(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 5973919, 123782] NotebookOptionsPosition[ 5913003, 122723] NotebookOutlinePosition[ 5913611, 122744] CellTagsIndexPosition[ 5913568, 122741] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["MEC-E8001 Finite Element Analysis 2022", "Title", CellChangeTimes->{ 3.4430806364968*^9, {3.4453166713873997`*^9, 3.4453166747414*^9}, { 3.447462264275*^9, 3.4474622644154*^9}, {3.4695731321116*^9, 3.4695731359491997`*^9}, 3.473055186341*^9, {3.4730552472860003`*^9, 3.47305524884*^9}, {3.473055399782*^9, 3.473055419801*^9}, { 3.4734696760778*^9, 3.4734697047349997`*^9}, {3.4770537891542*^9, 3.4770537950354*^9}, {3.4932799754514*^9, 3.4932799779161997`*^9}, { 3.4945558951644*^9, 3.4945558957416*^9}, {3.4957646303032*^9, 3.4957646329084*^9}, {3.497581602118*^9, 3.4975816042552*^9}, { 3.500960505817*^9, 3.5009605094206*^9}, {3.556623836083009*^9, 3.5566238462386265`*^9}, 3.5568725629008207`*^9, {3.5568726649396567`*^9, 3.5568726677478175`*^9}, 3.618709835758954*^9, 3.629777498181036*^9, 3.661174828401641*^9, {3.685234578060045*^9, 3.6852345824842978`*^9}, { 3.68523485439185*^9, 3.6852348785262303`*^9}, {3.6852638608992662`*^9, 3.685263861779268*^9}, {3.6853203463091555`*^9, 3.6853203574191704`*^9}, { 3.688455489182722*^9, 3.688455490812724*^9}, {3.690793272858951*^9, 3.6907932833889694`*^9}, 3.692021062414472*^9, 3.723799076464348*^9, 3.7529075526728444`*^9, {3.786674520886054*^9, 3.78667452099538*^9}, { 3.787369077038349*^9, 3.787369078333099*^9}, {3.7873692589195013`*^9, 3.7873692634178495`*^9}, 3.816933053461233*^9, {3.817042959067622*^9, 3.817042966014656*^9}, {3.8191048779101887`*^9, 3.8191048783875504`*^9}, 3.8506134998997335`*^9},ExpressionUUID->"f9c2c148-a01a-4dcf-b5a2-\ 59c8faa291c7"], Cell[CellGroupData[{ Cell["FEM DEFINITIONS", "Section", CellChangeTimes->{ 3.4430806364968*^9, {3.4453166713873997`*^9, 3.4453166747414*^9}, { 3.447462264275*^9, 3.4474622644154*^9}, {3.4695731321116*^9, 3.4695731359491997`*^9}, 3.473055186341*^9, {3.4730552472860003`*^9, 3.47305524884*^9}, {3.473055399782*^9, 3.473055419801*^9}, { 3.4734696760778*^9, 3.4734697047349997`*^9}, {3.4770537891542*^9, 3.4770537950354*^9}, {3.4932799754514*^9, 3.4932799779161997`*^9}, { 3.4945558951644*^9, 3.4945558957416*^9}, {3.4957646303032*^9, 3.4957646329084*^9}, {3.497581602118*^9, 3.4975816042552*^9}, { 3.500960505817*^9, 3.5009605094206*^9}, {3.556623836083009*^9, 3.5566238462386265`*^9}, {3.5568725055395393`*^9, 3.5568725163821597`*^9}, {3.556872678728445*^9, 3.5568726810485783`*^9}, { 3.7323376045620503`*^9, 3.7323376086812124`*^9}},ExpressionUUID->"7b219000-c4f4-41ef-90a2-\ e545639024f2"], Cell[CellGroupData[{ Cell["DEFS defs ", "Subsection", CellChangeTimes->{{3.4770537307790003`*^9, 3.4770537313562*^9}},ExpressionUUID->"9f625864-b9bc-40ff-bf39-665b1dfd8d1c"], Cell[BoxData[{ RowBox[{ RowBox[{"Off", "[", RowBox[{"General", "::", "spell"}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Off", "[", RowBox[{"General", "::", "spell1"}], "]"}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Clear", "[", "\[Delta]", "]"}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", "exp_", "]"}], ":=", RowBox[{"exp", "/.", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"a", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]a", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"b", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]b", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"c", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]c", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"ux", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]ux", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"uy", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]uy", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"uz", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]uz", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Theta]x", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]\[Theta]x", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"\[Theta]y", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]\[Theta]y", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"\[Theta]z", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]\[Theta]z", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"uX", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]uX", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"uY", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]uY", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"uZ", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]uZ", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Theta]X", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]\[Theta]X", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"\[Theta]Y", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]\[Theta]Y", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"\[Theta]Z", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]\[Theta]Z", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"Fx", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]Fx", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"Fy", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]Fy", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"Fz", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]Fz", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"Mx", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]Mx", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"My", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]My", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"Mz", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]Mz", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"FX", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]FX", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"FY", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]FY", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"FZ", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]FZ", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"MX", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]MX", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"MY", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]MY", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"MZ", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]MZ", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"FN", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]FN", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"FT", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]FT", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"FB", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]FB", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"MN", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]MN", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"MT", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]MT", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"MB", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]MB", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[CurlyTheta]", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Delta]\[CurlyTheta]", "[", "any", "]"}]}]}], "}"}]}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]UN", "[", "exp_", "]"}], ":=", RowBox[{"exp", "/.", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"\[Delta]a", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"a", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"\[Delta]b", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"b", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]c", "[", "any__", "]"}], " ", "\[Rule]", RowBox[{"c", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", " ", RowBox[{ RowBox[{"\[Delta]ux", "[", "any__", "]"}], "\[Rule]", RowBox[{"ux", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]uy", "[", "any__", "]"}], "\[Rule]", RowBox[{"uy", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]uz", "[", "any__", "]"}], "\[Rule]", RowBox[{"uz", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", " ", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Theta]x", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Theta]y", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Theta]z", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", " ", RowBox[{ RowBox[{"\[Delta]uX", "[", "any__", "]"}], "\[Rule]", RowBox[{"uX", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]uY", "[", "any__", "]"}], "\[Rule]", RowBox[{"uY", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]uZ", "[", "any__", "]"}], "\[Rule]", RowBox[{"uZ", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", " ", RowBox[{ RowBox[{"\[Delta]\[Theta]X", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Theta]X", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]\[Theta]Y", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Theta]Y", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]\[Theta]Z", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[Theta]Z", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", " ", RowBox[{ RowBox[{"\[Delta]Fx", "[", "any__", "]"}], "\[Rule]", RowBox[{"Fx", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]Fy", "[", "any__", "]"}], "\[Rule]", RowBox[{"Fy", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]Fz", "[", "any__", "]"}], "\[Rule]", RowBox[{"Fz", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", " ", RowBox[{ RowBox[{"\[Delta]Mx", "[", "any__", "]"}], "\[Rule]", RowBox[{"Mx", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]My", "[", "any__", "]"}], "\[Rule]", RowBox[{"My", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]Mz", "[", "any__", "]"}], "\[Rule]", RowBox[{"Mz", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", " ", RowBox[{ RowBox[{"\[Delta]FX", "[", "any__", "]"}], "\[Rule]", RowBox[{"FX", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]FY", "[", "any__", "]"}], "\[Rule]", RowBox[{"FY", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]FZ", "[", "any__", "]"}], "\[Rule]", RowBox[{"FZ", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", " ", RowBox[{ RowBox[{"\[Delta]MX", "[", "any__", "]"}], "\[Rule]", RowBox[{"MX", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]MY", "[", "any__", "]"}], "\[Rule]", RowBox[{"MY", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]MZ", "[", "any__", "]"}], "\[Rule]", RowBox[{"MZ", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", " ", RowBox[{ RowBox[{"\[Delta]FN", "[", "any__", "]"}], "\[Rule]", RowBox[{"FN", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]FT", "[", "any__", "]"}], "\[Rule]", RowBox[{"FT", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]FB", "[", "any__", "]"}], "\[Rule]", RowBox[{"FB", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", " ", RowBox[{ RowBox[{"\[Delta]MN", "[", "any__", "]"}], "\[Rule]", RowBox[{"MN", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]MT", "[", "any__", "]"}], "\[Rule]", RowBox[{"MT", "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{"\[Delta]MB", "[", "any__", "]"}], "\[Rule]", RowBox[{"MB", "[", "any", "]"}]}], ",", "\[IndentingNewLine]", " ", RowBox[{ RowBox[{"\[Delta]\[CurlyTheta]", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[CurlyTheta]", "[", "any", "]"}]}]}], "}"}]}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"DOFS", "[", "exp_", "]"}], " ", ":=", RowBox[{"Union", "[", RowBox[{"Cases", "[", RowBox[{ RowBox[{"{", "exp", "}"}], ",", RowBox[{ RowBox[{"a", "[", "__", "]"}], "|", RowBox[{"b", "[", "__", "]"}], "|", RowBox[{"c", "[", "__", "]"}], " ", "|", RowBox[{"uX", "[", "__", "]"}], "|", RowBox[{"uY", "[", "__", "]"}], "|", RowBox[{"uZ", "[", "__", "]"}], "|", " ", RowBox[{"\[Theta]X", "[", "__", "]"}], "|", " ", RowBox[{"\[Theta]Y", "[", "__", "]"}], "|", RowBox[{"\[Theta]Z", "[", "__", "]"}], "|", RowBox[{"ux", "[", "__", "]"}], "|", RowBox[{"uy", "[", "__", "]"}], "|", RowBox[{"uz", "[", "__", "]"}], "|", " ", RowBox[{"\[Theta]x", "[", "__", "]"}], "|", " ", RowBox[{"\[Theta]y", "[", "__", "]"}], "|", RowBox[{"\[Theta]z", "[", "__", "]"}], "|", RowBox[{"FX", "[", "__", "]"}], "|", RowBox[{"FY", "[", "__", "]"}], "|", RowBox[{"FZ", "[", "__", "]"}], "|", " ", RowBox[{"MX", "[", "__", "]"}], "|", " ", RowBox[{"MY", "[", "__", "]"}], "|", RowBox[{"MZ", "[", "__", "]"}], "|", RowBox[{"FN", "[", "__", "]"}], "|", RowBox[{"FT", "[", "__", "]"}], "|", RowBox[{"FB", "[", "__", "]"}], "|", " ", RowBox[{"MN", "[", "__", "]"}], "|", " ", RowBox[{"MT", "[", "__", "]"}], "|", RowBox[{"MB", "[", "__", "]"}], "|", RowBox[{"Fx", "[", "__", "]"}], "|", RowBox[{"Fy", "[", "__", "]"}], "|", RowBox[{"Fz", "[", "__", "]"}], "|", " ", RowBox[{"Mx", "[", "__", "]"}], "|", " ", RowBox[{"My", "[", "__", "]"}], "|", RowBox[{"Mz", "[", "__", "]"}], "|", " ", RowBox[{"\[CurlyTheta]", "[", "__", "]"}]}], ",", "Infinity"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"DFFS", "[", "exp_", "]"}], " ", ":=", RowBox[{"Union", "[", RowBox[{"Cases", "[", RowBox[{ RowBox[{"{", "exp", "}"}], ",", RowBox[{ RowBox[{"FX", "[", "__", "]"}], "|", RowBox[{"FY", "[", "__", "]"}], "|", RowBox[{"FZ", "[", "__", "]"}], "|", " ", RowBox[{"MX", "[", "__", "]"}], "|", " ", RowBox[{"MY", "[", "__", "]"}], "|", RowBox[{"MZ", "[", "__", "]"}], "|", RowBox[{"FN", "[", "__", "]"}], "|", RowBox[{"FT", "[", "__", "]"}], "|", RowBox[{"FB", "[", "__", "]"}], "|", " ", RowBox[{"MN", "[", "__", "]"}], "|", " ", RowBox[{"MT", "[", "__", "]"}], "|", RowBox[{"MB", "[", "__", "]"}], "|", RowBox[{"Fx", "[", "__", "]"}], "|", RowBox[{"Fy", "[", "__", "]"}], "|", RowBox[{"Fz", "[", "__", "]"}], "|", " ", RowBox[{"Mx", "[", "__", "]"}], "|", " ", RowBox[{"My", "[", "__", "]"}], "|", RowBox[{"Mz", "[", "__", "]"}]}], ",", "Infinity"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]DFFS", "[", "exp_", "]"}], " ", ":=", RowBox[{"Union", "[", RowBox[{"Cases", "[", RowBox[{ RowBox[{"{", "exp", "}"}], ",", RowBox[{ RowBox[{"\[Delta]FX", "[", "__", "]"}], "|", RowBox[{"\[Delta]FY", "[", "__", "]"}], "|", RowBox[{"\[Delta]FZ", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]MX", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]MY", "[", "__", "]"}], "|", RowBox[{"\[Delta]MZ", "[", "__", "]"}], "|", RowBox[{"\[Delta]FN", "[", "__", "]"}], "|", RowBox[{"\[Delta]FT", "[", "__", "]"}], "|", RowBox[{"\[Delta]FB", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]MN", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]MT", "[", "__", "]"}], "|", RowBox[{"\[Delta]MB", "[", "__", "]"}], "|", RowBox[{"\[Delta]Fx", "[", "__", "]"}], "|", RowBox[{"\[Delta]Fy", "[", "__", "]"}], "|", RowBox[{"\[Delta]Fz", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]Mx", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]My", "[", "__", "]"}], "|", RowBox[{"\[Delta]Mz", "[", "__", "]"}]}], ",", "Infinity"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]DOFS", "[", "exp_", "]"}], " ", ":=", RowBox[{"Union", "[", RowBox[{"Cases", "[", RowBox[{ RowBox[{"{", "exp", "}"}], ",", RowBox[{ RowBox[{"\[Delta]a", "[", "__", "]"}], "|", RowBox[{"\[Delta]b", "[", "__", "]"}], "|", RowBox[{"\[Delta]c", "[", "__", "]"}], " ", "|", RowBox[{"\[Delta]uX", "[", "__", "]"}], "|", RowBox[{"\[Delta]uY", "[", "__", "]"}], "|", RowBox[{"\[Delta]uZ", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]\[Theta]X", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]\[Theta]Y", "[", "__", "]"}], "|", RowBox[{"\[Delta]\[Theta]Z", "[", "__", "]"}], "|", RowBox[{"\[Delta]ux", "[", "__", "]"}], "|", RowBox[{"\[Delta]uy", "[", "__", "]"}], "|", RowBox[{"\[Delta]uz", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]\[Theta]x", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]\[Theta]y", "[", "__", "]"}], "|", RowBox[{"\[Delta]\[Theta]z", "[", "__", "]"}], "|", RowBox[{"\[Delta]FX", "[", "__", "]"}], "|", RowBox[{"\[Delta]FY", "[", "__", "]"}], "|", RowBox[{"\[Delta]FZ", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]MX", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]MY", "[", "__", "]"}], "|", RowBox[{"\[Delta]MZ", "[", "__", "]"}], "|", RowBox[{"\[Delta]FN", "[", "__", "]"}], "|", RowBox[{"\[Delta]FT", "[", "__", "]"}], "|", RowBox[{"\[Delta]FB", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]MN", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]MT", "[", "__", "]"}], "|", RowBox[{"\[Delta]MB", "[", "__", "]"}], "|", RowBox[{"\[Delta]Fx", "[", "__", "]"}], "|", RowBox[{"\[Delta]Fy", "[", "__", "]"}], "|", RowBox[{"\[Delta]Fz", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]Mx", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]My", "[", "__", "]"}], "|", RowBox[{"\[Delta]Mz", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]\[CurlyTheta]", "[", "__", "]"}]}], ",", "Infinity"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"DOFS", "[", RowBox[{"exp_", ",", "n_"}], "]"}], " ", ":=", RowBox[{"Union", "[", RowBox[{"Cases", "[", RowBox[{ RowBox[{"{", "exp", "}"}], ",", RowBox[{ RowBox[{"a", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"b", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"c", "[", RowBox[{"__", ",", "n"}], "]"}], " ", "|", RowBox[{"uX", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"uY", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"uZ", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"\[Theta]X", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"\[Theta]Y", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Theta]Z", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"ux", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"uy", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"uz", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"\[Theta]x", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"\[Theta]y", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Theta]z", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"FX", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"FY", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"FZ", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"MX", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"MY", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"MZ", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"FN", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"FT", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"FB", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"MN", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"MT", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"MB", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"Fx", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"Fy", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"Fz", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"Mx", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"My", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"Mz", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"\[CurlyTheta]", "[", RowBox[{"__", ",", "n"}], "]"}]}], ",", "Infinity"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]DOFS", "[", RowBox[{"exp_", ",", "n_"}], "]"}], " ", ":=", RowBox[{"Union", "[", RowBox[{"Cases", "[", RowBox[{ RowBox[{"{", "exp", "}"}], ",", RowBox[{ RowBox[{"\[Delta]a", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]b", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]c", "[", RowBox[{"__", ",", "n"}], "]"}], " ", "|", RowBox[{"\[Delta]uX", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]uY", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]uZ", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"\[Delta]\[Theta]X", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"\[Delta]\[Theta]Y", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]\[Theta]Z", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]ux", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]uy", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]uz", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]FX", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]FY", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]FZ", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"\[Delta]MX", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"\[Delta]MY", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]MZ", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]FN", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]FT", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]FB", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"\[Delta]MN", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"\[Delta]MT", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]MB", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]Fx", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]Fy", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]Fz", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"\[Delta]Mx", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"\[Delta]My", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]Mz", "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{"\[Delta]\[CurlyTheta]", "[", RowBox[{"__", ",", "n"}], "]"}]}], ",", "Infinity"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"DRULE", "[", "n_", "]"}], ":=", " ", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"a", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"a", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"b", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"b", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"c", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"c", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"uX", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"uX", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"uY", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"uY", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"uZ", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"uZ", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Theta]X", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"\[Theta]X", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"\[Theta]Y", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"\[Theta]Y", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"\[Theta]Z", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"\[Theta]Z", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"ux", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"ux", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"uy", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"uy", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"uz", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"uz", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Theta]x", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"\[Theta]x", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"\[Theta]y", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"\[Theta]y", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"\[Theta]z", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"\[Theta]z", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"FX", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"FX", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"FY", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"FY", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"FZ", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"FZ", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"MX", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"MX", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"MY", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"MY", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"MZ", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"MZ", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"FN", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"FN", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"FT", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"FT", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"FB", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"FB", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"MN", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"MN", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"MT", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"MT", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"MB", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"MB", "[", RowBox[{"any", ",", "n"}], "]"}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", "u_", "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", "dof", "}"}], ",", RowBox[{ RowBox[{"dof", "=", RowBox[{"DOFS", "[", "u", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"dof", "==", RowBox[{"{", "}"}]}], " ", ",", RowBox[{"u", "*", "0"}], ",", RowBox[{ RowBox[{"D", "[", RowBox[{"u", ",", RowBox[{"{", "dof", "}"}]}], "]"}], ".", RowBox[{"\[Delta]", "[", "dof", "]"}]}]}], "]"}]}]}], "]"}]}], ";"}], " "}]}], "Input", InitializationCell->True, CellChangeTimes->{{3.4426462585778456`*^9, 3.4426462590770454`*^9}, 3.4770537732734003`*^9, {3.4770538084514*^9, 3.4770539107874002`*^9}, { 3.4770539837018003`*^9, 3.4770539840762*^9}, {3.6310184366218147`*^9, 3.631018437292616*^9}, {3.685233451807683*^9, 3.685233452477684*^9}, { 3.685234382901882*^9, 3.6852343866400967`*^9}, {3.6853442041034565`*^9, 3.6853443400412316`*^9}, {3.6853443751512394`*^9, 3.685344377332364*^9}, 3.6853454114825144`*^9, {3.6868316461612635`*^9, 3.6868318084514904`*^9}, { 3.686832766952832*^9, 3.6868328092028913`*^9}, {3.686832846372944*^9, 3.686832931023062*^9}, {3.6872635529744654`*^9, 3.6872635616644773`*^9}, { 3.6875150430418844`*^9, 3.6875151112847824`*^9}, {3.687743582879592*^9, 3.6877436675097103`*^9}, {3.687743698119753*^9, 3.6877437374098077`*^9}, { 3.6877437674998503`*^9, 3.687743819059922*^9}, {3.687744657251096*^9, 3.687744669171112*^9}, {3.692421446310708*^9, 3.69242161182094*^9}, { 3.6926015199824505`*^9, 3.692601820564872*^9}, {3.6926909355497313`*^9, 3.6926909367897334`*^9}, {3.6927677148447485`*^9, 3.692767777644837*^9}, { 3.692767831454912*^9, 3.6927678718849688`*^9}, {3.6942322376116867`*^9, 3.6942324085019264`*^9}, {3.694415508707368*^9, 3.694415535947406*^9}, { 3.6944156219175262`*^9, 3.6944156308775387`*^9}, {3.694415674217599*^9, 3.694415743297696*^9}, 3.6944162623784227`*^9, 3.694416759679119*^9, { 3.6946871199157624`*^9, 3.694687178045844*^9}, 3.6946872406459312`*^9, { 3.6948454377388935`*^9, 3.6948454739389443`*^9}, {3.694845622699153*^9, 3.694845623739154*^9}, {3.6948457209192905`*^9, 3.6948457976193976`*^9}, { 3.724304012886026*^9, 3.724304060229605*^9}, {3.73313814515314*^9, 3.7331381540290995`*^9}, {3.733138190908001*^9, 3.7331382926372166`*^9}, { 3.7458091168859*^9, 3.745809330453831*^9}, {3.7530811243190904`*^9, 3.7530811449186587`*^9}, {3.7561686396442633`*^9, 3.756168670119571*^9}, { 3.7600603151211576`*^9, 3.7600603156835256`*^9}, {3.7894796484099903`*^9, 3.789479649089468*^9}, {3.789479692503845*^9, 3.7894797188708086`*^9}, { 3.7894797500361404`*^9, 3.789479784847563*^9}, 3.7894799681885223`*^9, { 3.789480438163148*^9, 3.7894804422051945`*^9}, {3.7894806002852697`*^9, 3.789480655832934*^9}, {3.8166040129889574`*^9, 3.8166041495837865`*^9}, { 3.816604189186468*^9, 3.816604214802972*^9}, {3.8166042734773865`*^9, 3.8166043972850933`*^9}, {3.816604428267262*^9, 3.816604499850178*^9}, { 3.8166081703698654`*^9, 3.8166082203890176`*^9}, {3.8210655469757404`*^9, 3.821065597044009*^9}, {3.821065646217851*^9, 3.821065659621196*^9}, { 3.821065714586218*^9, 3.8210658123471637`*^9}, {3.8210658715411763`*^9, 3.821065940333043*^9}, 3.8210659934232154`*^9, {3.821151689134054*^9, 3.8211516901175613`*^9}}, CellLabel->"In[1]:=",ExpressionUUID->"e32c8819-c40a-4fc2-9333-bc065e3c69c0"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.686831884411597*^9, 3.6868318902216053`*^9}},ExpressionUUID->"4874a0c9-8cff-4280-8cb3-\ 1ff5c94a752a"] }, Closed]], Cell[CellGroupData[{ Cell["SHAPE defs ", "Subsection",ExpressionUUID->"eec57070-ff9d-4fae-86ab-c05296189c15"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"SHAPES1", "[", "h_", "]"}], ":=", " ", RowBox[{"{", RowBox[{ RowBox[{"1", "-", RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}]}], ",", RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SHAPES11", "[", "h_", "]"}], ":=", " ", RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", RowBox[{"x", "/", "h"}]}]}], ")"}]}], ",", RowBox[{"h", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{"2", " ", RowBox[{"x", "/", "h"}]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}], "2"]}], ",", RowBox[{"h", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"x", "/", "h"}]}], ")"}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"LAGRANGE", "[", RowBox[{"n_", ",", "h_"}], "]"}], ":=", " ", RowBox[{"Simplify", "[", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"#1", "/", RowBox[{"(", RowBox[{"#1", "/.", RowBox[{"x", "->", RowBox[{"h", "*", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}]}], ")"}]}], ")"}], "&"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"Apply", "[", RowBox[{"Times", ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"x", "-", RowBox[{"h", "*", RowBox[{ RowBox[{"(", RowBox[{"ii", "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", "n"}], "}"}]}], "]"}]}], "]"}], "/", RowBox[{"(", RowBox[{"x", "-", RowBox[{"h", "*", RowBox[{ RowBox[{"(", RowBox[{"jj", "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}], ")"}]}], ",", RowBox[{"{", RowBox[{"jj", ",", "1", ",", "n"}], "}"}]}], "]"}]}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"LAGRANGE", "[", RowBox[{"n_", ",", RowBox[{"{", RowBox[{"x0_", ",", "x1_"}], "}"}]}], "]"}], ":=", " ", RowBox[{"Simplify", "[", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"#1", "/", RowBox[{"(", RowBox[{"#1", "/.", RowBox[{"x", "\[Rule]", RowBox[{"x0", "+", RowBox[{ RowBox[{"(", RowBox[{"x1", "-", "x0"}], ")"}], "*", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}]}]}], ")"}]}], ")"}], "&"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"Apply", "[", RowBox[{"Times", ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"x", "-", RowBox[{"(", RowBox[{"x0", "+", RowBox[{ RowBox[{"(", RowBox[{"x1", "-", "x0"}], ")"}], "*", RowBox[{ RowBox[{"(", RowBox[{"ii", "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}], ")"}]}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", "n"}], "}"}]}], "]"}]}], "]"}], "/", RowBox[{"(", RowBox[{"x", "-", RowBox[{"(", RowBox[{"x0", "+", RowBox[{ RowBox[{"(", RowBox[{"x1", "-", "x0"}], ")"}], "*", RowBox[{ RowBox[{"(", RowBox[{"jj", "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}], ")"}]}], ")"}]}], ",", RowBox[{"{", RowBox[{"jj", ",", "1", ",", "n"}], "}"}]}], "]"}]}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"LAGRANGE", "[", RowBox[{"n_", ",", RowBox[{"{", RowBox[{"x", ",", RowBox[{"{", RowBox[{"x0_", ",", "x1_"}], "}"}]}], "}"}]}], "]"}], ":=", " ", RowBox[{"Simplify", "[", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"#1", "/", RowBox[{"(", RowBox[{"#1", "/.", RowBox[{"x", "\[Rule]", RowBox[{"x0", "+", RowBox[{ RowBox[{"(", RowBox[{"x1", "-", "x0"}], ")"}], "*", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}]}]}], ")"}]}], ")"}], "&"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"Apply", "[", RowBox[{"Times", ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"x", "-", RowBox[{"(", RowBox[{"x0", "+", RowBox[{ RowBox[{"(", RowBox[{"x1", "-", "x0"}], ")"}], "*", RowBox[{ RowBox[{"(", RowBox[{"ii", "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}], ")"}]}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", "n"}], "}"}]}], "]"}]}], "]"}], "/", RowBox[{"(", RowBox[{"x", "-", RowBox[{"(", RowBox[{"x0", "+", RowBox[{ RowBox[{"(", RowBox[{"x1", "-", "x0"}], ")"}], "*", RowBox[{ RowBox[{"(", RowBox[{"jj", "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}], ")"}]}], ")"}]}], ",", RowBox[{"{", RowBox[{"jj", ",", "1", ",", "n"}], "}"}]}], "]"}]}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SHAPES1", "[", RowBox[{"bas_", ",", "ver_"}], "]"}], ":=", " ", RowBox[{"Simplify", "[", RowBox[{"bas", " ", ".", " ", RowBox[{"Inverse", "[", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"{", "bas", "}"}], "/.", " ", RowBox[{"{", RowBox[{"x", "->", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "&"}], ",", " ", "ver"}], "]"}], ",", "1"}], "]"}], "]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SHAPES11", "[", RowBox[{"bas_", ",", "ver_"}], "]"}], ":=", " ", RowBox[{"bas", " ", ".", " ", RowBox[{"Inverse", "[", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"bas", ",", RowBox[{ SubscriptBox["\[PartialD]", "x"], "bas"}]}], "}"}], "/.", " ", RowBox[{"{", RowBox[{"x", "->", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "&"}], ",", " ", "ver"}], "]"}], ",", "1"}], "]"}], "]"}]}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SHAPES2", "[", RowBox[{"bas_", ",", "ver_"}], "]"}], ":=", " ", RowBox[{"bas", " ", ".", " ", RowBox[{"Inverse", "[", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"{", "bas", "}"}], "/.", " ", RowBox[{"{", RowBox[{ RowBox[{"x", "->", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", RowBox[{"y", "->", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}]}]}], "}"}]}], "&"}], ",", " ", "ver"}], "]"}], ",", "1"}], "]"}], "]"}]}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SHAPES21", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"x1_", ",", "y1_"}], "}"}], ",", RowBox[{"{", RowBox[{"x2_", ",", "y2_"}], "}"}]}], "}"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"Nx", ",", "Ny"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"Nx", "=", " ", RowBox[{"SHAPES11", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "x", ",", RowBox[{"x", "^", "2"}], ",", RowBox[{"x", "^", "3"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "x1", "}"}], ",", RowBox[{"{", "x2", "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Ny", "=", " ", RowBox[{ RowBox[{"SHAPES11", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "x", ",", RowBox[{"x", "^", "2"}], ",", RowBox[{"x", "^", "3"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "y1", "}"}], ",", RowBox[{"{", "y2", "}"}]}], "}"}]}], "]"}], " ", "/.", " ", RowBox[{"x", "\[Rule]", "y"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "2", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "4", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "2", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "3", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "3", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "4", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "3", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "4", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "3", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "4", "]"}], "]"}]}]}], "}"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SHAPES3", "[", RowBox[{"bas_", ",", "ver_"}], "]"}], ":=", " ", RowBox[{"bas", " ", ".", " ", RowBox[{"Inverse", "[", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"{", "bas", "}"}], "/.", " ", RowBox[{"{", RowBox[{ RowBox[{"x", "->", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", RowBox[{"y", "->", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}]}], ",", RowBox[{"z", "->", RowBox[{"#", "[", RowBox[{"[", "3", "]"}], "]"}]}]}], "}"}]}], "&"}], ",", " ", "ver"}], "]"}], ",", "1"}], "]"}], "]"}]}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SHAPES1", "[", "h_", "]"}], ":=", " ", RowBox[{"{", RowBox[{ RowBox[{"1", "-", RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}]}], ",", RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SHAPES11", "[", "h_", "]"}], ":=", " ", RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", RowBox[{"x", "/", "h"}]}]}], ")"}]}], ",", RowBox[{"h", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{"2", " ", RowBox[{"x", "/", "h"}]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}], "2"]}], ",", RowBox[{"h", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"x", "/", "h"}]}], ")"}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"LAGRANGE", "[", RowBox[{"n_", ",", "h_"}], "]"}], ":=", " ", RowBox[{"Simplify", "[", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"#1", "/", RowBox[{"(", RowBox[{"#1", "/.", RowBox[{"x", "->", RowBox[{"h", "*", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}]}], ")"}]}], ")"}], "&"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"Apply", "[", RowBox[{"Times", ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"x", "-", RowBox[{"h", "*", RowBox[{ RowBox[{"(", RowBox[{"ii", "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", "n"}], "}"}]}], "]"}]}], "]"}], "/", RowBox[{"(", RowBox[{"x", "-", RowBox[{"h", "*", RowBox[{ RowBox[{"(", RowBox[{"jj", "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}], ")"}]}], ",", RowBox[{"{", RowBox[{"jj", ",", "1", ",", "n"}], "}"}]}], "]"}]}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{"{", RowBox[{"n_", ",", "r_"}], "}"}], "}"}], "]"}], ":=", " ", RowBox[{"Simplify", "[", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"#1", "/", RowBox[{"(", RowBox[{"#1", "/.", RowBox[{"r", "->", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}], ")"}]}], ")"}], "&"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"Apply", "[", RowBox[{"Times", ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"r", "-", RowBox[{ RowBox[{"(", RowBox[{"ii", "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", "n"}], "}"}]}], "]"}]}], "]"}], "/", RowBox[{"(", RowBox[{"r", "-", RowBox[{ RowBox[{"(", RowBox[{"jj", "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}], ")"}]}], ",", RowBox[{"{", RowBox[{"jj", ",", "1", ",", "n"}], "}"}]}], "]"}]}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n_", ",", "r_"}], "}"}], ",", RowBox[{"{", RowBox[{"m_", ",", "s_"}], "}"}]}], "}"}], "]"}], ":=", " ", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{"{", RowBox[{"m", ",", "s"}], "}"}], "}"}], "]"}], ",", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{"{", RowBox[{"n", ",", "r"}], "}"}], "}"}], "]"}]}], "]"}], ",", "1"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n_", ",", "r_"}], "}"}], ",", RowBox[{"{", RowBox[{"m_", ",", "s_"}], "}"}], ",", RowBox[{"{", RowBox[{"k_", ",", "t_"}], "}"}]}], "}"}], "]"}], ":=", " ", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{"{", RowBox[{"k", ",", "t"}], "}"}], "}"}], "]"}], ",", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{"{", RowBox[{"m", ",", "s"}], "}"}], "}"}], "]"}], ",", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{"{", RowBox[{"n", ",", "r"}], "}"}], "}"}], "]"}]}], "]"}], ",", "2"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"LAGRANGE", "[", RowBox[{"n_", ",", RowBox[{"{", RowBox[{"x0_", ",", "x1_"}], "}"}]}], "]"}], ":=", " ", RowBox[{"Simplify", "[", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"#1", "/", RowBox[{"(", RowBox[{"#1", "/.", RowBox[{"x", "\[Rule]", RowBox[{"x0", "+", RowBox[{ RowBox[{"(", RowBox[{"x1", "-", "x0"}], ")"}], "*", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}]}]}], ")"}]}], ")"}], "&"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"Apply", "[", RowBox[{"Times", ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"x", "-", RowBox[{"(", RowBox[{"x0", "+", RowBox[{ RowBox[{"(", RowBox[{"x1", "-", "x0"}], ")"}], "*", RowBox[{ RowBox[{"(", RowBox[{"ii", "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}], ")"}]}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", "n"}], "}"}]}], "]"}]}], "]"}], "/", RowBox[{"(", RowBox[{"x", "-", RowBox[{"(", RowBox[{"x0", "+", RowBox[{ RowBox[{"(", RowBox[{"x1", "-", "x0"}], ")"}], "*", RowBox[{ RowBox[{"(", RowBox[{"jj", "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}], ")"}]}], ")"}]}], ",", RowBox[{"{", RowBox[{"jj", ",", "1", ",", "n"}], "}"}]}], "]"}]}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"LAGRANGE", "[", RowBox[{"n_", ",", RowBox[{"{", RowBox[{"x", ",", RowBox[{"{", RowBox[{"x0_", ",", "x1_"}], "}"}]}], "}"}]}], "]"}], ":=", " ", RowBox[{"Simplify", "[", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"#1", "/", RowBox[{"(", RowBox[{"#1", "/.", RowBox[{"x", "\[Rule]", RowBox[{"x0", "+", RowBox[{ RowBox[{"(", RowBox[{"x1", "-", "x0"}], ")"}], "*", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}]}]}], ")"}]}], ")"}], "&"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"Apply", "[", RowBox[{"Times", ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"x", "-", RowBox[{"(", RowBox[{"x0", "+", RowBox[{ RowBox[{"(", RowBox[{"x1", "-", "x0"}], ")"}], "*", RowBox[{ RowBox[{"(", RowBox[{"ii", "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}], ")"}]}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", "n"}], "}"}]}], "]"}]}], "]"}], "/", RowBox[{"(", RowBox[{"x", "-", RowBox[{"(", RowBox[{"x0", "+", RowBox[{ RowBox[{"(", RowBox[{"x1", "-", "x0"}], ")"}], "*", RowBox[{ RowBox[{"(", RowBox[{"jj", "-", "1"}], ")"}], "/", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}], ")"}]}], ")"}]}], ",", RowBox[{"{", RowBox[{"jj", ",", "1", ",", "n"}], "}"}]}], "]"}]}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SHAPES1", "[", RowBox[{"bas_", ",", "ver_"}], "]"}], ":=", " ", RowBox[{"Simplify", "[", RowBox[{"bas", " ", ".", " ", RowBox[{"Inverse", "[", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"{", "bas", "}"}], "/.", " ", RowBox[{"{", RowBox[{"x", "->", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "&"}], ",", " ", "ver"}], "]"}], ",", "1"}], "]"}], "]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SHAPES11", "[", RowBox[{"bas_", ",", "ver_"}], "]"}], ":=", " ", RowBox[{"bas", " ", ".", " ", RowBox[{"Inverse", "[", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"bas", ",", RowBox[{ SubscriptBox["\[PartialD]", "x"], "bas"}]}], "}"}], "/.", " ", RowBox[{"{", RowBox[{"x", "->", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "&"}], ",", " ", "ver"}], "]"}], ",", "1"}], "]"}], "]"}]}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SHAPES2", "[", RowBox[{"bas_", ",", "ver_"}], "]"}], ":=", " ", RowBox[{"bas", " ", ".", " ", RowBox[{"Inverse", "[", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"{", "bas", "}"}], "/.", " ", RowBox[{"{", RowBox[{ RowBox[{"x", "->", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", RowBox[{"y", "->", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}]}]}], "}"}]}], "&"}], ",", " ", "ver"}], "]"}], ",", "1"}], "]"}], "]"}]}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SHAPES21", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"x1_", ",", "y1_"}], "}"}], ",", RowBox[{"{", RowBox[{"x2_", ",", "y2_"}], "}"}]}], "}"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"Nx", ",", "Ny"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"Nx", "=", " ", RowBox[{"SHAPES11", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "x", ",", RowBox[{"x", "^", "2"}], ",", RowBox[{"x", "^", "3"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "x1", "}"}], ",", RowBox[{"{", "x2", "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Ny", "=", " ", RowBox[{ RowBox[{"SHAPES11", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "x", ",", RowBox[{"x", "^", "2"}], ",", RowBox[{"x", "^", "3"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "y1", "}"}], ",", RowBox[{"{", "y2", "}"}]}], "}"}]}], "]"}], " ", "/.", " ", RowBox[{"x", "\[Rule]", "y"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "2", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "4", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "2", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "3", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "3", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "4", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "3", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "4", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "3", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"Nx", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"Ny", "[", RowBox[{"[", "4", "]"}], "]"}]}]}], "}"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SHAPES3", "[", RowBox[{"bas_", ",", "ver_"}], "]"}], ":=", " ", RowBox[{"bas", " ", ".", " ", RowBox[{"Inverse", "[", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"{", "bas", "}"}], "/.", " ", RowBox[{"{", RowBox[{ RowBox[{"x", "->", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", RowBox[{"y", "->", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}]}], ",", RowBox[{"z", "->", RowBox[{"#", "[", RowBox[{"[", "3", "]"}], "]"}]}]}], "}"}]}], "&"}], ",", " ", "ver"}], "]"}], ",", "1"}], "]"}], "]"}]}]}], ";"}], "\[IndentingNewLine]"}], "Input", InitializationCell->True, CellChangeTimes->{{3.4670783931368*^9, 3.4670784098444*^9}, { 3.468067594204*^9, 3.4680678179392*^9}, 3.4680680234556*^9, { 3.468068073126*^9, 3.4680681447455997`*^9}, {3.4680681751188*^9, 3.46806831009*^9}, {3.4684605671832*^9, 3.4684605726744003`*^9}, { 3.471399186098*^9, 3.4713991974236*^9}, {3.471404873455*^9, 3.4714048739854*^9}, {3.4820580083386*^9, 3.4820580095086*^9}, { 3.4820588874835997`*^9, 3.4820588977016*^9}, {3.6187193088566475`*^9, 3.6187193100797176`*^9}}, CellLabel->"In[14]:=",ExpressionUUID->"0d84d048-10b8-4020-80f1-474bbf6e6928"] }, Closed]], Cell[CellGroupData[{ Cell["QUAD defs ", "Subsection",ExpressionUUID->"bb23d42e-ddee-4fa6-b7ad-482b53d6586c"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"LIN1", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"w", ",", "p"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", RowBox[{ RowBox[{"{", RowBox[{"{", "1", "}"}], "}"}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"{", "1", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"LIN2", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"w", ",", "p"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "1", "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"LIN2G", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"w", ",", "p"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", RowBox[{"{", RowBox[{ RowBox[{"{", "0.21132486540518713", "}"}], ",", RowBox[{"{", "0.7886751345948129", "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"LIN3", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"w", ",", "p"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "1", "}"}], ",", RowBox[{"{", "2", "}"}]}], "}"}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "4", ",", "1"}], "}"}], "/", "6"}]}], ";", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"LIN3G", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"w", ",", "p"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", RowBox[{"{", RowBox[{ RowBox[{"{", "0.1127016653792583", "}"}], ",", RowBox[{"{", "0.5", "}"}], ",", RowBox[{"{", "0.8872983346207417", "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"{", RowBox[{ "0.2777777777777777", ",", "0.44444444444444453", ",", "0.2777777777777777"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"LIN5", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"w", ",", "p"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "1", "}"}], ",", RowBox[{"{", "2", "}"}], ",", RowBox[{"{", "3", "}"}], ",", RowBox[{"{", "4", "}"}]}], "}"}], "/", "4"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"{", RowBox[{"7", ",", "32", ",", "12", ",", "32", ",", "7"}], "}"}], "/", "90"}]}], ";", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"w", ",", "p"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "1", "}"}], ",", RowBox[{"{", "2", "}"}], ",", RowBox[{"{", "3", "}"}], ",", RowBox[{"{", "4", "}"}], ",", RowBox[{"{", "5", "}"}], ",", RowBox[{"{", "6", "}"}]}], "}"}], "/", "6"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"{", RowBox[{ "41", ",", "216", ",", "27", ",", "272", ",", "27", ",", "216", ",", "41"}], "}"}], "/", "840"}]}], ";", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"LIN14", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"w", ",", "p"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", RowBox[{ RowBox[{"Table", "[", RowBox[{"ii", ",", RowBox[{"{", RowBox[{"ii", ",", "0", ",", "13"}], "}"}]}], "]"}], "/", "13"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"{", RowBox[{ FractionBox["8181904909", "402361344000"], ",", FractionBox["56280729661", "402361344000"], ",", RowBox[{"-", FractionBox["1737125143", "22353408000"]}], ",", FractionBox["11148172711", "28740096000"], ",", RowBox[{"-", FractionBox["6066382933", "16094453760"]}], ",", FractionBox["22964826443", "44706816000"], ",", RowBox[{"-", FractionBox["3592666051", "33530112000"]}], ",", RowBox[{"-", FractionBox["3592666051", "33530112000"]}], ",", FractionBox["22964826443", "44706816000"], ",", RowBox[{"-", FractionBox["6066382933", "16094453760"]}], ",", FractionBox["11148172711", "28740096000"], ",", RowBox[{"-", FractionBox["1737125143", "22353408000"]}], ",", FractionBox["56280729661", "402361344000"], ",", FractionBox["8181904909", "402361344000"]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI1", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"w", ",", "p"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "}"}], "/", "3"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"{", "1", "}"}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI3", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"w", ",", "p"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", "1"}], "}"}], "/", "6"}]}], ";", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI4", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"w", ",", "p"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "/", "3"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"1", "/", "24"}], "*", RowBox[{"{", RowBox[{"1", ",", "1", ",", "1", ",", "9"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI41", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"w", ",", "p"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], "/", "2"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "/", "2"}], ",", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], "/", "2"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "/", "3"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"1", "/", "120"}], "*", RowBox[{"{", RowBox[{"11", ",", "11", ",", "11", ",", "27"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"w", ",", "p"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"1", "/", "2"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"1", "/", "2"}], ",", RowBox[{"1", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"1", "/", "3"}], ",", RowBox[{"1", "/", "3"}]}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "/", "40"}], ",", RowBox[{"1", "/", "15"}], ",", RowBox[{"1", "/", "40"}], ",", RowBox[{"1", "/", "15"}], ",", RowBox[{"1", "/", "40"}], ",", RowBox[{"1", "/", "15"}], ",", RowBox[{"9", "/", "40"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI12", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"w", ",", "p"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "1"}], "}"}]}], "}"}], "/", "4"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"{", RowBox[{"4", ",", RowBox[{"-", "1"}], ",", "4", ",", "4", ",", "8", ",", "8", ",", "4", ",", RowBox[{"-", "1"}], ",", "8", ",", RowBox[{"-", "1"}], ",", "4", ",", "4"}], "}"}], "/", "90"}]}], ";", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI28", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"w", ",", "p"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "5"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "6"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "5"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"5", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"5", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"6", ",", "0"}], "}"}]}], "}"}], "/", "6"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "36", ",", RowBox[{"-", "27"}], ",", "64", ",", RowBox[{"-", "27"}], ",", "36", ",", "0", ",", "36", ",", "72", ",", "72", ",", "72", ",", "72", ",", "36", ",", RowBox[{"-", "27"}], ",", "72", ",", RowBox[{"-", "54"}], ",", "72", ",", RowBox[{"-", "27"}], ",", "64", ",", "72", ",", "72", ",", "64", ",", RowBox[{"-", "27"}], ",", "72", ",", RowBox[{"-", "27"}], ",", "36", ",", "36", ",", "0"}], "}"}], "/", RowBox[{"(", RowBox[{"3.", "*", "560"}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"REC9", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"w", ",", "p"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}]}], "}"}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"{", RowBox[{ "1", ",", "4", ",", "1", ",", "4", ",", "16", ",", "4", ",", "1", ",", "4", ",", "1"}], "}"}], "/", "36"}]}], ";", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"HEX27", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"w", ",", "p"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "2", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "2", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "0", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "2", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "2", ",", "2"}], "}"}]}], "}"}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"{", RowBox[{ "1", ",", "4", ",", "1", ",", "4", ",", "16", ",", "4", ",", "1", ",", "4", ",", "1", ",", "4", ",", "16", ",", "4", ",", "16", ",", "64", ",", "16", ",", "4", ",", "16", ",", "4", ",", "1", ",", "4", ",", "1", ",", "4", ",", "16", ",", "4", ",", "1", ",", "4", ",", "1"}], "}"}], "/", RowBox[{"6", "^", "3"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TET5", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"w", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "16"}], ",", "9", ",", "9", ",", "9", ",", "9"}], "}"}], "/", "120"}]}], ",", RowBox[{"p", "=", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "4"}], ",", RowBox[{"1", "/", "2"}], ",", RowBox[{"1", "/", "6"}], ",", RowBox[{"1", "/", "6"}], ",", RowBox[{"1", "/", "6"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"1", "/", "4"}], ",", RowBox[{"1", "/", "6"}], ",", RowBox[{"1", "/", "6"}], ",", RowBox[{"1", "/", "6"}], ",", RowBox[{"1", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"1", "/", "4"}], ",", RowBox[{"1", "/", "6"}], ",", RowBox[{"1", "/", "6"}], ",", RowBox[{"1", "/", "2"}], ",", RowBox[{"1", "/", "6"}]}], "}"}]}], "}"}], "]"}]}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TET10", ",", "exp_", ",", "var_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"w", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", "4", ",", "4", ",", "4", ",", "4", ",", "4", ",", "4"}], "}"}], "/", "120"}]}], ",", RowBox[{"p", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", "0"}], "}"}], "/", "2"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "1"}], "}"}], "/", "2"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], "/", "2"}], ",", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1", ",", "1"}], "}"}], "/", "2"}], ",", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], "/", "2"}], ",", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}], "/", "2"}]}], "}"}]}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"w", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "*", "exp"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "\[Rule]", "#1"}], "]"}]}], "&"}], ",", "p"}], "]"}]}], "]"}]}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.4426462761434455`*^9, {3.4426463580278454`*^9, 3.4426463672786455`*^9}, 3.4461855349388*^9, {3.4468649264091997`*^9, 3.4468649477656*^9}, 3.4770653198157997`*^9, {3.4771016648258*^9, 3.4771016703638*^9}, 3.4773012612406*^9, 3.4773013118782*^9, {3.4773017793166*^9, 3.4773018115618*^9}, {3.4818081970202*^9, 3.4818082252406*^9}, { 3.4822977608296003`*^9, 3.48229777267*^9}, {3.482298444565*^9, 3.4822984493698*^9}, {3.4822986565578003`*^9, 3.4822987152293997`*^9}, { 3.4822987471470003`*^9, 3.4822988202018003`*^9}, {3.4823218768966*^9, 3.4823219047738*^9}, {3.6320400759127555`*^9, 3.6320400774188414`*^9}, { 3.6339410644178886`*^9, 3.633941069742193*^9}, {3.633942002306533*^9, 3.6339420034775996`*^9}, 3.6565732333204584`*^9, {3.685329942084824*^9, 3.6853299995431104`*^9}, {3.6881195224183316`*^9, 3.6881195236983337`*^9}, {3.6881195571483803`*^9, 3.6881195915584283`*^9}, {3.688120564569791*^9, 3.6881205683897963`*^9}, { 3.6881206185098658`*^9, 3.688120642069899*^9}, {3.688284719785588*^9, 3.688284729985602*^9}, {3.6882848245567346`*^9, 3.688284827776739*^9}, { 3.688284875506806*^9, 3.6882848867468214`*^9}, {3.688350375413198*^9, 3.688350378173202*^9}, 3.6883504111932483`*^9, {3.7455544449212356`*^9, 3.745554465572897*^9}, {3.7455544990494084`*^9, 3.7455545172795343`*^9}, { 3.74644306965172*^9, 3.746443076505107*^9}, {3.7468733511314077`*^9, 3.7468733665022874`*^9}, {3.763815192640204*^9, 3.7638152262175827`*^9}, { 3.76381555999401*^9, 3.763815576658593*^9}, {3.763815629456071*^9, 3.7638156433643184`*^9}, {3.7638156760642715`*^9, 3.763815680110509*^9}, { 3.763816314054133*^9, 3.763816315160985*^9}, {3.7641283974818926`*^9, 3.7641284022168202`*^9}, {3.764128466623234*^9, 3.764128512308055*^9}, { 3.7641285516285644`*^9, 3.764128597474304*^9}, {3.7641286389761047`*^9, 3.764128668115802*^9}, {3.7661439599999857`*^9, 3.766144017439571*^9}, { 3.8413897282608337`*^9, 3.8413897551839*^9}, {3.8413907066897593`*^9, 3.841390726628026*^9}, 3.8413907607649965`*^9, {3.8435604066446185`*^9, 3.843560438358281*^9}, {3.8435605553679347`*^9, 3.843560556538128*^9}, { 3.8435617747579966`*^9, 3.8435617981268296`*^9}, {3.8435621954269557`*^9, 3.8435621959062867`*^9}, {3.8445744705479603`*^9, 3.84457448460798*^9}, { 3.844574539146332*^9, 3.844574603163684*^9}, 3.8445746860003757`*^9}, CellLabel->"In[37]:=",ExpressionUUID->"576b99af-d39f-40c6-a17e-774066c43b83"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"tet", "=", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", "0"}], "}"}], "/", "2"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "1"}], "}"}], "/", "2"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], "/", "2"}], ",", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1", ",", "1"}], "}"}], "/", "2"}], ",", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], "/", "2"}], ",", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}], "/", "2"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", "=", RowBox[{"{", RowBox[{"1", ",", "x", ",", "y", ",", "z", ",", RowBox[{"x", " ", "y"}], ",", RowBox[{"x", " ", "z"}], ",", " ", RowBox[{"y", " ", "z"}], ",", " ", RowBox[{"x", "^", "2"}], ",", " ", RowBox[{"y", "^", "2"}], ",", RowBox[{"z", "^", "2"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"eq", "[", "i_", "]"}], ":=", " ", RowBox[{ RowBox[{ RowBox[{"Array", "[", RowBox[{"w", ",", "10"}], "]"}], ".", RowBox[{"(", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", "i", "]"}], "]"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}], "->", "#"}], "]"}]}], "&"}], ",", "p"}], "]"}], ")"}]}], "-", RowBox[{"Integrate", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", "i", "]"}], "]"}], ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}], StyleBox["\[Element]", "OperatorCharacter"], StyleBox["tet", "OperatorCharacter"]}]}], StyleBox["]", "OperatorCharacter"]}]}]}], StyleBox[";", "OperatorCharacter"]}], StyleBox["\[IndentingNewLine]", "OperatorCharacter"], "\[IndentingNewLine]", RowBox[{ RowBox[{"sol", "=", RowBox[{ RowBox[{ StyleBox["Solve", "OperatorCharacter"], StyleBox["[", "OperatorCharacter"], RowBox[{ RowBox[{"Thread", "[", RowBox[{ RowBox[{ StyleBox["Table", "OperatorCharacter"], StyleBox["[", "OperatorCharacter"], RowBox[{ RowBox[{"eq", "[", "i", "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "10"}], "}"}]}], "]"}], "==", "0"}], "]"}], ",", RowBox[{"Array", "[", RowBox[{"w", ",", "10"}], "]"}]}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"120", "*", RowBox[{"Array", "[", RowBox[{"w", ",", "10"}], "]"}]}], " ", "/.", "sol"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{ RowBox[{"Array", "[", RowBox[{"w", ",", "10"}], "]"}], " ", "/.", "sol"}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.8413897580019073`*^9, 3.8413905824006023`*^9}, { 3.841390641631239*^9, 3.841390651680857*^9}, {3.841390686922451*^9, 3.841390692801841*^9}}, CellLabel-> "In[116]:=",ExpressionUUID->"b6207a37-a9af-46be-93c2-e328fab05069"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", "4", ",", "4", ",", "4", ",", "4", ",", "4", ",", "4"}], "}"}]], "Output", CellChangeTimes->{ 3.8413900780711346`*^9, 3.8413901203216476`*^9, 3.841390186370854*^9, 3.841390445057602*^9, 3.841390476814777*^9, {3.841390518910721*^9, 3.841390583991149*^9}, 3.841390653783507*^9, 3.8413906934544754`*^9}, CellLabel-> "Out[121]=",ExpressionUUID->"70d10832-ca9d-4b10-bbb7-f22345d51098"], Cell[BoxData[ FractionBox["1", "6"]], "Output", CellChangeTimes->{ 3.8413900780711346`*^9, 3.8413901203216476`*^9, 3.841390186370854*^9, 3.841390445057602*^9, 3.841390476814777*^9, {3.841390518910721*^9, 3.841390583991149*^9}, 3.841390653783507*^9, 3.8413906934584646`*^9}, CellLabel-> "Out[122]=",ExpressionUUID->"80ac7773-60a7-42e9-878a-b3857f105846"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["INTEGRATE defs ", "Subsection",ExpressionUUID->"86802962-6405-448c-bfca-277c3d443e13"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"INTEGRATE", "[", RowBox[{ RowBox[{"{", RowBox[{"LINE", ",", "exp_"}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{ RowBox[{"{", RowBox[{"LINLINE", ",", "exp"}], "}"}], ",", "#"}], "]"}], "&"}], ",", "ele"}], "]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"RULE", "[", RowBox[{"{", RowBox[{"LINE", ",", RowBox[{"{", "iy_", "}"}], ",", "list_"}], "}"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"ix", ",", "iz", ",", "hx", ",", "nn"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ix", ",", "hx"}], "}"}], " ", "=", " ", RowBox[{"UNIT", "[", RowBox[{ RowBox[{"XYZ", "[", RowBox[{"Last", "[", "list", "]"}], "]"}], "-", RowBox[{"XYZ", "[", RowBox[{"First", "[", "list", "]"}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz", " ", "=", " ", RowBox[{"CROSS", "[", RowBox[{"ix", ",", "iy"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"nn", " ", "=", " ", RowBox[{"Length", "[", "list", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"xrule", " ", "=", " ", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"x", "[", "ii", "]"}], "\[Rule]", " ", RowBox[{"ix", ".", RowBox[{"XYZ", "[", RowBox[{"list", "[", RowBox[{"[", "ii", "]"}], "]"}], "]"}]}]}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", "nn"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"yrule", " ", "=", " ", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"y", "[", "ii", "]"}], "\[Rule]", " ", RowBox[{"iy", ".", RowBox[{"XYZ", "[", RowBox[{"list", "[", RowBox[{"[", "ii", "]"}], "]"}], "]"}]}]}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", "nn"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"zrule", " ", "=", " ", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"z", "[", "ii", "]"}], "\[Rule]", " ", RowBox[{"iz", ".", RowBox[{"XYZ", "[", RowBox[{"list", "[", RowBox[{"[", "ii", "]"}], "]"}], "]"}]}]}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", "nn"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Flatten", "[", RowBox[{"Join", "[", RowBox[{"xrule", ",", "yrule", ",", "zrule"}], "]"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"QUAD", "[", RowBox[{ RowBox[{"{", RowBox[{"LINLINE", ",", "exp_"}], "}"}], ",", "element_"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "NN", ",", "rule", ",", "xx", ",", "yy", ",", "zz", ",", "J", ",", "int"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", " ", "=", " ", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Xi]"}], ",", "\[Xi]"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rule", " ", "=", " ", RowBox[{"RULE", "[", "element", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"xx", " ", "=", " ", RowBox[{ RowBox[{"NN", ".", RowBox[{"{", RowBox[{ RowBox[{"x", "[", "1", "]"}], ",", RowBox[{"x", "[", "2", "]"}]}], "}"}]}], " ", "/.", " ", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"yy", " ", "=", " ", RowBox[{ RowBox[{"NN", ".", RowBox[{"{", RowBox[{ RowBox[{"y", "[", "1", "]"}], ",", RowBox[{"y", "[", "2", "]"}]}], "}"}]}], " ", "/.", " ", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"zz", " ", "=", " ", RowBox[{ RowBox[{"NN", ".", RowBox[{"{", RowBox[{ RowBox[{"z", "[", "1", "]"}], ",", RowBox[{"z", "[", "2", "]"}]}], "}"}]}], " ", "/.", " ", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"J", " ", "=", " ", RowBox[{"Sqrt", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "xx"}], ")"}], "^", "2"}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "yy"}], ")"}], "^", "2"}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "zz"}], ")"}], "^", "2"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"int", " ", "=", " ", RowBox[{ RowBox[{"J", "*", "exp"}], " ", "/.", " ", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "xx"}], ",", " ", RowBox[{"y", "\[Rule]", "yy"}], ",", " ", RowBox[{"z", "\[Rule]", "zz"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUADE", "[", RowBox[{"QTYPE", ",", RowBox[{ RowBox[{"(", RowBox[{"int", " ", "/.", " ", RowBox[{"\[Xi]", "\[Rule]", " ", "#1"}]}], ")"}], "&"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUADE", "[", RowBox[{"LINE1", ",", "exp_"}], "]"}], ":=", " ", RowBox[{ RowBox[{"exp", "[", RowBox[{"{", RowBox[{"1", "/", "2"}], "}"}], "]"}], ".", RowBox[{"{", "1", "}"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUADE", "[", RowBox[{"LINE2", ",", "exp_"}], "]"}], ":=", " ", RowBox[{ RowBox[{ RowBox[{"exp", "[", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "/", "2"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"QUADE", "[", RowBox[{"LINE3", ",", "exp_"}], "]"}], ":=", " ", RowBox[{ RowBox[{ RowBox[{"exp", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1", ",", "2"}], "}"}], "/", "2"}], "]"}], ".", RowBox[{"{", RowBox[{"1", ",", "4", ",", "1"}], "}"}]}], "/", "6"}]}], ";"}]}], "Input", InitializationCell->True, CellLabel->"In[56]:=",ExpressionUUID->"07a8cdfb-4723-40a1-a6c6-318acecc057a"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["FORCE MODEL", "Section", CellChangeTimes->{ 3.4430806364968*^9, {3.4453166713873997`*^9, 3.4453166747414*^9}, { 3.447462264275*^9, 3.4474622644154*^9}, {3.4695731321116*^9, 3.4695731359491997`*^9}, 3.473055186341*^9, {3.4730552472860003`*^9, 3.47305524884*^9}, {3.473055399782*^9, 3.473055419801*^9}, { 3.4734696760778*^9, 3.4734697047349997`*^9}, {3.4770537891542*^9, 3.4770537950354*^9}, {3.4932799754514*^9, 3.4932799779161997`*^9}, { 3.4945558951644*^9, 3.4945558957416*^9}, {3.4957646303032*^9, 3.4957646329084*^9}, {3.497581602118*^9, 3.4975816042552*^9}, { 3.500960505817*^9, 3.5009605094206*^9}, {3.556623836083009*^9, 3.5566238462386265`*^9}, {3.5568725055395393`*^9, 3.5568725163821597`*^9}, {3.556872678728445*^9, 3.5568726810485783`*^9}, { 3.7323376045620503`*^9, 3.7323376086812124`*^9}, {3.7335630623483887`*^9, 3.733563072583865*^9}, {3.733563130246215*^9, 3.733563131355714*^9}, { 3.817531303014368*^9, 3.8175313048303127`*^9}, {3.8175314979069576`*^9, 3.8175315153006535`*^9}, 3.817531608989934*^9},ExpressionUUID->"11730195-1052-43dc-a707-\ b2ccaa2937d3"], Cell[CellGroupData[{ Cell["NULL ELEMENT defs ", "Subsection", CellChangeTimes->{{3.6926098999374723`*^9, 3.6926099165674953`*^9}, { 3.7606078822118464`*^9, 3.7606078873319845`*^9}, {3.7606079926026382`*^9, 3.7606079992085595`*^9}},ExpressionUUID->"10a3b971-55d0-4ff8-9913-\ 748f6b1fc9a3"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"MEC", "-", "E1050"}], "|", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"should", " ", "anything", " ", "go", " ", "wrong"}], ",", " ", RowBox[{"do", " ", "this"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"analysistype_", ",", "ele_", ",", "fun_"}], "]"}], ":=", "0"}], ";"}]}]], "Input", CellChangeTimes->{{3.7606079691729827`*^9, 3.7606079699771805`*^9}, { 3.760608006624578*^9, 3.760608064931302*^9}, {3.7880761427660694`*^9, 3.788076155873885*^9}, {3.788424805091097*^9, 3.7884248740992002`*^9}, { 3.817531967792331*^9, 3.817531969861539*^9}},ExpressionUUID->"f8ae57a5-1c27-407e-9962-\ 6e5080babd59"] }, Closed]], Cell[CellGroupData[{ Cell["FORCE ELEMENT (disp) defs ", "Subsection", CellChangeTimes->{{3.6926098999374723`*^9, 3.6926099165674953`*^9}, { 3.7606078822118464`*^9, 3.7606078873319845`*^9}, {3.766555151642228*^9, 3.7665551755834265`*^9}, {3.774244544239236*^9, 3.7742445459997997`*^9}, { 3.787895139092532*^9, 3.787895139619763*^9}},ExpressionUUID->"b572a4a7-8c0c-4655-8d88-\ 90163b53d75b"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"MEC", "-", "E1050"}], "|", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"FX_", ",", "FY_", ",", "FZ_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1", "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ "FX_", ",", "FY_", ",", "FZ_", ",", "MX_", ",", "MY_", ",", "MZ_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ"}], "}"}], ".", RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"{", RowBox[{"MX", ",", "MY", ",", "MZ"}], "}"}], ".", RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], "]"}]}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX", ",", "fX"}], "}"}], ",", RowBox[{"{", RowBox[{"fY", ",", "fY"}], "}"}], ",", RowBox[{"{", RowBox[{"fZ", ",", "fZ"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX1_", ",", "fX2_"}], "}"}], ",", RowBox[{"{", RowBox[{"fY1_", ",", "fY2_"}], "}"}], ",", RowBox[{"{", RowBox[{"fZ1_", ",", "fZ2_"}], "}"}]}], "}"}], " ", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"nl", ",", "r0", ",", "h0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"h0", "/", "6"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{"fX1", ",", "fX2"}], "}"}]}], " ", "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{"fY1", ",", "fY2"}], "}"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{"fZ1", ",", "fZ2"}], "}"}]}]}], ")"}]}]}]}], " ", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"area", " ", "force"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}], " ", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX", ",", "fX", ",", "fX"}], "}"}], ",", RowBox[{"{", RowBox[{"fY", ",", "fY", ",", "fY"}], "}"}], ",", RowBox[{"{", RowBox[{"fZ", ",", "fZ", ",", "fZ"}], "}"}]}], "}"}], " ", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX1_", ",", "fX2_", ",", "fX3_"}], "}"}], ",", RowBox[{"{", RowBox[{"fY1_", ",", "fY2_", ",", "fY3_"}], "}"}], ",", RowBox[{"{", RowBox[{"fZ1_", ",", "fZ2_", ",", "fZ3_"}], "}"}]}], "}"}], " ", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Area", "[", RowBox[{"Polygon", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "1"}], "]"}], "]"}], "]"}], "]"}], "/", "12"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "2"}], "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{"fX1", ",", "fX2", ",", "fX3"}], "}"}]}], " ", "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "2"}], "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{"fY1", ",", "fY2", ",", "fY3"}], "}"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "2"}], "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{"fZ1", ",", "fZ2", ",", "fZ3"}], "}"}]}]}], ")"}]}]}], " ", ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.5002027395954*^9, {3.5007051491098003`*^9, 3.5007051504826*^9}, { 3.5007158972342*^9, 3.500715901961*^9}, {3.557660909440528*^9, 3.5576609113281307`*^9}, {3.557660948393796*^9, 3.5576609720746374`*^9}, { 3.557661012619109*^9, 3.5576610278447356`*^9}, {3.557661136342926*^9, 3.557661147387746*^9}, {3.6297908563470783`*^9, 3.629791071268656*^9}, 3.6297911922156687`*^9, 3.629791337951124*^9, 3.630659123489007*^9, { 3.6306802085628467`*^9, 3.630680256501731*^9}, {3.6306810828067827`*^9, 3.630681095411605*^9}, {3.6336810185255365`*^9, 3.6336810782549524`*^9}, { 3.685253847224399*^9, 3.68525389391807*^9}, 3.6853217521711235`*^9, { 3.6853402653249354`*^9, 3.6853402673449383`*^9}, {3.6881771903780155`*^9, 3.688177478668419*^9}, {3.688177519198476*^9, 3.688177565838541*^9}, { 3.6881807547137823`*^9, 3.6881807650437965`*^9}, {3.6881808240138793`*^9, 3.688180876463952*^9}, {3.6881809499540553`*^9, 3.688181051294197*^9}, { 3.688181093904257*^9, 3.6881812886945295`*^9}, {3.688181328234585*^9, 3.6881813304845877`*^9}, {3.688181453674761*^9, 3.6881815439948874`*^9}, { 3.6881825493903384`*^9, 3.6881825553503466`*^9}, {3.6888686424940867`*^9, 3.688868654634104*^9}, {3.6889603910835114`*^9, 3.688960395673517*^9}, { 3.6892196168325553`*^9, 3.6892196711326313`*^9}, {3.6892225677866864`*^9, 3.689222572486693*^9}, {3.692609973477575*^9, 3.6926099745275764`*^9}, { 3.6926155402795706`*^9, 3.692615635319703*^9}, {3.692615764369884*^9, 3.6926157969499297`*^9}, {3.6926158381999874`*^9, 3.6926159127500916`*^9}, {3.69261598286019*^9, 3.6926159923902035`*^9}, { 3.692616041680272*^9, 3.692616050660285*^9}, {3.692616114410374*^9, 3.692616301970637*^9}, 3.6926169967516093`*^9, {3.692617055031691*^9, 3.6926170726717157`*^9}, {3.6926171281517935`*^9, 3.6926171424118137`*^9}, {3.693017729825803*^9, 3.693017759355844*^9}, { 3.693017854095977*^9, 3.6930178839960184`*^9}, {3.693017945736105*^9, 3.6930179921261697`*^9}, {3.693716924097577*^9, 3.693716939187598*^9}, { 3.694845162608508*^9, 3.6948452135185795`*^9}, {3.6948452490186296`*^9, 3.6948452827886767`*^9}, {3.724757160342552*^9, 3.7247571958524694`*^9}, 3.724757226606532*^9, {3.724757277132578*^9, 3.7247573049427323`*^9}, { 3.7247573425972123`*^9, 3.724757343668002*^9}, {3.724757406051021*^9, 3.7247574182226624`*^9}, {3.72475750713536*^9, 3.724757523005001*^9}, { 3.7247575654114623`*^9, 3.724757565695835*^9}, {3.725367981062604*^9, 3.7253680379435987`*^9}, {3.753080180213684*^9, 3.75308023490277*^9}, { 3.7531760736894627`*^9, 3.7531760867433243`*^9}, {3.753176152767415*^9, 3.753176188588335*^9}, {3.7531763657274866`*^9, 3.7531763780597005`*^9}, { 3.7557233277936163`*^9, 3.7557233738564167`*^9}, {3.760607910807132*^9, 3.760607911704075*^9}, {3.766555201350331*^9, 3.7665553560217686`*^9}, { 3.7665553926814957`*^9, 3.766555405620928*^9}, {3.76663078538684*^9, 3.766630788445305*^9}, {3.7666308695077744`*^9, 3.7666309155844073`*^9}, { 3.766630963805001*^9, 3.766630964328018*^9}, {3.7666310063775616`*^9, 3.766631007597319*^9}, {3.766631053754822*^9, 3.7666310557693295`*^9}, { 3.766631102143116*^9, 3.766631182053177*^9}, {3.774244592505701*^9, 3.774244606024996*^9}, {3.774244666999945*^9, 3.774244780885934*^9}, { 3.7742448195924053`*^9, 3.7742448333656425`*^9}, {3.7742448971593103`*^9, 3.7742449615049114`*^9}, {3.774245098242358*^9, 3.7742451238780427`*^9}, { 3.77424518753212*^9, 3.7742451943686037`*^9}, {3.7742452586200476`*^9, 3.7742453104279203`*^9}, {3.7742469442792187`*^9, 3.7742472465608587`*^9}, {3.774247297716411*^9, 3.774247331264948*^9}, { 3.78807546567931*^9, 3.7880755830304527`*^9}, 3.78807562415361*^9, { 3.788075666988602*^9, 3.7880756768677874`*^9}, 3.788075710101962*^9, { 3.788075747380065*^9, 3.7880757482704797`*^9}, {3.7880760000927234`*^9, 3.788076030825418*^9}, 3.817437852364077*^9, {3.8408458462334127`*^9, 3.8408458682568913`*^9}, {3.840847529962968*^9, 3.840847547834058*^9}}, CellLabel->"In[62]:=",ExpressionUUID->"4ef1200c-ad4e-4c34-8e06-2931ac75ffb3"] }, Closed]], Cell[CellGroupData[{ Cell["FORCE ELEMENT (evnt) defs ", "Subsection", CellChangeTimes->{{3.6926098999374723`*^9, 3.6926099165674953`*^9}, { 3.7606078822118464`*^9, 3.7606078873319845`*^9}, {3.766555151642228*^9, 3.7665551755834265`*^9}, {3.774244544239236*^9, 3.7742445459997997`*^9}, { 3.787895139092532*^9, 3.787895139619763*^9}, {3.817437626458826*^9, 3.8174376276248903`*^9}, 3.8223693711432643`*^9},ExpressionUUID->"eb02d56d-6103-4cea-b42e-\ 30117bb7222f"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"MEC", "-", "E1050"}], "|", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"EVENT", ",", RowBox[{"{", RowBox[{"s0_", ",", "sol0_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"FORCE", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.5002027395954*^9, {3.5007051491098003`*^9, 3.5007051504826*^9}, { 3.5007158972342*^9, 3.500715901961*^9}, {3.557660909440528*^9, 3.5576609113281307`*^9}, {3.557660948393796*^9, 3.5576609720746374`*^9}, { 3.557661012619109*^9, 3.5576610278447356`*^9}, {3.557661136342926*^9, 3.557661147387746*^9}, {3.6297908563470783`*^9, 3.629791071268656*^9}, 3.6297911922156687`*^9, 3.629791337951124*^9, 3.630659123489007*^9, { 3.6306802085628467`*^9, 3.630680256501731*^9}, {3.6306810828067827`*^9, 3.630681095411605*^9}, {3.6336810185255365`*^9, 3.6336810782549524`*^9}, { 3.685253847224399*^9, 3.68525389391807*^9}, 3.6853217521711235`*^9, { 3.6853402653249354`*^9, 3.6853402673449383`*^9}, {3.6881771903780155`*^9, 3.688177478668419*^9}, {3.688177519198476*^9, 3.688177565838541*^9}, { 3.6881807547137823`*^9, 3.6881807650437965`*^9}, {3.6881808240138793`*^9, 3.688180876463952*^9}, {3.6881809499540553`*^9, 3.688181051294197*^9}, { 3.688181093904257*^9, 3.6881812886945295`*^9}, {3.688181328234585*^9, 3.6881813304845877`*^9}, {3.688181453674761*^9, 3.6881815439948874`*^9}, { 3.6881825493903384`*^9, 3.6881825553503466`*^9}, {3.6888686424940867`*^9, 3.688868654634104*^9}, {3.6889603910835114`*^9, 3.688960395673517*^9}, { 3.6892196168325553`*^9, 3.6892196711326313`*^9}, {3.6892225677866864`*^9, 3.689222572486693*^9}, {3.692609973477575*^9, 3.6926099745275764`*^9}, { 3.6926155402795706`*^9, 3.692615635319703*^9}, {3.692615764369884*^9, 3.6926157969499297`*^9}, {3.6926158381999874`*^9, 3.6926159127500916`*^9}, {3.69261598286019*^9, 3.6926159923902035`*^9}, { 3.692616041680272*^9, 3.692616050660285*^9}, {3.692616114410374*^9, 3.692616301970637*^9}, 3.6926169967516093`*^9, {3.692617055031691*^9, 3.6926170726717157`*^9}, {3.6926171281517935`*^9, 3.6926171424118137`*^9}, {3.693017729825803*^9, 3.693017759355844*^9}, { 3.693017854095977*^9, 3.6930178839960184`*^9}, {3.693017945736105*^9, 3.6930179921261697`*^9}, {3.693716924097577*^9, 3.693716939187598*^9}, { 3.694845162608508*^9, 3.6948452135185795`*^9}, {3.6948452490186296`*^9, 3.6948452827886767`*^9}, {3.724757160342552*^9, 3.7247571958524694`*^9}, 3.724757226606532*^9, {3.724757277132578*^9, 3.7247573049427323`*^9}, { 3.7247573425972123`*^9, 3.724757343668002*^9}, {3.724757406051021*^9, 3.7247574182226624`*^9}, {3.72475750713536*^9, 3.724757523005001*^9}, { 3.7247575654114623`*^9, 3.724757565695835*^9}, {3.725367981062604*^9, 3.7253680379435987`*^9}, {3.753080180213684*^9, 3.75308023490277*^9}, { 3.7531760736894627`*^9, 3.7531760867433243`*^9}, {3.753176152767415*^9, 3.753176188588335*^9}, {3.7531763657274866`*^9, 3.7531763780597005`*^9}, { 3.7557233277936163`*^9, 3.7557233738564167`*^9}, {3.760607910807132*^9, 3.760607911704075*^9}, {3.766555201350331*^9, 3.7665553560217686`*^9}, { 3.7665553926814957`*^9, 3.766555405620928*^9}, {3.76663078538684*^9, 3.766630788445305*^9}, {3.7666308695077744`*^9, 3.7666309155844073`*^9}, { 3.766630963805001*^9, 3.766630964328018*^9}, {3.7666310063775616`*^9, 3.766631007597319*^9}, {3.766631053754822*^9, 3.7666310557693295`*^9}, { 3.766631102143116*^9, 3.766631182053177*^9}, {3.774244592505701*^9, 3.774244606024996*^9}, {3.774244666999945*^9, 3.774244780885934*^9}, { 3.7742448195924053`*^9, 3.7742448333656425`*^9}, {3.7742448971593103`*^9, 3.7742449615049114`*^9}, {3.774245098242358*^9, 3.7742451238780427`*^9}, { 3.77424518753212*^9, 3.7742451943686037`*^9}, {3.7742452586200476`*^9, 3.7742453104279203`*^9}, {3.7742469442792187`*^9, 3.7742472465608587`*^9}, {3.774247297716411*^9, 3.774247331264948*^9}, { 3.78807546567931*^9, 3.7880755830304527`*^9}, 3.78807562415361*^9, { 3.788075666988602*^9, 3.7880756768677874`*^9}, 3.788075710101962*^9, { 3.788075747380065*^9, 3.7880757482704797`*^9}, {3.7880760000927234`*^9, 3.788076030825418*^9}, {3.817437636844257*^9, 3.817437649087758*^9}, { 3.8174378054427986`*^9, 3.8174378405468597`*^9}, {3.8174388645560064`*^9, 3.817438902212788*^9}, 3.8175212166525545`*^9}, CellLabel->"In[68]:=",ExpressionUUID->"5a76afda-3e2b-407f-828d-a064af3284c8"] }, Closed]], Cell[CellGroupData[{ Cell["FORCE ELEMENT (vibr) defs ", "Subsection", CellChangeTimes->{{3.6926098999374723`*^9, 3.6926099165674953`*^9}, { 3.760607890234026*^9, 3.760607893763776*^9}, {3.787895219181797*^9, 3.787895220119398*^9}},ExpressionUUID->"66e83de4-cdf2-4efb-953b-\ 7b1ca775f27d"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"FX_", ",", "FY_", ",", "FZ_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1", "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ "FX_", ",", "FY_", ",", "FZ_", ",", "MX_", ",", "MY_", ",", "MZ_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ"}], "}"}], ".", RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}]}], "+", RowBox[{ RowBox[{"{", RowBox[{"MX", ",", "MY", ",", "MZ"}], "}"}], ".", RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}]}]}], ")"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX", ",", "fX"}], "}"}], ",", RowBox[{"{", RowBox[{"fY", ",", "fY"}], "}"}], ",", RowBox[{"{", RowBox[{"fZ", ",", "fZ"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX1_", ",", "fX2_"}], "}"}], ",", RowBox[{"{", RowBox[{"fY1_", ",", "fY2_"}], "}"}], ",", RowBox[{"{", RowBox[{"fZ1_", ",", "fZ2_"}], "}"}]}], "}"}], " ", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"nl", ",", "r0", ",", "h0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(", RowBox[{ RowBox[{"h0", "/", "6"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{"fX1", ",", "fX2"}], "}"}]}], " ", "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{"fY1", ",", "fY2"}], "}"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{"fZ1", ",", "fZ2"}], "}"}]}]}], ")"}]}], ")"}]}]}], " ", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}], " ", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX", ",", "fX", ",", "fX"}], "}"}], ",", RowBox[{"{", RowBox[{"fY", ",", "fY", ",", "fY"}], "}"}], ",", RowBox[{"{", RowBox[{"fZ", ",", "fZ", ",", "fZ"}], "}"}]}], "}"}], " ", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX1_", ",", "fX2_", ",", "fX3_"}], "}"}], ",", RowBox[{"{", RowBox[{"fY1_", ",", "fY2_", ",", "fY3_"}], "}"}], ",", RowBox[{"{", RowBox[{"fZ1_", ",", "fZ2_", ",", "fZ3_"}], "}"}]}], "}"}], " ", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", " ", RowBox[{ RowBox[{ RowBox[{"Area", "[", RowBox[{"Polygon", "[", RowBox[{"fun", "[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "1"}], "]"}], "]"}], "]"}], "/", "12"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "2"}], "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{"fX1", ",", "fX2", ",", "fX3"}], "}"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "2"}], "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{"fY1", ",", "fY2", ",", "fY3"}], "}"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "2"}], "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{"fZ1", ",", "fZ2", ",", "fZ3"}], "}"}]}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"{", "m_", "}"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "m"}], " ", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}], ")"}], ".", " ", RowBox[{"(", RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}], ")"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"{", RowBox[{"m_", ",", "J_"}], "}"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"m", ",", "J"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1", "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"m_", ",", "J_"}], "}"}], ",", RowBox[{"{", RowBox[{"ix_", ",", "iy_"}], "}"}]}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"iz", "=", RowBox[{"ix", StyleBox["\[Cross]", "OperatorCharacter"], StyleBox["iy", "OperatorCharacter"]}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"m", " ", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}], ")"}], ".", RowBox[{"(", " ", RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}], ")"}]}]}], "-", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"J", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}], ")"}], ".", RowBox[{"(", RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"for", " ", "detailed", " ", "graphics"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"m_", ",", "J_"}], "}"}], ",", RowBox[{"{", RowBox[{"ix_", ",", "iy_"}], "}"}], ",", RowBox[{"{", RowBox[{"xyz_", ",", "obj_"}], "}"}]}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"m", ",", "J"}], "}"}], ",", RowBox[{"{", RowBox[{"ix", ",", "iy"}], "}"}]}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1", "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.5002027395954*^9, {3.5007051491098003`*^9, 3.5007051504826*^9}, { 3.5007158972342*^9, 3.500715901961*^9}, {3.557660909440528*^9, 3.5576609113281307`*^9}, {3.557660948393796*^9, 3.5576609720746374`*^9}, { 3.557661012619109*^9, 3.5576610278447356`*^9}, {3.557661136342926*^9, 3.557661147387746*^9}, {3.6297908563470783`*^9, 3.629791071268656*^9}, 3.6297911922156687`*^9, 3.629791337951124*^9, 3.630659123489007*^9, { 3.6306802085628467`*^9, 3.630680256501731*^9}, {3.6306810828067827`*^9, 3.630681095411605*^9}, {3.6336810185255365`*^9, 3.6336810782549524`*^9}, { 3.685253847224399*^9, 3.68525389391807*^9}, 3.6853217521711235`*^9, { 3.6853402653249354`*^9, 3.6853402673449383`*^9}, {3.6881771903780155`*^9, 3.688177478668419*^9}, {3.688177519198476*^9, 3.688177565838541*^9}, { 3.6881807547137823`*^9, 3.6881807650437965`*^9}, {3.6881808240138793`*^9, 3.688180876463952*^9}, {3.6881809499540553`*^9, 3.688181051294197*^9}, { 3.688181093904257*^9, 3.6881812886945295`*^9}, {3.688181328234585*^9, 3.6881813304845877`*^9}, {3.688181453674761*^9, 3.6881815439948874`*^9}, { 3.6881825493903384`*^9, 3.6881825553503466`*^9}, {3.6888686424940867`*^9, 3.688868654634104*^9}, {3.6889603910835114`*^9, 3.688960395673517*^9}, { 3.6892196168325553`*^9, 3.6892196711326313`*^9}, {3.6892225677866864`*^9, 3.689222572486693*^9}, {3.692609973477575*^9, 3.6926099745275764`*^9}, { 3.6926155402795706`*^9, 3.692615635319703*^9}, {3.692615764369884*^9, 3.6926157969499297`*^9}, {3.6926158381999874`*^9, 3.6926159127500916`*^9}, {3.69261598286019*^9, 3.6926159923902035`*^9}, { 3.692616041680272*^9, 3.692616050660285*^9}, {3.692616114410374*^9, 3.692616301970637*^9}, 3.6926169967516093`*^9, {3.692617055031691*^9, 3.6926170726717157`*^9}, {3.6926171281517935`*^9, 3.6926171424118137`*^9}, {3.693017729825803*^9, 3.693017759355844*^9}, { 3.693017854095977*^9, 3.6930178839960184`*^9}, {3.693017945736105*^9, 3.6930179921261697`*^9}, {3.693716924097577*^9, 3.693716939187598*^9}, { 3.694845162608508*^9, 3.6948452135185795`*^9}, {3.6948452490186296`*^9, 3.6948452827886767`*^9}, {3.724757160342552*^9, 3.7247571958524694`*^9}, 3.724757226606532*^9, {3.724757277132578*^9, 3.7247573049427323`*^9}, { 3.7247573425972123`*^9, 3.724757343668002*^9}, {3.724757406051021*^9, 3.7247574182226624`*^9}, {3.72475750713536*^9, 3.724757523005001*^9}, { 3.7247575654114623`*^9, 3.724757565695835*^9}, {3.725367981062604*^9, 3.7253680379435987`*^9}, {3.753080180213684*^9, 3.75308023490277*^9}, { 3.7531760736894627`*^9, 3.7531760867433243`*^9}, {3.753176152767415*^9, 3.753176188588335*^9}, {3.7531763657274866`*^9, 3.7531763780597005`*^9}, { 3.7557233277936163`*^9, 3.7557233738564167`*^9}, {3.760607934362851*^9, 3.7606079386004443`*^9}, {3.760608196677984*^9, 3.7606082206131644`*^9}, { 3.7650816994300117`*^9, 3.76508188551581*^9}, {3.765081961656807*^9, 3.765082049591256*^9}, {3.7650820808183804`*^9, 3.765082093155528*^9}, { 3.765082452422645*^9, 3.7650825105342064`*^9}, {3.76508255601999*^9, 3.765082685611348*^9}, {3.765082742570591*^9, 3.7650827441033616`*^9}, { 3.7650827973670535`*^9, 3.7650828162989264`*^9}, {3.7650828756452084`*^9, 3.76508291725654*^9}, {3.787989785884842*^9, 3.7879897861538515`*^9}, { 3.787989950939253*^9, 3.7879899714860353`*^9}, {3.787990031945051*^9, 3.7879900904605694`*^9}, {3.7880748631855245`*^9, 3.788074907396145*^9}, { 3.788074983681623*^9, 3.7880749851875305`*^9}, {3.7880752108539596`*^9, 3.7880753460848837`*^9}, {3.7880753955492105`*^9, 3.7880754495543413`*^9}, 3.7880757985887327`*^9, {3.7880758550342417`*^9, 3.7880758814237986`*^9}, { 3.7880759143167744`*^9, 3.7880759877586217`*^9}, {3.788076059772026*^9, 3.788076102767933*^9}, 3.7881670103681445`*^9, {3.788424742599498*^9, 3.7884247886832037`*^9}, {3.820469573319458*^9, 3.8204696119241095`*^9}, { 3.820469713680828*^9, 3.820469726202425*^9}, {3.820469774985937*^9, 3.8204697820405493`*^9}, {3.8204709818632145`*^9, 3.8204709829070034`*^9}, {3.8211506205514607`*^9, 3.8211506410480547`*^9}, {3.821150731307102*^9, 3.821150735471115*^9}, { 3.821151423923393*^9, 3.82115148698011*^9}, {3.821151531470887*^9, 3.8211516059392166`*^9}, {3.8298844266880245`*^9, 3.8298844622541885`*^9}, {3.829890944882238*^9, 3.8298909629438314`*^9}, { 3.829891002598065*^9, 3.8298910041502285`*^9}, {3.8298910779119153`*^9, 3.8298911107781134`*^9}, {3.8298912682866173`*^9, 3.829891271409994*^9}}, CellLabel->"In[69]:=",ExpressionUUID->"a0f62632-6cb5-4616-a306-7f3d44298dc4"] }, Closed]], Cell[CellGroupData[{ Cell["FORCE ELEMENT (stab) defs ", "Subsection", CellChangeTimes->{{3.6926098999374723`*^9, 3.6926099165674953`*^9}, { 3.760607890234026*^9, 3.760607893763776*^9}, {3.787895219181797*^9, 3.787895220119398*^9}, {3.788574649818136*^9, 3.7885746509362783`*^9}},ExpressionUUID->"00760fe3-96a5-4648-a12e-\ bd9d44d56567"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"FX_", ",", "FY_", ",", "FZ_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1", "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ "FX_", ",", "FY_", ",", "FZ_", ",", "MX_", ",", "MY_", ",", "MZ_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ "FX", ",", "FY", ",", "FZ", ",", "MX", ",", "MY", ",", "MZ"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1", "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX1_", ",", "fX2_"}], "}"}], ",", RowBox[{"{", RowBox[{"fY1_", ",", "fY2_"}], "}"}], ",", RowBox[{"{", RowBox[{"fZ1_", ",", "fZ2_"}], "}"}]}], "}"}], " ", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX1", ",", "fX2"}], "}"}], ",", RowBox[{"{", RowBox[{"fY1", ",", "fY2"}], "}"}], ",", RowBox[{"{", RowBox[{"fZ1", ",", "fZ2"}], "}"}]}], "}"}], " ", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}], " ", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}], " ", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX1_", ",", "fX2_", ",", "fX3_"}], "}"}], ",", RowBox[{"{", RowBox[{"fY1_", ",", "fY2_", ",", "fY3_"}], "}"}], ",", RowBox[{"{", RowBox[{"fZ1_", ",", "fZ2_", ",", "fZ3_"}], "}"}]}], "}"}], " ", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", " ", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX1", ",", "fX2", ",", "fX3"}], "}"}], ",", RowBox[{"{", RowBox[{"fY1", ",", "fY2", ",", "fY3"}], "}"}], ",", RowBox[{"{", RowBox[{"fZ1", ",", "fZ2", ",", "fZ3"}], "}"}]}], "}"}], " ", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.5002027395954*^9, {3.5007051491098003`*^9, 3.5007051504826*^9}, { 3.5007158972342*^9, 3.500715901961*^9}, {3.557660909440528*^9, 3.5576609113281307`*^9}, {3.557660948393796*^9, 3.5576609720746374`*^9}, { 3.557661012619109*^9, 3.5576610278447356`*^9}, {3.557661136342926*^9, 3.557661147387746*^9}, {3.6297908563470783`*^9, 3.629791071268656*^9}, 3.6297911922156687`*^9, 3.629791337951124*^9, 3.630659123489007*^9, { 3.6306802085628467`*^9, 3.630680256501731*^9}, {3.6306810828067827`*^9, 3.630681095411605*^9}, {3.6336810185255365`*^9, 3.6336810782549524`*^9}, { 3.685253847224399*^9, 3.68525389391807*^9}, 3.6853217521711235`*^9, { 3.6853402653249354`*^9, 3.6853402673449383`*^9}, {3.6881771903780155`*^9, 3.688177478668419*^9}, {3.688177519198476*^9, 3.688177565838541*^9}, { 3.6881807547137823`*^9, 3.6881807650437965`*^9}, {3.6881808240138793`*^9, 3.688180876463952*^9}, {3.6881809499540553`*^9, 3.688181051294197*^9}, { 3.688181093904257*^9, 3.6881812886945295`*^9}, {3.688181328234585*^9, 3.6881813304845877`*^9}, {3.688181453674761*^9, 3.6881815439948874`*^9}, { 3.6881825493903384`*^9, 3.6881825553503466`*^9}, {3.6888686424940867`*^9, 3.688868654634104*^9}, {3.6889603910835114`*^9, 3.688960395673517*^9}, { 3.6892196168325553`*^9, 3.6892196711326313`*^9}, {3.6892225677866864`*^9, 3.689222572486693*^9}, {3.692609973477575*^9, 3.6926099745275764`*^9}, { 3.6926155402795706`*^9, 3.692615635319703*^9}, {3.692615764369884*^9, 3.6926157969499297`*^9}, {3.6926158381999874`*^9, 3.6926159127500916`*^9}, {3.69261598286019*^9, 3.6926159923902035`*^9}, { 3.692616041680272*^9, 3.692616050660285*^9}, {3.692616114410374*^9, 3.692616301970637*^9}, 3.6926169967516093`*^9, {3.692617055031691*^9, 3.6926170726717157`*^9}, {3.6926171281517935`*^9, 3.6926171424118137`*^9}, {3.693017729825803*^9, 3.693017759355844*^9}, { 3.693017854095977*^9, 3.6930178839960184`*^9}, {3.693017945736105*^9, 3.6930179921261697`*^9}, {3.693716924097577*^9, 3.693716939187598*^9}, { 3.694845162608508*^9, 3.6948452135185795`*^9}, {3.6948452490186296`*^9, 3.6948452827886767`*^9}, {3.724757160342552*^9, 3.7247571958524694`*^9}, 3.724757226606532*^9, {3.724757277132578*^9, 3.7247573049427323`*^9}, { 3.7247573425972123`*^9, 3.724757343668002*^9}, {3.724757406051021*^9, 3.7247574182226624`*^9}, {3.72475750713536*^9, 3.724757523005001*^9}, { 3.7247575654114623`*^9, 3.724757565695835*^9}, {3.725367981062604*^9, 3.7253680379435987`*^9}, {3.753080180213684*^9, 3.75308023490277*^9}, { 3.7531760736894627`*^9, 3.7531760867433243`*^9}, {3.753176152767415*^9, 3.753176188588335*^9}, {3.7531763657274866`*^9, 3.7531763780597005`*^9}, { 3.7557233277936163`*^9, 3.7557233738564167`*^9}, {3.760607934362851*^9, 3.7606079386004443`*^9}, {3.760608196677984*^9, 3.7606082206131644`*^9}, { 3.7650816994300117`*^9, 3.76508188551581*^9}, {3.765081961656807*^9, 3.765082049591256*^9}, {3.7650820808183804`*^9, 3.765082093155528*^9}, { 3.765082452422645*^9, 3.7650825105342064`*^9}, {3.76508255601999*^9, 3.765082685611348*^9}, {3.765082742570591*^9, 3.7650827441033616`*^9}, { 3.7650827973670535`*^9, 3.7650828162989264`*^9}, {3.7650828756452084`*^9, 3.76508291725654*^9}, {3.787989785884842*^9, 3.7879897861538515`*^9}, { 3.787989950939253*^9, 3.7879899714860353`*^9}, {3.787990031945051*^9, 3.7879900904605694`*^9}, {3.7880748631855245`*^9, 3.788074907396145*^9}, { 3.788074983681623*^9, 3.7880749851875305`*^9}, {3.7880752108539596`*^9, 3.7880753460848837`*^9}, {3.7880753955492105`*^9, 3.7880754495543413`*^9}, 3.7880757985887327`*^9, {3.7880758550342417`*^9, 3.7880758814237986`*^9}, { 3.7880759143167744`*^9, 3.7880759877586217`*^9}, {3.788076059772026*^9, 3.788076102767933*^9}, 3.7881670103681445`*^9, {3.788424742599498*^9, 3.7884247886832037`*^9}, {3.788574662089695*^9, 3.7885746993059206`*^9}, { 3.7885747319173193`*^9, 3.7885747927154846`*^9}, {3.788833131233985*^9, 3.788833188690298*^9}, {3.821150888214839*^9, 3.8211509294646425`*^9}, { 3.8211509603238955`*^9, 3.8211510555185704`*^9}, {3.8211511473842373`*^9, 3.821151233654641*^9}}, CellLabel->"In[79]:=",ExpressionUUID->"89d5eea9-5a18-4852-9d52-bb525ff9ee28"] }, Closed]], Cell[CellGroupData[{ Cell["FORCE ELEMENT (nonl) defs ", "Subsection", CellChangeTimes->{{3.6926098999374723`*^9, 3.6926099165674953`*^9}, { 3.760607890234026*^9, 3.760607893763776*^9}, {3.787895219181797*^9, 3.787895220119398*^9}, {3.788574649818136*^9, 3.7885746509362783`*^9}, { 3.789441075232401*^9, 3.7894410761072865`*^9}},ExpressionUUID->"05f18933-8805-4dd4-9044-\ 2c67ffb9e9ee"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"FX_", ",", "FY_", ",", "FZ_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1", "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ "FX_", ",", "FY_", ",", "FZ_", ",", "MX_", ",", "MY_", ",", "MZ_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ"}], "}"}], ".", RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "]"}]}], "+", RowBox[{"MY", "*", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3", ",", "3"}], "]"}], "]"}]}], "*", RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3", ",", "1"}], "]"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"1", "+", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3", ",", "1"}], "]"}], "]"}]}], ")"}], "*", " ", RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3", ",", "3"}], "]"}], "]"}], "]"}]}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "+", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3", ",", "1"}], "]"}], "]"}]}], ")"}], "^", "2"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3", ",", "3"}], "]"}], "]"}], "^", "2"}]}], ")"}]}]}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"area", " ", "force"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}], " ", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX", ",", "fX", ",", "fX"}], "}"}], ",", RowBox[{"{", RowBox[{"fY", ",", "fY", ",", "fY"}], "}"}], ",", RowBox[{"{", RowBox[{"fZ", ",", "fZ", ",", "fZ"}], "}"}]}], "}"}], " ", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX1_", ",", "fX2_", ",", "fX3_"}], "}"}], ",", RowBox[{"{", RowBox[{"fY1_", ",", "fY2_", ",", "fY3_"}], "}"}], ",", RowBox[{"{", RowBox[{"fZ1_", ",", "fZ2_", ",", "fZ3_"}], "}"}]}], "}"}], " ", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX1", ",", "fX2", ",", "fX3"}], "}"}], ",", RowBox[{"{", RowBox[{"fY1", ",", "fY2", ",", "fY3"}], "}"}], ",", RowBox[{"{", RowBox[{"fZ1", ",", "fZ2", ",", "fZ3"}], "}"}]}], "}"}], " ", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.5002027395954*^9, {3.5007051491098003`*^9, 3.5007051504826*^9}, { 3.5007158972342*^9, 3.500715901961*^9}, {3.557660909440528*^9, 3.5576609113281307`*^9}, {3.557660948393796*^9, 3.5576609720746374`*^9}, { 3.557661012619109*^9, 3.5576610278447356`*^9}, {3.557661136342926*^9, 3.557661147387746*^9}, {3.6297908563470783`*^9, 3.629791071268656*^9}, 3.6297911922156687`*^9, 3.629791337951124*^9, 3.630659123489007*^9, { 3.6306802085628467`*^9, 3.630680256501731*^9}, {3.6306810828067827`*^9, 3.630681095411605*^9}, {3.6336810185255365`*^9, 3.6336810782549524`*^9}, { 3.685253847224399*^9, 3.68525389391807*^9}, 3.6853217521711235`*^9, { 3.6853402653249354`*^9, 3.6853402673449383`*^9}, {3.6881771903780155`*^9, 3.688177478668419*^9}, {3.688177519198476*^9, 3.688177565838541*^9}, { 3.6881807547137823`*^9, 3.6881807650437965`*^9}, {3.6881808240138793`*^9, 3.688180876463952*^9}, {3.6881809499540553`*^9, 3.688181051294197*^9}, { 3.688181093904257*^9, 3.6881812886945295`*^9}, {3.688181328234585*^9, 3.6881813304845877`*^9}, {3.688181453674761*^9, 3.6881815439948874`*^9}, { 3.6881825493903384`*^9, 3.6881825553503466`*^9}, {3.6888686424940867`*^9, 3.688868654634104*^9}, {3.6889603910835114`*^9, 3.688960395673517*^9}, { 3.6892196168325553`*^9, 3.6892196711326313`*^9}, {3.6892225677866864`*^9, 3.689222572486693*^9}, {3.692609973477575*^9, 3.6926099745275764`*^9}, { 3.6926155402795706`*^9, 3.692615635319703*^9}, {3.692615764369884*^9, 3.6926157969499297`*^9}, {3.6926158381999874`*^9, 3.6926159127500916`*^9}, {3.69261598286019*^9, 3.6926159923902035`*^9}, { 3.692616041680272*^9, 3.692616050660285*^9}, {3.692616114410374*^9, 3.692616301970637*^9}, 3.6926169967516093`*^9, {3.692617055031691*^9, 3.6926170726717157`*^9}, {3.6926171281517935`*^9, 3.6926171424118137`*^9}, {3.693017729825803*^9, 3.693017759355844*^9}, { 3.693017854095977*^9, 3.6930178839960184`*^9}, {3.693017945736105*^9, 3.6930179921261697`*^9}, {3.693716924097577*^9, 3.693716939187598*^9}, { 3.694845162608508*^9, 3.6948452135185795`*^9}, {3.6948452490186296`*^9, 3.6948452827886767`*^9}, {3.724757160342552*^9, 3.7247571958524694`*^9}, 3.724757226606532*^9, {3.724757277132578*^9, 3.7247573049427323`*^9}, { 3.7247573425972123`*^9, 3.724757343668002*^9}, {3.724757406051021*^9, 3.7247574182226624`*^9}, {3.72475750713536*^9, 3.724757523005001*^9}, { 3.7247575654114623`*^9, 3.724757565695835*^9}, {3.725367981062604*^9, 3.7253680379435987`*^9}, {3.753080180213684*^9, 3.75308023490277*^9}, { 3.7531760736894627`*^9, 3.7531760867433243`*^9}, {3.753176152767415*^9, 3.753176188588335*^9}, {3.7531763657274866`*^9, 3.7531763780597005`*^9}, { 3.7557233277936163`*^9, 3.7557233738564167`*^9}, {3.760607934362851*^9, 3.7606079386004443`*^9}, {3.760608196677984*^9, 3.7606082206131644`*^9}, { 3.7650816994300117`*^9, 3.76508188551581*^9}, {3.765081961656807*^9, 3.765082049591256*^9}, {3.7650820808183804`*^9, 3.765082093155528*^9}, { 3.765082452422645*^9, 3.7650825105342064`*^9}, {3.76508255601999*^9, 3.765082685611348*^9}, {3.765082742570591*^9, 3.7650827441033616`*^9}, { 3.7650827973670535`*^9, 3.7650828162989264`*^9}, {3.7650828756452084`*^9, 3.76508291725654*^9}, {3.787989785884842*^9, 3.7879897861538515`*^9}, { 3.787989950939253*^9, 3.7879899714860353`*^9}, {3.787990031945051*^9, 3.7879900904605694`*^9}, {3.7880748631855245`*^9, 3.788074907396145*^9}, { 3.788074983681623*^9, 3.7880749851875305`*^9}, {3.7880752108539596`*^9, 3.7880753460848837`*^9}, {3.7880753955492105`*^9, 3.7880754495543413`*^9}, 3.7880757985887327`*^9, {3.7880758550342417`*^9, 3.7880758814237986`*^9}, { 3.7880759143167744`*^9, 3.7880759877586217`*^9}, {3.788076059772026*^9, 3.788076102767933*^9}, 3.7881670103681445`*^9, {3.788424742599498*^9, 3.7884247886832037`*^9}, {3.788574662089695*^9, 3.7885746993059206`*^9}, { 3.7885747319173193`*^9, 3.7885747927154846`*^9}, {3.788833131233985*^9, 3.788833188690298*^9}, {3.789441083494993*^9, 3.7894410929575987`*^9}, { 3.7894411329012265`*^9, 3.789441135103803*^9}, {3.8216139632647324`*^9, 3.821614000501048*^9}, {3.821778980163827*^9, 3.821779023170026*^9}, { 3.8526149197908554`*^9, 3.8526149264241767`*^9}, {3.8526150097945175`*^9, 3.8526151076594424`*^9}, {3.8526151937844095`*^9, 3.8526153799795046`*^9}, {3.8526154236433077`*^9, 3.852615428357727*^9}, 3.852615738143323*^9, {3.85261577369608*^9, 3.8526157754718657`*^9}, { 3.852615819281072*^9, 3.8526158733183727`*^9}, 3.8526167397965617`*^9, { 3.85261723461384*^9, 3.8526172417322617`*^9}, {3.8526178141348553`*^9, 3.8526178535724907`*^9}, 3.852617953477276*^9, {3.8526936587753305`*^9, 3.852693709451621*^9}, {3.8526943296373367`*^9, 3.852694418011649*^9}, { 3.852694451913797*^9, 3.852694569753277*^9}, {3.852699051213097*^9, 3.85269906934655*^9}, {3.8526991193491087`*^9, 3.85269912274557*^9}}, CellLabel->"In[85]:=",ExpressionUUID->"754cb2f7-16f1-484b-b777-131739da99a4"] }, Open ]], Cell[CellGroupData[{ Cell["FORCE ELEMENT (tmec) defs ", "Subsection", CellChangeTimes->{{3.6926098999374723`*^9, 3.6926099165674953`*^9}, { 3.760607890234026*^9, 3.760607893763776*^9}, {3.787895219181797*^9, 3.787895220119398*^9}, {3.788574649818136*^9, 3.7885746509362783`*^9}, { 3.789441075232401*^9, 3.7894410761072865`*^9}, {3.8223693498062468`*^9, 3.8223693569381757`*^9}},ExpressionUUID->"4a94c2a2-6f79-4c85-bf73-\ 05c16b93f2ed"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"TMEC", ",", RowBox[{"{", RowBox[{"FORCE", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.5002027395954*^9, {3.5007051491098003`*^9, 3.5007051504826*^9}, { 3.5007158972342*^9, 3.500715901961*^9}, {3.557660909440528*^9, 3.5576609113281307`*^9}, {3.557660948393796*^9, 3.5576609720746374`*^9}, { 3.557661012619109*^9, 3.5576610278447356`*^9}, {3.557661136342926*^9, 3.557661147387746*^9}, {3.6297908563470783`*^9, 3.629791071268656*^9}, 3.6297911922156687`*^9, 3.629791337951124*^9, 3.630659123489007*^9, { 3.6306802085628467`*^9, 3.630680256501731*^9}, {3.6306810828067827`*^9, 3.630681095411605*^9}, {3.6336810185255365`*^9, 3.6336810782549524`*^9}, { 3.685253847224399*^9, 3.68525389391807*^9}, 3.6853217521711235`*^9, { 3.6853402653249354`*^9, 3.6853402673449383`*^9}, {3.6881771903780155`*^9, 3.688177478668419*^9}, {3.688177519198476*^9, 3.688177565838541*^9}, { 3.6881807547137823`*^9, 3.6881807650437965`*^9}, {3.6881808240138793`*^9, 3.688180876463952*^9}, {3.6881809499540553`*^9, 3.688181051294197*^9}, { 3.688181093904257*^9, 3.6881812886945295`*^9}, {3.688181328234585*^9, 3.6881813304845877`*^9}, {3.688181453674761*^9, 3.6881815439948874`*^9}, { 3.6881825493903384`*^9, 3.6881825553503466`*^9}, {3.6888686424940867`*^9, 3.688868654634104*^9}, {3.6889603910835114`*^9, 3.688960395673517*^9}, { 3.6892196168325553`*^9, 3.6892196711326313`*^9}, {3.6892225677866864`*^9, 3.689222572486693*^9}, {3.692609973477575*^9, 3.6926099745275764`*^9}, { 3.6926155402795706`*^9, 3.692615635319703*^9}, {3.692615764369884*^9, 3.6926157969499297`*^9}, {3.6926158381999874`*^9, 3.6926159127500916`*^9}, {3.69261598286019*^9, 3.6926159923902035`*^9}, { 3.692616041680272*^9, 3.692616050660285*^9}, {3.692616114410374*^9, 3.692616301970637*^9}, 3.6926169967516093`*^9, {3.692617055031691*^9, 3.6926170726717157`*^9}, {3.6926171281517935`*^9, 3.6926171424118137`*^9}, {3.693017729825803*^9, 3.693017759355844*^9}, { 3.693017854095977*^9, 3.6930178839960184`*^9}, {3.693017945736105*^9, 3.6930179921261697`*^9}, {3.693716924097577*^9, 3.693716939187598*^9}, { 3.694845162608508*^9, 3.6948452135185795`*^9}, {3.6948452490186296`*^9, 3.6948452827886767`*^9}, {3.724757160342552*^9, 3.7247571958524694`*^9}, 3.724757226606532*^9, {3.724757277132578*^9, 3.7247573049427323`*^9}, { 3.7247573425972123`*^9, 3.724757343668002*^9}, {3.724757406051021*^9, 3.7247574182226624`*^9}, {3.72475750713536*^9, 3.724757523005001*^9}, { 3.7247575654114623`*^9, 3.724757565695835*^9}, {3.725367981062604*^9, 3.7253680379435987`*^9}, {3.753080180213684*^9, 3.75308023490277*^9}, { 3.7531760736894627`*^9, 3.7531760867433243`*^9}, {3.753176152767415*^9, 3.753176188588335*^9}, {3.7531763657274866`*^9, 3.7531763780597005`*^9}, { 3.7557233277936163`*^9, 3.7557233738564167`*^9}, {3.760607934362851*^9, 3.7606079386004443`*^9}, {3.760608196677984*^9, 3.7606082206131644`*^9}, { 3.7650816994300117`*^9, 3.76508188551581*^9}, {3.765081961656807*^9, 3.765082049591256*^9}, {3.7650820808183804`*^9, 3.765082093155528*^9}, { 3.765082452422645*^9, 3.7650825105342064`*^9}, {3.76508255601999*^9, 3.765082685611348*^9}, {3.765082742570591*^9, 3.7650827441033616`*^9}, { 3.7650827973670535`*^9, 3.7650828162989264`*^9}, {3.7650828756452084`*^9, 3.76508291725654*^9}, {3.787989785884842*^9, 3.7879897861538515`*^9}, { 3.787989950939253*^9, 3.7879899714860353`*^9}, {3.787990031945051*^9, 3.7879900904605694`*^9}, {3.7880748631855245`*^9, 3.788074907396145*^9}, { 3.788074983681623*^9, 3.7880749851875305`*^9}, {3.7880752108539596`*^9, 3.7880753460848837`*^9}, {3.7880753955492105`*^9, 3.7880754495543413`*^9}, 3.7880757985887327`*^9, {3.7880758550342417`*^9, 3.7880758814237986`*^9}, { 3.7880759143167744`*^9, 3.7880759877586217`*^9}, {3.788076059772026*^9, 3.788076102767933*^9}, 3.7881670103681445`*^9, {3.788424742599498*^9, 3.7884247886832037`*^9}, {3.788574662089695*^9, 3.7885746993059206`*^9}, { 3.7885747319173193`*^9, 3.7885747927154846`*^9}, {3.788833131233985*^9, 3.788833188690298*^9}, {3.789441083494993*^9, 3.7894410929575987`*^9}, { 3.7894411329012265`*^9, 3.789441135103803*^9}, {3.8216139632647324`*^9, 3.821614000501048*^9}, {3.821778980163827*^9, 3.821779023170026*^9}, { 3.822369386549012*^9, 3.822369387709909*^9}}, CellLabel->"In[89]:=",ExpressionUUID->"01ec5291-3a5a-46f6-af67-96b1daf55db2"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["CONSTRAINT MODEL", "Section", CellChangeTimes->{ 3.4430806364968*^9, {3.4453166713873997`*^9, 3.4453166747414*^9}, { 3.447462264275*^9, 3.4474622644154*^9}, {3.4695731321116*^9, 3.4695731359491997`*^9}, 3.473055186341*^9, {3.4730552472860003`*^9, 3.47305524884*^9}, {3.473055399782*^9, 3.473055419801*^9}, { 3.4734696760778*^9, 3.4734697047349997`*^9}, {3.4770537891542*^9, 3.4770537950354*^9}, {3.4932799754514*^9, 3.4932799779161997`*^9}, { 3.4945558951644*^9, 3.4945558957416*^9}, {3.4957646303032*^9, 3.4957646329084*^9}, {3.497581602118*^9, 3.4975816042552*^9}, { 3.500960505817*^9, 3.5009605094206*^9}, {3.556623836083009*^9, 3.5566238462386265`*^9}, {3.5568725055395393`*^9, 3.5568725163821597`*^9}, {3.556872678728445*^9, 3.5568726810485783`*^9}, { 3.7323376045620503`*^9, 3.7323376086812124`*^9}, {3.7335630623483887`*^9, 3.733563072583865*^9}, {3.733563130246215*^9, 3.733563131355714*^9}, { 3.8175313791665382`*^9, 3.8175313820813637`*^9}, {3.817531489041069*^9, 3.81753151263837*^9}, 3.817531603785071*^9},ExpressionUUID->"cc1def21-86d8-4618-aebf-\ 14e5a843c2c6"], Cell[CellGroupData[{ Cell["CONSTRAINT ELEMENT (disp) defs ", "Subsection", CellChangeTimes->{{3.632187277028809*^9, 3.63218727949695*^9}, 3.632188602208605*^9, {3.632189487917265*^9, 3.6321894914104643`*^9}, { 3.68532054956944*^9, 3.6853205513594418`*^9}, {3.687743079248886*^9, 3.6877430854888954`*^9}, {3.76507863996914*^9, 3.7650786436977797`*^9}, { 3.7880762440580482`*^9, 3.7880762616852336`*^9}, {3.788076337785893*^9, 3.7880763394484987`*^9}, {3.817437563190297*^9, 3.817437574730232*^9}},ExpressionUUID->"e06fe3be-e95c-4877-90ee-\ 4a809db41a90"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"MEC", "-", "E1050"}], "|", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"RIGID", ",", RowBox[{"{", "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"RIGID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1", "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"RIGID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"uX1_", ",", "uY1_", ",", "uZ1_"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Theta]X1_", ",", "\[Theta]Y1_", ",", "\[Theta]Z1_"}], "}"}]}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "-", RowBox[{"{", RowBox[{"uX1", ",", "uY1", ",", "uZ1"}], "}"}]}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{"FX", "[", "n1", "]"}], ",", RowBox[{"FY", "[", "n1", "]"}], ",", RowBox[{"FZ", "[", "n1", "]"}]}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], "-", RowBox[{"{", RowBox[{"\[Theta]X1", ",", "\[Theta]Y1", ",", "\[Theta]Z1"}], "}"}]}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{"MX", "[", "n1", "]"}], ",", RowBox[{"MY", "[", "n1", "]"}], ",", RowBox[{"MZ", "[", "n1", "]"}]}], "}"}]}], "]"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"RIGID", ",", RowBox[{"{", "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "-", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], StyleBox["\[Cross]", "OperatorCharacter"], RowBox[{ StyleBox["(", "OperatorCharacter"], RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}], ")"}]}]}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{"FX", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"FY", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"FZ", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}]}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}], ")"}], ".", RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"MX", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"MY", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"MZ", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}]}], "}"}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"FX", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"FY", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"FZ", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}]}], "}"}], StyleBox["\[Cross]", "OperatorCharacter"], RowBox[{ StyleBox["(", "OperatorCharacter"], RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}], ")"}]}]}], ")"}]}], "]"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"JOINT", ",", RowBox[{"{", "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"FX", "[", "n1", "]"}], ",", RowBox[{"FY", "[", "n1", "]"}], ",", RowBox[{"FZ", "[", "n1", "]"}]}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"JOINT", ",", RowBox[{"{", RowBox[{"uX1_", ",", "uY1_", ",", "uZ1_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "-", RowBox[{"{", RowBox[{"uX1", ",", "uY1", ",", "uZ1"}], "}"}]}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{"FX", "[", "n1", "]"}], ",", RowBox[{"FY", "[", "n1", "]"}], ",", RowBox[{"FZ", "[", "n1", "]"}]}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"JOINT", ",", RowBox[{"{", "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{"FX", "[", "n1", "]"}], ",", RowBox[{"FY", "[", "n1", "]"}], ",", RowBox[{"FZ", "[", "n1", "]"}]}], "}"}]}], "]"}]}], " ", ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SLIDER", ",", RowBox[{"{", RowBox[{"nX_", ",", "nY_", ",", "nZ_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{"nX", ",", "nY", ",", "nZ"}], "}"}]}], ")"}], "*", RowBox[{"FN", "[", "n1", "]"}]}], "]"}]}], " ", ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.496939383309*^9, 3.4969394213417997`*^9}, { 3.559961640310264*^9, 3.559961656783893*^9}, {3.5599617303692226`*^9, 3.5599617392300377`*^9}, {3.5601312763250604`*^9, 3.5601312794606657`*^9}, {3.5601313134219255`*^9, 3.560131324388745*^9}, { 3.560132497854006*^9, 3.5601324981348066`*^9}, {3.63023183959678*^9, 3.630231884758859*^9}, {3.630649684386073*^9, 3.630649712146661*^9}, { 3.630649747889705*^9, 3.6306497780604305`*^9}, {3.630649843969201*^9, 3.6306501496326838`*^9}, {3.6306501928641567`*^9, 3.630650252234552*^9}, { 3.630650308727783*^9, 3.6306503113519335`*^9}, {3.630650349614122*^9, 3.630650420974203*^9}, {3.630650474367257*^9, 3.630650601725542*^9}, { 3.630651184910898*^9, 3.630651194788463*^9}, {3.6306517131931143`*^9, 3.6306517167213163`*^9}, {3.6306573863011556`*^9, 3.6306574164092083`*^9}, {3.6306574511192694`*^9, 3.630657474862511*^9}, { 3.6306575678542747`*^9, 3.6306576670080485`*^9}, {3.6306577117645273`*^9, 3.6306579038944645`*^9}, {3.630658012221055*^9, 3.630658091874795*^9}, { 3.6306581291432605`*^9, 3.630658226440631*^9}, {3.63065827139991*^9, 3.6306582739115143`*^9}, 3.630658635254949*^9, {3.6306586682178073`*^9, 3.6306586813998303`*^9}, {3.6306590619156985`*^9, 3.630659069606512*^9}, { 3.6321872976489887`*^9, 3.6321873151349883`*^9}, 3.6321874056671667`*^9, { 3.632187463194457*^9, 3.6321878547998557`*^9}, {3.632187889913864*^9, 3.6321878942471123`*^9}, {3.632187976697828*^9, 3.632187979874009*^9}, { 3.6321886111201143`*^9, 3.63218861505834*^9}, {3.632188654528598*^9, 3.6321886640741434`*^9}, {3.632189320010661*^9, 3.632189331931343*^9}, { 3.6853206095995235`*^9, 3.685320631309554*^9}, {3.6853206843496284`*^9, 3.685320754049726*^9}, {3.685320792059779*^9, 3.685320823639823*^9}, { 3.685321020360099*^9, 3.6853211351402597`*^9}, {3.6853211801403227`*^9, 3.685321665981003*^9}, {3.6853216989010487`*^9, 3.6853217094910636`*^9}, { 3.6853217810511637`*^9, 3.6853220138814898`*^9}, {3.6853225388622246`*^9, 3.6853226020023127`*^9}, {3.687743095218909*^9, 3.6877431192189426`*^9}, { 3.687743169079012*^9, 3.687743170319014*^9}, {3.6877432521091285`*^9, 3.68774331760922*^9}, {3.6877433494492645`*^9, 3.6877434507694063`*^9}, { 3.6877434824794507`*^9, 3.687743525179511*^9}, {3.6877442207004843`*^9, 3.68774423869051*^9}, {3.687744273840559*^9, 3.6877443377106485`*^9}, { 3.687744434080783*^9, 3.6877445463509407`*^9}, {3.687744848891364*^9, 3.6877448558313737`*^9}, {3.6877638336712008`*^9, 3.68776389741129*^9}, { 3.687763938681348*^9, 3.6877639455213575`*^9}, {3.6877641776516824`*^9, 3.6877642483817816`*^9}, {3.687764508142145*^9, 3.6877645655122256`*^9}, { 3.687778690246417*^9, 3.687778699786431*^9}, {3.6892208471842775`*^9, 3.6892208613442974`*^9}, {3.6892209340143995`*^9, 3.689220966944445*^9}, { 3.6892211581147127`*^9, 3.689221214324792*^9}, {3.689221265414863*^9, 3.689221335944962*^9}, 3.6892213742150154`*^9, {3.6892214353151007`*^9, 3.689221472385153*^9}, {3.689221514295212*^9, 3.689221800835613*^9}, { 3.6892221753761373`*^9, 3.689222181266145*^9}, 3.689222955217229*^9, { 3.6892232691076684`*^9, 3.689223331877756*^9}, {3.693460221154632*^9, 3.6934602635146914`*^9}, {3.6948453326087465`*^9, 3.6948453439687624`*^9}, {3.7348680727026668`*^9, 3.73486817909155*^9}, { 3.746150241146084*^9, 3.746150271873185*^9}, {3.7530805273958597`*^9, 3.7530805538372126`*^9}, {3.7530806121866155`*^9, 3.753080612619146*^9}, { 3.7530807812083597`*^9, 3.753080855476215*^9}, {3.7530808933957005`*^9, 3.753080928261367*^9}, {3.7530812010856276`*^9, 3.753081304984929*^9}, { 3.753081363847283*^9, 3.753081510980585*^9}, {3.7530830896227846`*^9, 3.7530831670560236`*^9}, {3.753083282189464*^9, 3.753083319143241*^9}, { 3.753083522782399*^9, 3.7530836451470532`*^9}, {3.753083680478052*^9, 3.7530837044483657`*^9}, {3.7530839780537753`*^9, 3.7530840044915133`*^9}, {3.7530841230935698`*^9, 3.7530841439684134`*^9}, {3.753084174787207*^9, 3.753084175438378*^9}, { 3.7531753489377103`*^9, 3.7531753521812167`*^9}, {3.7531753986744366`*^9, 3.753175401639263*^9}, {3.7531757699701395`*^9, 3.7531757819468718`*^9}, { 3.7531758502951393`*^9, 3.753176036147319*^9}, {3.7650793717088127`*^9, 3.765079384414342*^9}, {3.7650794145018706`*^9, 3.7650794160024643`*^9}, { 3.765080191205142*^9, 3.7650801957605696`*^9}, {3.765080316588634*^9, 3.765080334411024*^9}, {3.7650804146979465`*^9, 3.765080452046597*^9}, { 3.7650805125970893`*^9, 3.765080538042729*^9}, {3.7650806025099554`*^9, 3.765080640706174*^9}, {3.765081132572468*^9, 3.765081149288616*^9}, { 3.7843471628441577`*^9, 3.784347230545391*^9}, 3.788076396075549*^9, { 3.7880764597653866`*^9, 3.78807658689421*^9}, {3.7880766192477016`*^9, 3.78807666464567*^9}, 3.790134342393529*^9, {3.81147586433552*^9, 3.8114758660676584`*^9}, {3.8114759011903524`*^9, 3.8114759016633973`*^9}, 3.8114759988439693`*^9, 3.8114761633171883`*^9, {3.816603834074288*^9, 3.8166039336563835`*^9}, {3.8170006770430465`*^9, 3.817000724749156*^9}, { 3.8170007595398445`*^9, 3.817000786405624*^9}, 3.8170037199219055`*^9, { 3.8170045080782423`*^9, 3.8170045294203014`*^9}, {3.81700457884058*^9, 3.81700458306651*^9}, {3.8170046136020584`*^9, 3.8170046363287716`*^9}, { 3.8170054362323685`*^9, 3.817005516642319*^9}, {3.817005553771696*^9, 3.8170057022018414`*^9}, {3.817438004752759*^9, 3.817438079208784*^9}, { 3.8174381095342855`*^9, 3.817438111564824*^9}, {3.817438162423845*^9, 3.81743817388716*^9}, 3.8174382117090836`*^9, 3.8174382843486643`*^9, 3.817438365153536*^9, {3.8174384271840076`*^9, 3.817438431575055*^9}, { 3.817438579668557*^9, 3.8174385809774275`*^9}, {3.817438614371037*^9, 3.817438652378895*^9}, {3.8456995036286135`*^9, 3.845699532708929*^9}}, CellLabel->"In[90]:=",ExpressionUUID->"4addbcb1-2ea6-496d-981f-9f7e1be7e07d"] }, Closed]], Cell[CellGroupData[{ Cell["CONSTRAINT ELEMENT (evnt) defs ", "Subsection", CellChangeTimes->{{3.632187277028809*^9, 3.63218727949695*^9}, 3.632188602208605*^9, {3.632189487917265*^9, 3.6321894914104643`*^9}, { 3.68532054956944*^9, 3.6853205513594418`*^9}, {3.687743079248886*^9, 3.6877430854888954`*^9}, {3.76507863996914*^9, 3.7650786436977797`*^9}, { 3.7880762440580482`*^9, 3.7880762616852336`*^9}, {3.788076337785893*^9, 3.7880763394484987`*^9}, {3.817437563190297*^9, 3.817437574730232*^9}, { 3.8174387848423214`*^9, 3.817438785964677*^9}, 3.8431826672012787`*^9},ExpressionUUID->"6d6aaea5-f790-4af3-bf7c-\ 3274b903fd14"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"EVNT", ",", RowBox[{"{", RowBox[{"s0_", ",", "sol0_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"RIGID", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"RIGID", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"EVNT", ",", RowBox[{"{", RowBox[{"s0_", ",", "sol0_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"JOINT", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"JOINT", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"EVNT", ",", RowBox[{"{", RowBox[{"s0_", ",", "sol0_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"SLIDER", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SLIDER", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"EVNT", ",", RowBox[{"{", RowBox[{"s0_", ",", "sol0_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"CONTACT", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"nX_", ",", "nY_", ",", "nZ_"}], "}"}], ",", "d_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"U", ",", "F", ",", "U0", ",", "dU0", ",", "F0", ",", "dF0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"(*", "events", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"U", "=", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"nX", ",", "nY", ",", "nZ"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], "-", "d"}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"F", "=", RowBox[{"FN", "[", "n1", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"U0", "=", RowBox[{"U", "/.", "sol0"}]}], ";", RowBox[{"dU0", "=", RowBox[{"D", "[", RowBox[{"U0", ",", "s"}], "]"}]}], ";", RowBox[{"U0", "=", RowBox[{"U0", "/.", RowBox[{"s", "\[Rule]", "s0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"F0", "=", RowBox[{"F", "/.", "sol0"}]}], ";", RowBox[{"dF0", "=", RowBox[{"D", "[", RowBox[{"F0", ",", "s"}], "]"}]}], ";", RowBox[{"F0", "=", RowBox[{"F0", "/.", RowBox[{"s", "\[Rule]", "s0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"{", RowBox[{"U0", ",", "dU0", ",", "F0", ",", "dF0"}], "}"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"pick", " ", "the", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"Which", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"U0", "\[Equal]", "0"}], ")"}], "&&", " ", RowBox[{"(", RowBox[{"F0", ">", "0"}], ")"}]}], ",", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{"F", "*", "U"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{"U0", "\[Equal]", "0"}], ")"}], "&&", " ", RowBox[{"(", RowBox[{"F0", "<", "0"}], ")"}]}], ",", RowBox[{ RowBox[{"Print", "[", "\"\\"", "]"}], ";", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{"F", "*", "F"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{"F0", "\[Equal]", "0"}], ")"}], "&&", " ", RowBox[{"(", RowBox[{"U0", ">", "0"}], ")"}]}], ",", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{"F", "*", "F"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{"F0", "\[Equal]", "0"}], ")"}], "&&", " ", RowBox[{"(", RowBox[{"U0", "<", "0"}], ")"}]}], ",", RowBox[{ RowBox[{"Print", "[", "\"\\"", "]"}], ";", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{"F", "*", "U"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{"F0", "\[Equal]", "0"}], ")"}], "&&", " ", RowBox[{"(", RowBox[{"U0", "==", "0"}], ")"}], "&&", " ", RowBox[{"(", RowBox[{"dU0", ">", "0"}], ")"}]}], ",", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{"F", "*", "F"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{"F0", "\[Equal]", "0"}], ")"}], "&&", " ", RowBox[{"(", RowBox[{"U0", "==", "0"}], ")"}], "&&", " ", RowBox[{"(", RowBox[{"dU0", "<", "0"}], ")"}]}], ",", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{"U", "*", "F"}], "]"}], ",", "True", ",", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{"U", "*", "F"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"EVNTPOST", ",", RowBox[{"{", RowBox[{"s0_", ",", "sol0_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"CONTACT", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"nX_", ",", "nY_", ",", "nZ_"}], "}"}], ",", "d_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"UF", ",", "k", ",", "UF0", ",", "\[CapitalDelta]s"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"(*", "events", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"UF", "=", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"nX", ",", "nY", ",", "nZ"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], "-", "d"}], ")"}], "+", RowBox[{"FN", "[", "n1", "]"}]}], ")"}], " ", "/.", "sol0"}], " ", "/.", RowBox[{"s", "->", RowBox[{"s0", "+", "\[CapitalDelta]s"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"UF0", "=", RowBox[{"UF", " ", "/.", RowBox[{"\[CapitalDelta]s", "\[Rule]", "0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"k", "=", RowBox[{"D", "[", RowBox[{"UF", ",", "\[CapitalDelta]s"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalDelta]s", "=", RowBox[{"Max", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"k", StyleBox["\[NotEqual]", "OperatorCharacter"], StyleBox["0", "OperatorCharacter"]}], ",", RowBox[{ RowBox[{"-", "UF0"}], "/", "k"}], ",", "0"}], "]"}], ",", "0"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"\[CapitalDelta]s", "\[Equal]", "0"}], ",", RowBox[{"1", "-", "s0"}], ",", "\[CapitalDelta]s"}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.496939383309*^9, 3.4969394213417997`*^9}, { 3.559961640310264*^9, 3.559961656783893*^9}, {3.5599617303692226`*^9, 3.5599617392300377`*^9}, {3.5601312763250604`*^9, 3.5601312794606657`*^9}, {3.5601313134219255`*^9, 3.560131324388745*^9}, { 3.560132497854006*^9, 3.5601324981348066`*^9}, {3.63023183959678*^9, 3.630231884758859*^9}, {3.630649684386073*^9, 3.630649712146661*^9}, { 3.630649747889705*^9, 3.6306497780604305`*^9}, {3.630649843969201*^9, 3.6306501496326838`*^9}, {3.6306501928641567`*^9, 3.630650252234552*^9}, { 3.630650308727783*^9, 3.6306503113519335`*^9}, {3.630650349614122*^9, 3.630650420974203*^9}, {3.630650474367257*^9, 3.630650601725542*^9}, { 3.630651184910898*^9, 3.630651194788463*^9}, {3.6306517131931143`*^9, 3.6306517167213163`*^9}, {3.6306573863011556`*^9, 3.6306574164092083`*^9}, {3.6306574511192694`*^9, 3.630657474862511*^9}, { 3.6306575678542747`*^9, 3.6306576670080485`*^9}, {3.6306577117645273`*^9, 3.6306579038944645`*^9}, {3.630658012221055*^9, 3.630658091874795*^9}, { 3.6306581291432605`*^9, 3.630658226440631*^9}, {3.63065827139991*^9, 3.6306582739115143`*^9}, 3.630658635254949*^9, {3.6306586682178073`*^9, 3.6306586813998303`*^9}, {3.6306590619156985`*^9, 3.630659069606512*^9}, { 3.6321872976489887`*^9, 3.6321873151349883`*^9}, 3.6321874056671667`*^9, { 3.632187463194457*^9, 3.6321878547998557`*^9}, {3.632187889913864*^9, 3.6321878942471123`*^9}, {3.632187976697828*^9, 3.632187979874009*^9}, { 3.6321886111201143`*^9, 3.63218861505834*^9}, {3.632188654528598*^9, 3.6321886640741434`*^9}, {3.632189320010661*^9, 3.632189331931343*^9}, { 3.6853206095995235`*^9, 3.685320631309554*^9}, {3.6853206843496284`*^9, 3.685320754049726*^9}, {3.685320792059779*^9, 3.685320823639823*^9}, { 3.685321020360099*^9, 3.6853211351402597`*^9}, {3.6853211801403227`*^9, 3.685321665981003*^9}, {3.6853216989010487`*^9, 3.6853217094910636`*^9}, { 3.6853217810511637`*^9, 3.6853220138814898`*^9}, {3.6853225388622246`*^9, 3.6853226020023127`*^9}, {3.687743095218909*^9, 3.6877431192189426`*^9}, { 3.687743169079012*^9, 3.687743170319014*^9}, {3.6877432521091285`*^9, 3.68774331760922*^9}, {3.6877433494492645`*^9, 3.6877434507694063`*^9}, { 3.6877434824794507`*^9, 3.687743525179511*^9}, {3.6877442207004843`*^9, 3.68774423869051*^9}, {3.687744273840559*^9, 3.6877443377106485`*^9}, { 3.687744434080783*^9, 3.6877445463509407`*^9}, {3.687744848891364*^9, 3.6877448558313737`*^9}, {3.6877638336712008`*^9, 3.68776389741129*^9}, { 3.687763938681348*^9, 3.6877639455213575`*^9}, {3.6877641776516824`*^9, 3.6877642483817816`*^9}, {3.687764508142145*^9, 3.6877645655122256`*^9}, { 3.687778690246417*^9, 3.687778699786431*^9}, {3.6892208471842775`*^9, 3.6892208613442974`*^9}, {3.6892209340143995`*^9, 3.689220966944445*^9}, { 3.6892211581147127`*^9, 3.689221214324792*^9}, {3.689221265414863*^9, 3.689221335944962*^9}, 3.6892213742150154`*^9, {3.6892214353151007`*^9, 3.689221472385153*^9}, {3.689221514295212*^9, 3.689221800835613*^9}, { 3.6892221753761373`*^9, 3.689222181266145*^9}, 3.689222955217229*^9, { 3.6892232691076684`*^9, 3.689223331877756*^9}, {3.693460221154632*^9, 3.6934602635146914`*^9}, {3.6948453326087465`*^9, 3.6948453439687624`*^9}, {3.7348680727026668`*^9, 3.73486817909155*^9}, { 3.746150241146084*^9, 3.746150271873185*^9}, {3.7530805273958597`*^9, 3.7530805538372126`*^9}, {3.7530806121866155`*^9, 3.753080612619146*^9}, { 3.7530807812083597`*^9, 3.753080855476215*^9}, {3.7530808933957005`*^9, 3.753080928261367*^9}, {3.7530812010856276`*^9, 3.753081304984929*^9}, { 3.753081363847283*^9, 3.753081510980585*^9}, {3.7530830896227846`*^9, 3.7530831670560236`*^9}, {3.753083282189464*^9, 3.753083319143241*^9}, { 3.753083522782399*^9, 3.7530836451470532`*^9}, {3.753083680478052*^9, 3.7530837044483657`*^9}, {3.7530839780537753`*^9, 3.7530840044915133`*^9}, {3.7530841230935698`*^9, 3.7530841439684134`*^9}, {3.753084174787207*^9, 3.753084175438378*^9}, { 3.7531753489377103`*^9, 3.7531753521812167`*^9}, {3.7531753986744366`*^9, 3.753175401639263*^9}, {3.7531757699701395`*^9, 3.7531757819468718`*^9}, { 3.7531758502951393`*^9, 3.753176036147319*^9}, {3.7650793717088127`*^9, 3.765079384414342*^9}, {3.7650794145018706`*^9, 3.7650794160024643`*^9}, { 3.765080191205142*^9, 3.7650801957605696`*^9}, {3.765080316588634*^9, 3.765080334411024*^9}, {3.7650804146979465`*^9, 3.765080452046597*^9}, { 3.7650805125970893`*^9, 3.765080538042729*^9}, {3.7650806025099554`*^9, 3.765080640706174*^9}, {3.765081132572468*^9, 3.765081149288616*^9}, { 3.7843471628441577`*^9, 3.784347230545391*^9}, 3.788076396075549*^9, { 3.7880764597653866`*^9, 3.78807658689421*^9}, {3.7880766192477016`*^9, 3.78807666464567*^9}, 3.790134342393529*^9, {3.81147586433552*^9, 3.8114758660676584`*^9}, {3.8114759011903524`*^9, 3.8114759016633973`*^9}, 3.8114759988439693`*^9, 3.8114761633171883`*^9, {3.816603834074288*^9, 3.8166039336563835`*^9}, {3.8170006770430465`*^9, 3.817000724749156*^9}, { 3.8170007595398445`*^9, 3.817000786405624*^9}, 3.8170037199219055`*^9, { 3.8170045080782423`*^9, 3.8170045294203014`*^9}, {3.81700457884058*^9, 3.81700458306651*^9}, {3.8170046136020584`*^9, 3.8170046363287716`*^9}, { 3.8170054362323685`*^9, 3.817005516642319*^9}, {3.817005553771696*^9, 3.8170057022018414`*^9}, {3.817438004752759*^9, 3.817438079208784*^9}, { 3.8174381095342855`*^9, 3.817438111564824*^9}, {3.817438162423845*^9, 3.81743817388716*^9}, 3.8174382117090836`*^9, 3.8174382843486643`*^9, 3.817438365153536*^9, {3.8174384271840076`*^9, 3.817438431575055*^9}, { 3.817438579668557*^9, 3.8174385809774275`*^9}, {3.817438614371037*^9, 3.817438652378895*^9}, {3.817438930825718*^9, 3.8174390943730135`*^9}, { 3.8174391259139147`*^9, 3.817439141253656*^9}, {3.817521077883604*^9, 3.817521080728553*^9}, {3.8175211772242155`*^9, 3.8175212036088133`*^9}, { 3.8175674512925177`*^9, 3.817567623935768*^9}, {3.8175676609349613`*^9, 3.817567723697788*^9}, {3.817568085932104*^9, 3.8175680987457275`*^9}, { 3.817569108580055*^9, 3.817569117864359*^9}, {3.817569150118846*^9, 3.8175691557258625`*^9}, {3.8176216772973127`*^9, 3.817621692611002*^9}, { 3.8176217285430126`*^9, 3.817621790585905*^9}, {3.817786782380433*^9, 3.8177868741990595`*^9}, {3.8177916370767837`*^9, 3.817791664037953*^9}, 3.8177919725788736`*^9, {3.817797728334919*^9, 3.8177979470877533`*^9}, { 3.817798048009226*^9, 3.8177980720019073`*^9}, {3.8177981782154303`*^9, 3.8177982245972304`*^9}, {3.817874042594287*^9, 3.8178740483145275`*^9}, 3.817874104353353*^9, {3.817874161520626*^9, 3.817874247753765*^9}, { 3.817875812854987*^9, 3.8178758350526857`*^9}, 3.8178759752202544`*^9, { 3.843182718463587*^9, 3.84318273860385*^9}}, CellLabel->"In[97]:=",ExpressionUUID->"3b98d934-ed89-4766-ae8f-7f3b11c7602b"] }, Closed]], Cell[CellGroupData[{ Cell["CONSTRAINT ELEMENT (vibr) defs", "Subsection", CellChangeTimes->{{3.632187277028809*^9, 3.63218727949695*^9}, 3.632188602208605*^9, {3.632189487917265*^9, 3.6321894914104643`*^9}, { 3.68532054956944*^9, 3.6853205513594418`*^9}, {3.687743079248886*^9, 3.6877430854888954`*^9}, {3.765078647709998*^9, 3.7650786536233745`*^9}, { 3.787894934272877*^9, 3.787894940030588*^9}, 3.8174375910297575`*^9},ExpressionUUID->"ac4d2151-f977-47ab-89d2-\ cba20d90a0c1"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"RIGID", ",", RowBox[{"{", "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], " ", ".", RowBox[{"{", RowBox[{ RowBox[{"FX", "[", "n1", "]"}], ",", RowBox[{"FY", "[", "n1", "]"}], ",", RowBox[{"FZ", "[", "n1", "]"}]}], "}"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"MX", "[", "n1", "]"}], ",", RowBox[{"MY", "[", "n1", "]"}], ",", RowBox[{"MZ", "[", "n1", "]"}]}], "}"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"RIGID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"uX1_", ",", "uY1_", ",", "uZ1_"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Theta]X1_", ",", "\[Theta]Y1_", ",", "\[Theta]Z1_"}], "}"}]}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "-", RowBox[{"{", RowBox[{"uX1", ",", "uY1", ",", "uZ1"}], "}"}]}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{"FX", "[", "n1", "]"}], ",", RowBox[{"FY", "[", "n1", "]"}], ",", RowBox[{"FZ", "[", "n1", "]"}]}], "}"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], "-", RowBox[{"{", RowBox[{"\[Theta]X1", ",", "\[Theta]Y1", ",", "\[Theta]Z1"}], "}"}]}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{"MX", "[", "n1", "]"}], ",", RowBox[{"MY", "[", "n1", "]"}], ",", RowBox[{"MZ", "[", "n1", "]"}]}], "}"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"RIGID", ",", RowBox[{"{", "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "-", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], StyleBox["\[Cross]", "OperatorCharacter"], RowBox[{ StyleBox["(", "OperatorCharacter"], RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}], ")"}]}]}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{"FX", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"FY", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"FZ", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}]}], "}"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}], ")"}], ".", RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"MX", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"MY", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"MZ", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}]}], "}"}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"FX", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"FY", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"FZ", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}]}], "}"}], StyleBox["\[Cross]", "OperatorCharacter"], RowBox[{ StyleBox["(", "OperatorCharacter"], RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}], ")"}]}]}], ")"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"JOINT", ",", RowBox[{"{", "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"FX", "[", "n1", "]"}], ",", RowBox[{"FY", "[", "n1", "]"}], ",", RowBox[{"FZ", "[", "n1", "]"}]}], "}"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"JOINT", ",", RowBox[{"{", RowBox[{"uX1_", ",", "uY1_", ",", "uZ1_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "-", RowBox[{"{", RowBox[{"uX1", ",", "uY1", ",", "uZ1"}], "}"}]}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{"FX", "[", "n1", "]"}], ",", RowBox[{"FY", "[", "n1", "]"}], ",", RowBox[{"FZ", "[", "n1", "]"}]}], "}"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"JOINT", ",", RowBox[{"{", "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{"FX", "[", "n1", "]"}], ",", RowBox[{"FY", "[", "n1", "]"}], ",", RowBox[{"FZ", "[", "n1", "]"}]}], "}"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}]}], " ", ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"SLIDER", ",", RowBox[{"{", RowBox[{"nX_", ",", "nY_", ",", "nZ_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{"nX", ",", "nY", ",", "nZ"}], "}"}]}], ")"}], "*", RowBox[{"FN", "[", "n1", "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}]}], " ", ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.496939383309*^9, 3.4969394213417997`*^9}, { 3.559961640310264*^9, 3.559961656783893*^9}, {3.5599617303692226`*^9, 3.5599617392300377`*^9}, {3.5601312763250604`*^9, 3.5601312794606657`*^9}, {3.5601313134219255`*^9, 3.560131324388745*^9}, { 3.560132497854006*^9, 3.5601324981348066`*^9}, {3.63023183959678*^9, 3.630231884758859*^9}, {3.630649684386073*^9, 3.630649712146661*^9}, { 3.630649747889705*^9, 3.6306497780604305`*^9}, {3.630649843969201*^9, 3.6306501496326838`*^9}, {3.6306501928641567`*^9, 3.630650252234552*^9}, { 3.630650308727783*^9, 3.6306503113519335`*^9}, {3.630650349614122*^9, 3.630650420974203*^9}, {3.630650474367257*^9, 3.630650601725542*^9}, { 3.630651184910898*^9, 3.630651194788463*^9}, {3.6306517131931143`*^9, 3.6306517167213163`*^9}, {3.6306573863011556`*^9, 3.6306574164092083`*^9}, {3.6306574511192694`*^9, 3.630657474862511*^9}, { 3.6306575678542747`*^9, 3.6306576670080485`*^9}, {3.6306577117645273`*^9, 3.6306579038944645`*^9}, {3.630658012221055*^9, 3.630658091874795*^9}, { 3.6306581291432605`*^9, 3.630658226440631*^9}, {3.63065827139991*^9, 3.6306582739115143`*^9}, 3.630658635254949*^9, {3.6306586682178073`*^9, 3.6306586813998303`*^9}, {3.6306590619156985`*^9, 3.630659069606512*^9}, { 3.6321872976489887`*^9, 3.6321873151349883`*^9}, 3.6321874056671667`*^9, { 3.632187463194457*^9, 3.6321878547998557`*^9}, {3.632187889913864*^9, 3.6321878942471123`*^9}, {3.632187976697828*^9, 3.632187979874009*^9}, { 3.6321886111201143`*^9, 3.63218861505834*^9}, {3.632188654528598*^9, 3.6321886640741434`*^9}, {3.632189320010661*^9, 3.632189331931343*^9}, { 3.6853206095995235`*^9, 3.685320631309554*^9}, {3.6853206843496284`*^9, 3.685320754049726*^9}, {3.685320792059779*^9, 3.685320823639823*^9}, { 3.685321020360099*^9, 3.6853211351402597`*^9}, {3.6853211801403227`*^9, 3.685321665981003*^9}, {3.6853216989010487`*^9, 3.6853217094910636`*^9}, { 3.6853217810511637`*^9, 3.6853220138814898`*^9}, {3.6853225388622246`*^9, 3.6853226020023127`*^9}, {3.687743095218909*^9, 3.6877431192189426`*^9}, { 3.687743169079012*^9, 3.687743170319014*^9}, {3.6877432521091285`*^9, 3.68774331760922*^9}, {3.6877433494492645`*^9, 3.6877434507694063`*^9}, { 3.6877434824794507`*^9, 3.687743525179511*^9}, {3.6877442207004843`*^9, 3.68774423869051*^9}, {3.687744273840559*^9, 3.6877443377106485`*^9}, { 3.687744434080783*^9, 3.6877445463509407`*^9}, {3.687744848891364*^9, 3.6877448558313737`*^9}, {3.6877638336712008`*^9, 3.68776389741129*^9}, { 3.687763938681348*^9, 3.6877639455213575`*^9}, {3.6877641776516824`*^9, 3.6877642483817816`*^9}, {3.687764508142145*^9, 3.6877645655122256`*^9}, { 3.687778690246417*^9, 3.687778699786431*^9}, {3.6892208471842775`*^9, 3.6892208613442974`*^9}, {3.6892209340143995`*^9, 3.689220966944445*^9}, { 3.6892211581147127`*^9, 3.689221214324792*^9}, {3.689221265414863*^9, 3.689221335944962*^9}, 3.6892213742150154`*^9, {3.6892214353151007`*^9, 3.689221472385153*^9}, {3.689221514295212*^9, 3.689221800835613*^9}, { 3.6892221753761373`*^9, 3.689222181266145*^9}, 3.689222955217229*^9, { 3.6892232691076684`*^9, 3.689223331877756*^9}, {3.693460221154632*^9, 3.6934602635146914`*^9}, {3.6948453326087465`*^9, 3.6948453439687624`*^9}, {3.7348680727026668`*^9, 3.73486817909155*^9}, { 3.746150241146084*^9, 3.746150271873185*^9}, {3.7530805273958597`*^9, 3.7530805538372126`*^9}, {3.7530806121866155`*^9, 3.753080612619146*^9}, { 3.7530807812083597`*^9, 3.753080855476215*^9}, {3.7530808933957005`*^9, 3.753080928261367*^9}, {3.7530812010856276`*^9, 3.753081304984929*^9}, { 3.753081363847283*^9, 3.753081510980585*^9}, {3.7530830896227846`*^9, 3.7530831670560236`*^9}, {3.753083282189464*^9, 3.753083319143241*^9}, { 3.753083522782399*^9, 3.7530836451470532`*^9}, {3.753083680478052*^9, 3.7530837044483657`*^9}, {3.7530839780537753`*^9, 3.7530840044915133`*^9}, {3.7530841230935698`*^9, 3.7530841439684134`*^9}, {3.753084174787207*^9, 3.753084175438378*^9}, { 3.7531753489377103`*^9, 3.7531753521812167`*^9}, {3.7531753986744366`*^9, 3.753175401639263*^9}, {3.7531757699701395`*^9, 3.7531757819468718`*^9}, { 3.7531758502951393`*^9, 3.753176036147319*^9}, {3.7650786786571007`*^9, 3.765078730242957*^9}, {3.765079011319233*^9, 3.7650790213991427`*^9}, { 3.765079090426065*^9, 3.7650790915198584`*^9}, {3.7880750541013985`*^9, 3.7880751871791787`*^9}, 3.7880763476153545`*^9, {3.7880764088125978`*^9, 3.788076439490058*^9}, {3.788076727654149*^9, 3.788076736195205*^9}, { 3.7880769509878035`*^9, 3.788076996669318*^9}, {3.788157806923176*^9, 3.7881578103397293`*^9}, {3.788157887685897*^9, 3.7881579246081514`*^9}, 3.788166841222316*^9, {3.788245673127977*^9, 3.7882457332638197`*^9}, { 3.7884249270350504`*^9, 3.788424928787249*^9}, {3.796348073487073*^9, 3.796348235983635*^9}, 3.8204695675454354`*^9, 3.8210644461664095`*^9, { 3.8211518525046625`*^9, 3.8211518941528387`*^9}, {3.821151937357603*^9, 3.821152092267825*^9}, {3.8211521441264668`*^9, 3.821152293547024*^9}}, CellLabel-> "In[102]:=",ExpressionUUID->"5ae1b60c-b700-40b1-9a48-e53a1cc07540"] }, Closed]], Cell[CellGroupData[{ Cell["CONSTRAINT ELEMENT (stab) defs ", "Subsection", CellChangeTimes->{{3.632187277028809*^9, 3.63218727949695*^9}, 3.632188602208605*^9, {3.632189487917265*^9, 3.6321894914104643`*^9}, { 3.68532054956944*^9, 3.6853205513594418`*^9}, {3.687743079248886*^9, 3.6877430854888954`*^9}, {3.76507863996914*^9, 3.7650786436977797`*^9}, { 3.7880762440580482`*^9, 3.7880762616852336`*^9}, {3.788076337785893*^9, 3.7880763394484987`*^9}, {3.7890210020583797`*^9, 3.7890210028862896`*^9}, 3.8174375960916395`*^9},ExpressionUUID->"ce934794-0db1-42c7-9127-\ acf682062b33"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"RIGID", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"RIGID", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"JOINT", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"JOINT", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"SLIDER", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SLIDER", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.496939383309*^9, 3.4969394213417997`*^9}, { 3.559961640310264*^9, 3.559961656783893*^9}, {3.5599617303692226`*^9, 3.5599617392300377`*^9}, {3.5601312763250604`*^9, 3.5601312794606657`*^9}, {3.5601313134219255`*^9, 3.560131324388745*^9}, { 3.560132497854006*^9, 3.5601324981348066`*^9}, {3.63023183959678*^9, 3.630231884758859*^9}, {3.630649684386073*^9, 3.630649712146661*^9}, { 3.630649747889705*^9, 3.6306497780604305`*^9}, {3.630649843969201*^9, 3.6306501496326838`*^9}, {3.6306501928641567`*^9, 3.630650252234552*^9}, { 3.630650308727783*^9, 3.6306503113519335`*^9}, {3.630650349614122*^9, 3.630650420974203*^9}, {3.630650474367257*^9, 3.630650601725542*^9}, { 3.630651184910898*^9, 3.630651194788463*^9}, {3.6306517131931143`*^9, 3.6306517167213163`*^9}, {3.6306573863011556`*^9, 3.6306574164092083`*^9}, {3.6306574511192694`*^9, 3.630657474862511*^9}, { 3.6306575678542747`*^9, 3.6306576670080485`*^9}, {3.6306577117645273`*^9, 3.6306579038944645`*^9}, {3.630658012221055*^9, 3.630658091874795*^9}, { 3.6306581291432605`*^9, 3.630658226440631*^9}, {3.63065827139991*^9, 3.6306582739115143`*^9}, 3.630658635254949*^9, {3.6306586682178073`*^9, 3.6306586813998303`*^9}, {3.6306590619156985`*^9, 3.630659069606512*^9}, { 3.6321872976489887`*^9, 3.6321873151349883`*^9}, 3.6321874056671667`*^9, { 3.632187463194457*^9, 3.6321878547998557`*^9}, {3.632187889913864*^9, 3.6321878942471123`*^9}, {3.632187976697828*^9, 3.632187979874009*^9}, { 3.6321886111201143`*^9, 3.63218861505834*^9}, {3.632188654528598*^9, 3.6321886640741434`*^9}, {3.632189320010661*^9, 3.632189331931343*^9}, { 3.6853206095995235`*^9, 3.685320631309554*^9}, {3.6853206843496284`*^9, 3.685320754049726*^9}, {3.685320792059779*^9, 3.685320823639823*^9}, { 3.685321020360099*^9, 3.6853211351402597`*^9}, {3.6853211801403227`*^9, 3.685321665981003*^9}, {3.6853216989010487`*^9, 3.6853217094910636`*^9}, { 3.6853217810511637`*^9, 3.6853220138814898`*^9}, {3.6853225388622246`*^9, 3.6853226020023127`*^9}, {3.687743095218909*^9, 3.6877431192189426`*^9}, { 3.687743169079012*^9, 3.687743170319014*^9}, {3.6877432521091285`*^9, 3.68774331760922*^9}, {3.6877433494492645`*^9, 3.6877434507694063`*^9}, { 3.6877434824794507`*^9, 3.687743525179511*^9}, {3.6877442207004843`*^9, 3.68774423869051*^9}, {3.687744273840559*^9, 3.6877443377106485`*^9}, { 3.687744434080783*^9, 3.6877445463509407`*^9}, {3.687744848891364*^9, 3.6877448558313737`*^9}, {3.6877638336712008`*^9, 3.68776389741129*^9}, { 3.687763938681348*^9, 3.6877639455213575`*^9}, {3.6877641776516824`*^9, 3.6877642483817816`*^9}, {3.687764508142145*^9, 3.6877645655122256`*^9}, { 3.687778690246417*^9, 3.687778699786431*^9}, {3.6892208471842775`*^9, 3.6892208613442974`*^9}, {3.6892209340143995`*^9, 3.689220966944445*^9}, { 3.6892211581147127`*^9, 3.689221214324792*^9}, {3.689221265414863*^9, 3.689221335944962*^9}, 3.6892213742150154`*^9, {3.6892214353151007`*^9, 3.689221472385153*^9}, {3.689221514295212*^9, 3.689221800835613*^9}, { 3.6892221753761373`*^9, 3.689222181266145*^9}, 3.689222955217229*^9, { 3.6892232691076684`*^9, 3.689223331877756*^9}, {3.693460221154632*^9, 3.6934602635146914`*^9}, {3.6948453326087465`*^9, 3.6948453439687624`*^9}, {3.7348680727026668`*^9, 3.73486817909155*^9}, { 3.746150241146084*^9, 3.746150271873185*^9}, {3.7530805273958597`*^9, 3.7530805538372126`*^9}, {3.7530806121866155`*^9, 3.753080612619146*^9}, { 3.7530807812083597`*^9, 3.753080855476215*^9}, {3.7530808933957005`*^9, 3.753080928261367*^9}, {3.7530812010856276`*^9, 3.753081304984929*^9}, { 3.753081363847283*^9, 3.753081510980585*^9}, {3.7530830896227846`*^9, 3.7530831670560236`*^9}, {3.753083282189464*^9, 3.753083319143241*^9}, { 3.753083522782399*^9, 3.7530836451470532`*^9}, {3.753083680478052*^9, 3.7530837044483657`*^9}, {3.7530839780537753`*^9, 3.7530840044915133`*^9}, {3.7530841230935698`*^9, 3.7530841439684134`*^9}, {3.753084174787207*^9, 3.753084175438378*^9}, { 3.7531753489377103`*^9, 3.7531753521812167`*^9}, {3.7531753986744366`*^9, 3.753175401639263*^9}, {3.7531757699701395`*^9, 3.7531757819468718`*^9}, { 3.7531758502951393`*^9, 3.753176036147319*^9}, {3.7650793717088127`*^9, 3.765079384414342*^9}, {3.7650794145018706`*^9, 3.7650794160024643`*^9}, { 3.765080191205142*^9, 3.7650801957605696`*^9}, {3.765080316588634*^9, 3.765080334411024*^9}, {3.7650804146979465`*^9, 3.765080452046597*^9}, { 3.7650805125970893`*^9, 3.765080538042729*^9}, {3.7650806025099554`*^9, 3.765080640706174*^9}, {3.765081132572468*^9, 3.765081149288616*^9}, { 3.7843471628441577`*^9, 3.784347230545391*^9}, 3.788076396075549*^9, { 3.7880764597653866`*^9, 3.78807658689421*^9}, {3.7880766192477016`*^9, 3.78807666464567*^9}, {3.7890210098488555`*^9, 3.7890210223821774`*^9}, { 3.7890210765394955`*^9, 3.789021101390154*^9}, {3.821064422910862*^9, 3.821064437263141*^9}, {3.821064504769821*^9, 3.82106453846552*^9}, { 3.82106460185704*^9, 3.821064667240161*^9}, {3.821064704521668*^9, 3.821064854939661*^9}, {3.821064886734498*^9, 3.8210649097711177`*^9}}, CellLabel-> "In[109]:=",ExpressionUUID->"c4542834-7089-48fe-bac4-7e114ab3a12b"] }, Closed]], Cell[CellGroupData[{ Cell["CONSTRAINT ELEMENT (nonl) defs ", "Subsection", CellChangeTimes->{{3.632187277028809*^9, 3.63218727949695*^9}, 3.632188602208605*^9, {3.632189487917265*^9, 3.6321894914104643`*^9}, { 3.68532054956944*^9, 3.6853205513594418`*^9}, {3.687743079248886*^9, 3.6877430854888954`*^9}, {3.76507863996914*^9, 3.7650786436977797`*^9}, { 3.7880762440580482`*^9, 3.7880762616852336`*^9}, {3.788076337785893*^9, 3.7880763394484987`*^9}, {3.7890210020583797`*^9, 3.7890210028862896`*^9}, 3.8174375960916395`*^9, {3.8216140745704536`*^9, 3.8216140795088263`*^9}},ExpressionUUID->"707c619e-862d-4a34-9d6f-\ 9ce5b5329e63"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"RIGID", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"RIGID", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"JOINT", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"JOINT", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"SLIDER", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SLIDER", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.496939383309*^9, 3.4969394213417997`*^9}, { 3.559961640310264*^9, 3.559961656783893*^9}, {3.5599617303692226`*^9, 3.5599617392300377`*^9}, {3.5601312763250604`*^9, 3.5601312794606657`*^9}, {3.5601313134219255`*^9, 3.560131324388745*^9}, { 3.560132497854006*^9, 3.5601324981348066`*^9}, {3.63023183959678*^9, 3.630231884758859*^9}, {3.630649684386073*^9, 3.630649712146661*^9}, { 3.630649747889705*^9, 3.6306497780604305`*^9}, {3.630649843969201*^9, 3.6306501496326838`*^9}, {3.6306501928641567`*^9, 3.630650252234552*^9}, { 3.630650308727783*^9, 3.6306503113519335`*^9}, {3.630650349614122*^9, 3.630650420974203*^9}, {3.630650474367257*^9, 3.630650601725542*^9}, { 3.630651184910898*^9, 3.630651194788463*^9}, {3.6306517131931143`*^9, 3.6306517167213163`*^9}, {3.6306573863011556`*^9, 3.6306574164092083`*^9}, {3.6306574511192694`*^9, 3.630657474862511*^9}, { 3.6306575678542747`*^9, 3.6306576670080485`*^9}, {3.6306577117645273`*^9, 3.6306579038944645`*^9}, {3.630658012221055*^9, 3.630658091874795*^9}, { 3.6306581291432605`*^9, 3.630658226440631*^9}, {3.63065827139991*^9, 3.6306582739115143`*^9}, 3.630658635254949*^9, {3.6306586682178073`*^9, 3.6306586813998303`*^9}, {3.6306590619156985`*^9, 3.630659069606512*^9}, { 3.6321872976489887`*^9, 3.6321873151349883`*^9}, 3.6321874056671667`*^9, { 3.632187463194457*^9, 3.6321878547998557`*^9}, {3.632187889913864*^9, 3.6321878942471123`*^9}, {3.632187976697828*^9, 3.632187979874009*^9}, { 3.6321886111201143`*^9, 3.63218861505834*^9}, {3.632188654528598*^9, 3.6321886640741434`*^9}, {3.632189320010661*^9, 3.632189331931343*^9}, { 3.6853206095995235`*^9, 3.685320631309554*^9}, {3.6853206843496284`*^9, 3.685320754049726*^9}, {3.685320792059779*^9, 3.685320823639823*^9}, { 3.685321020360099*^9, 3.6853211351402597`*^9}, {3.6853211801403227`*^9, 3.685321665981003*^9}, {3.6853216989010487`*^9, 3.6853217094910636`*^9}, { 3.6853217810511637`*^9, 3.6853220138814898`*^9}, {3.6853225388622246`*^9, 3.6853226020023127`*^9}, {3.687743095218909*^9, 3.6877431192189426`*^9}, { 3.687743169079012*^9, 3.687743170319014*^9}, {3.6877432521091285`*^9, 3.68774331760922*^9}, {3.6877433494492645`*^9, 3.6877434507694063`*^9}, { 3.6877434824794507`*^9, 3.687743525179511*^9}, {3.6877442207004843`*^9, 3.68774423869051*^9}, {3.687744273840559*^9, 3.6877443377106485`*^9}, { 3.687744434080783*^9, 3.6877445463509407`*^9}, {3.687744848891364*^9, 3.6877448558313737`*^9}, {3.6877638336712008`*^9, 3.68776389741129*^9}, { 3.687763938681348*^9, 3.6877639455213575`*^9}, {3.6877641776516824`*^9, 3.6877642483817816`*^9}, {3.687764508142145*^9, 3.6877645655122256`*^9}, { 3.687778690246417*^9, 3.687778699786431*^9}, {3.6892208471842775`*^9, 3.6892208613442974`*^9}, {3.6892209340143995`*^9, 3.689220966944445*^9}, { 3.6892211581147127`*^9, 3.689221214324792*^9}, {3.689221265414863*^9, 3.689221335944962*^9}, 3.6892213742150154`*^9, {3.6892214353151007`*^9, 3.689221472385153*^9}, {3.689221514295212*^9, 3.689221800835613*^9}, { 3.6892221753761373`*^9, 3.689222181266145*^9}, 3.689222955217229*^9, { 3.6892232691076684`*^9, 3.689223331877756*^9}, {3.693460221154632*^9, 3.6934602635146914`*^9}, {3.6948453326087465`*^9, 3.6948453439687624`*^9}, {3.7348680727026668`*^9, 3.73486817909155*^9}, { 3.746150241146084*^9, 3.746150271873185*^9}, {3.7530805273958597`*^9, 3.7530805538372126`*^9}, {3.7530806121866155`*^9, 3.753080612619146*^9}, { 3.7530807812083597`*^9, 3.753080855476215*^9}, {3.7530808933957005`*^9, 3.753080928261367*^9}, {3.7530812010856276`*^9, 3.753081304984929*^9}, { 3.753081363847283*^9, 3.753081510980585*^9}, {3.7530830896227846`*^9, 3.7530831670560236`*^9}, {3.753083282189464*^9, 3.753083319143241*^9}, { 3.753083522782399*^9, 3.7530836451470532`*^9}, {3.753083680478052*^9, 3.7530837044483657`*^9}, {3.7530839780537753`*^9, 3.7530840044915133`*^9}, {3.7530841230935698`*^9, 3.7530841439684134`*^9}, {3.753084174787207*^9, 3.753084175438378*^9}, { 3.7531753489377103`*^9, 3.7531753521812167`*^9}, {3.7531753986744366`*^9, 3.753175401639263*^9}, {3.7531757699701395`*^9, 3.7531757819468718`*^9}, { 3.7531758502951393`*^9, 3.753176036147319*^9}, {3.7650793717088127`*^9, 3.765079384414342*^9}, {3.7650794145018706`*^9, 3.7650794160024643`*^9}, { 3.765080191205142*^9, 3.7650801957605696`*^9}, {3.765080316588634*^9, 3.765080334411024*^9}, {3.7650804146979465`*^9, 3.765080452046597*^9}, { 3.7650805125970893`*^9, 3.765080538042729*^9}, {3.7650806025099554`*^9, 3.765080640706174*^9}, {3.765081132572468*^9, 3.765081149288616*^9}, { 3.7843471628441577`*^9, 3.784347230545391*^9}, 3.788076396075549*^9, { 3.7880764597653866`*^9, 3.78807658689421*^9}, {3.7880766192477016`*^9, 3.78807666464567*^9}, {3.7890210098488555`*^9, 3.7890210223821774`*^9}, { 3.7890210765394955`*^9, 3.789021101390154*^9}, {3.821064422910862*^9, 3.821064437263141*^9}, {3.821064504769821*^9, 3.82106453846552*^9}, { 3.82106460185704*^9, 3.821064667240161*^9}, {3.821064704521668*^9, 3.821064854939661*^9}, {3.821064886734498*^9, 3.8210649097711177`*^9}, { 3.8216140898940353`*^9, 3.821614102548308*^9}}, CellLabel-> "In[112]:=",ExpressionUUID->"36b01e2c-345f-4788-8083-087747d27a4d"] }, Closed]], Cell[CellGroupData[{ Cell["CONSTRAINT ELEMENT (tmec) defs ", "Subsection", CellChangeTimes->{{3.632187277028809*^9, 3.63218727949695*^9}, 3.632188602208605*^9, {3.632189487917265*^9, 3.6321894914104643`*^9}, { 3.68532054956944*^9, 3.6853205513594418`*^9}, {3.687743079248886*^9, 3.6877430854888954`*^9}, {3.76507863996914*^9, 3.7650786436977797`*^9}, { 3.7880762440580482`*^9, 3.7880762616852336`*^9}, {3.788076337785893*^9, 3.7880763394484987`*^9}, {3.7890210020583797`*^9, 3.7890210028862896`*^9}, 3.8174375960916395`*^9, {3.8216140745704536`*^9, 3.8216140795088263`*^9}, { 3.8223694156960897`*^9, 3.8223694175391617`*^9}},ExpressionUUID->"24fcb166-9cd4-4b87-a143-\ f5a36af4d49f"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"TMEC", ",", RowBox[{"{", RowBox[{"RIGID", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"RIGID", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"TMEC", ",", RowBox[{"{", RowBox[{"JOINT", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"JOINT", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"TMEC", ",", RowBox[{"{", RowBox[{"SLIDER", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SLIDER", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.496939383309*^9, 3.4969394213417997`*^9}, { 3.559961640310264*^9, 3.559961656783893*^9}, {3.5599617303692226`*^9, 3.5599617392300377`*^9}, {3.5601312763250604`*^9, 3.5601312794606657`*^9}, {3.5601313134219255`*^9, 3.560131324388745*^9}, { 3.560132497854006*^9, 3.5601324981348066`*^9}, {3.63023183959678*^9, 3.630231884758859*^9}, {3.630649684386073*^9, 3.630649712146661*^9}, { 3.630649747889705*^9, 3.6306497780604305`*^9}, {3.630649843969201*^9, 3.6306501496326838`*^9}, {3.6306501928641567`*^9, 3.630650252234552*^9}, { 3.630650308727783*^9, 3.6306503113519335`*^9}, {3.630650349614122*^9, 3.630650420974203*^9}, {3.630650474367257*^9, 3.630650601725542*^9}, { 3.630651184910898*^9, 3.630651194788463*^9}, {3.6306517131931143`*^9, 3.6306517167213163`*^9}, {3.6306573863011556`*^9, 3.6306574164092083`*^9}, {3.6306574511192694`*^9, 3.630657474862511*^9}, { 3.6306575678542747`*^9, 3.6306576670080485`*^9}, {3.6306577117645273`*^9, 3.6306579038944645`*^9}, {3.630658012221055*^9, 3.630658091874795*^9}, { 3.6306581291432605`*^9, 3.630658226440631*^9}, {3.63065827139991*^9, 3.6306582739115143`*^9}, 3.630658635254949*^9, {3.6306586682178073`*^9, 3.6306586813998303`*^9}, {3.6306590619156985`*^9, 3.630659069606512*^9}, { 3.6321872976489887`*^9, 3.6321873151349883`*^9}, 3.6321874056671667`*^9, { 3.632187463194457*^9, 3.6321878547998557`*^9}, {3.632187889913864*^9, 3.6321878942471123`*^9}, {3.632187976697828*^9, 3.632187979874009*^9}, { 3.6321886111201143`*^9, 3.63218861505834*^9}, {3.632188654528598*^9, 3.6321886640741434`*^9}, {3.632189320010661*^9, 3.632189331931343*^9}, { 3.6853206095995235`*^9, 3.685320631309554*^9}, {3.6853206843496284`*^9, 3.685320754049726*^9}, {3.685320792059779*^9, 3.685320823639823*^9}, { 3.685321020360099*^9, 3.6853211351402597`*^9}, {3.6853211801403227`*^9, 3.685321665981003*^9}, {3.6853216989010487`*^9, 3.6853217094910636`*^9}, { 3.6853217810511637`*^9, 3.6853220138814898`*^9}, {3.6853225388622246`*^9, 3.6853226020023127`*^9}, {3.687743095218909*^9, 3.6877431192189426`*^9}, { 3.687743169079012*^9, 3.687743170319014*^9}, {3.6877432521091285`*^9, 3.68774331760922*^9}, {3.6877433494492645`*^9, 3.6877434507694063`*^9}, { 3.6877434824794507`*^9, 3.687743525179511*^9}, {3.6877442207004843`*^9, 3.68774423869051*^9}, {3.687744273840559*^9, 3.6877443377106485`*^9}, { 3.687744434080783*^9, 3.6877445463509407`*^9}, {3.687744848891364*^9, 3.6877448558313737`*^9}, {3.6877638336712008`*^9, 3.68776389741129*^9}, { 3.687763938681348*^9, 3.6877639455213575`*^9}, {3.6877641776516824`*^9, 3.6877642483817816`*^9}, {3.687764508142145*^9, 3.6877645655122256`*^9}, { 3.687778690246417*^9, 3.687778699786431*^9}, {3.6892208471842775`*^9, 3.6892208613442974`*^9}, {3.6892209340143995`*^9, 3.689220966944445*^9}, { 3.6892211581147127`*^9, 3.689221214324792*^9}, {3.689221265414863*^9, 3.689221335944962*^9}, 3.6892213742150154`*^9, {3.6892214353151007`*^9, 3.689221472385153*^9}, {3.689221514295212*^9, 3.689221800835613*^9}, { 3.6892221753761373`*^9, 3.689222181266145*^9}, 3.689222955217229*^9, { 3.6892232691076684`*^9, 3.689223331877756*^9}, {3.693460221154632*^9, 3.6934602635146914`*^9}, {3.6948453326087465`*^9, 3.6948453439687624`*^9}, {3.7348680727026668`*^9, 3.73486817909155*^9}, { 3.746150241146084*^9, 3.746150271873185*^9}, {3.7530805273958597`*^9, 3.7530805538372126`*^9}, {3.7530806121866155`*^9, 3.753080612619146*^9}, { 3.7530807812083597`*^9, 3.753080855476215*^9}, {3.7530808933957005`*^9, 3.753080928261367*^9}, {3.7530812010856276`*^9, 3.753081304984929*^9}, { 3.753081363847283*^9, 3.753081510980585*^9}, {3.7530830896227846`*^9, 3.7530831670560236`*^9}, {3.753083282189464*^9, 3.753083319143241*^9}, { 3.753083522782399*^9, 3.7530836451470532`*^9}, {3.753083680478052*^9, 3.7530837044483657`*^9}, {3.7530839780537753`*^9, 3.7530840044915133`*^9}, {3.7530841230935698`*^9, 3.7530841439684134`*^9}, {3.753084174787207*^9, 3.753084175438378*^9}, { 3.7531753489377103`*^9, 3.7531753521812167`*^9}, {3.7531753986744366`*^9, 3.753175401639263*^9}, {3.7531757699701395`*^9, 3.7531757819468718`*^9}, { 3.7531758502951393`*^9, 3.753176036147319*^9}, {3.7650793717088127`*^9, 3.765079384414342*^9}, {3.7650794145018706`*^9, 3.7650794160024643`*^9}, { 3.765080191205142*^9, 3.7650801957605696`*^9}, {3.765080316588634*^9, 3.765080334411024*^9}, {3.7650804146979465`*^9, 3.765080452046597*^9}, { 3.7650805125970893`*^9, 3.765080538042729*^9}, {3.7650806025099554`*^9, 3.765080640706174*^9}, {3.765081132572468*^9, 3.765081149288616*^9}, { 3.7843471628441577`*^9, 3.784347230545391*^9}, 3.788076396075549*^9, { 3.7880764597653866`*^9, 3.78807658689421*^9}, {3.7880766192477016`*^9, 3.78807666464567*^9}, {3.7890210098488555`*^9, 3.7890210223821774`*^9}, { 3.7890210765394955`*^9, 3.789021101390154*^9}, {3.821064422910862*^9, 3.821064437263141*^9}, {3.821064504769821*^9, 3.82106453846552*^9}, { 3.82106460185704*^9, 3.821064667240161*^9}, {3.821064704521668*^9, 3.821064854939661*^9}, {3.821064886734498*^9, 3.8210649097711177`*^9}, { 3.8216140898940353`*^9, 3.821614102548308*^9}, {3.8223694278575764`*^9, 3.8223694427926483`*^9}}, CellLabel-> "In[115]:=",ExpressionUUID->"cb46ea58-8ee7-4f83-8317-3c04612e4669"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["BEAM MODEL", "Section", CellChangeTimes->{ 3.4430806364968*^9, {3.4453166713873997`*^9, 3.4453166747414*^9}, { 3.447462264275*^9, 3.4474622644154*^9}, {3.4695731321116*^9, 3.4695731359491997`*^9}, 3.473055186341*^9, {3.4730552472860003`*^9, 3.47305524884*^9}, {3.473055399782*^9, 3.473055419801*^9}, { 3.4734696760778*^9, 3.4734697047349997`*^9}, {3.4770537891542*^9, 3.4770537950354*^9}, {3.4932799754514*^9, 3.4932799779161997`*^9}, { 3.4945558951644*^9, 3.4945558957416*^9}, {3.4957646303032*^9, 3.4957646329084*^9}, {3.497581602118*^9, 3.4975816042552*^9}, { 3.500960505817*^9, 3.5009605094206*^9}, {3.556623836083009*^9, 3.5566238462386265`*^9}, {3.5568725055395393`*^9, 3.5568725163821597`*^9}, {3.556872678728445*^9, 3.5568726810485783`*^9}, { 3.7323376045620503`*^9, 3.7323376086812124`*^9}, {3.7335630623483887`*^9, 3.733563072583865*^9}, {3.733563130246215*^9, 3.733563131355714*^9}, { 3.8175314748809648`*^9, 3.817531482757032*^9}, {3.8175315215912895`*^9, 3.817531523916857*^9}, 3.8175315939049935`*^9},ExpressionUUID->"05a7c66b-fbed-4e48-83b3-\ e8cfa2f8e9b8"], Cell[CellGroupData[{ Cell["BAR ELEMENT (disp) defs", "Subsection", InitializationCell->True, CellChangeTimes->{{3.753018875511382*^9, 3.7530188786265306`*^9}, { 3.7878946919412775`*^9, 3.7878946924724035`*^9}, 3.7878949434473147`*^9},ExpressionUUID->"6bfc85ed-f105-4a6b-85be-\ 4228df237726"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"MEC", "-", "E1050"}], "|", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "iy_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE", "}"}], ",", RowBox[{"{", "AA", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "iy_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE", "}"}], ",", RowBox[{"{", "AA", "}"}], ",", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", "AA_", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE", "}"}], ",", RowBox[{"{", "AA", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", "AA_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "ix0", ",", "ux", ",", "\[Delta]ux", ",", "EE1", ",", "EE2", ",", "EE3", ",", "AA1", ",", "AA2", ",", "AA3", ",", "fx1", ",", "fx2", ",", "fx3", ",", "nl", ",", "rule"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", " ", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ux", "[", "i_", "]"}], ":=", RowBox[{"ix0", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"nl", "[", RowBox[{"[", "i", "]"}], "]"}], ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]ux", "[", "i_", "]"}], ":=", RowBox[{"\[Delta]", "[", RowBox[{"ux", "[", "i", "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"rule", " ", ":=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"a1_", ",", "a2_", ",", "a3_"}], "}"}], "\[Rule]", RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3"}], "}"}]}], ",", RowBox[{ RowBox[{"{", RowBox[{"a1_", ",", "a2_"}], "}"}], "\[Rule]", RowBox[{"{", RowBox[{"a1", ",", RowBox[{ RowBox[{"(", RowBox[{"a1", "+", "a2"}], ")"}], "/", "2"}], ",", "a2"}], "}"}]}], ",", RowBox[{"a1_", "\[Rule]", RowBox[{"{", RowBox[{"a1", ",", "a1", ",", "a1"}], "}"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"EE1", ",", "EE2", ",", "EE3"}], "}"}], "=", RowBox[{"EE", " ", "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"AA1", ",", "AA2", ",", "AA3"}], "}"}], "=", RowBox[{"AA", " ", "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"fx1", ",", "fx2", ",", "fx3"}], "}"}], "=", RowBox[{"ix0", ".", RowBox[{"{", RowBox[{ RowBox[{"fX", " ", "/.", "rule"}], ",", RowBox[{"fY", " ", "/.", "rule"}], ",", RowBox[{"fZ", " ", "/.", "rule"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ FractionBox["1", RowBox[{"30", " ", SuperscriptBox["h0", "2"]}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"AA1", " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", "EE1"}], "+", RowBox[{"2", " ", "EE2"}], "-", "EE3"}], ")"}]}], "+", RowBox[{"2", " ", "AA2", " ", RowBox[{"(", RowBox[{"EE1", "+", RowBox[{"8", " ", "EE2"}], "+", "EE3"}], ")"}]}], "+", RowBox[{"AA3", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "EE1"}], "+", RowBox[{"2", " ", "EE2"}], "+", RowBox[{"4", " ", "EE3"}]}], ")"}]}]}], ")"}]}], " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"ux", "[", "1", "]"}]}], "+", RowBox[{"ux", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"5", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"fx1", " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"fx3", " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"2", " ", "fx2", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", "AA_", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE", "}"}], ",", RowBox[{"{", "AA", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", "AA_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "ix0", ",", "ux", ",", "\[Delta]ux", ",", "EE1", ",", "EE2", ",", "EE3", ",", "AA1", ",", "AA2", ",", "AA3", ",", "fx1", ",", "fx2", ",", "fx3", ",", "nl", ",", "rule"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", " ", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n3", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", " ", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ux", "[", "i_", "]"}], ":=", RowBox[{"ix0", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"nl", "[", RowBox[{"[", "i", "]"}], "]"}], ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]ux", "[", "i_", "]"}], ":=", RowBox[{"\[Delta]", "[", RowBox[{"ux", "[", "i", "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"rule", " ", ":=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"a1_", ",", "a2_", ",", "a3_"}], "}"}], "\[Rule]", RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3"}], "}"}]}], ",", RowBox[{ RowBox[{"{", RowBox[{"a1_", ",", "a2_"}], "}"}], "\[Rule]", RowBox[{"{", RowBox[{"a1", ",", RowBox[{ RowBox[{"(", RowBox[{"a1", "+", "a2"}], ")"}], "/", "2"}], ",", "a2"}], "}"}]}], ",", RowBox[{"a1_", "\[Rule]", RowBox[{"{", RowBox[{"a1", ",", "a1", ",", "a1"}], "}"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"EE1", ",", "EE2", ",", "EE3"}], "}"}], "=", RowBox[{"EE", " ", "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"AA1", ",", "AA2", ",", "AA3"}], "}"}], "=", RowBox[{"AA", " ", "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"fx1", ",", "fx2", ",", "fx3"}], "}"}], "=", RowBox[{"ix0", ".", RowBox[{"{", RowBox[{ RowBox[{"fX", " ", "/.", "rule"}], ",", RowBox[{"fY", " ", "/.", "rule"}], ",", RowBox[{"fZ", " ", "/.", "rule"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"-", FractionBox["1", RowBox[{"210", " ", "h0"}]]}], RowBox[{"(", RowBox[{ RowBox[{"7", " ", "fx3", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"184", " ", "AA1", " ", "EE1", " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"94", " ", "AA2", " ", "EE1", " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "-", RowBox[{"19", " ", "AA3", " ", "EE1", " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"94", " ", "AA1", " ", "EE2", " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"176", " ", "AA2", " ", "EE2", " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "-", RowBox[{"18", " ", "AA3", " ", "EE2", " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "-", RowBox[{"19", " ", "AA1", " ", "EE3", " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "-", RowBox[{"18", " ", "AA2", " ", "EE3", " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"16", " ", "AA3", " ", "EE3", " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "-", RowBox[{"228", " ", "AA1", " ", "EE1", " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "-", RowBox[{"104", " ", "AA2", " ", "EE1", " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"24", " ", "AA3", " ", "EE1", " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "-", RowBox[{"104", " ", "AA1", " ", "EE2", " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "-", RowBox[{"128", " ", "AA2", " ", "EE2", " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"8", " ", "AA3", " ", "EE2", " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"24", " ", "AA1", " ", "EE3", " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"8", " ", "AA2", " ", "EE3", " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "-", RowBox[{"60", " ", "AA3", " ", "EE3", " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"44", " ", "AA1", " ", "EE1", " ", RowBox[{"ux", "[", "3", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"10", " ", "AA2", " ", "EE1", " ", RowBox[{"ux", "[", "3", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "-", RowBox[{"5", " ", "AA3", " ", "EE1", " ", RowBox[{"ux", "[", "3", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"10", " ", "AA1", " ", "EE2", " ", RowBox[{"ux", "[", "3", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "-", RowBox[{"48", " ", "AA2", " ", "EE2", " ", RowBox[{"ux", "[", "3", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"10", " ", "AA3", " ", "EE2", " ", RowBox[{"ux", "[", "3", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "-", RowBox[{"5", " ", "AA1", " ", "EE3", " ", RowBox[{"ux", "[", "3", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"10", " ", "AA2", " ", "EE3", " ", RowBox[{"ux", "[", "3", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"44", " ", "AA3", " ", "EE3", " ", RowBox[{"ux", "[", "3", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "-", RowBox[{"14", " ", "fx3", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "-", RowBox[{"228", " ", "AA1", " ", "EE1", " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "-", RowBox[{"104", " ", "AA2", " ", "EE1", " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"24", " ", "AA3", " ", "EE1", " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "-", RowBox[{"104", " ", "AA1", " ", "EE2", " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "-", RowBox[{"128", " ", "AA2", " ", "EE2", " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"8", " ", "AA3", " ", "EE2", " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"24", " ", "AA1", " ", "EE3", " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"8", " ", "AA2", " ", "EE3", " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "-", RowBox[{"60", " ", "AA3", " ", "EE3", " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"288", " ", "AA1", " ", "EE1", " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"96", " ", "AA2", " ", "EE1", " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "-", RowBox[{"48", " ", "AA3", " ", "EE1", " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"96", " ", "AA1", " ", "EE2", " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"256", " ", "AA2", " ", "EE2", " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"96", " ", "AA3", " ", "EE2", " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "-", RowBox[{"48", " ", "AA1", " ", "EE3", " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"96", " ", "AA2", " ", "EE3", " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"288", " ", "AA3", " ", "EE3", " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "-", RowBox[{"60", " ", "AA1", " ", "EE1", " ", RowBox[{"ux", "[", "3", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"8", " ", "AA2", " ", "EE1", " ", RowBox[{"ux", "[", "3", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"24", " ", "AA3", " ", "EE1", " ", RowBox[{"ux", "[", "3", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"8", " ", "AA1", " ", "EE2", " ", RowBox[{"ux", "[", "3", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "-", RowBox[{"128", " ", "AA2", " ", "EE2", " ", RowBox[{"ux", "[", "3", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "-", RowBox[{"104", " ", "AA3", " ", "EE2", " ", RowBox[{"ux", "[", "3", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"24", " ", "AA1", " ", "EE3", " ", RowBox[{"ux", "[", "3", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "-", RowBox[{"104", " ", "AA2", " ", "EE3", " ", RowBox[{"ux", "[", "3", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "-", RowBox[{"228", " ", "AA3", " ", "EE3", " ", RowBox[{"ux", "[", "3", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "28"}], " ", "fx3", " ", SuperscriptBox["h0", "2"]}], "+", RowBox[{"AA1", " ", RowBox[{"(", RowBox[{ RowBox[{"44", " ", "EE1", " ", RowBox[{"ux", "[", "1", "]"}]}], "+", RowBox[{"10", " ", "EE2", " ", RowBox[{"ux", "[", "1", "]"}]}], "-", RowBox[{"5", " ", "EE3", " ", RowBox[{"ux", "[", "1", "]"}]}], "-", RowBox[{"60", " ", "EE1", " ", RowBox[{"ux", "[", "2", "]"}]}], "+", RowBox[{"8", " ", "EE2", " ", RowBox[{"ux", "[", "2", "]"}]}], "+", RowBox[{"24", " ", "EE3", " ", RowBox[{"ux", "[", "2", "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"16", " ", "EE1"}], "-", RowBox[{"18", " ", "EE2"}], "-", RowBox[{"19", " ", "EE3"}]}], ")"}], " ", RowBox[{"ux", "[", "3", "]"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "AA2", " ", RowBox[{"(", RowBox[{ RowBox[{"5", " ", "EE1", " ", RowBox[{"ux", "[", "1", "]"}]}], "-", RowBox[{"24", " ", "EE2", " ", RowBox[{"ux", "[", "1", "]"}]}], "+", RowBox[{"5", " ", "EE3", " ", RowBox[{"ux", "[", "1", "]"}]}], "+", RowBox[{"4", " ", "EE1", " ", RowBox[{"ux", "[", "2", "]"}]}], "-", RowBox[{"64", " ", "EE2", " ", RowBox[{"ux", "[", "2", "]"}]}], "-", RowBox[{"52", " ", "EE3", " ", RowBox[{"ux", "[", "2", "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "9"}], " ", "EE1"}], "+", RowBox[{"88", " ", "EE2"}], "+", RowBox[{"47", " ", "EE3"}]}], ")"}], " ", RowBox[{"ux", "[", "3", "]"}]}]}], ")"}]}], "+", RowBox[{"AA3", " ", RowBox[{"(", RowBox[{ RowBox[{"EE1", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "5"}], " ", RowBox[{"ux", "[", "1", "]"}]}], "+", RowBox[{"24", " ", RowBox[{"ux", "[", "2", "]"}]}], "-", RowBox[{"19", " ", RowBox[{"ux", "[", "3", "]"}]}]}], ")"}]}], "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE3", " ", RowBox[{"(", RowBox[{ RowBox[{"11", " ", RowBox[{"ux", "[", "1", "]"}]}], "-", RowBox[{"57", " ", RowBox[{"ux", "[", "2", "]"}]}], "+", RowBox[{"46", " ", RowBox[{"ux", "[", "3", "]"}]}]}], ")"}]}], "+", RowBox[{"EE2", " ", RowBox[{"(", RowBox[{ RowBox[{"5", " ", RowBox[{"ux", "[", "1", "]"}]}], "-", RowBox[{"52", " ", RowBox[{"ux", "[", "2", "]"}]}], "+", RowBox[{"47", " ", RowBox[{"ux", "[", "3", "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"\[Delta]ux", "[", "3", "]"}]}], "+", RowBox[{"7", " ", "fx1", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "-", RowBox[{"2", " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"\[Delta]ux", "[", "3", "]"}]}], ")"}]}], "-", RowBox[{"14", " ", "fx2", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "+", RowBox[{"8", " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"\[Delta]ux", "[", "3", "]"}]}], ")"}]}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, { 3.7530189177531705`*^9, 3.753018918350237*^9}, {3.753018991800671*^9, 3.753019041865839*^9}, {3.7530191095313196`*^9, 3.7530191100576744`*^9}, 3.753019155952956*^9, {3.7530192458219423`*^9, 3.753019353286773*^9}, { 3.773986323215969*^9, 3.7739864366876383`*^9}, {3.7739864700193005`*^9, 3.7739865885966825`*^9}, {3.7739869332783327`*^9, 3.7739870501829805`*^9}, 3.773987085528166*^9, {3.7739872536160583`*^9, 3.773987270466986*^9}, { 3.773987482712697*^9, 3.7739875221812735`*^9}, {3.773987740298462*^9, 3.7739877466065903`*^9}, {3.7739878599976892`*^9, 3.7739878861137896`*^9}, {3.773987965425336*^9, 3.7739879715632877`*^9}, 3.773988098774023*^9, 3.7739883193781385`*^9, {3.7739884099852057`*^9, 3.7739885862960095`*^9}, {3.773988628922502*^9, 3.773988632767228*^9}, { 3.7739891227568517`*^9, 3.77398915009042*^9}, {3.7739892774900556`*^9, 3.773989291800435*^9}, {3.7739896060525217`*^9, 3.773989635013425*^9}, { 3.7751890832095585`*^9, 3.7751890882413054`*^9}, {3.7751894923762302`*^9, 3.7751895008441906`*^9}, {3.7751911834227276`*^9, 3.775191222686661*^9}, 3.7751912606478214`*^9, {3.7751943412188396`*^9, 3.775194461553982*^9}, { 3.775194496052539*^9, 3.7751945353727713`*^9}, {3.7751945737174063`*^9, 3.775194621343042*^9}, {3.775194667862669*^9, 3.7751947598351893`*^9}, { 3.7751948235734253`*^9, 3.7751949415953684`*^9}, {3.775195100078847*^9, 3.77519512113822*^9}, {3.7751954506873007`*^9, 3.775195467864645*^9}, { 3.775270786870551*^9, 3.775270796325161*^9}, {3.7752708274391947`*^9, 3.775270839737406*^9}, {3.7752709283091574`*^9, 3.7752709474534383`*^9}, { 3.7752710502850266`*^9, 3.7752711744130797`*^9}, {3.7752712273079033`*^9, 3.7752713060364757`*^9}, {3.775271448825513*^9, 3.7752714699277525`*^9}, { 3.775271509321142*^9, 3.775271585609558*^9}, {3.775271620653377*^9, 3.77527180192237*^9}, {3.781671264558541*^9, 3.7816712751556396`*^9}, { 3.7816715257512035`*^9, 3.781671526206021*^9}, 3.781671612475748*^9, { 3.781672177985033*^9, 3.7816722548545895`*^9}, {3.7816755757937236`*^9, 3.7816756936745577`*^9}, 3.781675873086305*^9, {3.7816761808096905`*^9, 3.7816762075777946`*^9}, {3.788077170199604*^9, 3.7880772443461285`*^9}, 3.8175324221718016`*^9, {3.817532645653172*^9, 3.817532680712221*^9}, { 3.8200248875082335`*^9, 3.8200249266511517`*^9}, 3.8200249735130763`*^9, { 3.8217742761087155`*^9, 3.821774333135168*^9}, {3.821774750423011*^9, 3.8217747610558224`*^9}, {3.8217747912447248`*^9, 3.8217749904455633`*^9}, {3.8217750368892345`*^9, 3.8217752594972935`*^9}, {3.8217752941944513`*^9, 3.8217753660612097`*^9}, {3.843624690905726*^9, 3.843624714964343*^9}, { 3.843625137403534*^9, 3.8436253106688747`*^9}, {3.8436254114664454`*^9, 3.843625482254491*^9}, {3.8436258314013753`*^9, 3.843625832963335*^9}, { 3.84362587330585*^9, 3.8436258882972155`*^9}, {3.843625938953411*^9, 3.8436259929118633`*^9}, {3.8530325799408607`*^9, 3.8530325954117217`*^9}, 3.8530326372114444`*^9}, CellLabel-> "In[118]:=",ExpressionUUID->"8da43dad-153a-4069-a012-c6a592fa09b0"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "iy_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE", "}"}], ",", RowBox[{"{", "AA", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "iy_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE", "}"}], ",", RowBox[{"{", "AA", "}"}], ",", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", "AA_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "ix0", ",", "iz0", ",", "ux", ",", "\[Delta]ux", ",", "EE1", ",", "EE2", ",", "EE3", ",", "AA1", ",", "AA2", ",", "AA3", ",", "fx", ",", "fx1", ",", "fx2", ",", "fx3", ",", "nl", ",", "rule"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", " ", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ux", "[", "i_", "]"}], ":=", RowBox[{"ix0", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"nl", "[", RowBox[{"[", "i", "]"}], "]"}], ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]ux", "[", "i_", "]"}], ":=", RowBox[{"\[Delta]", "[", RowBox[{"ux", "[", "i", "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"rule", " ", ":=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"a1_", ",", "a2_", ",", "a3_"}], "}"}], "\[Rule]", RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3"}], "}"}]}], ",", RowBox[{ RowBox[{"{", RowBox[{"a1_", ",", "a2_"}], "}"}], "\[Rule]", RowBox[{"{", RowBox[{"a1", ",", RowBox[{ RowBox[{"(", RowBox[{"a1", "+", "a2"}], ")"}], "/", "2"}], ",", "a2"}], "}"}]}], ",", RowBox[{"a1_", "\[Rule]", RowBox[{"{", RowBox[{"a1", ",", "a1", ",", "a1"}], "}"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"fx", " ", "=", RowBox[{ RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"EE1", ",", "EE2", ",", "EE3"}], "}"}], "=", RowBox[{"EE", " ", "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"AA1", ",", "AA2", ",", "AA3"}], "}"}], "=", RowBox[{"AA", " ", "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"fx1", ",", "fx2", ",", "fx3"}], "}"}], "=", RowBox[{"fx", " ", "/.", "rule"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ FractionBox["1", RowBox[{"30", " ", SuperscriptBox["h0", "2"]}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"AA1", " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", "EE1"}], "+", RowBox[{"2", " ", "EE2"}], "-", "EE3"}], ")"}]}], "+", RowBox[{"2", " ", "AA2", " ", RowBox[{"(", RowBox[{"EE1", "+", RowBox[{"8", " ", "EE2"}], "+", "EE3"}], ")"}]}], "+", RowBox[{"AA3", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "EE1"}], "+", RowBox[{"2", " ", "EE2"}], "+", RowBox[{"4", " ", "EE3"}]}], ")"}]}]}], ")"}]}], " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"ux", "[", "1", "]"}]}], "+", RowBox[{"ux", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"5", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"fx1", " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"fx3", " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"2", " ", "fx2", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", "AA_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "ix0", ",", "ux", ",", "\[Delta]ux", ",", "\[Delta]Wint", ",", "\[Delta]Wext"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", " ", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ux", "[", "1", "]"}], "=", RowBox[{"ix0", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"ux", "[", "2", "]"}], "=", RowBox[{"ix0", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"ux", "[", "1", "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]ux", "[", "2", "]"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"ux", "[", "2", "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]Wint", "=", RowBox[{ RowBox[{"-", "AA"}], " ", RowBox[{"EE", "/", "h0"}], " ", "*", RowBox[{"(", RowBox[{ RowBox[{"ux", "[", "1", "]"}], "-", RowBox[{"ux", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "-", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]Wext", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}], "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "*", RowBox[{"h0", "/", "2"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]Wint", "+", "\[Delta]Wext"}]}]}], "]"}]}], ";"}]}]}]], "Input", CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, { 3.7530189177531705`*^9, 3.753018918350237*^9}, {3.753018991800671*^9, 3.753019041865839*^9}, {3.7530191095313196`*^9, 3.7530191100576744`*^9}, 3.753019155952956*^9, {3.7530192458219423`*^9, 3.753019353286773*^9}, { 3.773986323215969*^9, 3.7739864366876383`*^9}, {3.7739864700193005`*^9, 3.7739865885966825`*^9}, {3.7739869332783327`*^9, 3.7739870501829805`*^9}, 3.773987085528166*^9, {3.7739872536160583`*^9, 3.773987270466986*^9}, { 3.773987482712697*^9, 3.7739875221812735`*^9}, {3.773987740298462*^9, 3.7739877466065903`*^9}, {3.7739878599976892`*^9, 3.7739878861137896`*^9}, {3.773987965425336*^9, 3.7739879715632877`*^9}, 3.773988098774023*^9, 3.7739883193781385`*^9, {3.7739884099852057`*^9, 3.7739885862960095`*^9}, {3.773988628922502*^9, 3.773988632767228*^9}, { 3.7739891227568517`*^9, 3.77398915009042*^9}, {3.7739892774900556`*^9, 3.773989291800435*^9}, {3.7739896060525217`*^9, 3.773989635013425*^9}, { 3.7751890832095585`*^9, 3.7751890882413054`*^9}, {3.7751894923762302`*^9, 3.7751895008441906`*^9}, {3.7751911834227276`*^9, 3.775191222686661*^9}, 3.7751912606478214`*^9, {3.7751943412188396`*^9, 3.775194461553982*^9}, { 3.775194496052539*^9, 3.7751945353727713`*^9}, {3.7751945737174063`*^9, 3.775194621343042*^9}, {3.775194667862669*^9, 3.7751947598351893`*^9}, { 3.7751948235734253`*^9, 3.7751949415953684`*^9}, {3.775195100078847*^9, 3.77519512113822*^9}, {3.7751954506873007`*^9, 3.775195467864645*^9}, { 3.775270786870551*^9, 3.775270796325161*^9}, {3.7752708274391947`*^9, 3.775270839737406*^9}, {3.7752709283091574`*^9, 3.7752709474534383`*^9}, { 3.7752710502850266`*^9, 3.7752711744130797`*^9}, {3.7752712273079033`*^9, 3.7752713060364757`*^9}, {3.775271448825513*^9, 3.7752714699277525`*^9}, { 3.775271509321142*^9, 3.775271585609558*^9}, {3.775271620653377*^9, 3.77527180192237*^9}, {3.781671264558541*^9, 3.7816712751556396`*^9}, { 3.7816715257512035`*^9, 3.781671526206021*^9}, 3.781671612475748*^9, { 3.781672177985033*^9, 3.7816722548545895`*^9}, {3.7816755757937236`*^9, 3.7816756936745577`*^9}, 3.781675873086305*^9, {3.7816761808096905`*^9, 3.7816762075777946`*^9}, {3.788077170199604*^9, 3.7880772443461285`*^9}, 3.8175324221718016`*^9, {3.817532645653172*^9, 3.817532680712221*^9}, { 3.8200248875082335`*^9, 3.8200249266511517`*^9}, 3.8200249735130763`*^9, { 3.8217742761087155`*^9, 3.821774333135168*^9}, {3.821774750423011*^9, 3.8217747610558224`*^9}, {3.8217747912447248`*^9, 3.8217749904455633`*^9}, {3.8217750368892345`*^9, 3.8217752594972935`*^9}, {3.8217752941944513`*^9, 3.8217753660612097`*^9}, {3.843624690905726*^9, 3.843624714964343*^9}, { 3.843625137403534*^9, 3.8436253106688747`*^9}, {3.8436254114664454`*^9, 3.843625482254491*^9}, {3.8436258314013753`*^9, 3.843625832963335*^9}, { 3.84362587330585*^9, 3.8436258882972155`*^9}, {3.843625938953411*^9, 3.843626019323427*^9}},ExpressionUUID->"29a8cc6d-3e9d-4cc8-b075-\ be9a813667e8"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"GENERICBAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", "A_", "}"}], ",", RowBox[{"{", "fx_", "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "NN", ",", "\[Xi]", ",", "r", ",", "r\[Xi]", ",", "h0", ",", "i\[Xi]", ",", "s", ",", "x", ",", "uu", ",", "\[Delta]uu", ",", "F", ",", "\[Delta]wint", ",", "\[Delta]wext"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "=", " ", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"Length", "[", "node", "]"}], ",", "\[Xi]"}], "}"}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"mapping", " ", "to", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"\[Xi]", "*", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"Last", "[", "node", "]"}], ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"First", "[", "node", "]"}], ",", "1"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Xi]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "r"}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r\[Xi]", ".", "r\[Xi]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"i\[Xi]", " ", "=", RowBox[{"r\[Xi]", "/", "h0"}]}], ";", "\[IndentingNewLine]", RowBox[{"s", "=", RowBox[{"i\[Xi]", " ", ".", "r"}]}], ";", "\[IndentingNewLine]", RowBox[{"x", "=", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"First", "[", "node", "]"}], ",", "1"}], "]"}], "]"}], ".", "i\[Xi]"}], "+", "s"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"(*", "approximation", "*)"}], "\[IndentingNewLine]", RowBox[{"uu", "=", " ", RowBox[{"i\[Xi]", ".", RowBox[{"(", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "2"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "resultant"}], "*)"}], "\[IndentingNewLine]", RowBox[{"F", " ", "=", RowBox[{ RowBox[{"EE", "[", "x", "]"}], "*", RowBox[{"A", "[", "x", "]"}], " ", "*", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "uu"}], "/", "h0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "uu"}], "/", "h0"}], "]"}]}], "*", "F"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uu", "]"}], "*", RowBox[{"fx", "[", "x", "]"}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "h0"}], ",", RowBox[{"{", RowBox[{"\[Xi]", ",", "0", ",", "1"}], "}"}]}], "]"}], ",", " ", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, { 3.7530189177531705`*^9, 3.753018918350237*^9}, {3.753018991800671*^9, 3.753019041865839*^9}, {3.7530191095313196`*^9, 3.7530191100576744`*^9}, 3.753019155952956*^9, {3.7530192458219423`*^9, 3.753019353286773*^9}, { 3.773986323215969*^9, 3.7739864366876383`*^9}, {3.7739864700193005`*^9, 3.7739865885966825`*^9}, {3.7739869332783327`*^9, 3.7739870501829805`*^9}, 3.773987085528166*^9, {3.7739872536160583`*^9, 3.773987270466986*^9}, { 3.773987482712697*^9, 3.7739875221812735`*^9}, {3.773987740298462*^9, 3.7739877466065903`*^9}, {3.7739878599976892`*^9, 3.7739878861137896`*^9}, {3.773987965425336*^9, 3.7739879715632877`*^9}, 3.773988098774023*^9, 3.7739883193781385`*^9, {3.7739884099852057`*^9, 3.7739885862960095`*^9}, {3.773988628922502*^9, 3.773988632767228*^9}, { 3.7739891227568517`*^9, 3.77398915009042*^9}, {3.7739892774900556`*^9, 3.773989291800435*^9}, {3.7739896060525217`*^9, 3.773989635013425*^9}, { 3.7751890832095585`*^9, 3.7751890882413054`*^9}, {3.7751894923762302`*^9, 3.7751895008441906`*^9}, {3.7751911834227276`*^9, 3.775191222686661*^9}, 3.7751912606478214`*^9, {3.7751943412188396`*^9, 3.775194461553982*^9}, { 3.775194496052539*^9, 3.7751945353727713`*^9}, {3.7751945737174063`*^9, 3.775194621343042*^9}, {3.775194667862669*^9, 3.7751947598351893`*^9}, { 3.7751948235734253`*^9, 3.7751949415953684`*^9}, {3.775195100078847*^9, 3.77519512113822*^9}, {3.7751954506873007`*^9, 3.775195467864645*^9}, { 3.775270786870551*^9, 3.775270796325161*^9}, {3.7752708274391947`*^9, 3.775270839737406*^9}, {3.7752709283091574`*^9, 3.7752709474534383`*^9}, { 3.7752710502850266`*^9, 3.7752711744130797`*^9}, {3.7752712273079033`*^9, 3.7752713060364757`*^9}, {3.775271448825513*^9, 3.7752714699277525`*^9}, { 3.775271509321142*^9, 3.775271585609558*^9}, {3.775271620653377*^9, 3.77527180192237*^9}, {3.781671264558541*^9, 3.7816712751556396`*^9}, { 3.7816715257512035`*^9, 3.781671526206021*^9}, 3.781671612475748*^9, { 3.781672177985033*^9, 3.7816722548545895`*^9}, {3.7816755757937236`*^9, 3.7816756936745577`*^9}, 3.781675873086305*^9, {3.7816761808096905`*^9, 3.7816762075777946`*^9}, {3.788077170199604*^9, 3.7880772443461285`*^9}, 3.8175324221718016`*^9, {3.817532645653172*^9, 3.817532680712221*^9}, { 3.8200248875082335`*^9, 3.8200249266511517`*^9}, 3.8200249735130763`*^9, 3.820025011696958*^9},ExpressionUUID->"8b48a7c8-e995-4bfa-aa44-\ 595f56c6c1f8"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"NEW", " ", "DEFS"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"RECTANGLE", "[", RowBox[{"ly_", ",", "lz_"}], "]"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"RECTANGLE", "[", RowBox[{"ly", ",", "lz", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"RECTANGLE", "[", RowBox[{"ly_", ",", "lz_"}], "]"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"RECTANGLE", "[", RowBox[{"ly", ",", "lz", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"RECTANGLE", "[", RowBox[{"ly_", ",", "lz_"}], "]"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", RowBox[{"ly", ",", "lz", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"RECTANGLE", "[", RowBox[{"ly_", ",", "lz_", ",", "iy_"}], "]"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "ix0", ",", "ux", ",", "\[Delta]ux", ",", "EE1", ",", "EE2", ",", "EE3", ",", "AA1", ",", "AA2", ",", "AA3", ",", "fx1", ",", "fx2", ",", "fx3", ",", "nl", ",", "rule"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", " ", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ux", "[", "i_", "]"}], ":=", RowBox[{"ix0", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"nl", "[", RowBox[{"[", "i", "]"}], "]"}], ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]ux", "[", "i_", "]"}], ":=", RowBox[{"\[Delta]", "[", RowBox[{"ux", "[", "i", "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"rule", " ", ":=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"a1_", ",", "a2_", ",", "a3_"}], "}"}], "\[Rule]", RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3"}], "}"}]}], ",", RowBox[{ RowBox[{"{", RowBox[{"a1_", ",", "a2_"}], "}"}], "\[Rule]", RowBox[{"{", RowBox[{"a1", ",", RowBox[{ RowBox[{"(", RowBox[{"a1", "+", "a2"}], ")"}], "/", "2"}], ",", "a2"}], "}"}]}], ",", RowBox[{"a1_", "\[Rule]", RowBox[{"{", RowBox[{"a1", ",", "a1", ",", "a1"}], "}"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"EE1", ",", "EE2", ",", "EE3"}], "}"}], "=", RowBox[{"EE", " ", "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"AA1", ",", "AA2", ",", "AA3"}], "}"}], "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}]}], "&"}], ",", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"ly", "/.", "rule"}], ",", RowBox[{"lz", "/.", "rule"}]}], "}"}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"fx1", ",", "fx2", ",", "fx3"}], "}"}], "=", " ", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"#", ".", "ix0"}], "&"}], ",", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"fX", "/.", "rule"}], ",", RowBox[{"fY", "/.", "rule"}], ",", RowBox[{"fZ", "/.", "rule"}]}], "}"}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ FractionBox["1", RowBox[{"30", " ", SuperscriptBox["h0", "2"]}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"AA1", " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", "EE1"}], "+", RowBox[{"2", " ", "EE2"}], "-", "EE3"}], ")"}]}], "+", RowBox[{"2", " ", "AA2", " ", RowBox[{"(", RowBox[{"EE1", "+", RowBox[{"8", " ", "EE2"}], "+", "EE3"}], ")"}]}], "+", RowBox[{"AA3", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "EE1"}], "+", RowBox[{"2", " ", "EE2"}], "+", RowBox[{"4", " ", "EE3"}]}], ")"}]}]}], ")"}]}], " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"ux", "[", "1", "]"}]}], "+", RowBox[{"ux", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"5", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"fx1", " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"fx3", " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"2", " ", "fx2", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"circle", " ", "cross"}], "-", "section"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"CIRCLE", "[", "d_", "]"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"CIRCLE", "[", RowBox[{"d", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"CIRCLE", "[", "d_", "]"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"CIRCLE", "[", RowBox[{"d", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"CIRCLE", "[", "d_", "]"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"CIRCLE", "[", RowBox[{"d", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"CIRCLE", "[", RowBox[{"d_", ",", "iy_"}], "]"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "ix0", ",", "ux", ",", "\[Delta]ux", ",", "EE1", ",", "EE2", ",", "EE3", ",", "AA1", ",", "AA2", ",", "AA3", ",", "fx1", ",", "fx2", ",", "fx3", ",", "nl", ",", "rule"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", " ", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ux", "[", "i_", "]"}], ":=", RowBox[{"ix0", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"nl", "[", RowBox[{"[", "i", "]"}], "]"}], ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]ux", "[", "i_", "]"}], ":=", RowBox[{"\[Delta]", "[", RowBox[{"ux", "[", "i", "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"rule", " ", ":=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"a1_", ",", "a2_", ",", "a3_"}], "}"}], "\[Rule]", RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3"}], "}"}]}], ",", RowBox[{ RowBox[{"{", RowBox[{"a1_", ",", "a2_"}], "}"}], "\[Rule]", RowBox[{"{", RowBox[{"a1", ",", RowBox[{ RowBox[{"(", RowBox[{"a1", "+", "a2"}], ")"}], "/", "2"}], ",", "a2"}], "}"}]}], ",", RowBox[{"a1_", "\[Rule]", RowBox[{"{", RowBox[{"a1", ",", "a1", ",", "a1"}], "}"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"EE1", ",", "EE2", ",", "EE3"}], "}"}], "=", RowBox[{"EE", " ", "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"AA1", ",", "AA2", ",", "AA3"}], "}"}], "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Pi", "/", "4"}], "*", RowBox[{"#", "^", "2"}]}], "&"}], ",", RowBox[{"d", "/.", "rule"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"fx1", ",", "fx2", ",", "fx3"}], "}"}], "=", " ", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"#", ".", "ix0"}], "&"}], ",", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"fX", "/.", "rule"}], ",", RowBox[{"fY", "/.", "rule"}], ",", RowBox[{"fZ", "/.", "rule"}]}], "}"}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ FractionBox["1", RowBox[{"30", " ", SuperscriptBox["h0", "2"]}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"AA1", " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", "EE1"}], "+", RowBox[{"2", " ", "EE2"}], "-", "EE3"}], ")"}]}], "+", RowBox[{"2", " ", "AA2", " ", RowBox[{"(", RowBox[{"EE1", "+", RowBox[{"8", " ", "EE2"}], "+", "EE3"}], ")"}]}], "+", RowBox[{"AA3", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "EE1"}], "+", RowBox[{"2", " ", "EE2"}], "+", RowBox[{"4", " ", "EE3"}]}], ")"}]}]}], ")"}]}], " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"ux", "[", "1", "]"}]}], "+", RowBox[{"ux", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"5", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"fx1", " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"fx3", " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"2", " ", "fx2", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}]}], "]"}]}], ";"}]}]}]], "Input", CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, { 3.7530189177531705`*^9, 3.753018918350237*^9}, {3.753018991800671*^9, 3.753019041865839*^9}, {3.7530191095313196`*^9, 3.7530191100576744`*^9}, 3.753019155952956*^9, {3.7530192458219423`*^9, 3.753019353286773*^9}, { 3.773986323215969*^9, 3.7739864366876383`*^9}, {3.7739864700193005`*^9, 3.7739865885966825`*^9}, {3.7739869332783327`*^9, 3.7739870501829805`*^9}, 3.773987085528166*^9, {3.7739872536160583`*^9, 3.773987270466986*^9}, { 3.773987482712697*^9, 3.7739875221812735`*^9}, {3.773987740298462*^9, 3.7739877466065903`*^9}, {3.7739878599976892`*^9, 3.7739878861137896`*^9}, {3.773987965425336*^9, 3.7739879715632877`*^9}, 3.773988098774023*^9, 3.7739883193781385`*^9, {3.7739884099852057`*^9, 3.7739885862960095`*^9}, {3.773988628922502*^9, 3.773988632767228*^9}, { 3.7739891227568517`*^9, 3.77398915009042*^9}, {3.7739892774900556`*^9, 3.773989291800435*^9}, {3.7739896060525217`*^9, 3.773989635013425*^9}, { 3.7751890832095585`*^9, 3.7751890882413054`*^9}, {3.7751894923762302`*^9, 3.7751895008441906`*^9}, {3.7751911834227276`*^9, 3.775191222686661*^9}, 3.7751912606478214`*^9, {3.7751943412188396`*^9, 3.775194461553982*^9}, { 3.775194496052539*^9, 3.7751945353727713`*^9}, {3.7751945737174063`*^9, 3.775194621343042*^9}, {3.775194667862669*^9, 3.7751947598351893`*^9}, { 3.7751948235734253`*^9, 3.7751949415953684`*^9}, {3.775195100078847*^9, 3.77519512113822*^9}, {3.7751954506873007`*^9, 3.775195467864645*^9}, { 3.775270786870551*^9, 3.775270796325161*^9}, {3.7752708274391947`*^9, 3.775270839737406*^9}, {3.7752709283091574`*^9, 3.7752709474534383`*^9}, { 3.7752710502850266`*^9, 3.7752711744130797`*^9}, {3.7752712273079033`*^9, 3.7752713060364757`*^9}, {3.775271448825513*^9, 3.7752714699277525`*^9}, { 3.775271509321142*^9, 3.775271585609558*^9}, {3.775271620653377*^9, 3.77527180192237*^9}, {3.781671264558541*^9, 3.7816712751556396`*^9}, { 3.7816715257512035`*^9, 3.781671526206021*^9}, 3.781671612475748*^9, { 3.781672177985033*^9, 3.7816722548545895`*^9}, {3.7816755757937236`*^9, 3.7816756936745577`*^9}, 3.781675873086305*^9, {3.7816761808096905`*^9, 3.7816762075777946`*^9}, {3.788077170199604*^9, 3.7880772443461285`*^9}, 3.8175324221718016`*^9, {3.817532645653172*^9, 3.817532680712221*^9}, { 3.8200248875082335`*^9, 3.8200249266511517`*^9}, 3.8200249735130763`*^9, 3.820025011696958*^9},ExpressionUUID->"8eee6ea7-8e3e-4fd6-a599-\ af158de67901"] }, Closed]], Cell[CellGroupData[{ Cell["BAR ELEMENT (evnt) defs", "Subsection", InitializationCell->True, CellChangeTimes->{{3.753018875511382*^9, 3.7530188786265306`*^9}, { 3.7878946919412775`*^9, 3.7878946924724035`*^9}, 3.7878949434473147`*^9, { 3.817439189246712*^9, 3.8174391911071873`*^9}, 3.8431828238589272`*^9},ExpressionUUID->"a33ee5fa-f607-4577-b5e4-\ 49dc900e2e2f"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"EVNT", ",", RowBox[{"{", RowBox[{"s0_", ",", "sol0_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"BAR", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, { 3.7530189177531705`*^9, 3.753018918350237*^9}, {3.753018991800671*^9, 3.753019041865839*^9}, {3.7530191095313196`*^9, 3.7530191100576744`*^9}, 3.753019155952956*^9, {3.7530192458219423`*^9, 3.753019353286773*^9}, { 3.773986323215969*^9, 3.7739864366876383`*^9}, {3.7739864700193005`*^9, 3.7739865885966825`*^9}, {3.7739869332783327`*^9, 3.7739870501829805`*^9}, 3.773987085528166*^9, {3.7739872536160583`*^9, 3.773987270466986*^9}, { 3.773987482712697*^9, 3.7739875221812735`*^9}, {3.773987740298462*^9, 3.7739877466065903`*^9}, {3.7739878599976892`*^9, 3.7739878861137896`*^9}, {3.773987965425336*^9, 3.7739879715632877`*^9}, 3.773988098774023*^9, 3.7739883193781385`*^9, {3.7739884099852057`*^9, 3.7739885862960095`*^9}, {3.773988628922502*^9, 3.773988632767228*^9}, { 3.7739891227568517`*^9, 3.77398915009042*^9}, {3.7739892774900556`*^9, 3.773989291800435*^9}, {3.7739896060525217`*^9, 3.773989635013425*^9}, { 3.7751890832095585`*^9, 3.7751890882413054`*^9}, {3.7751894923762302`*^9, 3.7751895008441906`*^9}, {3.7751911834227276`*^9, 3.775191222686661*^9}, 3.7751912606478214`*^9, {3.7751943412188396`*^9, 3.775194461553982*^9}, { 3.775194496052539*^9, 3.7751945353727713`*^9}, {3.7751945737174063`*^9, 3.775194621343042*^9}, {3.775194667862669*^9, 3.7751947598351893`*^9}, { 3.7751948235734253`*^9, 3.7751949415953684`*^9}, {3.775195100078847*^9, 3.77519512113822*^9}, {3.7751954506873007`*^9, 3.775195467864645*^9}, { 3.775270786870551*^9, 3.775270796325161*^9}, {3.7752708274391947`*^9, 3.775270839737406*^9}, {3.7752709283091574`*^9, 3.7752709474534383`*^9}, { 3.7752710502850266`*^9, 3.7752711744130797`*^9}, {3.7752712273079033`*^9, 3.7752713060364757`*^9}, {3.775271448825513*^9, 3.7752714699277525`*^9}, { 3.775271509321142*^9, 3.775271585609558*^9}, {3.775271620653377*^9, 3.77527180192237*^9}, {3.781671264558541*^9, 3.7816712751556396`*^9}, { 3.7816715257512035`*^9, 3.781671526206021*^9}, 3.781671612475748*^9, { 3.781672177985033*^9, 3.7816722548545895`*^9}, {3.7816755757937236`*^9, 3.7816756936745577`*^9}, 3.781675873086305*^9, {3.7816761808096905`*^9, 3.7816762075777946`*^9}, {3.788077170199604*^9, 3.7880772443461285`*^9}, { 3.817439204000356*^9, 3.8174392066998005`*^9}, {3.817439295580332*^9, 3.817439307456877*^9}, 3.817521235605838*^9, 3.843182831518036*^9}, CellLabel-> "In[124]:=",ExpressionUUID->"406b3cca-7d82-49dd-af4f-2774c3349319"] }, Closed]], Cell[CellGroupData[{ Cell["BAR ELEMENT (vibr) defs", "Subsection", InitializationCell->True, CellChangeTimes->{{3.7530188810407906`*^9, 3.753018884630788*^9}, { 3.7878946971705894`*^9, 3.7878946984332533`*^9}, 3.787894946958498*^9},ExpressionUUID->"f36d60ea-4a6a-4c2b-8982-\ 3cd23a80abe5"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "AA_", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", "AA", "}"}], ",", RowBox[{"{", "0", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "AA_", "}"}], ",", RowBox[{"{", "fx_", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "ix0", ",", "ux", ",", "\[Delta]ux", ",", "EE1", ",", "EE2", ",", "EE3", ",", "AA1", ",", "AA2", ",", "AA3", ",", "fx1", ",", "fx2", ",", "fx3", ",", "nl", ",", "rule"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", " ", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], "=", RowBox[{ RowBox[{"ix0", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "2"}], "]"}], "=", RowBox[{ RowBox[{"ix0", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}], "=", RowBox[{ RowBox[{"ix0", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"ux", "[", RowBox[{"2", ",", "2"}], "]"}], "=", RowBox[{ RowBox[{"ix0", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ FractionBox["1", RowBox[{"6", " ", "h0"}]], RowBox[{"(", RowBox[{ RowBox[{"3", " ", "fx", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{"AA", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["h0", "2"], " ", "\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"ux", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}]}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, { 3.753019452689951*^9, 3.753019484970434*^9}, {3.7530196011509657`*^9, 3.753019673352596*^9}, {3.753019831211974*^9, 3.75301989711664*^9}, 3.7530200045416303`*^9, {3.7885030525030107`*^9, 3.7885030592759047`*^9}, { 3.818904755546356*^9, 3.8189048128461294`*^9}, 3.820024775397682*^9}, CellLabel-> "In[125]:=",ExpressionUUID->"37832c68-eb7f-4a75-935e-0915a7e2a13a"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"GENERICBAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "AA_", "}"}], ",", RowBox[{"{", "ff_", "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "NN", ",", "\[Xi]", ",", "r", ",", "r\[Xi]", ",", "h0", ",", "i\[Xi]", ",", "s", ",", "x", ",", "uu", ",", "u0", ",", "u2", ",", "\[Delta]uu", ",", "F", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wine", ",", "AAA", ",", "EEE", ",", "\[Rho]\[Rho]\[Rho]", ",", "fff"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "=", " ", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"Length", "[", "node", "]"}], ",", "\[Xi]"}], "}"}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"mapping", " ", "to", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"\[Xi]", "*", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"Last", "[", "node", "]"}], ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"First", "[", "node", "]"}], ",", "1"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Xi]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "r"}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r\[Xi]", ".", "r\[Xi]"}], "]"}], ",", " ", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"i\[Xi]", " ", "=", RowBox[{"r\[Xi]", "/", "h0"}]}], ";", "\[IndentingNewLine]", RowBox[{"s", "=", RowBox[{"i\[Xi]", " ", ".", "r"}]}], ";", "\[IndentingNewLine]", RowBox[{"x", "=", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"First", "[", "node", "]"}], ",", "1"}], "]"}], "]"}], ".", "i\[Xi]"}], "+", "s"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"(*", "approximation", "*)"}], "\[IndentingNewLine]", RowBox[{"uu", "=", " ", RowBox[{"i\[Xi]", ".", RowBox[{"(", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "2"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"u0", "=", " ", RowBox[{"uu", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"u2", "=", " ", RowBox[{"uu", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "resultant"}], "*)"}], "\[IndentingNewLine]", RowBox[{"F", " ", "=", RowBox[{ RowBox[{"EE", "[", "x", "]"}], " ", RowBox[{"AA", "[", "x", "]"}], " ", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "u0"}], "/", "h0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "u0"}], "/", "h0"}], "]"}]}], " ", "F"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "u0", "]"}], " ", RowBox[{"ff", "[", "x", "]"}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wine", "=", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", "u0", "]"}]}], " ", RowBox[{"\[Rho]\[Rho]", "[", "x", "]"}], " ", RowBox[{"AA", "[", "x", "]"}], " ", "u2"}]}], ";", "\[IndentingNewLine]", RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wine"}], ")"}], "*", "h0"}], ",", RowBox[{"{", RowBox[{"\[Xi]", ",", "0", ",", "1"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, { 3.753019452689951*^9, 3.753019484970434*^9}, {3.7530196011509657`*^9, 3.753019673352596*^9}, {3.753019831211974*^9, 3.75301989711664*^9}, 3.7530200045416303`*^9, {3.7885030525030107`*^9, 3.7885030592759047`*^9}, { 3.818904755546356*^9, 3.8189048128461294`*^9}, 3.820024775397682*^9},ExpressionUUID->"91a94a3b-6460-4e61-9415-\ 5af8add0b018"] }, Closed]], Cell[CellGroupData[{ Cell["BAR ELEMENT (stab) defs ", "Subsection", InitializationCell->True, CellChangeTimes->{{3.753018875511382*^9, 3.7530188786265306`*^9}, { 3.756267607734783*^9, 3.756267609945469*^9}, 3.7878947030333853`*^9},ExpressionUUID->"304352cb-c654-483d-b6eb-\ 9e908263043a"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", "AA_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE", "}"}], ",", RowBox[{"{", "AA", "}"}], ",", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", "AA_", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE", "}"}], ",", RowBox[{"{", "AA", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, { 3.7530189177531705`*^9, 3.753018918350237*^9}, {3.753018991800671*^9, 3.753019041865839*^9}, {3.7530191095313196`*^9, 3.7530191100576744`*^9}, 3.753019155952956*^9, {3.7530192458219423`*^9, 3.753019353286773*^9}, { 3.7562676525896635`*^9, 3.756267707097726*^9}, {3.7606671297197995`*^9, 3.7606671693669567`*^9}, {3.7885030281334577`*^9, 3.78850303141934*^9}, { 3.7885030692138157`*^9, 3.7885030730711346`*^9}, {3.7888331112134047`*^9, 3.788833121736215*^9}, 3.7890211201729145`*^9, {3.850965595585096*^9, 3.8509656478473897`*^9}}, CellLabel-> "In[127]:=",ExpressionUUID->"a70afda4-fad2-4c81-a4da-50f7c3ab46c0"] }, Closed]], Cell[CellGroupData[{ Cell["BAR ELEMENT (nonl) defs ", "Subsection", InitializationCell->True, CellChangeTimes->{{3.7530188810407906`*^9, 3.753018884630788*^9}, { 3.753019375620509*^9, 3.753019378557259*^9}, {3.787894723689047*^9, 3.7878947246772313`*^9}},ExpressionUUID->"272f1965-2555-46e0-9de8-\ e1a410e2024b"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "CC_", "}"}], ",", RowBox[{"{", "AA_", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "CC", "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "CC_", "}"}], ",", RowBox[{"{", "AA_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "CC", "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "CC_", "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "iy_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "CC", "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "iy"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "CC_", "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "iy_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[CapitalDelta]h", ",", "h0", ",", "ix", ",", "iz", ",", "NN", ",", "fx", ",", "fy", ",", "fz", ",", "x", ",", "uu", ",", "vv", ",", "ww", ",", "EE", ",", "\[Delta]EE", ",", "\[Delta]wint", ",", "\[Delta]wext"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[CapitalDelta]h", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"\[CapitalDelta]h", ".", "\[CapitalDelta]h"}], "]"}], ",", " ", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix", "=", RowBox[{"\[CapitalDelta]h", "/", "h0"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz", "=", RowBox[{"ix", StyleBox["\[Cross]", "OperatorCharacter"], StyleBox["iy", "OperatorCharacter"]}]}], StyleBox[";", "OperatorCharacter"], "\[IndentingNewLine]", RowBox[{"NN", "=", " ", RowBox[{"{", RowBox[{ RowBox[{"1", "-", RowBox[{"x", "/", "h0"}]}], ",", RowBox[{"x", "/", "h0"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"fx", " ", "=", RowBox[{"ix", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"fy", " ", "=", RowBox[{"iy", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"fz", " ", "=", RowBox[{"iz", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"uu", "=", " ", RowBox[{"NN", ".", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "ix"}], ",", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "ix"}]}], "}"}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"vv", "=", " ", RowBox[{"NN", ".", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iy"}], ",", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iy"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"ww", "=", " ", RowBox[{"NN", ".", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iz"}], ",", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iz"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"EE", "=", " ", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "uu"}], "+", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], RowBox[{"{", RowBox[{"uu", ",", "vv", ",", "ww"}], "}"}]}], ".", RowBox[{ SubscriptBox["\[PartialD]", "x"], RowBox[{"{", RowBox[{"uu", ",", "vv", ",", "ww"}], "}"}]}]}], "/", "2"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]EE", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], "uu"}], "]"}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], RowBox[{"{", RowBox[{"uu", ",", "vv", ",", "ww"}], "}"}]}], "]"}], ".", RowBox[{ SubscriptBox["\[PartialD]", "x"], RowBox[{"{", RowBox[{"uu", ",", "vv", ",", "ww"}], "}"}]}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", "\[Delta]EE"}], " ", "CC", " ", "AA", " ", "EE"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"uu", ",", "vv", ",", "ww"}], "}"}], "]"}], ".", RowBox[{"{", " ", RowBox[{"fx", ",", "fy", ",", "fz"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"Integrate", "[", RowBox[{ RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "h0"}], "}"}]}], "]"}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, 3.753020083991325*^9, {3.7530201458865404`*^9, 3.753020147585074*^9}, { 3.7894406851054068`*^9, 3.7894406982798967`*^9}, {3.789456736272064*^9, 3.789456831643631*^9}, {3.8216141464350357`*^9, 3.821614249465634*^9}, { 3.8217727479052997`*^9, 3.8217727798972683`*^9}, {3.8217728196181326`*^9, 3.821772858846867*^9}, {3.8217733416981835`*^9, 3.8217733490574265`*^9}, { 3.852693331201587*^9, 3.8526934718702607`*^9}}, CellLabel-> "In[129]:=",ExpressionUUID->"7df3ec16-4b8b-45cb-8015-ca721564c3d5"] }, Closed]], Cell[CellGroupData[{ Cell["BAR ELEMENT (tmec) defs ", "Subsection", InitializationCell->True, CellChangeTimes->{{3.7530188810407906`*^9, 3.753018884630788*^9}, { 3.753019375620509*^9, 3.753019378557259*^9}, {3.7530200248509674`*^9, 3.7530200339415607`*^9}, 3.7575039589097877`*^9, {3.7878947510437098`*^9, 3.7878947515126114`*^9}, 3.7901298129642305`*^9},ExpressionUUID->"cfec64be-5244-4b11-aa3d-\ 7416a16cdcd9"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"TMEC", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Alpha]\[Alpha]_", ",", "kk_"}], "}"}], ",", RowBox[{"{", "AA_", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"ss_", ",", "\[CurlyTheta]0_"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"TMEC", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Alpha]\[Alpha]", ",", "kk"}], "}"}], ",", RowBox[{"{", "AA", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"ss", ",", "\[CurlyTheta]0"}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"TMEC", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Alpha]\[Alpha]_", ",", "kk_"}], "}"}], ",", RowBox[{"{", "AA_", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}], ",", RowBox[{"{", RowBox[{"ss_", ",", "\[CurlyTheta]0_"}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "NN", ",", "\[Xi]", ",", "r", ",", "r\[Xi]", ",", "h0", ",", "i\[Xi]", ",", "s", ",", "x", ",", "uu", ",", "\[CurlyTheta]\[CurlyTheta]", ",", "F", ",", "Q", ",", "\[Delta]w", ",", "\[Delta]p", ",", "AAA", ",", "EEE", ",", "ffX", ",", "ffY", ",", "ffZ", ",", "kkk", ",", "sss", ",", "\[Alpha]\[Alpha]\[Alpha]"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "=", " ", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"Length", "[", "node", "]"}], ",", "\[Xi]"}], "}"}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"mapping", " ", "to", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"\[Xi]", "*", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"Last", "[", "node", "]"}], ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"First", "[", "node", "]"}], ",", "1"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Xi]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "r"}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r\[Xi]", ".", "r\[Xi]"}], "]"}], ",", " ", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"i\[Xi]", " ", "=", RowBox[{"r\[Xi]", "/", "h0"}]}], ";", "\[IndentingNewLine]", RowBox[{"s", "=", RowBox[{"i\[Xi]", " ", ".", "r"}]}], ";", "\[IndentingNewLine]", RowBox[{"x", "=", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"First", "[", "node", "]"}], ",", "1"}], "]"}], "]"}], ".", "i\[Xi]"}], "+", "s"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", "approximation", "*)"}], "\[IndentingNewLine]", RowBox[{"uu", "=", " ", RowBox[{"i\[Xi]", ".", RowBox[{"(", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "2"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CurlyTheta]\[CurlyTheta]", "=", " ", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "4"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "resultant"}], "*)"}], "\[IndentingNewLine]", RowBox[{"AAA", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "AA", "]"}], "===", "Function"}], ",", RowBox[{"AA", "[", "x", "]"}], ",", "AA"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEE", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "EE", "]"}], "===", "Function"}], ",", RowBox[{"EE", "[", "x", "]"}], ",", "EE"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Alpha]\[Alpha]\[Alpha]", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "\[Alpha]\[Alpha]", "]"}], "===", "Function"}], ",", RowBox[{"\[Alpha]\[Alpha]", "[", "x", "]"}], ",", "\[Alpha]\[Alpha]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"kkk", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "kk", "]"}], "===", "Function"}], ",", RowBox[{"kk", "[", "x", "]"}], ",", "kk"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ffX", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "fX", "]"}], "===", "Function"}], ",", RowBox[{"fX", "[", "x", "]"}], ",", "fX"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ffY", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "fY", "]"}], "===", "Function"}], ",", RowBox[{"fY", "[", "x", "]"}], ",", "fY"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ffZ", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "fZ", "]"}], "===", "Function"}], ",", RowBox[{"fZ", "[", "x", "]"}], ",", "fZ"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sss", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "ss", "]"}], "===", "Function"}], ",", RowBox[{"ss", "[", "x", "]"}], ",", "ss"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"F", " ", "=", RowBox[{"EEE", " ", "AAA", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "uu"}], "/", "h0"}], "-", RowBox[{"\[Alpha]\[Alpha]\[Alpha]", " ", RowBox[{"(", RowBox[{"\[CurlyTheta]\[CurlyTheta]", "-", "\[CurlyTheta]0"}], ")"}]}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Q", "=", RowBox[{ RowBox[{"-", "kkk"}], " ", "AAA", " ", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "\[CurlyTheta]\[CurlyTheta]"}], "/", "h0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]w", "=", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "uu"}], "/", "h0"}], "]"}]}], " ", "F"}], "+", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", "uu", "]"}], " ", RowBox[{ RowBox[{"{", RowBox[{"ffX", ",", "ffY", ",", "ffZ"}], "}"}], ".", "i\[Xi]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]p", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "\[CurlyTheta]\[CurlyTheta]"}], "/", "h0"}], "]"}], " ", "Q"}], " ", "+", RowBox[{ RowBox[{ "\[Delta]\[Delta]", "[", "\[CurlyTheta]\[CurlyTheta]", "]"}], " ", "sss"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"\[Delta]w", "+", "\[Delta]p"}], ")"}], " ", "h0"}], ",", RowBox[{"{", RowBox[{"\[Xi]", ",", "0", ",", "1"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, 3.7530202209165316`*^9, {3.7898060059373465`*^9, 3.7898060199153595`*^9}, { 3.8223694609291615`*^9, 3.8223694626206393`*^9}, {3.850614635752848*^9, 3.850614714304345*^9}, {3.8506148466526003`*^9, 3.850615010959174*^9}, { 3.8506155810199738`*^9, 3.8506156273379755`*^9}}, CellLabel-> "In[133]:=",ExpressionUUID->"9eb002e1-9863-43c9-96e2-cfe763b385fd"] }, Closed]], Cell[CellGroupData[{ Cell["TORSION ELEMENT (disp) defs", "Subsection", InitializationCell->True, CellChangeTimes->{{3.753018875511382*^9, 3.7530188786265306`*^9}, { 3.781589886623744*^9, 3.7815898932426767`*^9}, {3.7878947601549573`*^9, 3.787894760728943*^9}, 3.7878948945295725`*^9},ExpressionUUID->"1d455053-ab43-4028-9372-\ 89426eb6cdbe"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", "E1050"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "GG_", "}"}], ",", RowBox[{"{", "JJ_", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "GG", "}"}], ",", RowBox[{"{", "JJ", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "GG_", "}"}], ",", RowBox[{"{", "JJ_", "}"}], ",", RowBox[{"{", RowBox[{"mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "ix0", ",", "\[Theta]x", ",", "\[Delta]\[Theta]x", ",", "GG1", ",", "GG2", ",", "GG3", ",", "JJ1", ",", "JJ2", ",", "JJ3", ",", "mx1", ",", "mx2", ",", "mx3", ",", "nl", ",", "rule"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", " ", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Theta]x", "[", "i_", "]"}], ":=", RowBox[{"ix0", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"nl", "[", RowBox[{"[", "i", "]"}], "]"}], ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", "i_", "]"}], ":=", RowBox[{"\[Delta]", "[", RowBox[{"\[Theta]x", "[", "i", "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"rule", " ", ":=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"a1_", ",", "a2_", ",", "a3_"}], "}"}], "\[Rule]", RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3"}], "}"}]}], ",", RowBox[{ RowBox[{"{", RowBox[{"a1_", ",", "a2_"}], "}"}], "\[Rule]", RowBox[{"{", RowBox[{"a1", ",", RowBox[{ RowBox[{"(", RowBox[{"a1", "+", "a2"}], ")"}], "/", "2"}], ",", "a2"}], "}"}]}], ",", RowBox[{"a1_", "\[Rule]", RowBox[{"{", RowBox[{"a1", ",", "a1", ",", "a1"}], "}"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"GG1", ",", "GG2", ",", "GG3"}], "}"}], "=", RowBox[{"GG", "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"JJ1", ",", "JJ2", ",", "JJ3"}], "}"}], "=", RowBox[{"JJ", " ", "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"mx1", ",", "mx2", ",", "mx3"}], "}"}], "=", RowBox[{"ix0", ".", RowBox[{"{", RowBox[{ RowBox[{"mX", " ", "/.", "rule"}], ",", RowBox[{"mY", " ", "/.", "rule"}], ",", RowBox[{"mZ", " ", "/.", "rule"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ FractionBox["1", RowBox[{"30", " ", SuperscriptBox["h0", "2"]}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"JJ1", " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", "GG1"}], "+", RowBox[{"2", " ", "GG2"}], "-", "GG3"}], ")"}]}], "+", RowBox[{"2", " ", "JJ2", " ", RowBox[{"(", RowBox[{"GG1", "+", RowBox[{"8", " ", "GG2"}], "+", "GG3"}], ")"}]}], "+", RowBox[{"JJ3", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "GG1"}], "+", RowBox[{"2", " ", "GG2"}], "+", RowBox[{"4", " ", "GG3"}]}], ")"}]}]}], ")"}]}], " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"\[Theta]x", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"5", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"mx1", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"mx3", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}]}], "+", RowBox[{"2", " ", "mx2", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, { 3.7530189177531705`*^9, 3.753018918350237*^9}, {3.753018991800671*^9, 3.753019041865839*^9}, {3.7530191095313196`*^9, 3.7530191100576744`*^9}, 3.753019155952956*^9, {3.7530192458219423`*^9, 3.753019353286773*^9}, { 3.773986323215969*^9, 3.7739864366876383`*^9}, {3.7739864700193005`*^9, 3.7739865885966825`*^9}, {3.7739869332783327`*^9, 3.7739870501829805`*^9}, 3.773987085528166*^9, {3.7739872536160583`*^9, 3.773987270466986*^9}, { 3.773987482712697*^9, 3.7739875221812735`*^9}, {3.773987740298462*^9, 3.7739877466065903`*^9}, {3.7739878599976892`*^9, 3.7739878861137896`*^9}, {3.773987965425336*^9, 3.7739879715632877`*^9}, 3.773988098774023*^9, 3.7739883193781385`*^9, {3.7739884099852057`*^9, 3.7739885862960095`*^9}, {3.773988628922502*^9, 3.773988632767228*^9}, { 3.7739891227568517`*^9, 3.77398915009042*^9}, {3.7739892774900556`*^9, 3.773989291800435*^9}, {3.7739896060525217`*^9, 3.773989635013425*^9}, { 3.7751890832095585`*^9, 3.7751890882413054`*^9}, {3.7751894923762302`*^9, 3.7751895008441906`*^9}, {3.7751911834227276`*^9, 3.775191222686661*^9}, 3.7751912606478214`*^9, {3.7751943412188396`*^9, 3.775194461553982*^9}, { 3.775194496052539*^9, 3.7751945353727713`*^9}, {3.7751945737174063`*^9, 3.775194621343042*^9}, {3.775194667862669*^9, 3.7751947598351893`*^9}, { 3.7751948235734253`*^9, 3.7751949415953684`*^9}, {3.775195100078847*^9, 3.77519512113822*^9}, {3.7751954506873007`*^9, 3.775195467864645*^9}, { 3.775270786870551*^9, 3.775270796325161*^9}, {3.7752708274391947`*^9, 3.775270839737406*^9}, {3.7752709283091574`*^9, 3.7752709474534383`*^9}, { 3.7752710502850266`*^9, 3.7752711744130797`*^9}, {3.7752712273079033`*^9, 3.7752713060364757`*^9}, {3.775271448825513*^9, 3.7752714699277525`*^9}, { 3.775271509321142*^9, 3.775271585609558*^9}, {3.775271620653377*^9, 3.77527180192237*^9}, {3.781589928213842*^9, 3.781590052438653*^9}, { 3.7815900898176003`*^9, 3.781590109307678*^9}, {3.781590201383393*^9, 3.7815902433873234`*^9}, {3.7815905445265956`*^9, 3.781590569573782*^9}, { 3.7815906952864275`*^9, 3.781590715680611*^9}, {3.7815908323678637`*^9, 3.781590881239719*^9}, {3.7815911048122363`*^9, 3.781591119274813*^9}, { 3.8175324830973916`*^9, 3.817532552103792*^9}, {3.843704806259609*^9, 3.843704863557214*^9}, {3.8437049017363043`*^9, 3.8437049180939226`*^9}}, CellLabel-> "In[135]:=",ExpressionUUID->"4d523384-9111-4e5f-bc74-e0e134ba5179"] }, Closed]], Cell[CellGroupData[{ Cell["TORSION ELEMENT (evnt) defs", "Subsection", InitializationCell->True, CellChangeTimes->{{3.753018875511382*^9, 3.7530188786265306`*^9}, { 3.781589886623744*^9, 3.7815898932426767`*^9}, {3.7878947601549573`*^9, 3.787894760728943*^9}, 3.7878948945295725`*^9, {3.817439343565061*^9, 3.8174393448082724`*^9}, 3.8431828477515774`*^9},ExpressionUUID->"8bf2b28f-bdbb-4c8e-b241-\ a461a8c907e5"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"EVNT", ",", RowBox[{"{", RowBox[{"s0_", ",", "sol0_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"TORSION", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"TORSION", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, { 3.7530189177531705`*^9, 3.753018918350237*^9}, {3.753018991800671*^9, 3.753019041865839*^9}, {3.7530191095313196`*^9, 3.7530191100576744`*^9}, 3.753019155952956*^9, {3.7530192458219423`*^9, 3.753019353286773*^9}, { 3.773986323215969*^9, 3.7739864366876383`*^9}, {3.7739864700193005`*^9, 3.7739865885966825`*^9}, {3.7739869332783327`*^9, 3.7739870501829805`*^9}, 3.773987085528166*^9, {3.7739872536160583`*^9, 3.773987270466986*^9}, { 3.773987482712697*^9, 3.7739875221812735`*^9}, {3.773987740298462*^9, 3.7739877466065903`*^9}, {3.7739878599976892`*^9, 3.7739878861137896`*^9}, {3.773987965425336*^9, 3.7739879715632877`*^9}, 3.773988098774023*^9, 3.7739883193781385`*^9, {3.7739884099852057`*^9, 3.7739885862960095`*^9}, {3.773988628922502*^9, 3.773988632767228*^9}, { 3.7739891227568517`*^9, 3.77398915009042*^9}, {3.7739892774900556`*^9, 3.773989291800435*^9}, {3.7739896060525217`*^9, 3.773989635013425*^9}, { 3.7751890832095585`*^9, 3.7751890882413054`*^9}, {3.7751894923762302`*^9, 3.7751895008441906`*^9}, {3.7751911834227276`*^9, 3.775191222686661*^9}, 3.7751912606478214`*^9, {3.7751943412188396`*^9, 3.775194461553982*^9}, { 3.775194496052539*^9, 3.7751945353727713`*^9}, {3.7751945737174063`*^9, 3.775194621343042*^9}, {3.775194667862669*^9, 3.7751947598351893`*^9}, { 3.7751948235734253`*^9, 3.7751949415953684`*^9}, {3.775195100078847*^9, 3.77519512113822*^9}, {3.7751954506873007`*^9, 3.775195467864645*^9}, { 3.775270786870551*^9, 3.775270796325161*^9}, {3.7752708274391947`*^9, 3.775270839737406*^9}, {3.7752709283091574`*^9, 3.7752709474534383`*^9}, { 3.7752710502850266`*^9, 3.7752711744130797`*^9}, {3.7752712273079033`*^9, 3.7752713060364757`*^9}, {3.775271448825513*^9, 3.7752714699277525`*^9}, { 3.775271509321142*^9, 3.775271585609558*^9}, {3.775271620653377*^9, 3.77527180192237*^9}, {3.781589928213842*^9, 3.781590052438653*^9}, { 3.7815900898176003`*^9, 3.781590109307678*^9}, {3.781590201383393*^9, 3.7815902433873234`*^9}, {3.7815905445265956`*^9, 3.781590569573782*^9}, { 3.7815906952864275`*^9, 3.781590715680611*^9}, {3.7815908323678637`*^9, 3.781590881239719*^9}, {3.7815911048122363`*^9, 3.781591119274813*^9}, { 3.817439386305109*^9, 3.8174394287787733`*^9}, 3.81752126940705*^9, 3.8431828427789755`*^9}, CellLabel-> "In[137]:=",ExpressionUUID->"7f1d8f80-4c88-4a1c-9118-d8f7367ce72a"] }, Closed]], Cell[CellGroupData[{ Cell["TORSION ELEMENT (vibr) defs", "Subsection", InitializationCell->True, CellChangeTimes->{{3.753018875511382*^9, 3.7530188786265306`*^9}, { 3.781589886623744*^9, 3.7815898932426767`*^9}, {3.7878947601549573`*^9, 3.787894760728943*^9}, 3.7878948945295725`*^9, {3.78815413936168*^9, 3.788154140564639*^9}},ExpressionUUID->"52d7337e-01ce-475c-9a61-\ 6b4210776b58"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "JJ_", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"GG", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", "JJ", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "JJ_", "}"}], ",", RowBox[{"{", RowBox[{"mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "ix0", ",", "\[Theta]x", ",", "\[Delta]\[Theta]x", ",", "rule", ",", "mx"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", " ", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "=", RowBox[{ RowBox[{"ix0", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}], "=", RowBox[{ RowBox[{"ix0", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], "=", RowBox[{ RowBox[{"ix0", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}]}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}], "=", RowBox[{ RowBox[{"ix0", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}]}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"mx", "=", RowBox[{"ix0", ".", RowBox[{"{", RowBox[{"mX", ",", "mY", ",", "mZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ FractionBox["1", RowBox[{"6", " ", "h0"}]], RowBox[{"(", RowBox[{ RowBox[{"3", " ", "mx", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{"JJ", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "GG", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["h0", "2"], " ", "\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, { 3.7530189177531705`*^9, 3.753018918350237*^9}, {3.753018991800671*^9, 3.753019041865839*^9}, {3.7530191095313196`*^9, 3.7530191100576744`*^9}, 3.753019155952956*^9, {3.7530192458219423`*^9, 3.753019353286773*^9}, { 3.773986323215969*^9, 3.7739864366876383`*^9}, {3.7739864700193005`*^9, 3.7739865885966825`*^9}, {3.7739869332783327`*^9, 3.7739870501829805`*^9}, 3.773987085528166*^9, {3.7739872536160583`*^9, 3.773987270466986*^9}, { 3.773987482712697*^9, 3.7739875221812735`*^9}, {3.773987740298462*^9, 3.7739877466065903`*^9}, {3.7739878599976892`*^9, 3.7739878861137896`*^9}, {3.773987965425336*^9, 3.7739879715632877`*^9}, 3.773988098774023*^9, 3.7739883193781385`*^9, {3.7739884099852057`*^9, 3.7739885862960095`*^9}, {3.773988628922502*^9, 3.773988632767228*^9}, { 3.7739891227568517`*^9, 3.77398915009042*^9}, {3.7739892774900556`*^9, 3.773989291800435*^9}, {3.7739896060525217`*^9, 3.773989635013425*^9}, { 3.7751890832095585`*^9, 3.7751890882413054`*^9}, {3.7751894923762302`*^9, 3.7751895008441906`*^9}, {3.7751911834227276`*^9, 3.775191222686661*^9}, 3.7751912606478214`*^9, {3.7751943412188396`*^9, 3.775194461553982*^9}, { 3.775194496052539*^9, 3.7751945353727713`*^9}, {3.7751945737174063`*^9, 3.775194621343042*^9}, {3.775194667862669*^9, 3.7751947598351893`*^9}, { 3.7751948235734253`*^9, 3.7751949415953684`*^9}, {3.775195100078847*^9, 3.77519512113822*^9}, {3.7751954506873007`*^9, 3.775195467864645*^9}, { 3.775270786870551*^9, 3.775270796325161*^9}, {3.7752708274391947`*^9, 3.775270839737406*^9}, {3.7752709283091574`*^9, 3.7752709474534383`*^9}, { 3.7752710502850266`*^9, 3.7752711744130797`*^9}, {3.7752712273079033`*^9, 3.7752713060364757`*^9}, {3.775271448825513*^9, 3.7752714699277525`*^9}, { 3.775271509321142*^9, 3.775271585609558*^9}, {3.775271620653377*^9, 3.77527180192237*^9}, {3.781589928213842*^9, 3.781590052438653*^9}, { 3.7815900898176003`*^9, 3.781590109307678*^9}, {3.781590201383393*^9, 3.7815902433873234`*^9}, {3.7815905445265956`*^9, 3.781590569573782*^9}, { 3.7815906952864275`*^9, 3.781590715680611*^9}, {3.7815908323678637`*^9, 3.781590881239719*^9}, {3.7815911048122363`*^9, 3.781591119274813*^9}, { 3.788154182393029*^9, 3.7881542008707867`*^9}, {3.788154262468212*^9, 3.788154413095205*^9}, {3.788154445865172*^9, 3.7881544989994373`*^9}, { 3.788154543552347*^9, 3.788154583606308*^9}, {3.8513960191034765`*^9, 3.851396064317687*^9}, {3.8513960979650345`*^9, 3.8513961553917027`*^9}, { 3.85139633477669*^9, 3.851396341122322*^9}}, CellLabel-> "In[138]:=",ExpressionUUID->"901b597d-d5c6-4937-9c30-705ce8a39225"] }, Closed]], Cell[CellGroupData[{ Cell["TORSION ELEMENT (stab) defs", "Subsection", InitializationCell->True, CellChangeTimes->{{3.753018875511382*^9, 3.7530188786265306`*^9}, { 3.781589886623744*^9, 3.7815898932426767`*^9}, {3.7878947601549573`*^9, 3.787894760728943*^9}, 3.7878948945295725`*^9, {3.7890211428141956`*^9, 3.7890211435642633`*^9}},ExpressionUUID->"009b90fc-3172-4340-a53d-\ 6b92288a94d3"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "GG_", "}"}], ",", RowBox[{"{", "JJ_", "}"}], ",", RowBox[{"{", "mx_", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "GG", "}"}], ",", RowBox[{"{", "JJ", "}"}], ",", RowBox[{"{", "mx", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, { 3.7530189177531705`*^9, 3.753018918350237*^9}, {3.753018991800671*^9, 3.753019041865839*^9}, {3.7530191095313196`*^9, 3.7530191100576744`*^9}, 3.753019155952956*^9, {3.7530192458219423`*^9, 3.753019353286773*^9}, { 3.773986323215969*^9, 3.7739864366876383`*^9}, {3.7739864700193005`*^9, 3.7739865885966825`*^9}, {3.7739869332783327`*^9, 3.7739870501829805`*^9}, 3.773987085528166*^9, {3.7739872536160583`*^9, 3.773987270466986*^9}, { 3.773987482712697*^9, 3.7739875221812735`*^9}, {3.773987740298462*^9, 3.7739877466065903`*^9}, {3.7739878599976892`*^9, 3.7739878861137896`*^9}, {3.773987965425336*^9, 3.7739879715632877`*^9}, 3.773988098774023*^9, 3.7739883193781385`*^9, {3.7739884099852057`*^9, 3.7739885862960095`*^9}, {3.773988628922502*^9, 3.773988632767228*^9}, { 3.7739891227568517`*^9, 3.77398915009042*^9}, {3.7739892774900556`*^9, 3.773989291800435*^9}, {3.7739896060525217`*^9, 3.773989635013425*^9}, { 3.7751890832095585`*^9, 3.7751890882413054`*^9}, {3.7751894923762302`*^9, 3.7751895008441906`*^9}, {3.7751911834227276`*^9, 3.775191222686661*^9}, 3.7751912606478214`*^9, {3.7751943412188396`*^9, 3.775194461553982*^9}, { 3.775194496052539*^9, 3.7751945353727713`*^9}, {3.7751945737174063`*^9, 3.775194621343042*^9}, {3.775194667862669*^9, 3.7751947598351893`*^9}, { 3.7751948235734253`*^9, 3.7751949415953684`*^9}, {3.775195100078847*^9, 3.77519512113822*^9}, {3.7751954506873007`*^9, 3.775195467864645*^9}, { 3.775270786870551*^9, 3.775270796325161*^9}, {3.7752708274391947`*^9, 3.775270839737406*^9}, {3.7752709283091574`*^9, 3.7752709474534383`*^9}, { 3.7752710502850266`*^9, 3.7752711744130797`*^9}, {3.7752712273079033`*^9, 3.7752713060364757`*^9}, {3.775271448825513*^9, 3.7752714699277525`*^9}, { 3.775271509321142*^9, 3.775271585609558*^9}, {3.775271620653377*^9, 3.77527180192237*^9}, {3.781589928213842*^9, 3.781590052438653*^9}, { 3.7815900898176003`*^9, 3.781590109307678*^9}, {3.781590201383393*^9, 3.7815902433873234`*^9}, {3.7815905445265956`*^9, 3.781590569573782*^9}, { 3.7815906952864275`*^9, 3.781590715680611*^9}, {3.7815908323678637`*^9, 3.781590881239719*^9}, {3.7815911048122363`*^9, 3.781591119274813*^9}, { 3.789021170161874*^9, 3.7890212153743477`*^9}}, CellLabel-> "In[140]:=",ExpressionUUID->"c74c377f-e765-4c55-8c9f-cc4ffa46a71f"] }, Closed]], Cell[CellGroupData[{ Cell["TORSION ELEMENT (nonl) defs", "Subsection", InitializationCell->True, CellChangeTimes->{{3.753018875511382*^9, 3.7530188786265306`*^9}, { 3.781589886623744*^9, 3.7815898932426767`*^9}, {3.7878947601549573`*^9, 3.787894760728943*^9}, 3.7878948945295725`*^9, {3.7890211428141956`*^9, 3.7890211435642633`*^9}, {3.8216143327381015`*^9, 3.8216143387229114`*^9}},ExpressionUUID->"98996e5f-4490-4a7e-bf15-\ b1b937f97cff"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"TORSION", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"TORSION", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, { 3.7530189177531705`*^9, 3.753018918350237*^9}, {3.753018991800671*^9, 3.753019041865839*^9}, {3.7530191095313196`*^9, 3.7530191100576744`*^9}, 3.753019155952956*^9, {3.7530192458219423`*^9, 3.753019353286773*^9}, { 3.773986323215969*^9, 3.7739864366876383`*^9}, {3.7739864700193005`*^9, 3.7739865885966825`*^9}, {3.7739869332783327`*^9, 3.7739870501829805`*^9}, 3.773987085528166*^9, {3.7739872536160583`*^9, 3.773987270466986*^9}, { 3.773987482712697*^9, 3.7739875221812735`*^9}, {3.773987740298462*^9, 3.7739877466065903`*^9}, {3.7739878599976892`*^9, 3.7739878861137896`*^9}, {3.773987965425336*^9, 3.7739879715632877`*^9}, 3.773988098774023*^9, 3.7739883193781385`*^9, {3.7739884099852057`*^9, 3.7739885862960095`*^9}, {3.773988628922502*^9, 3.773988632767228*^9}, { 3.7739891227568517`*^9, 3.77398915009042*^9}, {3.7739892774900556`*^9, 3.773989291800435*^9}, {3.7739896060525217`*^9, 3.773989635013425*^9}, { 3.7751890832095585`*^9, 3.7751890882413054`*^9}, {3.7751894923762302`*^9, 3.7751895008441906`*^9}, {3.7751911834227276`*^9, 3.775191222686661*^9}, 3.7751912606478214`*^9, {3.7751943412188396`*^9, 3.775194461553982*^9}, { 3.775194496052539*^9, 3.7751945353727713`*^9}, {3.7751945737174063`*^9, 3.775194621343042*^9}, {3.775194667862669*^9, 3.7751947598351893`*^9}, { 3.7751948235734253`*^9, 3.7751949415953684`*^9}, {3.775195100078847*^9, 3.77519512113822*^9}, {3.7751954506873007`*^9, 3.775195467864645*^9}, { 3.775270786870551*^9, 3.775270796325161*^9}, {3.7752708274391947`*^9, 3.775270839737406*^9}, {3.7752709283091574`*^9, 3.7752709474534383`*^9}, { 3.7752710502850266`*^9, 3.7752711744130797`*^9}, {3.7752712273079033`*^9, 3.7752713060364757`*^9}, {3.775271448825513*^9, 3.7752714699277525`*^9}, { 3.775271509321142*^9, 3.775271585609558*^9}, {3.775271620653377*^9, 3.77527180192237*^9}, {3.781589928213842*^9, 3.781590052438653*^9}, { 3.7815900898176003`*^9, 3.781590109307678*^9}, {3.781590201383393*^9, 3.7815902433873234`*^9}, {3.7815905445265956`*^9, 3.781590569573782*^9}, { 3.7815906952864275`*^9, 3.781590715680611*^9}, {3.7815908323678637`*^9, 3.781590881239719*^9}, {3.7815911048122363`*^9, 3.781591119274813*^9}, { 3.789021170161874*^9, 3.7890212153743477`*^9}, {3.8216143478699703`*^9, 3.821614443850371*^9}}, CellLabel-> "In[141]:=",ExpressionUUID->"7e4a66c0-0db9-40e8-94f5-29ce7f2b7e62"] }, Closed]], Cell[CellGroupData[{ Cell["BENDING ELEMENT (disp) defs ", "Subsection", CellChangeTimes->{{3.7530187996679964`*^9, 3.753018803413909*^9}, { 3.7633629633672647`*^9, 3.763362967100765*^9}, {3.787894773214689*^9, 3.7878947881941814`*^9}, {3.78789485671918*^9, 3.78789488217928*^9}, 3.7885197052606735`*^9, {3.788530025907043*^9, 3.7885300287809105`*^9}, 3.7885306781716957`*^9, {3.8200271989371843`*^9, 3.8200272016625395`*^9}, { 3.8200274346181693`*^9, 3.8200274405428553`*^9}, {3.851994139239622*^9, 3.8519941462255764`*^9}},ExpressionUUID->"238c2337-8ec9-471f-befd-\ 2926af1c9d23"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"MEC", "-", "E1050"}], "|", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BENDING", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", RowBox[{"Iyy_", ",", "Izz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "Iyy", ",", "Izz", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BENDING", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", RowBox[{"Iyy_", ",", "Izz_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "Iyy", ",", "Izz", ",", "iy0"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BENDING", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", RowBox[{"Iyy_", ",", "Izz_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "Iyy", ",", "Izz", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BENDING", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", RowBox[{"Iyy_", ",", "Izz_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "Iyy", ",", "Izz", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "mX", ",", "mY", ",", "mZ"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4430689313272*^9, 3.4430690080792*^9}, { 3.4430690869528*^9, 3.4430691077320004`*^9}, {3.4430691700116*^9, 3.4430691708072*^9}, {3.4430692071717997`*^9, 3.443069246359*^9}, { 3.4430772782732*^9, 3.4430773623416*^9}, {3.4430773978316*^9, 3.4430774104676*^9}, {3.4430775053780003`*^9, 3.4430776180598*^9}, { 3.4434109099524*^9, 3.4434109159584*^9}, {3.4438800815346003`*^9, 3.4438802689304*^9}, {3.443880362624*^9, 3.4438803824516*^9}, { 3.443929565615374*^9, 3.443929570232974*^9}, {3.443935321321974*^9, 3.443935335705174*^9}, {3.443935419945174*^9, 3.443935421489574*^9}, { 3.443935494013974*^9, 3.443935494715974*^9}, {3.443935617565974*^9, 3.4439357217895737`*^9}, {3.443935755360774*^9, 3.443935816107174*^9}, { 3.443942155230774*^9, 3.443942209939974*^9}, {3.443942305710374*^9, 3.4439423142123737`*^9}, {3.4439442908131742`*^9, 3.443944441181574*^9}, { 3.4439447830065737`*^9, 3.4439447917425737`*^9}, {3.443944908541774*^9, 3.443944916060974*^9}, {3.4442731097938004`*^9, 3.4442731115254*^9}, { 3.444273189229*^9, 3.4442732700526*^9}, {3.4442748430004*^9, 3.4442748605036*^9}, {3.4442748977438*^9, 3.4442748989762*^9}, { 3.4442749340762*^9, 3.4442749351057997`*^9}, 3.4442752313382*^9, { 3.4442919702026*^9, 3.4442919911846*^9}, {3.4442921151577997`*^9, 3.4442921271074*^9}, {3.4443811023684*^9, 3.4443811036632*^9}, { 3.4443814073171997`*^9, 3.4443814402956*^9}, {3.4443815036316*^9, 3.4443815147855997`*^9}, {3.4443815537232*^9, 3.4443815747676*^9}, { 3.4443816138143997`*^9, 3.444381633174*^9}, {3.4443816850439997`*^9, 3.4443817801728*^9}, 3.4443853618688*^9, {3.4443855607376003`*^9, 3.4443856337924*^9}, {3.4443861200444*^9, 3.4443861523676*^9}, { 3.4443862280495996`*^9, 3.444386291448*^9}, {3.4443864047352*^9, 3.4443864135336*^9}, {3.4443870026832*^9, 3.4443870095316*^9}, { 3.4444082055056*^9, 3.4444082437412*^9}, {3.4444082797148*^9, 3.4444084583816*^9}, {3.4444084889108*^9, 3.4444085087539997`*^9}, { 3.444408942517*^9, 3.4444089563386*^9}, {3.4444091419564*^9, 3.4444091647167997`*^9}, {3.4444092206428003`*^9, 3.4444092944463997`*^9}, {3.4444093856284*^9, 3.4444094281071997`*^9}, { 3.4444094976988*^9, 3.4444095275104*^9}, {3.444409611064*^9, 3.4444096125772*^9}, 3.4444098504616003`*^9, {3.444409913392*^9, 3.4444099166056004`*^9}, 3.4444100178496*^9, {3.4444103063248*^9, 3.4444103358712*^9}, {3.4444103868208*^9, 3.4444104432460003`*^9}, { 3.4444921219564*^9, 3.4444921256224003`*^9}, {3.444492194824*^9, 3.4444921973668003`*^9}, {3.4444922814351997`*^9, 3.4444922853508*^9}, { 3.4444923330868*^9, 3.4444923345844*^9}, {3.444492366424*^9, 3.4444923855808*^9}, {3.4453153475226*^9, 3.445315360689*^9}, { 3.4465518166373653`*^9, 3.446551863016165*^9}, {3.446551894231765*^9, 3.446552159384965*^9}, {3.446552232377365*^9, 3.4465522555589647`*^9}, { 3.446553347388365*^9, 3.4465533616155653`*^9}, {3.4466058525769997`*^9, 3.4466058529046*^9}, {3.4466064371219997`*^9, 3.4466065097244*^9}, { 3.4466127725788*^9, 3.4466127766036*^9}, {3.4466128124835997`*^9, 3.4466130037864*^9}, {3.4466131532696*^9, 3.4466131761703997`*^9}, { 3.4466133992192*^9, 3.4466134478756*^9}, {3.446613483584*^9, 3.4466134932092*^9}, {3.4466135740952*^9, 3.4466135794927998`*^9}, { 3.4466137283948*^9, 3.4466137341356*^9}, {3.4466138994342003`*^9, 3.4466139023826*^9}, {3.4466139549858*^9, 3.4466139579653997`*^9}, { 3.4466142109818*^9, 3.4466142245226*^9}, {3.4466142793878*^9, 3.4466143652033997`*^9}, {3.4466144712834*^9, 3.4466145978929996`*^9}, { 3.4466146992618*^9, 3.4466147509914*^9}, {3.4466151283086*^9, 3.4466152768986*^9}, {3.4466153107506*^9, 3.4466153406558*^9}, { 3.4466194331976*^9, 3.4466194377528*^9}, {3.4466194847712*^9, 3.446619488718*^9}, {3.4466389495861998`*^9, 3.4466389768238*^9}, { 3.4466391218414*^9, 3.446639306561*^9}, {3.4466393990222*^9, 3.4466394004886*^9}, {3.4466394475694*^9, 3.4466394487706003`*^9}, { 3.4466395034174*^9, 3.4466395049462*^9}, 3.4466395515755997`*^9, { 3.4466396000176*^9, 3.4466396190808*^9}, {3.4466397459088*^9, 3.446639748826*^9}, {3.4466397974356003`*^9, 3.446639798668*^9}, 3.4466398447816*^9, {3.446639894218*^9, 3.4466399201556*^9}, { 3.4466399570964003`*^9, 3.4466399583288*^9}, {3.446639994006*^9, 3.4466400056904*^9}, {3.4466400383568*^9, 3.4466400395892*^9}, { 3.4466400745643997`*^9, 3.4466401025976*^9}, {3.4466401660834*^9, 3.4466401806070004`*^9}, {3.4466402251294003`*^9, 3.446640227407*^9}, { 3.446640260479*^9, 3.4466402657674*^9}, {3.4466404133122*^9, 3.4466405185654*^9}, 3.4466405830462*^9, {3.4467273294214*^9, 3.4467273777813997`*^9}, {3.4467274366558*^9, 3.4467275620954*^9}, { 3.446727593311*^9, 3.4467277412614*^9}, {3.4467283334639997`*^9, 3.4467283356012*^9}, {3.4467283707636003`*^9, 3.4467283727604*^9}, { 3.4467289882664003`*^9, 3.4467291276836*^9}, {3.446778464322*^9, 3.4467786797424*^9}, {3.4467801953803997`*^9, 3.4467802409792*^9}, { 3.4467802998691998`*^9, 3.4467804023456*^9}, 3.4467804345596*^9, { 3.4467808656344*^9, 3.4467808670852003`*^9}, 3.4467818107525997`*^9, { 3.446781855509*^9, 3.446781874385*^9}, {3.4467826737914*^9, 3.4467827381726*^9}, {3.4467828623018*^9, 3.4467831045386*^9}, { 3.4470344113984003`*^9, 3.4470344123344*^9}, {3.4470344628316*^9, 3.4470345343108*^9}, {3.447043591118539*^9, 3.447043642192939*^9}, { 3.447045649625739*^9, 3.447045718437339*^9}, {3.447054774023939*^9, 3.447054834198939*^9}, {3.4470549103449388`*^9, 3.4470549116169386`*^9}, { 3.447054943902939*^9, 3.4470553027109385`*^9}, {3.447055334559939*^9, 3.447055353684939*^9}, {3.447057311918539*^9, 3.447057369747739*^9}, { 3.4470575058577385`*^9, 3.4470575951365385`*^9}, {3.4470581848789387`*^9, 3.4470582040825386`*^9}, {3.451276121243*^9, 3.4512761425838003`*^9}, { 3.4512762022382*^9, 3.4512762064346*^9}, {3.4512762476966*^9, 3.4512762827654*^9}, {3.451276489091*^9, 3.451276541975*^9}, { 3.4512765853118*^9, 3.4512766132046003`*^9}, {3.4512773470306*^9, 3.4512773766082*^9}, {3.4512776069110003`*^9, 3.4512777499318*^9}, 3.4512777831286*^9, {3.4512778785538*^9, 3.451277881627*^9}, { 3.4512780242734003`*^9, 3.4512780302794*^9}, 3.4512780737878*^9, { 3.4512781866226*^9, 3.4512781930810003`*^9}, {3.4512863325078*^9, 3.4512863539266*^9}, {3.4568019250434*^9, 3.4568022712698*^9}, { 3.4568023177422*^9, 3.4568024125278*^9}, {3.4568024694365997`*^9, 3.4568024750369997`*^9}, {3.4568026914402*^9, 3.4568028101094*^9}, { 3.4568028406698*^9, 3.4568028564726*^9}, 3.4568028886085997`*^9, { 3.4568030489454*^9, 3.4568030800986*^9}, 3.4568032004128*^9, { 3.4568035073698*^9, 3.4568035176034*^9}, {3.4568040146596003`*^9, 3.4568040844852*^9}, {3.4568043016684*^9, 3.4568043154744*^9}, { 3.4568045482264*^9, 3.4568045486632*^9}, {3.4568048944996*^9, 3.4568049806116*^9}, {3.4660560628582*^9, 3.4660560753538*^9}, { 3.4660676729379997`*^9, 3.4660676735931997`*^9}, {3.4660677244024*^9, 3.4660677277251997`*^9}, {3.4742646771287394`*^9, 3.47426469439174*^9}, { 3.47426489921974*^9, 3.4742649800437393`*^9}, {3.4801246373348*^9, 3.4801246860536003`*^9}, {3.4801247748176003`*^9, 3.4801247821028*^9}, { 3.4801248161264*^9, 3.4801248295736*^9}, {3.4801248810692*^9, 3.4801248964508*^9}, {3.4801249330484*^9, 3.480124947884*^9}, 3.4801249886468*^9, {3.4801251139147997`*^9, 3.48012512588*^9}, { 3.4838339444988003`*^9, 3.4838339567448*^9}, 3.4838341692012*^9, { 3.4838344350408*^9, 3.4838344353684*^9}, {3.4938987575920324`*^9, 3.4938987586840324`*^9}, {3.4941630624049997`*^9, 3.4941631381274*^9}, { 3.4941632311345997`*^9, 3.4941632492306004`*^9}, 3.4941633249217997`*^9, { 3.4941633940922003`*^9, 3.4941634063538*^9}, {3.4941634538402*^9, 3.4941635051642*^9}, {3.494163565115*^9, 3.4941636341762*^9}, { 3.4941636853442*^9, 3.4941639323234*^9}, {3.4941640277798*^9, 3.4941641455754004`*^9}, {3.4941641790374002`*^9, 3.4941641803789997`*^9}, {3.4941642676142*^9, 3.4941643277678003`*^9}, 3.4941644677018003`*^9, {3.4941646208938*^9, 3.4941646322349997`*^9}, { 3.4941652592693996`*^9, 3.4941652807194*^9}, {3.4941653119038*^9, 3.494165416299*^9}, {3.494165453895*^9, 3.4941654544722*^9}, { 3.4950990979779997`*^9, 3.495099142701*^9}, {3.495099172958*^9, 3.4950991806289997`*^9}, {3.495099227097*^9, 3.495099238113*^9}, 3.495099290797*^9, {3.495099346084*^9, 3.495099359507*^9}, { 3.495099456308*^9, 3.495099464091*^9}, 3.495099683108*^9, { 3.495100428112*^9, 3.495100434958*^9}, {3.4951006496219997`*^9, 3.495100649992*^9}, {3.4987235265018*^9, 3.4987235939094*^9}, { 3.4987236420666*^9, 3.4987236530646*^9}, {3.4987237305341997`*^9, 3.4987237396914*^9}, {3.498733136159*^9, 3.4987332972446003`*^9}, { 3.4987364783094*^9, 3.4987364860626*^9}, {3.4987366201134*^9, 3.4987366236078*^9}, {3.4987367272386*^9, 3.4987367464890003`*^9}, { 3.4987369428462*^9, 3.4987369670886*^9}, {3.4987370134518003`*^9, 3.4987370259941998`*^9}, {3.4987370944002*^9, 3.4987371027618*^9}, { 3.4987371921029997`*^9, 3.498737193663*^9}, {3.4987372660938*^9, 3.4987372935498*^9}, {3.4987373290554*^9, 3.4987377176202*^9}, { 3.4987377520182*^9, 3.4987379139462*^9}, {3.4987382030216*^9, 3.4987382667078*^9}, {3.4987888391818*^9, 3.4987888608346*^9}, { 3.4988785131146*^9, 3.4988785160162*^9}, {3.5007170967096*^9, 3.5007170999076*^9}, 3.5007182237316*^9, {3.5007182772864*^9, 3.5007182987832003`*^9}, {3.5009573226744003`*^9, 3.5009573940444*^9}, 3.5009574358710003`*^9, 3.5009604278482*^9, {3.5009897246173353`*^9, 3.5009898480289354`*^9}, {3.5009901464413357`*^9, 3.5009901475333357`*^9}, {3.5009901801997356`*^9, 3.500990274096135*^9}, { 3.5010475253292*^9, 3.5010475852332*^9}, {3.5010605722018003`*^9, 3.5010606739762*^9}, {3.5010607202146*^9, 3.5010607323358*^9}, { 3.5010607920526*^9, 3.501061118467*^9}, {3.5010612022078*^9, 3.5010612277138*^9}, {3.5010616467766*^9, 3.5010617938534*^9}, { 3.5010618406222*^9, 3.5010619950778*^9}, {3.5010621500638*^9, 3.5010622514014*^9}, {3.5010625292218*^9, 3.5010625409374*^9}, { 3.5010626043046*^9, 3.5010626313862*^9}, {3.5010626787166*^9, 3.5010626790754004`*^9}, {3.501074457561*^9, 3.5010744671082*^9}, 3.5010763029458*^9, {3.5032210899309998`*^9, 3.5032212413900003`*^9}, { 3.557658203404973*^9, 3.557658219644601*^9}, {3.5576584433801947`*^9, 3.557658496030287*^9}, {3.5576585501779823`*^9, 3.5576586046064777`*^9}, { 3.557658648910555*^9, 3.557658754600741*^9}, {3.557658963945511*^9, 3.5576589782507353`*^9}, {3.557659009949991*^9, 3.5576591437514267`*^9}, { 3.557659182221094*^9, 3.5576592187719584`*^9}, 3.557659413865901*^9, { 3.557659921100792*^9, 3.5576599556392527`*^9}, {3.557660706920972*^9, 3.5576607248454037`*^9}, {3.557661209085854*^9, 3.557661209413454*^9}, { 3.5577526651911488`*^9, 3.5577526932087984`*^9}, {3.5577527272480583`*^9, 3.557752747122493*^9}, {3.5577528374934516`*^9, 3.557752838523053*^9}, { 3.557752881204728*^9, 3.557752891313546*^9}, {3.557752938612829*^9, 3.5577529469120436`*^9}, {3.557753060714244*^9, 3.557753062633047*^9}, { 3.5577536609544907`*^9, 3.5577536637936954`*^9}, {3.5577537824631042`*^9, 3.557753810184353*^9}, {3.557753841025607*^9, 3.5577540648392*^9}, 3.5577541920574236`*^9, {3.5577547033327217`*^9, 3.557754716967146*^9}, { 3.5577547716296415`*^9, 3.557754802112095*^9}, {3.5577549509363565`*^9, 3.5577549771444025`*^9}, 3.5577551382302856`*^9, {3.55775527184452*^9, 3.557755272858522*^9}, {3.557755881555991*^9, 3.557755886548*^9}, { 3.557756158316077*^9, 3.557756231885806*^9}, {3.5577572408487787`*^9, 3.557757248835993*^9}, {3.5577572834368534`*^9, 3.5577575888229895`*^9}, { 3.5577578129641833`*^9, 3.557757862837471*^9}, {3.557758025514557*^9, 3.557758079272251*^9}, 3.557810586960072*^9, {3.5578240262005973`*^9, 3.5578240345360737`*^9}, {3.557824091429328*^9, 3.5578241008156557`*^9}, { 3.557831525255726*^9, 3.5578315319793377`*^9}, 3.5578315716190076`*^9, { 3.557831606079468*^9, 3.557831629432709*^9}, {3.5578316663267736`*^9, 3.5578317569473333`*^9}, {3.5578322144181366`*^9, 3.557832218084143*^9}, { 3.557836356693412*^9, 3.557836473771618*^9}, {3.5578365201660995`*^9, 3.5578365974018345`*^9}, {3.5578366426731143`*^9, 3.557836658865943*^9}, { 3.557836691017599*^9, 3.5578367924957776`*^9}, {3.5578368305442443`*^9, 3.557836888279946*^9}, {3.5578369382156334`*^9, 3.5578370776642785`*^9}, { 3.5578383536061196`*^9, 3.5578383735117545`*^9}, {3.5578385892445335`*^9, 3.5578385978869486`*^9}, {3.5578386713006773`*^9, 3.557838700113928*^9}, { 3.5578387451200075`*^9, 3.5578387467892103`*^9}, {3.5578388951454706`*^9, 3.5578389248635225`*^9}, {3.5578389679351983`*^9, 3.557838983535226*^9}, { 3.5578390227692947`*^9, 3.557839023143696*^9}, {3.557839097696226*^9, 3.5578391125162525`*^9}, {3.5578391553539276`*^9, 3.557839199892006*^9}, { 3.55783924184048*^9, 3.557839294490572*^9}, {3.5578393285922318`*^9, 3.557839398683155*^9}, {3.557839430522811*^9, 3.557839470162481*^9}, { 3.5578395370865984`*^9, 3.5578395446994114`*^9}, {3.5578396068499207`*^9, 3.5578396118575296`*^9}, 3.5578943518105097`*^9, {3.557894388361374*^9, 3.5578944029629993`*^9}, {3.5578944607611012`*^9, 3.5578944989499683`*^9}, {3.5578945393696394`*^9, 3.557894561537278*^9}, { 3.5578946028617506`*^9, 3.5578946188985786`*^9}, {3.557894650894235*^9, 3.5578947812636642`*^9}, {3.55789481884413*^9, 3.5578948191249304`*^9}, { 3.5578949768100076`*^9, 3.5578949836272197`*^9}, {3.5578967386805477`*^9, 3.55789678549623*^9}, {3.5578968804691963`*^9, 3.557896888643611*^9}, { 3.557897022491846*^9, 3.5578970341450663`*^9}, {3.557897620940097*^9, 3.55789765120415*^9}, {3.5579218072271147`*^9, 3.5579218263059483`*^9}, { 3.557922095312821*^9, 3.557922116965659*^9}, {3.557922178086566*^9, 3.557922188616585*^9}, {3.5579223258812256`*^9, 3.557922327066828*^9}, { 3.5579224596046605`*^9, 3.557922461804264*^9}, 3.5579805928465395`*^9, { 3.5579815200581703`*^9, 3.557981541711009*^9}, 3.557985544779242*^9, { 3.5579863164793987`*^9, 3.5579863339514294`*^9}, {3.557986523210962*^9, 3.557986568841042*^9}, 3.5579866122559185`*^9, 3.557986993536188*^9, { 3.5579871244716187`*^9, 3.5579871290580263`*^9}, 3.557987173486905*^9, 3.5579872166989803`*^9, {3.5599618621582537`*^9, 3.5599618642486577`*^9}, { 3.559961969720443*^9, 3.5599619894700775`*^9}, 3.559963611089726*^9, { 3.5601298891258235`*^9, 3.560129889422224*^9}, {3.560132445157113*^9, 3.5601324458591146`*^9}, {3.561978472080926*^9, 3.561978472392926*^9}, { 3.6297802564412937`*^9, 3.6297802957377625`*^9}, {3.62978033369263*^9, 3.629780429741998*^9}, {3.6297805790030603`*^9, 3.6297809429048996`*^9}, { 3.629780987957779*^9, 3.629781197575347*^9}, {3.629781240397422*^9, 3.629781337663593*^9}, {3.6297813946972933`*^9, 3.6297814529165955`*^9}, { 3.6297814952550697`*^9, 3.629781527578326*^9}, {3.62978162025529*^9, 3.629781647633338*^9}, {3.629781678833393*^9, 3.629781763120341*^9}, 3.6297818028224106`*^9, {3.6297818432108817`*^9, 3.629781872570133*^9}, { 3.629782355765382*^9, 3.629782427603508*^9}, {3.6297824692243814`*^9, 3.629782674863942*^9}, {3.629782707218399*^9, 3.6297829295343895`*^9}, { 3.629783005631323*^9, 3.6297830574702144`*^9}, {3.6297831098551064`*^9, 3.629783142786764*^9}, {3.629783433711675*^9, 3.629783442619291*^9}, { 3.6297834942397814`*^9, 3.6297835175930223`*^9}, 3.6297835794939313`*^9, { 3.6297836160291953`*^9, 3.6297837668970604`*^9}, {3.6297842042438283`*^9, 3.6297842697483435`*^9}, {3.6297843514456873`*^9, 3.629784370742921*^9}, { 3.629784443829049*^9, 3.6297844678842916`*^9}, {3.6297845252611923`*^9, 3.629784525588793*^9}, {3.6297846136821475`*^9, 3.629784629235375*^9}, { 3.629784814797701*^9, 3.629784927648299*^9}, {3.629785259960083*^9, 3.6297852602096834`*^9}, {3.6297858780175686`*^9, 3.629785917282837*^9}, { 3.629786048057867*^9, 3.629786048681868*^9}, 3.6297863278755584`*^9, { 3.6297867047133856`*^9, 3.629786748533863*^9}, {3.6297867791567163`*^9, 3.6297868491540394`*^9}, {3.6297875320748396`*^9, 3.629787569795706*^9}, { 3.6297876247234025`*^9, 3.6297877281983843`*^9}, {3.6297877681812544`*^9, 3.629787774015665*^9}, {3.629787831408166*^9, 3.6297878355265727`*^9}, { 3.6297878775686464`*^9, 3.6297878861174617`*^9}, {3.6297879185343184`*^9, 3.629787919064719*^9}, {3.6297880043032694`*^9, 3.62978800470887*^9}, 3.6297880488257475`*^9, {3.6297882100052304`*^9, 3.6297882174776435`*^9}, { 3.6297882697533355`*^9, 3.6297882948381796`*^9}, {3.6297883467550707`*^9, 3.6297883991087627`*^9}, {3.6297887361785545`*^9, 3.629788783961438*^9}, 3.629788825395111*^9, {3.629789006152629*^9, 3.6297890321266747`*^9}, { 3.6297891133248167`*^9, 3.629789145336073*^9}, {3.6297891926821566`*^9, 3.629789194257759*^9}, {3.629789255316266*^9, 3.6297892556282673`*^9}, { 3.629869102295367*^9, 3.629869160124668*^9}, {3.6298691942887287`*^9, 3.6298696149902673`*^9}, {3.6298696993864155`*^9, 3.62986975897852*^9}, { 3.6298698387726603`*^9, 3.629869912030389*^9}, {3.6298700722270703`*^9, 3.629870234560955*^9}, {3.629870580429163*^9, 3.629870630458451*^9}, { 3.630556081081209*^9, 3.630556104902451*^9}, {3.6305562643503313`*^9, 3.6305562763935523`*^9}, {3.6305563415080667`*^9, 3.630556480956712*^9}, { 3.630556692851884*^9, 3.630556695347888*^9}, {3.630556730042349*^9, 3.630556914528273*^9}, {3.6305653725974936`*^9, 3.6305656807121167`*^9}, { 3.630565758760581*^9, 3.6305657739024467`*^9}, {3.630565858170267*^9, 3.63056596644846*^9}, {3.6305661502619734`*^9, 3.6305661523230915`*^9}, { 3.6305662653385553`*^9, 3.630566370352562*^9}, {3.6305667786019125`*^9, 3.630566790535595*^9}, {3.6305668214773645`*^9, 3.630567044691132*^9}, { 3.6305670772499943`*^9, 3.6305670783710585`*^9}, 3.630567272031135*^9, { 3.630567303902958*^9, 3.630567409875019*^9}, {3.630568671196477*^9, 3.6305687195002403`*^9}, {3.6305687542132254`*^9, 3.630568758623478*^9}, { 3.630568855671028*^9, 3.630568859250233*^9}, {3.630569706514694*^9, 3.630569775526641*^9}, 3.630569982346471*^9, {3.6305701679130845`*^9, 3.630570205199217*^9}, {3.6305703751399374`*^9, 3.630570526177576*^9}, { 3.630587657039589*^9, 3.630587688367381*^9}, {3.6305880733027773`*^9, 3.6305883365376396`*^9}, {3.6305886689118233`*^9, 3.6305886717978287`*^9}, 3.6305889776831656`*^9, {3.6305890389444733`*^9, 3.6305890437180815`*^9}, { 3.630589093248169*^9, 3.6305891296430326`*^9}, 3.630589181700324*^9, { 3.6305892509956455`*^9, 3.6305892594820604`*^9}, {3.630589318949365*^9, 3.6305893334729905`*^9}, {3.630589630294712*^9, 3.6305896376267247`*^9}, { 3.630589683288005*^9, 3.630589684988408*^9}, {3.630597310538067*^9, 3.630597340080757*^9}, {3.630597391446695*^9, 3.630597400596218*^9}, { 3.6305974350611897`*^9, 3.6305974605306463`*^9}, {3.630633997622449*^9, 3.630634003125764*^9}, {3.630659322217756*^9, 3.63065932438616*^9}, { 3.6306611578252783`*^9, 3.6306611625988865`*^9}, {3.6306612541554475`*^9, 3.630661257587454*^9}, {3.6306613001287284`*^9, 3.6306613026715326`*^9}, { 3.6306613920752897`*^9, 3.6306613949768953`*^9}, {3.6306706377509866`*^9, 3.630670654957817*^9}, {3.6306749981919994`*^9, 3.630675005793434*^9}, { 3.6306751229631357`*^9, 3.630675150017683*^9}, {3.6306752035287437`*^9, 3.6306752096180925`*^9}, {3.630675315921172*^9, 3.6306753201514144`*^9}, { 3.6306757793287754`*^9, 3.6306757796257925`*^9}, {3.630675814406262*^9, 3.6306758147026625`*^9}, {3.6306760107574763`*^9, 3.6306760154417443`*^9}, {3.6306789722320743`*^9, 3.6306789870309205`*^9}, {3.6306790257051325`*^9, 3.630679028076268*^9}, { 3.6306800259177256`*^9, 3.6306800406129513`*^9}, {3.6306801239326982`*^9, 3.6306801300167084`*^9}, {3.630680769261832*^9, 3.6306807806186523`*^9}, { 3.630681157468514*^9, 3.6306811577649145`*^9}, {3.6306812744219193`*^9, 3.63068127471832*^9}, {3.6306817187418995`*^9, 3.6306817919060287`*^9}, { 3.630681879188182*^9, 3.6306819111526375`*^9}, {3.6306821191790032`*^9, 3.6306821283050194`*^9}, {3.630720543651497*^9, 3.6307205534300566`*^9}, { 3.630721035525631*^9, 3.630721092774905*^9}, {3.6307212510439577`*^9, 3.6307213064777765`*^9}, {3.6307477437169704`*^9, 3.6307478284095197`*^9}, {3.6307478614971776`*^9, 3.6307478785948076`*^9}, {3.6307479884814005`*^9, 3.630748002880226*^9}, { 3.630748045624301*^9, 3.630748063876333*^9}, {3.630748111596817*^9, 3.6307481498324842`*^9}, {3.6307489182430334`*^9, 3.6307489447786803`*^9}, {3.630749037427243*^9, 3.6307490443848553`*^9}, { 3.6307491041485605`*^9, 3.6307491384218206`*^9}, {3.6307491914151134`*^9, 3.630749196890723*^9}, {3.6307492445800066`*^9, 3.6307493439989815`*^9}, { 3.630749396212273*^9, 3.6307494766304145`*^9}, {3.6307495333989143`*^9, 3.6307495547241516`*^9}, {3.6307496525831237`*^9, 3.630749669571553*^9}, { 3.630750220602922*^9, 3.6307502881822405`*^9}, {3.6307510631916018`*^9, 3.630751068292811*^9}, {3.6307511226589065`*^9, 3.630751137962533*^9}, { 3.6307512555243397`*^9, 3.630751282777588*^9}, {3.630752266971757*^9, 3.630752414599744*^9}, {3.630752446407563*^9, 3.630752457388191*^9}, { 3.6307589380050273`*^9, 3.6307590266300964`*^9}, {3.6307591666721067`*^9, 3.63075923229886*^9}, 3.630760288282259*^9, {3.6307603547370596`*^9, 3.630760557414652*^9}, {3.630760654134184*^9, 3.63076065510824*^9}, { 3.6307606911683025`*^9, 3.6307606919283457`*^9}, {3.6307607642334814`*^9, 3.6307607648645177`*^9}, {3.630761455000991*^9, 3.6307614616743727`*^9}, { 3.630761507825012*^9, 3.630761605776615*^9}, {3.630761652999316*^9, 3.630761695865768*^9}, {3.630761771278081*^9, 3.6307617792215357`*^9}, 3.6307629478424797`*^9, {3.632205207880766*^9, 3.6322052561155243`*^9}, { 3.6322052892474194`*^9, 3.6322052915745525`*^9}, 3.6322053746993074`*^9, { 3.6322062705415463`*^9, 3.6322062726016645`*^9}, {3.6322063396935015`*^9, 3.63220636484194*^9}, {3.6322064410612993`*^9, 3.6322064491667633`*^9}, { 3.632206580308264*^9, 3.6322066373275256`*^9}, {3.6322066736436024`*^9, 3.6322067467737856`*^9}, {3.632206782260815*^9, 3.6322071351279984`*^9}, 3.6322071989226465`*^9, {3.632207270393735*^9, 3.6322073359894867`*^9}, { 3.6322073997741346`*^9, 3.6322074126708727`*^9}, {3.632207491777397*^9, 3.632207682289294*^9}, {3.632207809621577*^9, 3.632207827973626*^9}, { 3.6322079043859973`*^9, 3.6322079279443445`*^9}, {3.6322080916397076`*^9, 3.6322081666649985`*^9}, 3.634905258940913*^9, {3.634905370524296*^9, 3.6349054089004903`*^9}, {3.6349054472556844`*^9, 3.63490544787272*^9}, { 3.634905483492757*^9, 3.6349055164646425`*^9}, {3.634905574352954*^9, 3.634905628121029*^9}, {3.6349057012822137`*^9, 3.6349057207913294`*^9}, { 3.6349061371061416`*^9, 3.634906354438572*^9}, {3.6349063890455513`*^9, 3.6349064369332905`*^9}, {3.634906537696054*^9, 3.634906601859724*^9}, 3.634906706128688*^9, {3.6349069249442034`*^9, 3.6349069328326545`*^9}, { 3.6349070151973653`*^9, 3.6349070242298822`*^9}, {3.6349070817921743`*^9, 3.6349070822111983`*^9}, {3.634907723288866*^9, 3.634907739005765*^9}, { 3.6349079580732946`*^9, 3.6349079868219395`*^9}, {3.634908200284148*^9, 3.634908315195721*^9}, {3.6349083774582825`*^9, 3.6349084027997313`*^9}, { 3.63490844507615*^9, 3.634908448843365*^9}, {3.634914956333157*^9, 3.634915020054802*^9}, {3.634915050572547*^9, 3.6349150956171236`*^9}, { 3.6349539785771523`*^9, 3.634953978975175*^9}, {3.6349540728785458`*^9, 3.6349541681829967`*^9}, {3.634954211263461*^9, 3.6349542495746527`*^9}, { 3.6349543251259737`*^9, 3.634954355882733*^9}, {3.6349543892536416`*^9, 3.6349544742835045`*^9}, {3.634954547519694*^9, 3.6349545640246377`*^9}, { 3.6349547051657104`*^9, 3.6349547107930326`*^9}, {3.634954745355009*^9, 3.634954752101395*^9}, {3.6349547948858423`*^9, 3.6349548053894434`*^9}, { 3.634954904907135*^9, 3.6349549451084347`*^9}, {3.634955219605135*^9, 3.6349552640926795`*^9}, {3.634955320189888*^9, 3.634955348763522*^9}, { 3.634955386393675*^9, 3.6349555039273973`*^9}, {3.6349557669644423`*^9, 3.6349557672004557`*^9}, {3.634955894841756*^9, 3.634955902578199*^9}, { 3.6349559513739896`*^9, 3.6349560216320086`*^9}, {3.634956120144643*^9, 3.634956128996149*^9}, {3.6349561700724983`*^9, 3.6349561978900895`*^9}, { 3.6349562480719595`*^9, 3.634956254326318*^9}, {3.634956331684742*^9, 3.6349563460575643`*^9}, {3.634956379242462*^9, 3.63495642676418*^9}, 3.6349564696636343`*^9, {3.6351524116477795`*^9, 3.6351524153379908`*^9}, { 3.6352134400282927`*^9, 3.635213442148414*^9}, {3.6352134745862694`*^9, 3.635213495869487*^9}, {3.6352135383409157`*^9, 3.6352137157160616`*^9}, { 3.6352137493569856`*^9, 3.635213764522853*^9}, {3.635214215036621*^9, 3.635214227593339*^9}, {3.635214407257615*^9, 3.63521441713218*^9}, { 3.635215297101512*^9, 3.635215303964904*^9}, {3.6352154111120324`*^9, 3.635215431504199*^9}, {3.635216346055508*^9, 3.635216494371991*^9}, { 3.635216631050809*^9, 3.6352166603244834`*^9}, {3.635216763034358*^9, 3.635216764164423*^9}, {3.6352168771938877`*^9, 3.635216888828553*^9}, 3.6352169832479534`*^9, 3.635217037668066*^9, {3.6352172024924936`*^9, 3.6352172054526625`*^9}, {3.635217344025589*^9, 3.635217346898753*^9}, 3.6352173863770113`*^9, {3.635217519639633*^9, 3.6352175507014103`*^9}, 3.635217615445113*^9, {3.6352178715087595`*^9, 3.635217880460271*^9}, { 3.6352185912849283`*^9, 3.635218598444338*^9}, {3.6352186995721216`*^9, 3.635218714955002*^9}, {3.6352189761749425`*^9, 3.6352189789341*^9}, { 3.6352195060322485`*^9, 3.635219509972474*^9}, 3.6352195673477554`*^9, 3.6352195994635925`*^9, {3.6352197336482677`*^9, 3.635219737452485*^9}, { 3.6352197706093817`*^9, 3.6352197723214793`*^9}, {3.635219941784172*^9, 3.6352199485115566`*^9}, {3.6352200714185867`*^9, 3.6352200854323883`*^9}, {3.6352202085694313`*^9, 3.635220235849992*^9}, { 3.6352202816336107`*^9, 3.6352203110962954`*^9}, {3.6352204980449886`*^9, 3.6352205276526823`*^9}, {3.6352253191447396`*^9, 3.6352253299913597`*^9}, {3.6352253611111403`*^9, 3.6352253637572913`*^9}, {3.635225409322898*^9, 3.6352255965196047`*^9}, { 3.6352260914249115`*^9, 3.6352261698393965`*^9}, {3.63522638233055*^9, 3.6352264188036366`*^9}, {3.635227493469104*^9, 3.635227556935734*^9}, { 3.6352276745764627`*^9, 3.635227730116639*^9}, {3.6352287979917183`*^9, 3.6352288587651944`*^9}, {3.635228894237223*^9, 3.635228948324317*^9}, { 3.635229365252164*^9, 3.6352293902275925`*^9}, {3.63522947690555*^9, 3.6352294807837715`*^9}, {3.6352492831123204`*^9, 3.6352492983621926`*^9}, 3.6356569054520617`*^9, {3.6363778004499054`*^9, 3.636377802787039*^9}, { 3.6363778414932528`*^9, 3.6363778525308843`*^9}, {3.636384436335312*^9, 3.6363846409950175`*^9}, {3.636384971250907*^9, 3.6363849738080535`*^9}, { 3.6363850170465264`*^9, 3.636385030729309*^9}, {3.6363851286779118`*^9, 3.636385138359465*^9}, {3.6363851699712734`*^9, 3.636385223111313*^9}, { 3.656076172452749*^9, 3.656076182171566*^9}, {3.6560765578514256`*^9, 3.656076619019133*^9}, 3.6560772545486493`*^9, {3.6630719749029694`*^9, 3.6630719878027077`*^9}, {3.6630720702554235`*^9, 3.6630720807290225`*^9}, {3.6630721155740156`*^9, 3.6630721713712068`*^9}, {3.663072270834896*^9, 3.6630722882218904`*^9}, 3.6630724099968557`*^9, {3.685234767958906*^9, 3.685234768480936*^9}, { 3.685252204033695*^9, 3.6852522340537376`*^9}, {3.6852522757137957`*^9, 3.6852523115138454`*^9}, {3.68525376314359*^9, 3.6852537725041256`*^9}, { 3.6852539763277836`*^9, 3.6852539861693463`*^9}, 3.6852540682470407`*^9, 3.6852541660656357`*^9, {3.6852604801645336`*^9, 3.6852605060345697`*^9}, { 3.6852605373446136`*^9, 3.6852605977846985`*^9}, 3.685260655254779*^9, { 3.6853280002218475`*^9, 3.685328019561875*^9}, 3.685328064721938*^9, { 3.6853280953119807`*^9, 3.6853282636022167`*^9}, {3.685328356242346*^9, 3.685328598671985*^9}, {3.6853286682069626`*^9, 3.6853287982524004`*^9}, { 3.6853288753368096`*^9, 3.6853289367033195`*^9}, {3.685328968274125*^9, 3.685328978713722*^9}, {3.685329033941881*^9, 3.685329044950511*^9}, { 3.685329173522865*^9, 3.6853294420842257`*^9}, {3.6853296024223967`*^9, 3.6853296124319687`*^9}, {3.6853297221712456`*^9, 3.685329733349885*^9}, { 3.6853298076291337`*^9, 3.6853298739599276`*^9}, {3.685330038474337*^9, 3.685330051652091*^9}, {3.6853311309428225`*^9, 3.685331168378964*^9}, { 3.685340142134763*^9, 3.685340180544817*^9}, {3.6853583292043543`*^9, 3.685358334834362*^9}, {3.685358366084406*^9, 3.685358366954407*^9}, { 3.685358408404465*^9, 3.685358518294619*^9}, 3.685358620174762*^9, 3.6853586578748145`*^9, {3.6853588750151186`*^9, 3.6853588857151337`*^9}, { 3.6853589302051954`*^9, 3.685358938995208*^9}, {3.685359014715314*^9, 3.6853590296653347`*^9}, 3.685359148315501*^9, 3.6853598281764526`*^9, { 3.6853683109000263`*^9, 3.685368382250126*^9}, {3.685368420160179*^9, 3.6853684704302497`*^9}, {3.6853685194503183`*^9, 3.685368742860631*^9}, { 3.685369008901004*^9, 3.68536902061102*^9}, {3.6853690791611023`*^9, 3.685369132301176*^9}, {3.6853693219914417`*^9, 3.6853693304114532`*^9}, 3.6853696089118433`*^9, {3.6858758911429157`*^9, 3.685875951793*^9}, { 3.6859484099082212`*^9, 3.6859484970032024`*^9}, {3.686052829875022*^9, 3.686052906242383*^9}, {3.6860535326822133`*^9, 3.686053598029951*^9}, { 3.68605365168902*^9, 3.6860541446091995`*^9}, {3.6860541846064873`*^9, 3.68605440393201*^9}, {3.686054713802734*^9, 3.6860547858298535`*^9}, { 3.6860548280202665`*^9, 3.686054837219793*^9}, {3.686054874127904*^9, 3.686054892139934*^9}, {3.686055136014883*^9, 3.6860551460584574`*^9}, { 3.686055211281188*^9, 3.6860552301962633`*^9}, {3.6860553465409174`*^9, 3.6860553998749685`*^9}, {3.6860556017188663`*^9, 3.6860556050188704`*^9}, {3.6862923512707715`*^9, 3.686292363600789*^9}, { 3.686292409650853*^9, 3.6862924109708548`*^9}, {3.6862924536109147`*^9, 3.6862924596309233`*^9}, {3.686292542221039*^9, 3.6862925430110397`*^9}, { 3.686292988803664*^9, 3.686293001033681*^9}, {3.6866504529025555`*^9, 3.686650526682659*^9}, {3.686650671852862*^9, 3.6866507242929354`*^9}, { 3.6866507657529936`*^9, 3.6866507887630253`*^9}, {3.6866508208230705`*^9, 3.6866509100531955`*^9}, {3.6866509593932643`*^9, 3.686650971113281*^9}, { 3.686651007793332*^9, 3.6866511595335445`*^9}, {3.686651223513634*^9, 3.686651234033649*^9}, {3.686651304763748*^9, 3.6866513363837924`*^9}, { 3.6866514102038956`*^9, 3.686651429943923*^9}, {3.686652993837468*^9, 3.6866530046274834`*^9}, {3.686804398511652*^9, 3.6868044081516657`*^9}, { 3.6868046315619783`*^9, 3.686804631801979*^9}, {3.686804685872054*^9, 3.686804707092084*^9}, {3.6868047382021275`*^9, 3.686804767812169*^9}, { 3.686804824012248*^9, 3.6868048404922705`*^9}, {3.686804942142413*^9, 3.6868049633424425`*^9}, {3.6868050765526013`*^9, 3.686805101092636*^9}, { 3.6868051463526993`*^9, 3.6868052234228067`*^9}, {3.686805307602925*^9, 3.686805311682931*^9}, {3.68680577547358*^9, 3.686805788923599*^9}, { 3.686821702197342*^9, 3.6868217282873783`*^9}, {3.6868225192884855`*^9, 3.686822538368512*^9}, {3.6868226306886415`*^9, 3.6868226683086944`*^9}, { 3.6868227318887835`*^9, 3.6868227627088265`*^9}, {3.686822801638881*^9, 3.6868230490692277`*^9}, {3.686823122979331*^9, 3.6868231833294153`*^9}, { 3.6868232450595016`*^9, 3.6868233753996844`*^9}, {3.6868234153897405`*^9, 3.686823451379791*^9}, {3.6868236736101017`*^9, 3.6868236786601086`*^9}, { 3.6868237164601617`*^9, 3.68682375072021*^9}, {3.68682389396041*^9, 3.68682390087042*^9}, {3.686823940790476*^9, 3.6868239416904774`*^9}, { 3.6868239808805323`*^9, 3.6868239872905407`*^9}, {3.686824051540631*^9, 3.6868240519006314`*^9}, {3.686824360861064*^9, 3.6868243761510854`*^9}, { 3.6868245440213203`*^9, 3.686824577221367*^9}, {3.686824685841519*^9, 3.6868246979115357`*^9}, 3.6868248012716804`*^9, 3.6868253582724605`*^9, { 3.6868255183026843`*^9, 3.686825518932685*^9}, {3.6868264466639843`*^9, 3.6868264497139883`*^9}, {3.6868267792744493`*^9, 3.6868268152945004`*^9}, {3.686827100164899*^9, 3.6868271210549283`*^9}, 3.686827162004986*^9, {3.6868272414950967`*^9, 3.686827327475217*^9}, { 3.686827953126093*^9, 3.686827976506126*^9}, {3.686829128577739*^9, 3.686829138957753*^9}, 3.6868292410978966`*^9, {3.6868292768379464`*^9, 3.686829282727955*^9}, {3.6868293820380936`*^9, 3.686829418138144*^9}, { 3.686829846748744*^9, 3.686829848298746*^9}, {3.6868313063207874`*^9, 3.686831307180789*^9}, {3.6868331276633377`*^9, 3.68683328653356*^9}, { 3.6868394697195063`*^9, 3.6868394933895392`*^9}, 3.686839530999592*^9, { 3.686839582829664*^9, 3.68683963686974*^9}, {3.6868397551199055`*^9, 3.68683979365996*^9}, {3.6868398344600167`*^9, 3.686839866200061*^9}, { 3.687092084401948*^9, 3.687092117031994*^9}, {3.6870922598621936`*^9, 3.6870922645422*^9}, {3.6870962086478376`*^9, 3.6870962658779182`*^9}, 3.687096444838168*^9, {3.687096500978247*^9, 3.687096501638248*^9}, { 3.6870965809883595`*^9, 3.687096592708376*^9}, 3.687096837948719*^9, { 3.68709688890879*^9, 3.687096985798926*^9}, {3.6870971015990877`*^9, 3.6870972179192505`*^9}, {3.6870972618993125`*^9, 3.687097305639374*^9}, { 3.6870973356794157`*^9, 3.6870975186496716`*^9}, {3.6870975796097574`*^9, 3.6870975953197794`*^9}, {3.6870976531898603`*^9, 3.6870976848899045`*^9}, 3.6870977782500353`*^9, {3.687413757687042*^9, 3.6874137834070783`*^9}, { 3.6874140542074575`*^9, 3.687414094417514*^9}, {3.6874143478878684`*^9, 3.687414485538061*^9}, {3.6874146116082373`*^9, 3.68741464894829*^9}, { 3.6874147451084247`*^9, 3.687414766118454*^9}, 3.6874149094486547`*^9, { 3.6874150416688395`*^9, 3.6874150634888706`*^9}, {3.6874152437091227`*^9, 3.687415268869158*^9}, 3.6874153442892637`*^9, {3.687415449879411*^9, 3.687415469659439*^9}, 3.687415529739523*^9, 3.687415564789572*^9, 3.687415645529685*^9, {3.6874168016913037`*^9, 3.687416803441306*^9}, { 3.687421022677213*^9, 3.6874212686075573`*^9}, {3.68742948209425*^9, 3.6874294906842623`*^9}, {3.687844340668378*^9, 3.6878443698084188`*^9}, { 3.6886534778571014`*^9, 3.6886534911571198`*^9}, {3.688906380162199*^9, 3.6889064680223217`*^9}, {3.688906514222396*^9, 3.6889065193925257`*^9}, { 3.688908192623024*^9, 3.6889082006430354`*^9}, {3.688908261823121*^9, 3.688908271653135*^9}, {3.6889083776232834`*^9, 3.6889083922733035`*^9}, { 3.688908466073407*^9, 3.6889084993734536`*^9}, 3.688908533623502*^9, { 3.688908616683618*^9, 3.6889086271336327`*^9}, {3.6889086885637183`*^9, 3.6889087063437433`*^9}, {3.6889091647443852`*^9, 3.6889092012544365`*^9}, {3.6889093019045773`*^9, 3.6889093406746316`*^9}, 3.6889101071957045`*^9, {3.689905940063133*^9, 3.689905972983179*^9}, { 3.692530981927737*^9, 3.6925310416778207`*^9}, {3.692531099797902*^9, 3.6925311384779563`*^9}, {3.692531192258032*^9, 3.692531244668105*^9}, { 3.6925312919881716`*^9, 3.692531425418358*^9}, {3.6925315270885005`*^9, 3.692531643928664*^9}, {3.692535489534048*^9, 3.6925356485142703`*^9}, { 3.692535753564418*^9, 3.6925357992544813`*^9}, {3.6925358831745987`*^9, 3.692535899604622*^9}, {3.692536042584822*^9, 3.692536159384986*^9}, { 3.6925366121156197`*^9, 3.6925366207256317`*^9}, {3.6925367265057793`*^9, 3.69253672683578*^9}, {3.6925368590559654`*^9, 3.6925368636559715`*^9}, { 3.6925370880062857`*^9, 3.692537177856412*^9}, {3.692537322456614*^9, 3.6925373869767046`*^9}, {3.6925390913352747`*^9, 3.6925390925252767`*^9}, {3.692539644430175*^9, 3.6925396711502123`*^9}, { 3.692539727510291*^9, 3.692539730440295*^9}, {3.69253993367058*^9, 3.692539963780622*^9}, {3.6925400018406754`*^9, 3.692540003630678*^9}, { 3.6925401743409166`*^9, 3.6925401747509174`*^9}, {3.692540399111232*^9, 3.692540407981244*^9}, {3.69254047647134*^9, 3.6925404886113567`*^9}, { 3.6925406039715185`*^9, 3.69254060531152*^9}, {3.6925414948727655`*^9, 3.6925414953427663`*^9}, {3.6925415478528395`*^9, 3.692541613062931*^9}, 3.692541649332982*^9, {3.692541727633092*^9, 3.6925418840133104`*^9}, { 3.692541924473367*^9, 3.692542041693531*^9}, {3.6925421488836813`*^9, 3.6925422549438295`*^9}, {3.6925422976938896`*^9, 3.692542521444203*^9}, { 3.6925426221843443`*^9, 3.6925426357343626`*^9}, 3.692542739374508*^9, 3.692599799510878*^9, {3.692599834884901*^9, 3.6925998954663663`*^9}, { 3.692599925635092*^9, 3.6926000095928946`*^9}, {3.692600108929576*^9, 3.6926001456386757`*^9}, {3.6926001874800687`*^9, 3.692600454421337*^9}, { 3.692600503149027*^9, 3.6926006000391626`*^9}, {3.692600680251275*^9, 3.6926006814012766`*^9}, {3.6926009000215826`*^9, 3.6926009410816402`*^9}, 3.692601280532116*^9, {3.6926044914726114`*^9, 3.69260449774262*^9}, 3.6926045660127153`*^9, 3.6926046690228596`*^9, {3.69296647863291*^9, 3.6929664798829117`*^9}, {3.6929665643330297`*^9, 3.6929666141830997`*^9}, {3.6929670390036945`*^9, 3.6929670405536966`*^9}, {3.6929670861037607`*^9, 3.6929670952937737`*^9}, {3.6929671302538223`*^9, 3.6929671549438567`*^9}, {3.6929671904739065`*^9, 3.69296722137395*^9}, { 3.6929672596240034`*^9, 3.6929673352541094`*^9}, 3.6929678909232683`*^9, { 3.6930146982034283`*^9, 3.693014722713463*^9}, {3.6930148540136466`*^9, 3.693014857023651*^9}, {3.6930148913836985`*^9, 3.693014894823704*^9}, { 3.693014930903754*^9, 3.6930151942541227`*^9}, {3.693015247824198*^9, 3.693015430554454*^9}, {3.693015673794794*^9, 3.69301579223496*^9}, { 3.6930163123576884`*^9, 3.693016326897709*^9}, {3.6930164225678425`*^9, 3.693016429727853*^9}, {3.693016686718212*^9, 3.693016698128228*^9}, { 3.693016737038283*^9, 3.693016755068308*^9}, {3.6930168429225607`*^9, 3.6930168719926014`*^9}, {3.6930172049430676`*^9, 3.693017284063178*^9}, { 3.693017336433252*^9, 3.6930173662532935`*^9}, {3.6930180949163136`*^9, 3.6930180975563173`*^9}, {3.6930181870764427`*^9, 3.693018199956461*^9}, { 3.6930182954065943`*^9, 3.693018305996609*^9}, {3.693139886141657*^9, 3.6931399045016823`*^9}, {3.6931402916003532`*^9, 3.693140295770359*^9}, { 3.693140426020541*^9, 3.693140426530542*^9}, {3.6931410492237864`*^9, 3.6931410888738413`*^9}, {3.6931411194438844`*^9, 3.693141126553894*^9}, { 3.693141412004294*^9, 3.693141454164353*^9}, {3.6931415979955544`*^9, 3.6931417931758275`*^9}, {3.6932199559445915`*^9, 3.6932199772046213`*^9}, {3.6932201435748544`*^9, 3.693220170284892*^9}, { 3.693220713855653*^9, 3.693220721825664*^9}, {3.693625124589745*^9, 3.693625153729786*^9}, {3.6940907995669713`*^9, 3.6940909688872085`*^9}, { 3.6940913675677667`*^9, 3.6940914223978434`*^9}, {3.694091508037963*^9, 3.694091572118053*^9}, 3.694092009628666*^9, {3.6940920553287296`*^9, 3.694092229168973*^9}, {3.6940923053990793`*^9, 3.694092374419176*^9}, { 3.6940924537392874`*^9, 3.694092457789293*^9}, 3.694092642849552*^9, { 3.6940928573598523`*^9, 3.694092862379859*^9}, {3.6940945886222763`*^9, 3.694094601932295*^9}, 3.694094849542641*^9, {3.694095764293922*^9, 3.6940957644739223`*^9}, {3.6940960602743363`*^9, 3.6940960732243547`*^9}, {3.6940961211044216`*^9, 3.694096124194426*^9}, { 3.694665030960044*^9, 3.6946650634500895`*^9}, {3.6946652071402903`*^9, 3.6946653490404887`*^9}, {3.6946658702212186`*^9, 3.6946658881212435`*^9}, {3.694665923041292*^9, 3.694665953561335*^9}, { 3.694665995981395*^9, 3.6946660149414215`*^9}, {3.694666050571471*^9, 3.6946660547214766`*^9}, {3.694666169991638*^9, 3.694666292151809*^9}, { 3.6946663456618843`*^9, 3.6946663943919525`*^9}, 3.6946667526224537`*^9, 3.69466680700253*^9, 3.694687076625702*^9, {3.6946874316161985`*^9, 3.6946874621962414`*^9}, 3.694687499496294*^9, {3.694687567516389*^9, 3.694687642816495*^9}, {3.694687679006545*^9, 3.6946877198966026`*^9}, { 3.6946877714966745`*^9, 3.694687931746899*^9}, {3.723798739728607*^9, 3.723798744014243*^9}, {3.7237990126446104`*^9, 3.723799023974499*^9}, { 3.7244116671877546`*^9, 3.7244116733393917`*^9}, {3.724411761793063*^9, 3.7244117718753977`*^9}, {3.724411928386671*^9, 3.7244119682966137`*^9}, { 3.724412131847311*^9, 3.724412188341254*^9}, {3.729414981357122*^9, 3.7294149861075096`*^9}, {3.749817651293678*^9, 3.749817653108206*^9}, { 3.7498176831919456`*^9, 3.7498176846222315`*^9}, 3.7498177601545563`*^9, { 3.749817859674735*^9, 3.749817861044999*^9}, {3.7498179561547127`*^9, 3.749817964489929*^9}, {3.749818149334386*^9, 3.749818237397959*^9}, 3.749818617867873*^9, {3.7505621848002787`*^9, 3.7505622174085107`*^9}, { 3.75056238761455*^9, 3.750562431347901*^9}, {3.7505626332829456`*^9, 3.7505627331565337`*^9}, {3.7505627632642183`*^9, 3.7505627635859113`*^9}, {3.7515359581577415`*^9, 3.7515359614850826`*^9}, {3.751536071974715*^9, 3.7515360961721487`*^9}, 3.7515362040373974`*^9, {3.751536256080162*^9, 3.7515365099108534`*^9}, { 3.751549231137398*^9, 3.7515493334258356`*^9}, {3.7515496891619573`*^9, 3.751549689458767*^9}, 3.753020403650548*^9, {3.7530205114189386`*^9, 3.753020525224822*^9}, {3.753021995594639*^9, 3.753022011512741*^9}, { 3.760634689749445*^9, 3.7606348247488756`*^9}, {3.7606349119783344`*^9, 3.7606349350197754`*^9}, {3.76063496856853*^9, 3.7606349922504683`*^9}, { 3.760667269592998*^9, 3.760667271545692*^9}, 3.7606679283912125`*^9, 3.760668039709257*^9, {3.763302716900259*^9, 3.763302749083943*^9}, { 3.763304867499642*^9, 3.7633048681948185`*^9}, {3.763337978730939*^9, 3.763338014197137*^9}, {3.763338054806819*^9, 3.7633381289118147`*^9}, { 3.763338224472745*^9, 3.7633382447254143`*^9}, 3.763338501519575*^9, { 3.7633387342733064`*^9, 3.763338775483101*^9}, {3.7633388525735607`*^9, 3.7633390131554184`*^9}, {3.763360596353942*^9, 3.7633606328922167`*^9}, { 3.7633606638773637`*^9, 3.763360724941125*^9}, {3.763360812068123*^9, 3.763360863571327*^9}, {3.763361217769263*^9, 3.763361243271195*^9}, { 3.763361578316657*^9, 3.7633615820345063`*^9}, {3.763362291476118*^9, 3.763362301380039*^9}, {3.763362505004878*^9, 3.763362606421646*^9}, { 3.763362742167684*^9, 3.7633627524126663`*^9}, {3.7633628090243473`*^9, 3.763362931819517*^9}, 3.7633630680313087`*^9, {3.76336360941794*^9, 3.7633636782369685`*^9}, {3.763363813698273*^9, 3.763363822992702*^9}, { 3.7633837714269123`*^9, 3.763383775708086*^9}, {3.7633839861442327`*^9, 3.7633839966350546`*^9}, {3.7633846907375526`*^9, 3.76338471098131*^9}, 3.763426089635152*^9, {3.7634262143520336`*^9, 3.7634262475470448`*^9}, { 3.7634276458524485`*^9, 3.7634276705117846`*^9}, {3.7634292721860075`*^9, 3.7634292840439587`*^9}, {3.76352820463631*^9, 3.7635282147939873`*^9}, { 3.763528430960533*^9, 3.7635284413250494`*^9}, {3.7635285114344244`*^9, 3.763528537124817*^9}, {3.763528653934307*^9, 3.7635286747218256`*^9}, { 3.7635486952594075`*^9, 3.763548696007099*^9}, {3.7639579130072594`*^9, 3.7639579464687676`*^9}, {3.763957980699315*^9, 3.7639580928074217`*^9}, { 3.763959813173403*^9, 3.7639598134702053`*^9}, {3.7639608015345135`*^9, 3.7639608287155933`*^9}, {3.7645603385872726`*^9, 3.764560365934222*^9}, { 3.76456061596602*^9, 3.76456062636983*^9}, {3.7647257988231063`*^9, 3.7647258025896564`*^9}, {3.765077713031946*^9, 3.7650777913378534`*^9}, { 3.7740698865922914`*^9, 3.774069989744633*^9}, {3.7740700982535834`*^9, 3.774070098487667*^9}, {3.7740701415628414`*^9, 3.7740702370647106`*^9}, { 3.77407029325229*^9, 3.7740703348543596`*^9}, {3.774070397587008*^9, 3.774070454974152*^9}, {3.7740709929610343`*^9, 3.7740710067172923`*^9}, { 3.775190474681038*^9, 3.7751904884151363`*^9}, {3.7751905901325903`*^9, 3.775190642609686*^9}, 3.775190717712206*^9, {3.7751956728394384`*^9, 3.7751957010601625`*^9}, 3.7751957418100777`*^9, {3.7751958741450567`*^9, 3.775195882844048*^9}, {3.7751959530858574`*^9, 3.775196055684782*^9}, { 3.7836566506037264`*^9, 3.783656699859296*^9}, {3.783834162184903*^9, 3.7838342075157394`*^9}, {3.7838342453955064`*^9, 3.7838342564437876`*^9}, {3.783834288539219*^9, 3.783834289188504*^9}, { 3.783834319888338*^9, 3.783834404011998*^9}, {3.783835274452033*^9, 3.783835643262226*^9}, 3.783835673435833*^9, {3.783837186915415*^9, 3.783837252940491*^9}, 3.783838076793089*^9, {3.7838387026691084`*^9, 3.7838387106794033`*^9}, {3.7838387751330376`*^9, 3.78383877586726*^9}, 3.7885184612710266`*^9, {3.7885197610115976`*^9, 3.788519761667694*^9}, { 3.788519815581788*^9, 3.788519877459923*^9}, {3.788519910619506*^9, 3.7885199214314795`*^9}, {3.78852990807364*^9, 3.78852991935472*^9}, { 3.788529949778452*^9, 3.7885299511123505`*^9}, 3.7885729856546545`*^9, { 3.795769635061987*^9, 3.7957696738473544`*^9}, {3.7957698528454103`*^9, 3.795769867081932*^9}, {3.7963499268904905`*^9, 3.796349974573367*^9}, { 3.8116565658363085`*^9, 3.811656579625844*^9}, {3.8116566792733173`*^9, 3.811656696847624*^9}, {3.819778974172573*^9, 3.819778996370713*^9}, { 3.819779237456471*^9, 3.819779375493654*^9}, {3.819779556474127*^9, 3.8197797185600586`*^9}, 3.8200272939729*^9, 3.8200273875005593`*^9, 3.820027421880412*^9, {3.8200275035350485`*^9, 3.8200275049354267`*^9}, { 3.8459709950905457`*^9, 3.8459710017500772`*^9}, {3.8459711689546986`*^9, 3.8459711702691975`*^9}, {3.845971286165346*^9, 3.845971289846427*^9}, { 3.8459713248880577`*^9, 3.8459714501425343`*^9}, {3.845971579506527*^9, 3.8459716159320116`*^9}, {3.851994156946926*^9, 3.851994267451933*^9}, { 3.851994384355441*^9, 3.851994388857566*^9}, {3.8519946139658265`*^9, 3.8519947933175044`*^9}, {3.8519948506536093`*^9, 3.8519948668032107`*^9}, {3.8520795751469183`*^9, 3.852079576172632*^9}, { 3.852092396739352*^9, 3.8520925534144993`*^9}}, CellLabel-> "In[142]:=",ExpressionUUID->"90f2e58a-5392-4b26-b45d-dddeafd00cd0"] }, Closed]], Cell[CellGroupData[{ Cell["BENDING ELEMENT (vibr) defs ", "Subsection", CellChangeTimes->{{3.7530187996679964`*^9, 3.753018803413909*^9}, { 3.7633629633672647`*^9, 3.763362967100765*^9}, {3.787894773214689*^9, 3.7878947881941814`*^9}, {3.78789485671918*^9, 3.78789488217928*^9}, 3.7885197052606735`*^9, {3.788530025907043*^9, 3.7885300287809105`*^9}, 3.7885306781716957`*^9, {3.8200271989371843`*^9, 3.8200272016625395`*^9}, { 3.8200274346181693`*^9, 3.8200274405428553`*^9}, {3.851994139239622*^9, 3.8519941462255764`*^9}, {3.8520799546994066`*^9, 3.852079955796615*^9}},ExpressionUUID->"37b1c143-470c-45fd-bc65-\ 79466d47cc47"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BENDING", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "0", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iyy", ",", "Izz", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BENDING", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "0", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iyy", ",", "Izz", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BENDING", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "0", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iyy", ",", "Izz", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "mX", ",", "mY", ",", "mZ"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4430689313272*^9, 3.4430690080792*^9}, { 3.4430690869528*^9, 3.4430691077320004`*^9}, {3.4430691700116*^9, 3.4430691708072*^9}, {3.4430692071717997`*^9, 3.443069246359*^9}, { 3.4430772782732*^9, 3.4430773623416*^9}, {3.4430773978316*^9, 3.4430774104676*^9}, {3.4430775053780003`*^9, 3.4430776180598*^9}, { 3.4434109099524*^9, 3.4434109159584*^9}, {3.4438800815346003`*^9, 3.4438802689304*^9}, {3.443880362624*^9, 3.4438803824516*^9}, { 3.443929565615374*^9, 3.443929570232974*^9}, {3.443935321321974*^9, 3.443935335705174*^9}, {3.443935419945174*^9, 3.443935421489574*^9}, { 3.443935494013974*^9, 3.443935494715974*^9}, {3.443935617565974*^9, 3.4439357217895737`*^9}, {3.443935755360774*^9, 3.443935816107174*^9}, { 3.443942155230774*^9, 3.443942209939974*^9}, {3.443942305710374*^9, 3.4439423142123737`*^9}, {3.4439442908131742`*^9, 3.443944441181574*^9}, { 3.4439447830065737`*^9, 3.4439447917425737`*^9}, {3.443944908541774*^9, 3.443944916060974*^9}, {3.4442731097938004`*^9, 3.4442731115254*^9}, { 3.444273189229*^9, 3.4442732700526*^9}, {3.4442748430004*^9, 3.4442748605036*^9}, {3.4442748977438*^9, 3.4442748989762*^9}, { 3.4442749340762*^9, 3.4442749351057997`*^9}, 3.4442752313382*^9, { 3.4442919702026*^9, 3.4442919911846*^9}, {3.4442921151577997`*^9, 3.4442921271074*^9}, {3.4443811023684*^9, 3.4443811036632*^9}, { 3.4443814073171997`*^9, 3.4443814402956*^9}, {3.4443815036316*^9, 3.4443815147855997`*^9}, {3.4443815537232*^9, 3.4443815747676*^9}, { 3.4443816138143997`*^9, 3.444381633174*^9}, {3.4443816850439997`*^9, 3.4443817801728*^9}, 3.4443853618688*^9, {3.4443855607376003`*^9, 3.4443856337924*^9}, {3.4443861200444*^9, 3.4443861523676*^9}, { 3.4443862280495996`*^9, 3.444386291448*^9}, {3.4443864047352*^9, 3.4443864135336*^9}, {3.4443870026832*^9, 3.4443870095316*^9}, { 3.4444082055056*^9, 3.4444082437412*^9}, {3.4444082797148*^9, 3.4444084583816*^9}, {3.4444084889108*^9, 3.4444085087539997`*^9}, { 3.444408942517*^9, 3.4444089563386*^9}, {3.4444091419564*^9, 3.4444091647167997`*^9}, {3.4444092206428003`*^9, 3.4444092944463997`*^9}, {3.4444093856284*^9, 3.4444094281071997`*^9}, { 3.4444094976988*^9, 3.4444095275104*^9}, {3.444409611064*^9, 3.4444096125772*^9}, 3.4444098504616003`*^9, {3.444409913392*^9, 3.4444099166056004`*^9}, 3.4444100178496*^9, {3.4444103063248*^9, 3.4444103358712*^9}, {3.4444103868208*^9, 3.4444104432460003`*^9}, { 3.4444921219564*^9, 3.4444921256224003`*^9}, {3.444492194824*^9, 3.4444921973668003`*^9}, {3.4444922814351997`*^9, 3.4444922853508*^9}, { 3.4444923330868*^9, 3.4444923345844*^9}, {3.444492366424*^9, 3.4444923855808*^9}, {3.4453153475226*^9, 3.445315360689*^9}, { 3.4465518166373653`*^9, 3.446551863016165*^9}, {3.446551894231765*^9, 3.446552159384965*^9}, {3.446552232377365*^9, 3.4465522555589647`*^9}, { 3.446553347388365*^9, 3.4465533616155653`*^9}, {3.4466058525769997`*^9, 3.4466058529046*^9}, {3.4466064371219997`*^9, 3.4466065097244*^9}, { 3.4466127725788*^9, 3.4466127766036*^9}, {3.4466128124835997`*^9, 3.4466130037864*^9}, {3.4466131532696*^9, 3.4466131761703997`*^9}, { 3.4466133992192*^9, 3.4466134478756*^9}, {3.446613483584*^9, 3.4466134932092*^9}, {3.4466135740952*^9, 3.4466135794927998`*^9}, { 3.4466137283948*^9, 3.4466137341356*^9}, {3.4466138994342003`*^9, 3.4466139023826*^9}, {3.4466139549858*^9, 3.4466139579653997`*^9}, { 3.4466142109818*^9, 3.4466142245226*^9}, {3.4466142793878*^9, 3.4466143652033997`*^9}, {3.4466144712834*^9, 3.4466145978929996`*^9}, { 3.4466146992618*^9, 3.4466147509914*^9}, {3.4466151283086*^9, 3.4466152768986*^9}, {3.4466153107506*^9, 3.4466153406558*^9}, { 3.4466194331976*^9, 3.4466194377528*^9}, {3.4466194847712*^9, 3.446619488718*^9}, {3.4466389495861998`*^9, 3.4466389768238*^9}, { 3.4466391218414*^9, 3.446639306561*^9}, {3.4466393990222*^9, 3.4466394004886*^9}, {3.4466394475694*^9, 3.4466394487706003`*^9}, { 3.4466395034174*^9, 3.4466395049462*^9}, 3.4466395515755997`*^9, { 3.4466396000176*^9, 3.4466396190808*^9}, {3.4466397459088*^9, 3.446639748826*^9}, {3.4466397974356003`*^9, 3.446639798668*^9}, 3.4466398447816*^9, {3.446639894218*^9, 3.4466399201556*^9}, { 3.4466399570964003`*^9, 3.4466399583288*^9}, {3.446639994006*^9, 3.4466400056904*^9}, {3.4466400383568*^9, 3.4466400395892*^9}, { 3.4466400745643997`*^9, 3.4466401025976*^9}, {3.4466401660834*^9, 3.4466401806070004`*^9}, {3.4466402251294003`*^9, 3.446640227407*^9}, { 3.446640260479*^9, 3.4466402657674*^9}, {3.4466404133122*^9, 3.4466405185654*^9}, 3.4466405830462*^9, {3.4467273294214*^9, 3.4467273777813997`*^9}, {3.4467274366558*^9, 3.4467275620954*^9}, { 3.446727593311*^9, 3.4467277412614*^9}, {3.4467283334639997`*^9, 3.4467283356012*^9}, {3.4467283707636003`*^9, 3.4467283727604*^9}, { 3.4467289882664003`*^9, 3.4467291276836*^9}, {3.446778464322*^9, 3.4467786797424*^9}, {3.4467801953803997`*^9, 3.4467802409792*^9}, { 3.4467802998691998`*^9, 3.4467804023456*^9}, 3.4467804345596*^9, { 3.4467808656344*^9, 3.4467808670852003`*^9}, 3.4467818107525997`*^9, { 3.446781855509*^9, 3.446781874385*^9}, {3.4467826737914*^9, 3.4467827381726*^9}, {3.4467828623018*^9, 3.4467831045386*^9}, { 3.4470344113984003`*^9, 3.4470344123344*^9}, {3.4470344628316*^9, 3.4470345343108*^9}, {3.447043591118539*^9, 3.447043642192939*^9}, { 3.447045649625739*^9, 3.447045718437339*^9}, {3.447054774023939*^9, 3.447054834198939*^9}, {3.4470549103449388`*^9, 3.4470549116169386`*^9}, { 3.447054943902939*^9, 3.4470553027109385`*^9}, {3.447055334559939*^9, 3.447055353684939*^9}, {3.447057311918539*^9, 3.447057369747739*^9}, { 3.4470575058577385`*^9, 3.4470575951365385`*^9}, {3.4470581848789387`*^9, 3.4470582040825386`*^9}, {3.451276121243*^9, 3.4512761425838003`*^9}, { 3.4512762022382*^9, 3.4512762064346*^9}, {3.4512762476966*^9, 3.4512762827654*^9}, {3.451276489091*^9, 3.451276541975*^9}, { 3.4512765853118*^9, 3.4512766132046003`*^9}, {3.4512773470306*^9, 3.4512773766082*^9}, {3.4512776069110003`*^9, 3.4512777499318*^9}, 3.4512777831286*^9, {3.4512778785538*^9, 3.451277881627*^9}, { 3.4512780242734003`*^9, 3.4512780302794*^9}, 3.4512780737878*^9, { 3.4512781866226*^9, 3.4512781930810003`*^9}, {3.4512863325078*^9, 3.4512863539266*^9}, {3.4568019250434*^9, 3.4568022712698*^9}, { 3.4568023177422*^9, 3.4568024125278*^9}, {3.4568024694365997`*^9, 3.4568024750369997`*^9}, {3.4568026914402*^9, 3.4568028101094*^9}, { 3.4568028406698*^9, 3.4568028564726*^9}, 3.4568028886085997`*^9, { 3.4568030489454*^9, 3.4568030800986*^9}, 3.4568032004128*^9, { 3.4568035073698*^9, 3.4568035176034*^9}, {3.4568040146596003`*^9, 3.4568040844852*^9}, {3.4568043016684*^9, 3.4568043154744*^9}, { 3.4568045482264*^9, 3.4568045486632*^9}, {3.4568048944996*^9, 3.4568049806116*^9}, {3.4660560628582*^9, 3.4660560753538*^9}, { 3.4660676729379997`*^9, 3.4660676735931997`*^9}, {3.4660677244024*^9, 3.4660677277251997`*^9}, {3.4742646771287394`*^9, 3.47426469439174*^9}, { 3.47426489921974*^9, 3.4742649800437393`*^9}, {3.4801246373348*^9, 3.4801246860536003`*^9}, {3.4801247748176003`*^9, 3.4801247821028*^9}, { 3.4801248161264*^9, 3.4801248295736*^9}, {3.4801248810692*^9, 3.4801248964508*^9}, {3.4801249330484*^9, 3.480124947884*^9}, 3.4801249886468*^9, {3.4801251139147997`*^9, 3.48012512588*^9}, { 3.4838339444988003`*^9, 3.4838339567448*^9}, 3.4838341692012*^9, { 3.4838344350408*^9, 3.4838344353684*^9}, {3.4938987575920324`*^9, 3.4938987586840324`*^9}, {3.4941630624049997`*^9, 3.4941631381274*^9}, { 3.4941632311345997`*^9, 3.4941632492306004`*^9}, 3.4941633249217997`*^9, { 3.4941633940922003`*^9, 3.4941634063538*^9}, {3.4941634538402*^9, 3.4941635051642*^9}, {3.494163565115*^9, 3.4941636341762*^9}, { 3.4941636853442*^9, 3.4941639323234*^9}, {3.4941640277798*^9, 3.4941641455754004`*^9}, {3.4941641790374002`*^9, 3.4941641803789997`*^9}, {3.4941642676142*^9, 3.4941643277678003`*^9}, 3.4941644677018003`*^9, {3.4941646208938*^9, 3.4941646322349997`*^9}, { 3.4941652592693996`*^9, 3.4941652807194*^9}, {3.4941653119038*^9, 3.494165416299*^9}, {3.494165453895*^9, 3.4941654544722*^9}, { 3.4950990979779997`*^9, 3.495099142701*^9}, {3.495099172958*^9, 3.4950991806289997`*^9}, {3.495099227097*^9, 3.495099238113*^9}, 3.495099290797*^9, {3.495099346084*^9, 3.495099359507*^9}, { 3.495099456308*^9, 3.495099464091*^9}, 3.495099683108*^9, { 3.495100428112*^9, 3.495100434958*^9}, {3.4951006496219997`*^9, 3.495100649992*^9}, {3.4987235265018*^9, 3.4987235939094*^9}, { 3.4987236420666*^9, 3.4987236530646*^9}, {3.4987237305341997`*^9, 3.4987237396914*^9}, {3.498733136159*^9, 3.4987332972446003`*^9}, { 3.4987364783094*^9, 3.4987364860626*^9}, {3.4987366201134*^9, 3.4987366236078*^9}, {3.4987367272386*^9, 3.4987367464890003`*^9}, { 3.4987369428462*^9, 3.4987369670886*^9}, {3.4987370134518003`*^9, 3.4987370259941998`*^9}, {3.4987370944002*^9, 3.4987371027618*^9}, { 3.4987371921029997`*^9, 3.498737193663*^9}, {3.4987372660938*^9, 3.4987372935498*^9}, {3.4987373290554*^9, 3.4987377176202*^9}, { 3.4987377520182*^9, 3.4987379139462*^9}, {3.4987382030216*^9, 3.4987382667078*^9}, {3.4987888391818*^9, 3.4987888608346*^9}, { 3.4988785131146*^9, 3.4988785160162*^9}, {3.5007170967096*^9, 3.5007170999076*^9}, 3.5007182237316*^9, {3.5007182772864*^9, 3.5007182987832003`*^9}, {3.5009573226744003`*^9, 3.5009573940444*^9}, 3.5009574358710003`*^9, 3.5009604278482*^9, {3.5009897246173353`*^9, 3.5009898480289354`*^9}, {3.5009901464413357`*^9, 3.5009901475333357`*^9}, {3.5009901801997356`*^9, 3.500990274096135*^9}, { 3.5010475253292*^9, 3.5010475852332*^9}, {3.5010605722018003`*^9, 3.5010606739762*^9}, {3.5010607202146*^9, 3.5010607323358*^9}, { 3.5010607920526*^9, 3.501061118467*^9}, {3.5010612022078*^9, 3.5010612277138*^9}, {3.5010616467766*^9, 3.5010617938534*^9}, { 3.5010618406222*^9, 3.5010619950778*^9}, {3.5010621500638*^9, 3.5010622514014*^9}, {3.5010625292218*^9, 3.5010625409374*^9}, { 3.5010626043046*^9, 3.5010626313862*^9}, {3.5010626787166*^9, 3.5010626790754004`*^9}, {3.501074457561*^9, 3.5010744671082*^9}, 3.5010763029458*^9, {3.5032210899309998`*^9, 3.5032212413900003`*^9}, { 3.557658203404973*^9, 3.557658219644601*^9}, {3.5576584433801947`*^9, 3.557658496030287*^9}, {3.5576585501779823`*^9, 3.5576586046064777`*^9}, { 3.557658648910555*^9, 3.557658754600741*^9}, {3.557658963945511*^9, 3.5576589782507353`*^9}, {3.557659009949991*^9, 3.5576591437514267`*^9}, { 3.557659182221094*^9, 3.5576592187719584`*^9}, 3.557659413865901*^9, { 3.557659921100792*^9, 3.5576599556392527`*^9}, {3.557660706920972*^9, 3.5576607248454037`*^9}, {3.557661209085854*^9, 3.557661209413454*^9}, { 3.5577526651911488`*^9, 3.5577526932087984`*^9}, {3.5577527272480583`*^9, 3.557752747122493*^9}, {3.5577528374934516`*^9, 3.557752838523053*^9}, { 3.557752881204728*^9, 3.557752891313546*^9}, {3.557752938612829*^9, 3.5577529469120436`*^9}, {3.557753060714244*^9, 3.557753062633047*^9}, { 3.5577536609544907`*^9, 3.5577536637936954`*^9}, {3.5577537824631042`*^9, 3.557753810184353*^9}, {3.557753841025607*^9, 3.5577540648392*^9}, 3.5577541920574236`*^9, {3.5577547033327217`*^9, 3.557754716967146*^9}, { 3.5577547716296415`*^9, 3.557754802112095*^9}, {3.5577549509363565`*^9, 3.5577549771444025`*^9}, 3.5577551382302856`*^9, {3.55775527184452*^9, 3.557755272858522*^9}, {3.557755881555991*^9, 3.557755886548*^9}, { 3.557756158316077*^9, 3.557756231885806*^9}, {3.5577572408487787`*^9, 3.557757248835993*^9}, {3.5577572834368534`*^9, 3.5577575888229895`*^9}, { 3.5577578129641833`*^9, 3.557757862837471*^9}, {3.557758025514557*^9, 3.557758079272251*^9}, 3.557810586960072*^9, {3.5578240262005973`*^9, 3.5578240345360737`*^9}, {3.557824091429328*^9, 3.5578241008156557`*^9}, { 3.557831525255726*^9, 3.5578315319793377`*^9}, 3.5578315716190076`*^9, { 3.557831606079468*^9, 3.557831629432709*^9}, {3.5578316663267736`*^9, 3.5578317569473333`*^9}, {3.5578322144181366`*^9, 3.557832218084143*^9}, { 3.557836356693412*^9, 3.557836473771618*^9}, {3.5578365201660995`*^9, 3.5578365974018345`*^9}, {3.5578366426731143`*^9, 3.557836658865943*^9}, { 3.557836691017599*^9, 3.5578367924957776`*^9}, {3.5578368305442443`*^9, 3.557836888279946*^9}, {3.5578369382156334`*^9, 3.5578370776642785`*^9}, { 3.5578383536061196`*^9, 3.5578383735117545`*^9}, {3.5578385892445335`*^9, 3.5578385978869486`*^9}, {3.5578386713006773`*^9, 3.557838700113928*^9}, { 3.5578387451200075`*^9, 3.5578387467892103`*^9}, {3.5578388951454706`*^9, 3.5578389248635225`*^9}, {3.5578389679351983`*^9, 3.557838983535226*^9}, { 3.5578390227692947`*^9, 3.557839023143696*^9}, {3.557839097696226*^9, 3.5578391125162525`*^9}, {3.5578391553539276`*^9, 3.557839199892006*^9}, { 3.55783924184048*^9, 3.557839294490572*^9}, {3.5578393285922318`*^9, 3.557839398683155*^9}, {3.557839430522811*^9, 3.557839470162481*^9}, { 3.5578395370865984`*^9, 3.5578395446994114`*^9}, {3.5578396068499207`*^9, 3.5578396118575296`*^9}, 3.5578943518105097`*^9, {3.557894388361374*^9, 3.5578944029629993`*^9}, {3.5578944607611012`*^9, 3.5578944989499683`*^9}, {3.5578945393696394`*^9, 3.557894561537278*^9}, { 3.5578946028617506`*^9, 3.5578946188985786`*^9}, {3.557894650894235*^9, 3.5578947812636642`*^9}, {3.55789481884413*^9, 3.5578948191249304`*^9}, { 3.5578949768100076`*^9, 3.5578949836272197`*^9}, {3.5578967386805477`*^9, 3.55789678549623*^9}, {3.5578968804691963`*^9, 3.557896888643611*^9}, { 3.557897022491846*^9, 3.5578970341450663`*^9}, {3.557897620940097*^9, 3.55789765120415*^9}, {3.5579218072271147`*^9, 3.5579218263059483`*^9}, { 3.557922095312821*^9, 3.557922116965659*^9}, {3.557922178086566*^9, 3.557922188616585*^9}, {3.5579223258812256`*^9, 3.557922327066828*^9}, { 3.5579224596046605`*^9, 3.557922461804264*^9}, 3.5579805928465395`*^9, { 3.5579815200581703`*^9, 3.557981541711009*^9}, 3.557985544779242*^9, { 3.5579863164793987`*^9, 3.5579863339514294`*^9}, {3.557986523210962*^9, 3.557986568841042*^9}, 3.5579866122559185`*^9, 3.557986993536188*^9, { 3.5579871244716187`*^9, 3.5579871290580263`*^9}, 3.557987173486905*^9, 3.5579872166989803`*^9, {3.5599618621582537`*^9, 3.5599618642486577`*^9}, { 3.559961969720443*^9, 3.5599619894700775`*^9}, 3.559963611089726*^9, { 3.5601298891258235`*^9, 3.560129889422224*^9}, {3.560132445157113*^9, 3.5601324458591146`*^9}, {3.561978472080926*^9, 3.561978472392926*^9}, { 3.6297802564412937`*^9, 3.6297802957377625`*^9}, {3.62978033369263*^9, 3.629780429741998*^9}, {3.6297805790030603`*^9, 3.6297809429048996`*^9}, { 3.629780987957779*^9, 3.629781197575347*^9}, {3.629781240397422*^9, 3.629781337663593*^9}, {3.6297813946972933`*^9, 3.6297814529165955`*^9}, { 3.6297814952550697`*^9, 3.629781527578326*^9}, {3.62978162025529*^9, 3.629781647633338*^9}, {3.629781678833393*^9, 3.629781763120341*^9}, 3.6297818028224106`*^9, {3.6297818432108817`*^9, 3.629781872570133*^9}, { 3.629782355765382*^9, 3.629782427603508*^9}, {3.6297824692243814`*^9, 3.629782674863942*^9}, {3.629782707218399*^9, 3.6297829295343895`*^9}, { 3.629783005631323*^9, 3.6297830574702144`*^9}, {3.6297831098551064`*^9, 3.629783142786764*^9}, {3.629783433711675*^9, 3.629783442619291*^9}, { 3.6297834942397814`*^9, 3.6297835175930223`*^9}, 3.6297835794939313`*^9, { 3.6297836160291953`*^9, 3.6297837668970604`*^9}, {3.6297842042438283`*^9, 3.6297842697483435`*^9}, {3.6297843514456873`*^9, 3.629784370742921*^9}, { 3.629784443829049*^9, 3.6297844678842916`*^9}, {3.6297845252611923`*^9, 3.629784525588793*^9}, {3.6297846136821475`*^9, 3.629784629235375*^9}, { 3.629784814797701*^9, 3.629784927648299*^9}, {3.629785259960083*^9, 3.6297852602096834`*^9}, {3.6297858780175686`*^9, 3.629785917282837*^9}, { 3.629786048057867*^9, 3.629786048681868*^9}, 3.6297863278755584`*^9, { 3.6297867047133856`*^9, 3.629786748533863*^9}, {3.6297867791567163`*^9, 3.6297868491540394`*^9}, {3.6297875320748396`*^9, 3.629787569795706*^9}, { 3.6297876247234025`*^9, 3.6297877281983843`*^9}, {3.6297877681812544`*^9, 3.629787774015665*^9}, {3.629787831408166*^9, 3.6297878355265727`*^9}, { 3.6297878775686464`*^9, 3.6297878861174617`*^9}, {3.6297879185343184`*^9, 3.629787919064719*^9}, {3.6297880043032694`*^9, 3.62978800470887*^9}, 3.6297880488257475`*^9, {3.6297882100052304`*^9, 3.6297882174776435`*^9}, { 3.6297882697533355`*^9, 3.6297882948381796`*^9}, {3.6297883467550707`*^9, 3.6297883991087627`*^9}, {3.6297887361785545`*^9, 3.629788783961438*^9}, 3.629788825395111*^9, {3.629789006152629*^9, 3.6297890321266747`*^9}, { 3.6297891133248167`*^9, 3.629789145336073*^9}, {3.6297891926821566`*^9, 3.629789194257759*^9}, {3.629789255316266*^9, 3.6297892556282673`*^9}, { 3.629869102295367*^9, 3.629869160124668*^9}, {3.6298691942887287`*^9, 3.6298696149902673`*^9}, {3.6298696993864155`*^9, 3.62986975897852*^9}, { 3.6298698387726603`*^9, 3.629869912030389*^9}, {3.6298700722270703`*^9, 3.629870234560955*^9}, {3.629870580429163*^9, 3.629870630458451*^9}, { 3.630556081081209*^9, 3.630556104902451*^9}, {3.6305562643503313`*^9, 3.6305562763935523`*^9}, {3.6305563415080667`*^9, 3.630556480956712*^9}, { 3.630556692851884*^9, 3.630556695347888*^9}, {3.630556730042349*^9, 3.630556914528273*^9}, {3.6305653725974936`*^9, 3.6305656807121167`*^9}, { 3.630565758760581*^9, 3.6305657739024467`*^9}, {3.630565858170267*^9, 3.63056596644846*^9}, {3.6305661502619734`*^9, 3.6305661523230915`*^9}, { 3.6305662653385553`*^9, 3.630566370352562*^9}, {3.6305667786019125`*^9, 3.630566790535595*^9}, {3.6305668214773645`*^9, 3.630567044691132*^9}, { 3.6305670772499943`*^9, 3.6305670783710585`*^9}, 3.630567272031135*^9, { 3.630567303902958*^9, 3.630567409875019*^9}, {3.630568671196477*^9, 3.6305687195002403`*^9}, {3.6305687542132254`*^9, 3.630568758623478*^9}, { 3.630568855671028*^9, 3.630568859250233*^9}, {3.630569706514694*^9, 3.630569775526641*^9}, 3.630569982346471*^9, {3.6305701679130845`*^9, 3.630570205199217*^9}, {3.6305703751399374`*^9, 3.630570526177576*^9}, { 3.630587657039589*^9, 3.630587688367381*^9}, {3.6305880733027773`*^9, 3.6305883365376396`*^9}, {3.6305886689118233`*^9, 3.6305886717978287`*^9}, 3.6305889776831656`*^9, {3.6305890389444733`*^9, 3.6305890437180815`*^9}, { 3.630589093248169*^9, 3.6305891296430326`*^9}, 3.630589181700324*^9, { 3.6305892509956455`*^9, 3.6305892594820604`*^9}, {3.630589318949365*^9, 3.6305893334729905`*^9}, {3.630589630294712*^9, 3.6305896376267247`*^9}, { 3.630589683288005*^9, 3.630589684988408*^9}, {3.630597310538067*^9, 3.630597340080757*^9}, {3.630597391446695*^9, 3.630597400596218*^9}, { 3.6305974350611897`*^9, 3.6305974605306463`*^9}, {3.630633997622449*^9, 3.630634003125764*^9}, {3.630659322217756*^9, 3.63065932438616*^9}, { 3.6306611578252783`*^9, 3.6306611625988865`*^9}, {3.6306612541554475`*^9, 3.630661257587454*^9}, {3.6306613001287284`*^9, 3.6306613026715326`*^9}, { 3.6306613920752897`*^9, 3.6306613949768953`*^9}, {3.6306706377509866`*^9, 3.630670654957817*^9}, {3.6306749981919994`*^9, 3.630675005793434*^9}, { 3.6306751229631357`*^9, 3.630675150017683*^9}, {3.6306752035287437`*^9, 3.6306752096180925`*^9}, {3.630675315921172*^9, 3.6306753201514144`*^9}, { 3.6306757793287754`*^9, 3.6306757796257925`*^9}, {3.630675814406262*^9, 3.6306758147026625`*^9}, {3.6306760107574763`*^9, 3.6306760154417443`*^9}, {3.6306789722320743`*^9, 3.6306789870309205`*^9}, {3.6306790257051325`*^9, 3.630679028076268*^9}, { 3.6306800259177256`*^9, 3.6306800406129513`*^9}, {3.6306801239326982`*^9, 3.6306801300167084`*^9}, {3.630680769261832*^9, 3.6306807806186523`*^9}, { 3.630681157468514*^9, 3.6306811577649145`*^9}, {3.6306812744219193`*^9, 3.63068127471832*^9}, {3.6306817187418995`*^9, 3.6306817919060287`*^9}, { 3.630681879188182*^9, 3.6306819111526375`*^9}, {3.6306821191790032`*^9, 3.6306821283050194`*^9}, {3.630720543651497*^9, 3.6307205534300566`*^9}, { 3.630721035525631*^9, 3.630721092774905*^9}, {3.6307212510439577`*^9, 3.6307213064777765`*^9}, {3.6307477437169704`*^9, 3.6307478284095197`*^9}, {3.6307478614971776`*^9, 3.6307478785948076`*^9}, {3.6307479884814005`*^9, 3.630748002880226*^9}, { 3.630748045624301*^9, 3.630748063876333*^9}, {3.630748111596817*^9, 3.6307481498324842`*^9}, {3.6307489182430334`*^9, 3.6307489447786803`*^9}, {3.630749037427243*^9, 3.6307490443848553`*^9}, { 3.6307491041485605`*^9, 3.6307491384218206`*^9}, {3.6307491914151134`*^9, 3.630749196890723*^9}, {3.6307492445800066`*^9, 3.6307493439989815`*^9}, { 3.630749396212273*^9, 3.6307494766304145`*^9}, {3.6307495333989143`*^9, 3.6307495547241516`*^9}, {3.6307496525831237`*^9, 3.630749669571553*^9}, { 3.630750220602922*^9, 3.6307502881822405`*^9}, {3.6307510631916018`*^9, 3.630751068292811*^9}, {3.6307511226589065`*^9, 3.630751137962533*^9}, { 3.6307512555243397`*^9, 3.630751282777588*^9}, {3.630752266971757*^9, 3.630752414599744*^9}, {3.630752446407563*^9, 3.630752457388191*^9}, { 3.6307589380050273`*^9, 3.6307590266300964`*^9}, {3.6307591666721067`*^9, 3.63075923229886*^9}, 3.630760288282259*^9, {3.6307603547370596`*^9, 3.630760557414652*^9}, {3.630760654134184*^9, 3.63076065510824*^9}, { 3.6307606911683025`*^9, 3.6307606919283457`*^9}, {3.6307607642334814`*^9, 3.6307607648645177`*^9}, {3.630761455000991*^9, 3.6307614616743727`*^9}, { 3.630761507825012*^9, 3.630761605776615*^9}, {3.630761652999316*^9, 3.630761695865768*^9}, {3.630761771278081*^9, 3.6307617792215357`*^9}, 3.6307629478424797`*^9, {3.632205207880766*^9, 3.6322052561155243`*^9}, { 3.6322052892474194`*^9, 3.6322052915745525`*^9}, 3.6322053746993074`*^9, { 3.6322062705415463`*^9, 3.6322062726016645`*^9}, {3.6322063396935015`*^9, 3.63220636484194*^9}, {3.6322064410612993`*^9, 3.6322064491667633`*^9}, { 3.632206580308264*^9, 3.6322066373275256`*^9}, {3.6322066736436024`*^9, 3.6322067467737856`*^9}, {3.632206782260815*^9, 3.6322071351279984`*^9}, 3.6322071989226465`*^9, {3.632207270393735*^9, 3.6322073359894867`*^9}, { 3.6322073997741346`*^9, 3.6322074126708727`*^9}, {3.632207491777397*^9, 3.632207682289294*^9}, {3.632207809621577*^9, 3.632207827973626*^9}, { 3.6322079043859973`*^9, 3.6322079279443445`*^9}, {3.6322080916397076`*^9, 3.6322081666649985`*^9}, 3.634905258940913*^9, {3.634905370524296*^9, 3.6349054089004903`*^9}, {3.6349054472556844`*^9, 3.63490544787272*^9}, { 3.634905483492757*^9, 3.6349055164646425`*^9}, {3.634905574352954*^9, 3.634905628121029*^9}, {3.6349057012822137`*^9, 3.6349057207913294`*^9}, { 3.6349061371061416`*^9, 3.634906354438572*^9}, {3.6349063890455513`*^9, 3.6349064369332905`*^9}, {3.634906537696054*^9, 3.634906601859724*^9}, 3.634906706128688*^9, {3.6349069249442034`*^9, 3.6349069328326545`*^9}, { 3.6349070151973653`*^9, 3.6349070242298822`*^9}, {3.6349070817921743`*^9, 3.6349070822111983`*^9}, {3.634907723288866*^9, 3.634907739005765*^9}, { 3.6349079580732946`*^9, 3.6349079868219395`*^9}, {3.634908200284148*^9, 3.634908315195721*^9}, {3.6349083774582825`*^9, 3.6349084027997313`*^9}, { 3.63490844507615*^9, 3.634908448843365*^9}, {3.634914956333157*^9, 3.634915020054802*^9}, {3.634915050572547*^9, 3.6349150956171236`*^9}, { 3.6349539785771523`*^9, 3.634953978975175*^9}, {3.6349540728785458`*^9, 3.6349541681829967`*^9}, {3.634954211263461*^9, 3.6349542495746527`*^9}, { 3.6349543251259737`*^9, 3.634954355882733*^9}, {3.6349543892536416`*^9, 3.6349544742835045`*^9}, {3.634954547519694*^9, 3.6349545640246377`*^9}, { 3.6349547051657104`*^9, 3.6349547107930326`*^9}, {3.634954745355009*^9, 3.634954752101395*^9}, {3.6349547948858423`*^9, 3.6349548053894434`*^9}, { 3.634954904907135*^9, 3.6349549451084347`*^9}, {3.634955219605135*^9, 3.6349552640926795`*^9}, {3.634955320189888*^9, 3.634955348763522*^9}, { 3.634955386393675*^9, 3.6349555039273973`*^9}, {3.6349557669644423`*^9, 3.6349557672004557`*^9}, {3.634955894841756*^9, 3.634955902578199*^9}, { 3.6349559513739896`*^9, 3.6349560216320086`*^9}, {3.634956120144643*^9, 3.634956128996149*^9}, {3.6349561700724983`*^9, 3.6349561978900895`*^9}, { 3.6349562480719595`*^9, 3.634956254326318*^9}, {3.634956331684742*^9, 3.6349563460575643`*^9}, {3.634956379242462*^9, 3.63495642676418*^9}, 3.6349564696636343`*^9, {3.6351524116477795`*^9, 3.6351524153379908`*^9}, { 3.6352134400282927`*^9, 3.635213442148414*^9}, {3.6352134745862694`*^9, 3.635213495869487*^9}, {3.6352135383409157`*^9, 3.6352137157160616`*^9}, { 3.6352137493569856`*^9, 3.635213764522853*^9}, {3.635214215036621*^9, 3.635214227593339*^9}, {3.635214407257615*^9, 3.63521441713218*^9}, { 3.635215297101512*^9, 3.635215303964904*^9}, {3.6352154111120324`*^9, 3.635215431504199*^9}, {3.635216346055508*^9, 3.635216494371991*^9}, { 3.635216631050809*^9, 3.6352166603244834`*^9}, {3.635216763034358*^9, 3.635216764164423*^9}, {3.6352168771938877`*^9, 3.635216888828553*^9}, 3.6352169832479534`*^9, 3.635217037668066*^9, {3.6352172024924936`*^9, 3.6352172054526625`*^9}, {3.635217344025589*^9, 3.635217346898753*^9}, 3.6352173863770113`*^9, {3.635217519639633*^9, 3.6352175507014103`*^9}, 3.635217615445113*^9, {3.6352178715087595`*^9, 3.635217880460271*^9}, { 3.6352185912849283`*^9, 3.635218598444338*^9}, {3.6352186995721216`*^9, 3.635218714955002*^9}, {3.6352189761749425`*^9, 3.6352189789341*^9}, { 3.6352195060322485`*^9, 3.635219509972474*^9}, 3.6352195673477554`*^9, 3.6352195994635925`*^9, {3.6352197336482677`*^9, 3.635219737452485*^9}, { 3.6352197706093817`*^9, 3.6352197723214793`*^9}, {3.635219941784172*^9, 3.6352199485115566`*^9}, {3.6352200714185867`*^9, 3.6352200854323883`*^9}, {3.6352202085694313`*^9, 3.635220235849992*^9}, { 3.6352202816336107`*^9, 3.6352203110962954`*^9}, {3.6352204980449886`*^9, 3.6352205276526823`*^9}, {3.6352253191447396`*^9, 3.6352253299913597`*^9}, {3.6352253611111403`*^9, 3.6352253637572913`*^9}, {3.635225409322898*^9, 3.6352255965196047`*^9}, { 3.6352260914249115`*^9, 3.6352261698393965`*^9}, {3.63522638233055*^9, 3.6352264188036366`*^9}, {3.635227493469104*^9, 3.635227556935734*^9}, { 3.6352276745764627`*^9, 3.635227730116639*^9}, {3.6352287979917183`*^9, 3.6352288587651944`*^9}, {3.635228894237223*^9, 3.635228948324317*^9}, { 3.635229365252164*^9, 3.6352293902275925`*^9}, {3.63522947690555*^9, 3.6352294807837715`*^9}, {3.6352492831123204`*^9, 3.6352492983621926`*^9}, 3.6356569054520617`*^9, {3.6363778004499054`*^9, 3.636377802787039*^9}, { 3.6363778414932528`*^9, 3.6363778525308843`*^9}, {3.636384436335312*^9, 3.6363846409950175`*^9}, {3.636384971250907*^9, 3.6363849738080535`*^9}, { 3.6363850170465264`*^9, 3.636385030729309*^9}, {3.6363851286779118`*^9, 3.636385138359465*^9}, {3.6363851699712734`*^9, 3.636385223111313*^9}, { 3.656076172452749*^9, 3.656076182171566*^9}, {3.6560765578514256`*^9, 3.656076619019133*^9}, 3.6560772545486493`*^9, {3.6630719749029694`*^9, 3.6630719878027077`*^9}, {3.6630720702554235`*^9, 3.6630720807290225`*^9}, {3.6630721155740156`*^9, 3.6630721713712068`*^9}, {3.663072270834896*^9, 3.6630722882218904`*^9}, 3.6630724099968557`*^9, {3.685234767958906*^9, 3.685234768480936*^9}, { 3.685252204033695*^9, 3.6852522340537376`*^9}, {3.6852522757137957`*^9, 3.6852523115138454`*^9}, {3.68525376314359*^9, 3.6852537725041256`*^9}, { 3.6852539763277836`*^9, 3.6852539861693463`*^9}, 3.6852540682470407`*^9, 3.6852541660656357`*^9, {3.6852604801645336`*^9, 3.6852605060345697`*^9}, { 3.6852605373446136`*^9, 3.6852605977846985`*^9}, 3.685260655254779*^9, { 3.6853280002218475`*^9, 3.685328019561875*^9}, 3.685328064721938*^9, { 3.6853280953119807`*^9, 3.6853282636022167`*^9}, {3.685328356242346*^9, 3.685328598671985*^9}, {3.6853286682069626`*^9, 3.6853287982524004`*^9}, { 3.6853288753368096`*^9, 3.6853289367033195`*^9}, {3.685328968274125*^9, 3.685328978713722*^9}, {3.685329033941881*^9, 3.685329044950511*^9}, { 3.685329173522865*^9, 3.6853294420842257`*^9}, {3.6853296024223967`*^9, 3.6853296124319687`*^9}, {3.6853297221712456`*^9, 3.685329733349885*^9}, { 3.6853298076291337`*^9, 3.6853298739599276`*^9}, {3.685330038474337*^9, 3.685330051652091*^9}, {3.6853311309428225`*^9, 3.685331168378964*^9}, { 3.685340142134763*^9, 3.685340180544817*^9}, {3.6853583292043543`*^9, 3.685358334834362*^9}, {3.685358366084406*^9, 3.685358366954407*^9}, { 3.685358408404465*^9, 3.685358518294619*^9}, 3.685358620174762*^9, 3.6853586578748145`*^9, {3.6853588750151186`*^9, 3.6853588857151337`*^9}, { 3.6853589302051954`*^9, 3.685358938995208*^9}, {3.685359014715314*^9, 3.6853590296653347`*^9}, 3.685359148315501*^9, 3.6853598281764526`*^9, { 3.6853683109000263`*^9, 3.685368382250126*^9}, {3.685368420160179*^9, 3.6853684704302497`*^9}, {3.6853685194503183`*^9, 3.685368742860631*^9}, { 3.685369008901004*^9, 3.68536902061102*^9}, {3.6853690791611023`*^9, 3.685369132301176*^9}, {3.6853693219914417`*^9, 3.6853693304114532`*^9}, 3.6853696089118433`*^9, {3.6858758911429157`*^9, 3.685875951793*^9}, { 3.6859484099082212`*^9, 3.6859484970032024`*^9}, {3.686052829875022*^9, 3.686052906242383*^9}, {3.6860535326822133`*^9, 3.686053598029951*^9}, { 3.68605365168902*^9, 3.6860541446091995`*^9}, {3.6860541846064873`*^9, 3.68605440393201*^9}, {3.686054713802734*^9, 3.6860547858298535`*^9}, { 3.6860548280202665`*^9, 3.686054837219793*^9}, {3.686054874127904*^9, 3.686054892139934*^9}, {3.686055136014883*^9, 3.6860551460584574`*^9}, { 3.686055211281188*^9, 3.6860552301962633`*^9}, {3.6860553465409174`*^9, 3.6860553998749685`*^9}, {3.6860556017188663`*^9, 3.6860556050188704`*^9}, {3.6862923512707715`*^9, 3.686292363600789*^9}, { 3.686292409650853*^9, 3.6862924109708548`*^9}, {3.6862924536109147`*^9, 3.6862924596309233`*^9}, {3.686292542221039*^9, 3.6862925430110397`*^9}, { 3.686292988803664*^9, 3.686293001033681*^9}, {3.6866504529025555`*^9, 3.686650526682659*^9}, {3.686650671852862*^9, 3.6866507242929354`*^9}, { 3.6866507657529936`*^9, 3.6866507887630253`*^9}, {3.6866508208230705`*^9, 3.6866509100531955`*^9}, {3.6866509593932643`*^9, 3.686650971113281*^9}, { 3.686651007793332*^9, 3.6866511595335445`*^9}, {3.686651223513634*^9, 3.686651234033649*^9}, {3.686651304763748*^9, 3.6866513363837924`*^9}, { 3.6866514102038956`*^9, 3.686651429943923*^9}, {3.686652993837468*^9, 3.6866530046274834`*^9}, {3.686804398511652*^9, 3.6868044081516657`*^9}, { 3.6868046315619783`*^9, 3.686804631801979*^9}, {3.686804685872054*^9, 3.686804707092084*^9}, {3.6868047382021275`*^9, 3.686804767812169*^9}, { 3.686804824012248*^9, 3.6868048404922705`*^9}, {3.686804942142413*^9, 3.6868049633424425`*^9}, {3.6868050765526013`*^9, 3.686805101092636*^9}, { 3.6868051463526993`*^9, 3.6868052234228067`*^9}, {3.686805307602925*^9, 3.686805311682931*^9}, {3.68680577547358*^9, 3.686805788923599*^9}, { 3.686821702197342*^9, 3.6868217282873783`*^9}, {3.6868225192884855`*^9, 3.686822538368512*^9}, {3.6868226306886415`*^9, 3.6868226683086944`*^9}, { 3.6868227318887835`*^9, 3.6868227627088265`*^9}, {3.686822801638881*^9, 3.6868230490692277`*^9}, {3.686823122979331*^9, 3.6868231833294153`*^9}, { 3.6868232450595016`*^9, 3.6868233753996844`*^9}, {3.6868234153897405`*^9, 3.686823451379791*^9}, {3.6868236736101017`*^9, 3.6868236786601086`*^9}, { 3.6868237164601617`*^9, 3.68682375072021*^9}, {3.68682389396041*^9, 3.68682390087042*^9}, {3.686823940790476*^9, 3.6868239416904774`*^9}, { 3.6868239808805323`*^9, 3.6868239872905407`*^9}, {3.686824051540631*^9, 3.6868240519006314`*^9}, {3.686824360861064*^9, 3.6868243761510854`*^9}, { 3.6868245440213203`*^9, 3.686824577221367*^9}, {3.686824685841519*^9, 3.6868246979115357`*^9}, 3.6868248012716804`*^9, 3.6868253582724605`*^9, { 3.6868255183026843`*^9, 3.686825518932685*^9}, {3.6868264466639843`*^9, 3.6868264497139883`*^9}, {3.6868267792744493`*^9, 3.6868268152945004`*^9}, {3.686827100164899*^9, 3.6868271210549283`*^9}, 3.686827162004986*^9, {3.6868272414950967`*^9, 3.686827327475217*^9}, { 3.686827953126093*^9, 3.686827976506126*^9}, {3.686829128577739*^9, 3.686829138957753*^9}, 3.6868292410978966`*^9, {3.6868292768379464`*^9, 3.686829282727955*^9}, {3.6868293820380936`*^9, 3.686829418138144*^9}, { 3.686829846748744*^9, 3.686829848298746*^9}, {3.6868313063207874`*^9, 3.686831307180789*^9}, {3.6868331276633377`*^9, 3.68683328653356*^9}, { 3.6868394697195063`*^9, 3.6868394933895392`*^9}, 3.686839530999592*^9, { 3.686839582829664*^9, 3.68683963686974*^9}, {3.6868397551199055`*^9, 3.68683979365996*^9}, {3.6868398344600167`*^9, 3.686839866200061*^9}, { 3.687092084401948*^9, 3.687092117031994*^9}, {3.6870922598621936`*^9, 3.6870922645422*^9}, {3.6870962086478376`*^9, 3.6870962658779182`*^9}, 3.687096444838168*^9, {3.687096500978247*^9, 3.687096501638248*^9}, { 3.6870965809883595`*^9, 3.687096592708376*^9}, 3.687096837948719*^9, { 3.68709688890879*^9, 3.687096985798926*^9}, {3.6870971015990877`*^9, 3.6870972179192505`*^9}, {3.6870972618993125`*^9, 3.687097305639374*^9}, { 3.6870973356794157`*^9, 3.6870975186496716`*^9}, {3.6870975796097574`*^9, 3.6870975953197794`*^9}, {3.6870976531898603`*^9, 3.6870976848899045`*^9}, 3.6870977782500353`*^9, {3.687413757687042*^9, 3.6874137834070783`*^9}, { 3.6874140542074575`*^9, 3.687414094417514*^9}, {3.6874143478878684`*^9, 3.687414485538061*^9}, {3.6874146116082373`*^9, 3.68741464894829*^9}, { 3.6874147451084247`*^9, 3.687414766118454*^9}, 3.6874149094486547`*^9, { 3.6874150416688395`*^9, 3.6874150634888706`*^9}, {3.6874152437091227`*^9, 3.687415268869158*^9}, 3.6874153442892637`*^9, {3.687415449879411*^9, 3.687415469659439*^9}, 3.687415529739523*^9, 3.687415564789572*^9, 3.687415645529685*^9, {3.6874168016913037`*^9, 3.687416803441306*^9}, { 3.687421022677213*^9, 3.6874212686075573`*^9}, {3.68742948209425*^9, 3.6874294906842623`*^9}, {3.687844340668378*^9, 3.6878443698084188`*^9}, { 3.6886534778571014`*^9, 3.6886534911571198`*^9}, {3.688906380162199*^9, 3.6889064680223217`*^9}, {3.688906514222396*^9, 3.6889065193925257`*^9}, { 3.688908192623024*^9, 3.6889082006430354`*^9}, {3.688908261823121*^9, 3.688908271653135*^9}, {3.6889083776232834`*^9, 3.6889083922733035`*^9}, { 3.688908466073407*^9, 3.6889084993734536`*^9}, 3.688908533623502*^9, { 3.688908616683618*^9, 3.6889086271336327`*^9}, {3.6889086885637183`*^9, 3.6889087063437433`*^9}, {3.6889091647443852`*^9, 3.6889092012544365`*^9}, {3.6889093019045773`*^9, 3.6889093406746316`*^9}, 3.6889101071957045`*^9, {3.689905940063133*^9, 3.689905972983179*^9}, { 3.692530981927737*^9, 3.6925310416778207`*^9}, {3.692531099797902*^9, 3.6925311384779563`*^9}, {3.692531192258032*^9, 3.692531244668105*^9}, { 3.6925312919881716`*^9, 3.692531425418358*^9}, {3.6925315270885005`*^9, 3.692531643928664*^9}, {3.692535489534048*^9, 3.6925356485142703`*^9}, { 3.692535753564418*^9, 3.6925357992544813`*^9}, {3.6925358831745987`*^9, 3.692535899604622*^9}, {3.692536042584822*^9, 3.692536159384986*^9}, { 3.6925366121156197`*^9, 3.6925366207256317`*^9}, {3.6925367265057793`*^9, 3.69253672683578*^9}, {3.6925368590559654`*^9, 3.6925368636559715`*^9}, { 3.6925370880062857`*^9, 3.692537177856412*^9}, {3.692537322456614*^9, 3.6925373869767046`*^9}, {3.6925390913352747`*^9, 3.6925390925252767`*^9}, {3.692539644430175*^9, 3.6925396711502123`*^9}, { 3.692539727510291*^9, 3.692539730440295*^9}, {3.69253993367058*^9, 3.692539963780622*^9}, {3.6925400018406754`*^9, 3.692540003630678*^9}, { 3.6925401743409166`*^9, 3.6925401747509174`*^9}, {3.692540399111232*^9, 3.692540407981244*^9}, {3.69254047647134*^9, 3.6925404886113567`*^9}, { 3.6925406039715185`*^9, 3.69254060531152*^9}, {3.6925414948727655`*^9, 3.6925414953427663`*^9}, {3.6925415478528395`*^9, 3.692541613062931*^9}, 3.692541649332982*^9, {3.692541727633092*^9, 3.6925418840133104`*^9}, { 3.692541924473367*^9, 3.692542041693531*^9}, {3.6925421488836813`*^9, 3.6925422549438295`*^9}, {3.6925422976938896`*^9, 3.692542521444203*^9}, { 3.6925426221843443`*^9, 3.6925426357343626`*^9}, 3.692542739374508*^9, 3.692599799510878*^9, {3.692599834884901*^9, 3.6925998954663663`*^9}, { 3.692599925635092*^9, 3.6926000095928946`*^9}, {3.692600108929576*^9, 3.6926001456386757`*^9}, {3.6926001874800687`*^9, 3.692600454421337*^9}, { 3.692600503149027*^9, 3.6926006000391626`*^9}, {3.692600680251275*^9, 3.6926006814012766`*^9}, {3.6926009000215826`*^9, 3.6926009410816402`*^9}, 3.692601280532116*^9, {3.6926044914726114`*^9, 3.69260449774262*^9}, 3.6926045660127153`*^9, 3.6926046690228596`*^9, {3.69296647863291*^9, 3.6929664798829117`*^9}, {3.6929665643330297`*^9, 3.6929666141830997`*^9}, {3.6929670390036945`*^9, 3.6929670405536966`*^9}, {3.6929670861037607`*^9, 3.6929670952937737`*^9}, {3.6929671302538223`*^9, 3.6929671549438567`*^9}, {3.6929671904739065`*^9, 3.69296722137395*^9}, { 3.6929672596240034`*^9, 3.6929673352541094`*^9}, 3.6929678909232683`*^9, { 3.6930146982034283`*^9, 3.693014722713463*^9}, {3.6930148540136466`*^9, 3.693014857023651*^9}, {3.6930148913836985`*^9, 3.693014894823704*^9}, { 3.693014930903754*^9, 3.6930151942541227`*^9}, {3.693015247824198*^9, 3.693015430554454*^9}, {3.693015673794794*^9, 3.69301579223496*^9}, { 3.6930163123576884`*^9, 3.693016326897709*^9}, {3.6930164225678425`*^9, 3.693016429727853*^9}, {3.693016686718212*^9, 3.693016698128228*^9}, { 3.693016737038283*^9, 3.693016755068308*^9}, {3.6930168429225607`*^9, 3.6930168719926014`*^9}, {3.6930172049430676`*^9, 3.693017284063178*^9}, { 3.693017336433252*^9, 3.6930173662532935`*^9}, {3.6930180949163136`*^9, 3.6930180975563173`*^9}, {3.6930181870764427`*^9, 3.693018199956461*^9}, { 3.6930182954065943`*^9, 3.693018305996609*^9}, {3.693139886141657*^9, 3.6931399045016823`*^9}, {3.6931402916003532`*^9, 3.693140295770359*^9}, { 3.693140426020541*^9, 3.693140426530542*^9}, {3.6931410492237864`*^9, 3.6931410888738413`*^9}, {3.6931411194438844`*^9, 3.693141126553894*^9}, { 3.693141412004294*^9, 3.693141454164353*^9}, {3.6931415979955544`*^9, 3.6931417931758275`*^9}, {3.6932199559445915`*^9, 3.6932199772046213`*^9}, {3.6932201435748544`*^9, 3.693220170284892*^9}, { 3.693220713855653*^9, 3.693220721825664*^9}, {3.693625124589745*^9, 3.693625153729786*^9}, {3.6940907995669713`*^9, 3.6940909688872085`*^9}, { 3.6940913675677667`*^9, 3.6940914223978434`*^9}, {3.694091508037963*^9, 3.694091572118053*^9}, 3.694092009628666*^9, {3.6940920553287296`*^9, 3.694092229168973*^9}, {3.6940923053990793`*^9, 3.694092374419176*^9}, { 3.6940924537392874`*^9, 3.694092457789293*^9}, 3.694092642849552*^9, { 3.6940928573598523`*^9, 3.694092862379859*^9}, {3.6940945886222763`*^9, 3.694094601932295*^9}, 3.694094849542641*^9, {3.694095764293922*^9, 3.6940957644739223`*^9}, {3.6940960602743363`*^9, 3.6940960732243547`*^9}, {3.6940961211044216`*^9, 3.694096124194426*^9}, { 3.694665030960044*^9, 3.6946650634500895`*^9}, {3.6946652071402903`*^9, 3.6946653490404887`*^9}, {3.6946658702212186`*^9, 3.6946658881212435`*^9}, {3.694665923041292*^9, 3.694665953561335*^9}, { 3.694665995981395*^9, 3.6946660149414215`*^9}, {3.694666050571471*^9, 3.6946660547214766`*^9}, {3.694666169991638*^9, 3.694666292151809*^9}, { 3.6946663456618843`*^9, 3.6946663943919525`*^9}, 3.6946667526224537`*^9, 3.69466680700253*^9, 3.694687076625702*^9, {3.6946874316161985`*^9, 3.6946874621962414`*^9}, 3.694687499496294*^9, {3.694687567516389*^9, 3.694687642816495*^9}, {3.694687679006545*^9, 3.6946877198966026`*^9}, { 3.6946877714966745`*^9, 3.694687931746899*^9}, {3.723798739728607*^9, 3.723798744014243*^9}, {3.7237990126446104`*^9, 3.723799023974499*^9}, { 3.7244116671877546`*^9, 3.7244116733393917`*^9}, {3.724411761793063*^9, 3.7244117718753977`*^9}, {3.724411928386671*^9, 3.7244119682966137`*^9}, { 3.724412131847311*^9, 3.724412188341254*^9}, {3.729414981357122*^9, 3.7294149861075096`*^9}, {3.749817651293678*^9, 3.749817653108206*^9}, { 3.7498176831919456`*^9, 3.7498176846222315`*^9}, 3.7498177601545563`*^9, { 3.749817859674735*^9, 3.749817861044999*^9}, {3.7498179561547127`*^9, 3.749817964489929*^9}, {3.749818149334386*^9, 3.749818237397959*^9}, 3.749818617867873*^9, {3.7505621848002787`*^9, 3.7505622174085107`*^9}, { 3.75056238761455*^9, 3.750562431347901*^9}, {3.7505626332829456`*^9, 3.7505627331565337`*^9}, {3.7505627632642183`*^9, 3.7505627635859113`*^9}, {3.7515359581577415`*^9, 3.7515359614850826`*^9}, {3.751536071974715*^9, 3.7515360961721487`*^9}, 3.7515362040373974`*^9, {3.751536256080162*^9, 3.7515365099108534`*^9}, { 3.751549231137398*^9, 3.7515493334258356`*^9}, {3.7515496891619573`*^9, 3.751549689458767*^9}, {3.763384318028655*^9, 3.763384321230183*^9}, 3.7633844800900145`*^9, {3.7650666220235834`*^9, 3.765066676848461*^9}, { 3.7650667705927696`*^9, 3.765066781277461*^9}, {3.7650668220493402`*^9, 3.7650670769609847`*^9}, {3.765075343296377*^9, 3.765075345014902*^9}, { 3.765075479631569*^9, 3.7650755114191623`*^9}, {3.765075617307859*^9, 3.7650756180851874`*^9}, {3.76507585422694*^9, 3.765075872425325*^9}, { 3.7650760811750383`*^9, 3.7650762635610576`*^9}, {3.7650763100785646`*^9, 3.765076323109063*^9}, {3.7650763765120716`*^9, 3.765076385469493*^9}, { 3.7650764317497897`*^9, 3.7650764864127855`*^9}, 3.765076672990033*^9, { 3.7650767604139767`*^9, 3.7650767965644426`*^9}, {3.765076849411788*^9, 3.76507688334435*^9}, {3.765076928656023*^9, 3.7650769388747053`*^9}, 3.76507697239373*^9, {3.7650770147173185`*^9, 3.7650770820420313`*^9}, { 3.765077138264634*^9, 3.765077175747029*^9}, {3.765077340035742*^9, 3.765077493212038*^9}, {3.7650775254837503`*^9, 3.765077573524544*^9}, { 3.765077619369755*^9, 3.7650776808294816`*^9}, {3.765088266857733*^9, 3.765088281236836*^9}, {3.76508836959641*^9, 3.765088394392946*^9}, { 3.7650900504082956`*^9, 3.765090052695187*^9}, {3.7650900911122713`*^9, 3.765090094160341*^9}, {3.765090519594511*^9, 3.7650905411898503`*^9}, { 3.7885193337832556`*^9, 3.788519339935099*^9}, {3.788519391172593*^9, 3.7885194472501445`*^9}, {3.7885195529105897`*^9, 3.788519558251149*^9}, { 3.7885305232444134`*^9, 3.788530576893549*^9}, 3.788530695024667*^9, { 3.7885307280202837`*^9, 3.788530769626217*^9}, {3.7963483332994423`*^9, 3.796348466639106*^9}, {3.820027614612806*^9, 3.8200276304022093`*^9}, 3.8200276853924747`*^9, {3.829884589354769*^9, 3.8298846124571314`*^9}, 3.8520842379402337`*^9, {3.8520842684576464`*^9, 3.8520843062238846`*^9}, { 3.852084804512635*^9, 3.8520849353565645`*^9}, {3.8520851998691287`*^9, 3.852085265248603*^9}}, CellLabel-> "In[146]:=",ExpressionUUID->"b35ad1d3-1e12-4044-a4b6-3a447654c9a1"] }, Closed]], Cell[CellGroupData[{ Cell["BENDING ELEMENT (nonl) defs ", "Subsection", CellChangeTimes->{{3.7530187996679964`*^9, 3.753018803413909*^9}, { 3.7633629633672647`*^9, 3.763362967100765*^9}, {3.787894773214689*^9, 3.7878947881941814`*^9}, {3.78789485671918*^9, 3.78789488217928*^9}, 3.7885197052606735`*^9, {3.788530025907043*^9, 3.7885300287809105`*^9}, 3.7885306781716957`*^9, {3.8200271989371843`*^9, 3.8200272016625395`*^9}, { 3.8200274346181693`*^9, 3.8200274405428553`*^9}, {3.851994139239622*^9, 3.8519941462255764`*^9}, {3.852427723407469*^9, 3.852427728727656*^9}},ExpressionUUID->"bc4db6e1-aed8-42a6-b88c-\ 38ede4d891c1"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"BENDING", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BENDING", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4430689313272*^9, 3.4430690080792*^9}, { 3.4430690869528*^9, 3.4430691077320004`*^9}, {3.4430691700116*^9, 3.4430691708072*^9}, {3.4430692071717997`*^9, 3.443069246359*^9}, { 3.4430772782732*^9, 3.4430773623416*^9}, {3.4430773978316*^9, 3.4430774104676*^9}, {3.4430775053780003`*^9, 3.4430776180598*^9}, { 3.4434109099524*^9, 3.4434109159584*^9}, {3.4438800815346003`*^9, 3.4438802689304*^9}, {3.443880362624*^9, 3.4438803824516*^9}, { 3.443929565615374*^9, 3.443929570232974*^9}, {3.443935321321974*^9, 3.443935335705174*^9}, {3.443935419945174*^9, 3.443935421489574*^9}, { 3.443935494013974*^9, 3.443935494715974*^9}, {3.443935617565974*^9, 3.4439357217895737`*^9}, {3.443935755360774*^9, 3.443935816107174*^9}, { 3.443942155230774*^9, 3.443942209939974*^9}, {3.443942305710374*^9, 3.4439423142123737`*^9}, {3.4439442908131742`*^9, 3.443944441181574*^9}, { 3.4439447830065737`*^9, 3.4439447917425737`*^9}, {3.443944908541774*^9, 3.443944916060974*^9}, {3.4442731097938004`*^9, 3.4442731115254*^9}, { 3.444273189229*^9, 3.4442732700526*^9}, {3.4442748430004*^9, 3.4442748605036*^9}, {3.4442748977438*^9, 3.4442748989762*^9}, { 3.4442749340762*^9, 3.4442749351057997`*^9}, 3.4442752313382*^9, { 3.4442919702026*^9, 3.4442919911846*^9}, {3.4442921151577997`*^9, 3.4442921271074*^9}, {3.4443811023684*^9, 3.4443811036632*^9}, { 3.4443814073171997`*^9, 3.4443814402956*^9}, {3.4443815036316*^9, 3.4443815147855997`*^9}, {3.4443815537232*^9, 3.4443815747676*^9}, { 3.4443816138143997`*^9, 3.444381633174*^9}, {3.4443816850439997`*^9, 3.4443817801728*^9}, 3.4443853618688*^9, {3.4443855607376003`*^9, 3.4443856337924*^9}, {3.4443861200444*^9, 3.4443861523676*^9}, { 3.4443862280495996`*^9, 3.444386291448*^9}, {3.4443864047352*^9, 3.4443864135336*^9}, {3.4443870026832*^9, 3.4443870095316*^9}, { 3.4444082055056*^9, 3.4444082437412*^9}, {3.4444082797148*^9, 3.4444084583816*^9}, {3.4444084889108*^9, 3.4444085087539997`*^9}, { 3.444408942517*^9, 3.4444089563386*^9}, {3.4444091419564*^9, 3.4444091647167997`*^9}, {3.4444092206428003`*^9, 3.4444092944463997`*^9}, {3.4444093856284*^9, 3.4444094281071997`*^9}, { 3.4444094976988*^9, 3.4444095275104*^9}, {3.444409611064*^9, 3.4444096125772*^9}, 3.4444098504616003`*^9, {3.444409913392*^9, 3.4444099166056004`*^9}, 3.4444100178496*^9, {3.4444103063248*^9, 3.4444103358712*^9}, {3.4444103868208*^9, 3.4444104432460003`*^9}, { 3.4444921219564*^9, 3.4444921256224003`*^9}, {3.444492194824*^9, 3.4444921973668003`*^9}, {3.4444922814351997`*^9, 3.4444922853508*^9}, { 3.4444923330868*^9, 3.4444923345844*^9}, {3.444492366424*^9, 3.4444923855808*^9}, {3.4453153475226*^9, 3.445315360689*^9}, { 3.4465518166373653`*^9, 3.446551863016165*^9}, {3.446551894231765*^9, 3.446552159384965*^9}, {3.446552232377365*^9, 3.4465522555589647`*^9}, { 3.446553347388365*^9, 3.4465533616155653`*^9}, {3.4466058525769997`*^9, 3.4466058529046*^9}, {3.4466064371219997`*^9, 3.4466065097244*^9}, { 3.4466127725788*^9, 3.4466127766036*^9}, {3.4466128124835997`*^9, 3.4466130037864*^9}, {3.4466131532696*^9, 3.4466131761703997`*^9}, { 3.4466133992192*^9, 3.4466134478756*^9}, {3.446613483584*^9, 3.4466134932092*^9}, {3.4466135740952*^9, 3.4466135794927998`*^9}, { 3.4466137283948*^9, 3.4466137341356*^9}, {3.4466138994342003`*^9, 3.4466139023826*^9}, {3.4466139549858*^9, 3.4466139579653997`*^9}, { 3.4466142109818*^9, 3.4466142245226*^9}, {3.4466142793878*^9, 3.4466143652033997`*^9}, {3.4466144712834*^9, 3.4466145978929996`*^9}, { 3.4466146992618*^9, 3.4466147509914*^9}, {3.4466151283086*^9, 3.4466152768986*^9}, {3.4466153107506*^9, 3.4466153406558*^9}, { 3.4466194331976*^9, 3.4466194377528*^9}, {3.4466194847712*^9, 3.446619488718*^9}, {3.4466389495861998`*^9, 3.4466389768238*^9}, { 3.4466391218414*^9, 3.446639306561*^9}, {3.4466393990222*^9, 3.4466394004886*^9}, {3.4466394475694*^9, 3.4466394487706003`*^9}, { 3.4466395034174*^9, 3.4466395049462*^9}, 3.4466395515755997`*^9, { 3.4466396000176*^9, 3.4466396190808*^9}, {3.4466397459088*^9, 3.446639748826*^9}, {3.4466397974356003`*^9, 3.446639798668*^9}, 3.4466398447816*^9, {3.446639894218*^9, 3.4466399201556*^9}, { 3.4466399570964003`*^9, 3.4466399583288*^9}, {3.446639994006*^9, 3.4466400056904*^9}, {3.4466400383568*^9, 3.4466400395892*^9}, { 3.4466400745643997`*^9, 3.4466401025976*^9}, {3.4466401660834*^9, 3.4466401806070004`*^9}, {3.4466402251294003`*^9, 3.446640227407*^9}, { 3.446640260479*^9, 3.4466402657674*^9}, {3.4466404133122*^9, 3.4466405185654*^9}, 3.4466405830462*^9, {3.4467273294214*^9, 3.4467273777813997`*^9}, {3.4467274366558*^9, 3.4467275620954*^9}, { 3.446727593311*^9, 3.4467277412614*^9}, {3.4467283334639997`*^9, 3.4467283356012*^9}, {3.4467283707636003`*^9, 3.4467283727604*^9}, { 3.4467289882664003`*^9, 3.4467291276836*^9}, {3.446778464322*^9, 3.4467786797424*^9}, {3.4467801953803997`*^9, 3.4467802409792*^9}, { 3.4467802998691998`*^9, 3.4467804023456*^9}, 3.4467804345596*^9, { 3.4467808656344*^9, 3.4467808670852003`*^9}, 3.4467818107525997`*^9, { 3.446781855509*^9, 3.446781874385*^9}, {3.4467826737914*^9, 3.4467827381726*^9}, {3.4467828623018*^9, 3.4467831045386*^9}, { 3.4470344113984003`*^9, 3.4470344123344*^9}, {3.4470344628316*^9, 3.4470345343108*^9}, {3.447043591118539*^9, 3.447043642192939*^9}, { 3.447045649625739*^9, 3.447045718437339*^9}, {3.447054774023939*^9, 3.447054834198939*^9}, {3.4470549103449388`*^9, 3.4470549116169386`*^9}, { 3.447054943902939*^9, 3.4470553027109385`*^9}, {3.447055334559939*^9, 3.447055353684939*^9}, {3.447057311918539*^9, 3.447057369747739*^9}, { 3.4470575058577385`*^9, 3.4470575951365385`*^9}, {3.4470581848789387`*^9, 3.4470582040825386`*^9}, {3.451276121243*^9, 3.4512761425838003`*^9}, { 3.4512762022382*^9, 3.4512762064346*^9}, {3.4512762476966*^9, 3.4512762827654*^9}, {3.451276489091*^9, 3.451276541975*^9}, { 3.4512765853118*^9, 3.4512766132046003`*^9}, {3.4512773470306*^9, 3.4512773766082*^9}, {3.4512776069110003`*^9, 3.4512777499318*^9}, 3.4512777831286*^9, {3.4512778785538*^9, 3.451277881627*^9}, { 3.4512780242734003`*^9, 3.4512780302794*^9}, 3.4512780737878*^9, { 3.4512781866226*^9, 3.4512781930810003`*^9}, {3.4512863325078*^9, 3.4512863539266*^9}, {3.4568019250434*^9, 3.4568022712698*^9}, { 3.4568023177422*^9, 3.4568024125278*^9}, {3.4568024694365997`*^9, 3.4568024750369997`*^9}, {3.4568026914402*^9, 3.4568028101094*^9}, { 3.4568028406698*^9, 3.4568028564726*^9}, 3.4568028886085997`*^9, { 3.4568030489454*^9, 3.4568030800986*^9}, 3.4568032004128*^9, { 3.4568035073698*^9, 3.4568035176034*^9}, {3.4568040146596003`*^9, 3.4568040844852*^9}, {3.4568043016684*^9, 3.4568043154744*^9}, { 3.4568045482264*^9, 3.4568045486632*^9}, {3.4568048944996*^9, 3.4568049806116*^9}, {3.4660560628582*^9, 3.4660560753538*^9}, { 3.4660676729379997`*^9, 3.4660676735931997`*^9}, {3.4660677244024*^9, 3.4660677277251997`*^9}, {3.4742646771287394`*^9, 3.47426469439174*^9}, { 3.47426489921974*^9, 3.4742649800437393`*^9}, {3.4801246373348*^9, 3.4801246860536003`*^9}, {3.4801247748176003`*^9, 3.4801247821028*^9}, { 3.4801248161264*^9, 3.4801248295736*^9}, {3.4801248810692*^9, 3.4801248964508*^9}, {3.4801249330484*^9, 3.480124947884*^9}, 3.4801249886468*^9, {3.4801251139147997`*^9, 3.48012512588*^9}, { 3.4838339444988003`*^9, 3.4838339567448*^9}, 3.4838341692012*^9, { 3.4838344350408*^9, 3.4838344353684*^9}, {3.4938987575920324`*^9, 3.4938987586840324`*^9}, {3.4941630624049997`*^9, 3.4941631381274*^9}, { 3.4941632311345997`*^9, 3.4941632492306004`*^9}, 3.4941633249217997`*^9, { 3.4941633940922003`*^9, 3.4941634063538*^9}, {3.4941634538402*^9, 3.4941635051642*^9}, {3.494163565115*^9, 3.4941636341762*^9}, { 3.4941636853442*^9, 3.4941639323234*^9}, {3.4941640277798*^9, 3.4941641455754004`*^9}, {3.4941641790374002`*^9, 3.4941641803789997`*^9}, {3.4941642676142*^9, 3.4941643277678003`*^9}, 3.4941644677018003`*^9, {3.4941646208938*^9, 3.4941646322349997`*^9}, { 3.4941652592693996`*^9, 3.4941652807194*^9}, {3.4941653119038*^9, 3.494165416299*^9}, {3.494165453895*^9, 3.4941654544722*^9}, { 3.4950990979779997`*^9, 3.495099142701*^9}, {3.495099172958*^9, 3.4950991806289997`*^9}, {3.495099227097*^9, 3.495099238113*^9}, 3.495099290797*^9, {3.495099346084*^9, 3.495099359507*^9}, { 3.495099456308*^9, 3.495099464091*^9}, 3.495099683108*^9, { 3.495100428112*^9, 3.495100434958*^9}, {3.4951006496219997`*^9, 3.495100649992*^9}, {3.4987235265018*^9, 3.4987235939094*^9}, { 3.4987236420666*^9, 3.4987236530646*^9}, {3.4987237305341997`*^9, 3.4987237396914*^9}, {3.498733136159*^9, 3.4987332972446003`*^9}, { 3.4987364783094*^9, 3.4987364860626*^9}, {3.4987366201134*^9, 3.4987366236078*^9}, {3.4987367272386*^9, 3.4987367464890003`*^9}, { 3.4987369428462*^9, 3.4987369670886*^9}, {3.4987370134518003`*^9, 3.4987370259941998`*^9}, {3.4987370944002*^9, 3.4987371027618*^9}, { 3.4987371921029997`*^9, 3.498737193663*^9}, {3.4987372660938*^9, 3.4987372935498*^9}, {3.4987373290554*^9, 3.4987377176202*^9}, { 3.4987377520182*^9, 3.4987379139462*^9}, {3.4987382030216*^9, 3.4987382667078*^9}, {3.4987888391818*^9, 3.4987888608346*^9}, { 3.4988785131146*^9, 3.4988785160162*^9}, {3.5007170967096*^9, 3.5007170999076*^9}, 3.5007182237316*^9, {3.5007182772864*^9, 3.5007182987832003`*^9}, {3.5009573226744003`*^9, 3.5009573940444*^9}, 3.5009574358710003`*^9, 3.5009604278482*^9, {3.5009897246173353`*^9, 3.5009898480289354`*^9}, {3.5009901464413357`*^9, 3.5009901475333357`*^9}, {3.5009901801997356`*^9, 3.500990274096135*^9}, { 3.5010475253292*^9, 3.5010475852332*^9}, {3.5010605722018003`*^9, 3.5010606739762*^9}, {3.5010607202146*^9, 3.5010607323358*^9}, { 3.5010607920526*^9, 3.501061118467*^9}, {3.5010612022078*^9, 3.5010612277138*^9}, {3.5010616467766*^9, 3.5010617938534*^9}, { 3.5010618406222*^9, 3.5010619950778*^9}, {3.5010621500638*^9, 3.5010622514014*^9}, {3.5010625292218*^9, 3.5010625409374*^9}, { 3.5010626043046*^9, 3.5010626313862*^9}, {3.5010626787166*^9, 3.5010626790754004`*^9}, {3.501074457561*^9, 3.5010744671082*^9}, 3.5010763029458*^9, {3.5032210899309998`*^9, 3.5032212413900003`*^9}, { 3.557658203404973*^9, 3.557658219644601*^9}, {3.5576584433801947`*^9, 3.557658496030287*^9}, {3.5576585501779823`*^9, 3.5576586046064777`*^9}, { 3.557658648910555*^9, 3.557658754600741*^9}, {3.557658963945511*^9, 3.5576589782507353`*^9}, {3.557659009949991*^9, 3.5576591437514267`*^9}, { 3.557659182221094*^9, 3.5576592187719584`*^9}, 3.557659413865901*^9, { 3.557659921100792*^9, 3.5576599556392527`*^9}, {3.557660706920972*^9, 3.5576607248454037`*^9}, {3.557661209085854*^9, 3.557661209413454*^9}, { 3.5577526651911488`*^9, 3.5577526932087984`*^9}, {3.5577527272480583`*^9, 3.557752747122493*^9}, {3.5577528374934516`*^9, 3.557752838523053*^9}, { 3.557752881204728*^9, 3.557752891313546*^9}, {3.557752938612829*^9, 3.5577529469120436`*^9}, {3.557753060714244*^9, 3.557753062633047*^9}, { 3.5577536609544907`*^9, 3.5577536637936954`*^9}, {3.5577537824631042`*^9, 3.557753810184353*^9}, {3.557753841025607*^9, 3.5577540648392*^9}, 3.5577541920574236`*^9, {3.5577547033327217`*^9, 3.557754716967146*^9}, { 3.5577547716296415`*^9, 3.557754802112095*^9}, {3.5577549509363565`*^9, 3.5577549771444025`*^9}, 3.5577551382302856`*^9, {3.55775527184452*^9, 3.557755272858522*^9}, {3.557755881555991*^9, 3.557755886548*^9}, { 3.557756158316077*^9, 3.557756231885806*^9}, {3.5577572408487787`*^9, 3.557757248835993*^9}, {3.5577572834368534`*^9, 3.5577575888229895`*^9}, { 3.5577578129641833`*^9, 3.557757862837471*^9}, {3.557758025514557*^9, 3.557758079272251*^9}, 3.557810586960072*^9, {3.5578240262005973`*^9, 3.5578240345360737`*^9}, {3.557824091429328*^9, 3.5578241008156557`*^9}, { 3.557831525255726*^9, 3.5578315319793377`*^9}, 3.5578315716190076`*^9, { 3.557831606079468*^9, 3.557831629432709*^9}, {3.5578316663267736`*^9, 3.5578317569473333`*^9}, {3.5578322144181366`*^9, 3.557832218084143*^9}, { 3.557836356693412*^9, 3.557836473771618*^9}, {3.5578365201660995`*^9, 3.5578365974018345`*^9}, {3.5578366426731143`*^9, 3.557836658865943*^9}, { 3.557836691017599*^9, 3.5578367924957776`*^9}, {3.5578368305442443`*^9, 3.557836888279946*^9}, {3.5578369382156334`*^9, 3.5578370776642785`*^9}, { 3.5578383536061196`*^9, 3.5578383735117545`*^9}, {3.5578385892445335`*^9, 3.5578385978869486`*^9}, {3.5578386713006773`*^9, 3.557838700113928*^9}, { 3.5578387451200075`*^9, 3.5578387467892103`*^9}, {3.5578388951454706`*^9, 3.5578389248635225`*^9}, {3.5578389679351983`*^9, 3.557838983535226*^9}, { 3.5578390227692947`*^9, 3.557839023143696*^9}, {3.557839097696226*^9, 3.5578391125162525`*^9}, {3.5578391553539276`*^9, 3.557839199892006*^9}, { 3.55783924184048*^9, 3.557839294490572*^9}, {3.5578393285922318`*^9, 3.557839398683155*^9}, {3.557839430522811*^9, 3.557839470162481*^9}, { 3.5578395370865984`*^9, 3.5578395446994114`*^9}, {3.5578396068499207`*^9, 3.5578396118575296`*^9}, 3.5578943518105097`*^9, {3.557894388361374*^9, 3.5578944029629993`*^9}, {3.5578944607611012`*^9, 3.5578944989499683`*^9}, {3.5578945393696394`*^9, 3.557894561537278*^9}, { 3.5578946028617506`*^9, 3.5578946188985786`*^9}, {3.557894650894235*^9, 3.5578947812636642`*^9}, {3.55789481884413*^9, 3.5578948191249304`*^9}, { 3.5578949768100076`*^9, 3.5578949836272197`*^9}, {3.5578967386805477`*^9, 3.55789678549623*^9}, {3.5578968804691963`*^9, 3.557896888643611*^9}, { 3.557897022491846*^9, 3.5578970341450663`*^9}, {3.557897620940097*^9, 3.55789765120415*^9}, {3.5579218072271147`*^9, 3.5579218263059483`*^9}, { 3.557922095312821*^9, 3.557922116965659*^9}, {3.557922178086566*^9, 3.557922188616585*^9}, {3.5579223258812256`*^9, 3.557922327066828*^9}, { 3.5579224596046605`*^9, 3.557922461804264*^9}, 3.5579805928465395`*^9, { 3.5579815200581703`*^9, 3.557981541711009*^9}, 3.557985544779242*^9, { 3.5579863164793987`*^9, 3.5579863339514294`*^9}, {3.557986523210962*^9, 3.557986568841042*^9}, 3.5579866122559185`*^9, 3.557986993536188*^9, { 3.5579871244716187`*^9, 3.5579871290580263`*^9}, 3.557987173486905*^9, 3.5579872166989803`*^9, {3.5599618621582537`*^9, 3.5599618642486577`*^9}, { 3.559961969720443*^9, 3.5599619894700775`*^9}, 3.559963611089726*^9, { 3.5601298891258235`*^9, 3.560129889422224*^9}, {3.560132445157113*^9, 3.5601324458591146`*^9}, {3.561978472080926*^9, 3.561978472392926*^9}, { 3.6297802564412937`*^9, 3.6297802957377625`*^9}, {3.62978033369263*^9, 3.629780429741998*^9}, {3.6297805790030603`*^9, 3.6297809429048996`*^9}, { 3.629780987957779*^9, 3.629781197575347*^9}, {3.629781240397422*^9, 3.629781337663593*^9}, {3.6297813946972933`*^9, 3.6297814529165955`*^9}, { 3.6297814952550697`*^9, 3.629781527578326*^9}, {3.62978162025529*^9, 3.629781647633338*^9}, {3.629781678833393*^9, 3.629781763120341*^9}, 3.6297818028224106`*^9, {3.6297818432108817`*^9, 3.629781872570133*^9}, { 3.629782355765382*^9, 3.629782427603508*^9}, {3.6297824692243814`*^9, 3.629782674863942*^9}, {3.629782707218399*^9, 3.6297829295343895`*^9}, { 3.629783005631323*^9, 3.6297830574702144`*^9}, {3.6297831098551064`*^9, 3.629783142786764*^9}, {3.629783433711675*^9, 3.629783442619291*^9}, { 3.6297834942397814`*^9, 3.6297835175930223`*^9}, 3.6297835794939313`*^9, { 3.6297836160291953`*^9, 3.6297837668970604`*^9}, {3.6297842042438283`*^9, 3.6297842697483435`*^9}, {3.6297843514456873`*^9, 3.629784370742921*^9}, { 3.629784443829049*^9, 3.6297844678842916`*^9}, {3.6297845252611923`*^9, 3.629784525588793*^9}, {3.6297846136821475`*^9, 3.629784629235375*^9}, { 3.629784814797701*^9, 3.629784927648299*^9}, {3.629785259960083*^9, 3.6297852602096834`*^9}, {3.6297858780175686`*^9, 3.629785917282837*^9}, { 3.629786048057867*^9, 3.629786048681868*^9}, 3.6297863278755584`*^9, { 3.6297867047133856`*^9, 3.629786748533863*^9}, {3.6297867791567163`*^9, 3.6297868491540394`*^9}, {3.6297875320748396`*^9, 3.629787569795706*^9}, { 3.6297876247234025`*^9, 3.6297877281983843`*^9}, {3.6297877681812544`*^9, 3.629787774015665*^9}, {3.629787831408166*^9, 3.6297878355265727`*^9}, { 3.6297878775686464`*^9, 3.6297878861174617`*^9}, {3.6297879185343184`*^9, 3.629787919064719*^9}, {3.6297880043032694`*^9, 3.62978800470887*^9}, 3.6297880488257475`*^9, {3.6297882100052304`*^9, 3.6297882174776435`*^9}, { 3.6297882697533355`*^9, 3.6297882948381796`*^9}, {3.6297883467550707`*^9, 3.6297883991087627`*^9}, {3.6297887361785545`*^9, 3.629788783961438*^9}, 3.629788825395111*^9, {3.629789006152629*^9, 3.6297890321266747`*^9}, { 3.6297891133248167`*^9, 3.629789145336073*^9}, {3.6297891926821566`*^9, 3.629789194257759*^9}, {3.629789255316266*^9, 3.6297892556282673`*^9}, { 3.629869102295367*^9, 3.629869160124668*^9}, {3.6298691942887287`*^9, 3.6298696149902673`*^9}, {3.6298696993864155`*^9, 3.62986975897852*^9}, { 3.6298698387726603`*^9, 3.629869912030389*^9}, {3.6298700722270703`*^9, 3.629870234560955*^9}, {3.629870580429163*^9, 3.629870630458451*^9}, { 3.630556081081209*^9, 3.630556104902451*^9}, {3.6305562643503313`*^9, 3.6305562763935523`*^9}, {3.6305563415080667`*^9, 3.630556480956712*^9}, { 3.630556692851884*^9, 3.630556695347888*^9}, {3.630556730042349*^9, 3.630556914528273*^9}, {3.6305653725974936`*^9, 3.6305656807121167`*^9}, { 3.630565758760581*^9, 3.6305657739024467`*^9}, {3.630565858170267*^9, 3.63056596644846*^9}, {3.6305661502619734`*^9, 3.6305661523230915`*^9}, { 3.6305662653385553`*^9, 3.630566370352562*^9}, {3.6305667786019125`*^9, 3.630566790535595*^9}, {3.6305668214773645`*^9, 3.630567044691132*^9}, { 3.6305670772499943`*^9, 3.6305670783710585`*^9}, 3.630567272031135*^9, { 3.630567303902958*^9, 3.630567409875019*^9}, {3.630568671196477*^9, 3.6305687195002403`*^9}, {3.6305687542132254`*^9, 3.630568758623478*^9}, { 3.630568855671028*^9, 3.630568859250233*^9}, {3.630569706514694*^9, 3.630569775526641*^9}, 3.630569982346471*^9, {3.6305701679130845`*^9, 3.630570205199217*^9}, {3.6305703751399374`*^9, 3.630570526177576*^9}, { 3.630587657039589*^9, 3.630587688367381*^9}, {3.6305880733027773`*^9, 3.6305883365376396`*^9}, {3.6305886689118233`*^9, 3.6305886717978287`*^9}, 3.6305889776831656`*^9, {3.6305890389444733`*^9, 3.6305890437180815`*^9}, { 3.630589093248169*^9, 3.6305891296430326`*^9}, 3.630589181700324*^9, { 3.6305892509956455`*^9, 3.6305892594820604`*^9}, {3.630589318949365*^9, 3.6305893334729905`*^9}, {3.630589630294712*^9, 3.6305896376267247`*^9}, { 3.630589683288005*^9, 3.630589684988408*^9}, {3.630597310538067*^9, 3.630597340080757*^9}, {3.630597391446695*^9, 3.630597400596218*^9}, { 3.6305974350611897`*^9, 3.6305974605306463`*^9}, {3.630633997622449*^9, 3.630634003125764*^9}, {3.630659322217756*^9, 3.63065932438616*^9}, { 3.6306611578252783`*^9, 3.6306611625988865`*^9}, {3.6306612541554475`*^9, 3.630661257587454*^9}, {3.6306613001287284`*^9, 3.6306613026715326`*^9}, { 3.6306613920752897`*^9, 3.6306613949768953`*^9}, {3.6306706377509866`*^9, 3.630670654957817*^9}, {3.6306749981919994`*^9, 3.630675005793434*^9}, { 3.6306751229631357`*^9, 3.630675150017683*^9}, {3.6306752035287437`*^9, 3.6306752096180925`*^9}, {3.630675315921172*^9, 3.6306753201514144`*^9}, { 3.6306757793287754`*^9, 3.6306757796257925`*^9}, {3.630675814406262*^9, 3.6306758147026625`*^9}, {3.6306760107574763`*^9, 3.6306760154417443`*^9}, {3.6306789722320743`*^9, 3.6306789870309205`*^9}, {3.6306790257051325`*^9, 3.630679028076268*^9}, { 3.6306800259177256`*^9, 3.6306800406129513`*^9}, {3.6306801239326982`*^9, 3.6306801300167084`*^9}, {3.630680769261832*^9, 3.6306807806186523`*^9}, { 3.630681157468514*^9, 3.6306811577649145`*^9}, {3.6306812744219193`*^9, 3.63068127471832*^9}, {3.6306817187418995`*^9, 3.6306817919060287`*^9}, { 3.630681879188182*^9, 3.6306819111526375`*^9}, {3.6306821191790032`*^9, 3.6306821283050194`*^9}, {3.630720543651497*^9, 3.6307205534300566`*^9}, { 3.630721035525631*^9, 3.630721092774905*^9}, {3.6307212510439577`*^9, 3.6307213064777765`*^9}, {3.6307477437169704`*^9, 3.6307478284095197`*^9}, {3.6307478614971776`*^9, 3.6307478785948076`*^9}, {3.6307479884814005`*^9, 3.630748002880226*^9}, { 3.630748045624301*^9, 3.630748063876333*^9}, {3.630748111596817*^9, 3.6307481498324842`*^9}, {3.6307489182430334`*^9, 3.6307489447786803`*^9}, {3.630749037427243*^9, 3.6307490443848553`*^9}, { 3.6307491041485605`*^9, 3.6307491384218206`*^9}, {3.6307491914151134`*^9, 3.630749196890723*^9}, {3.6307492445800066`*^9, 3.6307493439989815`*^9}, { 3.630749396212273*^9, 3.6307494766304145`*^9}, {3.6307495333989143`*^9, 3.6307495547241516`*^9}, {3.6307496525831237`*^9, 3.630749669571553*^9}, { 3.630750220602922*^9, 3.6307502881822405`*^9}, {3.6307510631916018`*^9, 3.630751068292811*^9}, {3.6307511226589065`*^9, 3.630751137962533*^9}, { 3.6307512555243397`*^9, 3.630751282777588*^9}, {3.630752266971757*^9, 3.630752414599744*^9}, {3.630752446407563*^9, 3.630752457388191*^9}, { 3.6307589380050273`*^9, 3.6307590266300964`*^9}, {3.6307591666721067`*^9, 3.63075923229886*^9}, 3.630760288282259*^9, {3.6307603547370596`*^9, 3.630760557414652*^9}, {3.630760654134184*^9, 3.63076065510824*^9}, { 3.6307606911683025`*^9, 3.6307606919283457`*^9}, {3.6307607642334814`*^9, 3.6307607648645177`*^9}, {3.630761455000991*^9, 3.6307614616743727`*^9}, { 3.630761507825012*^9, 3.630761605776615*^9}, {3.630761652999316*^9, 3.630761695865768*^9}, {3.630761771278081*^9, 3.6307617792215357`*^9}, 3.6307629478424797`*^9, {3.632205207880766*^9, 3.6322052561155243`*^9}, { 3.6322052892474194`*^9, 3.6322052915745525`*^9}, 3.6322053746993074`*^9, { 3.6322062705415463`*^9, 3.6322062726016645`*^9}, {3.6322063396935015`*^9, 3.63220636484194*^9}, {3.6322064410612993`*^9, 3.6322064491667633`*^9}, { 3.632206580308264*^9, 3.6322066373275256`*^9}, {3.6322066736436024`*^9, 3.6322067467737856`*^9}, {3.632206782260815*^9, 3.6322071351279984`*^9}, 3.6322071989226465`*^9, {3.632207270393735*^9, 3.6322073359894867`*^9}, { 3.6322073997741346`*^9, 3.6322074126708727`*^9}, {3.632207491777397*^9, 3.632207682289294*^9}, {3.632207809621577*^9, 3.632207827973626*^9}, { 3.6322079043859973`*^9, 3.6322079279443445`*^9}, {3.6322080916397076`*^9, 3.6322081666649985`*^9}, 3.634905258940913*^9, {3.634905370524296*^9, 3.6349054089004903`*^9}, {3.6349054472556844`*^9, 3.63490544787272*^9}, { 3.634905483492757*^9, 3.6349055164646425`*^9}, {3.634905574352954*^9, 3.634905628121029*^9}, {3.6349057012822137`*^9, 3.6349057207913294`*^9}, { 3.6349061371061416`*^9, 3.634906354438572*^9}, {3.6349063890455513`*^9, 3.6349064369332905`*^9}, {3.634906537696054*^9, 3.634906601859724*^9}, 3.634906706128688*^9, {3.6349069249442034`*^9, 3.6349069328326545`*^9}, { 3.6349070151973653`*^9, 3.6349070242298822`*^9}, {3.6349070817921743`*^9, 3.6349070822111983`*^9}, {3.634907723288866*^9, 3.634907739005765*^9}, { 3.6349079580732946`*^9, 3.6349079868219395`*^9}, {3.634908200284148*^9, 3.634908315195721*^9}, {3.6349083774582825`*^9, 3.6349084027997313`*^9}, { 3.63490844507615*^9, 3.634908448843365*^9}, {3.634914956333157*^9, 3.634915020054802*^9}, {3.634915050572547*^9, 3.6349150956171236`*^9}, { 3.6349539785771523`*^9, 3.634953978975175*^9}, {3.6349540728785458`*^9, 3.6349541681829967`*^9}, {3.634954211263461*^9, 3.6349542495746527`*^9}, { 3.6349543251259737`*^9, 3.634954355882733*^9}, {3.6349543892536416`*^9, 3.6349544742835045`*^9}, {3.634954547519694*^9, 3.6349545640246377`*^9}, { 3.6349547051657104`*^9, 3.6349547107930326`*^9}, {3.634954745355009*^9, 3.634954752101395*^9}, {3.6349547948858423`*^9, 3.6349548053894434`*^9}, { 3.634954904907135*^9, 3.6349549451084347`*^9}, {3.634955219605135*^9, 3.6349552640926795`*^9}, {3.634955320189888*^9, 3.634955348763522*^9}, { 3.634955386393675*^9, 3.6349555039273973`*^9}, {3.6349557669644423`*^9, 3.6349557672004557`*^9}, {3.634955894841756*^9, 3.634955902578199*^9}, { 3.6349559513739896`*^9, 3.6349560216320086`*^9}, {3.634956120144643*^9, 3.634956128996149*^9}, {3.6349561700724983`*^9, 3.6349561978900895`*^9}, { 3.6349562480719595`*^9, 3.634956254326318*^9}, {3.634956331684742*^9, 3.6349563460575643`*^9}, {3.634956379242462*^9, 3.63495642676418*^9}, 3.6349564696636343`*^9, {3.6351524116477795`*^9, 3.6351524153379908`*^9}, { 3.6352134400282927`*^9, 3.635213442148414*^9}, {3.6352134745862694`*^9, 3.635213495869487*^9}, {3.6352135383409157`*^9, 3.6352137157160616`*^9}, { 3.6352137493569856`*^9, 3.635213764522853*^9}, {3.635214215036621*^9, 3.635214227593339*^9}, {3.635214407257615*^9, 3.63521441713218*^9}, { 3.635215297101512*^9, 3.635215303964904*^9}, {3.6352154111120324`*^9, 3.635215431504199*^9}, {3.635216346055508*^9, 3.635216494371991*^9}, { 3.635216631050809*^9, 3.6352166603244834`*^9}, {3.635216763034358*^9, 3.635216764164423*^9}, {3.6352168771938877`*^9, 3.635216888828553*^9}, 3.6352169832479534`*^9, 3.635217037668066*^9, {3.6352172024924936`*^9, 3.6352172054526625`*^9}, {3.635217344025589*^9, 3.635217346898753*^9}, 3.6352173863770113`*^9, {3.635217519639633*^9, 3.6352175507014103`*^9}, 3.635217615445113*^9, {3.6352178715087595`*^9, 3.635217880460271*^9}, { 3.6352185912849283`*^9, 3.635218598444338*^9}, {3.6352186995721216`*^9, 3.635218714955002*^9}, {3.6352189761749425`*^9, 3.6352189789341*^9}, { 3.6352195060322485`*^9, 3.635219509972474*^9}, 3.6352195673477554`*^9, 3.6352195994635925`*^9, {3.6352197336482677`*^9, 3.635219737452485*^9}, { 3.6352197706093817`*^9, 3.6352197723214793`*^9}, {3.635219941784172*^9, 3.6352199485115566`*^9}, {3.6352200714185867`*^9, 3.6352200854323883`*^9}, {3.6352202085694313`*^9, 3.635220235849992*^9}, { 3.6352202816336107`*^9, 3.6352203110962954`*^9}, {3.6352204980449886`*^9, 3.6352205276526823`*^9}, {3.6352253191447396`*^9, 3.6352253299913597`*^9}, {3.6352253611111403`*^9, 3.6352253637572913`*^9}, {3.635225409322898*^9, 3.6352255965196047`*^9}, { 3.6352260914249115`*^9, 3.6352261698393965`*^9}, {3.63522638233055*^9, 3.6352264188036366`*^9}, {3.635227493469104*^9, 3.635227556935734*^9}, { 3.6352276745764627`*^9, 3.635227730116639*^9}, {3.6352287979917183`*^9, 3.6352288587651944`*^9}, {3.635228894237223*^9, 3.635228948324317*^9}, { 3.635229365252164*^9, 3.6352293902275925`*^9}, {3.63522947690555*^9, 3.6352294807837715`*^9}, {3.6352492831123204`*^9, 3.6352492983621926`*^9}, 3.6356569054520617`*^9, {3.6363778004499054`*^9, 3.636377802787039*^9}, { 3.6363778414932528`*^9, 3.6363778525308843`*^9}, {3.636384436335312*^9, 3.6363846409950175`*^9}, {3.636384971250907*^9, 3.6363849738080535`*^9}, { 3.6363850170465264`*^9, 3.636385030729309*^9}, {3.6363851286779118`*^9, 3.636385138359465*^9}, {3.6363851699712734`*^9, 3.636385223111313*^9}, { 3.656076172452749*^9, 3.656076182171566*^9}, {3.6560765578514256`*^9, 3.656076619019133*^9}, 3.6560772545486493`*^9, {3.6630719749029694`*^9, 3.6630719878027077`*^9}, {3.6630720702554235`*^9, 3.6630720807290225`*^9}, {3.6630721155740156`*^9, 3.6630721713712068`*^9}, {3.663072270834896*^9, 3.6630722882218904`*^9}, 3.6630724099968557`*^9, {3.685234767958906*^9, 3.685234768480936*^9}, { 3.685252204033695*^9, 3.6852522340537376`*^9}, {3.6852522757137957`*^9, 3.6852523115138454`*^9}, {3.68525376314359*^9, 3.6852537725041256`*^9}, { 3.6852539763277836`*^9, 3.6852539861693463`*^9}, 3.6852540682470407`*^9, 3.6852541660656357`*^9, {3.6852604801645336`*^9, 3.6852605060345697`*^9}, { 3.6852605373446136`*^9, 3.6852605977846985`*^9}, 3.685260655254779*^9, { 3.6853280002218475`*^9, 3.685328019561875*^9}, 3.685328064721938*^9, { 3.6853280953119807`*^9, 3.6853282636022167`*^9}, {3.685328356242346*^9, 3.685328598671985*^9}, {3.6853286682069626`*^9, 3.6853287982524004`*^9}, { 3.6853288753368096`*^9, 3.6853289367033195`*^9}, {3.685328968274125*^9, 3.685328978713722*^9}, {3.685329033941881*^9, 3.685329044950511*^9}, { 3.685329173522865*^9, 3.6853294420842257`*^9}, {3.6853296024223967`*^9, 3.6853296124319687`*^9}, {3.6853297221712456`*^9, 3.685329733349885*^9}, { 3.6853298076291337`*^9, 3.6853298739599276`*^9}, {3.685330038474337*^9, 3.685330051652091*^9}, {3.6853311309428225`*^9, 3.685331168378964*^9}, { 3.685340142134763*^9, 3.685340180544817*^9}, {3.6853583292043543`*^9, 3.685358334834362*^9}, {3.685358366084406*^9, 3.685358366954407*^9}, { 3.685358408404465*^9, 3.685358518294619*^9}, 3.685358620174762*^9, 3.6853586578748145`*^9, {3.6853588750151186`*^9, 3.6853588857151337`*^9}, { 3.6853589302051954`*^9, 3.685358938995208*^9}, {3.685359014715314*^9, 3.6853590296653347`*^9}, 3.685359148315501*^9, 3.6853598281764526`*^9, { 3.6853683109000263`*^9, 3.685368382250126*^9}, {3.685368420160179*^9, 3.6853684704302497`*^9}, {3.6853685194503183`*^9, 3.685368742860631*^9}, { 3.685369008901004*^9, 3.68536902061102*^9}, {3.6853690791611023`*^9, 3.685369132301176*^9}, {3.6853693219914417`*^9, 3.6853693304114532`*^9}, 3.6853696089118433`*^9, {3.6858758911429157`*^9, 3.685875951793*^9}, { 3.6859484099082212`*^9, 3.6859484970032024`*^9}, {3.686052829875022*^9, 3.686052906242383*^9}, {3.6860535326822133`*^9, 3.686053598029951*^9}, { 3.68605365168902*^9, 3.6860541446091995`*^9}, {3.6860541846064873`*^9, 3.68605440393201*^9}, {3.686054713802734*^9, 3.6860547858298535`*^9}, { 3.6860548280202665`*^9, 3.686054837219793*^9}, {3.686054874127904*^9, 3.686054892139934*^9}, {3.686055136014883*^9, 3.6860551460584574`*^9}, { 3.686055211281188*^9, 3.6860552301962633`*^9}, {3.6860553465409174`*^9, 3.6860553998749685`*^9}, {3.6860556017188663`*^9, 3.6860556050188704`*^9}, {3.6862923512707715`*^9, 3.686292363600789*^9}, { 3.686292409650853*^9, 3.6862924109708548`*^9}, {3.6862924536109147`*^9, 3.6862924596309233`*^9}, {3.686292542221039*^9, 3.6862925430110397`*^9}, { 3.686292988803664*^9, 3.686293001033681*^9}, {3.6866504529025555`*^9, 3.686650526682659*^9}, {3.686650671852862*^9, 3.6866507242929354`*^9}, { 3.6866507657529936`*^9, 3.6866507887630253`*^9}, {3.6866508208230705`*^9, 3.6866509100531955`*^9}, {3.6866509593932643`*^9, 3.686650971113281*^9}, { 3.686651007793332*^9, 3.6866511595335445`*^9}, {3.686651223513634*^9, 3.686651234033649*^9}, {3.686651304763748*^9, 3.6866513363837924`*^9}, { 3.6866514102038956`*^9, 3.686651429943923*^9}, {3.686652993837468*^9, 3.6866530046274834`*^9}, {3.686804398511652*^9, 3.6868044081516657`*^9}, { 3.6868046315619783`*^9, 3.686804631801979*^9}, {3.686804685872054*^9, 3.686804707092084*^9}, {3.6868047382021275`*^9, 3.686804767812169*^9}, { 3.686804824012248*^9, 3.6868048404922705`*^9}, {3.686804942142413*^9, 3.6868049633424425`*^9}, {3.6868050765526013`*^9, 3.686805101092636*^9}, { 3.6868051463526993`*^9, 3.6868052234228067`*^9}, {3.686805307602925*^9, 3.686805311682931*^9}, {3.68680577547358*^9, 3.686805788923599*^9}, { 3.686821702197342*^9, 3.6868217282873783`*^9}, {3.6868225192884855`*^9, 3.686822538368512*^9}, {3.6868226306886415`*^9, 3.6868226683086944`*^9}, { 3.6868227318887835`*^9, 3.6868227627088265`*^9}, {3.686822801638881*^9, 3.6868230490692277`*^9}, {3.686823122979331*^9, 3.6868231833294153`*^9}, { 3.6868232450595016`*^9, 3.6868233753996844`*^9}, {3.6868234153897405`*^9, 3.686823451379791*^9}, {3.6868236736101017`*^9, 3.6868236786601086`*^9}, { 3.6868237164601617`*^9, 3.68682375072021*^9}, {3.68682389396041*^9, 3.68682390087042*^9}, {3.686823940790476*^9, 3.6868239416904774`*^9}, { 3.6868239808805323`*^9, 3.6868239872905407`*^9}, {3.686824051540631*^9, 3.6868240519006314`*^9}, {3.686824360861064*^9, 3.6868243761510854`*^9}, { 3.6868245440213203`*^9, 3.686824577221367*^9}, {3.686824685841519*^9, 3.6868246979115357`*^9}, 3.6868248012716804`*^9, 3.6868253582724605`*^9, { 3.6868255183026843`*^9, 3.686825518932685*^9}, {3.6868264466639843`*^9, 3.6868264497139883`*^9}, {3.6868267792744493`*^9, 3.6868268152945004`*^9}, {3.686827100164899*^9, 3.6868271210549283`*^9}, 3.686827162004986*^9, {3.6868272414950967`*^9, 3.686827327475217*^9}, { 3.686827953126093*^9, 3.686827976506126*^9}, {3.686829128577739*^9, 3.686829138957753*^9}, 3.6868292410978966`*^9, {3.6868292768379464`*^9, 3.686829282727955*^9}, {3.6868293820380936`*^9, 3.686829418138144*^9}, { 3.686829846748744*^9, 3.686829848298746*^9}, {3.6868313063207874`*^9, 3.686831307180789*^9}, {3.6868331276633377`*^9, 3.68683328653356*^9}, { 3.6868394697195063`*^9, 3.6868394933895392`*^9}, 3.686839530999592*^9, { 3.686839582829664*^9, 3.68683963686974*^9}, {3.6868397551199055`*^9, 3.68683979365996*^9}, {3.6868398344600167`*^9, 3.686839866200061*^9}, { 3.687092084401948*^9, 3.687092117031994*^9}, {3.6870922598621936`*^9, 3.6870922645422*^9}, {3.6870962086478376`*^9, 3.6870962658779182`*^9}, 3.687096444838168*^9, {3.687096500978247*^9, 3.687096501638248*^9}, { 3.6870965809883595`*^9, 3.687096592708376*^9}, 3.687096837948719*^9, { 3.68709688890879*^9, 3.687096985798926*^9}, {3.6870971015990877`*^9, 3.6870972179192505`*^9}, {3.6870972618993125`*^9, 3.687097305639374*^9}, { 3.6870973356794157`*^9, 3.6870975186496716`*^9}, {3.6870975796097574`*^9, 3.6870975953197794`*^9}, {3.6870976531898603`*^9, 3.6870976848899045`*^9}, 3.6870977782500353`*^9, {3.687413757687042*^9, 3.6874137834070783`*^9}, { 3.6874140542074575`*^9, 3.687414094417514*^9}, {3.6874143478878684`*^9, 3.687414485538061*^9}, {3.6874146116082373`*^9, 3.68741464894829*^9}, { 3.6874147451084247`*^9, 3.687414766118454*^9}, 3.6874149094486547`*^9, { 3.6874150416688395`*^9, 3.6874150634888706`*^9}, {3.6874152437091227`*^9, 3.687415268869158*^9}, 3.6874153442892637`*^9, {3.687415449879411*^9, 3.687415469659439*^9}, 3.687415529739523*^9, 3.687415564789572*^9, 3.687415645529685*^9, {3.6874168016913037`*^9, 3.687416803441306*^9}, { 3.687421022677213*^9, 3.6874212686075573`*^9}, {3.68742948209425*^9, 3.6874294906842623`*^9}, {3.687844340668378*^9, 3.6878443698084188`*^9}, { 3.6886534778571014`*^9, 3.6886534911571198`*^9}, {3.688906380162199*^9, 3.6889064680223217`*^9}, {3.688906514222396*^9, 3.6889065193925257`*^9}, { 3.688908192623024*^9, 3.6889082006430354`*^9}, {3.688908261823121*^9, 3.688908271653135*^9}, {3.6889083776232834`*^9, 3.6889083922733035`*^9}, { 3.688908466073407*^9, 3.6889084993734536`*^9}, 3.688908533623502*^9, { 3.688908616683618*^9, 3.6889086271336327`*^9}, {3.6889086885637183`*^9, 3.6889087063437433`*^9}, {3.6889091647443852`*^9, 3.6889092012544365`*^9}, {3.6889093019045773`*^9, 3.6889093406746316`*^9}, 3.6889101071957045`*^9, {3.689905940063133*^9, 3.689905972983179*^9}, { 3.692530981927737*^9, 3.6925310416778207`*^9}, {3.692531099797902*^9, 3.6925311384779563`*^9}, {3.692531192258032*^9, 3.692531244668105*^9}, { 3.6925312919881716`*^9, 3.692531425418358*^9}, {3.6925315270885005`*^9, 3.692531643928664*^9}, {3.692535489534048*^9, 3.6925356485142703`*^9}, { 3.692535753564418*^9, 3.6925357992544813`*^9}, {3.6925358831745987`*^9, 3.692535899604622*^9}, {3.692536042584822*^9, 3.692536159384986*^9}, { 3.6925366121156197`*^9, 3.6925366207256317`*^9}, {3.6925367265057793`*^9, 3.69253672683578*^9}, {3.6925368590559654`*^9, 3.6925368636559715`*^9}, { 3.6925370880062857`*^9, 3.692537177856412*^9}, {3.692537322456614*^9, 3.6925373869767046`*^9}, {3.6925390913352747`*^9, 3.6925390925252767`*^9}, {3.692539644430175*^9, 3.6925396711502123`*^9}, { 3.692539727510291*^9, 3.692539730440295*^9}, {3.69253993367058*^9, 3.692539963780622*^9}, {3.6925400018406754`*^9, 3.692540003630678*^9}, { 3.6925401743409166`*^9, 3.6925401747509174`*^9}, {3.692540399111232*^9, 3.692540407981244*^9}, {3.69254047647134*^9, 3.6925404886113567`*^9}, { 3.6925406039715185`*^9, 3.69254060531152*^9}, {3.6925414948727655`*^9, 3.6925414953427663`*^9}, {3.6925415478528395`*^9, 3.692541613062931*^9}, 3.692541649332982*^9, {3.692541727633092*^9, 3.6925418840133104`*^9}, { 3.692541924473367*^9, 3.692542041693531*^9}, {3.6925421488836813`*^9, 3.6925422549438295`*^9}, {3.6925422976938896`*^9, 3.692542521444203*^9}, { 3.6925426221843443`*^9, 3.6925426357343626`*^9}, 3.692542739374508*^9, 3.692599799510878*^9, {3.692599834884901*^9, 3.6925998954663663`*^9}, { 3.692599925635092*^9, 3.6926000095928946`*^9}, {3.692600108929576*^9, 3.6926001456386757`*^9}, {3.6926001874800687`*^9, 3.692600454421337*^9}, { 3.692600503149027*^9, 3.6926006000391626`*^9}, {3.692600680251275*^9, 3.6926006814012766`*^9}, {3.6926009000215826`*^9, 3.6926009410816402`*^9}, 3.692601280532116*^9, {3.6926044914726114`*^9, 3.69260449774262*^9}, 3.6926045660127153`*^9, 3.6926046690228596`*^9, {3.69296647863291*^9, 3.6929664798829117`*^9}, {3.6929665643330297`*^9, 3.6929666141830997`*^9}, {3.6929670390036945`*^9, 3.6929670405536966`*^9}, {3.6929670861037607`*^9, 3.6929670952937737`*^9}, {3.6929671302538223`*^9, 3.6929671549438567`*^9}, {3.6929671904739065`*^9, 3.69296722137395*^9}, { 3.6929672596240034`*^9, 3.6929673352541094`*^9}, 3.6929678909232683`*^9, { 3.6930146982034283`*^9, 3.693014722713463*^9}, {3.6930148540136466`*^9, 3.693014857023651*^9}, {3.6930148913836985`*^9, 3.693014894823704*^9}, { 3.693014930903754*^9, 3.6930151942541227`*^9}, {3.693015247824198*^9, 3.693015430554454*^9}, {3.693015673794794*^9, 3.69301579223496*^9}, { 3.6930163123576884`*^9, 3.693016326897709*^9}, {3.6930164225678425`*^9, 3.693016429727853*^9}, {3.693016686718212*^9, 3.693016698128228*^9}, { 3.693016737038283*^9, 3.693016755068308*^9}, {3.6930168429225607`*^9, 3.6930168719926014`*^9}, {3.6930172049430676`*^9, 3.693017284063178*^9}, { 3.693017336433252*^9, 3.6930173662532935`*^9}, {3.6930180949163136`*^9, 3.6930180975563173`*^9}, {3.6930181870764427`*^9, 3.693018199956461*^9}, { 3.6930182954065943`*^9, 3.693018305996609*^9}, {3.693139886141657*^9, 3.6931399045016823`*^9}, {3.6931402916003532`*^9, 3.693140295770359*^9}, { 3.693140426020541*^9, 3.693140426530542*^9}, {3.6931410492237864`*^9, 3.6931410888738413`*^9}, {3.6931411194438844`*^9, 3.693141126553894*^9}, { 3.693141412004294*^9, 3.693141454164353*^9}, {3.6931415979955544`*^9, 3.6931417931758275`*^9}, {3.6932199559445915`*^9, 3.6932199772046213`*^9}, {3.6932201435748544`*^9, 3.693220170284892*^9}, { 3.693220713855653*^9, 3.693220721825664*^9}, {3.693625124589745*^9, 3.693625153729786*^9}, {3.6940907995669713`*^9, 3.6940909688872085`*^9}, { 3.6940913675677667`*^9, 3.6940914223978434`*^9}, {3.694091508037963*^9, 3.694091572118053*^9}, 3.694092009628666*^9, {3.6940920553287296`*^9, 3.694092229168973*^9}, {3.6940923053990793`*^9, 3.694092374419176*^9}, { 3.6940924537392874`*^9, 3.694092457789293*^9}, 3.694092642849552*^9, { 3.6940928573598523`*^9, 3.694092862379859*^9}, {3.6940945886222763`*^9, 3.694094601932295*^9}, 3.694094849542641*^9, {3.694095764293922*^9, 3.6940957644739223`*^9}, {3.6940960602743363`*^9, 3.6940960732243547`*^9}, {3.6940961211044216`*^9, 3.694096124194426*^9}, { 3.694665030960044*^9, 3.6946650634500895`*^9}, {3.6946652071402903`*^9, 3.6946653490404887`*^9}, {3.6946658702212186`*^9, 3.6946658881212435`*^9}, {3.694665923041292*^9, 3.694665953561335*^9}, { 3.694665995981395*^9, 3.6946660149414215`*^9}, {3.694666050571471*^9, 3.6946660547214766`*^9}, {3.694666169991638*^9, 3.694666292151809*^9}, { 3.6946663456618843`*^9, 3.6946663943919525`*^9}, 3.6946667526224537`*^9, 3.69466680700253*^9, 3.694687076625702*^9, {3.6946874316161985`*^9, 3.6946874621962414`*^9}, 3.694687499496294*^9, {3.694687567516389*^9, 3.694687642816495*^9}, {3.694687679006545*^9, 3.6946877198966026`*^9}, { 3.6946877714966745`*^9, 3.694687931746899*^9}, {3.723798739728607*^9, 3.723798744014243*^9}, {3.7237990126446104`*^9, 3.723799023974499*^9}, { 3.7244116671877546`*^9, 3.7244116733393917`*^9}, {3.724411761793063*^9, 3.7244117718753977`*^9}, {3.724411928386671*^9, 3.7244119682966137`*^9}, { 3.724412131847311*^9, 3.724412188341254*^9}, {3.729414981357122*^9, 3.7294149861075096`*^9}, {3.749817651293678*^9, 3.749817653108206*^9}, { 3.7498176831919456`*^9, 3.7498176846222315`*^9}, 3.7498177601545563`*^9, { 3.749817859674735*^9, 3.749817861044999*^9}, {3.7498179561547127`*^9, 3.749817964489929*^9}, {3.749818149334386*^9, 3.749818237397959*^9}, 3.749818617867873*^9, {3.7505621848002787`*^9, 3.7505622174085107`*^9}, { 3.75056238761455*^9, 3.750562431347901*^9}, {3.7505626332829456`*^9, 3.7505627331565337`*^9}, {3.7505627632642183`*^9, 3.7505627635859113`*^9}, {3.7515359581577415`*^9, 3.7515359614850826`*^9}, {3.751536071974715*^9, 3.7515360961721487`*^9}, 3.7515362040373974`*^9, {3.751536256080162*^9, 3.7515365099108534`*^9}, { 3.751549231137398*^9, 3.7515493334258356`*^9}, {3.7515496891619573`*^9, 3.751549689458767*^9}, 3.753020403650548*^9, {3.7530205114189386`*^9, 3.753020525224822*^9}, {3.753021995594639*^9, 3.753022011512741*^9}, { 3.760634689749445*^9, 3.7606348247488756`*^9}, {3.7606349119783344`*^9, 3.7606349350197754`*^9}, {3.76063496856853*^9, 3.7606349922504683`*^9}, { 3.760667269592998*^9, 3.760667271545692*^9}, 3.7606679283912125`*^9, 3.760668039709257*^9, {3.763302716900259*^9, 3.763302749083943*^9}, { 3.763304867499642*^9, 3.7633048681948185`*^9}, {3.763337978730939*^9, 3.763338014197137*^9}, {3.763338054806819*^9, 3.7633381289118147`*^9}, { 3.763338224472745*^9, 3.7633382447254143`*^9}, 3.763338501519575*^9, { 3.7633387342733064`*^9, 3.763338775483101*^9}, {3.7633388525735607`*^9, 3.7633390131554184`*^9}, {3.763360596353942*^9, 3.7633606328922167`*^9}, { 3.7633606638773637`*^9, 3.763360724941125*^9}, {3.763360812068123*^9, 3.763360863571327*^9}, {3.763361217769263*^9, 3.763361243271195*^9}, { 3.763361578316657*^9, 3.7633615820345063`*^9}, {3.763362291476118*^9, 3.763362301380039*^9}, {3.763362505004878*^9, 3.763362606421646*^9}, { 3.763362742167684*^9, 3.7633627524126663`*^9}, {3.7633628090243473`*^9, 3.763362931819517*^9}, 3.7633630680313087`*^9, {3.76336360941794*^9, 3.7633636782369685`*^9}, {3.763363813698273*^9, 3.763363822992702*^9}, { 3.7633837714269123`*^9, 3.763383775708086*^9}, {3.7633839861442327`*^9, 3.7633839966350546`*^9}, {3.7633846907375526`*^9, 3.76338471098131*^9}, 3.763426089635152*^9, {3.7634262143520336`*^9, 3.7634262475470448`*^9}, { 3.7634276458524485`*^9, 3.7634276705117846`*^9}, {3.7634292721860075`*^9, 3.7634292840439587`*^9}, {3.76352820463631*^9, 3.7635282147939873`*^9}, { 3.763528430960533*^9, 3.7635284413250494`*^9}, {3.7635285114344244`*^9, 3.763528537124817*^9}, {3.763528653934307*^9, 3.7635286747218256`*^9}, { 3.7635486952594075`*^9, 3.763548696007099*^9}, {3.7639579130072594`*^9, 3.7639579464687676`*^9}, {3.763957980699315*^9, 3.7639580928074217`*^9}, { 3.763959813173403*^9, 3.7639598134702053`*^9}, {3.7639608015345135`*^9, 3.7639608287155933`*^9}, {3.7645603385872726`*^9, 3.764560365934222*^9}, { 3.76456061596602*^9, 3.76456062636983*^9}, {3.7647257988231063`*^9, 3.7647258025896564`*^9}, {3.765077713031946*^9, 3.7650777913378534`*^9}, { 3.7740698865922914`*^9, 3.774069989744633*^9}, {3.7740700982535834`*^9, 3.774070098487667*^9}, {3.7740701415628414`*^9, 3.7740702370647106`*^9}, { 3.77407029325229*^9, 3.7740703348543596`*^9}, {3.774070397587008*^9, 3.774070454974152*^9}, {3.7740709929610343`*^9, 3.7740710067172923`*^9}, { 3.775190474681038*^9, 3.7751904884151363`*^9}, {3.7751905901325903`*^9, 3.775190642609686*^9}, 3.775190717712206*^9, {3.7751956728394384`*^9, 3.7751957010601625`*^9}, 3.7751957418100777`*^9, {3.7751958741450567`*^9, 3.775195882844048*^9}, {3.7751959530858574`*^9, 3.775196055684782*^9}, { 3.7836566506037264`*^9, 3.783656699859296*^9}, {3.783834162184903*^9, 3.7838342075157394`*^9}, {3.7838342453955064`*^9, 3.7838342564437876`*^9}, {3.783834288539219*^9, 3.783834289188504*^9}, { 3.783834319888338*^9, 3.783834404011998*^9}, {3.783835274452033*^9, 3.783835643262226*^9}, 3.783835673435833*^9, {3.783837186915415*^9, 3.783837252940491*^9}, 3.783838076793089*^9, {3.7838387026691084`*^9, 3.7838387106794033`*^9}, {3.7838387751330376`*^9, 3.78383877586726*^9}, 3.7885184612710266`*^9, {3.7885197610115976`*^9, 3.788519761667694*^9}, { 3.788519815581788*^9, 3.788519877459923*^9}, {3.788519910619506*^9, 3.7885199214314795`*^9}, {3.78852990807364*^9, 3.78852991935472*^9}, { 3.788529949778452*^9, 3.7885299511123505`*^9}, 3.7885729856546545`*^9, { 3.795769635061987*^9, 3.7957696738473544`*^9}, {3.7957698528454103`*^9, 3.795769867081932*^9}, {3.7963499268904905`*^9, 3.796349974573367*^9}, { 3.8116565658363085`*^9, 3.811656579625844*^9}, {3.8116566792733173`*^9, 3.811656696847624*^9}, {3.819778974172573*^9, 3.819778996370713*^9}, { 3.819779237456471*^9, 3.819779375493654*^9}, {3.819779556474127*^9, 3.8197797185600586`*^9}, 3.8200272939729*^9, 3.8200273875005593`*^9, 3.820027421880412*^9, {3.8200275035350485`*^9, 3.8200275049354267`*^9}, { 3.8459709950905457`*^9, 3.8459710017500772`*^9}, {3.8459711689546986`*^9, 3.8459711702691975`*^9}, {3.845971286165346*^9, 3.845971289846427*^9}, { 3.8459713248880577`*^9, 3.8459714501425343`*^9}, {3.845971579506527*^9, 3.8459716159320116`*^9}, {3.851994156946926*^9, 3.851994267451933*^9}, { 3.851994384355441*^9, 3.851994388857566*^9}, {3.8519946139658265`*^9, 3.8519947933175044`*^9}, {3.8519948506536093`*^9, 3.8519948668032107`*^9}, {3.8520795751469183`*^9, 3.852079576172632*^9}, { 3.852092396739352*^9, 3.8520925534144993`*^9}, {3.85242776319461*^9, 3.852427782014557*^9}}, CellLabel-> "In[149]:=",ExpressionUUID->"e31964a9-fd10-447e-9cb9-0775bb52af68"] }, Closed]], Cell[CellGroupData[{ Cell["BEAM ELEMENT (disp) defs ", "Subsection", CellChangeTimes->{{3.7530187996679964`*^9, 3.753018803413909*^9}, { 3.7633629633672647`*^9, 3.763362967100765*^9}, {3.787894773214689*^9, 3.7878947881941814`*^9}, {3.78789485671918*^9, 3.78789488217928*^9}, 3.7885197052606735`*^9, {3.788530025907043*^9, 3.7885300287809105`*^9}, 3.7885306781716957`*^9, {3.8200271989371843`*^9, 3.8200272016625395`*^9}, { 3.8200274346181693`*^9, 3.8200274405428553`*^9}, {3.851995002562483*^9, 3.851995003043193*^9}},ExpressionUUID->"49cc3388-fa6c-4867-a3aa-\ e5d8eb58f69b"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"MEC", "-", "E1050"}], "|", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iyy", ",", "Izz", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iyy", ",", "Izz", ",", "iy0"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iyy", ",", "Izz", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iyy", ",", "Izz", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "mX", ",", "mY", ",", "mZ"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "ix0", ",", "iz0", ",", "ux", ",", "uy", " ", ",", "uz", " ", ",", "\[Theta]x", " ", ",", "\[Theta]y", " ", ",", "\[Theta]z", " ", ",", "\[Delta]ux", " ", ",", "\[Delta]uy", ",", "\[Delta]uz", ",", "\[Delta]\[Theta]x", ",", "\[Delta]\[Theta]y", ",", "\[Delta]\[Theta]z", ",", "fx1", ",", "fx2", ",", "fy1", ",", "fy2", ",", "fz1", ",", "fz2", ",", "mx1", ",", "mx2", ",", "my1", ",", "my2", ",", "mz1", ",", "mz2", ",", "EEm", ",", "GGm", ",", "AAm", ",", "Iyym", ",", "Izzm"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "mapping", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz0", "=", RowBox[{"ix0", "\[Cross]", "iy0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", "1", "]"}], ",", RowBox[{"uy", "[", "1", "]"}], ",", RowBox[{"uz", "[", "1", "]"}]}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", "2", "]"}], ",", RowBox[{"uy", "[", "2", "]"}], ",", RowBox[{"uz", "[", "2", "]"}]}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", "1", "]"}], ",", RowBox[{"\[Theta]y", "[", "1", "]"}], ",", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", "2", "]"}], ",", RowBox[{"\[Theta]y", "[", "2", "]"}], ",", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], ",", RowBox[{"\[Delta]uy", "[", "1", "]"}], ",", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", "1", "]"}], ",", RowBox[{"uy", "[", "1", "]"}], ",", RowBox[{"uz", "[", "1", "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]ux", "[", "2", "]"}], ",", RowBox[{"\[Delta]uy", "[", "2", "]"}], ",", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", "2", "]"}], ",", RowBox[{"uy", "[", "2", "]"}], ",", RowBox[{"uz", "[", "2", "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], ",", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], ",", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", "1", "]"}], ",", RowBox[{"\[Theta]y", "[", "1", "]"}], ",", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], ",", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}], ",", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", "2", "]"}], ",", RowBox[{"\[Theta]y", "[", "2", "]"}], ",", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"EEm", "=", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], ".", RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "EE"}], ")"}]}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"GGm", "=", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], ".", RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "GG"}], ")"}]}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"AAm", "=", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], ".", RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "AA"}], ")"}]}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"Iyym", "=", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], ".", RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "Iyy"}], ")"}]}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"Izzm", "=", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], ".", RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "Izz"}], ")"}]}], "/", "2"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"fx1", ",", "fx2"}], "}"}], "=", RowBox[{"ix0", ".", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fX"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fY"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fZ"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"fy1", ",", "fy2"}], "}"}], "=", RowBox[{"iy0", ".", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fX"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fY"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fZ"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"fz1", ",", "fz2"}], "}"}], "=", RowBox[{"iz0", ".", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fX"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fY"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fZ"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"mx1", ",", "mx2"}], "}"}], "=", RowBox[{"ix0", ".", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "mX"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "mY"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "mZ"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"my1", ",", "my2"}], "}"}], "=", RowBox[{"iy0", ".", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "mX"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "mY"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "mZ"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"mz1", ",", "mz2"}], "}"}], "=", RowBox[{"iz0", ".", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "mX"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "mY"}], ",", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "mZ"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ FractionBox["1", RowBox[{"60", " ", SuperscriptBox["h0", "3"]}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "60"}], " ", "AAm", " ", "EEm", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"60", " ", "AAm", " ", "EEm", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"60", " ", "AAm", " ", "EEm", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "-", RowBox[{"60", " ", "AAm", " ", "EEm", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"10", " ", "fx1", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"10", " ", "fx2", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}]}], ")"}]}], "+", RowBox[{"21", " ", "fy1", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "+", RowBox[{"9", " ", "fy2", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "-", RowBox[{"30", " ", SuperscriptBox["h0", "3"], " ", "mz1", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "-", RowBox[{"30", " ", SuperscriptBox["h0", "3"], " ", "mz2", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "-", RowBox[{"720", " ", "EEm", " ", "Izzm", " ", RowBox[{"uy", "[", "1", "]"}], " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "+", RowBox[{"720", " ", "EEm", " ", "Izzm", " ", RowBox[{"uy", "[", "2", "]"}], " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "+", RowBox[{"9", " ", "fy1", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"21", " ", "fy2", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"30", " ", SuperscriptBox["h0", "3"], " ", "mz1", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"30", " ", SuperscriptBox["h0", "3"], " ", "mz2", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"720", " ", "EEm", " ", "Izzm", " ", RowBox[{"uy", "[", "1", "]"}], " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "-", RowBox[{"720", " ", "EEm", " ", "Izzm", " ", RowBox[{"uy", "[", "2", "]"}], " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"21", " ", "fz1", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"9", " ", "fz2", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"30", " ", SuperscriptBox["h0", "3"], " ", "my1", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"30", " ", SuperscriptBox["h0", "3"], " ", "my2", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "-", RowBox[{"720", " ", "EEm", " ", "Iyym", " ", RowBox[{"uz", "[", "1", "]"}], " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"720", " ", "EEm", " ", "Iyym", " ", RowBox[{"uz", "[", "2", "]"}], " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"9", " ", "fz1", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "+", RowBox[{"21", " ", "fz2", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "-", RowBox[{"30", " ", SuperscriptBox["h0", "3"], " ", "my1", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "-", RowBox[{"30", " ", SuperscriptBox["h0", "3"], " ", "my2", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "+", RowBox[{"720", " ", "EEm", " ", "Iyym", " ", RowBox[{"uz", "[", "1", "]"}], " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "-", RowBox[{"720", " ", "EEm", " ", "Iyym", " ", RowBox[{"uz", "[", "2", "]"}], " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "+", RowBox[{"20", " ", SuperscriptBox["h0", "4"], " ", "mx1", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"10", " ", SuperscriptBox["h0", "4"], " ", "mx2", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"10", " ", SuperscriptBox["h0", "4"], " ", "mx1", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}]}], "+", RowBox[{"20", " ", SuperscriptBox["h0", "4"], " ", "mx2", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}]}], "-", RowBox[{"3", " ", "fz1", " ", SuperscriptBox["h0", "5"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"2", " ", "fz2", " ", SuperscriptBox["h0", "5"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"5", " ", SuperscriptBox["h0", "4"], " ", "my1", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"5", " ", SuperscriptBox["h0", "4"], " ", "my2", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h0", " ", "Iyym", " ", RowBox[{"uz", "[", "1", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h0", " ", "Iyym", " ", RowBox[{"uz", "[", "2", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"2", " ", "fz1", " ", SuperscriptBox["h0", "5"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"3", " ", "fz2", " ", SuperscriptBox["h0", "5"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "-", RowBox[{"5", " ", SuperscriptBox["h0", "4"], " ", "my1", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"5", " ", SuperscriptBox["h0", "4"], " ", "my2", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h0", " ", "Iyym", " ", RowBox[{"uz", "[", "1", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h0", " ", "Iyym", " ", RowBox[{"uz", "[", "2", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"3", " ", "fy1", " ", SuperscriptBox["h0", "5"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"2", " ", "fy2", " ", SuperscriptBox["h0", "5"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"5", " ", SuperscriptBox["h0", "4"], " ", "mz1", " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"5", " ", SuperscriptBox["h0", "4"], " ", "mz2", " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h0", " ", "Izzm", " ", RowBox[{"uy", "[", "1", "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h0", " ", "Izzm", " ", RowBox[{"uy", "[", "2", "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"2", " ", "fy1", " ", SuperscriptBox["h0", "5"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"3", " ", "fy2", " ", SuperscriptBox["h0", "5"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"5", " ", SuperscriptBox["h0", "4"], " ", "mz1", " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "+", RowBox[{"5", " ", SuperscriptBox["h0", "4"], " ", "mz2", " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h0", " ", "Izzm", " ", RowBox[{"uy", "[", "1", "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h0", " ", "Izzm", " ", RowBox[{"uy", "[", "2", "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h0", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], " ", RowBox[{"\[Theta]x", "[", "1", "]"}]}], "-", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h0", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], " ", RowBox[{"\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h0", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], " ", RowBox[{"\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h0", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], " ", RowBox[{"\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h0", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], " ", RowBox[{"\[Theta]x", "[", "2", "]"}]}], "+", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h0", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], " ", RowBox[{"\[Theta]x", "[", "2", "]"}]}], "-", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h0", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], " ", RowBox[{"\[Theta]x", "[", "2", "]"}]}], "-", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h0", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], " ", RowBox[{"\[Theta]x", "[", "2", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h0", " ", "Iyym", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h0", " ", "Iyym", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"240", " ", "EEm", " ", SuperscriptBox["h0", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"120", " ", "EEm", " ", SuperscriptBox["h0", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h0", " ", "Iyym", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h0", " ", "Iyym", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "-", RowBox[{"120", " ", "EEm", " ", SuperscriptBox["h0", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "-", RowBox[{"240", " ", "EEm", " ", SuperscriptBox["h0", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h0", " ", "Izzm", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h0", " ", "Izzm", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"240", " ", "EEm", " ", SuperscriptBox["h0", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"120", " ", "EEm", " ", SuperscriptBox["h0", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h0", " ", "Izzm", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h0", " ", "Izzm", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"120", " ", "EEm", " ", SuperscriptBox["h0", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"240", " ", "EEm", " ", SuperscriptBox["h0", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}]}], ")"}]}]}]}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4430689313272*^9, 3.4430690080792*^9}, { 3.4430690869528*^9, 3.4430691077320004`*^9}, {3.4430691700116*^9, 3.4430691708072*^9}, {3.4430692071717997`*^9, 3.443069246359*^9}, { 3.4430772782732*^9, 3.4430773623416*^9}, {3.4430773978316*^9, 3.4430774104676*^9}, {3.4430775053780003`*^9, 3.4430776180598*^9}, { 3.4434109099524*^9, 3.4434109159584*^9}, {3.4438800815346003`*^9, 3.4438802689304*^9}, {3.443880362624*^9, 3.4438803824516*^9}, { 3.443929565615374*^9, 3.443929570232974*^9}, {3.443935321321974*^9, 3.443935335705174*^9}, {3.443935419945174*^9, 3.443935421489574*^9}, { 3.443935494013974*^9, 3.443935494715974*^9}, {3.443935617565974*^9, 3.4439357217895737`*^9}, {3.443935755360774*^9, 3.443935816107174*^9}, { 3.443942155230774*^9, 3.443942209939974*^9}, {3.443942305710374*^9, 3.4439423142123737`*^9}, {3.4439442908131742`*^9, 3.443944441181574*^9}, { 3.4439447830065737`*^9, 3.4439447917425737`*^9}, {3.443944908541774*^9, 3.443944916060974*^9}, {3.4442731097938004`*^9, 3.4442731115254*^9}, { 3.444273189229*^9, 3.4442732700526*^9}, {3.4442748430004*^9, 3.4442748605036*^9}, {3.4442748977438*^9, 3.4442748989762*^9}, { 3.4442749340762*^9, 3.4442749351057997`*^9}, 3.4442752313382*^9, { 3.4442919702026*^9, 3.4442919911846*^9}, {3.4442921151577997`*^9, 3.4442921271074*^9}, {3.4443811023684*^9, 3.4443811036632*^9}, { 3.4443814073171997`*^9, 3.4443814402956*^9}, {3.4443815036316*^9, 3.4443815147855997`*^9}, {3.4443815537232*^9, 3.4443815747676*^9}, { 3.4443816138143997`*^9, 3.444381633174*^9}, {3.4443816850439997`*^9, 3.4443817801728*^9}, 3.4443853618688*^9, {3.4443855607376003`*^9, 3.4443856337924*^9}, {3.4443861200444*^9, 3.4443861523676*^9}, { 3.4443862280495996`*^9, 3.444386291448*^9}, {3.4443864047352*^9, 3.4443864135336*^9}, {3.4443870026832*^9, 3.4443870095316*^9}, { 3.4444082055056*^9, 3.4444082437412*^9}, {3.4444082797148*^9, 3.4444084583816*^9}, {3.4444084889108*^9, 3.4444085087539997`*^9}, { 3.444408942517*^9, 3.4444089563386*^9}, {3.4444091419564*^9, 3.4444091647167997`*^9}, {3.4444092206428003`*^9, 3.4444092944463997`*^9}, {3.4444093856284*^9, 3.4444094281071997`*^9}, { 3.4444094976988*^9, 3.4444095275104*^9}, {3.444409611064*^9, 3.4444096125772*^9}, 3.4444098504616003`*^9, {3.444409913392*^9, 3.4444099166056004`*^9}, 3.4444100178496*^9, {3.4444103063248*^9, 3.4444103358712*^9}, {3.4444103868208*^9, 3.4444104432460003`*^9}, { 3.4444921219564*^9, 3.4444921256224003`*^9}, {3.444492194824*^9, 3.4444921973668003`*^9}, {3.4444922814351997`*^9, 3.4444922853508*^9}, { 3.4444923330868*^9, 3.4444923345844*^9}, {3.444492366424*^9, 3.4444923855808*^9}, {3.4453153475226*^9, 3.445315360689*^9}, { 3.4465518166373653`*^9, 3.446551863016165*^9}, {3.446551894231765*^9, 3.446552159384965*^9}, {3.446552232377365*^9, 3.4465522555589647`*^9}, { 3.446553347388365*^9, 3.4465533616155653`*^9}, {3.4466058525769997`*^9, 3.4466058529046*^9}, {3.4466064371219997`*^9, 3.4466065097244*^9}, { 3.4466127725788*^9, 3.4466127766036*^9}, {3.4466128124835997`*^9, 3.4466130037864*^9}, {3.4466131532696*^9, 3.4466131761703997`*^9}, { 3.4466133992192*^9, 3.4466134478756*^9}, {3.446613483584*^9, 3.4466134932092*^9}, {3.4466135740952*^9, 3.4466135794927998`*^9}, { 3.4466137283948*^9, 3.4466137341356*^9}, {3.4466138994342003`*^9, 3.4466139023826*^9}, {3.4466139549858*^9, 3.4466139579653997`*^9}, { 3.4466142109818*^9, 3.4466142245226*^9}, {3.4466142793878*^9, 3.4466143652033997`*^9}, {3.4466144712834*^9, 3.4466145978929996`*^9}, { 3.4466146992618*^9, 3.4466147509914*^9}, {3.4466151283086*^9, 3.4466152768986*^9}, {3.4466153107506*^9, 3.4466153406558*^9}, { 3.4466194331976*^9, 3.4466194377528*^9}, {3.4466194847712*^9, 3.446619488718*^9}, {3.4466389495861998`*^9, 3.4466389768238*^9}, { 3.4466391218414*^9, 3.446639306561*^9}, {3.4466393990222*^9, 3.4466394004886*^9}, {3.4466394475694*^9, 3.4466394487706003`*^9}, { 3.4466395034174*^9, 3.4466395049462*^9}, 3.4466395515755997`*^9, { 3.4466396000176*^9, 3.4466396190808*^9}, {3.4466397459088*^9, 3.446639748826*^9}, {3.4466397974356003`*^9, 3.446639798668*^9}, 3.4466398447816*^9, {3.446639894218*^9, 3.4466399201556*^9}, { 3.4466399570964003`*^9, 3.4466399583288*^9}, {3.446639994006*^9, 3.4466400056904*^9}, {3.4466400383568*^9, 3.4466400395892*^9}, { 3.4466400745643997`*^9, 3.4466401025976*^9}, {3.4466401660834*^9, 3.4466401806070004`*^9}, {3.4466402251294003`*^9, 3.446640227407*^9}, { 3.446640260479*^9, 3.4466402657674*^9}, {3.4466404133122*^9, 3.4466405185654*^9}, 3.4466405830462*^9, {3.4467273294214*^9, 3.4467273777813997`*^9}, {3.4467274366558*^9, 3.4467275620954*^9}, { 3.446727593311*^9, 3.4467277412614*^9}, {3.4467283334639997`*^9, 3.4467283356012*^9}, {3.4467283707636003`*^9, 3.4467283727604*^9}, { 3.4467289882664003`*^9, 3.4467291276836*^9}, {3.446778464322*^9, 3.4467786797424*^9}, {3.4467801953803997`*^9, 3.4467802409792*^9}, { 3.4467802998691998`*^9, 3.4467804023456*^9}, 3.4467804345596*^9, { 3.4467808656344*^9, 3.4467808670852003`*^9}, 3.4467818107525997`*^9, { 3.446781855509*^9, 3.446781874385*^9}, {3.4467826737914*^9, 3.4467827381726*^9}, {3.4467828623018*^9, 3.4467831045386*^9}, { 3.4470344113984003`*^9, 3.4470344123344*^9}, {3.4470344628316*^9, 3.4470345343108*^9}, {3.447043591118539*^9, 3.447043642192939*^9}, { 3.447045649625739*^9, 3.447045718437339*^9}, {3.447054774023939*^9, 3.447054834198939*^9}, {3.4470549103449388`*^9, 3.4470549116169386`*^9}, { 3.447054943902939*^9, 3.4470553027109385`*^9}, {3.447055334559939*^9, 3.447055353684939*^9}, {3.447057311918539*^9, 3.447057369747739*^9}, { 3.4470575058577385`*^9, 3.4470575951365385`*^9}, {3.4470581848789387`*^9, 3.4470582040825386`*^9}, {3.451276121243*^9, 3.4512761425838003`*^9}, { 3.4512762022382*^9, 3.4512762064346*^9}, {3.4512762476966*^9, 3.4512762827654*^9}, {3.451276489091*^9, 3.451276541975*^9}, { 3.4512765853118*^9, 3.4512766132046003`*^9}, {3.4512773470306*^9, 3.4512773766082*^9}, {3.4512776069110003`*^9, 3.4512777499318*^9}, 3.4512777831286*^9, {3.4512778785538*^9, 3.451277881627*^9}, { 3.4512780242734003`*^9, 3.4512780302794*^9}, 3.4512780737878*^9, { 3.4512781866226*^9, 3.4512781930810003`*^9}, {3.4512863325078*^9, 3.4512863539266*^9}, {3.4568019250434*^9, 3.4568022712698*^9}, { 3.4568023177422*^9, 3.4568024125278*^9}, {3.4568024694365997`*^9, 3.4568024750369997`*^9}, {3.4568026914402*^9, 3.4568028101094*^9}, { 3.4568028406698*^9, 3.4568028564726*^9}, 3.4568028886085997`*^9, { 3.4568030489454*^9, 3.4568030800986*^9}, 3.4568032004128*^9, { 3.4568035073698*^9, 3.4568035176034*^9}, {3.4568040146596003`*^9, 3.4568040844852*^9}, {3.4568043016684*^9, 3.4568043154744*^9}, { 3.4568045482264*^9, 3.4568045486632*^9}, {3.4568048944996*^9, 3.4568049806116*^9}, {3.4660560628582*^9, 3.4660560753538*^9}, { 3.4660676729379997`*^9, 3.4660676735931997`*^9}, {3.4660677244024*^9, 3.4660677277251997`*^9}, {3.4742646771287394`*^9, 3.47426469439174*^9}, { 3.47426489921974*^9, 3.4742649800437393`*^9}, {3.4801246373348*^9, 3.4801246860536003`*^9}, {3.4801247748176003`*^9, 3.4801247821028*^9}, { 3.4801248161264*^9, 3.4801248295736*^9}, {3.4801248810692*^9, 3.4801248964508*^9}, {3.4801249330484*^9, 3.480124947884*^9}, 3.4801249886468*^9, {3.4801251139147997`*^9, 3.48012512588*^9}, { 3.4838339444988003`*^9, 3.4838339567448*^9}, 3.4838341692012*^9, { 3.4838344350408*^9, 3.4838344353684*^9}, {3.4938987575920324`*^9, 3.4938987586840324`*^9}, {3.4941630624049997`*^9, 3.4941631381274*^9}, { 3.4941632311345997`*^9, 3.4941632492306004`*^9}, 3.4941633249217997`*^9, { 3.4941633940922003`*^9, 3.4941634063538*^9}, {3.4941634538402*^9, 3.4941635051642*^9}, {3.494163565115*^9, 3.4941636341762*^9}, { 3.4941636853442*^9, 3.4941639323234*^9}, {3.4941640277798*^9, 3.4941641455754004`*^9}, {3.4941641790374002`*^9, 3.4941641803789997`*^9}, {3.4941642676142*^9, 3.4941643277678003`*^9}, 3.4941644677018003`*^9, {3.4941646208938*^9, 3.4941646322349997`*^9}, { 3.4941652592693996`*^9, 3.4941652807194*^9}, {3.4941653119038*^9, 3.494165416299*^9}, {3.494165453895*^9, 3.4941654544722*^9}, { 3.4950990979779997`*^9, 3.495099142701*^9}, {3.495099172958*^9, 3.4950991806289997`*^9}, {3.495099227097*^9, 3.495099238113*^9}, 3.495099290797*^9, {3.495099346084*^9, 3.495099359507*^9}, { 3.495099456308*^9, 3.495099464091*^9}, 3.495099683108*^9, { 3.495100428112*^9, 3.495100434958*^9}, {3.4951006496219997`*^9, 3.495100649992*^9}, {3.4987235265018*^9, 3.4987235939094*^9}, { 3.4987236420666*^9, 3.4987236530646*^9}, {3.4987237305341997`*^9, 3.4987237396914*^9}, {3.498733136159*^9, 3.4987332972446003`*^9}, { 3.4987364783094*^9, 3.4987364860626*^9}, {3.4987366201134*^9, 3.4987366236078*^9}, {3.4987367272386*^9, 3.4987367464890003`*^9}, { 3.4987369428462*^9, 3.4987369670886*^9}, {3.4987370134518003`*^9, 3.4987370259941998`*^9}, {3.4987370944002*^9, 3.4987371027618*^9}, { 3.4987371921029997`*^9, 3.498737193663*^9}, {3.4987372660938*^9, 3.4987372935498*^9}, {3.4987373290554*^9, 3.4987377176202*^9}, { 3.4987377520182*^9, 3.4987379139462*^9}, {3.4987382030216*^9, 3.4987382667078*^9}, {3.4987888391818*^9, 3.4987888608346*^9}, { 3.4988785131146*^9, 3.4988785160162*^9}, {3.5007170967096*^9, 3.5007170999076*^9}, 3.5007182237316*^9, {3.5007182772864*^9, 3.5007182987832003`*^9}, {3.5009573226744003`*^9, 3.5009573940444*^9}, 3.5009574358710003`*^9, 3.5009604278482*^9, {3.5009897246173353`*^9, 3.5009898480289354`*^9}, {3.5009901464413357`*^9, 3.5009901475333357`*^9}, {3.5009901801997356`*^9, 3.500990274096135*^9}, { 3.5010475253292*^9, 3.5010475852332*^9}, {3.5010605722018003`*^9, 3.5010606739762*^9}, {3.5010607202146*^9, 3.5010607323358*^9}, { 3.5010607920526*^9, 3.501061118467*^9}, {3.5010612022078*^9, 3.5010612277138*^9}, {3.5010616467766*^9, 3.5010617938534*^9}, { 3.5010618406222*^9, 3.5010619950778*^9}, {3.5010621500638*^9, 3.5010622514014*^9}, {3.5010625292218*^9, 3.5010625409374*^9}, { 3.5010626043046*^9, 3.5010626313862*^9}, {3.5010626787166*^9, 3.5010626790754004`*^9}, {3.501074457561*^9, 3.5010744671082*^9}, 3.5010763029458*^9, {3.5032210899309998`*^9, 3.5032212413900003`*^9}, { 3.557658203404973*^9, 3.557658219644601*^9}, {3.5576584433801947`*^9, 3.557658496030287*^9}, {3.5576585501779823`*^9, 3.5576586046064777`*^9}, { 3.557658648910555*^9, 3.557658754600741*^9}, {3.557658963945511*^9, 3.5576589782507353`*^9}, {3.557659009949991*^9, 3.5576591437514267`*^9}, { 3.557659182221094*^9, 3.5576592187719584`*^9}, 3.557659413865901*^9, { 3.557659921100792*^9, 3.5576599556392527`*^9}, {3.557660706920972*^9, 3.5576607248454037`*^9}, {3.557661209085854*^9, 3.557661209413454*^9}, { 3.5577526651911488`*^9, 3.5577526932087984`*^9}, {3.5577527272480583`*^9, 3.557752747122493*^9}, {3.5577528374934516`*^9, 3.557752838523053*^9}, { 3.557752881204728*^9, 3.557752891313546*^9}, {3.557752938612829*^9, 3.5577529469120436`*^9}, {3.557753060714244*^9, 3.557753062633047*^9}, { 3.5577536609544907`*^9, 3.5577536637936954`*^9}, {3.5577537824631042`*^9, 3.557753810184353*^9}, {3.557753841025607*^9, 3.5577540648392*^9}, 3.5577541920574236`*^9, {3.5577547033327217`*^9, 3.557754716967146*^9}, { 3.5577547716296415`*^9, 3.557754802112095*^9}, {3.5577549509363565`*^9, 3.5577549771444025`*^9}, 3.5577551382302856`*^9, {3.55775527184452*^9, 3.557755272858522*^9}, {3.557755881555991*^9, 3.557755886548*^9}, { 3.557756158316077*^9, 3.557756231885806*^9}, {3.5577572408487787`*^9, 3.557757248835993*^9}, {3.5577572834368534`*^9, 3.5577575888229895`*^9}, { 3.5577578129641833`*^9, 3.557757862837471*^9}, {3.557758025514557*^9, 3.557758079272251*^9}, 3.557810586960072*^9, {3.5578240262005973`*^9, 3.5578240345360737`*^9}, {3.557824091429328*^9, 3.5578241008156557`*^9}, { 3.557831525255726*^9, 3.5578315319793377`*^9}, 3.5578315716190076`*^9, { 3.557831606079468*^9, 3.557831629432709*^9}, {3.5578316663267736`*^9, 3.5578317569473333`*^9}, {3.5578322144181366`*^9, 3.557832218084143*^9}, { 3.557836356693412*^9, 3.557836473771618*^9}, {3.5578365201660995`*^9, 3.5578365974018345`*^9}, {3.5578366426731143`*^9, 3.557836658865943*^9}, { 3.557836691017599*^9, 3.5578367924957776`*^9}, {3.5578368305442443`*^9, 3.557836888279946*^9}, {3.5578369382156334`*^9, 3.5578370776642785`*^9}, { 3.5578383536061196`*^9, 3.5578383735117545`*^9}, {3.5578385892445335`*^9, 3.5578385978869486`*^9}, {3.5578386713006773`*^9, 3.557838700113928*^9}, { 3.5578387451200075`*^9, 3.5578387467892103`*^9}, {3.5578388951454706`*^9, 3.5578389248635225`*^9}, {3.5578389679351983`*^9, 3.557838983535226*^9}, { 3.5578390227692947`*^9, 3.557839023143696*^9}, {3.557839097696226*^9, 3.5578391125162525`*^9}, {3.5578391553539276`*^9, 3.557839199892006*^9}, { 3.55783924184048*^9, 3.557839294490572*^9}, {3.5578393285922318`*^9, 3.557839398683155*^9}, {3.557839430522811*^9, 3.557839470162481*^9}, { 3.5578395370865984`*^9, 3.5578395446994114`*^9}, {3.5578396068499207`*^9, 3.5578396118575296`*^9}, 3.5578943518105097`*^9, {3.557894388361374*^9, 3.5578944029629993`*^9}, {3.5578944607611012`*^9, 3.5578944989499683`*^9}, {3.5578945393696394`*^9, 3.557894561537278*^9}, { 3.5578946028617506`*^9, 3.5578946188985786`*^9}, {3.557894650894235*^9, 3.5578947812636642`*^9}, {3.55789481884413*^9, 3.5578948191249304`*^9}, { 3.5578949768100076`*^9, 3.5578949836272197`*^9}, {3.5578967386805477`*^9, 3.55789678549623*^9}, {3.5578968804691963`*^9, 3.557896888643611*^9}, { 3.557897022491846*^9, 3.5578970341450663`*^9}, {3.557897620940097*^9, 3.55789765120415*^9}, {3.5579218072271147`*^9, 3.5579218263059483`*^9}, { 3.557922095312821*^9, 3.557922116965659*^9}, {3.557922178086566*^9, 3.557922188616585*^9}, {3.5579223258812256`*^9, 3.557922327066828*^9}, { 3.5579224596046605`*^9, 3.557922461804264*^9}, 3.5579805928465395`*^9, { 3.5579815200581703`*^9, 3.557981541711009*^9}, 3.557985544779242*^9, { 3.5579863164793987`*^9, 3.5579863339514294`*^9}, {3.557986523210962*^9, 3.557986568841042*^9}, 3.5579866122559185`*^9, 3.557986993536188*^9, { 3.5579871244716187`*^9, 3.5579871290580263`*^9}, 3.557987173486905*^9, 3.5579872166989803`*^9, {3.5599618621582537`*^9, 3.5599618642486577`*^9}, { 3.559961969720443*^9, 3.5599619894700775`*^9}, 3.559963611089726*^9, { 3.5601298891258235`*^9, 3.560129889422224*^9}, {3.560132445157113*^9, 3.5601324458591146`*^9}, {3.561978472080926*^9, 3.561978472392926*^9}, { 3.6297802564412937`*^9, 3.6297802957377625`*^9}, {3.62978033369263*^9, 3.629780429741998*^9}, {3.6297805790030603`*^9, 3.6297809429048996`*^9}, { 3.629780987957779*^9, 3.629781197575347*^9}, {3.629781240397422*^9, 3.629781337663593*^9}, {3.6297813946972933`*^9, 3.6297814529165955`*^9}, { 3.6297814952550697`*^9, 3.629781527578326*^9}, {3.62978162025529*^9, 3.629781647633338*^9}, {3.629781678833393*^9, 3.629781763120341*^9}, 3.6297818028224106`*^9, {3.6297818432108817`*^9, 3.629781872570133*^9}, { 3.629782355765382*^9, 3.629782427603508*^9}, {3.6297824692243814`*^9, 3.629782674863942*^9}, {3.629782707218399*^9, 3.6297829295343895`*^9}, { 3.629783005631323*^9, 3.6297830574702144`*^9}, {3.6297831098551064`*^9, 3.629783142786764*^9}, {3.629783433711675*^9, 3.629783442619291*^9}, { 3.6297834942397814`*^9, 3.6297835175930223`*^9}, 3.6297835794939313`*^9, { 3.6297836160291953`*^9, 3.6297837668970604`*^9}, {3.6297842042438283`*^9, 3.6297842697483435`*^9}, {3.6297843514456873`*^9, 3.629784370742921*^9}, { 3.629784443829049*^9, 3.6297844678842916`*^9}, {3.6297845252611923`*^9, 3.629784525588793*^9}, {3.6297846136821475`*^9, 3.629784629235375*^9}, { 3.629784814797701*^9, 3.629784927648299*^9}, {3.629785259960083*^9, 3.6297852602096834`*^9}, {3.6297858780175686`*^9, 3.629785917282837*^9}, { 3.629786048057867*^9, 3.629786048681868*^9}, 3.6297863278755584`*^9, { 3.6297867047133856`*^9, 3.629786748533863*^9}, {3.6297867791567163`*^9, 3.6297868491540394`*^9}, {3.6297875320748396`*^9, 3.629787569795706*^9}, { 3.6297876247234025`*^9, 3.6297877281983843`*^9}, {3.6297877681812544`*^9, 3.629787774015665*^9}, {3.629787831408166*^9, 3.6297878355265727`*^9}, { 3.6297878775686464`*^9, 3.6297878861174617`*^9}, {3.6297879185343184`*^9, 3.629787919064719*^9}, {3.6297880043032694`*^9, 3.62978800470887*^9}, 3.6297880488257475`*^9, {3.6297882100052304`*^9, 3.6297882174776435`*^9}, { 3.6297882697533355`*^9, 3.6297882948381796`*^9}, {3.6297883467550707`*^9, 3.6297883991087627`*^9}, {3.6297887361785545`*^9, 3.629788783961438*^9}, 3.629788825395111*^9, {3.629789006152629*^9, 3.6297890321266747`*^9}, { 3.6297891133248167`*^9, 3.629789145336073*^9}, {3.6297891926821566`*^9, 3.629789194257759*^9}, {3.629789255316266*^9, 3.6297892556282673`*^9}, { 3.629869102295367*^9, 3.629869160124668*^9}, {3.6298691942887287`*^9, 3.6298696149902673`*^9}, {3.6298696993864155`*^9, 3.62986975897852*^9}, { 3.6298698387726603`*^9, 3.629869912030389*^9}, {3.6298700722270703`*^9, 3.629870234560955*^9}, {3.629870580429163*^9, 3.629870630458451*^9}, { 3.630556081081209*^9, 3.630556104902451*^9}, {3.6305562643503313`*^9, 3.6305562763935523`*^9}, {3.6305563415080667`*^9, 3.630556480956712*^9}, { 3.630556692851884*^9, 3.630556695347888*^9}, {3.630556730042349*^9, 3.630556914528273*^9}, {3.6305653725974936`*^9, 3.6305656807121167`*^9}, { 3.630565758760581*^9, 3.6305657739024467`*^9}, {3.630565858170267*^9, 3.63056596644846*^9}, {3.6305661502619734`*^9, 3.6305661523230915`*^9}, { 3.6305662653385553`*^9, 3.630566370352562*^9}, {3.6305667786019125`*^9, 3.630566790535595*^9}, {3.6305668214773645`*^9, 3.630567044691132*^9}, { 3.6305670772499943`*^9, 3.6305670783710585`*^9}, 3.630567272031135*^9, { 3.630567303902958*^9, 3.630567409875019*^9}, {3.630568671196477*^9, 3.6305687195002403`*^9}, {3.6305687542132254`*^9, 3.630568758623478*^9}, { 3.630568855671028*^9, 3.630568859250233*^9}, {3.630569706514694*^9, 3.630569775526641*^9}, 3.630569982346471*^9, {3.6305701679130845`*^9, 3.630570205199217*^9}, {3.6305703751399374`*^9, 3.630570526177576*^9}, { 3.630587657039589*^9, 3.630587688367381*^9}, {3.6305880733027773`*^9, 3.6305883365376396`*^9}, {3.6305886689118233`*^9, 3.6305886717978287`*^9}, 3.6305889776831656`*^9, {3.6305890389444733`*^9, 3.6305890437180815`*^9}, { 3.630589093248169*^9, 3.6305891296430326`*^9}, 3.630589181700324*^9, { 3.6305892509956455`*^9, 3.6305892594820604`*^9}, {3.630589318949365*^9, 3.6305893334729905`*^9}, {3.630589630294712*^9, 3.6305896376267247`*^9}, { 3.630589683288005*^9, 3.630589684988408*^9}, {3.630597310538067*^9, 3.630597340080757*^9}, {3.630597391446695*^9, 3.630597400596218*^9}, { 3.6305974350611897`*^9, 3.6305974605306463`*^9}, {3.630633997622449*^9, 3.630634003125764*^9}, {3.630659322217756*^9, 3.63065932438616*^9}, { 3.6306611578252783`*^9, 3.6306611625988865`*^9}, {3.6306612541554475`*^9, 3.630661257587454*^9}, {3.6306613001287284`*^9, 3.6306613026715326`*^9}, { 3.6306613920752897`*^9, 3.6306613949768953`*^9}, {3.6306706377509866`*^9, 3.630670654957817*^9}, {3.6306749981919994`*^9, 3.630675005793434*^9}, { 3.6306751229631357`*^9, 3.630675150017683*^9}, {3.6306752035287437`*^9, 3.6306752096180925`*^9}, {3.630675315921172*^9, 3.6306753201514144`*^9}, { 3.6306757793287754`*^9, 3.6306757796257925`*^9}, {3.630675814406262*^9, 3.6306758147026625`*^9}, {3.6306760107574763`*^9, 3.6306760154417443`*^9}, {3.6306789722320743`*^9, 3.6306789870309205`*^9}, {3.6306790257051325`*^9, 3.630679028076268*^9}, { 3.6306800259177256`*^9, 3.6306800406129513`*^9}, {3.6306801239326982`*^9, 3.6306801300167084`*^9}, {3.630680769261832*^9, 3.6306807806186523`*^9}, { 3.630681157468514*^9, 3.6306811577649145`*^9}, {3.6306812744219193`*^9, 3.63068127471832*^9}, {3.6306817187418995`*^9, 3.6306817919060287`*^9}, { 3.630681879188182*^9, 3.6306819111526375`*^9}, {3.6306821191790032`*^9, 3.6306821283050194`*^9}, {3.630720543651497*^9, 3.6307205534300566`*^9}, { 3.630721035525631*^9, 3.630721092774905*^9}, {3.6307212510439577`*^9, 3.6307213064777765`*^9}, {3.6307477437169704`*^9, 3.6307478284095197`*^9}, {3.6307478614971776`*^9, 3.6307478785948076`*^9}, {3.6307479884814005`*^9, 3.630748002880226*^9}, { 3.630748045624301*^9, 3.630748063876333*^9}, {3.630748111596817*^9, 3.6307481498324842`*^9}, {3.6307489182430334`*^9, 3.6307489447786803`*^9}, {3.630749037427243*^9, 3.6307490443848553`*^9}, { 3.6307491041485605`*^9, 3.6307491384218206`*^9}, {3.6307491914151134`*^9, 3.630749196890723*^9}, {3.6307492445800066`*^9, 3.6307493439989815`*^9}, { 3.630749396212273*^9, 3.6307494766304145`*^9}, {3.6307495333989143`*^9, 3.6307495547241516`*^9}, {3.6307496525831237`*^9, 3.630749669571553*^9}, { 3.630750220602922*^9, 3.6307502881822405`*^9}, {3.6307510631916018`*^9, 3.630751068292811*^9}, {3.6307511226589065`*^9, 3.630751137962533*^9}, { 3.6307512555243397`*^9, 3.630751282777588*^9}, {3.630752266971757*^9, 3.630752414599744*^9}, {3.630752446407563*^9, 3.630752457388191*^9}, { 3.6307589380050273`*^9, 3.6307590266300964`*^9}, {3.6307591666721067`*^9, 3.63075923229886*^9}, 3.630760288282259*^9, {3.6307603547370596`*^9, 3.630760557414652*^9}, {3.630760654134184*^9, 3.63076065510824*^9}, { 3.6307606911683025`*^9, 3.6307606919283457`*^9}, {3.6307607642334814`*^9, 3.6307607648645177`*^9}, {3.630761455000991*^9, 3.6307614616743727`*^9}, { 3.630761507825012*^9, 3.630761605776615*^9}, {3.630761652999316*^9, 3.630761695865768*^9}, {3.630761771278081*^9, 3.6307617792215357`*^9}, 3.6307629478424797`*^9, {3.632205207880766*^9, 3.6322052561155243`*^9}, { 3.6322052892474194`*^9, 3.6322052915745525`*^9}, 3.6322053746993074`*^9, { 3.6322062705415463`*^9, 3.6322062726016645`*^9}, {3.6322063396935015`*^9, 3.63220636484194*^9}, {3.6322064410612993`*^9, 3.6322064491667633`*^9}, { 3.632206580308264*^9, 3.6322066373275256`*^9}, {3.6322066736436024`*^9, 3.6322067467737856`*^9}, {3.632206782260815*^9, 3.6322071351279984`*^9}, 3.6322071989226465`*^9, {3.632207270393735*^9, 3.6322073359894867`*^9}, { 3.6322073997741346`*^9, 3.6322074126708727`*^9}, {3.632207491777397*^9, 3.632207682289294*^9}, {3.632207809621577*^9, 3.632207827973626*^9}, { 3.6322079043859973`*^9, 3.6322079279443445`*^9}, {3.6322080916397076`*^9, 3.6322081666649985`*^9}, 3.634905258940913*^9, {3.634905370524296*^9, 3.6349054089004903`*^9}, {3.6349054472556844`*^9, 3.63490544787272*^9}, { 3.634905483492757*^9, 3.6349055164646425`*^9}, {3.634905574352954*^9, 3.634905628121029*^9}, {3.6349057012822137`*^9, 3.6349057207913294`*^9}, { 3.6349061371061416`*^9, 3.634906354438572*^9}, {3.6349063890455513`*^9, 3.6349064369332905`*^9}, {3.634906537696054*^9, 3.634906601859724*^9}, 3.634906706128688*^9, {3.6349069249442034`*^9, 3.6349069328326545`*^9}, { 3.6349070151973653`*^9, 3.6349070242298822`*^9}, {3.6349070817921743`*^9, 3.6349070822111983`*^9}, {3.634907723288866*^9, 3.634907739005765*^9}, { 3.6349079580732946`*^9, 3.6349079868219395`*^9}, {3.634908200284148*^9, 3.634908315195721*^9}, {3.6349083774582825`*^9, 3.6349084027997313`*^9}, { 3.63490844507615*^9, 3.634908448843365*^9}, {3.634914956333157*^9, 3.634915020054802*^9}, {3.634915050572547*^9, 3.6349150956171236`*^9}, { 3.6349539785771523`*^9, 3.634953978975175*^9}, {3.6349540728785458`*^9, 3.6349541681829967`*^9}, {3.634954211263461*^9, 3.6349542495746527`*^9}, { 3.6349543251259737`*^9, 3.634954355882733*^9}, {3.6349543892536416`*^9, 3.6349544742835045`*^9}, {3.634954547519694*^9, 3.6349545640246377`*^9}, { 3.6349547051657104`*^9, 3.6349547107930326`*^9}, {3.634954745355009*^9, 3.634954752101395*^9}, {3.6349547948858423`*^9, 3.6349548053894434`*^9}, { 3.634954904907135*^9, 3.6349549451084347`*^9}, {3.634955219605135*^9, 3.6349552640926795`*^9}, {3.634955320189888*^9, 3.634955348763522*^9}, { 3.634955386393675*^9, 3.6349555039273973`*^9}, {3.6349557669644423`*^9, 3.6349557672004557`*^9}, {3.634955894841756*^9, 3.634955902578199*^9}, { 3.6349559513739896`*^9, 3.6349560216320086`*^9}, {3.634956120144643*^9, 3.634956128996149*^9}, {3.6349561700724983`*^9, 3.6349561978900895`*^9}, { 3.6349562480719595`*^9, 3.634956254326318*^9}, {3.634956331684742*^9, 3.6349563460575643`*^9}, {3.634956379242462*^9, 3.63495642676418*^9}, 3.6349564696636343`*^9, {3.6351524116477795`*^9, 3.6351524153379908`*^9}, { 3.6352134400282927`*^9, 3.635213442148414*^9}, {3.6352134745862694`*^9, 3.635213495869487*^9}, {3.6352135383409157`*^9, 3.6352137157160616`*^9}, { 3.6352137493569856`*^9, 3.635213764522853*^9}, {3.635214215036621*^9, 3.635214227593339*^9}, {3.635214407257615*^9, 3.63521441713218*^9}, { 3.635215297101512*^9, 3.635215303964904*^9}, {3.6352154111120324`*^9, 3.635215431504199*^9}, {3.635216346055508*^9, 3.635216494371991*^9}, { 3.635216631050809*^9, 3.6352166603244834`*^9}, {3.635216763034358*^9, 3.635216764164423*^9}, {3.6352168771938877`*^9, 3.635216888828553*^9}, 3.6352169832479534`*^9, 3.635217037668066*^9, {3.6352172024924936`*^9, 3.6352172054526625`*^9}, {3.635217344025589*^9, 3.635217346898753*^9}, 3.6352173863770113`*^9, {3.635217519639633*^9, 3.6352175507014103`*^9}, 3.635217615445113*^9, {3.6352178715087595`*^9, 3.635217880460271*^9}, { 3.6352185912849283`*^9, 3.635218598444338*^9}, {3.6352186995721216`*^9, 3.635218714955002*^9}, {3.6352189761749425`*^9, 3.6352189789341*^9}, { 3.6352195060322485`*^9, 3.635219509972474*^9}, 3.6352195673477554`*^9, 3.6352195994635925`*^9, {3.6352197336482677`*^9, 3.635219737452485*^9}, { 3.6352197706093817`*^9, 3.6352197723214793`*^9}, {3.635219941784172*^9, 3.6352199485115566`*^9}, {3.6352200714185867`*^9, 3.6352200854323883`*^9}, {3.6352202085694313`*^9, 3.635220235849992*^9}, { 3.6352202816336107`*^9, 3.6352203110962954`*^9}, {3.6352204980449886`*^9, 3.6352205276526823`*^9}, {3.6352253191447396`*^9, 3.6352253299913597`*^9}, {3.6352253611111403`*^9, 3.6352253637572913`*^9}, {3.635225409322898*^9, 3.6352255965196047`*^9}, { 3.6352260914249115`*^9, 3.6352261698393965`*^9}, {3.63522638233055*^9, 3.6352264188036366`*^9}, {3.635227493469104*^9, 3.635227556935734*^9}, { 3.6352276745764627`*^9, 3.635227730116639*^9}, {3.6352287979917183`*^9, 3.6352288587651944`*^9}, {3.635228894237223*^9, 3.635228948324317*^9}, { 3.635229365252164*^9, 3.6352293902275925`*^9}, {3.63522947690555*^9, 3.6352294807837715`*^9}, {3.6352492831123204`*^9, 3.6352492983621926`*^9}, 3.6356569054520617`*^9, {3.6363778004499054`*^9, 3.636377802787039*^9}, { 3.6363778414932528`*^9, 3.6363778525308843`*^9}, {3.636384436335312*^9, 3.6363846409950175`*^9}, {3.636384971250907*^9, 3.6363849738080535`*^9}, { 3.6363850170465264`*^9, 3.636385030729309*^9}, {3.6363851286779118`*^9, 3.636385138359465*^9}, {3.6363851699712734`*^9, 3.636385223111313*^9}, { 3.656076172452749*^9, 3.656076182171566*^9}, {3.6560765578514256`*^9, 3.656076619019133*^9}, 3.6560772545486493`*^9, {3.6630719749029694`*^9, 3.6630719878027077`*^9}, {3.6630720702554235`*^9, 3.6630720807290225`*^9}, {3.6630721155740156`*^9, 3.6630721713712068`*^9}, {3.663072270834896*^9, 3.6630722882218904`*^9}, 3.6630724099968557`*^9, {3.685234767958906*^9, 3.685234768480936*^9}, { 3.685252204033695*^9, 3.6852522340537376`*^9}, {3.6852522757137957`*^9, 3.6852523115138454`*^9}, {3.68525376314359*^9, 3.6852537725041256`*^9}, { 3.6852539763277836`*^9, 3.6852539861693463`*^9}, 3.6852540682470407`*^9, 3.6852541660656357`*^9, {3.6852604801645336`*^9, 3.6852605060345697`*^9}, { 3.6852605373446136`*^9, 3.6852605977846985`*^9}, 3.685260655254779*^9, { 3.6853280002218475`*^9, 3.685328019561875*^9}, 3.685328064721938*^9, { 3.6853280953119807`*^9, 3.6853282636022167`*^9}, {3.685328356242346*^9, 3.685328598671985*^9}, {3.6853286682069626`*^9, 3.6853287982524004`*^9}, { 3.6853288753368096`*^9, 3.6853289367033195`*^9}, {3.685328968274125*^9, 3.685328978713722*^9}, {3.685329033941881*^9, 3.685329044950511*^9}, { 3.685329173522865*^9, 3.6853294420842257`*^9}, {3.6853296024223967`*^9, 3.6853296124319687`*^9}, {3.6853297221712456`*^9, 3.685329733349885*^9}, { 3.6853298076291337`*^9, 3.6853298739599276`*^9}, {3.685330038474337*^9, 3.685330051652091*^9}, {3.6853311309428225`*^9, 3.685331168378964*^9}, { 3.685340142134763*^9, 3.685340180544817*^9}, {3.6853583292043543`*^9, 3.685358334834362*^9}, {3.685358366084406*^9, 3.685358366954407*^9}, { 3.685358408404465*^9, 3.685358518294619*^9}, 3.685358620174762*^9, 3.6853586578748145`*^9, {3.6853588750151186`*^9, 3.6853588857151337`*^9}, { 3.6853589302051954`*^9, 3.685358938995208*^9}, {3.685359014715314*^9, 3.6853590296653347`*^9}, 3.685359148315501*^9, 3.6853598281764526`*^9, { 3.6853683109000263`*^9, 3.685368382250126*^9}, {3.685368420160179*^9, 3.6853684704302497`*^9}, {3.6853685194503183`*^9, 3.685368742860631*^9}, { 3.685369008901004*^9, 3.68536902061102*^9}, {3.6853690791611023`*^9, 3.685369132301176*^9}, {3.6853693219914417`*^9, 3.6853693304114532`*^9}, 3.6853696089118433`*^9, {3.6858758911429157`*^9, 3.685875951793*^9}, { 3.6859484099082212`*^9, 3.6859484970032024`*^9}, {3.686052829875022*^9, 3.686052906242383*^9}, {3.6860535326822133`*^9, 3.686053598029951*^9}, { 3.68605365168902*^9, 3.6860541446091995`*^9}, {3.6860541846064873`*^9, 3.68605440393201*^9}, {3.686054713802734*^9, 3.6860547858298535`*^9}, { 3.6860548280202665`*^9, 3.686054837219793*^9}, {3.686054874127904*^9, 3.686054892139934*^9}, {3.686055136014883*^9, 3.6860551460584574`*^9}, { 3.686055211281188*^9, 3.6860552301962633`*^9}, {3.6860553465409174`*^9, 3.6860553998749685`*^9}, {3.6860556017188663`*^9, 3.6860556050188704`*^9}, {3.6862923512707715`*^9, 3.686292363600789*^9}, { 3.686292409650853*^9, 3.6862924109708548`*^9}, {3.6862924536109147`*^9, 3.6862924596309233`*^9}, {3.686292542221039*^9, 3.6862925430110397`*^9}, { 3.686292988803664*^9, 3.686293001033681*^9}, {3.6866504529025555`*^9, 3.686650526682659*^9}, {3.686650671852862*^9, 3.6866507242929354`*^9}, { 3.6866507657529936`*^9, 3.6866507887630253`*^9}, {3.6866508208230705`*^9, 3.6866509100531955`*^9}, {3.6866509593932643`*^9, 3.686650971113281*^9}, { 3.686651007793332*^9, 3.6866511595335445`*^9}, {3.686651223513634*^9, 3.686651234033649*^9}, {3.686651304763748*^9, 3.6866513363837924`*^9}, { 3.6866514102038956`*^9, 3.686651429943923*^9}, {3.686652993837468*^9, 3.6866530046274834`*^9}, {3.686804398511652*^9, 3.6868044081516657`*^9}, { 3.6868046315619783`*^9, 3.686804631801979*^9}, {3.686804685872054*^9, 3.686804707092084*^9}, {3.6868047382021275`*^9, 3.686804767812169*^9}, { 3.686804824012248*^9, 3.6868048404922705`*^9}, {3.686804942142413*^9, 3.6868049633424425`*^9}, {3.6868050765526013`*^9, 3.686805101092636*^9}, { 3.6868051463526993`*^9, 3.6868052234228067`*^9}, {3.686805307602925*^9, 3.686805311682931*^9}, {3.68680577547358*^9, 3.686805788923599*^9}, { 3.686821702197342*^9, 3.6868217282873783`*^9}, {3.6868225192884855`*^9, 3.686822538368512*^9}, {3.6868226306886415`*^9, 3.6868226683086944`*^9}, { 3.6868227318887835`*^9, 3.6868227627088265`*^9}, {3.686822801638881*^9, 3.6868230490692277`*^9}, {3.686823122979331*^9, 3.6868231833294153`*^9}, { 3.6868232450595016`*^9, 3.6868233753996844`*^9}, {3.6868234153897405`*^9, 3.686823451379791*^9}, {3.6868236736101017`*^9, 3.6868236786601086`*^9}, { 3.6868237164601617`*^9, 3.68682375072021*^9}, {3.68682389396041*^9, 3.68682390087042*^9}, {3.686823940790476*^9, 3.6868239416904774`*^9}, { 3.6868239808805323`*^9, 3.6868239872905407`*^9}, {3.686824051540631*^9, 3.6868240519006314`*^9}, {3.686824360861064*^9, 3.6868243761510854`*^9}, { 3.6868245440213203`*^9, 3.686824577221367*^9}, {3.686824685841519*^9, 3.6868246979115357`*^9}, 3.6868248012716804`*^9, 3.6868253582724605`*^9, { 3.6868255183026843`*^9, 3.686825518932685*^9}, {3.6868264466639843`*^9, 3.6868264497139883`*^9}, {3.6868267792744493`*^9, 3.6868268152945004`*^9}, {3.686827100164899*^9, 3.6868271210549283`*^9}, 3.686827162004986*^9, {3.6868272414950967`*^9, 3.686827327475217*^9}, { 3.686827953126093*^9, 3.686827976506126*^9}, {3.686829128577739*^9, 3.686829138957753*^9}, 3.6868292410978966`*^9, {3.6868292768379464`*^9, 3.686829282727955*^9}, {3.6868293820380936`*^9, 3.686829418138144*^9}, { 3.686829846748744*^9, 3.686829848298746*^9}, {3.6868313063207874`*^9, 3.686831307180789*^9}, {3.6868331276633377`*^9, 3.68683328653356*^9}, { 3.6868394697195063`*^9, 3.6868394933895392`*^9}, 3.686839530999592*^9, { 3.686839582829664*^9, 3.68683963686974*^9}, {3.6868397551199055`*^9, 3.68683979365996*^9}, {3.6868398344600167`*^9, 3.686839866200061*^9}, { 3.687092084401948*^9, 3.687092117031994*^9}, {3.6870922598621936`*^9, 3.6870922645422*^9}, {3.6870962086478376`*^9, 3.6870962658779182`*^9}, 3.687096444838168*^9, {3.687096500978247*^9, 3.687096501638248*^9}, { 3.6870965809883595`*^9, 3.687096592708376*^9}, 3.687096837948719*^9, { 3.68709688890879*^9, 3.687096985798926*^9}, {3.6870971015990877`*^9, 3.6870972179192505`*^9}, {3.6870972618993125`*^9, 3.687097305639374*^9}, { 3.6870973356794157`*^9, 3.6870975186496716`*^9}, {3.6870975796097574`*^9, 3.6870975953197794`*^9}, {3.6870976531898603`*^9, 3.6870976848899045`*^9}, 3.6870977782500353`*^9, {3.687413757687042*^9, 3.6874137834070783`*^9}, { 3.6874140542074575`*^9, 3.687414094417514*^9}, {3.6874143478878684`*^9, 3.687414485538061*^9}, {3.6874146116082373`*^9, 3.68741464894829*^9}, { 3.6874147451084247`*^9, 3.687414766118454*^9}, 3.6874149094486547`*^9, { 3.6874150416688395`*^9, 3.6874150634888706`*^9}, {3.6874152437091227`*^9, 3.687415268869158*^9}, 3.6874153442892637`*^9, {3.687415449879411*^9, 3.687415469659439*^9}, 3.687415529739523*^9, 3.687415564789572*^9, 3.687415645529685*^9, {3.6874168016913037`*^9, 3.687416803441306*^9}, { 3.687421022677213*^9, 3.6874212686075573`*^9}, {3.68742948209425*^9, 3.6874294906842623`*^9}, {3.687844340668378*^9, 3.6878443698084188`*^9}, { 3.6886534778571014`*^9, 3.6886534911571198`*^9}, {3.688906380162199*^9, 3.6889064680223217`*^9}, {3.688906514222396*^9, 3.6889065193925257`*^9}, { 3.688908192623024*^9, 3.6889082006430354`*^9}, {3.688908261823121*^9, 3.688908271653135*^9}, {3.6889083776232834`*^9, 3.6889083922733035`*^9}, { 3.688908466073407*^9, 3.6889084993734536`*^9}, 3.688908533623502*^9, { 3.688908616683618*^9, 3.6889086271336327`*^9}, {3.6889086885637183`*^9, 3.6889087063437433`*^9}, {3.6889091647443852`*^9, 3.6889092012544365`*^9}, {3.6889093019045773`*^9, 3.6889093406746316`*^9}, 3.6889101071957045`*^9, {3.689905940063133*^9, 3.689905972983179*^9}, { 3.692530981927737*^9, 3.6925310416778207`*^9}, {3.692531099797902*^9, 3.6925311384779563`*^9}, {3.692531192258032*^9, 3.692531244668105*^9}, { 3.6925312919881716`*^9, 3.692531425418358*^9}, {3.6925315270885005`*^9, 3.692531643928664*^9}, {3.692535489534048*^9, 3.6925356485142703`*^9}, { 3.692535753564418*^9, 3.6925357992544813`*^9}, {3.6925358831745987`*^9, 3.692535899604622*^9}, {3.692536042584822*^9, 3.692536159384986*^9}, { 3.6925366121156197`*^9, 3.6925366207256317`*^9}, {3.6925367265057793`*^9, 3.69253672683578*^9}, {3.6925368590559654`*^9, 3.6925368636559715`*^9}, { 3.6925370880062857`*^9, 3.692537177856412*^9}, {3.692537322456614*^9, 3.6925373869767046`*^9}, {3.6925390913352747`*^9, 3.6925390925252767`*^9}, {3.692539644430175*^9, 3.6925396711502123`*^9}, { 3.692539727510291*^9, 3.692539730440295*^9}, {3.69253993367058*^9, 3.692539963780622*^9}, {3.6925400018406754`*^9, 3.692540003630678*^9}, { 3.6925401743409166`*^9, 3.6925401747509174`*^9}, {3.692540399111232*^9, 3.692540407981244*^9}, {3.69254047647134*^9, 3.6925404886113567`*^9}, { 3.6925406039715185`*^9, 3.69254060531152*^9}, {3.6925414948727655`*^9, 3.6925414953427663`*^9}, {3.6925415478528395`*^9, 3.692541613062931*^9}, 3.692541649332982*^9, {3.692541727633092*^9, 3.6925418840133104`*^9}, { 3.692541924473367*^9, 3.692542041693531*^9}, {3.6925421488836813`*^9, 3.6925422549438295`*^9}, {3.6925422976938896`*^9, 3.692542521444203*^9}, { 3.6925426221843443`*^9, 3.6925426357343626`*^9}, 3.692542739374508*^9, 3.692599799510878*^9, {3.692599834884901*^9, 3.6925998954663663`*^9}, { 3.692599925635092*^9, 3.6926000095928946`*^9}, {3.692600108929576*^9, 3.6926001456386757`*^9}, {3.6926001874800687`*^9, 3.692600454421337*^9}, { 3.692600503149027*^9, 3.6926006000391626`*^9}, {3.692600680251275*^9, 3.6926006814012766`*^9}, {3.6926009000215826`*^9, 3.6926009410816402`*^9}, 3.692601280532116*^9, {3.6926044914726114`*^9, 3.69260449774262*^9}, 3.6926045660127153`*^9, 3.6926046690228596`*^9, {3.69296647863291*^9, 3.6929664798829117`*^9}, {3.6929665643330297`*^9, 3.6929666141830997`*^9}, {3.6929670390036945`*^9, 3.6929670405536966`*^9}, {3.6929670861037607`*^9, 3.6929670952937737`*^9}, {3.6929671302538223`*^9, 3.6929671549438567`*^9}, {3.6929671904739065`*^9, 3.69296722137395*^9}, { 3.6929672596240034`*^9, 3.6929673352541094`*^9}, 3.6929678909232683`*^9, { 3.6930146982034283`*^9, 3.693014722713463*^9}, {3.6930148540136466`*^9, 3.693014857023651*^9}, {3.6930148913836985`*^9, 3.693014894823704*^9}, { 3.693014930903754*^9, 3.6930151942541227`*^9}, {3.693015247824198*^9, 3.693015430554454*^9}, {3.693015673794794*^9, 3.69301579223496*^9}, { 3.6930163123576884`*^9, 3.693016326897709*^9}, {3.6930164225678425`*^9, 3.693016429727853*^9}, {3.693016686718212*^9, 3.693016698128228*^9}, { 3.693016737038283*^9, 3.693016755068308*^9}, {3.6930168429225607`*^9, 3.6930168719926014`*^9}, {3.6930172049430676`*^9, 3.693017284063178*^9}, { 3.693017336433252*^9, 3.6930173662532935`*^9}, {3.6930180949163136`*^9, 3.6930180975563173`*^9}, {3.6930181870764427`*^9, 3.693018199956461*^9}, { 3.6930182954065943`*^9, 3.693018305996609*^9}, {3.693139886141657*^9, 3.6931399045016823`*^9}, {3.6931402916003532`*^9, 3.693140295770359*^9}, { 3.693140426020541*^9, 3.693140426530542*^9}, {3.6931410492237864`*^9, 3.6931410888738413`*^9}, {3.6931411194438844`*^9, 3.693141126553894*^9}, { 3.693141412004294*^9, 3.693141454164353*^9}, {3.6931415979955544`*^9, 3.6931417931758275`*^9}, {3.6932199559445915`*^9, 3.6932199772046213`*^9}, {3.6932201435748544`*^9, 3.693220170284892*^9}, { 3.693220713855653*^9, 3.693220721825664*^9}, {3.693625124589745*^9, 3.693625153729786*^9}, {3.6940907995669713`*^9, 3.6940909688872085`*^9}, { 3.6940913675677667`*^9, 3.6940914223978434`*^9}, {3.694091508037963*^9, 3.694091572118053*^9}, 3.694092009628666*^9, {3.6940920553287296`*^9, 3.694092229168973*^9}, {3.6940923053990793`*^9, 3.694092374419176*^9}, { 3.6940924537392874`*^9, 3.694092457789293*^9}, 3.694092642849552*^9, { 3.6940928573598523`*^9, 3.694092862379859*^9}, {3.6940945886222763`*^9, 3.694094601932295*^9}, 3.694094849542641*^9, {3.694095764293922*^9, 3.6940957644739223`*^9}, {3.6940960602743363`*^9, 3.6940960732243547`*^9}, {3.6940961211044216`*^9, 3.694096124194426*^9}, { 3.694665030960044*^9, 3.6946650634500895`*^9}, {3.6946652071402903`*^9, 3.6946653490404887`*^9}, {3.6946658702212186`*^9, 3.6946658881212435`*^9}, {3.694665923041292*^9, 3.694665953561335*^9}, { 3.694665995981395*^9, 3.6946660149414215`*^9}, {3.694666050571471*^9, 3.6946660547214766`*^9}, {3.694666169991638*^9, 3.694666292151809*^9}, { 3.6946663456618843`*^9, 3.6946663943919525`*^9}, 3.6946667526224537`*^9, 3.69466680700253*^9, 3.694687076625702*^9, {3.6946874316161985`*^9, 3.6946874621962414`*^9}, 3.694687499496294*^9, {3.694687567516389*^9, 3.694687642816495*^9}, {3.694687679006545*^9, 3.6946877198966026`*^9}, { 3.6946877714966745`*^9, 3.694687931746899*^9}, {3.723798739728607*^9, 3.723798744014243*^9}, {3.7237990126446104`*^9, 3.723799023974499*^9}, { 3.7244116671877546`*^9, 3.7244116733393917`*^9}, {3.724411761793063*^9, 3.7244117718753977`*^9}, {3.724411928386671*^9, 3.7244119682966137`*^9}, { 3.724412131847311*^9, 3.724412188341254*^9}, {3.729414981357122*^9, 3.7294149861075096`*^9}, {3.749817651293678*^9, 3.749817653108206*^9}, { 3.7498176831919456`*^9, 3.7498176846222315`*^9}, 3.7498177601545563`*^9, { 3.749817859674735*^9, 3.749817861044999*^9}, {3.7498179561547127`*^9, 3.749817964489929*^9}, {3.749818149334386*^9, 3.749818237397959*^9}, 3.749818617867873*^9, {3.7505621848002787`*^9, 3.7505622174085107`*^9}, { 3.75056238761455*^9, 3.750562431347901*^9}, {3.7505626332829456`*^9, 3.7505627331565337`*^9}, {3.7505627632642183`*^9, 3.7505627635859113`*^9}, {3.7515359581577415`*^9, 3.7515359614850826`*^9}, {3.751536071974715*^9, 3.7515360961721487`*^9}, 3.7515362040373974`*^9, {3.751536256080162*^9, 3.7515365099108534`*^9}, { 3.751549231137398*^9, 3.7515493334258356`*^9}, {3.7515496891619573`*^9, 3.751549689458767*^9}, 3.753020403650548*^9, {3.7530205114189386`*^9, 3.753020525224822*^9}, {3.753021995594639*^9, 3.753022011512741*^9}, { 3.760634689749445*^9, 3.7606348247488756`*^9}, {3.7606349119783344`*^9, 3.7606349350197754`*^9}, {3.76063496856853*^9, 3.7606349922504683`*^9}, { 3.760667269592998*^9, 3.760667271545692*^9}, 3.7606679283912125`*^9, 3.760668039709257*^9, {3.763302716900259*^9, 3.763302749083943*^9}, { 3.763304867499642*^9, 3.7633048681948185`*^9}, {3.763337978730939*^9, 3.763338014197137*^9}, {3.763338054806819*^9, 3.7633381289118147`*^9}, { 3.763338224472745*^9, 3.7633382447254143`*^9}, 3.763338501519575*^9, { 3.7633387342733064`*^9, 3.763338775483101*^9}, {3.7633388525735607`*^9, 3.7633390131554184`*^9}, {3.763360596353942*^9, 3.7633606328922167`*^9}, { 3.7633606638773637`*^9, 3.763360724941125*^9}, {3.763360812068123*^9, 3.763360863571327*^9}, {3.763361217769263*^9, 3.763361243271195*^9}, { 3.763361578316657*^9, 3.7633615820345063`*^9}, {3.763362291476118*^9, 3.763362301380039*^9}, {3.763362505004878*^9, 3.763362606421646*^9}, { 3.763362742167684*^9, 3.7633627524126663`*^9}, {3.7633628090243473`*^9, 3.763362931819517*^9}, 3.7633630680313087`*^9, {3.76336360941794*^9, 3.7633636782369685`*^9}, {3.763363813698273*^9, 3.763363822992702*^9}, { 3.7633837714269123`*^9, 3.763383775708086*^9}, {3.7633839861442327`*^9, 3.7633839966350546`*^9}, {3.7633846907375526`*^9, 3.76338471098131*^9}, 3.763426089635152*^9, {3.7634262143520336`*^9, 3.7634262475470448`*^9}, { 3.7634276458524485`*^9, 3.7634276705117846`*^9}, {3.7634292721860075`*^9, 3.7634292840439587`*^9}, {3.76352820463631*^9, 3.7635282147939873`*^9}, { 3.763528430960533*^9, 3.7635284413250494`*^9}, {3.7635285114344244`*^9, 3.763528537124817*^9}, {3.763528653934307*^9, 3.7635286747218256`*^9}, { 3.7635486952594075`*^9, 3.763548696007099*^9}, {3.7639579130072594`*^9, 3.7639579464687676`*^9}, {3.763957980699315*^9, 3.7639580928074217`*^9}, { 3.763959813173403*^9, 3.7639598134702053`*^9}, {3.7639608015345135`*^9, 3.7639608287155933`*^9}, {3.7645603385872726`*^9, 3.764560365934222*^9}, { 3.76456061596602*^9, 3.76456062636983*^9}, {3.7647257988231063`*^9, 3.7647258025896564`*^9}, {3.765077713031946*^9, 3.7650777913378534`*^9}, { 3.7740698865922914`*^9, 3.774069989744633*^9}, {3.7740700982535834`*^9, 3.774070098487667*^9}, {3.7740701415628414`*^9, 3.7740702370647106`*^9}, { 3.77407029325229*^9, 3.7740703348543596`*^9}, {3.774070397587008*^9, 3.774070454974152*^9}, {3.7740709929610343`*^9, 3.7740710067172923`*^9}, { 3.775190474681038*^9, 3.7751904884151363`*^9}, {3.7751905901325903`*^9, 3.775190642609686*^9}, 3.775190717712206*^9, {3.7751956728394384`*^9, 3.7751957010601625`*^9}, 3.7751957418100777`*^9, {3.7751958741450567`*^9, 3.775195882844048*^9}, {3.7751959530858574`*^9, 3.775196055684782*^9}, { 3.7836566506037264`*^9, 3.783656699859296*^9}, {3.783834162184903*^9, 3.7838342075157394`*^9}, {3.7838342453955064`*^9, 3.7838342564437876`*^9}, {3.783834288539219*^9, 3.783834289188504*^9}, { 3.783834319888338*^9, 3.783834404011998*^9}, {3.783835274452033*^9, 3.783835643262226*^9}, 3.783835673435833*^9, {3.783837186915415*^9, 3.783837252940491*^9}, 3.783838076793089*^9, {3.7838387026691084`*^9, 3.7838387106794033`*^9}, {3.7838387751330376`*^9, 3.78383877586726*^9}, 3.7885184612710266`*^9, {3.7885197610115976`*^9, 3.788519761667694*^9}, { 3.788519815581788*^9, 3.788519877459923*^9}, {3.788519910619506*^9, 3.7885199214314795`*^9}, {3.78852990807364*^9, 3.78852991935472*^9}, { 3.788529949778452*^9, 3.7885299511123505`*^9}, 3.7885729856546545`*^9, { 3.795769635061987*^9, 3.7957696738473544`*^9}, {3.7957698528454103`*^9, 3.795769867081932*^9}, {3.7963499268904905`*^9, 3.796349974573367*^9}, { 3.8116565658363085`*^9, 3.811656579625844*^9}, {3.8116566792733173`*^9, 3.811656696847624*^9}, {3.819778974172573*^9, 3.819778996370713*^9}, { 3.819779237456471*^9, 3.819779375493654*^9}, {3.819779556474127*^9, 3.8197797185600586`*^9}, 3.8200272939729*^9, 3.8200273875005593`*^9, 3.820027421880412*^9, {3.8200275035350485`*^9, 3.8200275049354267`*^9}, { 3.8459709950905457`*^9, 3.8459710017500772`*^9}, {3.8459711689546986`*^9, 3.8459711702691975`*^9}, {3.845971286165346*^9, 3.845971289846427*^9}, { 3.8459713248880577`*^9, 3.8459714501425343`*^9}, {3.845971579506527*^9, 3.8459716159320116`*^9}}, CellLabel-> "In[150]:=",ExpressionUUID->"902fe585-897b-4259-aabb-f537011656bc"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"element", " ", "build", " ", "defs"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"GENERICBEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"GENERICBEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG"}], "}"}], ",", RowBox[{"{", RowBox[{ "AA", ",", "0", ",", "0", ",", "Iyy", ",", "Izz", ",", "0", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ "fx", ",", "fy", ",", "fz", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"GENERICBEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fx_", ",", "fy_", ",", "fz_", ",", "mx_", ",", "my_", ",", "mz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"GENERICBEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG"}], "}"}], ",", RowBox[{"{", RowBox[{ "AA", ",", "0", ",", "0", ",", "Iyy", ",", "Izz", ",", "0", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ "fx", ",", "fy", ",", "fz", ",", "mx", ",", "my", ",", "mz"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Sy_", ",", "Sz_", ",", "Iyy_", ",", "Izz_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"GENERICBEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG"}], "}"}], ",", RowBox[{"{", RowBox[{ "AA", ",", "Sy", ",", "Sz", ",", "Iyy", ",", "Izz", ",", "0", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ "fx", ",", "fy", ",", "fz", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"GENERICBEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Kappa]x_"}], "}"}], ",", RowBox[{"{", RowBox[{ "AA_", ",", "Sy_", ",", "Sz_", ",", "Iyy_", ",", "Izz_", ",", "Iyz_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fx_", ",", "fy_", ",", "fz_", ",", "mx_", ",", "my_", ",", "mz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "NN", ",", "r0", ",", "r\[Alpha]0", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "ix0", ",", "iz0", ",", "s", ",", "x", ",", "jac", ",", "FF", ",", "FFINV", ",", "PP", ",", "ns", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]", ",", "EEEE", ",", "AE", ",", "CE", ",", "BE", ",", "\[Epsilon]", ",", "\[Kappa]", ",", "Irr", ",", "F", ",", "M", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wbrn", ",", "\[Delta]WW", ",", "equ", ",", "sol", ",", "bl", ",", "EEE", ",", "GGG", ",", "\[Kappa]\[Kappa]\[Kappa]", ",", "AAA", ",", "SSz", ",", "SSy", ",", "IIyy", ",", "IIzz", ",", "IIyz", ",", "ffx", ",", "ffy", ",", "ffz", ",", "mmx", ",", "mmy", ",", "mmz", ",", "\[Alpha]"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"mapping", " ", "to", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{"\[Alpha]", "*", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]0", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r0"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Alpha]0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r\[Alpha]0", ".", "r\[Alpha]0"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"i\[Alpha]0", " ", "=", RowBox[{"r\[Alpha]0", "/", "h\[Alpha]0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"iz0", "=", RowBox[{"ix0", "\[Cross]", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"s", "=", RowBox[{"i\[Alpha]0", ".", "r0"}]}], ";", "\[IndentingNewLine]", RowBox[{"x", "=", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], ".", "ix0"}], "+", "s"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"jac", " ", "=", "h\[Alpha]0"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"simple", " ", "metrics"}], "*)"}], "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"PP", "=", RowBox[{"LeviCivitaTensor", "[", "3", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"use", " ", "two", " ", "internal", " ", "nodes"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", " ", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{"{", RowBox[{"4", ",", "\[Alpha]"}], "}"}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"b", "[", "1", "]"}], ",", RowBox[{"b", "[", "2", "]"}], ",", RowBox[{"b", "[", "3", "]"}]}], "}"}], " ", ",", RowBox[{"{", RowBox[{ RowBox[{"b", "[", "4", "]"}], ",", RowBox[{"b", "[", "5", "]"}], ",", RowBox[{"b", "[", "6", "]"}]}], "}"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"b", "[", "7", "]"}], ",", RowBox[{"b", "[", "8", "]"}], ",", RowBox[{"b", "[", "9", "]"}]}], "}"}], " ", ",", RowBox[{"{", RowBox[{ RowBox[{"b", "[", "10", "]"}], ",", RowBox[{"b", "[", "11", "]"}], ",", RowBox[{"b", "[", "12", "]"}]}], "}"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"transform", " ", "to", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], ".", "FFINV"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], ".", "FFINV"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"elasticity", " ", "dyad", " ", "and", " ", "cross"}], "-", RowBox[{ "section", " ", "properties", " ", "are", " ", "known", " ", "in", " ", "the", " ", "material", " ", "system"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"EEE", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "EE", "]"}], "===", "Function"}], ",", RowBox[{"EE", "[", "x", "]"}], ",", "EE"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GGG", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "GG", "]"}], "===", "Function"}], ",", RowBox[{"GG", "[", "x", "]"}], ",", "GG"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"AAA", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "AA", "]"}], "===", "Function"}], ",", RowBox[{"AA", "[", "x", "]"}], ",", "AA"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"SSz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Sz", "]"}], "===", "Function"}], ",", RowBox[{"Sz", "[", "x", "]"}], ",", "Sz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"SSy", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Sy", "]"}], "===", "Function"}], ",", RowBox[{"Sy", "[", "x", "]"}], ",", "Sy"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIyy", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Iyy", "]"}], "===", "Function"}], ",", RowBox[{"Iyy", "[", "x", "]"}], ",", "Iyy"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIzz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Izz", "]"}], "===", "Function"}], ",", RowBox[{"Izz", "[", "x", "]"}], ",", "Izz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIyz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Iyz", "]"}], "===", "Function"}], ",", RowBox[{"Iyz", "[", "x", "]"}], ",", "Iyz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ffx", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "fx", "]"}], "===", "Function"}], ",", RowBox[{"fx", "[", "x", "]"}], ",", "fx"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ffy", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "fy", "]"}], "===", "Function"}], ",", RowBox[{"fy", "[", "x", "]"}], ",", "fy"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ffz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "fz", "]"}], "===", "Function"}], ",", RowBox[{"fz", "[", "x", "]"}], ",", "fz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"mmx", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "mx", "]"}], "===", "Function"}], ",", RowBox[{"mx", "[", "x", "]"}], ",", "mx"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"mmy", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "my", "]"}], "===", "Function"}], ",", RowBox[{"my", "[", "x", "]"}], ",", "my"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"mmz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "mz", "]"}], "===", "Function"}], ",", RowBox[{"mz", "[", "x", "]"}], ",", "mz"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"elasticity", " ", "dyad", " ", "and", " ", "cross"}], "-", RowBox[{ "section", " ", "properties", " ", "are", " ", "known", " ", "in", " ", "the", " ", "material", " ", "system"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"AE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EEE", " ", "AAA"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"GGG", " ", "AAA"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"GGG", " ", "AAA"}]}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"CE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"EEE", " ", "SSy"}], ",", RowBox[{ RowBox[{"-", "EEE"}], " ", "SSz"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "GGG"}], " ", "SSy"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"GGG", " ", "SSz"}], ",", "0", ",", "0"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"BE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Kappa]x", "*", RowBox[{"(", RowBox[{ RowBox[{"GGG", " ", "IIyy"}], "+", RowBox[{"GGG", " ", "IIzz"}]}], ")"}]}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"EEE", " ", "IIyy"}], ",", RowBox[{ RowBox[{"-", "EEE"}], " ", "IIyz"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"-", "EEE"}], " ", "IIyz"}], ",", RowBox[{"EEE", " ", "IIzz"}]}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"strain", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}]}], "/", "h\[Alpha]0"}], "+", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], "\[Cross]", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}]}], "/", "h\[Alpha]0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "resultants"}], "*)"}], "\[IndentingNewLine]", RowBox[{"F", "=", RowBox[{ RowBox[{"AE", ".", "\[Epsilon]"}], "+", RowBox[{"CE", ".", "\[Kappa]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M", "=", RowBox[{ RowBox[{ RowBox[{"Transpose", "[", "CE", "]"}], ".", "\[Epsilon]"}], "+", RowBox[{"BE", ".", "\[Kappa]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expressions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], ".", "F"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Kappa]", "]"}], ".", "M"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"ffx", ",", "ffy", ",", "ffz"}], "}"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"mmx", ",", "mmy", ",", "mmz"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wbrn", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"2", ";;", "3"}], "]"}], "]"}], "]"}], ".", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"2", ";;", "3"}], "]"}], "]"}]}], "*", "bl"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wbrn"}], ")"}], "*", "jac"}], ",", RowBox[{"{", "\[Alpha]", "}"}]}], "]"}]}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wbrn"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "0", ",", "1"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"eliminate", " ", "internals"}], "*)"}], "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", RowBox[{"Table", "[", RowBox[{ RowBox[{"\[Delta]b", "[", "ii", "]"}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", "12"}], "}"}]}], "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"equ", "\[Equal]", "0"}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"b", "[", "ii", "]"}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", "12"}], "}"}]}], "]"}]}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "go", " ", "to", " ", "the", " ", "Bernoulli", " ", "limit"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"Limit", "[", RowBox[{ RowBox[{"\[Delta]WW", " ", "/.", "sol"}], ",", RowBox[{"bl", "\[Rule]", "Infinity"}]}], "]"}]}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"GENERICBEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{ "AA_", ",", "Sy_", ",", "Sz_", ",", "Iyy_", ",", "Izz_", ",", "Iyz_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fx_", ",", "fy_", ",", "fz_", ",", "mx_", ",", "my_", ",", "mz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "NN", ",", "r0", ",", "r\[Alpha]0", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "ix0", ",", "iz0", ",", "s", ",", "x", ",", "jac", ",", "FF", ",", "FFINV", ",", "PP", ",", "ns", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]", ",", "EEEE", ",", "AE", ",", "CE", ",", "BE", ",", "\[Epsilon]", ",", "\[Kappa]", ",", "Irr", ",", "F", ",", "M", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wbrn", ",", "\[Delta]WW", ",", "equ", ",", "sol", ",", "bl", ",", "EEE", ",", "GGG", ",", "\[Kappa]\[Kappa]\[Kappa]", ",", "AAA", ",", "SSz", ",", "SSy", ",", "IIyy", ",", "IIzz", ",", "IIyz", ",", "ffx", ",", "ffy", ",", "ffz", ",", "mmx", ",", "mmy", ",", "mmz", ",", "\[Alpha]"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"mapping", " ", "to", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{"\[Alpha]", "*", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]0", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r0"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Alpha]0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r\[Alpha]0", ".", "r\[Alpha]0"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"i\[Alpha]0", " ", "=", RowBox[{"r\[Alpha]0", "/", "h\[Alpha]0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"iz0", "=", RowBox[{"ix0", "\[Cross]", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"s", "=", RowBox[{"i\[Alpha]0", ".", "r0"}]}], ";", "\[IndentingNewLine]", RowBox[{"x", "=", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], ".", "ix0"}], "+", "s"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"jac", " ", "=", "h\[Alpha]0"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"simple", " ", "metrics"}], "*)"}], "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"PP", "=", RowBox[{"LeviCivitaTensor", "[", "3", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"use", " ", "two", " ", "internal", " ", "nodes"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", " ", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{"{", RowBox[{"4", ",", "\[Alpha]"}], "}"}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"b", "[", "1", "]"}], ",", RowBox[{"b", "[", "2", "]"}], ",", RowBox[{"b", "[", "3", "]"}]}], "}"}], " ", ",", RowBox[{"{", RowBox[{ RowBox[{"b", "[", "4", "]"}], ",", RowBox[{"b", "[", "5", "]"}], ",", RowBox[{"b", "[", "6", "]"}]}], "}"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"b", "[", "7", "]"}], ",", RowBox[{"b", "[", "8", "]"}], ",", RowBox[{"b", "[", "9", "]"}]}], "}"}], " ", ",", RowBox[{"{", RowBox[{ RowBox[{"b", "[", "10", "]"}], ",", RowBox[{"b", "[", "11", "]"}], ",", RowBox[{"b", "[", "12", "]"}]}], "}"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"transform", " ", "to", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], ".", "FFINV"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], ".", "FFINV"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"elasticity", " ", "dyad", " ", "and", " ", "cross"}], "-", RowBox[{ "section", " ", "properties", " ", "are", " ", "known", " ", "in", " ", "the", " ", "material", " ", "system"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"EEE", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "EE", "]"}], "===", "Function"}], ",", RowBox[{"EE", "[", "x", "]"}], ",", "EE"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GGG", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "GG", "]"}], "===", "Function"}], ",", RowBox[{"GG", "[", "x", "]"}], ",", "GG"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"AAA", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "AA", "]"}], "===", "Function"}], ",", RowBox[{"AA", "[", "x", "]"}], ",", "AA"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"SSz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Sz", "]"}], "===", "Function"}], ",", RowBox[{"Sz", "[", "x", "]"}], ",", "Sz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"SSy", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Sy", "]"}], "===", "Function"}], ",", RowBox[{"Sy", "[", "x", "]"}], ",", "Sy"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIyy", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Iyy", "]"}], "===", "Function"}], ",", RowBox[{"Iyy", "[", "x", "]"}], ",", "Iyy"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIzz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Izz", "]"}], "===", "Function"}], ",", RowBox[{"Izz", "[", "x", "]"}], ",", "Izz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIyz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Iyz", "]"}], "===", "Function"}], ",", RowBox[{"Iyz", "[", "x", "]"}], ",", "Iyz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ffx", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "fx", "]"}], "===", "Function"}], ",", RowBox[{"fx", "[", "x", "]"}], ",", "fx"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ffy", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "fy", "]"}], "===", "Function"}], ",", RowBox[{"fy", "[", "x", "]"}], ",", "fy"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ffz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "fz", "]"}], "===", "Function"}], ",", RowBox[{"fz", "[", "x", "]"}], ",", "fz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"mmx", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "mx", "]"}], "===", "Function"}], ",", RowBox[{"mx", "[", "x", "]"}], ",", "mx"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"mmy", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "my", "]"}], "===", "Function"}], ",", RowBox[{"my", "[", "x", "]"}], ",", "my"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"mmz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "mz", "]"}], "===", "Function"}], ",", RowBox[{"mz", "[", "x", "]"}], ",", "mz"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"elasticity", " ", "dyad", " ", "and", " ", "cross"}], "-", RowBox[{ "section", " ", "properties", " ", "are", " ", "known", " ", "in", " ", "the", " ", "material", " ", "system"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"AE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EEE", " ", "AAA"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"GGG", " ", "AAA"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"GGG", " ", "AAA"}]}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"CE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"EEE", " ", "SSy"}], ",", RowBox[{ RowBox[{"-", "EEE"}], " ", "SSz"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "GGG"}], " ", "SSy"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"GGG", " ", "SSz"}], ",", "0", ",", "0"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"BE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"GGG", " ", "IIyy"}], "+", RowBox[{"GGG", " ", "IIzz"}]}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"EEE", " ", "IIyy"}], ",", RowBox[{ RowBox[{"-", "EEE"}], " ", "IIyz"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"-", "EEE"}], " ", "IIyz"}], ",", RowBox[{"EEE", " ", "IIzz"}]}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"strain", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}]}], "/", "h\[Alpha]0"}], "+", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], "\[Cross]", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}]}], "/", "h\[Alpha]0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "resultants"}], "*)"}], "\[IndentingNewLine]", RowBox[{"F", "=", RowBox[{ RowBox[{"AE", ".", "\[Epsilon]"}], "+", RowBox[{"CE", ".", "\[Kappa]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M", "=", RowBox[{ RowBox[{ RowBox[{"Transpose", "[", "CE", "]"}], ".", "\[Epsilon]"}], "+", RowBox[{"BE", ".", "\[Kappa]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expressions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], ".", "F"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Kappa]", "]"}], ".", "M"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"ffx", ",", "ffy", ",", "ffz"}], "}"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"mmx", ",", "mmy", ",", "mmz"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wbrn", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"2", ";;", "3"}], "]"}], "]"}], "]"}], ".", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"2", ";;", "3"}], "]"}], "]"}]}], "*", "bl"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wbrn"}], ")"}], "*", "jac"}], ",", RowBox[{"{", "\[Alpha]", "}"}]}], "]"}]}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wbrn"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "0", ",", "1"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"eliminate", " ", "internals"}], "*)"}], "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", RowBox[{"Table", "[", RowBox[{ RowBox[{"\[Delta]b", "[", "ii", "]"}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", "12"}], "}"}]}], "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"equ", "\[Equal]", "0"}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"b", "[", "ii", "]"}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", "12"}], "}"}]}], "]"}]}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "go", " ", "to", " ", "the", " ", "Bernoulli", " ", "limit"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"Limit", "[", RowBox[{ RowBox[{"\[Delta]WW", " ", "/.", "sol"}], ",", RowBox[{"bl", "\[Rule]", "Infinity"}]}], "]"}]}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.4430689313272*^9, 3.4430690080792*^9}, { 3.4430690869528*^9, 3.4430691077320004`*^9}, {3.4430691700116*^9, 3.4430691708072*^9}, {3.4430692071717997`*^9, 3.443069246359*^9}, { 3.4430772782732*^9, 3.4430773623416*^9}, {3.4430773978316*^9, 3.4430774104676*^9}, {3.4430775053780003`*^9, 3.4430776180598*^9}, { 3.4434109099524*^9, 3.4434109159584*^9}, {3.4438800815346003`*^9, 3.4438802689304*^9}, {3.443880362624*^9, 3.4438803824516*^9}, { 3.443929565615374*^9, 3.443929570232974*^9}, {3.443935321321974*^9, 3.443935335705174*^9}, {3.443935419945174*^9, 3.443935421489574*^9}, { 3.443935494013974*^9, 3.443935494715974*^9}, {3.443935617565974*^9, 3.4439357217895737`*^9}, {3.443935755360774*^9, 3.443935816107174*^9}, { 3.443942155230774*^9, 3.443942209939974*^9}, {3.443942305710374*^9, 3.4439423142123737`*^9}, {3.4439442908131742`*^9, 3.443944441181574*^9}, { 3.4439447830065737`*^9, 3.4439447917425737`*^9}, {3.443944908541774*^9, 3.443944916060974*^9}, {3.4442731097938004`*^9, 3.4442731115254*^9}, { 3.444273189229*^9, 3.4442732700526*^9}, {3.4442748430004*^9, 3.4442748605036*^9}, {3.4442748977438*^9, 3.4442748989762*^9}, { 3.4442749340762*^9, 3.4442749351057997`*^9}, 3.4442752313382*^9, { 3.4442919702026*^9, 3.4442919911846*^9}, {3.4442921151577997`*^9, 3.4442921271074*^9}, {3.4443811023684*^9, 3.4443811036632*^9}, { 3.4443814073171997`*^9, 3.4443814402956*^9}, {3.4443815036316*^9, 3.4443815147855997`*^9}, {3.4443815537232*^9, 3.4443815747676*^9}, { 3.4443816138143997`*^9, 3.444381633174*^9}, {3.4443816850439997`*^9, 3.4443817801728*^9}, 3.4443853618688*^9, {3.4443855607376003`*^9, 3.4443856337924*^9}, {3.4443861200444*^9, 3.4443861523676*^9}, { 3.4443862280495996`*^9, 3.444386291448*^9}, {3.4443864047352*^9, 3.4443864135336*^9}, {3.4443870026832*^9, 3.4443870095316*^9}, { 3.4444082055056*^9, 3.4444082437412*^9}, {3.4444082797148*^9, 3.4444084583816*^9}, {3.4444084889108*^9, 3.4444085087539997`*^9}, { 3.444408942517*^9, 3.4444089563386*^9}, {3.4444091419564*^9, 3.4444091647167997`*^9}, {3.4444092206428003`*^9, 3.4444092944463997`*^9}, {3.4444093856284*^9, 3.4444094281071997`*^9}, { 3.4444094976988*^9, 3.4444095275104*^9}, {3.444409611064*^9, 3.4444096125772*^9}, 3.4444098504616003`*^9, {3.444409913392*^9, 3.4444099166056004`*^9}, 3.4444100178496*^9, {3.4444103063248*^9, 3.4444103358712*^9}, {3.4444103868208*^9, 3.4444104432460003`*^9}, { 3.4444921219564*^9, 3.4444921256224003`*^9}, {3.444492194824*^9, 3.4444921973668003`*^9}, {3.4444922814351997`*^9, 3.4444922853508*^9}, { 3.4444923330868*^9, 3.4444923345844*^9}, {3.444492366424*^9, 3.4444923855808*^9}, {3.4453153475226*^9, 3.445315360689*^9}, { 3.4465518166373653`*^9, 3.446551863016165*^9}, {3.446551894231765*^9, 3.446552159384965*^9}, {3.446552232377365*^9, 3.4465522555589647`*^9}, { 3.446553347388365*^9, 3.4465533616155653`*^9}, {3.4466058525769997`*^9, 3.4466058529046*^9}, {3.4466064371219997`*^9, 3.4466065097244*^9}, { 3.4466127725788*^9, 3.4466127766036*^9}, {3.4466128124835997`*^9, 3.4466130037864*^9}, {3.4466131532696*^9, 3.4466131761703997`*^9}, { 3.4466133992192*^9, 3.4466134478756*^9}, {3.446613483584*^9, 3.4466134932092*^9}, {3.4466135740952*^9, 3.4466135794927998`*^9}, { 3.4466137283948*^9, 3.4466137341356*^9}, {3.4466138994342003`*^9, 3.4466139023826*^9}, {3.4466139549858*^9, 3.4466139579653997`*^9}, { 3.4466142109818*^9, 3.4466142245226*^9}, {3.4466142793878*^9, 3.4466143652033997`*^9}, {3.4466144712834*^9, 3.4466145978929996`*^9}, { 3.4466146992618*^9, 3.4466147509914*^9}, {3.4466151283086*^9, 3.4466152768986*^9}, {3.4466153107506*^9, 3.4466153406558*^9}, { 3.4466194331976*^9, 3.4466194377528*^9}, {3.4466194847712*^9, 3.446619488718*^9}, {3.4466389495861998`*^9, 3.4466389768238*^9}, { 3.4466391218414*^9, 3.446639306561*^9}, {3.4466393990222*^9, 3.4466394004886*^9}, {3.4466394475694*^9, 3.4466394487706003`*^9}, { 3.4466395034174*^9, 3.4466395049462*^9}, 3.4466395515755997`*^9, { 3.4466396000176*^9, 3.4466396190808*^9}, {3.4466397459088*^9, 3.446639748826*^9}, {3.4466397974356003`*^9, 3.446639798668*^9}, 3.4466398447816*^9, {3.446639894218*^9, 3.4466399201556*^9}, { 3.4466399570964003`*^9, 3.4466399583288*^9}, {3.446639994006*^9, 3.4466400056904*^9}, {3.4466400383568*^9, 3.4466400395892*^9}, { 3.4466400745643997`*^9, 3.4466401025976*^9}, {3.4466401660834*^9, 3.4466401806070004`*^9}, {3.4466402251294003`*^9, 3.446640227407*^9}, { 3.446640260479*^9, 3.4466402657674*^9}, {3.4466404133122*^9, 3.4466405185654*^9}, 3.4466405830462*^9, {3.4467273294214*^9, 3.4467273777813997`*^9}, {3.4467274366558*^9, 3.4467275620954*^9}, { 3.446727593311*^9, 3.4467277412614*^9}, {3.4467283334639997`*^9, 3.4467283356012*^9}, {3.4467283707636003`*^9, 3.4467283727604*^9}, { 3.4467289882664003`*^9, 3.4467291276836*^9}, {3.446778464322*^9, 3.4467786797424*^9}, {3.4467801953803997`*^9, 3.4467802409792*^9}, { 3.4467802998691998`*^9, 3.4467804023456*^9}, 3.4467804345596*^9, { 3.4467808656344*^9, 3.4467808670852003`*^9}, 3.4467818107525997`*^9, { 3.446781855509*^9, 3.446781874385*^9}, {3.4467826737914*^9, 3.4467827381726*^9}, {3.4467828623018*^9, 3.4467831045386*^9}, { 3.4470344113984003`*^9, 3.4470344123344*^9}, {3.4470344628316*^9, 3.4470345343108*^9}, {3.447043591118539*^9, 3.447043642192939*^9}, { 3.447045649625739*^9, 3.447045718437339*^9}, {3.447054774023939*^9, 3.447054834198939*^9}, {3.4470549103449388`*^9, 3.4470549116169386`*^9}, { 3.447054943902939*^9, 3.4470553027109385`*^9}, {3.447055334559939*^9, 3.447055353684939*^9}, {3.447057311918539*^9, 3.447057369747739*^9}, { 3.4470575058577385`*^9, 3.4470575951365385`*^9}, {3.4470581848789387`*^9, 3.4470582040825386`*^9}, {3.451276121243*^9, 3.4512761425838003`*^9}, { 3.4512762022382*^9, 3.4512762064346*^9}, {3.4512762476966*^9, 3.4512762827654*^9}, {3.451276489091*^9, 3.451276541975*^9}, { 3.4512765853118*^9, 3.4512766132046003`*^9}, {3.4512773470306*^9, 3.4512773766082*^9}, {3.4512776069110003`*^9, 3.4512777499318*^9}, 3.4512777831286*^9, {3.4512778785538*^9, 3.451277881627*^9}, { 3.4512780242734003`*^9, 3.4512780302794*^9}, 3.4512780737878*^9, { 3.4512781866226*^9, 3.4512781930810003`*^9}, {3.4512863325078*^9, 3.4512863539266*^9}, {3.4568019250434*^9, 3.4568022712698*^9}, { 3.4568023177422*^9, 3.4568024125278*^9}, {3.4568024694365997`*^9, 3.4568024750369997`*^9}, {3.4568026914402*^9, 3.4568028101094*^9}, { 3.4568028406698*^9, 3.4568028564726*^9}, 3.4568028886085997`*^9, { 3.4568030489454*^9, 3.4568030800986*^9}, 3.4568032004128*^9, { 3.4568035073698*^9, 3.4568035176034*^9}, {3.4568040146596003`*^9, 3.4568040844852*^9}, {3.4568043016684*^9, 3.4568043154744*^9}, { 3.4568045482264*^9, 3.4568045486632*^9}, {3.4568048944996*^9, 3.4568049806116*^9}, {3.4660560628582*^9, 3.4660560753538*^9}, { 3.4660676729379997`*^9, 3.4660676735931997`*^9}, {3.4660677244024*^9, 3.4660677277251997`*^9}, {3.4742646771287394`*^9, 3.47426469439174*^9}, { 3.47426489921974*^9, 3.4742649800437393`*^9}, {3.4801246373348*^9, 3.4801246860536003`*^9}, {3.4801247748176003`*^9, 3.4801247821028*^9}, { 3.4801248161264*^9, 3.4801248295736*^9}, {3.4801248810692*^9, 3.4801248964508*^9}, {3.4801249330484*^9, 3.480124947884*^9}, 3.4801249886468*^9, {3.4801251139147997`*^9, 3.48012512588*^9}, { 3.4838339444988003`*^9, 3.4838339567448*^9}, 3.4838341692012*^9, { 3.4838344350408*^9, 3.4838344353684*^9}, {3.4938987575920324`*^9, 3.4938987586840324`*^9}, {3.4941630624049997`*^9, 3.4941631381274*^9}, { 3.4941632311345997`*^9, 3.4941632492306004`*^9}, 3.4941633249217997`*^9, { 3.4941633940922003`*^9, 3.4941634063538*^9}, {3.4941634538402*^9, 3.4941635051642*^9}, {3.494163565115*^9, 3.4941636341762*^9}, { 3.4941636853442*^9, 3.4941639323234*^9}, {3.4941640277798*^9, 3.4941641455754004`*^9}, {3.4941641790374002`*^9, 3.4941641803789997`*^9}, {3.4941642676142*^9, 3.4941643277678003`*^9}, 3.4941644677018003`*^9, {3.4941646208938*^9, 3.4941646322349997`*^9}, { 3.4941652592693996`*^9, 3.4941652807194*^9}, {3.4941653119038*^9, 3.494165416299*^9}, {3.494165453895*^9, 3.4941654544722*^9}, { 3.4950990979779997`*^9, 3.495099142701*^9}, {3.495099172958*^9, 3.4950991806289997`*^9}, {3.495099227097*^9, 3.495099238113*^9}, 3.495099290797*^9, {3.495099346084*^9, 3.495099359507*^9}, { 3.495099456308*^9, 3.495099464091*^9}, 3.495099683108*^9, { 3.495100428112*^9, 3.495100434958*^9}, {3.4951006496219997`*^9, 3.495100649992*^9}, {3.4987235265018*^9, 3.4987235939094*^9}, { 3.4987236420666*^9, 3.4987236530646*^9}, {3.4987237305341997`*^9, 3.4987237396914*^9}, {3.498733136159*^9, 3.4987332972446003`*^9}, { 3.4987364783094*^9, 3.4987364860626*^9}, {3.4987366201134*^9, 3.4987366236078*^9}, {3.4987367272386*^9, 3.4987367464890003`*^9}, { 3.4987369428462*^9, 3.4987369670886*^9}, {3.4987370134518003`*^9, 3.4987370259941998`*^9}, {3.4987370944002*^9, 3.4987371027618*^9}, { 3.4987371921029997`*^9, 3.498737193663*^9}, {3.4987372660938*^9, 3.4987372935498*^9}, {3.4987373290554*^9, 3.4987377176202*^9}, { 3.4987377520182*^9, 3.4987379139462*^9}, {3.4987382030216*^9, 3.4987382667078*^9}, {3.4987888391818*^9, 3.4987888608346*^9}, { 3.4988785131146*^9, 3.4988785160162*^9}, {3.5007170967096*^9, 3.5007170999076*^9}, 3.5007182237316*^9, {3.5007182772864*^9, 3.5007182987832003`*^9}, {3.5009573226744003`*^9, 3.5009573940444*^9}, 3.5009574358710003`*^9, 3.5009604278482*^9, {3.5009897246173353`*^9, 3.5009898480289354`*^9}, {3.5009901464413357`*^9, 3.5009901475333357`*^9}, {3.5009901801997356`*^9, 3.500990274096135*^9}, { 3.5010475253292*^9, 3.5010475852332*^9}, {3.5010605722018003`*^9, 3.5010606739762*^9}, {3.5010607202146*^9, 3.5010607323358*^9}, { 3.5010607920526*^9, 3.501061118467*^9}, {3.5010612022078*^9, 3.5010612277138*^9}, {3.5010616467766*^9, 3.5010617938534*^9}, { 3.5010618406222*^9, 3.5010619950778*^9}, {3.5010621500638*^9, 3.5010622514014*^9}, {3.5010625292218*^9, 3.5010625409374*^9}, { 3.5010626043046*^9, 3.5010626313862*^9}, {3.5010626787166*^9, 3.5010626790754004`*^9}, {3.501074457561*^9, 3.5010744671082*^9}, 3.5010763029458*^9, {3.5032210899309998`*^9, 3.5032212413900003`*^9}, { 3.557658203404973*^9, 3.557658219644601*^9}, {3.5576584433801947`*^9, 3.557658496030287*^9}, {3.5576585501779823`*^9, 3.5576586046064777`*^9}, { 3.557658648910555*^9, 3.557658754600741*^9}, {3.557658963945511*^9, 3.5576589782507353`*^9}, {3.557659009949991*^9, 3.5576591437514267`*^9}, { 3.557659182221094*^9, 3.5576592187719584`*^9}, 3.557659413865901*^9, { 3.557659921100792*^9, 3.5576599556392527`*^9}, {3.557660706920972*^9, 3.5576607248454037`*^9}, {3.557661209085854*^9, 3.557661209413454*^9}, { 3.5577526651911488`*^9, 3.5577526932087984`*^9}, {3.5577527272480583`*^9, 3.557752747122493*^9}, {3.5577528374934516`*^9, 3.557752838523053*^9}, { 3.557752881204728*^9, 3.557752891313546*^9}, {3.557752938612829*^9, 3.5577529469120436`*^9}, {3.557753060714244*^9, 3.557753062633047*^9}, { 3.5577536609544907`*^9, 3.5577536637936954`*^9}, {3.5577537824631042`*^9, 3.557753810184353*^9}, {3.557753841025607*^9, 3.5577540648392*^9}, 3.5577541920574236`*^9, {3.5577547033327217`*^9, 3.557754716967146*^9}, { 3.5577547716296415`*^9, 3.557754802112095*^9}, {3.5577549509363565`*^9, 3.5577549771444025`*^9}, 3.5577551382302856`*^9, {3.55775527184452*^9, 3.557755272858522*^9}, {3.557755881555991*^9, 3.557755886548*^9}, { 3.557756158316077*^9, 3.557756231885806*^9}, {3.5577572408487787`*^9, 3.557757248835993*^9}, {3.5577572834368534`*^9, 3.5577575888229895`*^9}, { 3.5577578129641833`*^9, 3.557757862837471*^9}, {3.557758025514557*^9, 3.557758079272251*^9}, 3.557810586960072*^9, {3.5578240262005973`*^9, 3.5578240345360737`*^9}, {3.557824091429328*^9, 3.5578241008156557`*^9}, { 3.557831525255726*^9, 3.5578315319793377`*^9}, 3.5578315716190076`*^9, { 3.557831606079468*^9, 3.557831629432709*^9}, {3.5578316663267736`*^9, 3.5578317569473333`*^9}, {3.5578322144181366`*^9, 3.557832218084143*^9}, { 3.557836356693412*^9, 3.557836473771618*^9}, {3.5578365201660995`*^9, 3.5578365974018345`*^9}, {3.5578366426731143`*^9, 3.557836658865943*^9}, { 3.557836691017599*^9, 3.5578367924957776`*^9}, {3.5578368305442443`*^9, 3.557836888279946*^9}, {3.5578369382156334`*^9, 3.5578370776642785`*^9}, { 3.5578383536061196`*^9, 3.5578383735117545`*^9}, {3.5578385892445335`*^9, 3.5578385978869486`*^9}, {3.5578386713006773`*^9, 3.557838700113928*^9}, { 3.5578387451200075`*^9, 3.5578387467892103`*^9}, {3.5578388951454706`*^9, 3.5578389248635225`*^9}, {3.5578389679351983`*^9, 3.557838983535226*^9}, { 3.5578390227692947`*^9, 3.557839023143696*^9}, {3.557839097696226*^9, 3.5578391125162525`*^9}, {3.5578391553539276`*^9, 3.557839199892006*^9}, { 3.55783924184048*^9, 3.557839294490572*^9}, {3.5578393285922318`*^9, 3.557839398683155*^9}, {3.557839430522811*^9, 3.557839470162481*^9}, { 3.5578395370865984`*^9, 3.5578395446994114`*^9}, {3.5578396068499207`*^9, 3.5578396118575296`*^9}, 3.5578943518105097`*^9, {3.557894388361374*^9, 3.5578944029629993`*^9}, {3.5578944607611012`*^9, 3.5578944989499683`*^9}, {3.5578945393696394`*^9, 3.557894561537278*^9}, { 3.5578946028617506`*^9, 3.5578946188985786`*^9}, {3.557894650894235*^9, 3.5578947812636642`*^9}, {3.55789481884413*^9, 3.5578948191249304`*^9}, { 3.5578949768100076`*^9, 3.5578949836272197`*^9}, {3.5578967386805477`*^9, 3.55789678549623*^9}, {3.5578968804691963`*^9, 3.557896888643611*^9}, { 3.557897022491846*^9, 3.5578970341450663`*^9}, {3.557897620940097*^9, 3.55789765120415*^9}, {3.5579218072271147`*^9, 3.5579218263059483`*^9}, { 3.557922095312821*^9, 3.557922116965659*^9}, {3.557922178086566*^9, 3.557922188616585*^9}, {3.5579223258812256`*^9, 3.557922327066828*^9}, { 3.5579224596046605`*^9, 3.557922461804264*^9}, 3.5579805928465395`*^9, { 3.5579815200581703`*^9, 3.557981541711009*^9}, 3.557985544779242*^9, { 3.5579863164793987`*^9, 3.5579863339514294`*^9}, {3.557986523210962*^9, 3.557986568841042*^9}, 3.5579866122559185`*^9, 3.557986993536188*^9, { 3.5579871244716187`*^9, 3.5579871290580263`*^9}, 3.557987173486905*^9, 3.5579872166989803`*^9, {3.5599618621582537`*^9, 3.5599618642486577`*^9}, { 3.559961969720443*^9, 3.5599619894700775`*^9}, 3.559963611089726*^9, { 3.5601298891258235`*^9, 3.560129889422224*^9}, {3.560132445157113*^9, 3.5601324458591146`*^9}, {3.561978472080926*^9, 3.561978472392926*^9}, { 3.6297802564412937`*^9, 3.6297802957377625`*^9}, {3.62978033369263*^9, 3.629780429741998*^9}, {3.6297805790030603`*^9, 3.6297809429048996`*^9}, { 3.629780987957779*^9, 3.629781197575347*^9}, {3.629781240397422*^9, 3.629781337663593*^9}, {3.6297813946972933`*^9, 3.6297814529165955`*^9}, { 3.6297814952550697`*^9, 3.629781527578326*^9}, {3.62978162025529*^9, 3.629781647633338*^9}, {3.629781678833393*^9, 3.629781763120341*^9}, 3.6297818028224106`*^9, {3.6297818432108817`*^9, 3.629781872570133*^9}, { 3.629782355765382*^9, 3.629782427603508*^9}, {3.6297824692243814`*^9, 3.629782674863942*^9}, {3.629782707218399*^9, 3.6297829295343895`*^9}, { 3.629783005631323*^9, 3.6297830574702144`*^9}, {3.6297831098551064`*^9, 3.629783142786764*^9}, {3.629783433711675*^9, 3.629783442619291*^9}, { 3.6297834942397814`*^9, 3.6297835175930223`*^9}, 3.6297835794939313`*^9, { 3.6297836160291953`*^9, 3.6297837668970604`*^9}, {3.6297842042438283`*^9, 3.6297842697483435`*^9}, {3.6297843514456873`*^9, 3.629784370742921*^9}, { 3.629784443829049*^9, 3.6297844678842916`*^9}, {3.6297845252611923`*^9, 3.629784525588793*^9}, {3.6297846136821475`*^9, 3.629784629235375*^9}, { 3.629784814797701*^9, 3.629784927648299*^9}, {3.629785259960083*^9, 3.6297852602096834`*^9}, {3.6297858780175686`*^9, 3.629785917282837*^9}, { 3.629786048057867*^9, 3.629786048681868*^9}, 3.6297863278755584`*^9, { 3.6297867047133856`*^9, 3.629786748533863*^9}, {3.6297867791567163`*^9, 3.6297868491540394`*^9}, {3.6297875320748396`*^9, 3.629787569795706*^9}, { 3.6297876247234025`*^9, 3.6297877281983843`*^9}, {3.6297877681812544`*^9, 3.629787774015665*^9}, {3.629787831408166*^9, 3.6297878355265727`*^9}, { 3.6297878775686464`*^9, 3.6297878861174617`*^9}, {3.6297879185343184`*^9, 3.629787919064719*^9}, {3.6297880043032694`*^9, 3.62978800470887*^9}, 3.6297880488257475`*^9, {3.6297882100052304`*^9, 3.6297882174776435`*^9}, { 3.6297882697533355`*^9, 3.6297882948381796`*^9}, {3.6297883467550707`*^9, 3.6297883991087627`*^9}, {3.6297887361785545`*^9, 3.629788783961438*^9}, 3.629788825395111*^9, {3.629789006152629*^9, 3.6297890321266747`*^9}, { 3.6297891133248167`*^9, 3.629789145336073*^9}, {3.6297891926821566`*^9, 3.629789194257759*^9}, {3.629789255316266*^9, 3.6297892556282673`*^9}, { 3.629869102295367*^9, 3.629869160124668*^9}, {3.6298691942887287`*^9, 3.6298696149902673`*^9}, {3.6298696993864155`*^9, 3.62986975897852*^9}, { 3.6298698387726603`*^9, 3.629869912030389*^9}, {3.6298700722270703`*^9, 3.629870234560955*^9}, {3.629870580429163*^9, 3.629870630458451*^9}, { 3.630556081081209*^9, 3.630556104902451*^9}, {3.6305562643503313`*^9, 3.6305562763935523`*^9}, {3.6305563415080667`*^9, 3.630556480956712*^9}, { 3.630556692851884*^9, 3.630556695347888*^9}, {3.630556730042349*^9, 3.630556914528273*^9}, {3.6305653725974936`*^9, 3.6305656807121167`*^9}, { 3.630565758760581*^9, 3.6305657739024467`*^9}, {3.630565858170267*^9, 3.63056596644846*^9}, {3.6305661502619734`*^9, 3.6305661523230915`*^9}, { 3.6305662653385553`*^9, 3.630566370352562*^9}, {3.6305667786019125`*^9, 3.630566790535595*^9}, {3.6305668214773645`*^9, 3.630567044691132*^9}, { 3.6305670772499943`*^9, 3.6305670783710585`*^9}, 3.630567272031135*^9, { 3.630567303902958*^9, 3.630567409875019*^9}, {3.630568671196477*^9, 3.6305687195002403`*^9}, {3.6305687542132254`*^9, 3.630568758623478*^9}, { 3.630568855671028*^9, 3.630568859250233*^9}, {3.630569706514694*^9, 3.630569775526641*^9}, 3.630569982346471*^9, {3.6305701679130845`*^9, 3.630570205199217*^9}, {3.6305703751399374`*^9, 3.630570526177576*^9}, { 3.630587657039589*^9, 3.630587688367381*^9}, {3.6305880733027773`*^9, 3.6305883365376396`*^9}, {3.6305886689118233`*^9, 3.6305886717978287`*^9}, 3.6305889776831656`*^9, {3.6305890389444733`*^9, 3.6305890437180815`*^9}, { 3.630589093248169*^9, 3.6305891296430326`*^9}, 3.630589181700324*^9, { 3.6305892509956455`*^9, 3.6305892594820604`*^9}, {3.630589318949365*^9, 3.6305893334729905`*^9}, {3.630589630294712*^9, 3.6305896376267247`*^9}, { 3.630589683288005*^9, 3.630589684988408*^9}, {3.630597310538067*^9, 3.630597340080757*^9}, {3.630597391446695*^9, 3.630597400596218*^9}, { 3.6305974350611897`*^9, 3.6305974605306463`*^9}, {3.630633997622449*^9, 3.630634003125764*^9}, {3.630659322217756*^9, 3.63065932438616*^9}, { 3.6306611578252783`*^9, 3.6306611625988865`*^9}, {3.6306612541554475`*^9, 3.630661257587454*^9}, {3.6306613001287284`*^9, 3.6306613026715326`*^9}, { 3.6306613920752897`*^9, 3.6306613949768953`*^9}, {3.6306706377509866`*^9, 3.630670654957817*^9}, {3.6306749981919994`*^9, 3.630675005793434*^9}, { 3.6306751229631357`*^9, 3.630675150017683*^9}, {3.6306752035287437`*^9, 3.6306752096180925`*^9}, {3.630675315921172*^9, 3.6306753201514144`*^9}, { 3.6306757793287754`*^9, 3.6306757796257925`*^9}, {3.630675814406262*^9, 3.6306758147026625`*^9}, {3.6306760107574763`*^9, 3.6306760154417443`*^9}, {3.6306789722320743`*^9, 3.6306789870309205`*^9}, {3.6306790257051325`*^9, 3.630679028076268*^9}, { 3.6306800259177256`*^9, 3.6306800406129513`*^9}, {3.6306801239326982`*^9, 3.6306801300167084`*^9}, {3.630680769261832*^9, 3.6306807806186523`*^9}, { 3.630681157468514*^9, 3.6306811577649145`*^9}, {3.6306812744219193`*^9, 3.63068127471832*^9}, {3.6306817187418995`*^9, 3.6306817919060287`*^9}, { 3.630681879188182*^9, 3.6306819111526375`*^9}, {3.6306821191790032`*^9, 3.6306821283050194`*^9}, {3.630720543651497*^9, 3.6307205534300566`*^9}, { 3.630721035525631*^9, 3.630721092774905*^9}, {3.6307212510439577`*^9, 3.6307213064777765`*^9}, {3.6307477437169704`*^9, 3.6307478284095197`*^9}, {3.6307478614971776`*^9, 3.6307478785948076`*^9}, {3.6307479884814005`*^9, 3.630748002880226*^9}, { 3.630748045624301*^9, 3.630748063876333*^9}, {3.630748111596817*^9, 3.6307481498324842`*^9}, {3.6307489182430334`*^9, 3.6307489447786803`*^9}, {3.630749037427243*^9, 3.6307490443848553`*^9}, { 3.6307491041485605`*^9, 3.6307491384218206`*^9}, {3.6307491914151134`*^9, 3.630749196890723*^9}, {3.6307492445800066`*^9, 3.6307493439989815`*^9}, { 3.630749396212273*^9, 3.6307494766304145`*^9}, {3.6307495333989143`*^9, 3.6307495547241516`*^9}, {3.6307496525831237`*^9, 3.630749669571553*^9}, { 3.630750220602922*^9, 3.6307502881822405`*^9}, {3.6307510631916018`*^9, 3.630751068292811*^9}, {3.6307511226589065`*^9, 3.630751137962533*^9}, { 3.6307512555243397`*^9, 3.630751282777588*^9}, {3.630752266971757*^9, 3.630752414599744*^9}, {3.630752446407563*^9, 3.630752457388191*^9}, { 3.6307589380050273`*^9, 3.6307590266300964`*^9}, {3.6307591666721067`*^9, 3.63075923229886*^9}, 3.630760288282259*^9, {3.6307603547370596`*^9, 3.630760557414652*^9}, {3.630760654134184*^9, 3.63076065510824*^9}, { 3.6307606911683025`*^9, 3.6307606919283457`*^9}, {3.6307607642334814`*^9, 3.6307607648645177`*^9}, {3.630761455000991*^9, 3.6307614616743727`*^9}, { 3.630761507825012*^9, 3.630761605776615*^9}, {3.630761652999316*^9, 3.630761695865768*^9}, {3.630761771278081*^9, 3.6307617792215357`*^9}, 3.6307629478424797`*^9, {3.632205207880766*^9, 3.6322052561155243`*^9}, { 3.6322052892474194`*^9, 3.6322052915745525`*^9}, 3.6322053746993074`*^9, { 3.6322062705415463`*^9, 3.6322062726016645`*^9}, {3.6322063396935015`*^9, 3.63220636484194*^9}, {3.6322064410612993`*^9, 3.6322064491667633`*^9}, { 3.632206580308264*^9, 3.6322066373275256`*^9}, {3.6322066736436024`*^9, 3.6322067467737856`*^9}, {3.632206782260815*^9, 3.6322071351279984`*^9}, 3.6322071989226465`*^9, {3.632207270393735*^9, 3.6322073359894867`*^9}, { 3.6322073997741346`*^9, 3.6322074126708727`*^9}, {3.632207491777397*^9, 3.632207682289294*^9}, {3.632207809621577*^9, 3.632207827973626*^9}, { 3.6322079043859973`*^9, 3.6322079279443445`*^9}, {3.6322080916397076`*^9, 3.6322081666649985`*^9}, 3.634905258940913*^9, {3.634905370524296*^9, 3.6349054089004903`*^9}, {3.6349054472556844`*^9, 3.63490544787272*^9}, { 3.634905483492757*^9, 3.6349055164646425`*^9}, {3.634905574352954*^9, 3.634905628121029*^9}, {3.6349057012822137`*^9, 3.6349057207913294`*^9}, { 3.6349061371061416`*^9, 3.634906354438572*^9}, {3.6349063890455513`*^9, 3.6349064369332905`*^9}, {3.634906537696054*^9, 3.634906601859724*^9}, 3.634906706128688*^9, {3.6349069249442034`*^9, 3.6349069328326545`*^9}, { 3.6349070151973653`*^9, 3.6349070242298822`*^9}, {3.6349070817921743`*^9, 3.6349070822111983`*^9}, {3.634907723288866*^9, 3.634907739005765*^9}, { 3.6349079580732946`*^9, 3.6349079868219395`*^9}, {3.634908200284148*^9, 3.634908315195721*^9}, {3.6349083774582825`*^9, 3.6349084027997313`*^9}, { 3.63490844507615*^9, 3.634908448843365*^9}, {3.634914956333157*^9, 3.634915020054802*^9}, {3.634915050572547*^9, 3.6349150956171236`*^9}, { 3.6349539785771523`*^9, 3.634953978975175*^9}, {3.6349540728785458`*^9, 3.6349541681829967`*^9}, {3.634954211263461*^9, 3.6349542495746527`*^9}, { 3.6349543251259737`*^9, 3.634954355882733*^9}, {3.6349543892536416`*^9, 3.6349544742835045`*^9}, {3.634954547519694*^9, 3.6349545640246377`*^9}, { 3.6349547051657104`*^9, 3.6349547107930326`*^9}, {3.634954745355009*^9, 3.634954752101395*^9}, {3.6349547948858423`*^9, 3.6349548053894434`*^9}, { 3.634954904907135*^9, 3.6349549451084347`*^9}, {3.634955219605135*^9, 3.6349552640926795`*^9}, {3.634955320189888*^9, 3.634955348763522*^9}, { 3.634955386393675*^9, 3.6349555039273973`*^9}, {3.6349557669644423`*^9, 3.6349557672004557`*^9}, {3.634955894841756*^9, 3.634955902578199*^9}, { 3.6349559513739896`*^9, 3.6349560216320086`*^9}, {3.634956120144643*^9, 3.634956128996149*^9}, {3.6349561700724983`*^9, 3.6349561978900895`*^9}, { 3.6349562480719595`*^9, 3.634956254326318*^9}, {3.634956331684742*^9, 3.6349563460575643`*^9}, {3.634956379242462*^9, 3.63495642676418*^9}, 3.6349564696636343`*^9, {3.6351524116477795`*^9, 3.6351524153379908`*^9}, { 3.6352134400282927`*^9, 3.635213442148414*^9}, {3.6352134745862694`*^9, 3.635213495869487*^9}, {3.6352135383409157`*^9, 3.6352137157160616`*^9}, { 3.6352137493569856`*^9, 3.635213764522853*^9}, {3.635214215036621*^9, 3.635214227593339*^9}, {3.635214407257615*^9, 3.63521441713218*^9}, { 3.635215297101512*^9, 3.635215303964904*^9}, {3.6352154111120324`*^9, 3.635215431504199*^9}, {3.635216346055508*^9, 3.635216494371991*^9}, { 3.635216631050809*^9, 3.6352166603244834`*^9}, {3.635216763034358*^9, 3.635216764164423*^9}, {3.6352168771938877`*^9, 3.635216888828553*^9}, 3.6352169832479534`*^9, 3.635217037668066*^9, {3.6352172024924936`*^9, 3.6352172054526625`*^9}, {3.635217344025589*^9, 3.635217346898753*^9}, 3.6352173863770113`*^9, {3.635217519639633*^9, 3.6352175507014103`*^9}, 3.635217615445113*^9, {3.6352178715087595`*^9, 3.635217880460271*^9}, { 3.6352185912849283`*^9, 3.635218598444338*^9}, {3.6352186995721216`*^9, 3.635218714955002*^9}, {3.6352189761749425`*^9, 3.6352189789341*^9}, { 3.6352195060322485`*^9, 3.635219509972474*^9}, 3.6352195673477554`*^9, 3.6352195994635925`*^9, {3.6352197336482677`*^9, 3.635219737452485*^9}, { 3.6352197706093817`*^9, 3.6352197723214793`*^9}, {3.635219941784172*^9, 3.6352199485115566`*^9}, {3.6352200714185867`*^9, 3.6352200854323883`*^9}, {3.6352202085694313`*^9, 3.635220235849992*^9}, { 3.6352202816336107`*^9, 3.6352203110962954`*^9}, {3.6352204980449886`*^9, 3.6352205276526823`*^9}, {3.6352253191447396`*^9, 3.6352253299913597`*^9}, {3.6352253611111403`*^9, 3.6352253637572913`*^9}, {3.635225409322898*^9, 3.6352255965196047`*^9}, { 3.6352260914249115`*^9, 3.6352261698393965`*^9}, {3.63522638233055*^9, 3.6352264188036366`*^9}, {3.635227493469104*^9, 3.635227556935734*^9}, { 3.6352276745764627`*^9, 3.635227730116639*^9}, {3.6352287979917183`*^9, 3.6352288587651944`*^9}, {3.635228894237223*^9, 3.635228948324317*^9}, { 3.635229365252164*^9, 3.6352293902275925`*^9}, {3.63522947690555*^9, 3.6352294807837715`*^9}, {3.6352492831123204`*^9, 3.6352492983621926`*^9}, 3.6356569054520617`*^9, {3.6363778004499054`*^9, 3.636377802787039*^9}, { 3.6363778414932528`*^9, 3.6363778525308843`*^9}, {3.636384436335312*^9, 3.6363846409950175`*^9}, {3.636384971250907*^9, 3.6363849738080535`*^9}, { 3.6363850170465264`*^9, 3.636385030729309*^9}, {3.6363851286779118`*^9, 3.636385138359465*^9}, {3.6363851699712734`*^9, 3.636385223111313*^9}, { 3.656076172452749*^9, 3.656076182171566*^9}, {3.6560765578514256`*^9, 3.656076619019133*^9}, 3.6560772545486493`*^9, {3.6630719749029694`*^9, 3.6630719878027077`*^9}, {3.6630720702554235`*^9, 3.6630720807290225`*^9}, {3.6630721155740156`*^9, 3.6630721713712068`*^9}, {3.663072270834896*^9, 3.6630722882218904`*^9}, 3.6630724099968557`*^9, {3.685234767958906*^9, 3.685234768480936*^9}, { 3.685252204033695*^9, 3.6852522340537376`*^9}, {3.6852522757137957`*^9, 3.6852523115138454`*^9}, {3.68525376314359*^9, 3.6852537725041256`*^9}, { 3.6852539763277836`*^9, 3.6852539861693463`*^9}, 3.6852540682470407`*^9, 3.6852541660656357`*^9, {3.6852604801645336`*^9, 3.6852605060345697`*^9}, { 3.6852605373446136`*^9, 3.6852605977846985`*^9}, 3.685260655254779*^9, { 3.6853280002218475`*^9, 3.685328019561875*^9}, 3.685328064721938*^9, { 3.6853280953119807`*^9, 3.6853282636022167`*^9}, {3.685328356242346*^9, 3.685328598671985*^9}, {3.6853286682069626`*^9, 3.6853287982524004`*^9}, { 3.6853288753368096`*^9, 3.6853289367033195`*^9}, {3.685328968274125*^9, 3.685328978713722*^9}, {3.685329033941881*^9, 3.685329044950511*^9}, { 3.685329173522865*^9, 3.6853294420842257`*^9}, {3.6853296024223967`*^9, 3.6853296124319687`*^9}, {3.6853297221712456`*^9, 3.685329733349885*^9}, { 3.6853298076291337`*^9, 3.6853298739599276`*^9}, {3.685330038474337*^9, 3.685330051652091*^9}, {3.6853311309428225`*^9, 3.685331168378964*^9}, { 3.685340142134763*^9, 3.685340180544817*^9}, {3.6853583292043543`*^9, 3.685358334834362*^9}, {3.685358366084406*^9, 3.685358366954407*^9}, { 3.685358408404465*^9, 3.685358518294619*^9}, 3.685358620174762*^9, 3.6853586578748145`*^9, {3.6853588750151186`*^9, 3.6853588857151337`*^9}, { 3.6853589302051954`*^9, 3.685358938995208*^9}, {3.685359014715314*^9, 3.6853590296653347`*^9}, 3.685359148315501*^9, 3.6853598281764526`*^9, { 3.6853683109000263`*^9, 3.685368382250126*^9}, {3.685368420160179*^9, 3.6853684704302497`*^9}, {3.6853685194503183`*^9, 3.685368742860631*^9}, { 3.685369008901004*^9, 3.68536902061102*^9}, {3.6853690791611023`*^9, 3.685369132301176*^9}, {3.6853693219914417`*^9, 3.6853693304114532`*^9}, 3.6853696089118433`*^9, {3.6858758911429157`*^9, 3.685875951793*^9}, { 3.6859484099082212`*^9, 3.6859484970032024`*^9}, {3.686052829875022*^9, 3.686052906242383*^9}, {3.6860535326822133`*^9, 3.686053598029951*^9}, { 3.68605365168902*^9, 3.6860541446091995`*^9}, {3.6860541846064873`*^9, 3.68605440393201*^9}, {3.686054713802734*^9, 3.6860547858298535`*^9}, { 3.6860548280202665`*^9, 3.686054837219793*^9}, {3.686054874127904*^9, 3.686054892139934*^9}, {3.686055136014883*^9, 3.6860551460584574`*^9}, { 3.686055211281188*^9, 3.6860552301962633`*^9}, {3.6860553465409174`*^9, 3.6860553998749685`*^9}, {3.6860556017188663`*^9, 3.6860556050188704`*^9}, {3.6862923512707715`*^9, 3.686292363600789*^9}, { 3.686292409650853*^9, 3.6862924109708548`*^9}, {3.6862924536109147`*^9, 3.6862924596309233`*^9}, {3.686292542221039*^9, 3.6862925430110397`*^9}, { 3.686292988803664*^9, 3.686293001033681*^9}, {3.6866504529025555`*^9, 3.686650526682659*^9}, {3.686650671852862*^9, 3.6866507242929354`*^9}, { 3.6866507657529936`*^9, 3.6866507887630253`*^9}, {3.6866508208230705`*^9, 3.6866509100531955`*^9}, {3.6866509593932643`*^9, 3.686650971113281*^9}, { 3.686651007793332*^9, 3.6866511595335445`*^9}, {3.686651223513634*^9, 3.686651234033649*^9}, {3.686651304763748*^9, 3.6866513363837924`*^9}, { 3.6866514102038956`*^9, 3.686651429943923*^9}, {3.686652993837468*^9, 3.6866530046274834`*^9}, {3.686804398511652*^9, 3.6868044081516657`*^9}, { 3.6868046315619783`*^9, 3.686804631801979*^9}, {3.686804685872054*^9, 3.686804707092084*^9}, {3.6868047382021275`*^9, 3.686804767812169*^9}, { 3.686804824012248*^9, 3.6868048404922705`*^9}, {3.686804942142413*^9, 3.6868049633424425`*^9}, {3.6868050765526013`*^9, 3.686805101092636*^9}, { 3.6868051463526993`*^9, 3.6868052234228067`*^9}, {3.686805307602925*^9, 3.686805311682931*^9}, {3.68680577547358*^9, 3.686805788923599*^9}, { 3.686821702197342*^9, 3.6868217282873783`*^9}, {3.6868225192884855`*^9, 3.686822538368512*^9}, {3.6868226306886415`*^9, 3.6868226683086944`*^9}, { 3.6868227318887835`*^9, 3.6868227627088265`*^9}, {3.686822801638881*^9, 3.6868230490692277`*^9}, {3.686823122979331*^9, 3.6868231833294153`*^9}, { 3.6868232450595016`*^9, 3.6868233753996844`*^9}, {3.6868234153897405`*^9, 3.686823451379791*^9}, {3.6868236736101017`*^9, 3.6868236786601086`*^9}, { 3.6868237164601617`*^9, 3.68682375072021*^9}, {3.68682389396041*^9, 3.68682390087042*^9}, {3.686823940790476*^9, 3.6868239416904774`*^9}, { 3.6868239808805323`*^9, 3.6868239872905407`*^9}, {3.686824051540631*^9, 3.6868240519006314`*^9}, {3.686824360861064*^9, 3.6868243761510854`*^9}, { 3.6868245440213203`*^9, 3.686824577221367*^9}, {3.686824685841519*^9, 3.6868246979115357`*^9}, 3.6868248012716804`*^9, 3.6868253582724605`*^9, { 3.6868255183026843`*^9, 3.686825518932685*^9}, {3.6868264466639843`*^9, 3.6868264497139883`*^9}, {3.6868267792744493`*^9, 3.6868268152945004`*^9}, {3.686827100164899*^9, 3.6868271210549283`*^9}, 3.686827162004986*^9, {3.6868272414950967`*^9, 3.686827327475217*^9}, { 3.686827953126093*^9, 3.686827976506126*^9}, {3.686829128577739*^9, 3.686829138957753*^9}, 3.6868292410978966`*^9, {3.6868292768379464`*^9, 3.686829282727955*^9}, {3.6868293820380936`*^9, 3.686829418138144*^9}, { 3.686829846748744*^9, 3.686829848298746*^9}, {3.6868313063207874`*^9, 3.686831307180789*^9}, {3.6868331276633377`*^9, 3.68683328653356*^9}, { 3.6868394697195063`*^9, 3.6868394933895392`*^9}, 3.686839530999592*^9, { 3.686839582829664*^9, 3.68683963686974*^9}, {3.6868397551199055`*^9, 3.68683979365996*^9}, {3.6868398344600167`*^9, 3.686839866200061*^9}, { 3.687092084401948*^9, 3.687092117031994*^9}, {3.6870922598621936`*^9, 3.6870922645422*^9}, {3.6870962086478376`*^9, 3.6870962658779182`*^9}, 3.687096444838168*^9, {3.687096500978247*^9, 3.687096501638248*^9}, { 3.6870965809883595`*^9, 3.687096592708376*^9}, 3.687096837948719*^9, { 3.68709688890879*^9, 3.687096985798926*^9}, {3.6870971015990877`*^9, 3.6870972179192505`*^9}, {3.6870972618993125`*^9, 3.687097305639374*^9}, { 3.6870973356794157`*^9, 3.6870975186496716`*^9}, {3.6870975796097574`*^9, 3.6870975953197794`*^9}, {3.6870976531898603`*^9, 3.6870976848899045`*^9}, 3.6870977782500353`*^9, {3.687413757687042*^9, 3.6874137834070783`*^9}, { 3.6874140542074575`*^9, 3.687414094417514*^9}, {3.6874143478878684`*^9, 3.687414485538061*^9}, {3.6874146116082373`*^9, 3.68741464894829*^9}, { 3.6874147451084247`*^9, 3.687414766118454*^9}, 3.6874149094486547`*^9, { 3.6874150416688395`*^9, 3.6874150634888706`*^9}, {3.6874152437091227`*^9, 3.687415268869158*^9}, 3.6874153442892637`*^9, {3.687415449879411*^9, 3.687415469659439*^9}, 3.687415529739523*^9, 3.687415564789572*^9, 3.687415645529685*^9, {3.6874168016913037`*^9, 3.687416803441306*^9}, { 3.687421022677213*^9, 3.6874212686075573`*^9}, {3.68742948209425*^9, 3.6874294906842623`*^9}, {3.687844340668378*^9, 3.6878443698084188`*^9}, { 3.6886534778571014`*^9, 3.6886534911571198`*^9}, {3.688906380162199*^9, 3.6889064680223217`*^9}, {3.688906514222396*^9, 3.6889065193925257`*^9}, { 3.688908192623024*^9, 3.6889082006430354`*^9}, {3.688908261823121*^9, 3.688908271653135*^9}, {3.6889083776232834`*^9, 3.6889083922733035`*^9}, { 3.688908466073407*^9, 3.6889084993734536`*^9}, 3.688908533623502*^9, { 3.688908616683618*^9, 3.6889086271336327`*^9}, {3.6889086885637183`*^9, 3.6889087063437433`*^9}, {3.6889091647443852`*^9, 3.6889092012544365`*^9}, {3.6889093019045773`*^9, 3.6889093406746316`*^9}, 3.6889101071957045`*^9, {3.689905940063133*^9, 3.689905972983179*^9}, { 3.692530981927737*^9, 3.6925310416778207`*^9}, {3.692531099797902*^9, 3.6925311384779563`*^9}, {3.692531192258032*^9, 3.692531244668105*^9}, { 3.6925312919881716`*^9, 3.692531425418358*^9}, {3.6925315270885005`*^9, 3.692531643928664*^9}, {3.692535489534048*^9, 3.6925356485142703`*^9}, { 3.692535753564418*^9, 3.6925357992544813`*^9}, {3.6925358831745987`*^9, 3.692535899604622*^9}, {3.692536042584822*^9, 3.692536159384986*^9}, { 3.6925366121156197`*^9, 3.6925366207256317`*^9}, {3.6925367265057793`*^9, 3.69253672683578*^9}, {3.6925368590559654`*^9, 3.6925368636559715`*^9}, { 3.6925370880062857`*^9, 3.692537177856412*^9}, {3.692537322456614*^9, 3.6925373869767046`*^9}, {3.6925390913352747`*^9, 3.6925390925252767`*^9}, {3.692539644430175*^9, 3.6925396711502123`*^9}, { 3.692539727510291*^9, 3.692539730440295*^9}, {3.69253993367058*^9, 3.692539963780622*^9}, {3.6925400018406754`*^9, 3.692540003630678*^9}, { 3.6925401743409166`*^9, 3.6925401747509174`*^9}, {3.692540399111232*^9, 3.692540407981244*^9}, {3.69254047647134*^9, 3.6925404886113567`*^9}, { 3.6925406039715185`*^9, 3.69254060531152*^9}, {3.6925414948727655`*^9, 3.6925414953427663`*^9}, {3.6925415478528395`*^9, 3.692541613062931*^9}, 3.692541649332982*^9, {3.692541727633092*^9, 3.6925418840133104`*^9}, { 3.692541924473367*^9, 3.692542041693531*^9}, {3.6925421488836813`*^9, 3.6925422549438295`*^9}, {3.6925422976938896`*^9, 3.692542521444203*^9}, { 3.6925426221843443`*^9, 3.6925426357343626`*^9}, 3.692542739374508*^9, 3.692599799510878*^9, {3.692599834884901*^9, 3.6925998954663663`*^9}, { 3.692599925635092*^9, 3.6926000095928946`*^9}, {3.692600108929576*^9, 3.6926001456386757`*^9}, {3.6926001874800687`*^9, 3.692600454421337*^9}, { 3.692600503149027*^9, 3.6926006000391626`*^9}, {3.692600680251275*^9, 3.6926006814012766`*^9}, {3.6926009000215826`*^9, 3.6926009410816402`*^9}, 3.692601280532116*^9, {3.6926044914726114`*^9, 3.69260449774262*^9}, 3.6926045660127153`*^9, 3.6926046690228596`*^9, {3.69296647863291*^9, 3.6929664798829117`*^9}, {3.6929665643330297`*^9, 3.6929666141830997`*^9}, {3.6929670390036945`*^9, 3.6929670405536966`*^9}, {3.6929670861037607`*^9, 3.6929670952937737`*^9}, {3.6929671302538223`*^9, 3.6929671549438567`*^9}, {3.6929671904739065`*^9, 3.69296722137395*^9}, { 3.6929672596240034`*^9, 3.6929673352541094`*^9}, 3.6929678909232683`*^9, { 3.6930146982034283`*^9, 3.693014722713463*^9}, {3.6930148540136466`*^9, 3.693014857023651*^9}, {3.6930148913836985`*^9, 3.693014894823704*^9}, { 3.693014930903754*^9, 3.6930151942541227`*^9}, {3.693015247824198*^9, 3.693015430554454*^9}, {3.693015673794794*^9, 3.69301579223496*^9}, { 3.6930163123576884`*^9, 3.693016326897709*^9}, {3.6930164225678425`*^9, 3.693016429727853*^9}, {3.693016686718212*^9, 3.693016698128228*^9}, { 3.693016737038283*^9, 3.693016755068308*^9}, {3.6930168429225607`*^9, 3.6930168719926014`*^9}, {3.6930172049430676`*^9, 3.693017284063178*^9}, { 3.693017336433252*^9, 3.6930173662532935`*^9}, {3.6930180949163136`*^9, 3.6930180975563173`*^9}, {3.6930181870764427`*^9, 3.693018199956461*^9}, { 3.6930182954065943`*^9, 3.693018305996609*^9}, {3.693139886141657*^9, 3.6931399045016823`*^9}, {3.6931402916003532`*^9, 3.693140295770359*^9}, { 3.693140426020541*^9, 3.693140426530542*^9}, {3.6931410492237864`*^9, 3.6931410888738413`*^9}, {3.6931411194438844`*^9, 3.693141126553894*^9}, { 3.693141412004294*^9, 3.693141454164353*^9}, {3.6931415979955544`*^9, 3.6931417931758275`*^9}, {3.6932199559445915`*^9, 3.6932199772046213`*^9}, {3.6932201435748544`*^9, 3.693220170284892*^9}, { 3.693220713855653*^9, 3.693220721825664*^9}, {3.693625124589745*^9, 3.693625153729786*^9}, {3.6940907995669713`*^9, 3.6940909688872085`*^9}, { 3.6940913675677667`*^9, 3.6940914223978434`*^9}, {3.694091508037963*^9, 3.694091572118053*^9}, 3.694092009628666*^9, {3.6940920553287296`*^9, 3.694092229168973*^9}, {3.6940923053990793`*^9, 3.694092374419176*^9}, { 3.6940924537392874`*^9, 3.694092457789293*^9}, 3.694092642849552*^9, { 3.6940928573598523`*^9, 3.694092862379859*^9}, {3.6940945886222763`*^9, 3.694094601932295*^9}, 3.694094849542641*^9, {3.694095764293922*^9, 3.6940957644739223`*^9}, {3.6940960602743363`*^9, 3.6940960732243547`*^9}, {3.6940961211044216`*^9, 3.694096124194426*^9}, { 3.694665030960044*^9, 3.6946650634500895`*^9}, {3.6946652071402903`*^9, 3.6946653490404887`*^9}, {3.6946658702212186`*^9, 3.6946658881212435`*^9}, {3.694665923041292*^9, 3.694665953561335*^9}, { 3.694665995981395*^9, 3.6946660149414215`*^9}, {3.694666050571471*^9, 3.6946660547214766`*^9}, {3.694666169991638*^9, 3.694666292151809*^9}, { 3.6946663456618843`*^9, 3.6946663943919525`*^9}, 3.6946667526224537`*^9, 3.69466680700253*^9, 3.694687076625702*^9, {3.6946874316161985`*^9, 3.6946874621962414`*^9}, 3.694687499496294*^9, {3.694687567516389*^9, 3.694687642816495*^9}, {3.694687679006545*^9, 3.6946877198966026`*^9}, { 3.6946877714966745`*^9, 3.694687931746899*^9}, {3.723798739728607*^9, 3.723798744014243*^9}, {3.7237990126446104`*^9, 3.723799023974499*^9}, { 3.7244116671877546`*^9, 3.7244116733393917`*^9}, {3.724411761793063*^9, 3.7244117718753977`*^9}, {3.724411928386671*^9, 3.7244119682966137`*^9}, { 3.724412131847311*^9, 3.724412188341254*^9}, {3.729414981357122*^9, 3.7294149861075096`*^9}, {3.749817651293678*^9, 3.749817653108206*^9}, { 3.7498176831919456`*^9, 3.7498176846222315`*^9}, 3.7498177601545563`*^9, { 3.749817859674735*^9, 3.749817861044999*^9}, {3.7498179561547127`*^9, 3.749817964489929*^9}, {3.749818149334386*^9, 3.749818237397959*^9}, 3.749818617867873*^9, {3.7505621848002787`*^9, 3.7505622174085107`*^9}, { 3.75056238761455*^9, 3.750562431347901*^9}, {3.7505626332829456`*^9, 3.7505627331565337`*^9}, {3.7505627632642183`*^9, 3.7505627635859113`*^9}, {3.7515359581577415`*^9, 3.7515359614850826`*^9}, {3.751536071974715*^9, 3.7515360961721487`*^9}, 3.7515362040373974`*^9, {3.751536256080162*^9, 3.7515365099108534`*^9}, { 3.751549231137398*^9, 3.7515493334258356`*^9}, {3.7515496891619573`*^9, 3.751549689458767*^9}, 3.753020403650548*^9, {3.7530205114189386`*^9, 3.753020525224822*^9}, {3.753021995594639*^9, 3.753022011512741*^9}, { 3.760634689749445*^9, 3.7606348247488756`*^9}, {3.7606349119783344`*^9, 3.7606349350197754`*^9}, {3.76063496856853*^9, 3.7606349922504683`*^9}, { 3.760667269592998*^9, 3.760667271545692*^9}, 3.7606679283912125`*^9, 3.760668039709257*^9, {3.763302716900259*^9, 3.763302749083943*^9}, { 3.763304867499642*^9, 3.7633048681948185`*^9}, {3.763337978730939*^9, 3.763338014197137*^9}, {3.763338054806819*^9, 3.7633381289118147`*^9}, { 3.763338224472745*^9, 3.7633382447254143`*^9}, 3.763338501519575*^9, { 3.7633387342733064`*^9, 3.763338775483101*^9}, {3.7633388525735607`*^9, 3.7633390131554184`*^9}, {3.763360596353942*^9, 3.7633606328922167`*^9}, { 3.7633606638773637`*^9, 3.763360724941125*^9}, {3.763360812068123*^9, 3.763360863571327*^9}, {3.763361217769263*^9, 3.763361243271195*^9}, { 3.763361578316657*^9, 3.7633615820345063`*^9}, {3.763362291476118*^9, 3.763362301380039*^9}, {3.763362505004878*^9, 3.763362606421646*^9}, { 3.763362742167684*^9, 3.7633627524126663`*^9}, {3.7633628090243473`*^9, 3.763362931819517*^9}, 3.7633630680313087`*^9, {3.76336360941794*^9, 3.7633636782369685`*^9}, {3.763363813698273*^9, 3.763363822992702*^9}, { 3.7633837714269123`*^9, 3.763383775708086*^9}, {3.7633839861442327`*^9, 3.7633839966350546`*^9}, {3.7633846907375526`*^9, 3.76338471098131*^9}, 3.763426089635152*^9, {3.7634262143520336`*^9, 3.7634262475470448`*^9}, { 3.7634276458524485`*^9, 3.7634276705117846`*^9}, {3.7634292721860075`*^9, 3.7634292840439587`*^9}, {3.76352820463631*^9, 3.7635282147939873`*^9}, { 3.763528430960533*^9, 3.7635284413250494`*^9}, {3.7635285114344244`*^9, 3.763528537124817*^9}, {3.763528653934307*^9, 3.7635286747218256`*^9}, { 3.7635486952594075`*^9, 3.763548696007099*^9}, {3.7639579130072594`*^9, 3.7639579464687676`*^9}, {3.763957980699315*^9, 3.7639580928074217`*^9}, { 3.763959813173403*^9, 3.7639598134702053`*^9}, {3.7639608015345135`*^9, 3.7639608287155933`*^9}, {3.7645603385872726`*^9, 3.764560365934222*^9}, { 3.76456061596602*^9, 3.76456062636983*^9}, {3.7647257988231063`*^9, 3.7647258025896564`*^9}, {3.765077713031946*^9, 3.7650777913378534`*^9}, { 3.7740698865922914`*^9, 3.774069989744633*^9}, {3.7740700982535834`*^9, 3.774070098487667*^9}, {3.7740701415628414`*^9, 3.7740702370647106`*^9}, { 3.77407029325229*^9, 3.7740703348543596`*^9}, {3.774070397587008*^9, 3.774070454974152*^9}, {3.7740709929610343`*^9, 3.7740710067172923`*^9}, { 3.775190474681038*^9, 3.7751904884151363`*^9}, {3.7751905901325903`*^9, 3.775190642609686*^9}, 3.775190717712206*^9, {3.7751956728394384`*^9, 3.7751957010601625`*^9}, 3.7751957418100777`*^9, {3.7751958741450567`*^9, 3.775195882844048*^9}, {3.7751959530858574`*^9, 3.775196055684782*^9}, { 3.7836566506037264`*^9, 3.783656699859296*^9}, {3.783834162184903*^9, 3.7838342075157394`*^9}, {3.7838342453955064`*^9, 3.7838342564437876`*^9}, {3.783834288539219*^9, 3.783834289188504*^9}, { 3.783834319888338*^9, 3.783834404011998*^9}, {3.783835274452033*^9, 3.783835643262226*^9}, 3.783835673435833*^9, {3.783837186915415*^9, 3.783837252940491*^9}, 3.783838076793089*^9, {3.7838387026691084`*^9, 3.7838387106794033`*^9}, {3.7838387751330376`*^9, 3.78383877586726*^9}, 3.7885184612710266`*^9, {3.7885197610115976`*^9, 3.788519761667694*^9}, { 3.788519815581788*^9, 3.788519877459923*^9}, {3.788519910619506*^9, 3.7885199214314795`*^9}, {3.78852990807364*^9, 3.78852991935472*^9}, { 3.788529949778452*^9, 3.7885299511123505`*^9}, 3.7885729856546545`*^9, 3.851995321450799*^9, 3.8519953606861525`*^9},ExpressionUUID->"f5dc159b-dfac-430e-a432-\ c1a7b9bafe16"] }, Closed]], Cell[CellGroupData[{ Cell["BEAM ELEMENT (disp 1:st) defs ", "Subsection", CellChangeTimes->{{3.7530187996679964`*^9, 3.753018803413909*^9}, { 3.7633629633672647`*^9, 3.763362982159668*^9}, {3.787894778048681*^9, 3.7878948056524777`*^9}, {3.787894853900061*^9, 3.7878948799797325`*^9}, 3.788518934866293*^9, {3.7885300329539347`*^9, 3.7885300364009333`*^9}, 3.788530671733654*^9, {3.8200271779079833`*^9, 3.8200271816696315`*^9}, { 3.820027559976658*^9, 3.820027565268735*^9}, {3.8519950922439923`*^9, 3.8519950951031284`*^9}, {3.852092988966981*^9, 3.852092991459448*^9}},ExpressionUUID->"14357180-6a08-4b4a-b9da-\ b727a3841e7e"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"MEC", "-", "E1050"}], "|", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Kappa]y_", ",", "kz_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iy_", ",", "Iz_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG", ",", "\[Kappa]y", ",", "kz", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iy", ",", "Iz", ",", RowBox[{"Iy", "+", "Iz"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fz"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Kappa]y_", ",", "kz_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iy_", ",", "Iz_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG", ",", "\[Kappa]y", ",", "kz", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iy", ",", "Iz", ",", RowBox[{"Iy", "+", "Iz"}], ",", "iy0"}], "}"}], ",", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fz"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"first", " ", "order", " ", "theory", " ", "defs"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "ky_", ",", "kz_", ",", "ez_"}], "}"}], ",", RowBox[{"{", RowBox[{ "AA_", ",", "Iy_", ",", "Iz_", ",", "Jx_", ",", "iy0_", ",", "cpol_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG", ",", "ky", ",", "kz", ",", "ez"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iy", ",", "Iz", ",", "Jx", ",", "iy0"}], "}"}], ",", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "ky_", ",", "kz_", ",", "ez_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iy_", ",", "Iz_", ",", "Jx_", ",", RowBox[{"{", RowBox[{"iyr_", ",", "\[Alpha]_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "ixr", ",", "izr", ",", "ix0", ",", "iy0", ",", "iz0", ",", "ux1", ",", "uy1", " ", ",", "uz1", " ", ",", "\[Theta]x1", " ", ",", "\[Theta]y1", ",", "\[Theta]z1", " ", ",", "\[Delta]ux1", " ", ",", "\[Delta]uy1", ",", "\[Delta]uz1", ",", "\[Delta]\[Theta]x1", ",", "\[Delta]\[Theta]y1", ",", "\[Delta]\[Theta]z1", ",", "ux2", ",", "uy2", " ", ",", "uz2", " ", ",", "\[Theta]x2", " ", ",", "\[Theta]y2", ",", "\[Theta]z2", " ", ",", "\[Delta]ux2", " ", ",", "\[Delta]uy2", ",", "\[Delta]uz2", ",", "\[Delta]\[Theta]x2", ",", "\[Delta]\[Theta]y2", ",", "\[Delta]\[Theta]z2", ",", "bx", ",", "by", ",", "bz"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "mapping", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"\[Alpha]", " ", "rotation", " ", "along", " ", "x"}], "-", RowBox[{"axis", " ", "for", " ", "symmetry"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{"with", " ", "respect", " ", "to", " ", "z"}], "-", "axis"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ixr", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", RowBox[{"izr", "=", RowBox[{"ixr", "\[Cross]", "iyr"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", " ", "=", "ixr"}], ";", "\[IndentingNewLine]", RowBox[{"iy0", " ", "=", RowBox[{ RowBox[{ RowBox[{"Cos", "[", "\[Alpha]", "]"}], " ", "iyr"}], "+", RowBox[{ RowBox[{"Sin", "[", "\[Alpha]", "]"}], "izr"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"iz0", " ", "=", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"Sin", "[", "\[Alpha]", "]"}]}], " ", "iyr"}], "+", RowBox[{ RowBox[{"Cos", "[", "\[Alpha]", "]"}], "izr"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"ux1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "ix0"}]}], ";", " ", RowBox[{"ux2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{"uy1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iy0"}]}], ";", " ", RowBox[{"uy2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"uz1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iz0"}]}], ";", " ", RowBox[{"uz2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]x1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "ix0"}]}], ";", " ", RowBox[{"\[Theta]x2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]y1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iy0"}]}], ";", " ", RowBox[{"\[Theta]y2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]z1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iz0"}]}], ";", " ", RowBox[{"\[Theta]z2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]ux1", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "]"}], ".", "ix0"}]}], ";", " ", RowBox[{"\[Delta]ux2", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "]"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]uy1", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "]"}], ".", "iy0"}]}], ";", " ", RowBox[{"\[Delta]uy2", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "]"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]uz1", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "]"}], ".", "iz0"}]}], ";", " ", RowBox[{"\[Delta]uz2", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "]"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]\[Theta]x1", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], "]"}], ".", "ix0"}]}], ";", " ", RowBox[{"\[Delta]\[Theta]x2", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "]"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]\[Theta]y1", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], "]"}], ".", "iy0"}]}], ";", " ", RowBox[{"\[Delta]\[Theta]y2", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "]"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]\[Theta]z1", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], "]"}], ".", "iz0"}]}], ";", " ", RowBox[{"\[Delta]\[Theta]z2", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "]"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", RowBox[{"bx", " ", "=", RowBox[{ RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{"by", " ", "=", RowBox[{ RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"bz", " ", "=", RowBox[{ RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ FractionBox[ RowBox[{"bx", " ", "h0", " ", "\[Delta]ux1"}], "2"], "+", FractionBox[ RowBox[{"AA", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "ux1"}], "+", "ux2"}], ")"}], " ", "\[Delta]ux1"}], "h0"], "+", FractionBox[ RowBox[{"bx", " ", "h0", " ", "\[Delta]ux2"}], "2"], "+", FractionBox[ RowBox[{"AA", " ", "EE", " ", RowBox[{"(", RowBox[{"ux1", "-", "ux2"}], ")"}], " ", "\[Delta]ux2"}], "h0"], "+", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]uz2", " ", RowBox[{"(", RowBox[{ RowBox[{"bz", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", SuperscriptBox["h0", "2"], " ", "Iy"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", "kz"}]}], ")"}]}], "-", RowBox[{ "12", " ", "AA", " ", "EE", " ", "GG", " ", "Iy", " ", "kz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "uz1"}], "+", RowBox[{"2", " ", "uz2"}], "+", RowBox[{"h0", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "+", "\[Theta]y2"}], ")"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"24", " ", "EE", " ", "h0", " ", "Iy"}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "kz"}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]uz1", " ", RowBox[{"(", RowBox[{ RowBox[{"bz", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", SuperscriptBox["h0", "2"], " ", "Iy"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", "kz"}]}], ")"}]}], "+", RowBox[{ "12", " ", "AA", " ", "EE", " ", "GG", " ", "Iy", " ", "kz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "uz1"}], "+", RowBox[{"2", " ", "uz2"}], "+", RowBox[{"h0", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "+", "\[Theta]y2"}], ")"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"24", " ", "EE", " ", "h0", " ", "Iy"}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "kz"}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]\[Theta]y1", " ", RowBox[{"(", RowBox[{ RowBox[{"bz", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iy"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "kz"}]}], ")"}]}], "+", RowBox[{"24", " ", "EE", " ", "Iy", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "EE", " ", "Iy", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "-", "\[Theta]y2"}], ")"}]}], "+", RowBox[{"AA", " ", "GG", " ", "h0", " ", "kz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", "uz1"}], "+", RowBox[{"3", " ", "uz2"}], "+", RowBox[{"2", " ", "h0", " ", "\[Theta]y1"}], "+", RowBox[{"h0", " ", "\[Theta]y2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", "h0", " ", "Iy"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "kz"}]}], ")"}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]\[Theta]y2", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "bz"}], " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iy"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "kz"}]}], ")"}]}], "+", RowBox[{"24", " ", "EE", " ", "Iy", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "EE", " ", "Iy", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Theta]y1"}], "+", "\[Theta]y2"}], ")"}]}], "+", RowBox[{"AA", " ", "GG", " ", "h0", " ", "kz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", "uz1"}], "+", RowBox[{"3", " ", "uz2"}], "+", RowBox[{"h0", " ", "\[Theta]y1"}], "+", RowBox[{"2", " ", "h0", " ", "\[Theta]y2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", "h0", " ", "Iy"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "kz"}]}], ")"}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]uy1", " ", RowBox[{"(", RowBox[{ RowBox[{"by", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", SuperscriptBox["h0", "2"], " ", "Iz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", "ky"}]}], ")"}]}], "-", RowBox[{ "12", " ", "AA", " ", "EE", " ", "GG", " ", "Iz", " ", "ky", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "uy1"}], "-", RowBox[{"2", " ", "uy2"}], "-", RowBox[{"2", " ", "ez", " ", "\[Theta]x1"}], "+", RowBox[{"2", " ", "ez", " ", "\[Theta]x2"}], "+", RowBox[{"h0", " ", "\[Theta]z1"}], "+", RowBox[{"h0", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"24", " ", "EE", " ", "h0", " ", "Iz"}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky"}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]uy2", " ", RowBox[{"(", RowBox[{ RowBox[{"by", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", SuperscriptBox["h0", "2"], " ", "Iz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", "ky"}]}], ")"}]}], "+", RowBox[{ "12", " ", "AA", " ", "EE", " ", "GG", " ", "Iz", " ", "ky", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "uy1"}], "-", RowBox[{"2", " ", "uy2"}], "-", RowBox[{"2", " ", "ez", " ", "\[Theta]x1"}], "+", RowBox[{"2", " ", "ez", " ", "\[Theta]x2"}], "+", RowBox[{"h0", " ", "\[Theta]z1"}], "+", RowBox[{"h0", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"24", " ", "EE", " ", "h0", " ", "Iz"}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky"}]}], ")"}]}], "-", RowBox[{ FractionBox["1", RowBox[{ RowBox[{"12", " ", "EE", " ", "h0", " ", "Iz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky"}]}]], "GG", " ", "\[Delta]\[Theta]x1", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", "Iz", " ", "Jx", " ", RowBox[{"(", RowBox[{"\[Theta]x1", "-", "\[Theta]x2"}], ")"}]}], "+", RowBox[{"AA", " ", "ky", " ", RowBox[{"(", RowBox[{ RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", RowBox[{"(", RowBox[{"\[Theta]x1", "-", "\[Theta]x2"}], ")"}]}], "+", RowBox[{"6", " ", "EE", " ", "ez", " ", "Iz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "uy1"}], "+", RowBox[{"2", " ", "uy2"}], "+", RowBox[{"2", " ", "ez", " ", "\[Theta]x1"}], "-", RowBox[{"2", " ", "ez", " ", "\[Theta]x2"}], "-", RowBox[{"h0", " ", "\[Theta]z1"}], "-", RowBox[{"h0", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{ FractionBox["1", RowBox[{ RowBox[{"12", " ", "EE", " ", "h0", " ", "Iz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky"}]}]], "GG", " ", "\[Delta]\[Theta]x2", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", "Iz", " ", "Jx", " ", RowBox[{"(", RowBox[{"\[Theta]x1", "-", "\[Theta]x2"}], ")"}]}], "+", RowBox[{"AA", " ", "ky", " ", RowBox[{"(", RowBox[{ RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", RowBox[{"(", RowBox[{"\[Theta]x1", "-", "\[Theta]x2"}], ")"}]}], "+", RowBox[{"6", " ", "EE", " ", "ez", " ", "Iz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "uy1"}], "+", RowBox[{"2", " ", "uy2"}], "+", RowBox[{"2", " ", "ez", " ", "\[Theta]x1"}], "-", RowBox[{"2", " ", "ez", " ", "\[Theta]x2"}], "-", RowBox[{"h0", " ", "\[Theta]z1"}], "-", RowBox[{"h0", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]\[Theta]z1", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "by"}], " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "ky"}]}], ")"}]}], "+", RowBox[{"24", " ", "EE", " ", "Iz", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "EE", " ", "Iz", " ", RowBox[{"(", RowBox[{"\[Theta]z1", "-", "\[Theta]z2"}], ")"}]}], "+", RowBox[{"AA", " ", "GG", " ", "h0", " ", "ky", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", "uy1"}], "-", RowBox[{"3", " ", "uy2"}], "-", RowBox[{"3", " ", "ez", " ", "\[Theta]x1"}], "+", RowBox[{"3", " ", "ez", " ", "\[Theta]x2"}], "+", RowBox[{"2", " ", "h0", " ", "\[Theta]z1"}], "+", RowBox[{"h0", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", "h0", " ", "Iz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky"}]}], ")"}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]\[Theta]z2", " ", RowBox[{"(", RowBox[{ RowBox[{"by", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "ky"}]}], ")"}]}], "-", RowBox[{"24", " ", "EE", " ", "Iz", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "EE", " ", "Iz", " ", RowBox[{"(", RowBox[{"\[Theta]z1", "-", "\[Theta]z2"}], ")"}]}], "-", RowBox[{"AA", " ", "GG", " ", "h0", " ", "ky", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", "uy1"}], "-", RowBox[{"3", " ", "uy2"}], "-", RowBox[{"3", " ", "ez", " ", "\[Theta]x1"}], "+", RowBox[{"3", " ", "ez", " ", "\[Theta]x2"}], "+", RowBox[{"h0", " ", "\[Theta]z1"}], "+", RowBox[{"2", " ", "h0", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", "h0", " ", "Iz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky"}]}], ")"}]}], ")"}]}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "ky_", ",", "kz_", ",", "ez_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iy_", ",", "Iz_", ",", "Jx_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "ix0", ",", "iz0", ",", "ux1", ",", "uy1", " ", ",", "uz1", " ", ",", "\[Theta]x1", " ", ",", "\[Theta]y1", ",", "\[Theta]z1", " ", ",", "\[Delta]ux1", " ", ",", "\[Delta]uy1", ",", "\[Delta]uz1", ",", "\[Delta]\[Theta]x1", ",", "\[Delta]\[Theta]y1", ",", "\[Delta]\[Theta]z1", ",", "ux2", ",", "uy2", " ", ",", "uz2", " ", ",", "\[Theta]x2", " ", ",", "\[Theta]y2", ",", "\[Theta]z2", " ", ",", "\[Delta]ux2", " ", ",", "\[Delta]uy2", ",", "\[Delta]uz2", ",", "\[Delta]\[Theta]x2", ",", "\[Delta]\[Theta]y2", ",", "\[Delta]\[Theta]z2", ",", "bx", ",", "by", ",", "bz"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "mapping", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz0", "=", RowBox[{"ix0", "\[Cross]", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"ux1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "ix0"}]}], ";", " ", RowBox[{"ux2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{"uy1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iy0"}]}], ";", " ", RowBox[{"uy2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"uz1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iz0"}]}], ";", " ", RowBox[{"uz2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]x1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "ix0"}]}], ";", " ", RowBox[{"\[Theta]x2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]y1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iy0"}]}], ";", " ", RowBox[{"\[Theta]y2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]z1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iz0"}]}], ";", " ", RowBox[{"\[Theta]z2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]ux1", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "]"}], ".", "ix0"}]}], ";", " ", RowBox[{"\[Delta]ux2", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "]"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]uy1", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "]"}], ".", "iy0"}]}], ";", " ", RowBox[{"\[Delta]uy2", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "]"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]uz1", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "]"}], ".", "iz0"}]}], ";", " ", RowBox[{"\[Delta]uz2", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "]"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]\[Theta]x1", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], "]"}], ".", "ix0"}]}], ";", " ", RowBox[{"\[Delta]\[Theta]x2", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "]"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]\[Theta]y1", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], "]"}], ".", "iy0"}]}], ";", " ", RowBox[{"\[Delta]\[Theta]y2", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "]"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]\[Theta]z1", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], "]"}], ".", "iz0"}]}], ";", " ", RowBox[{"\[Delta]\[Theta]z2", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "]"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", RowBox[{"bx", " ", "=", RowBox[{ RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{"by", " ", "=", RowBox[{ RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"bz", " ", "=", RowBox[{ RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ FractionBox[ RowBox[{"bx", " ", "h0", " ", "\[Delta]ux1"}], "2"], "+", FractionBox[ RowBox[{"AA", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "ux1"}], "+", "ux2"}], ")"}], " ", "\[Delta]ux1"}], "h0"], "+", FractionBox[ RowBox[{"bx", " ", "h0", " ", "\[Delta]ux2"}], "2"], "+", FractionBox[ RowBox[{"AA", " ", "EE", " ", RowBox[{"(", RowBox[{"ux1", "-", "ux2"}], ")"}], " ", "\[Delta]ux2"}], "h0"], "+", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]uz2", " ", RowBox[{"(", RowBox[{ RowBox[{"bz", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", SuperscriptBox["h0", "2"], " ", "Iy"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", "kz"}]}], ")"}]}], "-", RowBox[{ "12", " ", "AA", " ", "EE", " ", "GG", " ", "Iy", " ", "kz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "uz1"}], "+", RowBox[{"2", " ", "uz2"}], "+", RowBox[{"h0", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "+", "\[Theta]y2"}], ")"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"24", " ", "EE", " ", "h0", " ", "Iy"}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "kz"}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]uz1", " ", RowBox[{"(", RowBox[{ RowBox[{"bz", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", SuperscriptBox["h0", "2"], " ", "Iy"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", "kz"}]}], ")"}]}], "+", RowBox[{ "12", " ", "AA", " ", "EE", " ", "GG", " ", "Iy", " ", "kz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "uz1"}], "+", RowBox[{"2", " ", "uz2"}], "+", RowBox[{"h0", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "+", "\[Theta]y2"}], ")"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"24", " ", "EE", " ", "h0", " ", "Iy"}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "kz"}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]\[Theta]y1", " ", RowBox[{"(", RowBox[{ RowBox[{"bz", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iy"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "kz"}]}], ")"}]}], "+", RowBox[{"24", " ", "EE", " ", "Iy", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "EE", " ", "Iy", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "-", "\[Theta]y2"}], ")"}]}], "+", RowBox[{"AA", " ", "GG", " ", "h0", " ", "kz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", "uz1"}], "+", RowBox[{"3", " ", "uz2"}], "+", RowBox[{"2", " ", "h0", " ", "\[Theta]y1"}], "+", RowBox[{"h0", " ", "\[Theta]y2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", "h0", " ", "Iy"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "kz"}]}], ")"}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]\[Theta]y2", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "bz"}], " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iy"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "kz"}]}], ")"}]}], "+", RowBox[{"24", " ", "EE", " ", "Iy", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "EE", " ", "Iy", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Theta]y1"}], "+", "\[Theta]y2"}], ")"}]}], "+", RowBox[{"AA", " ", "GG", " ", "h0", " ", "kz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", "uz1"}], "+", RowBox[{"3", " ", "uz2"}], "+", RowBox[{"h0", " ", "\[Theta]y1"}], "+", RowBox[{"2", " ", "h0", " ", "\[Theta]y2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", "h0", " ", "Iy"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "kz"}]}], ")"}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]uy1", " ", RowBox[{"(", RowBox[{ RowBox[{"by", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", SuperscriptBox["h0", "2"], " ", "Iz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", "ky"}]}], ")"}]}], "-", RowBox[{ "12", " ", "AA", " ", "EE", " ", "GG", " ", "Iz", " ", "ky", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "uy1"}], "-", RowBox[{"2", " ", "uy2"}], "-", RowBox[{"2", " ", "ez", " ", "\[Theta]x1"}], "+", RowBox[{"2", " ", "ez", " ", "\[Theta]x2"}], "+", RowBox[{"h0", " ", "\[Theta]z1"}], "+", RowBox[{"h0", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"24", " ", "EE", " ", "h0", " ", "Iz"}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky"}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]uy2", " ", RowBox[{"(", RowBox[{ RowBox[{"by", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", SuperscriptBox["h0", "2"], " ", "Iz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", "ky"}]}], ")"}]}], "+", RowBox[{ "12", " ", "AA", " ", "EE", " ", "GG", " ", "Iz", " ", "ky", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "uy1"}], "-", RowBox[{"2", " ", "uy2"}], "-", RowBox[{"2", " ", "ez", " ", "\[Theta]x1"}], "+", RowBox[{"2", " ", "ez", " ", "\[Theta]x2"}], "+", RowBox[{"h0", " ", "\[Theta]z1"}], "+", RowBox[{"h0", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"24", " ", "EE", " ", "h0", " ", "Iz"}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky"}]}], ")"}]}], "-", RowBox[{ FractionBox["1", RowBox[{ RowBox[{"12", " ", "EE", " ", "h0", " ", "Iz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky"}]}]], "GG", " ", "\[Delta]\[Theta]x1", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", "Iz", " ", "Jx", " ", RowBox[{"(", RowBox[{"\[Theta]x1", "-", "\[Theta]x2"}], ")"}]}], "+", RowBox[{"AA", " ", "ky", " ", RowBox[{"(", RowBox[{ RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", RowBox[{"(", RowBox[{"\[Theta]x1", "-", "\[Theta]x2"}], ")"}]}], "+", RowBox[{"6", " ", "EE", " ", "ez", " ", "Iz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "uy1"}], "+", RowBox[{"2", " ", "uy2"}], "+", RowBox[{"2", " ", "ez", " ", "\[Theta]x1"}], "-", RowBox[{"2", " ", "ez", " ", "\[Theta]x2"}], "-", RowBox[{"h0", " ", "\[Theta]z1"}], "-", RowBox[{"h0", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{ FractionBox["1", RowBox[{ RowBox[{"12", " ", "EE", " ", "h0", " ", "Iz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky"}]}]], "GG", " ", "\[Delta]\[Theta]x2", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", "Iz", " ", "Jx", " ", RowBox[{"(", RowBox[{"\[Theta]x1", "-", "\[Theta]x2"}], ")"}]}], "+", RowBox[{"AA", " ", "ky", " ", RowBox[{"(", RowBox[{ RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", RowBox[{"(", RowBox[{"\[Theta]x1", "-", "\[Theta]x2"}], ")"}]}], "+", RowBox[{"6", " ", "EE", " ", "ez", " ", "Iz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "uy1"}], "+", RowBox[{"2", " ", "uy2"}], "+", RowBox[{"2", " ", "ez", " ", "\[Theta]x1"}], "-", RowBox[{"2", " ", "ez", " ", "\[Theta]x2"}], "-", RowBox[{"h0", " ", "\[Theta]z1"}], "-", RowBox[{"h0", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]\[Theta]z1", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "by"}], " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "ky"}]}], ")"}]}], "+", RowBox[{"24", " ", "EE", " ", "Iz", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "EE", " ", "Iz", " ", RowBox[{"(", RowBox[{"\[Theta]z1", "-", "\[Theta]z2"}], ")"}]}], "+", RowBox[{"AA", " ", "GG", " ", "h0", " ", "ky", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", "uy1"}], "-", RowBox[{"3", " ", "uy2"}], "-", RowBox[{"3", " ", "ez", " ", "\[Theta]x1"}], "+", RowBox[{"3", " ", "ez", " ", "\[Theta]x2"}], "+", RowBox[{"2", " ", "h0", " ", "\[Theta]z1"}], "+", RowBox[{"h0", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", "h0", " ", "Iz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky"}]}], ")"}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]\[Theta]z2", " ", RowBox[{"(", RowBox[{ RowBox[{"by", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "ky"}]}], ")"}]}], "-", RowBox[{"24", " ", "EE", " ", "Iz", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "EE", " ", "Iz", " ", RowBox[{"(", RowBox[{"\[Theta]z1", "-", "\[Theta]z2"}], ")"}]}], "-", RowBox[{"AA", " ", "GG", " ", "h0", " ", "ky", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", "uy1"}], "-", RowBox[{"3", " ", "uy2"}], "-", RowBox[{"3", " ", "ez", " ", "\[Theta]x1"}], "+", RowBox[{"3", " ", "ez", " ", "\[Theta]x2"}], "+", RowBox[{"h0", " ", "\[Theta]z1"}], "+", RowBox[{"2", " ", "h0", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", "h0", " ", "Iz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky"}]}], ")"}]}], ")"}]}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "first", " ", "order", " ", "offset", " ", "beam", " ", "theory", " ", "defs"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Sy_", ",", "Sz_", ",", "Iy_", ",", "Iz_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE", ",", "GG", ",", "1", ",", "1", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ "AA", ",", "Sy", ",", "Sz", ",", "Iy", ",", "Iz", ",", "0", ",", RowBox[{"Iy", "+", "Iz"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE_", ",", "GG_", ",", "ky_", ",", "kz_", ",", "kyz_", ",", "ey_", ",", "ez_"}], "}"}], ",", RowBox[{"{", RowBox[{ "AA_", ",", "Sy_", ",", "Sz_", ",", "Iy_", ",", "Iz_", ",", "Iyz_", ",", "Jx_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "ix0", ",", "iz0", ",", "ux1", ",", "uy1", " ", ",", "uz1", " ", ",", "\[Theta]x1", " ", ",", "\[Theta]y1", ",", "\[Theta]z1", " ", ",", "\[Delta]ux1", " ", ",", "\[Delta]uy1", ",", "\[Delta]uz1", ",", "\[Delta]\[Theta]x1", ",", "\[Delta]\[Theta]y1", ",", "\[Delta]\[Theta]z1", ",", "ux2", ",", "uy2", " ", ",", "uz2", " ", ",", "\[Theta]x2", " ", ",", "\[Theta]y2", ",", "\[Theta]z2", " ", ",", "\[Delta]ux2", " ", ",", "\[Delta]uy2", ",", "\[Delta]uz2", ",", "\[Delta]\[Theta]x2", ",", "\[Delta]\[Theta]y2", ",", "\[Delta]\[Theta]z2", ",", "bx", ",", "by", ",", "bz", ",", "cx", ",", "cy", ",", "cz"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "mapping", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz0", "=", RowBox[{"ix0", "\[Cross]", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"ux1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "ix0"}]}], ";", " ", RowBox[{"ux2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{"uy1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iy0"}]}], ";", " ", RowBox[{"uy2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"uz1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iz0"}]}], ";", " ", RowBox[{"uz2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]x1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "ix0"}]}], ";", " ", RowBox[{"\[Theta]x2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]y1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iy0"}]}], ";", " ", RowBox[{"\[Theta]y2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]z1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iz0"}]}], ";", " ", RowBox[{"\[Theta]z2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]ux1", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "]"}], ".", "ix0"}]}], ";", " ", RowBox[{"\[Delta]ux2", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "]"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]uy1", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "]"}], ".", "iy0"}]}], ";", " ", RowBox[{"\[Delta]uy2", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "]"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]uz1", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "]"}], ".", "iz0"}]}], ";", " ", RowBox[{"\[Delta]uz2", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "]"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]\[Theta]x1", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], "]"}], ".", "ix0"}]}], ";", " ", RowBox[{"\[Delta]\[Theta]x2", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "]"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]\[Theta]y1", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], "]"}], ".", "iy0"}]}], ";", " ", RowBox[{"\[Delta]\[Theta]y2", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "]"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]\[Theta]z1", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], "]"}], ".", "iz0"}]}], ";", " ", RowBox[{"\[Delta]\[Theta]z2", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "]"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", RowBox[{"bx", " ", "=", RowBox[{ RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{"by", " ", "=", RowBox[{ RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"bz", " ", "=", RowBox[{ RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", RowBox[{"cx", " ", "=", RowBox[{ RowBox[{"{", RowBox[{"mX", ",", "mY", ",", "mZ"}], "}"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{"cy", " ", "=", RowBox[{ RowBox[{"{", RowBox[{"mX", ",", "mY", ",", "mZ"}], "}"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"cz", " ", "=", RowBox[{ RowBox[{"{", RowBox[{"mX", ",", "mY", ",", "mZ"}], "}"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "6"}], " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", SuperscriptBox["AA", "2"], " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "ky"}], "-", RowBox[{"2", " ", "Iyz", " ", "kyz"}], "+", RowBox[{"Iz", " ", "kz"}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["AA", "3"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", SuperscriptBox["kyz", "2"]}], "+", RowBox[{"ky", " ", "kz"}]}], ")"}]}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "Iyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "Sz"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"12", " ", "AA", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}]}], "+", RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", SuperscriptBox["Sy", "2"]}], "-", RowBox[{"2", " ", "kyz", " ", "Sy", " ", "Sz"}], "+", RowBox[{"kz", " ", SuperscriptBox["Sz", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", "\[Delta]ux1", " ", RowBox[{"(", RowBox[{ RowBox[{"bx", " ", SuperscriptBox["h0", "2"]}], "+", RowBox[{"2", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"AA", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "ux1"}], "+", "ux2"}], ")"}]}], "-", RowBox[{"Sy", " ", "\[Theta]y1"}], "+", RowBox[{"Sy", " ", "\[Theta]y2"}], "+", RowBox[{"Sz", " ", "\[Theta]z1"}], "-", RowBox[{"Sz", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"6", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", SuperscriptBox["AA", "2"], " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "ky"}], "-", RowBox[{"2", " ", "Iyz", " ", "kyz"}], "+", RowBox[{"Iz", " ", "kz"}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["AA", "3"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", SuperscriptBox["kyz", "2"]}], "+", RowBox[{"ky", " ", "kz"}]}], ")"}]}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "Iyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "Sz"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"12", " ", "AA", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}]}], "+", RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", SuperscriptBox["Sy", "2"]}], "-", RowBox[{"2", " ", "kyz", " ", "Sy", " ", "Sz"}], "+", RowBox[{"kz", " ", SuperscriptBox["Sz", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", "\[Delta]ux2", " ", RowBox[{"(", RowBox[{ RowBox[{"bx", " ", SuperscriptBox["h0", "2"]}], "+", RowBox[{"2", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"AA", " ", RowBox[{"(", RowBox[{"ux1", "-", "ux2"}], ")"}]}], "+", RowBox[{"Sy", " ", "\[Theta]y1"}], "-", RowBox[{"Sy", " ", "\[Theta]y2"}], "-", RowBox[{"Sz", " ", "\[Theta]z1"}], "+", RowBox[{"Sz", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"6", " ", "\[Delta]\[Theta]x1", " ", RowBox[{"(", RowBox[{ RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "Iyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "Sz"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"cx", " ", SuperscriptBox["h0", "2"]}], "+", RowBox[{"2", " ", "GG", " ", "Jx", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Theta]x1"}], "+", "\[Theta]x2"}], ")"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["AA", "3"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["kyz", "2"], "-", RowBox[{"ky", " ", "kz"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "cy", " ", "ey", " ", SuperscriptBox["h0", "3"]}], "+", RowBox[{"2", " ", "cz", " ", "ez", " ", SuperscriptBox["h0", "3"]}], "+", RowBox[{"cx", " ", SuperscriptBox["h0", "4"]}], "-", RowBox[{"24", " ", "EE", " ", "ey", " ", "Iyz", " ", "uy1"}], "+", RowBox[{"24", " ", "EE", " ", "ez", " ", "Iz", " ", "uy1"}], "+", RowBox[{"24", " ", "EE", " ", "ey", " ", "Iyz", " ", "uy2"}], "-", RowBox[{"24", " ", "EE", " ", "ez", " ", "Iz", " ", "uy2"}], "-", RowBox[{"24", " ", "EE", " ", "ey", " ", "Iy", " ", "uz1"}], "+", RowBox[{"24", " ", "EE", " ", "ez", " ", "Iyz", " ", "uz1"}], "+", RowBox[{"24", " ", "EE", " ", "ey", " ", "Iy", " ", "uz2"}], "-", RowBox[{"24", " ", "EE", " ", "ez", " ", "Iyz", " ", "uz2"}], "-", RowBox[{"24", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "Iy", " ", "\[Theta]x1"}], "+", RowBox[{ "48", " ", "EE", " ", "ey", " ", "ez", " ", "Iyz", " ", "\[Theta]x1"}], "-", RowBox[{"24", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "Iz", " ", "\[Theta]x1"}], "-", RowBox[{"2", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", "\[Theta]x1"}], "+", RowBox[{"24", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "Iy", " ", "\[Theta]x2"}], "-", RowBox[{ "48", " ", "EE", " ", "ey", " ", "ez", " ", "Iyz", " ", "\[Theta]x2"}], "+", RowBox[{"24", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "Iz", " ", "\[Theta]x2"}], "+", RowBox[{"2", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", "\[Theta]x2"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "h0", " ", "Iy", " ", "\[Theta]y1"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "h0", " ", "Iyz", " ", "\[Theta]y1"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "h0", " ", "Iy", " ", "\[Theta]y2"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "h0", " ", "Iyz", " ", "\[Theta]y2"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "h0", " ", "Iyz", " ", "\[Theta]z1"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "h0", " ", "Iz", " ", "\[Theta]z1"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "h0", " ", "Iyz", " ", "\[Theta]z2"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "h0", " ", "Iz", " ", "\[Theta]z2"}]}], ")"}]}], "-", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", "GG", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "cy", " ", "EE", " ", "ez", " ", SuperscriptBox["h0", "3"], " ", "Iyz", " ", "ky"}], "-", RowBox[{"12", " ", "cy", " ", "EE", " ", "ey", " ", SuperscriptBox["h0", "3"], " ", "Iyz", " ", "kyz"}], "-", RowBox[{"12", " ", "cy", " ", "EE", " ", "ez", " ", SuperscriptBox["h0", "3"], " ", "Iz", " ", "kyz"}], "+", RowBox[{"12", " ", "cy", " ", "EE", " ", "ey", " ", SuperscriptBox["h0", "3"], " ", "Iz", " ", "kz"}], "+", RowBox[{"12", " ", "cz", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"ez", " ", "Iy", " ", "ky"}], "-", RowBox[{"ey", " ", "Iy", " ", "kyz"}], "-", RowBox[{"ez", " ", "Iyz", " ", "kyz"}], "+", RowBox[{"ey", " ", "Iyz", " ", "kz"}]}], ")"}]}], "+", RowBox[{"6", " ", "cx", " ", "EE", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "ky"}], "-", RowBox[{"2", " ", "Iyz", " ", "kyz"}], "+", RowBox[{"Iz", " ", "kz"}]}], ")"}]}], "+", RowBox[{"bx", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", SuperscriptBox["kyz", "2"], " ", "Sy"}], "-", RowBox[{"bx", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "ky", " ", "kz", " ", "Sy"}], "-", RowBox[{"bx", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", SuperscriptBox["kyz", "2"], " ", "Sz"}], "+", RowBox[{"bx", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "ky", " ", "kz", " ", "Sz"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "uy1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "ky", " ", "uy1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uy1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kyz", " ", "uy1"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uy1"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uy1"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "uy2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "ky", " ", "uy2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uy2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kyz", " ", "uy2"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uy2"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uy2"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uz1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "kyz", " ", "uz1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "uz1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kz", " ", "uz1"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uz1"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uz2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "kyz", " ", "uz2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "uz2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kz", " ", "uz2"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uz2"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["ez", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["ez", "2"], " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Iy", " ", "Jx", " ", "ky", " ", "\[Theta]x1"}], "-", RowBox[{"288", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x1"}], "+", RowBox[{"288", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "ez", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x1"}], "+", RowBox[{"24", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Iyz", " ", "Jx", " ", "kyz", " ", "\[Theta]x1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["ey", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["ey", "2"], " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Iz", " ", "Jx", " ", "kz", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "+", RowBox[{ "24", " ", "EE", " ", "ey", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{ "24", " ", "EE", " ", "ey", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["ez", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]x2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["ez", "2"], " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Iy", " ", "Jx", " ", "ky", " ", "\[Theta]x2"}], "+", RowBox[{"288", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x2"}], "-", RowBox[{"288", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "ez", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x2"}], "-", RowBox[{"24", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Iyz", " ", "Jx", " ", "kyz", " ", "\[Theta]x2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["ey", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]x2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["ey", "2"], " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Iz", " ", "Jx", " ", "kz", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "-", RowBox[{ "24", " ", "EE", " ", "ey", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{ "24", " ", "EE", " ", "ey", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]y1"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]y1"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]y1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "h0", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]y1"}], "+", RowBox[{"6", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "-", RowBox[{"6", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "-", RowBox[{"6", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "+", RowBox[{"6", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]y2"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]y2"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]y2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "h0", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]y2"}], "+", RowBox[{"6", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "-", RowBox[{"6", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "-", RowBox[{"6", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "+", RowBox[{"6", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]z1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "h0", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]z1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]z1"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]z1"}], "-", RowBox[{"6", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "+", RowBox[{"6", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "+", RowBox[{"6", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "-", RowBox[{"6", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]z2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "h0", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]z2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]z2"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]z2"}], "-", RowBox[{"6", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}], "+", RowBox[{"6", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}], "+", RowBox[{"6", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}], "-", RowBox[{"6", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}]}], ")"}]}], "+", RowBox[{"12", " ", "AA", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"cx", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}]}], "+", RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "kyz", " ", "Sy"}], "+", RowBox[{"kz", " ", "Sz"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "GG", " ", RowBox[{"(", RowBox[{ RowBox[{"cy", " ", "ez", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "Sy", " ", "Sz"}], "-", RowBox[{"cy", " ", "ey", " ", SuperscriptBox["h0", "3"], " ", "kyz", " ", "Sy", " ", "Sz"}], "-", RowBox[{"cy", " ", "ez", " ", SuperscriptBox["h0", "3"], " ", "kyz", " ", SuperscriptBox["Sz", "2"]}], "+", RowBox[{"cy", " ", "ey", " ", SuperscriptBox["h0", "3"], " ", "kz", " ", SuperscriptBox["Sz", "2"]}], "+", RowBox[{"cz", " ", SuperscriptBox["h0", "3"], " ", "Sy", " ", RowBox[{"(", RowBox[{ RowBox[{"ez", " ", "ky", " ", "Sy"}], "-", RowBox[{"ey", " ", "kyz", " ", "Sy"}], "-", RowBox[{"ez", " ", "kyz", " ", "Sz"}], "+", RowBox[{"ey", " ", "kz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"bx", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"ez", " ", RowBox[{"(", RowBox[{ RowBox[{"Iyz", " ", "ky", " ", "Sy"}], "-", RowBox[{"Iz", " ", "kyz", " ", "Sy"}], "-", RowBox[{"Iy", " ", "ky", " ", "Sz"}], "+", RowBox[{"Iyz", " ", "kyz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"ey", " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", "kz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "kyz", " ", "Sz"}], "-", RowBox[{"Iyz", " ", RowBox[{"(", RowBox[{ RowBox[{"kyz", " ", "Sy"}], "+", RowBox[{"kz", " ", "Sz"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "uy1"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "uy1"}], "-", RowBox[{ "24", " ", "EE", " ", "ez", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "uy1"}], "+", RowBox[{ "24", " ", "EE", " ", "ey", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "uy1"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "uy2"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "uy2"}], "+", RowBox[{ "24", " ", "EE", " ", "ez", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "uy2"}], "-", RowBox[{ "24", " ", "EE", " ", "ey", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "uy2"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "-", RowBox[{ "24", " ", "EE", " ", "ez", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "uz1"}], "+", RowBox[{ "24", " ", "EE", " ", "ey", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz1"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "uz1"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uz1"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "+", RowBox[{ "24", " ", "EE", " ", "ez", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "uz2"}], "-", RowBox[{ "24", " ", "EE", " ", "ey", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz2"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "uz2"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uz2"}], "-", RowBox[{"12", " ", "EE", " ", SuperscriptBox["Iyz", "2"], " ", "Jx", " ", "\[Theta]x1"}], "+", RowBox[{ "12", " ", "EE", " ", "Iy", " ", "Iz", " ", "Jx", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "-", RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "+", RowBox[{ "24", " ", "EE", " ", "ey", " ", "ez", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "+", RowBox[{"24", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{ "48", " ", "EE", " ", "ey", " ", "ez", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "+", RowBox[{"2", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "+", RowBox[{"24", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "+", RowBox[{ "24", " ", "EE", " ", "ey", " ", "ez", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "-", RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", SuperscriptBox["Iyz", "2"], " ", "Jx", " ", "\[Theta]x2"}], "-", RowBox[{ "12", " ", "EE", " ", "Iy", " ", "Iz", " ", "Jx", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "+", RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "-", RowBox[{ "24", " ", "EE", " ", "ey", " ", "ez", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "-", RowBox[{"24", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{ "48", " ", "EE", " ", "ey", " ", "ez", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "-", RowBox[{"2", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "-", RowBox[{"24", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "-", RowBox[{ "24", " ", "EE", " ", "ey", " ", "ez", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "+", RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "-", RowBox[{ "6", " ", "EE", " ", "ez", " ", "h0", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "+", RowBox[{ "6", " ", "EE", " ", "ey", " ", "h0", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "h0", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "-", RowBox[{ "6", " ", "EE", " ", "ez", " ", "h0", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]y1"}], "+", RowBox[{ "6", " ", "EE", " ", "ey", " ", "h0", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]y1"}], "-", RowBox[{ "6", " ", "EE", " ", "ez", " ", "h0", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "+", RowBox[{ "6", " ", "EE", " ", "ey", " ", "h0", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "h0", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "-", RowBox[{ "6", " ", "EE", " ", "ez", " ", "h0", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]y2"}], "+", RowBox[{ "6", " ", "EE", " ", "ey", " ", "h0", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]y2"}], "+", RowBox[{ "6", " ", "EE", " ", "ez", " ", "h0", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]z1"}], "-", RowBox[{ "6", " ", "EE", " ", "ey", " ", "h0", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]z1"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "h0", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "+", RowBox[{ "6", " ", "EE", " ", "ez", " ", "h0", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "-", RowBox[{ "6", " ", "EE", " ", "ey", " ", "h0", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "+", RowBox[{ "6", " ", "EE", " ", "ez", " ", "h0", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]z2"}], "-", RowBox[{ "6", " ", "EE", " ", "ey", " ", "h0", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]z2"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "h0", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}], "+", RowBox[{ "6", " ", "EE", " ", "ez", " ", "h0", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}], "-", RowBox[{ "6", " ", "EE", " ", "ey", " ", "h0", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"6", " ", "\[Delta]\[Theta]x2", " ", RowBox[{"(", RowBox[{ RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "Iyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "Sz"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"cx", " ", SuperscriptBox["h0", "2"]}], "+", RowBox[{"2", " ", "GG", " ", "Jx", " ", RowBox[{"(", RowBox[{"\[Theta]x1", "-", "\[Theta]x2"}], ")"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["AA", "3"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["kyz", "2"], "-", RowBox[{"ky", " ", "kz"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "cy", " ", "ey", " ", SuperscriptBox["h0", "3"]}], "-", RowBox[{"2", " ", "cz", " ", "ez", " ", SuperscriptBox["h0", "3"]}], "+", RowBox[{"cx", " ", SuperscriptBox["h0", "4"]}], "+", RowBox[{"24", " ", "EE", " ", "ey", " ", "Iyz", " ", "uy1"}], "-", RowBox[{"24", " ", "EE", " ", "ez", " ", "Iz", " ", "uy1"}], "-", RowBox[{"24", " ", "EE", " ", "ey", " ", "Iyz", " ", "uy2"}], "+", RowBox[{"24", " ", "EE", " ", "ez", " ", "Iz", " ", "uy2"}], "+", RowBox[{"24", " ", "EE", " ", "ey", " ", "Iy", " ", "uz1"}], "-", RowBox[{"24", " ", "EE", " ", "ez", " ", "Iyz", " ", "uz1"}], "-", RowBox[{"24", " ", "EE", " ", "ey", " ", "Iy", " ", "uz2"}], "+", RowBox[{"24", " ", "EE", " ", "ez", " ", "Iyz", " ", "uz2"}], "+", RowBox[{"24", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "Iy", " ", "\[Theta]x1"}], "-", RowBox[{ "48", " ", "EE", " ", "ey", " ", "ez", " ", "Iyz", " ", "\[Theta]x1"}], "+", RowBox[{"24", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "Iz", " ", "\[Theta]x1"}], "+", RowBox[{"2", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", "\[Theta]x1"}], "-", RowBox[{"24", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "Iy", " ", "\[Theta]x2"}], "+", RowBox[{ "48", " ", "EE", " ", "ey", " ", "ez", " ", "Iyz", " ", "\[Theta]x2"}], "-", RowBox[{"24", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "Iz", " ", "\[Theta]x2"}], "-", RowBox[{"2", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", "\[Theta]x2"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "h0", " ", "Iy", " ", "\[Theta]y1"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "h0", " ", "Iyz", " ", "\[Theta]y1"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "h0", " ", "Iy", " ", "\[Theta]y2"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "h0", " ", "Iyz", " ", "\[Theta]y2"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "h0", " ", "Iyz", " ", "\[Theta]z1"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "h0", " ", "Iz", " ", "\[Theta]z1"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "h0", " ", "Iyz", " ", "\[Theta]z2"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "h0", " ", "Iz", " ", "\[Theta]z2"}]}], ")"}]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", "GG", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "cy", " ", "EE", " ", "ez", " ", SuperscriptBox["h0", "3"], " ", "Iyz", " ", "ky"}], "-", RowBox[{"12", " ", "cy", " ", "EE", " ", "ey", " ", SuperscriptBox["h0", "3"], " ", "Iyz", " ", "kyz"}], "-", RowBox[{"12", " ", "cy", " ", "EE", " ", "ez", " ", SuperscriptBox["h0", "3"], " ", "Iz", " ", "kyz"}], "+", RowBox[{"12", " ", "cy", " ", "EE", " ", "ey", " ", SuperscriptBox["h0", "3"], " ", "Iz", " ", "kz"}], "+", RowBox[{"12", " ", "cz", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"ez", " ", "Iy", " ", "ky"}], "-", RowBox[{"ey", " ", "Iy", " ", "kyz"}], "-", RowBox[{"ez", " ", "Iyz", " ", "kyz"}], "+", RowBox[{"ey", " ", "Iyz", " ", "kz"}]}], ")"}]}], "-", RowBox[{"6", " ", "cx", " ", "EE", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "ky"}], "-", RowBox[{"2", " ", "Iyz", " ", "kyz"}], "+", RowBox[{"Iz", " ", "kz"}]}], ")"}]}], "+", RowBox[{"bx", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", SuperscriptBox["kyz", "2"], " ", "Sy"}], "-", RowBox[{"bx", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "ky", " ", "kz", " ", "Sy"}], "-", RowBox[{"bx", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", SuperscriptBox["kyz", "2"], " ", "Sz"}], "+", RowBox[{"bx", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "ky", " ", "kz", " ", "Sz"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "uy1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "ky", " ", "uy1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uy1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kyz", " ", "uy1"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uy1"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uy1"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "uy2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "ky", " ", "uy2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uy2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kyz", " ", "uy2"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uy2"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uy2"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uz1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "kyz", " ", "uz1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "uz1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kz", " ", "uz1"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uz1"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uz2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "kyz", " ", "uz2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "uz2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kz", " ", "uz2"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uz2"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["ez", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["ez", "2"], " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Iy", " ", "Jx", " ", "ky", " ", "\[Theta]x1"}], "-", RowBox[{"288", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x1"}], "+", RowBox[{"288", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "ez", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x1"}], "+", RowBox[{"24", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Iyz", " ", "Jx", " ", "kyz", " ", "\[Theta]x1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["ey", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["ey", "2"], " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Iz", " ", "Jx", " ", "kz", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "+", RowBox[{ "24", " ", "EE", " ", "ey", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{ "24", " ", "EE", " ", "ey", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["ez", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]x2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["ez", "2"], " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Iy", " ", "Jx", " ", "ky", " ", "\[Theta]x2"}], "+", RowBox[{"288", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x2"}], "-", RowBox[{"288", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "ez", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x2"}], "-", RowBox[{"24", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Iyz", " ", "Jx", " ", "kyz", " ", "\[Theta]x2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["ey", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]x2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["ey", "2"], " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Iz", " ", "Jx", " ", "kz", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "-", RowBox[{ "24", " ", "EE", " ", "ey", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{ "24", " ", "EE", " ", "ey", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]y1"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]y1"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]y1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "h0", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]y1"}], "+", RowBox[{"6", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "-", RowBox[{"6", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "-", RowBox[{"6", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "+", RowBox[{"6", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]y2"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]y2"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]y2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "h0", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]y2"}], "+", RowBox[{"6", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "-", RowBox[{"6", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "-", RowBox[{"6", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "+", RowBox[{"6", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]z1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "h0", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]z1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]z1"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]z1"}], "-", RowBox[{"6", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "+", RowBox[{"6", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "+", RowBox[{"6", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "-", RowBox[{"6", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]z2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "h0", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]z2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]z2"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]z2"}], "-", RowBox[{"6", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}], "+", RowBox[{"6", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}], "+", RowBox[{"6", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}], "-", RowBox[{"6", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}]}], ")"}]}], "+", RowBox[{"12", " ", "AA", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"cx", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}]}], "+", RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "kyz", " ", "Sy"}], "+", RowBox[{"kz", " ", "Sz"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "cy"}], " ", "ez", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "Sy", " ", "Sz"}], "+", RowBox[{"cy", " ", "ey", " ", SuperscriptBox["h0", "3"], " ", "kyz", " ", "Sy", " ", "Sz"}], "+", RowBox[{"cy", " ", "ez", " ", SuperscriptBox["h0", "3"], " ", "kyz", " ", SuperscriptBox["Sz", "2"]}], "-", RowBox[{"cy", " ", "ey", " ", SuperscriptBox["h0", "3"], " ", "kz", " ", SuperscriptBox["Sz", "2"]}], "+", RowBox[{"cz", " ", SuperscriptBox["h0", "3"], " ", "Sy", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "ez"}], " ", "ky", " ", "Sy"}], "+", RowBox[{"ey", " ", "kyz", " ", "Sy"}], "+", RowBox[{"ez", " ", "kyz", " ", "Sz"}], "-", RowBox[{"ey", " ", "kz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"bx", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"ey", " ", RowBox[{"(", RowBox[{ RowBox[{"Iyz", " ", "kyz", " ", "Sy"}], "-", RowBox[{"Iz", " ", "kz", " ", "Sy"}], "-", RowBox[{"Iy", " ", "kyz", " ", "Sz"}], "+", RowBox[{"Iyz", " ", "kz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"ez", " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", "kyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "ky", " ", "Sz"}], "-", RowBox[{"Iyz", " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", "Sy"}], "+", RowBox[{"kyz", " ", "Sz"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "uy1"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "uy1"}], "+", RowBox[{ "24", " ", "EE", " ", "ez", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "uy1"}], "-", RowBox[{ "24", " ", "EE", " ", "ey", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "uy1"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "uy2"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "uy2"}], "-", RowBox[{ "24", " ", "EE", " ", "ez", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "uy2"}], "+", RowBox[{ "24", " ", "EE", " ", "ey", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "uy2"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "+", RowBox[{ "24", " ", "EE", " ", "ez", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "uz1"}], "-", RowBox[{ "24", " ", "EE", " ", "ey", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz1"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "uz1"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uz1"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "-", RowBox[{ "24", " ", "EE", " ", "ez", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "uz2"}], "+", RowBox[{ "24", " ", "EE", " ", "ey", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz2"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "uz2"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uz2"}], "+", RowBox[{"12", " ", "EE", " ", SuperscriptBox["Iyz", "2"], " ", "Jx", " ", "\[Theta]x1"}], "-", RowBox[{ "12", " ", "EE", " ", "Iy", " ", "Iz", " ", "Jx", " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "+", RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "-", RowBox[{ "24", " ", "EE", " ", "ey", " ", "ez", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "-", RowBox[{"24", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "+", RowBox[{ "48", " ", "EE", " ", "ey", " ", "ez", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{"2", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{"24", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "-", RowBox[{ "24", " ", "EE", " ", "ey", " ", "ez", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "+", RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", SuperscriptBox["Iyz", "2"], " ", "Jx", " ", "\[Theta]x2"}], "+", RowBox[{ "12", " ", "EE", " ", "Iy", " ", "Iz", " ", "Jx", " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "-", RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "+", RowBox[{ "24", " ", "EE", " ", "ey", " ", "ez", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "+", RowBox[{"24", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "-", RowBox[{ "48", " ", "EE", " ", "ey", " ", "ez", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{"2", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{"24", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ez", "2"], " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "+", RowBox[{ "24", " ", "EE", " ", "ey", " ", "ez", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", SuperscriptBox["ey", "2"], " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "-", RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", "Jx", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "+", RowBox[{ "6", " ", "EE", " ", "ez", " ", "h0", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "-", RowBox[{ "6", " ", "EE", " ", "ey", " ", "h0", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "h0", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "+", RowBox[{ "6", " ", "EE", " ", "ez", " ", "h0", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]y1"}], "-", RowBox[{ "6", " ", "EE", " ", "ey", " ", "h0", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]y1"}], "+", RowBox[{ "6", " ", "EE", " ", "ez", " ", "h0", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "-", RowBox[{ "6", " ", "EE", " ", "ey", " ", "h0", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "h0", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "+", RowBox[{ "6", " ", "EE", " ", "ez", " ", "h0", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]y2"}], "-", RowBox[{ "6", " ", "EE", " ", "ey", " ", "h0", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]y2"}], "-", RowBox[{ "6", " ", "EE", " ", "ez", " ", "h0", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]z1"}], "+", RowBox[{ "6", " ", "EE", " ", "ey", " ", "h0", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]z1"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "h0", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "-", RowBox[{ "6", " ", "EE", " ", "ez", " ", "h0", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "+", RowBox[{ "6", " ", "EE", " ", "ey", " ", "h0", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "-", RowBox[{ "6", " ", "EE", " ", "ez", " ", "h0", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]z2"}], "+", RowBox[{ "6", " ", "EE", " ", "ey", " ", "h0", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]z2"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "h0", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}], "-", RowBox[{ "6", " ", "EE", " ", "ez", " ", "h0", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}], "+", RowBox[{ "6", " ", "EE", " ", "ey", " ", "h0", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"6", " ", "\[Delta]uz1", " ", RowBox[{"(", RowBox[{ RowBox[{"144", " ", "bz", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "Iyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "Sz"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", "GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "12"}], " ", "cy", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iyz", " ", "kyz"}], "+", RowBox[{"12", " ", "cy", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iz", " ", "kz"}], "-", RowBox[{"12", " ", "cz", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "kyz"}], "-", RowBox[{"Iyz", " ", "kz"}]}], ")"}]}], "+", RowBox[{"6", " ", "bz", " ", "EE", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "ky"}], "-", RowBox[{"2", " ", "Iyz", " ", "kyz"}], "+", RowBox[{"Iz", " ", "kz"}]}], ")"}]}], "+", RowBox[{"bx", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", SuperscriptBox["kyz", "2"], " ", "Sy"}], "-", RowBox[{"bx", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "ky", " ", "kz", " ", "Sy"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uy1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kyz", " ", "uy1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uy1"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uy1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uy2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kyz", " ", "uy2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uy2"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uy2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "uz1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kz", " ", "uz1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "uz2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kz", " ", "uz2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]x2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]y1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]y1"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]y2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]y2"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]z1"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]z1"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]z2"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]z2"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}]}], ")"}]}], "+", RowBox[{"12", " ", "AA", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"bz", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}]}], "+", RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "kyz", " ", "Sy"}], "+", RowBox[{"kz", " ", "Sz"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "cy"}], " ", SuperscriptBox["h0", "3"], " ", "kyz", " ", "Sy", " ", "Sz"}], "+", RowBox[{"cy", " ", SuperscriptBox["h0", "3"], " ", "kz", " ", SuperscriptBox["Sz", "2"]}], "+", RowBox[{"cz", " ", SuperscriptBox["h0", "3"], " ", "Sy", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "kyz"}], " ", "Sy"}], "+", RowBox[{"kz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"bx", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", "kz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "kyz", " ", "Sz"}], "-", RowBox[{"Iyz", " ", RowBox[{"(", RowBox[{ RowBox[{"kyz", " ", "Sy"}], "+", RowBox[{"kz", " ", "Sz"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"12", " ", "EE", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "uy1"}], "+", RowBox[{ "24", " ", "EE", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "uy1"}], "-", RowBox[{"12", " ", "EE", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "+", RowBox[{"12", " ", "EE", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "uy2"}], "-", RowBox[{ "24", " ", "EE", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "uy2"}], "+", RowBox[{"12", " ", "EE", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "-", RowBox[{"12", " ", "EE", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "+", RowBox[{ "24", " ", "EE", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz1"}], "-", RowBox[{"12", " ", "EE", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uz1"}], "+", RowBox[{"12", " ", "EE", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "-", RowBox[{ "24", " ", "EE", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz2"}], "+", RowBox[{"12", " ", "EE", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uz2"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "-", RowBox[{ "24", " ", "EE", " ", "ez", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "+", RowBox[{ "24", " ", "EE", " ", "ey", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "+", RowBox[{ "24", " ", "EE", " ", "ez", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "-", RowBox[{ "24", " ", "EE", " ", "ey", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "+", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "-", RowBox[{ "12", " ", "EE", " ", "h0", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "+", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]y1"}], "+", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "-", RowBox[{ "12", " ", "EE", " ", "h0", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "+", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]y2"}], "-", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]z1"}], "+", RowBox[{ "12", " ", "EE", " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "-", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "-", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]z2"}], "+", RowBox[{ "12", " ", "EE", " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}], "-", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["AA", "3"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["kyz", "2"], "-", RowBox[{"ky", " ", "kz"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "cy", " ", SuperscriptBox["h0", "3"]}], "+", RowBox[{"bz", " ", SuperscriptBox["h0", "4"]}], "-", RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "uz1"}], "-", RowBox[{"2", " ", "uz2"}], "+", RowBox[{"2", " ", "ey", " ", "\[Theta]x1"}], "-", RowBox[{"2", " ", "ey", " ", "\[Theta]x2"}], "-", RowBox[{"h0", " ", "\[Theta]y1"}], "-", RowBox[{"h0", " ", "\[Theta]y2"}]}], ")"}]}], "+", RowBox[{"Iyz", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "uy1"}], "-", RowBox[{"2", " ", "uy2"}], "-", RowBox[{"2", " ", "ez", " ", "\[Theta]x1"}], "+", RowBox[{"2", " ", "ez", " ", "\[Theta]x2"}], "+", RowBox[{"h0", " ", "\[Theta]z1"}], "+", RowBox[{"h0", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"6", " ", "\[Delta]uz2", " ", RowBox[{"(", RowBox[{ RowBox[{"144", " ", "bz", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "Iyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "Sz"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", "GG", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "cy", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iyz", " ", "kyz"}], "-", RowBox[{"12", " ", "cy", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iz", " ", "kz"}], "+", RowBox[{"12", " ", "cz", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "kyz"}], "-", RowBox[{"Iyz", " ", "kz"}]}], ")"}]}], "+", RowBox[{"6", " ", "bz", " ", "EE", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "ky"}], "-", RowBox[{"2", " ", "Iyz", " ", "kyz"}], "+", RowBox[{"Iz", " ", "kz"}]}], ")"}]}], "-", RowBox[{"bx", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", SuperscriptBox["kyz", "2"], " ", "Sy"}], "+", RowBox[{"bx", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "ky", " ", "kz", " ", "Sy"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uy1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kyz", " ", "uy1"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uy1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uy1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uy2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kyz", " ", "uy2"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uy2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uy2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "uz1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kz", " ", "uz1"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "uz2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kz", " ", "uz2"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]x1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]x2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]y1"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]y1"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]y2"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]y2"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]z1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]z1"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]z2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]z2"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}]}], ")"}]}], "+", RowBox[{"12", " ", "AA", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"bz", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}]}], "+", RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "kyz", " ", "Sy"}], "+", RowBox[{"kz", " ", "Sz"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "GG", " ", RowBox[{"(", RowBox[{ RowBox[{"cy", " ", SuperscriptBox["h0", "3"], " ", "kyz", " ", "Sy", " ", "Sz"}], "-", RowBox[{"cy", " ", SuperscriptBox["h0", "3"], " ", "kz", " ", SuperscriptBox["Sz", "2"]}], "+", RowBox[{"cz", " ", SuperscriptBox["h0", "3"], " ", "Sy", " ", RowBox[{"(", RowBox[{ RowBox[{"kyz", " ", "Sy"}], "-", RowBox[{"kz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"bx", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iyz", " ", "kyz", " ", "Sy"}], "-", RowBox[{"Iz", " ", "kz", " ", "Sy"}], "-", RowBox[{"Iy", " ", "kyz", " ", "Sz"}], "+", RowBox[{"Iyz", " ", "kz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"12", " ", "EE", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "uy1"}], "-", RowBox[{ "24", " ", "EE", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "uy1"}], "+", RowBox[{"12", " ", "EE", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "-", RowBox[{"12", " ", "EE", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "uy2"}], "+", RowBox[{ "24", " ", "EE", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "uy2"}], "-", RowBox[{"12", " ", "EE", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "+", RowBox[{"12", " ", "EE", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "-", RowBox[{ "24", " ", "EE", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz1"}], "+", RowBox[{"12", " ", "EE", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uz1"}], "-", RowBox[{"12", " ", "EE", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "+", RowBox[{ "24", " ", "EE", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz2"}], "-", RowBox[{"12", " ", "EE", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uz2"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "+", RowBox[{ "24", " ", "EE", " ", "ez", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{ "24", " ", "EE", " ", "ey", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "-", RowBox[{ "24", " ", "EE", " ", "ez", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{ "24", " ", "EE", " ", "ey", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "-", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "+", RowBox[{ "12", " ", "EE", " ", "h0", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "-", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]y1"}], "-", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iz", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "+", RowBox[{ "12", " ", "EE", " ", "h0", " ", "Iyz", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "-", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iy", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]y2"}], "+", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]z1"}], "-", RowBox[{ "12", " ", "EE", " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "+", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "+", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]z2"}], "-", RowBox[{ "12", " ", "EE", " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}], "+", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["AA", "3"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["kyz", "2"], "-", RowBox[{"ky", " ", "kz"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "cy", " ", SuperscriptBox["h0", "3"]}], "+", RowBox[{"bz", " ", SuperscriptBox["h0", "4"]}], "+", RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "uz1"}], "-", RowBox[{"2", " ", "uz2"}], "+", RowBox[{"2", " ", "ey", " ", "\[Theta]x1"}], "-", RowBox[{"2", " ", "ey", " ", "\[Theta]x2"}], "-", RowBox[{"h0", " ", "\[Theta]y1"}], "-", RowBox[{"h0", " ", "\[Theta]y2"}]}], ")"}]}], "+", RowBox[{"Iyz", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "uy1"}], "-", RowBox[{"2", " ", "uy2"}], "-", RowBox[{"2", " ", "ez", " ", "\[Theta]x1"}], "+", RowBox[{"2", " ", "ez", " ", "\[Theta]x2"}], "+", RowBox[{"h0", " ", "\[Theta]z1"}], "+", RowBox[{"h0", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"6", " ", "\[Delta]uy1", " ", RowBox[{"(", RowBox[{ RowBox[{"144", " ", "by", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "Iyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "Sz"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", "GG", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "cy", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iyz", " ", "ky"}], "-", RowBox[{"12", " ", "cy", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iz", " ", "kyz"}], "+", RowBox[{"12", " ", "cz", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "ky"}], "-", RowBox[{"Iyz", " ", "kyz"}]}], ")"}]}], "-", RowBox[{"6", " ", "by", " ", "EE", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "ky"}], "-", RowBox[{"2", " ", "Iyz", " ", "kyz"}], "+", RowBox[{"Iz", " ", "kz"}]}], ")"}]}], "-", RowBox[{"bx", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", SuperscriptBox["kyz", "2"], " ", "Sz"}], "+", RowBox[{"bx", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "ky", " ", "kz", " ", "Sz"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "uy1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "ky", " ", "uy1"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "uy2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "ky", " ", "uy2"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uz1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kyz", " ", "uz1"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uz1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uz2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kyz", " ", "uz2"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uz2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]x2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]x2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]y1"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]y1"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]y2"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]y2"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]z1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]z1"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]z2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]z2"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}]}], ")"}]}], "+", RowBox[{"12", " ", "AA", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"by", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}]}], "+", RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "kyz", " ", "Sy"}], "+", RowBox[{"kz", " ", "Sz"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "cy"}], " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "Sy", " ", "Sz"}], "+", RowBox[{"cy", " ", SuperscriptBox["h0", "3"], " ", "kyz", " ", SuperscriptBox["Sz", "2"]}], "+", RowBox[{"cz", " ", SuperscriptBox["h0", "3"], " ", "Sy", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "ky"}], " ", "Sy"}], "+", RowBox[{"kyz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"bx", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", "kyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "ky", " ", "Sz"}], "-", RowBox[{"Iyz", " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", "Sy"}], "+", RowBox[{"kyz", " ", "Sz"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"12", " ", "EE", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "uy1"}], "+", RowBox[{ "24", " ", "EE", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "uy1"}], "-", RowBox[{"12", " ", "EE", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "+", RowBox[{"12", " ", "EE", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "uy2"}], "-", RowBox[{ "24", " ", "EE", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "uy2"}], "+", RowBox[{"12", " ", "EE", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "-", RowBox[{"12", " ", "EE", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "+", RowBox[{ "24", " ", "EE", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "uz1"}], "-", RowBox[{"12", " ", "EE", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "uz1"}], "+", RowBox[{"12", " ", "EE", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "-", RowBox[{ "24", " ", "EE", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "uz2"}], "+", RowBox[{"12", " ", "EE", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "uz2"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "-", RowBox[{ "24", " ", "EE", " ", "ez", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "+", RowBox[{ "24", " ", "EE", " ", "ey", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "+", RowBox[{ "24", " ", "EE", " ", "ez", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "-", RowBox[{ "24", " ", "EE", " ", "ey", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "+", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "-", RowBox[{ "12", " ", "EE", " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "+", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]y1"}], "+", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "-", RowBox[{ "12", " ", "EE", " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "+", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]y2"}], "-", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]z1"}], "+", RowBox[{ "12", " ", "EE", " ", "h0", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "-", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "-", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]z2"}], "+", RowBox[{ "12", " ", "EE", " ", "h0", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}], "-", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["AA", "3"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["kyz", "2"], "-", RowBox[{"ky", " ", "kz"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "cz", " ", SuperscriptBox["h0", "3"]}], "+", RowBox[{"by", " ", SuperscriptBox["h0", "4"]}], "-", RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"Iyz", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "uz1"}], "-", RowBox[{"2", " ", "uz2"}], "+", RowBox[{"2", " ", "ey", " ", "\[Theta]x1"}], "-", RowBox[{"2", " ", "ey", " ", "\[Theta]x2"}], "-", RowBox[{"h0", " ", "\[Theta]y1"}], "-", RowBox[{"h0", " ", "\[Theta]y2"}]}], ")"}]}], "+", RowBox[{"Iz", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "uy1"}], "-", RowBox[{"2", " ", "uy2"}], "-", RowBox[{"2", " ", "ez", " ", "\[Theta]x1"}], "+", RowBox[{"2", " ", "ez", " ", "\[Theta]x2"}], "+", RowBox[{"h0", " ", "\[Theta]z1"}], "+", RowBox[{"h0", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"6", " ", "\[Delta]uy2", " ", RowBox[{"(", RowBox[{ RowBox[{"144", " ", "by", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "Iyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "Sz"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", "GG", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "cy", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iyz", " ", "ky"}], "-", RowBox[{"12", " ", "cy", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iz", " ", "kyz"}], "+", RowBox[{"12", " ", "cz", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "ky"}], "-", RowBox[{"Iyz", " ", "kyz"}]}], ")"}]}], "+", RowBox[{"6", " ", "by", " ", "EE", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "ky"}], "-", RowBox[{"2", " ", "Iyz", " ", "kyz"}], "+", RowBox[{"Iz", " ", "kz"}]}], ")"}]}], "-", RowBox[{"bx", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", SuperscriptBox["kyz", "2"], " ", "Sz"}], "+", RowBox[{"bx", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "ky", " ", "kz", " ", "Sz"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "uy1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "ky", " ", "uy1"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "uy2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "ky", " ", "uy2"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uz1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kyz", " ", "uz1"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uz1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uz2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kyz", " ", "uz2"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uz2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]x2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]x2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]y1"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]y1"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]y2"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]y2"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]z1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]z1"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]z2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]z2"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}]}], ")"}]}], "+", RowBox[{"12", " ", "AA", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"by", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}]}], "+", RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "kyz", " ", "Sy"}], "+", RowBox[{"kz", " ", "Sz"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "GG", " ", RowBox[{"(", RowBox[{ RowBox[{"cy", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "Sy", " ", "Sz"}], "-", RowBox[{"cy", " ", SuperscriptBox["h0", "3"], " ", "kyz", " ", SuperscriptBox["Sz", "2"]}], "+", RowBox[{"cz", " ", SuperscriptBox["h0", "3"], " ", "Sy", " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", "Sy"}], "-", RowBox[{"kyz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"bx", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iyz", " ", "ky", " ", "Sy"}], "-", RowBox[{"Iz", " ", "kyz", " ", "Sy"}], "-", RowBox[{"Iy", " ", "ky", " ", "Sz"}], "+", RowBox[{"Iyz", " ", "kyz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"12", " ", "EE", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "uy1"}], "-", RowBox[{ "24", " ", "EE", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "uy1"}], "+", RowBox[{"12", " ", "EE", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "-", RowBox[{"12", " ", "EE", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "uy2"}], "+", RowBox[{ "24", " ", "EE", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "uy2"}], "-", RowBox[{"12", " ", "EE", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "+", RowBox[{"12", " ", "EE", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "-", RowBox[{ "24", " ", "EE", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "uz1"}], "+", RowBox[{"12", " ", "EE", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "uz1"}], "-", RowBox[{"12", " ", "EE", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "+", RowBox[{ "24", " ", "EE", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "uz2"}], "-", RowBox[{"12", " ", "EE", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "uz2"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "+", RowBox[{ "24", " ", "EE", " ", "ez", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{ "24", " ", "EE", " ", "ey", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "+", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "-", RowBox[{ "24", " ", "EE", " ", "ez", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{ "24", " ", "EE", " ", "ey", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{ "12", " ", "EE", " ", "ez", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "-", RowBox[{ "12", " ", "EE", " ", "ey", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "-", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "+", RowBox[{ "12", " ", "EE", " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "-", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]y1"}], "-", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iz", " ", "kyz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "+", RowBox[{ "12", " ", "EE", " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "-", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iy", " ", "kyz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]y2"}], "+", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]z1"}], "-", RowBox[{ "12", " ", "EE", " ", "h0", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "+", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "+", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iz", " ", "ky", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]z2"}], "-", RowBox[{ "12", " ", "EE", " ", "h0", " ", "Iyz", " ", "ky", " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}], "+", RowBox[{ "6", " ", "EE", " ", "h0", " ", "Iy", " ", "ky", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["AA", "3"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["kyz", "2"], "-", RowBox[{"ky", " ", "kz"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "cz", " ", SuperscriptBox["h0", "3"]}], "+", RowBox[{"by", " ", SuperscriptBox["h0", "4"]}], "+", RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"Iyz", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "uz1"}], "-", RowBox[{"2", " ", "uz2"}], "+", RowBox[{"2", " ", "ey", " ", "\[Theta]x1"}], "-", RowBox[{"2", " ", "ey", " ", "\[Theta]x2"}], "-", RowBox[{"h0", " ", "\[Theta]y1"}], "-", RowBox[{"h0", " ", "\[Theta]y2"}]}], ")"}]}], "+", RowBox[{"Iz", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "uy1"}], "-", RowBox[{"2", " ", "uy2"}], "-", RowBox[{"2", " ", "ez", " ", "\[Theta]x1"}], "+", RowBox[{"2", " ", "ez", " ", "\[Theta]x2"}], "+", RowBox[{"h0", " ", "\[Theta]z1"}], "+", RowBox[{"h0", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"\[Delta]\[Theta]z2", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", SuperscriptBox["AA", "2"], " ", "GG", " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "cz", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iyz", " ", "kyz"}], "+", RowBox[{"12", " ", "cy", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iyz", " ", "ky"}], "-", RowBox[{"Iz", " ", "kyz"}]}], ")"}]}], "-", RowBox[{"12", " ", "cz", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iz", " ", "kz"}], "+", RowBox[{"2", " ", "by", " ", "EE", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "ky"}], "-", RowBox[{"2", " ", "Iyz", " ", "kyz"}], "+", RowBox[{"Iz", " ", "kz"}]}], ")"}]}], "-", RowBox[{"bx", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", SuperscriptBox["kyz", "2"], " ", "Sz"}], "+", RowBox[{"bx", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "ky", " ", "kz", " ", "Sz"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "ky", " ", "Sz", " ", "ux1"}], "-", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sz", " ", "ux1"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iz", " ", "kz", " ", "Sz", " ", "ux1"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "ky", " ", "Sz", " ", "ux2"}], "+", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sz", " ", "ux2"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iz", " ", "kz", " ", "Sz", " ", "ux2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "uy1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "ky", " ", "uy1"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "uy2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "ky", " ", "uy2"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uz1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kyz", " ", "uz1"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uz1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uz2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kyz", " ", "uz2"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uz2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]x2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]x2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iyz", " ", "ky", " ", "\[Theta]y1"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]y1"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]y1"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "Iz", " ", "kz", " ", "\[Theta]y1"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iyz", " ", "ky", " ", "\[Theta]y2"}], "+", RowBox[{"120", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]y2"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]y2"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "Iz", " ", "kz", " ", "\[Theta]y2"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]z1"}], "+", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]z1"}], "+", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "Iz", " ", "kyz", " ", "\[Theta]z1"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iz", "2"], " ", "kz", " ", "\[Theta]z1"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "-", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]z2"}], "+", RowBox[{"96", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]z2"}], "-", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "Iz", " ", "kyz", " ", "\[Theta]z2"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iz", "2"], " ", "kz", " ", "\[Theta]z2"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}]}], ")"}]}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "Iyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "Sz"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "cz", " ", SuperscriptBox["h0", "2"]}], "-", RowBox[{"by", " ", SuperscriptBox["h0", "3"]}], "-", RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"Sz", " ", "ux1"}], "-", RowBox[{"Sz", " ", "ux2"}], "+", RowBox[{"Iyz", " ", "\[Theta]y1"}], "-", RowBox[{"Iyz", " ", "\[Theta]y2"}], "-", RowBox[{"Iz", " ", "\[Theta]z1"}], "+", RowBox[{"Iz", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{ SuperscriptBox["AA", "3"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["kyz", "2"], "-", RowBox[{"ky", " ", "kz"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"by", " ", SuperscriptBox["h0", "4"]}], "+", RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"h0", " ", "Sz", " ", RowBox[{"(", RowBox[{"ux1", "-", "ux2"}], ")"}]}], "+", RowBox[{"6", " ", "Iyz", " ", RowBox[{"(", RowBox[{"uz1", "-", "uz2", "+", RowBox[{"ey", " ", RowBox[{"(", RowBox[{"\[Theta]x1", "-", "\[Theta]x2"}], ")"}]}]}], ")"}]}], "+", RowBox[{"6", " ", "Iz", " ", RowBox[{"(", RowBox[{"uy1", "-", "uy2", "+", RowBox[{"ez", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Theta]x1"}], "+", "\[Theta]x2"}], ")"}]}]}], ")"}]}], "-", RowBox[{"2", " ", "h0", " ", "Iyz", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "+", RowBox[{"2", " ", "\[Theta]y2"}]}], ")"}]}], "+", RowBox[{"2", " ", "h0", " ", "Iz", " ", RowBox[{"(", RowBox[{"\[Theta]z1", "+", RowBox[{"2", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"12", " ", "AA", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "72"}], " ", "cz", " ", "EE", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}]}], "+", RowBox[{"12", " ", "by", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}]}], "+", RowBox[{"6", " ", "cy", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", "Sz", " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", "Sy"}], "-", RowBox[{"kyz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"6", " ", "bx", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iyz", " ", "ky", " ", "Sy"}], "-", RowBox[{"Iz", " ", "kyz", " ", "Sy"}], "-", RowBox[{"Iy", " ", "ky", " ", "Sz"}], "+", RowBox[{"Iyz", " ", "kyz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"6", " ", "cz", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", "Sz", " ", RowBox[{"(", RowBox[{ RowBox[{"kyz", " ", "Sy"}], "-", RowBox[{"kz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"by", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "kyz", " ", "Sy"}], "+", RowBox[{"kz", " ", "Sz"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Sz", " ", RowBox[{"(", RowBox[{"ux1", "-", "ux2"}], ")"}]}], "+", RowBox[{"Iyz", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "-", "\[Theta]y2"}], ")"}]}], "+", RowBox[{"Iz", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Theta]z1"}], "+", "\[Theta]z2"}], ")"}]}]}], ")"}]}], "+", RowBox[{"GG", " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "Iyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "Sz"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"kyz", " ", RowBox[{"(", RowBox[{"uz1", "-", "uz2", "+", RowBox[{"ey", " ", "\[Theta]x1"}], "-", RowBox[{"ey", " ", "\[Theta]x2"}]}], ")"}]}], "+", RowBox[{"ky", " ", RowBox[{"(", RowBox[{"uy1", "-", "uy2", "-", RowBox[{"ez", " ", "\[Theta]x1"}], "+", RowBox[{"ez", " ", "\[Theta]x2"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"h0", " ", RowBox[{"(", RowBox[{ RowBox[{"kz", " ", SuperscriptBox["Sz", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Sz", " ", RowBox[{"(", RowBox[{"ux1", "-", "ux2"}], ")"}]}], "+", RowBox[{"Iyz", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "-", "\[Theta]y2"}], ")"}]}], "+", RowBox[{"Iz", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Theta]z1"}], "+", "\[Theta]z2"}], ")"}]}]}], ")"}]}], "+", RowBox[{"ky", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "6"}], " ", "Iyz", " ", "Sy", " ", "Sz", " ", RowBox[{"(", RowBox[{"\[Theta]z1", "+", "\[Theta]z2"}], ")"}]}], "+", RowBox[{"3", " ", "Iy", " ", SuperscriptBox["Sz", "2"], " ", RowBox[{"(", RowBox[{"\[Theta]z1", "+", "\[Theta]z2"}], ")"}]}], "+", RowBox[{ SuperscriptBox["Sy", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Sz", " ", RowBox[{"(", RowBox[{"ux1", "-", "ux2"}], ")"}]}], "+", RowBox[{"Iyz", " ", "\[Theta]y1"}], "-", RowBox[{"Iyz", " ", "\[Theta]y2"}], "+", RowBox[{"2", " ", "Iz", " ", "\[Theta]z1"}], "+", RowBox[{"4", " ", "Iz", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"kyz", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", "Iz", " ", SuperscriptBox["Sy", "2"], " ", RowBox[{"(", RowBox[{"\[Theta]y1", "+", "\[Theta]y2"}], ")"}]}], "+", RowBox[{"3", " ", "Iy", " ", SuperscriptBox["Sz", "2"], " ", RowBox[{"(", RowBox[{"\[Theta]y1", "+", "\[Theta]y2"}], ")"}]}], "+", RowBox[{"2", " ", "Sy", " ", "Sz", " ", RowBox[{"(", RowBox[{ RowBox[{"Sz", " ", RowBox[{"(", RowBox[{"ux1", "-", "ux2"}], ")"}]}], "-", RowBox[{"2", " ", "Iyz", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "+", RowBox[{"2", " ", "\[Theta]y2"}]}], ")"}]}], "+", RowBox[{"Iz", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Theta]z1"}], "+", "\[Theta]z2"}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"\[Delta]\[Theta]y1", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", SuperscriptBox["AA", "2"], " ", "GG", " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "cz", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iy", " ", "kyz"}], "+", RowBox[{"12", " ", "cy", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "ky"}], "-", RowBox[{"Iyz", " ", "kyz"}]}], ")"}]}], "-", RowBox[{"12", " ", "cz", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iyz", " ", "kz"}], "-", RowBox[{"2", " ", "bz", " ", "EE", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "ky"}], "-", RowBox[{"2", " ", "Iyz", " ", "kyz"}], "+", RowBox[{"Iz", " ", "kz"}]}], ")"}]}], "-", RowBox[{"bx", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", SuperscriptBox["kyz", "2"], " ", "Sy"}], "+", RowBox[{"bx", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "ky", " ", "kz", " ", "Sy"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "ky", " ", "Sy", " ", "ux1"}], "+", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "ux1"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iz", " ", "kz", " ", "Sy", " ", "ux1"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "ky", " ", "Sy", " ", "ux2"}], "-", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "ux2"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iz", " ", "kz", " ", "Sy", " ", "ux2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uy1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kyz", " ", "uy1"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uy1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uy1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uy2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kyz", " ", "uy2"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uy2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uy2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "uz1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kz", " ", "uz1"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "uz2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kz", " ", "uz2"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]x1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]x2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iy", "2"], " ", "ky", " ", "\[Theta]y1"}], "+", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iyz", " ", "kyz", " ", "\[Theta]y1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]y1"}], "-", RowBox[{"96", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]y1"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iy", "2"], " ", "ky", " ", "\[Theta]y2"}], "-", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iyz", " ", "kyz", " ", "\[Theta]y2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]y2"}], "-", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]y2"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iyz", " ", "ky", " ", "\[Theta]z1"}], "-", RowBox[{"120", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]z1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]z1"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "Iz", " ", "kz", " ", "\[Theta]z1"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iyz", " ", "ky", " ", "\[Theta]z2"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]z2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]z2"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "Iz", " ", "kz", " ", "\[Theta]z2"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}]}], ")"}]}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "Iyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "Sz"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "6"}], " ", "cy", " ", SuperscriptBox["h0", "2"]}], "+", RowBox[{"bz", " ", SuperscriptBox["h0", "3"]}], "+", RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"Sy", " ", "ux1"}], "-", RowBox[{"Sy", " ", "ux2"}], "+", RowBox[{"Iy", " ", "\[Theta]y1"}], "-", RowBox[{"Iy", " ", "\[Theta]y2"}], "-", RowBox[{"Iyz", " ", "\[Theta]z1"}], "+", RowBox[{"Iyz", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["AA", "3"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["kyz", "2"], "-", RowBox[{"ky", " ", "kz"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"bz", " ", SuperscriptBox["h0", "4"]}], "-", RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"h0", " ", "Sy", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "ux1"}], "+", "ux2"}], ")"}]}], "+", RowBox[{"6", " ", "Iy", " ", RowBox[{"(", RowBox[{"uz1", "-", "uz2", "+", RowBox[{"ey", " ", RowBox[{"(", RowBox[{"\[Theta]x1", "-", "\[Theta]x2"}], ")"}]}]}], ")"}]}], "+", RowBox[{"6", " ", "Iyz", " ", RowBox[{"(", RowBox[{"uy1", "-", "uy2", "+", RowBox[{"ez", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Theta]x1"}], "+", "\[Theta]x2"}], ")"}]}]}], ")"}]}], "-", RowBox[{"2", " ", "h0", " ", "Iy", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "\[Theta]y1"}], "+", "\[Theta]y2"}], ")"}]}], "+", RowBox[{"2", " ", "h0", " ", "Iyz", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "\[Theta]z1"}], "+", "\[Theta]z2"}], ")"}]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"12", " ", "AA", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"72", " ", "cy", " ", "EE", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}]}], "-", RowBox[{"12", " ", "bz", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}]}], "+", RowBox[{"6", " ", "cy", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", "Sy", " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", "Sy"}], "-", RowBox[{"kyz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"6", " ", "cz", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", "Sy", " ", RowBox[{"(", RowBox[{ RowBox[{"kyz", " ", "Sy"}], "-", RowBox[{"kz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"6", " ", "bx", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iyz", " ", "kyz", " ", "Sy"}], "-", RowBox[{"Iz", " ", "kz", " ", "Sy"}], "-", RowBox[{"Iy", " ", "kyz", " ", "Sz"}], "+", RowBox[{"Iyz", " ", "kz", " ", "Sz"}]}], ")"}]}], "-", RowBox[{"bz", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "kyz", " ", "Sy"}], "+", RowBox[{"kz", " ", "Sz"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Sy", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "ux1"}], "+", "ux2"}], ")"}]}], "+", RowBox[{"Iy", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Theta]y1"}], "+", "\[Theta]y2"}], ")"}]}], "+", RowBox[{"Iyz", " ", RowBox[{"(", RowBox[{"\[Theta]z1", "-", "\[Theta]z2"}], ")"}]}]}], ")"}]}], "+", RowBox[{"GG", " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "Iyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "Sz"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"kz", " ", RowBox[{"(", RowBox[{"uz1", "-", "uz2", "+", RowBox[{"ey", " ", "\[Theta]x1"}], "-", RowBox[{"ey", " ", "\[Theta]x2"}]}], ")"}]}], "+", RowBox[{"kyz", " ", RowBox[{"(", RowBox[{"uy1", "-", "uy2", "-", RowBox[{"ez", " ", "\[Theta]x1"}], "+", RowBox[{"ez", " ", "\[Theta]x2"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"h0", " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", SuperscriptBox["Sy", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Sy", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "ux1"}], "+", "ux2"}], ")"}]}], "-", RowBox[{"Iy", " ", "\[Theta]y1"}], "+", RowBox[{"Iy", " ", "\[Theta]y2"}], "+", RowBox[{"Iyz", " ", "\[Theta]z1"}], "-", RowBox[{"Iyz", " ", "\[Theta]z2"}]}], ")"}]}], "-", RowBox[{"kz", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", "Iz", " ", SuperscriptBox["Sy", "2"], " ", RowBox[{"(", RowBox[{"\[Theta]y1", "+", "\[Theta]y2"}], ")"}]}], "+", RowBox[{"Sy", " ", "Sz", " ", RowBox[{"(", RowBox[{ RowBox[{"Sz", " ", RowBox[{"(", RowBox[{"ux1", "-", "ux2"}], ")"}]}], "-", RowBox[{"6", " ", "Iyz", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "+", "\[Theta]y2"}], ")"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["Sz", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "Iy", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "\[Theta]y1"}], "+", "\[Theta]y2"}], ")"}]}], "+", RowBox[{"Iyz", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Theta]z1"}], "+", "\[Theta]z2"}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"kyz", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", "Iy", " ", SuperscriptBox["Sz", "2"], " ", RowBox[{"(", RowBox[{"\[Theta]z1", "+", "\[Theta]z2"}], ")"}]}], "+", RowBox[{ SuperscriptBox["Sy", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "Sz", " ", RowBox[{"(", RowBox[{"ux1", "-", "ux2"}], ")"}]}], "+", RowBox[{"3", " ", "Iz", " ", RowBox[{"(", RowBox[{"\[Theta]z1", "+", "\[Theta]z2"}], ")"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "Sy", " ", "Sz", " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "-", "\[Theta]y2"}], ")"}]}], "-", RowBox[{"2", " ", "Iyz", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "\[Theta]z1"}], "+", "\[Theta]z2"}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"\[Delta]\[Theta]z1", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "6"}], " ", SuperscriptBox["AA", "2"], " ", "GG", " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "12"}], " ", "cz", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iyz", " ", "kyz"}], "-", RowBox[{"12", " ", "cy", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iyz", " ", "ky"}], "-", RowBox[{"Iz", " ", "kyz"}]}], ")"}]}], "+", RowBox[{"12", " ", "cz", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iz", " ", "kz"}], "+", RowBox[{"2", " ", "by", " ", "EE", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "ky"}], "-", RowBox[{"2", " ", "Iyz", " ", "kyz"}], "+", RowBox[{"Iz", " ", "kz"}]}], ")"}]}], "+", RowBox[{"bx", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", SuperscriptBox["kyz", "2"], " ", "Sz"}], "-", RowBox[{"bx", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "ky", " ", "kz", " ", "Sz"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "ky", " ", "Sz", " ", "ux1"}], "-", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sz", " ", "ux1"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iz", " ", "kz", " ", "Sz", " ", "ux1"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "ky", " ", "Sz", " ", "ux2"}], "+", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sz", " ", "ux2"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iz", " ", "kz", " ", "Sz", " ", "ux2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "uy1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "ky", " ", "uy1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uy1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "uy2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "ky", " ", "uy2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "uy2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uz1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kyz", " ", "uz1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uz1"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uz2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kyz", " ", "uz2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uz2"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uz2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]x1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]x1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]x2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]x2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]x2"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iyz", " ", "ky", " ", "\[Theta]y1"}], "-", RowBox[{"120", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]y1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]y1"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "Iz", " ", "kz", " ", "\[Theta]y1"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y1"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iyz", " ", "ky", " ", "\[Theta]y2"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]y2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]y2"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "Iz", " ", "kz", " ", "\[Theta]y2"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]y2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]z1"}], "-", RowBox[{"96", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]z1"}], "+", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "Iz", " ", "kyz", " ", "\[Theta]z1"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iz", "2"], " ", "kz", " ", "\[Theta]z1"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "ky", " ", "\[Theta]z2"}], "-", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "ky", " ", "\[Theta]z2"}], "-", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "Iz", " ", "kyz", " ", "\[Theta]z2"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iz", "2"], " ", "kz", " ", "\[Theta]z2"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sz", "2"], " ", "\[Theta]z2"}]}], ")"}]}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "Iyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "Sz"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "cz", " ", SuperscriptBox["h0", "2"]}], "+", RowBox[{"by", " ", SuperscriptBox["h0", "3"]}], "+", RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"Sz", " ", "ux1"}], "-", RowBox[{"Sz", " ", "ux2"}], "+", RowBox[{"Iyz", " ", "\[Theta]y1"}], "-", RowBox[{"Iyz", " ", "\[Theta]y2"}], "-", RowBox[{"Iz", " ", "\[Theta]z1"}], "+", RowBox[{"Iz", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["AA", "3"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["kyz", "2"], "-", RowBox[{"ky", " ", "kz"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"by", " ", SuperscriptBox["h0", "4"]}], "-", RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"h0", " ", "Sz", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "ux1"}], "+", "ux2"}], ")"}]}], "+", RowBox[{"6", " ", "Iyz", " ", RowBox[{"(", RowBox[{"uz1", "-", "uz2", "+", RowBox[{"ey", " ", RowBox[{"(", RowBox[{"\[Theta]x1", "-", "\[Theta]x2"}], ")"}]}]}], ")"}]}], "+", RowBox[{"6", " ", "Iz", " ", RowBox[{"(", RowBox[{"uy1", "-", "uy2", "+", RowBox[{"ez", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Theta]x1"}], "+", "\[Theta]x2"}], ")"}]}]}], ")"}]}], "-", RowBox[{"2", " ", "h0", " ", "Iyz", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "\[Theta]y1"}], "+", "\[Theta]y2"}], ")"}]}], "+", RowBox[{"2", " ", "h0", " ", "Iz", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "\[Theta]z1"}], "+", "\[Theta]z2"}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"12", " ", "AA", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"72", " ", "cz", " ", "EE", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}]}], "+", RowBox[{"12", " ", "by", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}]}], "+", RowBox[{"6", " ", "cy", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", "Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "ky"}], " ", "Sy"}], "+", RowBox[{"kyz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"6", " ", "cz", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", "Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "kyz"}], " ", "Sy"}], "+", RowBox[{"kz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"6", " ", "bx", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", "kyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "ky", " ", "Sz"}], "-", RowBox[{"Iyz", " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", "Sy"}], "+", RowBox[{"kyz", " ", "Sz"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"by", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "kyz", " ", "Sy"}], "+", RowBox[{"kz", " ", "Sz"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Sz", " ", RowBox[{"(", RowBox[{"ux1", "-", "ux2"}], ")"}]}], "+", RowBox[{"Iyz", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "-", "\[Theta]y2"}], ")"}]}], "+", RowBox[{"Iz", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Theta]z1"}], "+", "\[Theta]z2"}], ")"}]}]}], ")"}]}], "+", RowBox[{"GG", " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "6"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "Iyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "Sz"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"kyz", " ", RowBox[{"(", RowBox[{"uz1", "-", "uz2", "+", RowBox[{"ey", " ", "\[Theta]x1"}], "-", RowBox[{"ey", " ", "\[Theta]x2"}]}], ")"}]}], "+", RowBox[{"ky", " ", RowBox[{"(", RowBox[{"uy1", "-", "uy2", "-", RowBox[{"ez", " ", "\[Theta]x1"}], "+", RowBox[{"ez", " ", "\[Theta]x2"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"h0", " ", RowBox[{"(", RowBox[{ RowBox[{"kz", " ", SuperscriptBox["Sz", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Sz", " ", RowBox[{"(", RowBox[{"ux1", "-", "ux2"}], ")"}]}], "+", RowBox[{"Iyz", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "-", "\[Theta]y2"}], ")"}]}], "+", RowBox[{"Iz", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Theta]z1"}], "+", "\[Theta]z2"}], ")"}]}]}], ")"}]}], "+", RowBox[{"kyz", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", "Iz", " ", SuperscriptBox["Sy", "2"], " ", RowBox[{"(", RowBox[{"\[Theta]y1", "+", "\[Theta]y2"}], ")"}]}], "+", RowBox[{"3", " ", "Iy", " ", SuperscriptBox["Sz", "2"], " ", RowBox[{"(", RowBox[{"\[Theta]y1", "+", "\[Theta]y2"}], ")"}]}], "-", RowBox[{"2", " ", "Sy", " ", "Sz", " ", RowBox[{"(", RowBox[{ RowBox[{"Sz", " ", RowBox[{"(", RowBox[{"ux1", "-", "ux2"}], ")"}]}], "+", RowBox[{"4", " ", "Iyz", " ", "\[Theta]y1"}], "+", RowBox[{"2", " ", "Iyz", " ", "\[Theta]y2"}], "-", RowBox[{"Iz", " ", "\[Theta]z1"}], "+", RowBox[{"Iz", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"ky", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "Iyz", " ", "Sy", " ", "Sz", " ", RowBox[{"(", RowBox[{"\[Theta]z1", "+", "\[Theta]z2"}], ")"}]}], "-", RowBox[{"3", " ", "Iy", " ", SuperscriptBox["Sz", "2"], " ", RowBox[{"(", RowBox[{"\[Theta]z1", "+", "\[Theta]z2"}], ")"}]}], "+", RowBox[{ SuperscriptBox["Sy", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Sz", " ", RowBox[{"(", RowBox[{"ux1", "-", "ux2"}], ")"}]}], "+", RowBox[{"Iyz", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "-", "\[Theta]y2"}], ")"}]}], "-", RowBox[{"2", " ", "Iz", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "\[Theta]z1"}], "+", "\[Theta]z2"}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"\[Delta]\[Theta]y2", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "6"}], " ", SuperscriptBox["AA", "2"], " ", "GG", " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "cz", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iy", " ", "kyz"}], "+", RowBox[{"12", " ", "cy", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "ky"}], "-", RowBox[{"Iyz", " ", "kyz"}]}], ")"}]}], "-", RowBox[{"12", " ", "cz", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", "Iyz", " ", "kz"}], "+", RowBox[{"2", " ", "bz", " ", "EE", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "ky"}], "-", RowBox[{"2", " ", "Iyz", " ", "kyz"}], "+", RowBox[{"Iz", " ", "kz"}]}], ")"}]}], "-", RowBox[{"bx", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", SuperscriptBox["kyz", "2"], " ", "Sy"}], "+", RowBox[{"bx", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", "ky", " ", "kz", " ", "Sy"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "ky", " ", "Sy", " ", "ux1"}], "-", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "ux1"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iz", " ", "kz", " ", "Sy", " ", "ux1"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "ky", " ", "Sy", " ", "ux2"}], "+", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "kyz", " ", "Sy", " ", "ux2"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iz", " ", "kz", " ", "Sy", " ", "ux2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uy1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kyz", " ", "uy1"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uy1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uy1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "uy2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kyz", " ", "uy2"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "uy2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "uy2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "uz1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kz", " ", "uz1"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "uz2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "Iy", " ", "Iz", " ", "kz", " ", "uz2"}], "-", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "+", RowBox[{"12", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "uz2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]x1"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x1"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x1"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]x2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ez", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]x2"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]x2"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", "ey", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "ey", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]x2"}], "+", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "-", RowBox[{"12", " ", "EE", " ", "ez", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]x2"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iy", "2"], " ", "ky", " ", "\[Theta]y1"}], "-", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iyz", " ", "kyz", " ", "\[Theta]y1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]y1"}], "-", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]y1"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y1"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iy", "2"], " ", "ky", " ", "\[Theta]y2"}], "+", RowBox[{"48", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iyz", " ", "kyz", " ", "\[Theta]y2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kz", " ", "\[Theta]y2"}], "-", RowBox[{"96", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kz", " ", "\[Theta]y2"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", SuperscriptBox["Sy", "2"], " ", "\[Theta]y2"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iyz", " ", "ky", " ", "\[Theta]z1"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]z1"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]z1"}], "-", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "Iz", " ", "kz", " ", "\[Theta]z1"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]z1"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iyz", " ", "ky", " ", "\[Theta]z2"}], "-", RowBox[{"120", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", SuperscriptBox["Iyz", "2"], " ", "kyz", " ", "\[Theta]z2"}], "+", RowBox[{"72", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iy", " ", "Iz", " ", "kyz", " ", "\[Theta]z2"}], "+", RowBox[{"24", " ", SuperscriptBox["EE", "2"], " ", "h0", " ", "Iyz", " ", "Iz", " ", "kz", " ", "\[Theta]z2"}], "+", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", SuperscriptBox["kyz", "2"], " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}], "-", RowBox[{"6", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "3"], " ", "ky", " ", "kz", " ", "Sy", " ", "Sz", " ", "\[Theta]z2"}]}], ")"}]}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "Iyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "Sz"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "cy", " ", SuperscriptBox["h0", "2"]}], "+", RowBox[{"bz", " ", SuperscriptBox["h0", "3"]}], "+", RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"Sy", " ", "ux1"}], "-", RowBox[{"Sy", " ", "ux2"}], "+", RowBox[{"Iy", " ", "\[Theta]y1"}], "-", RowBox[{"Iy", " ", "\[Theta]y2"}], "-", RowBox[{"Iyz", " ", "\[Theta]z1"}], "+", RowBox[{"Iyz", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["AA", "3"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["kyz", "2"], "-", RowBox[{"ky", " ", "kz"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"bz", " ", SuperscriptBox["h0", "4"]}], "+", RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"h0", " ", "Sy", " ", RowBox[{"(", RowBox[{"ux1", "-", "ux2"}], ")"}]}], "+", RowBox[{"6", " ", "Iy", " ", RowBox[{"(", RowBox[{"uz1", "-", "uz2", "+", RowBox[{"ey", " ", RowBox[{"(", RowBox[{"\[Theta]x1", "-", "\[Theta]x2"}], ")"}]}]}], ")"}]}], "+", RowBox[{"6", " ", "Iyz", " ", RowBox[{"(", RowBox[{"uy1", "-", "uy2", "+", RowBox[{"ez", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Theta]x1"}], "+", "\[Theta]x2"}], ")"}]}]}], ")"}]}], "-", RowBox[{"2", " ", "h0", " ", "Iy", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "+", RowBox[{"2", " ", "\[Theta]y2"}]}], ")"}]}], "+", RowBox[{"2", " ", "h0", " ", "Iyz", " ", RowBox[{"(", RowBox[{"\[Theta]z1", "+", RowBox[{"2", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"12", " ", "AA", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"72", " ", "cy", " ", "EE", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}]}], "+", RowBox[{"12", " ", "bz", " ", "EE", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}]}], "+", RowBox[{"6", " ", "cy", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", "Sy", " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", "Sy"}], "-", RowBox[{"kyz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"6", " ", "cz", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", "Sy", " ", RowBox[{"(", RowBox[{ RowBox[{"kyz", " ", "Sy"}], "-", RowBox[{"kz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"6", " ", "bx", " ", "GG", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iyz", " ", "kyz", " ", "Sy"}], "-", RowBox[{"Iz", " ", "kz", " ", "Sy"}], "-", RowBox[{"Iy", " ", "kyz", " ", "Sz"}], "+", RowBox[{"Iyz", " ", "kz", " ", "Sz"}]}], ")"}]}], "+", RowBox[{"bz", " ", "GG", " ", SuperscriptBox["h0", "5"], " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "kyz", " ", "Sy"}], "+", RowBox[{"kz", " ", "Sz"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Sy", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "ux1"}], "+", "ux2"}], ")"}]}], "+", RowBox[{"Iy", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Theta]y1"}], "+", "\[Theta]y2"}], ")"}]}], "+", RowBox[{"Iyz", " ", RowBox[{"(", RowBox[{"\[Theta]z1", "-", "\[Theta]z2"}], ")"}]}]}], ")"}]}], "+", RowBox[{"GG", " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "6"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "Iyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "Sz"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"kz", " ", RowBox[{"(", RowBox[{"uz1", "-", "uz2", "+", RowBox[{"ey", " ", "\[Theta]x1"}], "-", RowBox[{"ey", " ", "\[Theta]x2"}]}], ")"}]}], "+", RowBox[{"kyz", " ", RowBox[{"(", RowBox[{"uy1", "-", "uy2", "-", RowBox[{"ez", " ", "\[Theta]x1"}], "+", RowBox[{"ez", " ", "\[Theta]x2"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"h0", " ", RowBox[{"(", RowBox[{ RowBox[{"kz", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", "Iz", " ", SuperscriptBox["Sy", "2"], " ", RowBox[{"(", RowBox[{"\[Theta]y1", "+", "\[Theta]y2"}], ")"}]}], "-", RowBox[{"Sy", " ", "Sz", " ", RowBox[{"(", RowBox[{ RowBox[{"Sz", " ", RowBox[{"(", RowBox[{"ux1", "-", "ux2"}], ")"}]}], "+", RowBox[{"6", " ", "Iyz", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "+", "\[Theta]y2"}], ")"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["Sz", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "Iy", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "+", RowBox[{"2", " ", "\[Theta]y2"}]}], ")"}]}], "+", RowBox[{"Iyz", " ", RowBox[{"(", RowBox[{"\[Theta]z1", "-", "\[Theta]z2"}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"ky", " ", SuperscriptBox["Sy", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Sy", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "ux1"}], "+", "ux2"}], ")"}]}], "-", RowBox[{"Iy", " ", "\[Theta]y1"}], "+", RowBox[{"Iy", " ", "\[Theta]y2"}], "+", RowBox[{"Iyz", " ", "\[Theta]z1"}], "-", RowBox[{"Iyz", " ", "\[Theta]z2"}]}], ")"}]}], "+", RowBox[{"kyz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", "Iy", " ", SuperscriptBox["Sz", "2"], " ", RowBox[{"(", RowBox[{"\[Theta]z1", "+", "\[Theta]z2"}], ")"}]}], "+", RowBox[{ SuperscriptBox["Sy", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "Sz", " ", RowBox[{"(", RowBox[{"ux1", "-", "ux2"}], ")"}]}], "-", RowBox[{"3", " ", "Iz", " ", RowBox[{"(", RowBox[{"\[Theta]z1", "+", "\[Theta]z2"}], ")"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "Sy", " ", "Sz", " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", RowBox[{"(", RowBox[{"\[Theta]y1", "-", "\[Theta]y2"}], ")"}]}], "+", RowBox[{"2", " ", "Iyz", " ", RowBox[{"(", RowBox[{"\[Theta]z1", "+", RowBox[{"2", " ", "\[Theta]z2"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}], "/", RowBox[{"(", RowBox[{"12", " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", SuperscriptBox["AA", "2"], " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iy", " ", "ky"}], "-", RowBox[{"2", " ", "Iyz", " ", "kyz"}], "+", RowBox[{"Iz", " ", "kz"}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["AA", "3"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", SuperscriptBox["kyz", "2"]}], "+", RowBox[{"ky", " ", "kz"}]}], ")"}]}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iz", " ", SuperscriptBox["Sy", "2"]}], "+", RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "Iyz", " ", "Sy"}], "+", RowBox[{"Iy", " ", "Sz"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"12", " ", "AA", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", RowBox[{"(", RowBox[{ SuperscriptBox["Iyz", "2"], "-", RowBox[{"Iy", " ", "Iz"}]}], ")"}]}], "+", RowBox[{"GG", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"ky", " ", SuperscriptBox["Sy", "2"]}], "-", RowBox[{"2", " ", "kyz", " ", "Sy", " ", "Sz"}], "+", RowBox[{"kz", " ", SuperscriptBox["Sz", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4430689313272*^9, 3.4430690080792*^9}, { 3.4430690869528*^9, 3.4430691077320004`*^9}, {3.4430691700116*^9, 3.4430691708072*^9}, {3.4430692071717997`*^9, 3.443069246359*^9}, { 3.4430772782732*^9, 3.4430773623416*^9}, {3.4430773978316*^9, 3.4430774104676*^9}, {3.4430775053780003`*^9, 3.4430776180598*^9}, { 3.4434109099524*^9, 3.4434109159584*^9}, {3.4438800815346003`*^9, 3.4438802689304*^9}, {3.443880362624*^9, 3.4438803824516*^9}, { 3.443929565615374*^9, 3.443929570232974*^9}, {3.443935321321974*^9, 3.443935335705174*^9}, {3.443935419945174*^9, 3.443935421489574*^9}, { 3.443935494013974*^9, 3.443935494715974*^9}, {3.443935617565974*^9, 3.4439357217895737`*^9}, {3.443935755360774*^9, 3.443935816107174*^9}, { 3.443942155230774*^9, 3.443942209939974*^9}, {3.443942305710374*^9, 3.4439423142123737`*^9}, {3.4439442908131742`*^9, 3.443944441181574*^9}, { 3.4439447830065737`*^9, 3.4439447917425737`*^9}, {3.443944908541774*^9, 3.443944916060974*^9}, {3.4442731097938004`*^9, 3.4442731115254*^9}, { 3.444273189229*^9, 3.4442732700526*^9}, {3.4442748430004*^9, 3.4442748605036*^9}, {3.4442748977438*^9, 3.4442748989762*^9}, { 3.4442749340762*^9, 3.4442749351057997`*^9}, 3.4442752313382*^9, { 3.4442919702026*^9, 3.4442919911846*^9}, {3.4442921151577997`*^9, 3.4442921271074*^9}, {3.4443811023684*^9, 3.4443811036632*^9}, { 3.4443814073171997`*^9, 3.4443814402956*^9}, {3.4443815036316*^9, 3.4443815147855997`*^9}, {3.4443815537232*^9, 3.4443815747676*^9}, { 3.4443816138143997`*^9, 3.444381633174*^9}, {3.4443816850439997`*^9, 3.4443817801728*^9}, 3.4443853618688*^9, {3.4443855607376003`*^9, 3.4443856337924*^9}, {3.4443861200444*^9, 3.4443861523676*^9}, { 3.4443862280495996`*^9, 3.444386291448*^9}, {3.4443864047352*^9, 3.4443864135336*^9}, {3.4443870026832*^9, 3.4443870095316*^9}, { 3.4444082055056*^9, 3.4444082437412*^9}, {3.4444082797148*^9, 3.4444084583816*^9}, {3.4444084889108*^9, 3.4444085087539997`*^9}, { 3.444408942517*^9, 3.4444089563386*^9}, {3.4444091419564*^9, 3.4444091647167997`*^9}, {3.4444092206428003`*^9, 3.4444092944463997`*^9}, {3.4444093856284*^9, 3.4444094281071997`*^9}, { 3.4444094976988*^9, 3.4444095275104*^9}, {3.444409611064*^9, 3.4444096125772*^9}, 3.4444098504616003`*^9, {3.444409913392*^9, 3.4444099166056004`*^9}, 3.4444100178496*^9, {3.4444103063248*^9, 3.4444103358712*^9}, {3.4444103868208*^9, 3.4444104432460003`*^9}, { 3.4444921219564*^9, 3.4444921256224003`*^9}, {3.444492194824*^9, 3.4444921973668003`*^9}, {3.4444922814351997`*^9, 3.4444922853508*^9}, { 3.4444923330868*^9, 3.4444923345844*^9}, {3.444492366424*^9, 3.4444923855808*^9}, {3.4453153475226*^9, 3.445315360689*^9}, { 3.4465518166373653`*^9, 3.446551863016165*^9}, {3.446551894231765*^9, 3.446552159384965*^9}, {3.446552232377365*^9, 3.4465522555589647`*^9}, { 3.446553347388365*^9, 3.4465533616155653`*^9}, {3.4466058525769997`*^9, 3.4466058529046*^9}, {3.4466064371219997`*^9, 3.4466065097244*^9}, { 3.4466127725788*^9, 3.4466127766036*^9}, {3.4466128124835997`*^9, 3.4466130037864*^9}, {3.4466131532696*^9, 3.4466131761703997`*^9}, { 3.4466133992192*^9, 3.4466134478756*^9}, {3.446613483584*^9, 3.4466134932092*^9}, {3.4466135740952*^9, 3.4466135794927998`*^9}, { 3.4466137283948*^9, 3.4466137341356*^9}, {3.4466138994342003`*^9, 3.4466139023826*^9}, {3.4466139549858*^9, 3.4466139579653997`*^9}, { 3.4466142109818*^9, 3.4466142245226*^9}, {3.4466142793878*^9, 3.4466143652033997`*^9}, {3.4466144712834*^9, 3.4466145978929996`*^9}, { 3.4466146992618*^9, 3.4466147509914*^9}, {3.4466151283086*^9, 3.4466152768986*^9}, {3.4466153107506*^9, 3.4466153406558*^9}, { 3.4466194331976*^9, 3.4466194377528*^9}, {3.4466194847712*^9, 3.446619488718*^9}, {3.4466389495861998`*^9, 3.4466389768238*^9}, { 3.4466391218414*^9, 3.446639306561*^9}, {3.4466393990222*^9, 3.4466394004886*^9}, {3.4466394475694*^9, 3.4466394487706003`*^9}, { 3.4466395034174*^9, 3.4466395049462*^9}, 3.4466395515755997`*^9, { 3.4466396000176*^9, 3.4466396190808*^9}, {3.4466397459088*^9, 3.446639748826*^9}, {3.4466397974356003`*^9, 3.446639798668*^9}, 3.4466398447816*^9, {3.446639894218*^9, 3.4466399201556*^9}, { 3.4466399570964003`*^9, 3.4466399583288*^9}, {3.446639994006*^9, 3.4466400056904*^9}, {3.4466400383568*^9, 3.4466400395892*^9}, { 3.4466400745643997`*^9, 3.4466401025976*^9}, {3.4466401660834*^9, 3.4466401806070004`*^9}, {3.4466402251294003`*^9, 3.446640227407*^9}, { 3.446640260479*^9, 3.4466402657674*^9}, {3.4466404133122*^9, 3.4466405185654*^9}, 3.4466405830462*^9, {3.4467273294214*^9, 3.4467273777813997`*^9}, {3.4467274366558*^9, 3.4467275620954*^9}, { 3.446727593311*^9, 3.4467277412614*^9}, {3.4467283334639997`*^9, 3.4467283356012*^9}, {3.4467283707636003`*^9, 3.4467283727604*^9}, { 3.4467289882664003`*^9, 3.4467291276836*^9}, {3.446778464322*^9, 3.4467786797424*^9}, {3.4467801953803997`*^9, 3.4467802409792*^9}, { 3.4467802998691998`*^9, 3.4467804023456*^9}, 3.4467804345596*^9, { 3.4467808656344*^9, 3.4467808670852003`*^9}, 3.4467818107525997`*^9, { 3.446781855509*^9, 3.446781874385*^9}, {3.4467826737914*^9, 3.4467827381726*^9}, {3.4467828623018*^9, 3.4467831045386*^9}, { 3.4470344113984003`*^9, 3.4470344123344*^9}, {3.4470344628316*^9, 3.4470345343108*^9}, {3.447043591118539*^9, 3.447043642192939*^9}, { 3.447045649625739*^9, 3.447045718437339*^9}, {3.447054774023939*^9, 3.447054834198939*^9}, {3.4470549103449388`*^9, 3.4470549116169386`*^9}, { 3.447054943902939*^9, 3.4470553027109385`*^9}, {3.447055334559939*^9, 3.447055353684939*^9}, {3.447057311918539*^9, 3.447057369747739*^9}, { 3.4470575058577385`*^9, 3.4470575951365385`*^9}, {3.4470581848789387`*^9, 3.4470582040825386`*^9}, {3.451276121243*^9, 3.4512761425838003`*^9}, { 3.4512762022382*^9, 3.4512762064346*^9}, {3.4512762476966*^9, 3.4512762827654*^9}, {3.451276489091*^9, 3.451276541975*^9}, { 3.4512765853118*^9, 3.4512766132046003`*^9}, {3.4512773470306*^9, 3.4512773766082*^9}, {3.4512776069110003`*^9, 3.4512777499318*^9}, 3.4512777831286*^9, {3.4512778785538*^9, 3.451277881627*^9}, { 3.4512780242734003`*^9, 3.4512780302794*^9}, 3.4512780737878*^9, { 3.4512781866226*^9, 3.4512781930810003`*^9}, {3.4512863325078*^9, 3.4512863539266*^9}, {3.4568019250434*^9, 3.4568022712698*^9}, { 3.4568023177422*^9, 3.4568024125278*^9}, {3.4568024694365997`*^9, 3.4568024750369997`*^9}, {3.4568026914402*^9, 3.4568028101094*^9}, { 3.4568028406698*^9, 3.4568028564726*^9}, 3.4568028886085997`*^9, { 3.4568030489454*^9, 3.4568030800986*^9}, 3.4568032004128*^9, { 3.4568035073698*^9, 3.4568035176034*^9}, {3.4568040146596003`*^9, 3.4568040844852*^9}, {3.4568043016684*^9, 3.4568043154744*^9}, { 3.4568045482264*^9, 3.4568045486632*^9}, {3.4568048944996*^9, 3.4568049806116*^9}, {3.4660560628582*^9, 3.4660560753538*^9}, { 3.4660676729379997`*^9, 3.4660676735931997`*^9}, {3.4660677244024*^9, 3.4660677277251997`*^9}, {3.4742646771287394`*^9, 3.47426469439174*^9}, { 3.47426489921974*^9, 3.4742649800437393`*^9}, {3.4801246373348*^9, 3.4801246860536003`*^9}, {3.4801247748176003`*^9, 3.4801247821028*^9}, { 3.4801248161264*^9, 3.4801248295736*^9}, {3.4801248810692*^9, 3.4801248964508*^9}, {3.4801249330484*^9, 3.480124947884*^9}, 3.4801249886468*^9, {3.4801251139147997`*^9, 3.48012512588*^9}, { 3.4838339444988003`*^9, 3.4838339567448*^9}, 3.4838341692012*^9, { 3.4838344350408*^9, 3.4838344353684*^9}, {3.4938987575920324`*^9, 3.4938987586840324`*^9}, {3.4941630624049997`*^9, 3.4941631381274*^9}, { 3.4941632311345997`*^9, 3.4941632492306004`*^9}, 3.4941633249217997`*^9, { 3.4941633940922003`*^9, 3.4941634063538*^9}, {3.4941634538402*^9, 3.4941635051642*^9}, {3.494163565115*^9, 3.4941636341762*^9}, { 3.4941636853442*^9, 3.4941639323234*^9}, {3.4941640277798*^9, 3.4941641455754004`*^9}, {3.4941641790374002`*^9, 3.4941641803789997`*^9}, {3.4941642676142*^9, 3.4941643277678003`*^9}, 3.4941644677018003`*^9, {3.4941646208938*^9, 3.4941646322349997`*^9}, { 3.4941652592693996`*^9, 3.4941652807194*^9}, {3.4941653119038*^9, 3.494165416299*^9}, {3.494165453895*^9, 3.4941654544722*^9}, { 3.4950990979779997`*^9, 3.495099142701*^9}, {3.495099172958*^9, 3.4950991806289997`*^9}, {3.495099227097*^9, 3.495099238113*^9}, 3.495099290797*^9, {3.495099346084*^9, 3.495099359507*^9}, { 3.495099456308*^9, 3.495099464091*^9}, 3.495099683108*^9, { 3.495100428112*^9, 3.495100434958*^9}, {3.4951006496219997`*^9, 3.495100649992*^9}, {3.4987235265018*^9, 3.4987235939094*^9}, { 3.4987236420666*^9, 3.4987236530646*^9}, {3.4987237305341997`*^9, 3.4987237396914*^9}, {3.498733136159*^9, 3.4987332972446003`*^9}, { 3.4987364783094*^9, 3.4987364860626*^9}, {3.4987366201134*^9, 3.4987366236078*^9}, {3.4987367272386*^9, 3.4987367464890003`*^9}, { 3.4987369428462*^9, 3.4987369670886*^9}, {3.4987370134518003`*^9, 3.4987370259941998`*^9}, {3.4987370944002*^9, 3.4987371027618*^9}, { 3.4987371921029997`*^9, 3.498737193663*^9}, {3.4987372660938*^9, 3.4987372935498*^9}, {3.4987373290554*^9, 3.4987377176202*^9}, { 3.4987377520182*^9, 3.4987379139462*^9}, {3.4987382030216*^9, 3.4987382667078*^9}, {3.4987888391818*^9, 3.4987888608346*^9}, { 3.4988785131146*^9, 3.4988785160162*^9}, {3.5007170967096*^9, 3.5007170999076*^9}, 3.5007182237316*^9, {3.5007182772864*^9, 3.5007182987832003`*^9}, {3.5009573226744003`*^9, 3.5009573940444*^9}, 3.5009574358710003`*^9, 3.5009604278482*^9, {3.5009897246173353`*^9, 3.5009898480289354`*^9}, {3.5009901464413357`*^9, 3.5009901475333357`*^9}, {3.5009901801997356`*^9, 3.500990274096135*^9}, { 3.5010475253292*^9, 3.5010475852332*^9}, {3.5010605722018003`*^9, 3.5010606739762*^9}, {3.5010607202146*^9, 3.5010607323358*^9}, { 3.5010607920526*^9, 3.501061118467*^9}, {3.5010612022078*^9, 3.5010612277138*^9}, {3.5010616467766*^9, 3.5010617938534*^9}, { 3.5010618406222*^9, 3.5010619950778*^9}, {3.5010621500638*^9, 3.5010622514014*^9}, {3.5010625292218*^9, 3.5010625409374*^9}, { 3.5010626043046*^9, 3.5010626313862*^9}, {3.5010626787166*^9, 3.5010626790754004`*^9}, {3.501074457561*^9, 3.5010744671082*^9}, 3.5010763029458*^9, {3.5032210899309998`*^9, 3.5032212413900003`*^9}, { 3.557658203404973*^9, 3.557658219644601*^9}, {3.5576584433801947`*^9, 3.557658496030287*^9}, {3.5576585501779823`*^9, 3.5576586046064777`*^9}, { 3.557658648910555*^9, 3.557658754600741*^9}, {3.557658963945511*^9, 3.5576589782507353`*^9}, {3.557659009949991*^9, 3.5576591437514267`*^9}, { 3.557659182221094*^9, 3.5576592187719584`*^9}, 3.557659413865901*^9, { 3.557659921100792*^9, 3.5576599556392527`*^9}, {3.557660706920972*^9, 3.5576607248454037`*^9}, {3.557661209085854*^9, 3.557661209413454*^9}, { 3.5577526651911488`*^9, 3.5577526932087984`*^9}, {3.5577527272480583`*^9, 3.557752747122493*^9}, {3.5577528374934516`*^9, 3.557752838523053*^9}, { 3.557752881204728*^9, 3.557752891313546*^9}, {3.557752938612829*^9, 3.5577529469120436`*^9}, {3.557753060714244*^9, 3.557753062633047*^9}, { 3.5577536609544907`*^9, 3.5577536637936954`*^9}, {3.5577537824631042`*^9, 3.557753810184353*^9}, {3.557753841025607*^9, 3.5577540648392*^9}, 3.5577541920574236`*^9, {3.5577547033327217`*^9, 3.557754716967146*^9}, { 3.5577547716296415`*^9, 3.557754802112095*^9}, {3.5577549509363565`*^9, 3.5577549771444025`*^9}, 3.5577551382302856`*^9, {3.55775527184452*^9, 3.557755272858522*^9}, {3.557755881555991*^9, 3.557755886548*^9}, { 3.557756158316077*^9, 3.557756231885806*^9}, {3.5577572408487787`*^9, 3.557757248835993*^9}, {3.5577572834368534`*^9, 3.5577575888229895`*^9}, { 3.5577578129641833`*^9, 3.557757862837471*^9}, {3.557758025514557*^9, 3.557758079272251*^9}, 3.557810586960072*^9, {3.5578240262005973`*^9, 3.5578240345360737`*^9}, {3.557824091429328*^9, 3.5578241008156557`*^9}, { 3.557831525255726*^9, 3.5578315319793377`*^9}, 3.5578315716190076`*^9, { 3.557831606079468*^9, 3.557831629432709*^9}, {3.5578316663267736`*^9, 3.5578317569473333`*^9}, {3.5578322144181366`*^9, 3.557832218084143*^9}, { 3.557836356693412*^9, 3.557836473771618*^9}, {3.5578365201660995`*^9, 3.5578365974018345`*^9}, {3.5578366426731143`*^9, 3.557836658865943*^9}, { 3.557836691017599*^9, 3.5578367924957776`*^9}, {3.5578368305442443`*^9, 3.557836888279946*^9}, {3.5578369382156334`*^9, 3.5578370776642785`*^9}, { 3.5578383536061196`*^9, 3.5578383735117545`*^9}, {3.5578385892445335`*^9, 3.5578385978869486`*^9}, {3.5578386713006773`*^9, 3.557838700113928*^9}, { 3.5578387451200075`*^9, 3.5578387467892103`*^9}, {3.5578388951454706`*^9, 3.5578389248635225`*^9}, {3.5578389679351983`*^9, 3.557838983535226*^9}, { 3.5578390227692947`*^9, 3.557839023143696*^9}, {3.557839097696226*^9, 3.5578391125162525`*^9}, {3.5578391553539276`*^9, 3.557839199892006*^9}, { 3.55783924184048*^9, 3.557839294490572*^9}, {3.5578393285922318`*^9, 3.557839398683155*^9}, {3.557839430522811*^9, 3.557839470162481*^9}, { 3.5578395370865984`*^9, 3.5578395446994114`*^9}, {3.5578396068499207`*^9, 3.5578396118575296`*^9}, 3.5578943518105097`*^9, {3.557894388361374*^9, 3.5578944029629993`*^9}, {3.5578944607611012`*^9, 3.5578944989499683`*^9}, {3.5578945393696394`*^9, 3.557894561537278*^9}, { 3.5578946028617506`*^9, 3.5578946188985786`*^9}, {3.557894650894235*^9, 3.5578947812636642`*^9}, {3.55789481884413*^9, 3.5578948191249304`*^9}, { 3.5578949768100076`*^9, 3.5578949836272197`*^9}, {3.5578967386805477`*^9, 3.55789678549623*^9}, {3.5578968804691963`*^9, 3.557896888643611*^9}, { 3.557897022491846*^9, 3.5578970341450663`*^9}, {3.557897620940097*^9, 3.55789765120415*^9}, {3.5579218072271147`*^9, 3.5579218263059483`*^9}, { 3.557922095312821*^9, 3.557922116965659*^9}, {3.557922178086566*^9, 3.557922188616585*^9}, {3.5579223258812256`*^9, 3.557922327066828*^9}, { 3.5579224596046605`*^9, 3.557922461804264*^9}, 3.5579805928465395`*^9, { 3.5579815200581703`*^9, 3.557981541711009*^9}, 3.557985544779242*^9, { 3.5579863164793987`*^9, 3.5579863339514294`*^9}, {3.557986523210962*^9, 3.557986568841042*^9}, 3.5579866122559185`*^9, 3.557986993536188*^9, { 3.5579871244716187`*^9, 3.5579871290580263`*^9}, 3.557987173486905*^9, 3.5579872166989803`*^9, {3.5599618621582537`*^9, 3.5599618642486577`*^9}, { 3.559961969720443*^9, 3.5599619894700775`*^9}, 3.559963611089726*^9, { 3.5601298891258235`*^9, 3.560129889422224*^9}, {3.560132445157113*^9, 3.5601324458591146`*^9}, {3.561978472080926*^9, 3.561978472392926*^9}, { 3.6297802564412937`*^9, 3.6297802957377625`*^9}, {3.62978033369263*^9, 3.629780429741998*^9}, {3.6297805790030603`*^9, 3.6297809429048996`*^9}, { 3.629780987957779*^9, 3.629781197575347*^9}, {3.629781240397422*^9, 3.629781337663593*^9}, {3.6297813946972933`*^9, 3.6297814529165955`*^9}, { 3.6297814952550697`*^9, 3.629781527578326*^9}, {3.62978162025529*^9, 3.629781647633338*^9}, {3.629781678833393*^9, 3.629781763120341*^9}, 3.6297818028224106`*^9, {3.6297818432108817`*^9, 3.629781872570133*^9}, { 3.629782355765382*^9, 3.629782427603508*^9}, {3.6297824692243814`*^9, 3.629782674863942*^9}, {3.629782707218399*^9, 3.6297829295343895`*^9}, { 3.629783005631323*^9, 3.6297830574702144`*^9}, {3.6297831098551064`*^9, 3.629783142786764*^9}, {3.629783433711675*^9, 3.629783442619291*^9}, { 3.6297834942397814`*^9, 3.6297835175930223`*^9}, 3.6297835794939313`*^9, { 3.6297836160291953`*^9, 3.6297837668970604`*^9}, {3.6297842042438283`*^9, 3.6297842697483435`*^9}, {3.6297843514456873`*^9, 3.629784370742921*^9}, { 3.629784443829049*^9, 3.6297844678842916`*^9}, {3.6297845252611923`*^9, 3.629784525588793*^9}, {3.6297846136821475`*^9, 3.629784629235375*^9}, { 3.629784814797701*^9, 3.629784927648299*^9}, {3.629785259960083*^9, 3.6297852602096834`*^9}, {3.6297858780175686`*^9, 3.629785917282837*^9}, { 3.629786048057867*^9, 3.629786048681868*^9}, 3.6297863278755584`*^9, { 3.6297867047133856`*^9, 3.629786748533863*^9}, {3.6297867791567163`*^9, 3.6297868491540394`*^9}, {3.6297875320748396`*^9, 3.629787569795706*^9}, { 3.6297876247234025`*^9, 3.6297877281983843`*^9}, {3.6297877681812544`*^9, 3.629787774015665*^9}, {3.629787831408166*^9, 3.6297878355265727`*^9}, { 3.6297878775686464`*^9, 3.6297878861174617`*^9}, {3.6297879185343184`*^9, 3.629787919064719*^9}, {3.6297880043032694`*^9, 3.62978800470887*^9}, 3.6297880488257475`*^9, {3.6297882100052304`*^9, 3.6297882174776435`*^9}, { 3.6297882697533355`*^9, 3.6297882948381796`*^9}, {3.6297883467550707`*^9, 3.6297883991087627`*^9}, {3.6297887361785545`*^9, 3.629788783961438*^9}, 3.629788825395111*^9, {3.629789006152629*^9, 3.6297890321266747`*^9}, { 3.6297891133248167`*^9, 3.629789145336073*^9}, {3.6297891926821566`*^9, 3.629789194257759*^9}, {3.629789255316266*^9, 3.6297892556282673`*^9}, { 3.629869102295367*^9, 3.629869160124668*^9}, {3.6298691942887287`*^9, 3.6298696149902673`*^9}, {3.6298696993864155`*^9, 3.62986975897852*^9}, { 3.6298698387726603`*^9, 3.629869912030389*^9}, {3.6298700722270703`*^9, 3.629870234560955*^9}, {3.629870580429163*^9, 3.629870630458451*^9}, { 3.630556081081209*^9, 3.630556104902451*^9}, {3.6305562643503313`*^9, 3.6305562763935523`*^9}, {3.6305563415080667`*^9, 3.630556480956712*^9}, { 3.630556692851884*^9, 3.630556695347888*^9}, {3.630556730042349*^9, 3.630556914528273*^9}, {3.6305653725974936`*^9, 3.6305656807121167`*^9}, { 3.630565758760581*^9, 3.6305657739024467`*^9}, {3.630565858170267*^9, 3.63056596644846*^9}, {3.6305661502619734`*^9, 3.6305661523230915`*^9}, { 3.6305662653385553`*^9, 3.630566370352562*^9}, {3.6305667786019125`*^9, 3.630566790535595*^9}, {3.6305668214773645`*^9, 3.630567044691132*^9}, { 3.6305670772499943`*^9, 3.6305670783710585`*^9}, 3.630567272031135*^9, { 3.630567303902958*^9, 3.630567409875019*^9}, {3.630568671196477*^9, 3.6305687195002403`*^9}, {3.6305687542132254`*^9, 3.630568758623478*^9}, { 3.630568855671028*^9, 3.630568859250233*^9}, {3.630569706514694*^9, 3.630569775526641*^9}, 3.630569982346471*^9, {3.6305701679130845`*^9, 3.630570205199217*^9}, {3.6305703751399374`*^9, 3.630570526177576*^9}, { 3.630587657039589*^9, 3.630587688367381*^9}, {3.6305880733027773`*^9, 3.6305883365376396`*^9}, {3.6305886689118233`*^9, 3.6305886717978287`*^9}, 3.6305889776831656`*^9, {3.6305890389444733`*^9, 3.6305890437180815`*^9}, { 3.630589093248169*^9, 3.6305891296430326`*^9}, 3.630589181700324*^9, { 3.6305892509956455`*^9, 3.6305892594820604`*^9}, {3.630589318949365*^9, 3.6305893334729905`*^9}, {3.630589630294712*^9, 3.6305896376267247`*^9}, { 3.630589683288005*^9, 3.630589684988408*^9}, {3.630597310538067*^9, 3.630597340080757*^9}, {3.630597391446695*^9, 3.630597400596218*^9}, { 3.6305974350611897`*^9, 3.6305974605306463`*^9}, {3.630633997622449*^9, 3.630634003125764*^9}, {3.630659322217756*^9, 3.63065932438616*^9}, { 3.6306611578252783`*^9, 3.6306611625988865`*^9}, {3.6306612541554475`*^9, 3.630661257587454*^9}, {3.6306613001287284`*^9, 3.6306613026715326`*^9}, { 3.6306613920752897`*^9, 3.6306613949768953`*^9}, {3.6306706377509866`*^9, 3.630670654957817*^9}, {3.6306749981919994`*^9, 3.630675005793434*^9}, { 3.6306751229631357`*^9, 3.630675150017683*^9}, {3.6306752035287437`*^9, 3.6306752096180925`*^9}, {3.630675315921172*^9, 3.6306753201514144`*^9}, { 3.6306757793287754`*^9, 3.6306757796257925`*^9}, {3.630675814406262*^9, 3.6306758147026625`*^9}, {3.6306760107574763`*^9, 3.6306760154417443`*^9}, {3.6306789722320743`*^9, 3.6306789870309205`*^9}, {3.6306790257051325`*^9, 3.630679028076268*^9}, { 3.6306800259177256`*^9, 3.6306800406129513`*^9}, {3.6306801239326982`*^9, 3.6306801300167084`*^9}, {3.630680769261832*^9, 3.6306807806186523`*^9}, { 3.630681157468514*^9, 3.6306811577649145`*^9}, {3.6306812744219193`*^9, 3.63068127471832*^9}, {3.6306817187418995`*^9, 3.6306817919060287`*^9}, { 3.630681879188182*^9, 3.6306819111526375`*^9}, {3.6306821191790032`*^9, 3.6306821283050194`*^9}, {3.630720543651497*^9, 3.6307205534300566`*^9}, { 3.630721035525631*^9, 3.630721092774905*^9}, {3.6307212510439577`*^9, 3.6307213064777765`*^9}, {3.6307477437169704`*^9, 3.6307478284095197`*^9}, {3.6307478614971776`*^9, 3.6307478785948076`*^9}, {3.6307479884814005`*^9, 3.630748002880226*^9}, { 3.630748045624301*^9, 3.630748063876333*^9}, {3.630748111596817*^9, 3.6307481498324842`*^9}, {3.6307489182430334`*^9, 3.6307489447786803`*^9}, {3.630749037427243*^9, 3.6307490443848553`*^9}, { 3.6307491041485605`*^9, 3.6307491384218206`*^9}, {3.6307491914151134`*^9, 3.630749196890723*^9}, {3.6307492445800066`*^9, 3.6307493439989815`*^9}, { 3.630749396212273*^9, 3.6307494766304145`*^9}, {3.6307495333989143`*^9, 3.6307495547241516`*^9}, {3.6307496525831237`*^9, 3.630749669571553*^9}, { 3.630750220602922*^9, 3.6307502881822405`*^9}, {3.6307510631916018`*^9, 3.630751068292811*^9}, {3.6307511226589065`*^9, 3.630751137962533*^9}, { 3.6307512555243397`*^9, 3.630751282777588*^9}, {3.630752266971757*^9, 3.630752414599744*^9}, {3.630752446407563*^9, 3.630752457388191*^9}, { 3.6307589380050273`*^9, 3.6307590266300964`*^9}, {3.6307591666721067`*^9, 3.63075923229886*^9}, 3.630760288282259*^9, {3.6307603547370596`*^9, 3.630760557414652*^9}, {3.630760654134184*^9, 3.63076065510824*^9}, { 3.6307606911683025`*^9, 3.6307606919283457`*^9}, {3.6307607642334814`*^9, 3.6307607648645177`*^9}, {3.630761455000991*^9, 3.6307614616743727`*^9}, { 3.630761507825012*^9, 3.630761605776615*^9}, {3.630761652999316*^9, 3.630761695865768*^9}, {3.630761771278081*^9, 3.6307617792215357`*^9}, 3.6307629478424797`*^9, {3.632205207880766*^9, 3.6322052561155243`*^9}, { 3.6322052892474194`*^9, 3.6322052915745525`*^9}, 3.6322053746993074`*^9, { 3.6322062705415463`*^9, 3.6322062726016645`*^9}, {3.6322063396935015`*^9, 3.63220636484194*^9}, {3.6322064410612993`*^9, 3.6322064491667633`*^9}, { 3.632206580308264*^9, 3.6322066373275256`*^9}, {3.6322066736436024`*^9, 3.6322067467737856`*^9}, {3.632206782260815*^9, 3.6322071351279984`*^9}, 3.6322071989226465`*^9, {3.632207270393735*^9, 3.6322073359894867`*^9}, { 3.6322073997741346`*^9, 3.6322074126708727`*^9}, {3.632207491777397*^9, 3.632207682289294*^9}, {3.632207809621577*^9, 3.632207827973626*^9}, { 3.6322079043859973`*^9, 3.6322079279443445`*^9}, {3.6322080916397076`*^9, 3.6322081666649985`*^9}, 3.634905258940913*^9, {3.634905370524296*^9, 3.6349054089004903`*^9}, {3.6349054472556844`*^9, 3.63490544787272*^9}, { 3.634905483492757*^9, 3.6349055164646425`*^9}, {3.634905574352954*^9, 3.634905628121029*^9}, {3.6349057012822137`*^9, 3.6349057207913294`*^9}, { 3.6349061371061416`*^9, 3.634906354438572*^9}, {3.6349063890455513`*^9, 3.6349064369332905`*^9}, {3.634906537696054*^9, 3.634906601859724*^9}, 3.634906706128688*^9, {3.6349069249442034`*^9, 3.6349069328326545`*^9}, { 3.6349070151973653`*^9, 3.6349070242298822`*^9}, {3.6349070817921743`*^9, 3.6349070822111983`*^9}, {3.634907723288866*^9, 3.634907739005765*^9}, { 3.6349079580732946`*^9, 3.6349079868219395`*^9}, {3.634908200284148*^9, 3.634908315195721*^9}, {3.6349083774582825`*^9, 3.6349084027997313`*^9}, { 3.63490844507615*^9, 3.634908448843365*^9}, {3.634914956333157*^9, 3.634915020054802*^9}, {3.634915050572547*^9, 3.6349150956171236`*^9}, { 3.6349539785771523`*^9, 3.634953978975175*^9}, {3.6349540728785458`*^9, 3.6349541681829967`*^9}, {3.634954211263461*^9, 3.6349542495746527`*^9}, { 3.6349543251259737`*^9, 3.634954355882733*^9}, {3.6349543892536416`*^9, 3.6349544742835045`*^9}, {3.634954547519694*^9, 3.6349545640246377`*^9}, { 3.6349547051657104`*^9, 3.6349547107930326`*^9}, {3.634954745355009*^9, 3.634954752101395*^9}, {3.6349547948858423`*^9, 3.6349548053894434`*^9}, { 3.634954904907135*^9, 3.6349549451084347`*^9}, {3.634955219605135*^9, 3.6349552640926795`*^9}, {3.634955320189888*^9, 3.634955348763522*^9}, { 3.634955386393675*^9, 3.6349555039273973`*^9}, {3.6349557669644423`*^9, 3.6349557672004557`*^9}, {3.634955894841756*^9, 3.634955902578199*^9}, { 3.6349559513739896`*^9, 3.6349560216320086`*^9}, {3.634956120144643*^9, 3.634956128996149*^9}, {3.6349561700724983`*^9, 3.6349561978900895`*^9}, { 3.6349562480719595`*^9, 3.634956254326318*^9}, {3.634956331684742*^9, 3.6349563460575643`*^9}, {3.634956379242462*^9, 3.63495642676418*^9}, 3.6349564696636343`*^9, {3.6351524116477795`*^9, 3.6351524153379908`*^9}, { 3.6352134400282927`*^9, 3.635213442148414*^9}, {3.6352134745862694`*^9, 3.635213495869487*^9}, {3.6352135383409157`*^9, 3.6352137157160616`*^9}, { 3.6352137493569856`*^9, 3.635213764522853*^9}, {3.635214215036621*^9, 3.635214227593339*^9}, {3.635214407257615*^9, 3.63521441713218*^9}, { 3.635215297101512*^9, 3.635215303964904*^9}, {3.6352154111120324`*^9, 3.635215431504199*^9}, {3.635216346055508*^9, 3.635216494371991*^9}, { 3.635216631050809*^9, 3.6352166603244834`*^9}, {3.635216763034358*^9, 3.635216764164423*^9}, {3.6352168771938877`*^9, 3.635216888828553*^9}, 3.6352169832479534`*^9, 3.635217037668066*^9, {3.6352172024924936`*^9, 3.6352172054526625`*^9}, {3.635217344025589*^9, 3.635217346898753*^9}, 3.6352173863770113`*^9, {3.635217519639633*^9, 3.6352175507014103`*^9}, 3.635217615445113*^9, {3.6352178715087595`*^9, 3.635217880460271*^9}, { 3.6352185912849283`*^9, 3.635218598444338*^9}, {3.6352186995721216`*^9, 3.635218714955002*^9}, {3.6352189761749425`*^9, 3.6352189789341*^9}, { 3.6352195060322485`*^9, 3.635219509972474*^9}, 3.6352195673477554`*^9, 3.6352195994635925`*^9, {3.6352197336482677`*^9, 3.635219737452485*^9}, { 3.6352197706093817`*^9, 3.6352197723214793`*^9}, {3.635219941784172*^9, 3.6352199485115566`*^9}, {3.6352200714185867`*^9, 3.6352200854323883`*^9}, {3.6352202085694313`*^9, 3.635220235849992*^9}, { 3.6352202816336107`*^9, 3.6352203110962954`*^9}, {3.6352204980449886`*^9, 3.6352205276526823`*^9}, {3.6352253191447396`*^9, 3.6352253299913597`*^9}, {3.6352253611111403`*^9, 3.6352253637572913`*^9}, {3.635225409322898*^9, 3.6352255965196047`*^9}, { 3.6352260914249115`*^9, 3.6352261698393965`*^9}, {3.63522638233055*^9, 3.6352264188036366`*^9}, {3.635227493469104*^9, 3.635227556935734*^9}, { 3.6352276745764627`*^9, 3.635227730116639*^9}, {3.6352287979917183`*^9, 3.6352288587651944`*^9}, {3.635228894237223*^9, 3.635228948324317*^9}, { 3.635229365252164*^9, 3.6352293902275925`*^9}, {3.63522947690555*^9, 3.6352294807837715`*^9}, {3.6352492831123204`*^9, 3.6352492983621926`*^9}, 3.6356569054520617`*^9, {3.6363778004499054`*^9, 3.636377802787039*^9}, { 3.6363778414932528`*^9, 3.6363778525308843`*^9}, {3.636384436335312*^9, 3.6363846409950175`*^9}, {3.636384971250907*^9, 3.6363849738080535`*^9}, { 3.6363850170465264`*^9, 3.636385030729309*^9}, {3.6363851286779118`*^9, 3.636385138359465*^9}, {3.6363851699712734`*^9, 3.636385223111313*^9}, { 3.656076172452749*^9, 3.656076182171566*^9}, {3.6560765578514256`*^9, 3.656076619019133*^9}, 3.6560772545486493`*^9, {3.6630719749029694`*^9, 3.6630719878027077`*^9}, {3.6630720702554235`*^9, 3.6630720807290225`*^9}, {3.6630721155740156`*^9, 3.6630721713712068`*^9}, {3.663072270834896*^9, 3.6630722882218904`*^9}, 3.6630724099968557`*^9, {3.685234767958906*^9, 3.685234768480936*^9}, { 3.685252204033695*^9, 3.6852522340537376`*^9}, {3.6852522757137957`*^9, 3.6852523115138454`*^9}, {3.68525376314359*^9, 3.6852537725041256`*^9}, { 3.6852539763277836`*^9, 3.6852539861693463`*^9}, 3.6852540682470407`*^9, 3.6852541660656357`*^9, {3.6852604801645336`*^9, 3.6852605060345697`*^9}, { 3.6852605373446136`*^9, 3.6852605977846985`*^9}, 3.685260655254779*^9, { 3.6853280002218475`*^9, 3.685328019561875*^9}, 3.685328064721938*^9, { 3.6853280953119807`*^9, 3.6853282636022167`*^9}, {3.685328356242346*^9, 3.685328598671985*^9}, {3.6853286682069626`*^9, 3.6853287982524004`*^9}, { 3.6853288753368096`*^9, 3.6853289367033195`*^9}, {3.685328968274125*^9, 3.685328978713722*^9}, {3.685329033941881*^9, 3.685329044950511*^9}, { 3.685329173522865*^9, 3.6853294420842257`*^9}, {3.6853296024223967`*^9, 3.6853296124319687`*^9}, {3.6853297221712456`*^9, 3.685329733349885*^9}, { 3.6853298076291337`*^9, 3.6853298739599276`*^9}, {3.685330038474337*^9, 3.685330051652091*^9}, {3.6853311309428225`*^9, 3.685331168378964*^9}, { 3.685340142134763*^9, 3.685340180544817*^9}, {3.6853583292043543`*^9, 3.685358334834362*^9}, {3.685358366084406*^9, 3.685358366954407*^9}, { 3.685358408404465*^9, 3.685358518294619*^9}, 3.685358620174762*^9, 3.6853586578748145`*^9, {3.6853588750151186`*^9, 3.6853588857151337`*^9}, { 3.6853589302051954`*^9, 3.685358938995208*^9}, {3.685359014715314*^9, 3.6853590296653347`*^9}, 3.685359148315501*^9, 3.6853598281764526`*^9, { 3.6853683109000263`*^9, 3.685368382250126*^9}, {3.685368420160179*^9, 3.6853684704302497`*^9}, {3.6853685194503183`*^9, 3.685368742860631*^9}, { 3.685369008901004*^9, 3.68536902061102*^9}, {3.6853690791611023`*^9, 3.685369132301176*^9}, {3.6853693219914417`*^9, 3.6853693304114532`*^9}, 3.6853696089118433`*^9, {3.6858758911429157`*^9, 3.685875951793*^9}, { 3.6859484099082212`*^9, 3.6859484970032024`*^9}, {3.686052829875022*^9, 3.686052906242383*^9}, {3.6860535326822133`*^9, 3.686053598029951*^9}, { 3.68605365168902*^9, 3.6860541446091995`*^9}, {3.6860541846064873`*^9, 3.68605440393201*^9}, {3.686054713802734*^9, 3.6860547858298535`*^9}, { 3.6860548280202665`*^9, 3.686054837219793*^9}, {3.686054874127904*^9, 3.686054892139934*^9}, {3.686055136014883*^9, 3.6860551460584574`*^9}, { 3.686055211281188*^9, 3.6860552301962633`*^9}, {3.6860553465409174`*^9, 3.6860553998749685`*^9}, {3.6860556017188663`*^9, 3.6860556050188704`*^9}, {3.6862923512707715`*^9, 3.686292363600789*^9}, { 3.686292409650853*^9, 3.6862924109708548`*^9}, {3.6862924536109147`*^9, 3.6862924596309233`*^9}, {3.686292542221039*^9, 3.6862925430110397`*^9}, { 3.686292988803664*^9, 3.686293001033681*^9}, {3.6866504529025555`*^9, 3.686650526682659*^9}, {3.686650671852862*^9, 3.6866507242929354`*^9}, { 3.6866507657529936`*^9, 3.6866507887630253`*^9}, {3.6866508208230705`*^9, 3.6866509100531955`*^9}, {3.6866509593932643`*^9, 3.686650971113281*^9}, { 3.686651007793332*^9, 3.6866511595335445`*^9}, {3.686651223513634*^9, 3.686651234033649*^9}, {3.686651304763748*^9, 3.6866513363837924`*^9}, { 3.6866514102038956`*^9, 3.686651429943923*^9}, {3.686652993837468*^9, 3.6866530046274834`*^9}, {3.686804398511652*^9, 3.6868044081516657`*^9}, { 3.6868046315619783`*^9, 3.686804631801979*^9}, {3.686804685872054*^9, 3.686804707092084*^9}, {3.6868047382021275`*^9, 3.686804767812169*^9}, { 3.686804824012248*^9, 3.6868048404922705`*^9}, {3.686804942142413*^9, 3.6868049633424425`*^9}, {3.6868050765526013`*^9, 3.686805101092636*^9}, { 3.6868051463526993`*^9, 3.6868052234228067`*^9}, {3.686805307602925*^9, 3.686805311682931*^9}, {3.68680577547358*^9, 3.686805788923599*^9}, { 3.686821702197342*^9, 3.6868217282873783`*^9}, {3.6868225192884855`*^9, 3.686822538368512*^9}, {3.6868226306886415`*^9, 3.6868226683086944`*^9}, { 3.6868227318887835`*^9, 3.6868227627088265`*^9}, {3.686822801638881*^9, 3.6868230490692277`*^9}, {3.686823122979331*^9, 3.6868231833294153`*^9}, { 3.6868232450595016`*^9, 3.6868233753996844`*^9}, {3.6868234153897405`*^9, 3.686823451379791*^9}, {3.6868236736101017`*^9, 3.6868236786601086`*^9}, { 3.6868237164601617`*^9, 3.68682375072021*^9}, {3.68682389396041*^9, 3.68682390087042*^9}, {3.686823940790476*^9, 3.6868239416904774`*^9}, { 3.6868239808805323`*^9, 3.6868239872905407`*^9}, {3.686824051540631*^9, 3.6868240519006314`*^9}, {3.686824360861064*^9, 3.6868243761510854`*^9}, { 3.6868245440213203`*^9, 3.686824577221367*^9}, {3.686824685841519*^9, 3.6868246979115357`*^9}, 3.6868248012716804`*^9, 3.6868253582724605`*^9, { 3.6868255183026843`*^9, 3.686825518932685*^9}, {3.6868264466639843`*^9, 3.6868264497139883`*^9}, {3.6868267792744493`*^9, 3.6868268152945004`*^9}, {3.686827100164899*^9, 3.6868271210549283`*^9}, 3.686827162004986*^9, {3.6868272414950967`*^9, 3.686827327475217*^9}, { 3.686827953126093*^9, 3.686827976506126*^9}, {3.686829128577739*^9, 3.686829138957753*^9}, 3.6868292410978966`*^9, {3.6868292768379464`*^9, 3.686829282727955*^9}, {3.6868293820380936`*^9, 3.686829418138144*^9}, { 3.686829846748744*^9, 3.686829848298746*^9}, {3.6868313063207874`*^9, 3.686831307180789*^9}, {3.6868331276633377`*^9, 3.68683328653356*^9}, { 3.6868394697195063`*^9, 3.6868394933895392`*^9}, 3.686839530999592*^9, { 3.686839582829664*^9, 3.68683963686974*^9}, {3.6868397551199055`*^9, 3.68683979365996*^9}, {3.6868398344600167`*^9, 3.686839866200061*^9}, { 3.687092084401948*^9, 3.687092117031994*^9}, {3.6870922598621936`*^9, 3.6870922645422*^9}, {3.6870962086478376`*^9, 3.6870962658779182`*^9}, 3.687096444838168*^9, {3.687096500978247*^9, 3.687096501638248*^9}, { 3.6870965809883595`*^9, 3.687096592708376*^9}, 3.687096837948719*^9, { 3.68709688890879*^9, 3.687096985798926*^9}, {3.6870971015990877`*^9, 3.6870972179192505`*^9}, {3.6870972618993125`*^9, 3.687097305639374*^9}, { 3.6870973356794157`*^9, 3.6870975186496716`*^9}, {3.6870975796097574`*^9, 3.6870975953197794`*^9}, {3.6870976531898603`*^9, 3.6870976848899045`*^9}, 3.6870977782500353`*^9, {3.687413757687042*^9, 3.6874137834070783`*^9}, { 3.6874140542074575`*^9, 3.687414094417514*^9}, {3.6874143478878684`*^9, 3.687414485538061*^9}, {3.6874146116082373`*^9, 3.68741464894829*^9}, { 3.6874147451084247`*^9, 3.687414766118454*^9}, 3.6874149094486547`*^9, { 3.6874150416688395`*^9, 3.6874150634888706`*^9}, {3.6874152437091227`*^9, 3.687415268869158*^9}, 3.6874153442892637`*^9, {3.687415449879411*^9, 3.687415469659439*^9}, 3.687415529739523*^9, 3.687415564789572*^9, 3.687415645529685*^9, {3.6874168016913037`*^9, 3.687416803441306*^9}, { 3.687421022677213*^9, 3.6874212686075573`*^9}, {3.68742948209425*^9, 3.6874294906842623`*^9}, {3.687844340668378*^9, 3.6878443698084188`*^9}, { 3.6886534778571014`*^9, 3.6886534911571198`*^9}, {3.688906380162199*^9, 3.6889064680223217`*^9}, {3.688906514222396*^9, 3.6889065193925257`*^9}, { 3.688908192623024*^9, 3.6889082006430354`*^9}, {3.688908261823121*^9, 3.688908271653135*^9}, {3.6889083776232834`*^9, 3.6889083922733035`*^9}, { 3.688908466073407*^9, 3.6889084993734536`*^9}, 3.688908533623502*^9, { 3.688908616683618*^9, 3.6889086271336327`*^9}, {3.6889086885637183`*^9, 3.6889087063437433`*^9}, {3.6889091647443852`*^9, 3.6889092012544365`*^9}, {3.6889093019045773`*^9, 3.6889093406746316`*^9}, 3.6889101071957045`*^9, {3.689905940063133*^9, 3.689905972983179*^9}, { 3.692530981927737*^9, 3.6925310416778207`*^9}, {3.692531099797902*^9, 3.6925311384779563`*^9}, {3.692531192258032*^9, 3.692531244668105*^9}, { 3.6925312919881716`*^9, 3.692531425418358*^9}, {3.6925315270885005`*^9, 3.692531643928664*^9}, {3.692535489534048*^9, 3.6925356485142703`*^9}, { 3.692535753564418*^9, 3.6925357992544813`*^9}, {3.6925358831745987`*^9, 3.692535899604622*^9}, {3.692536042584822*^9, 3.692536159384986*^9}, { 3.6925366121156197`*^9, 3.6925366207256317`*^9}, {3.6925367265057793`*^9, 3.69253672683578*^9}, {3.6925368590559654`*^9, 3.6925368636559715`*^9}, { 3.6925370880062857`*^9, 3.692537177856412*^9}, {3.692537322456614*^9, 3.6925373869767046`*^9}, {3.6925390913352747`*^9, 3.6925390925252767`*^9}, {3.692539644430175*^9, 3.6925396711502123`*^9}, { 3.692539727510291*^9, 3.692539730440295*^9}, {3.69253993367058*^9, 3.692539963780622*^9}, {3.6925400018406754`*^9, 3.692540003630678*^9}, { 3.6925401743409166`*^9, 3.6925401747509174`*^9}, {3.692540399111232*^9, 3.692540407981244*^9}, {3.69254047647134*^9, 3.6925404886113567`*^9}, { 3.6925406039715185`*^9, 3.69254060531152*^9}, {3.6925414948727655`*^9, 3.6925414953427663`*^9}, {3.6925415478528395`*^9, 3.692541613062931*^9}, 3.692541649332982*^9, {3.692541727633092*^9, 3.6925418840133104`*^9}, { 3.692541924473367*^9, 3.692542041693531*^9}, {3.6925421488836813`*^9, 3.6925422549438295`*^9}, {3.6925422976938896`*^9, 3.692542521444203*^9}, { 3.6925426221843443`*^9, 3.6925426357343626`*^9}, 3.692542739374508*^9, 3.692599799510878*^9, {3.692599834884901*^9, 3.6925998954663663`*^9}, { 3.692599925635092*^9, 3.6926000095928946`*^9}, {3.692600108929576*^9, 3.6926001456386757`*^9}, {3.6926001874800687`*^9, 3.692600454421337*^9}, { 3.692600503149027*^9, 3.6926006000391626`*^9}, {3.692600680251275*^9, 3.6926006814012766`*^9}, {3.6926009000215826`*^9, 3.6926009410816402`*^9}, 3.692601280532116*^9, {3.6926044914726114`*^9, 3.69260449774262*^9}, 3.6926045660127153`*^9, 3.6926046690228596`*^9, {3.69296647863291*^9, 3.6929664798829117`*^9}, {3.6929665643330297`*^9, 3.6929666141830997`*^9}, {3.6929670390036945`*^9, 3.6929670405536966`*^9}, {3.6929670861037607`*^9, 3.6929670952937737`*^9}, {3.6929671302538223`*^9, 3.6929671549438567`*^9}, {3.6929671904739065`*^9, 3.69296722137395*^9}, { 3.6929672596240034`*^9, 3.6929673352541094`*^9}, 3.6929678909232683`*^9, { 3.6930146982034283`*^9, 3.693014722713463*^9}, {3.6930148540136466`*^9, 3.693014857023651*^9}, {3.6930148913836985`*^9, 3.693014894823704*^9}, { 3.693014930903754*^9, 3.6930151942541227`*^9}, {3.693015247824198*^9, 3.693015430554454*^9}, {3.693015673794794*^9, 3.69301579223496*^9}, { 3.6930163123576884`*^9, 3.693016326897709*^9}, {3.6930164225678425`*^9, 3.693016429727853*^9}, {3.693016686718212*^9, 3.693016698128228*^9}, { 3.693016737038283*^9, 3.693016755068308*^9}, {3.6930168429225607`*^9, 3.6930168719926014`*^9}, {3.6930172049430676`*^9, 3.693017284063178*^9}, { 3.693017336433252*^9, 3.6930173662532935`*^9}, {3.6930180949163136`*^9, 3.6930180975563173`*^9}, {3.6930181870764427`*^9, 3.693018199956461*^9}, { 3.6930182954065943`*^9, 3.693018305996609*^9}, {3.693139886141657*^9, 3.6931399045016823`*^9}, {3.6931402916003532`*^9, 3.693140295770359*^9}, { 3.693140426020541*^9, 3.693140426530542*^9}, {3.6931410492237864`*^9, 3.6931410888738413`*^9}, {3.6931411194438844`*^9, 3.693141126553894*^9}, { 3.693141412004294*^9, 3.693141454164353*^9}, {3.6931415979955544`*^9, 3.6931417931758275`*^9}, {3.6932199559445915`*^9, 3.6932199772046213`*^9}, {3.6932201435748544`*^9, 3.693220170284892*^9}, { 3.693220713855653*^9, 3.693220721825664*^9}, {3.693625124589745*^9, 3.693625153729786*^9}, {3.6940907995669713`*^9, 3.6940909688872085`*^9}, { 3.6940913675677667`*^9, 3.6940914223978434`*^9}, {3.694091508037963*^9, 3.694091572118053*^9}, 3.694092009628666*^9, {3.6940920553287296`*^9, 3.694092229168973*^9}, {3.6940923053990793`*^9, 3.694092374419176*^9}, { 3.6940924537392874`*^9, 3.694092457789293*^9}, 3.694092642849552*^9, { 3.6940928573598523`*^9, 3.694092862379859*^9}, {3.6940945886222763`*^9, 3.694094601932295*^9}, 3.694094849542641*^9, {3.694095764293922*^9, 3.6940957644739223`*^9}, {3.6940960602743363`*^9, 3.6940960732243547`*^9}, {3.6940961211044216`*^9, 3.694096124194426*^9}, { 3.694665030960044*^9, 3.6946650634500895`*^9}, {3.6946652071402903`*^9, 3.6946653490404887`*^9}, {3.6946658702212186`*^9, 3.6946658881212435`*^9}, {3.694665923041292*^9, 3.694665953561335*^9}, { 3.694665995981395*^9, 3.6946660149414215`*^9}, {3.694666050571471*^9, 3.6946660547214766`*^9}, {3.694666169991638*^9, 3.694666292151809*^9}, { 3.6946663456618843`*^9, 3.6946663943919525`*^9}, 3.6946667526224537`*^9, 3.69466680700253*^9, 3.694687076625702*^9, {3.6946874316161985`*^9, 3.6946874621962414`*^9}, 3.694687499496294*^9, {3.694687567516389*^9, 3.694687642816495*^9}, {3.694687679006545*^9, 3.6946877198966026`*^9}, { 3.6946877714966745`*^9, 3.694687931746899*^9}, {3.723798739728607*^9, 3.723798744014243*^9}, {3.7237990126446104`*^9, 3.723799023974499*^9}, { 3.7244116671877546`*^9, 3.7244116733393917`*^9}, {3.724411761793063*^9, 3.7244117718753977`*^9}, {3.724411928386671*^9, 3.7244119682966137`*^9}, { 3.724412131847311*^9, 3.724412188341254*^9}, {3.729414981357122*^9, 3.7294149861075096`*^9}, {3.749817651293678*^9, 3.749817653108206*^9}, { 3.7498176831919456`*^9, 3.7498176846222315`*^9}, 3.7498177601545563`*^9, { 3.749817859674735*^9, 3.749817861044999*^9}, {3.7498179561547127`*^9, 3.749817964489929*^9}, {3.749818149334386*^9, 3.749818237397959*^9}, 3.749818617867873*^9, {3.7505621848002787`*^9, 3.7505622174085107`*^9}, { 3.75056238761455*^9, 3.750562431347901*^9}, {3.7505626332829456`*^9, 3.7505627331565337`*^9}, {3.7505627632642183`*^9, 3.7505627635859113`*^9}, {3.7515359581577415`*^9, 3.7515359614850826`*^9}, {3.751536071974715*^9, 3.7515360961721487`*^9}, 3.7515362040373974`*^9, {3.751536256080162*^9, 3.7515365099108534`*^9}, { 3.751549231137398*^9, 3.7515493334258356`*^9}, {3.7515496891619573`*^9, 3.751549689458767*^9}, 3.753020403650548*^9, {3.7530205114189386`*^9, 3.753020525224822*^9}, {3.753021995594639*^9, 3.753022011512741*^9}, { 3.760634689749445*^9, 3.7606348247488756`*^9}, {3.7606349119783344`*^9, 3.7606349350197754`*^9}, {3.76063496856853*^9, 3.7606349922504683`*^9}, { 3.760667269592998*^9, 3.760667271545692*^9}, 3.7606679283912125`*^9, 3.760668039709257*^9, {3.763302716900259*^9, 3.763302749083943*^9}, { 3.763304867499642*^9, 3.7633048681948185`*^9}, {3.763337978730939*^9, 3.763338014197137*^9}, {3.763338054806819*^9, 3.7633381289118147`*^9}, { 3.763338224472745*^9, 3.7633382447254143`*^9}, 3.763338501519575*^9, { 3.7633387342733064`*^9, 3.763338775483101*^9}, {3.7633388525735607`*^9, 3.7633390131554184`*^9}, {3.763360596353942*^9, 3.7633606328922167`*^9}, { 3.7633606638773637`*^9, 3.763360724941125*^9}, {3.763360812068123*^9, 3.763360863571327*^9}, {3.763361217769263*^9, 3.763361243271195*^9}, { 3.763361578316657*^9, 3.7633615820345063`*^9}, {3.763362291476118*^9, 3.763362301380039*^9}, {3.763362505004878*^9, 3.763362606421646*^9}, { 3.763362742167684*^9, 3.7633627524126663`*^9}, {3.7633628090243473`*^9, 3.763362931819517*^9}, {3.763363167452371*^9, 3.7633631784968414`*^9}, { 3.7633632517661986`*^9, 3.7633633364892464`*^9}, 3.763363375651574*^9, { 3.7633634067692766`*^9, 3.7633634260616302`*^9}, 3.7740707523990946`*^9, { 3.7740707829932833`*^9, 3.7740707878092556`*^9}, {3.7740708390374384`*^9, 3.7740708397395124`*^9}, {3.783227748950984*^9, 3.7832277492008963`*^9}, { 3.783227785707693*^9, 3.7832278143641577`*^9}, {3.7832278856705203`*^9, 3.7832279652392664`*^9}, {3.7832285261117268`*^9, 3.7832285921982536`*^9}, {3.783228737502862*^9, 3.78322877106949*^9}, { 3.783228913503404*^9, 3.783228974160059*^9}, {3.7832316543548126`*^9, 3.783231867293047*^9}, {3.78324783313018*^9, 3.7832478882254915`*^9}, { 3.783247918659526*^9, 3.783247936428216*^9}, {3.783247974038493*^9, 3.783247982976531*^9}, {3.783313226071577*^9, 3.7833132588540363`*^9}, 3.783313524738693*^9, 3.783314136984562*^9, 3.7834872060638447`*^9, 3.7837554878717237`*^9, {3.7837555335024405`*^9, 3.783755772186054*^9}, { 3.7838247043960843`*^9, 3.7838247173728824`*^9}, {3.7838316560507956`*^9, 3.7838316617616296`*^9}, 3.783831747278124*^9, {3.7838318003068686`*^9, 3.783831865083964*^9}, {3.783832157749748*^9, 3.7838321754150395`*^9}, 3.7838360879476986`*^9, {3.7838361186647277`*^9, 3.7838361777821407`*^9}, 3.7838382113157587`*^9, {3.78790294596488*^9, 3.7879029543299*^9}, { 3.7879030013387113`*^9, 3.7879030724054327`*^9}, {3.788518535581091*^9, 3.7885185816698837`*^9}, 3.7885186656840887`*^9, {3.788518750049559*^9, 3.7885188089248676`*^9}, {3.7922858050278015`*^9, 3.792285809644437*^9}, { 3.7922858997988377`*^9, 3.7922859032607307`*^9}, {3.792285934988084*^9, 3.7922859387881565`*^9}, {3.792286145687361*^9, 3.792286169387656*^9}, { 3.792286200995656*^9, 3.792286297490285*^9}, {3.792286331275391*^9, 3.792286495725276*^9}, {3.7922865286612988`*^9, 3.7922866344845324`*^9}, 3.792286868323101*^9, {3.792287008797488*^9, 3.792287076398588*^9}, { 3.847260050156146*^9, 3.8472600520411935`*^9}, {3.8472600827470026`*^9, 3.847260083816955*^9}, {3.847260159371749*^9, 3.8472603245136585`*^9}, { 3.8472610396461535`*^9, 3.847261042450612*^9}}, CellLabel-> "In[155]:=",ExpressionUUID->"1ab0d6bb-50b0-4ab4-a9e6-e185dc46e365"] }, Closed]], Cell[CellGroupData[{ Cell["BEAM ELEMENT (vibr) defs ", "Subsection", CellChangeTimes->{{3.7530187996679964`*^9, 3.753018818586525*^9}, { 3.7650665335992107`*^9, 3.765066539129182*^9}, {3.7878948161443896`*^9, 3.787894878450323*^9}, 3.7885192008078794`*^9, {3.8200277665922365`*^9, 3.8200277671230316`*^9}, {3.85199502324076*^9, 3.8519950237805815`*^9}},ExpressionUUID->"00c98f89-5b34-4350-9f2a-\ cbf0b8dc6dc8"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iyy", ",", "Izz", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iyy", ",", "Izz", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iyy", ",", "Izz", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "mX", ",", "mY", ",", "mZ"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "h", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "ix0", ",", "iz0", ",", "ux", ",", "uy", " ", ",", "uz", " ", ",", "\[Theta]x", " ", ",", "\[Theta]y", " ", ",", "\[Theta]z", " ", ",", "\[Delta]ux", " ", ",", "\[Delta]uy", ",", "\[Delta]uz", ",", "\[Delta]\[Theta]x", ",", "\[Delta]\[Theta]y", ",", "\[Delta]\[Theta]z", ",", "fx", ",", "fy", ",", "fz", ",", "mx", ",", "my", ",", "mz"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "mapping", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"h", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz0", "=", RowBox[{"ix0", "\[Cross]", "iy0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"2", ",", "2"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"fx", "=", RowBox[{"ix0", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"fy", "=", RowBox[{"iy0", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"fz", "=", RowBox[{"iz0", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"mx", "=", RowBox[{"ix0", ".", RowBox[{"{", RowBox[{"mX", ",", "mY", ",", "mZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"my", "=", RowBox[{"iy0", ".", RowBox[{"{", RowBox[{"mX", ",", "mY", ",", "mZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"mz", "=", RowBox[{"iz0", ".", RowBox[{"{", RowBox[{"mX", ",", "mY", ",", "mZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"-", FractionBox["1", RowBox[{"420", " ", SuperscriptBox["h", "3"]}]]}], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "210"}], " ", "fx", " ", SuperscriptBox["h", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"AA", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"420", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", "\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"70", " ", RowBox[{"ux", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"70", " ", RowBox[{"ux", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}], "+", RowBox[{"156", " ", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"54", " ", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"54", " ", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"156", " ", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"156", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"54", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"54", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"156", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"22", " ", "h", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"13", " ", "h", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"13", " ", "h", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"22", " ", "h", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"22", " ", "h", " ", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"13", " ", "h", " ", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"13", " ", "h", " ", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"22", " ", "h", " ", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"22", " ", "h", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"13", " ", "h", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"4", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"3", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"13", " ", "h", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"22", " ", "h", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"3", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"4", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"22", " ", "h", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"13", " ", "h", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"4", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"3", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"13", " ", "h", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"22", " ", "h", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"3", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"4", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"7", " ", RowBox[{"(", RowBox[{ RowBox[{"720", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"5", " ", "fz", " ", SuperscriptBox["h", "5"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{"5", " ", "fy", " ", SuperscriptBox["h", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"6", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"360", " ", "EE", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{ RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"uy", "[", RowBox[{"1", ",", "0"}], "]"}]}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"12", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], "-", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"5", " ", RowBox[{"(", RowBox[{ RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"2", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], "-", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"5", " ", RowBox[{"(", RowBox[{ RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"2", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"2", " ", SuperscriptBox["h", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"15", " ", "fz", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"15", " ", "mx", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{"\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"5", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}]}], "+", RowBox[{"5", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{"4", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"4", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"5", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}]}], "+", RowBox[{"5", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{"4", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"4", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"6", " ", SuperscriptBox["h", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"10", " ", "mz", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{"10", " ", "my", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}]}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}], "+", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{ RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}], "+", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"for", " ", "detailed", " ", "graphics"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_"}], "}"}], ",", "iy0_", ",", RowBox[{"{", RowBox[{"yz_", ",", "obj_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iyy", ",", "Izz", ",", "iy0"}], "}"}], ",", RowBox[{"{", RowBox[{ "fx", ",", "fy", ",", "fz", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4430689313272*^9, 3.4430690080792*^9}, { 3.4430690869528*^9, 3.4430691077320004`*^9}, {3.4430691700116*^9, 3.4430691708072*^9}, {3.4430692071717997`*^9, 3.443069246359*^9}, { 3.4430772782732*^9, 3.4430773623416*^9}, {3.4430773978316*^9, 3.4430774104676*^9}, {3.4430775053780003`*^9, 3.4430776180598*^9}, { 3.4434109099524*^9, 3.4434109159584*^9}, {3.4438800815346003`*^9, 3.4438802689304*^9}, {3.443880362624*^9, 3.4438803824516*^9}, { 3.443929565615374*^9, 3.443929570232974*^9}, {3.443935321321974*^9, 3.443935335705174*^9}, {3.443935419945174*^9, 3.443935421489574*^9}, { 3.443935494013974*^9, 3.443935494715974*^9}, {3.443935617565974*^9, 3.4439357217895737`*^9}, {3.443935755360774*^9, 3.443935816107174*^9}, { 3.443942155230774*^9, 3.443942209939974*^9}, {3.443942305710374*^9, 3.4439423142123737`*^9}, {3.4439442908131742`*^9, 3.443944441181574*^9}, { 3.4439447830065737`*^9, 3.4439447917425737`*^9}, {3.443944908541774*^9, 3.443944916060974*^9}, {3.4442731097938004`*^9, 3.4442731115254*^9}, { 3.444273189229*^9, 3.4442732700526*^9}, {3.4442748430004*^9, 3.4442748605036*^9}, {3.4442748977438*^9, 3.4442748989762*^9}, { 3.4442749340762*^9, 3.4442749351057997`*^9}, 3.4442752313382*^9, { 3.4442919702026*^9, 3.4442919911846*^9}, {3.4442921151577997`*^9, 3.4442921271074*^9}, {3.4443811023684*^9, 3.4443811036632*^9}, { 3.4443814073171997`*^9, 3.4443814402956*^9}, {3.4443815036316*^9, 3.4443815147855997`*^9}, {3.4443815537232*^9, 3.4443815747676*^9}, { 3.4443816138143997`*^9, 3.444381633174*^9}, {3.4443816850439997`*^9, 3.4443817801728*^9}, 3.4443853618688*^9, {3.4443855607376003`*^9, 3.4443856337924*^9}, {3.4443861200444*^9, 3.4443861523676*^9}, { 3.4443862280495996`*^9, 3.444386291448*^9}, {3.4443864047352*^9, 3.4443864135336*^9}, {3.4443870026832*^9, 3.4443870095316*^9}, { 3.4444082055056*^9, 3.4444082437412*^9}, {3.4444082797148*^9, 3.4444084583816*^9}, {3.4444084889108*^9, 3.4444085087539997`*^9}, { 3.444408942517*^9, 3.4444089563386*^9}, {3.4444091419564*^9, 3.4444091647167997`*^9}, {3.4444092206428003`*^9, 3.4444092944463997`*^9}, {3.4444093856284*^9, 3.4444094281071997`*^9}, { 3.4444094976988*^9, 3.4444095275104*^9}, {3.444409611064*^9, 3.4444096125772*^9}, 3.4444098504616003`*^9, {3.444409913392*^9, 3.4444099166056004`*^9}, 3.4444100178496*^9, {3.4444103063248*^9, 3.4444103358712*^9}, {3.4444103868208*^9, 3.4444104432460003`*^9}, { 3.4444921219564*^9, 3.4444921256224003`*^9}, {3.444492194824*^9, 3.4444921973668003`*^9}, {3.4444922814351997`*^9, 3.4444922853508*^9}, { 3.4444923330868*^9, 3.4444923345844*^9}, {3.444492366424*^9, 3.4444923855808*^9}, {3.4453153475226*^9, 3.445315360689*^9}, { 3.4465518166373653`*^9, 3.446551863016165*^9}, {3.446551894231765*^9, 3.446552159384965*^9}, {3.446552232377365*^9, 3.4465522555589647`*^9}, { 3.446553347388365*^9, 3.4465533616155653`*^9}, {3.4466058525769997`*^9, 3.4466058529046*^9}, {3.4466064371219997`*^9, 3.4466065097244*^9}, { 3.4466127725788*^9, 3.4466127766036*^9}, {3.4466128124835997`*^9, 3.4466130037864*^9}, {3.4466131532696*^9, 3.4466131761703997`*^9}, { 3.4466133992192*^9, 3.4466134478756*^9}, {3.446613483584*^9, 3.4466134932092*^9}, {3.4466135740952*^9, 3.4466135794927998`*^9}, { 3.4466137283948*^9, 3.4466137341356*^9}, {3.4466138994342003`*^9, 3.4466139023826*^9}, {3.4466139549858*^9, 3.4466139579653997`*^9}, { 3.4466142109818*^9, 3.4466142245226*^9}, {3.4466142793878*^9, 3.4466143652033997`*^9}, {3.4466144712834*^9, 3.4466145978929996`*^9}, { 3.4466146992618*^9, 3.4466147509914*^9}, {3.4466151283086*^9, 3.4466152768986*^9}, {3.4466153107506*^9, 3.4466153406558*^9}, { 3.4466194331976*^9, 3.4466194377528*^9}, {3.4466194847712*^9, 3.446619488718*^9}, {3.4466389495861998`*^9, 3.4466389768238*^9}, { 3.4466391218414*^9, 3.446639306561*^9}, {3.4466393990222*^9, 3.4466394004886*^9}, {3.4466394475694*^9, 3.4466394487706003`*^9}, { 3.4466395034174*^9, 3.4466395049462*^9}, 3.4466395515755997`*^9, { 3.4466396000176*^9, 3.4466396190808*^9}, {3.4466397459088*^9, 3.446639748826*^9}, {3.4466397974356003`*^9, 3.446639798668*^9}, 3.4466398447816*^9, {3.446639894218*^9, 3.4466399201556*^9}, { 3.4466399570964003`*^9, 3.4466399583288*^9}, {3.446639994006*^9, 3.4466400056904*^9}, {3.4466400383568*^9, 3.4466400395892*^9}, { 3.4466400745643997`*^9, 3.4466401025976*^9}, {3.4466401660834*^9, 3.4466401806070004`*^9}, {3.4466402251294003`*^9, 3.446640227407*^9}, { 3.446640260479*^9, 3.4466402657674*^9}, {3.4466404133122*^9, 3.4466405185654*^9}, 3.4466405830462*^9, {3.4467273294214*^9, 3.4467273777813997`*^9}, {3.4467274366558*^9, 3.4467275620954*^9}, { 3.446727593311*^9, 3.4467277412614*^9}, {3.4467283334639997`*^9, 3.4467283356012*^9}, {3.4467283707636003`*^9, 3.4467283727604*^9}, { 3.4467289882664003`*^9, 3.4467291276836*^9}, {3.446778464322*^9, 3.4467786797424*^9}, {3.4467801953803997`*^9, 3.4467802409792*^9}, { 3.4467802998691998`*^9, 3.4467804023456*^9}, 3.4467804345596*^9, { 3.4467808656344*^9, 3.4467808670852003`*^9}, 3.4467818107525997`*^9, { 3.446781855509*^9, 3.446781874385*^9}, {3.4467826737914*^9, 3.4467827381726*^9}, {3.4467828623018*^9, 3.4467831045386*^9}, { 3.4470344113984003`*^9, 3.4470344123344*^9}, {3.4470344628316*^9, 3.4470345343108*^9}, {3.447043591118539*^9, 3.447043642192939*^9}, { 3.447045649625739*^9, 3.447045718437339*^9}, {3.447054774023939*^9, 3.447054834198939*^9}, {3.4470549103449388`*^9, 3.4470549116169386`*^9}, { 3.447054943902939*^9, 3.4470553027109385`*^9}, {3.447055334559939*^9, 3.447055353684939*^9}, {3.447057311918539*^9, 3.447057369747739*^9}, { 3.4470575058577385`*^9, 3.4470575951365385`*^9}, {3.4470581848789387`*^9, 3.4470582040825386`*^9}, {3.451276121243*^9, 3.4512761425838003`*^9}, { 3.4512762022382*^9, 3.4512762064346*^9}, {3.4512762476966*^9, 3.4512762827654*^9}, {3.451276489091*^9, 3.451276541975*^9}, { 3.4512765853118*^9, 3.4512766132046003`*^9}, {3.4512773470306*^9, 3.4512773766082*^9}, {3.4512776069110003`*^9, 3.4512777499318*^9}, 3.4512777831286*^9, {3.4512778785538*^9, 3.451277881627*^9}, { 3.4512780242734003`*^9, 3.4512780302794*^9}, 3.4512780737878*^9, { 3.4512781866226*^9, 3.4512781930810003`*^9}, {3.4512863325078*^9, 3.4512863539266*^9}, {3.4568019250434*^9, 3.4568022712698*^9}, { 3.4568023177422*^9, 3.4568024125278*^9}, {3.4568024694365997`*^9, 3.4568024750369997`*^9}, {3.4568026914402*^9, 3.4568028101094*^9}, { 3.4568028406698*^9, 3.4568028564726*^9}, 3.4568028886085997`*^9, { 3.4568030489454*^9, 3.4568030800986*^9}, 3.4568032004128*^9, { 3.4568035073698*^9, 3.4568035176034*^9}, {3.4568040146596003`*^9, 3.4568040844852*^9}, {3.4568043016684*^9, 3.4568043154744*^9}, { 3.4568045482264*^9, 3.4568045486632*^9}, {3.4568048944996*^9, 3.4568049806116*^9}, {3.4660560628582*^9, 3.4660560753538*^9}, { 3.4660676729379997`*^9, 3.4660676735931997`*^9}, {3.4660677244024*^9, 3.4660677277251997`*^9}, {3.4742646771287394`*^9, 3.47426469439174*^9}, { 3.47426489921974*^9, 3.4742649800437393`*^9}, {3.4801246373348*^9, 3.4801246860536003`*^9}, {3.4801247748176003`*^9, 3.4801247821028*^9}, { 3.4801248161264*^9, 3.4801248295736*^9}, {3.4801248810692*^9, 3.4801248964508*^9}, {3.4801249330484*^9, 3.480124947884*^9}, 3.4801249886468*^9, {3.4801251139147997`*^9, 3.48012512588*^9}, { 3.4838339444988003`*^9, 3.4838339567448*^9}, 3.4838341692012*^9, { 3.4838344350408*^9, 3.4838344353684*^9}, {3.4938987575920324`*^9, 3.4938987586840324`*^9}, {3.4941630624049997`*^9, 3.4941631381274*^9}, { 3.4941632311345997`*^9, 3.4941632492306004`*^9}, 3.4941633249217997`*^9, { 3.4941633940922003`*^9, 3.4941634063538*^9}, {3.4941634538402*^9, 3.4941635051642*^9}, {3.494163565115*^9, 3.4941636341762*^9}, { 3.4941636853442*^9, 3.4941639323234*^9}, {3.4941640277798*^9, 3.4941641455754004`*^9}, {3.4941641790374002`*^9, 3.4941641803789997`*^9}, {3.4941642676142*^9, 3.4941643277678003`*^9}, 3.4941644677018003`*^9, {3.4941646208938*^9, 3.4941646322349997`*^9}, { 3.4941652592693996`*^9, 3.4941652807194*^9}, {3.4941653119038*^9, 3.494165416299*^9}, {3.494165453895*^9, 3.4941654544722*^9}, { 3.4950990979779997`*^9, 3.495099142701*^9}, {3.495099172958*^9, 3.4950991806289997`*^9}, {3.495099227097*^9, 3.495099238113*^9}, 3.495099290797*^9, {3.495099346084*^9, 3.495099359507*^9}, { 3.495099456308*^9, 3.495099464091*^9}, 3.495099683108*^9, { 3.495100428112*^9, 3.495100434958*^9}, {3.4951006496219997`*^9, 3.495100649992*^9}, {3.4987235265018*^9, 3.4987235939094*^9}, { 3.4987236420666*^9, 3.4987236530646*^9}, {3.4987237305341997`*^9, 3.4987237396914*^9}, {3.498733136159*^9, 3.4987332972446003`*^9}, { 3.4987364783094*^9, 3.4987364860626*^9}, {3.4987366201134*^9, 3.4987366236078*^9}, {3.4987367272386*^9, 3.4987367464890003`*^9}, { 3.4987369428462*^9, 3.4987369670886*^9}, {3.4987370134518003`*^9, 3.4987370259941998`*^9}, {3.4987370944002*^9, 3.4987371027618*^9}, { 3.4987371921029997`*^9, 3.498737193663*^9}, {3.4987372660938*^9, 3.4987372935498*^9}, {3.4987373290554*^9, 3.4987377176202*^9}, { 3.4987377520182*^9, 3.4987379139462*^9}, {3.4987382030216*^9, 3.4987382667078*^9}, {3.4987888391818*^9, 3.4987888608346*^9}, { 3.4988785131146*^9, 3.4988785160162*^9}, {3.5007170967096*^9, 3.5007170999076*^9}, 3.5007182237316*^9, {3.5007182772864*^9, 3.5007182987832003`*^9}, {3.5009573226744003`*^9, 3.5009573940444*^9}, 3.5009574358710003`*^9, 3.5009604278482*^9, {3.5009897246173353`*^9, 3.5009898480289354`*^9}, {3.5009901464413357`*^9, 3.5009901475333357`*^9}, {3.5009901801997356`*^9, 3.500990274096135*^9}, { 3.5010475253292*^9, 3.5010475852332*^9}, {3.5010605722018003`*^9, 3.5010606739762*^9}, {3.5010607202146*^9, 3.5010607323358*^9}, { 3.5010607920526*^9, 3.501061118467*^9}, {3.5010612022078*^9, 3.5010612277138*^9}, {3.5010616467766*^9, 3.5010617938534*^9}, { 3.5010618406222*^9, 3.5010619950778*^9}, {3.5010621500638*^9, 3.5010622514014*^9}, {3.5010625292218*^9, 3.5010625409374*^9}, { 3.5010626043046*^9, 3.5010626313862*^9}, {3.5010626787166*^9, 3.5010626790754004`*^9}, {3.501074457561*^9, 3.5010744671082*^9}, 3.5010763029458*^9, {3.5032210899309998`*^9, 3.5032212413900003`*^9}, { 3.557658203404973*^9, 3.557658219644601*^9}, {3.5576584433801947`*^9, 3.557658496030287*^9}, {3.5576585501779823`*^9, 3.5576586046064777`*^9}, { 3.557658648910555*^9, 3.557658754600741*^9}, {3.557658963945511*^9, 3.5576589782507353`*^9}, {3.557659009949991*^9, 3.5576591437514267`*^9}, { 3.557659182221094*^9, 3.5576592187719584`*^9}, 3.557659413865901*^9, { 3.557659921100792*^9, 3.5576599556392527`*^9}, {3.557660706920972*^9, 3.5576607248454037`*^9}, {3.557661209085854*^9, 3.557661209413454*^9}, { 3.5577526651911488`*^9, 3.5577526932087984`*^9}, {3.5577527272480583`*^9, 3.557752747122493*^9}, {3.5577528374934516`*^9, 3.557752838523053*^9}, { 3.557752881204728*^9, 3.557752891313546*^9}, {3.557752938612829*^9, 3.5577529469120436`*^9}, {3.557753060714244*^9, 3.557753062633047*^9}, { 3.5577536609544907`*^9, 3.5577536637936954`*^9}, {3.5577537824631042`*^9, 3.557753810184353*^9}, {3.557753841025607*^9, 3.5577540648392*^9}, 3.5577541920574236`*^9, {3.5577547033327217`*^9, 3.557754716967146*^9}, { 3.5577547716296415`*^9, 3.557754802112095*^9}, {3.5577549509363565`*^9, 3.5577549771444025`*^9}, 3.5577551382302856`*^9, {3.55775527184452*^9, 3.557755272858522*^9}, {3.557755881555991*^9, 3.557755886548*^9}, { 3.557756158316077*^9, 3.557756231885806*^9}, {3.5577572408487787`*^9, 3.557757248835993*^9}, {3.5577572834368534`*^9, 3.5577575888229895`*^9}, { 3.5577578129641833`*^9, 3.557757862837471*^9}, {3.557758025514557*^9, 3.557758079272251*^9}, 3.557810586960072*^9, {3.5578240262005973`*^9, 3.5578240345360737`*^9}, {3.557824091429328*^9, 3.5578241008156557`*^9}, { 3.557831525255726*^9, 3.5578315319793377`*^9}, 3.5578315716190076`*^9, { 3.557831606079468*^9, 3.557831629432709*^9}, {3.5578316663267736`*^9, 3.5578317569473333`*^9}, {3.5578322144181366`*^9, 3.557832218084143*^9}, { 3.557836356693412*^9, 3.557836473771618*^9}, {3.5578365201660995`*^9, 3.5578365974018345`*^9}, {3.5578366426731143`*^9, 3.557836658865943*^9}, { 3.557836691017599*^9, 3.5578367924957776`*^9}, {3.5578368305442443`*^9, 3.557836888279946*^9}, {3.5578369382156334`*^9, 3.5578370776642785`*^9}, { 3.5578383536061196`*^9, 3.5578383735117545`*^9}, {3.5578385892445335`*^9, 3.5578385978869486`*^9}, {3.5578386713006773`*^9, 3.557838700113928*^9}, { 3.5578387451200075`*^9, 3.5578387467892103`*^9}, {3.5578388951454706`*^9, 3.5578389248635225`*^9}, {3.5578389679351983`*^9, 3.557838983535226*^9}, { 3.5578390227692947`*^9, 3.557839023143696*^9}, {3.557839097696226*^9, 3.5578391125162525`*^9}, {3.5578391553539276`*^9, 3.557839199892006*^9}, { 3.55783924184048*^9, 3.557839294490572*^9}, {3.5578393285922318`*^9, 3.557839398683155*^9}, {3.557839430522811*^9, 3.557839470162481*^9}, { 3.5578395370865984`*^9, 3.5578395446994114`*^9}, {3.5578396068499207`*^9, 3.5578396118575296`*^9}, 3.5578943518105097`*^9, {3.557894388361374*^9, 3.5578944029629993`*^9}, {3.5578944607611012`*^9, 3.5578944989499683`*^9}, {3.5578945393696394`*^9, 3.557894561537278*^9}, { 3.5578946028617506`*^9, 3.5578946188985786`*^9}, {3.557894650894235*^9, 3.5578947812636642`*^9}, {3.55789481884413*^9, 3.5578948191249304`*^9}, { 3.5578949768100076`*^9, 3.5578949836272197`*^9}, {3.5578967386805477`*^9, 3.55789678549623*^9}, {3.5578968804691963`*^9, 3.557896888643611*^9}, { 3.557897022491846*^9, 3.5578970341450663`*^9}, {3.557897620940097*^9, 3.55789765120415*^9}, {3.5579218072271147`*^9, 3.5579218263059483`*^9}, { 3.557922095312821*^9, 3.557922116965659*^9}, {3.557922178086566*^9, 3.557922188616585*^9}, {3.5579223258812256`*^9, 3.557922327066828*^9}, { 3.5579224596046605`*^9, 3.557922461804264*^9}, 3.5579805928465395`*^9, { 3.5579815200581703`*^9, 3.557981541711009*^9}, 3.557985544779242*^9, { 3.5579863164793987`*^9, 3.5579863339514294`*^9}, {3.557986523210962*^9, 3.557986568841042*^9}, 3.5579866122559185`*^9, 3.557986993536188*^9, { 3.5579871244716187`*^9, 3.5579871290580263`*^9}, 3.557987173486905*^9, 3.5579872166989803`*^9, {3.5599618621582537`*^9, 3.5599618642486577`*^9}, { 3.559961969720443*^9, 3.5599619894700775`*^9}, 3.559963611089726*^9, { 3.5601298891258235`*^9, 3.560129889422224*^9}, {3.560132445157113*^9, 3.5601324458591146`*^9}, {3.561978472080926*^9, 3.561978472392926*^9}, { 3.6297802564412937`*^9, 3.6297802957377625`*^9}, {3.62978033369263*^9, 3.629780429741998*^9}, {3.6297805790030603`*^9, 3.6297809429048996`*^9}, { 3.629780987957779*^9, 3.629781197575347*^9}, {3.629781240397422*^9, 3.629781337663593*^9}, {3.6297813946972933`*^9, 3.6297814529165955`*^9}, { 3.6297814952550697`*^9, 3.629781527578326*^9}, {3.62978162025529*^9, 3.629781647633338*^9}, {3.629781678833393*^9, 3.629781763120341*^9}, 3.6297818028224106`*^9, {3.6297818432108817`*^9, 3.629781872570133*^9}, { 3.629782355765382*^9, 3.629782427603508*^9}, {3.6297824692243814`*^9, 3.629782674863942*^9}, {3.629782707218399*^9, 3.6297829295343895`*^9}, { 3.629783005631323*^9, 3.6297830574702144`*^9}, {3.6297831098551064`*^9, 3.629783142786764*^9}, {3.629783433711675*^9, 3.629783442619291*^9}, { 3.6297834942397814`*^9, 3.6297835175930223`*^9}, 3.6297835794939313`*^9, { 3.6297836160291953`*^9, 3.6297837668970604`*^9}, {3.6297842042438283`*^9, 3.6297842697483435`*^9}, {3.6297843514456873`*^9, 3.629784370742921*^9}, { 3.629784443829049*^9, 3.6297844678842916`*^9}, {3.6297845252611923`*^9, 3.629784525588793*^9}, {3.6297846136821475`*^9, 3.629784629235375*^9}, { 3.629784814797701*^9, 3.629784927648299*^9}, {3.629785259960083*^9, 3.6297852602096834`*^9}, {3.6297858780175686`*^9, 3.629785917282837*^9}, { 3.629786048057867*^9, 3.629786048681868*^9}, 3.6297863278755584`*^9, { 3.6297867047133856`*^9, 3.629786748533863*^9}, {3.6297867791567163`*^9, 3.6297868491540394`*^9}, {3.6297875320748396`*^9, 3.629787569795706*^9}, { 3.6297876247234025`*^9, 3.6297877281983843`*^9}, {3.6297877681812544`*^9, 3.629787774015665*^9}, {3.629787831408166*^9, 3.6297878355265727`*^9}, { 3.6297878775686464`*^9, 3.6297878861174617`*^9}, {3.6297879185343184`*^9, 3.629787919064719*^9}, {3.6297880043032694`*^9, 3.62978800470887*^9}, 3.6297880488257475`*^9, {3.6297882100052304`*^9, 3.6297882174776435`*^9}, { 3.6297882697533355`*^9, 3.6297882948381796`*^9}, {3.6297883467550707`*^9, 3.6297883991087627`*^9}, {3.6297887361785545`*^9, 3.629788783961438*^9}, 3.629788825395111*^9, {3.629789006152629*^9, 3.6297890321266747`*^9}, { 3.6297891133248167`*^9, 3.629789145336073*^9}, {3.6297891926821566`*^9, 3.629789194257759*^9}, {3.629789255316266*^9, 3.6297892556282673`*^9}, { 3.629869102295367*^9, 3.629869160124668*^9}, {3.6298691942887287`*^9, 3.6298696149902673`*^9}, {3.6298696993864155`*^9, 3.62986975897852*^9}, { 3.6298698387726603`*^9, 3.629869912030389*^9}, {3.6298700722270703`*^9, 3.629870234560955*^9}, {3.629870580429163*^9, 3.629870630458451*^9}, { 3.630556081081209*^9, 3.630556104902451*^9}, {3.6305562643503313`*^9, 3.6305562763935523`*^9}, {3.6305563415080667`*^9, 3.630556480956712*^9}, { 3.630556692851884*^9, 3.630556695347888*^9}, {3.630556730042349*^9, 3.630556914528273*^9}, {3.6305653725974936`*^9, 3.6305656807121167`*^9}, { 3.630565758760581*^9, 3.6305657739024467`*^9}, {3.630565858170267*^9, 3.63056596644846*^9}, {3.6305661502619734`*^9, 3.6305661523230915`*^9}, { 3.6305662653385553`*^9, 3.630566370352562*^9}, {3.6305667786019125`*^9, 3.630566790535595*^9}, {3.6305668214773645`*^9, 3.630567044691132*^9}, { 3.6305670772499943`*^9, 3.6305670783710585`*^9}, 3.630567272031135*^9, { 3.630567303902958*^9, 3.630567409875019*^9}, {3.630568671196477*^9, 3.6305687195002403`*^9}, {3.6305687542132254`*^9, 3.630568758623478*^9}, { 3.630568855671028*^9, 3.630568859250233*^9}, {3.630569706514694*^9, 3.630569775526641*^9}, 3.630569982346471*^9, {3.6305701679130845`*^9, 3.630570205199217*^9}, {3.6305703751399374`*^9, 3.630570526177576*^9}, { 3.630587657039589*^9, 3.630587688367381*^9}, {3.6305880733027773`*^9, 3.6305883365376396`*^9}, {3.6305886689118233`*^9, 3.6305886717978287`*^9}, 3.6305889776831656`*^9, {3.6305890389444733`*^9, 3.6305890437180815`*^9}, { 3.630589093248169*^9, 3.6305891296430326`*^9}, 3.630589181700324*^9, { 3.6305892509956455`*^9, 3.6305892594820604`*^9}, {3.630589318949365*^9, 3.6305893334729905`*^9}, {3.630589630294712*^9, 3.6305896376267247`*^9}, { 3.630589683288005*^9, 3.630589684988408*^9}, {3.630597310538067*^9, 3.630597340080757*^9}, {3.630597391446695*^9, 3.630597400596218*^9}, { 3.6305974350611897`*^9, 3.6305974605306463`*^9}, {3.630633997622449*^9, 3.630634003125764*^9}, {3.630659322217756*^9, 3.63065932438616*^9}, { 3.6306611578252783`*^9, 3.6306611625988865`*^9}, {3.6306612541554475`*^9, 3.630661257587454*^9}, {3.6306613001287284`*^9, 3.6306613026715326`*^9}, { 3.6306613920752897`*^9, 3.6306613949768953`*^9}, {3.6306706377509866`*^9, 3.630670654957817*^9}, {3.6306749981919994`*^9, 3.630675005793434*^9}, { 3.6306751229631357`*^9, 3.630675150017683*^9}, {3.6306752035287437`*^9, 3.6306752096180925`*^9}, {3.630675315921172*^9, 3.6306753201514144`*^9}, { 3.6306757793287754`*^9, 3.6306757796257925`*^9}, {3.630675814406262*^9, 3.6306758147026625`*^9}, {3.6306760107574763`*^9, 3.6306760154417443`*^9}, {3.6306789722320743`*^9, 3.6306789870309205`*^9}, {3.6306790257051325`*^9, 3.630679028076268*^9}, { 3.6306800259177256`*^9, 3.6306800406129513`*^9}, {3.6306801239326982`*^9, 3.6306801300167084`*^9}, {3.630680769261832*^9, 3.6306807806186523`*^9}, { 3.630681157468514*^9, 3.6306811577649145`*^9}, {3.6306812744219193`*^9, 3.63068127471832*^9}, {3.6306817187418995`*^9, 3.6306817919060287`*^9}, { 3.630681879188182*^9, 3.6306819111526375`*^9}, {3.6306821191790032`*^9, 3.6306821283050194`*^9}, {3.630720543651497*^9, 3.6307205534300566`*^9}, { 3.630721035525631*^9, 3.630721092774905*^9}, {3.6307212510439577`*^9, 3.6307213064777765`*^9}, {3.6307477437169704`*^9, 3.6307478284095197`*^9}, {3.6307478614971776`*^9, 3.6307478785948076`*^9}, {3.6307479884814005`*^9, 3.630748002880226*^9}, { 3.630748045624301*^9, 3.630748063876333*^9}, {3.630748111596817*^9, 3.6307481498324842`*^9}, {3.6307489182430334`*^9, 3.6307489447786803`*^9}, {3.630749037427243*^9, 3.6307490443848553`*^9}, { 3.6307491041485605`*^9, 3.6307491384218206`*^9}, {3.6307491914151134`*^9, 3.630749196890723*^9}, {3.6307492445800066`*^9, 3.6307493439989815`*^9}, { 3.630749396212273*^9, 3.6307494766304145`*^9}, {3.6307495333989143`*^9, 3.6307495547241516`*^9}, {3.6307496525831237`*^9, 3.630749669571553*^9}, { 3.630750220602922*^9, 3.6307502881822405`*^9}, {3.6307510631916018`*^9, 3.630751068292811*^9}, {3.6307511226589065`*^9, 3.630751137962533*^9}, { 3.6307512555243397`*^9, 3.630751282777588*^9}, {3.630752266971757*^9, 3.630752414599744*^9}, {3.630752446407563*^9, 3.630752457388191*^9}, { 3.6307589380050273`*^9, 3.6307590266300964`*^9}, {3.6307591666721067`*^9, 3.63075923229886*^9}, 3.630760288282259*^9, {3.6307603547370596`*^9, 3.630760557414652*^9}, {3.630760654134184*^9, 3.63076065510824*^9}, { 3.6307606911683025`*^9, 3.6307606919283457`*^9}, {3.6307607642334814`*^9, 3.6307607648645177`*^9}, {3.630761455000991*^9, 3.6307614616743727`*^9}, { 3.630761507825012*^9, 3.630761605776615*^9}, {3.630761652999316*^9, 3.630761695865768*^9}, {3.630761771278081*^9, 3.6307617792215357`*^9}, 3.6307629478424797`*^9, {3.632205207880766*^9, 3.6322052561155243`*^9}, { 3.6322052892474194`*^9, 3.6322052915745525`*^9}, 3.6322053746993074`*^9, { 3.6322062705415463`*^9, 3.6322062726016645`*^9}, {3.6322063396935015`*^9, 3.63220636484194*^9}, {3.6322064410612993`*^9, 3.6322064491667633`*^9}, { 3.632206580308264*^9, 3.6322066373275256`*^9}, {3.6322066736436024`*^9, 3.6322067467737856`*^9}, {3.632206782260815*^9, 3.6322071351279984`*^9}, 3.6322071989226465`*^9, {3.632207270393735*^9, 3.6322073359894867`*^9}, { 3.6322073997741346`*^9, 3.6322074126708727`*^9}, {3.632207491777397*^9, 3.632207682289294*^9}, {3.632207809621577*^9, 3.632207827973626*^9}, { 3.6322079043859973`*^9, 3.6322079279443445`*^9}, {3.6322080916397076`*^9, 3.6322081666649985`*^9}, 3.634905258940913*^9, {3.634905370524296*^9, 3.6349054089004903`*^9}, {3.6349054472556844`*^9, 3.63490544787272*^9}, { 3.634905483492757*^9, 3.6349055164646425`*^9}, {3.634905574352954*^9, 3.634905628121029*^9}, {3.6349057012822137`*^9, 3.6349057207913294`*^9}, { 3.6349061371061416`*^9, 3.634906354438572*^9}, {3.6349063890455513`*^9, 3.6349064369332905`*^9}, {3.634906537696054*^9, 3.634906601859724*^9}, 3.634906706128688*^9, {3.6349069249442034`*^9, 3.6349069328326545`*^9}, { 3.6349070151973653`*^9, 3.6349070242298822`*^9}, {3.6349070817921743`*^9, 3.6349070822111983`*^9}, {3.634907723288866*^9, 3.634907739005765*^9}, { 3.6349079580732946`*^9, 3.6349079868219395`*^9}, {3.634908200284148*^9, 3.634908315195721*^9}, {3.6349083774582825`*^9, 3.6349084027997313`*^9}, { 3.63490844507615*^9, 3.634908448843365*^9}, {3.634914956333157*^9, 3.634915020054802*^9}, {3.634915050572547*^9, 3.6349150956171236`*^9}, { 3.6349539785771523`*^9, 3.634953978975175*^9}, {3.6349540728785458`*^9, 3.6349541681829967`*^9}, {3.634954211263461*^9, 3.6349542495746527`*^9}, { 3.6349543251259737`*^9, 3.634954355882733*^9}, {3.6349543892536416`*^9, 3.6349544742835045`*^9}, {3.634954547519694*^9, 3.6349545640246377`*^9}, { 3.6349547051657104`*^9, 3.6349547107930326`*^9}, {3.634954745355009*^9, 3.634954752101395*^9}, {3.6349547948858423`*^9, 3.6349548053894434`*^9}, { 3.634954904907135*^9, 3.6349549451084347`*^9}, {3.634955219605135*^9, 3.6349552640926795`*^9}, {3.634955320189888*^9, 3.634955348763522*^9}, { 3.634955386393675*^9, 3.6349555039273973`*^9}, {3.6349557669644423`*^9, 3.6349557672004557`*^9}, {3.634955894841756*^9, 3.634955902578199*^9}, { 3.6349559513739896`*^9, 3.6349560216320086`*^9}, {3.634956120144643*^9, 3.634956128996149*^9}, {3.6349561700724983`*^9, 3.6349561978900895`*^9}, { 3.6349562480719595`*^9, 3.634956254326318*^9}, {3.634956331684742*^9, 3.6349563460575643`*^9}, {3.634956379242462*^9, 3.63495642676418*^9}, 3.6349564696636343`*^9, {3.6351524116477795`*^9, 3.6351524153379908`*^9}, { 3.6352134400282927`*^9, 3.635213442148414*^9}, {3.6352134745862694`*^9, 3.635213495869487*^9}, {3.6352135383409157`*^9, 3.6352137157160616`*^9}, { 3.6352137493569856`*^9, 3.635213764522853*^9}, {3.635214215036621*^9, 3.635214227593339*^9}, {3.635214407257615*^9, 3.63521441713218*^9}, { 3.635215297101512*^9, 3.635215303964904*^9}, {3.6352154111120324`*^9, 3.635215431504199*^9}, {3.635216346055508*^9, 3.635216494371991*^9}, { 3.635216631050809*^9, 3.6352166603244834`*^9}, {3.635216763034358*^9, 3.635216764164423*^9}, {3.6352168771938877`*^9, 3.635216888828553*^9}, 3.6352169832479534`*^9, 3.635217037668066*^9, {3.6352172024924936`*^9, 3.6352172054526625`*^9}, {3.635217344025589*^9, 3.635217346898753*^9}, 3.6352173863770113`*^9, {3.635217519639633*^9, 3.6352175507014103`*^9}, 3.635217615445113*^9, {3.6352178715087595`*^9, 3.635217880460271*^9}, { 3.6352185912849283`*^9, 3.635218598444338*^9}, {3.6352186995721216`*^9, 3.635218714955002*^9}, {3.6352189761749425`*^9, 3.6352189789341*^9}, { 3.6352195060322485`*^9, 3.635219509972474*^9}, 3.6352195673477554`*^9, 3.6352195994635925`*^9, {3.6352197336482677`*^9, 3.635219737452485*^9}, { 3.6352197706093817`*^9, 3.6352197723214793`*^9}, {3.635219941784172*^9, 3.6352199485115566`*^9}, {3.6352200714185867`*^9, 3.6352200854323883`*^9}, {3.6352202085694313`*^9, 3.635220235849992*^9}, { 3.6352202816336107`*^9, 3.6352203110962954`*^9}, {3.6352204980449886`*^9, 3.6352205276526823`*^9}, {3.6352253191447396`*^9, 3.6352253299913597`*^9}, {3.6352253611111403`*^9, 3.6352253637572913`*^9}, {3.635225409322898*^9, 3.6352255965196047`*^9}, { 3.6352260914249115`*^9, 3.6352261698393965`*^9}, {3.63522638233055*^9, 3.6352264188036366`*^9}, {3.635227493469104*^9, 3.635227556935734*^9}, { 3.6352276745764627`*^9, 3.635227730116639*^9}, {3.6352287979917183`*^9, 3.6352288587651944`*^9}, {3.635228894237223*^9, 3.635228948324317*^9}, { 3.635229365252164*^9, 3.6352293902275925`*^9}, {3.63522947690555*^9, 3.6352294807837715`*^9}, {3.6352492831123204`*^9, 3.6352492983621926`*^9}, 3.6356569054520617`*^9, {3.6363778004499054`*^9, 3.636377802787039*^9}, { 3.6363778414932528`*^9, 3.6363778525308843`*^9}, {3.636384436335312*^9, 3.6363846409950175`*^9}, {3.636384971250907*^9, 3.6363849738080535`*^9}, { 3.6363850170465264`*^9, 3.636385030729309*^9}, {3.6363851286779118`*^9, 3.636385138359465*^9}, {3.6363851699712734`*^9, 3.636385223111313*^9}, { 3.656076172452749*^9, 3.656076182171566*^9}, {3.6560765578514256`*^9, 3.656076619019133*^9}, 3.6560772545486493`*^9, {3.6630719749029694`*^9, 3.6630719878027077`*^9}, {3.6630720702554235`*^9, 3.6630720807290225`*^9}, {3.6630721155740156`*^9, 3.6630721713712068`*^9}, {3.663072270834896*^9, 3.6630722882218904`*^9}, 3.6630724099968557`*^9, {3.685234767958906*^9, 3.685234768480936*^9}, { 3.685252204033695*^9, 3.6852522340537376`*^9}, {3.6852522757137957`*^9, 3.6852523115138454`*^9}, {3.68525376314359*^9, 3.6852537725041256`*^9}, { 3.6852539763277836`*^9, 3.6852539861693463`*^9}, 3.6852540682470407`*^9, 3.6852541660656357`*^9, {3.6852604801645336`*^9, 3.6852605060345697`*^9}, { 3.6852605373446136`*^9, 3.6852605977846985`*^9}, 3.685260655254779*^9, { 3.6853280002218475`*^9, 3.685328019561875*^9}, 3.685328064721938*^9, { 3.6853280953119807`*^9, 3.6853282636022167`*^9}, {3.685328356242346*^9, 3.685328598671985*^9}, {3.6853286682069626`*^9, 3.6853287982524004`*^9}, { 3.6853288753368096`*^9, 3.6853289367033195`*^9}, {3.685328968274125*^9, 3.685328978713722*^9}, {3.685329033941881*^9, 3.685329044950511*^9}, { 3.685329173522865*^9, 3.6853294420842257`*^9}, {3.6853296024223967`*^9, 3.6853296124319687`*^9}, {3.6853297221712456`*^9, 3.685329733349885*^9}, { 3.6853298076291337`*^9, 3.6853298739599276`*^9}, {3.685330038474337*^9, 3.685330051652091*^9}, {3.6853311309428225`*^9, 3.685331168378964*^9}, { 3.685340142134763*^9, 3.685340180544817*^9}, {3.6853583292043543`*^9, 3.685358334834362*^9}, {3.685358366084406*^9, 3.685358366954407*^9}, { 3.685358408404465*^9, 3.685358518294619*^9}, 3.685358620174762*^9, 3.6853586578748145`*^9, {3.6853588750151186`*^9, 3.6853588857151337`*^9}, { 3.6853589302051954`*^9, 3.685358938995208*^9}, {3.685359014715314*^9, 3.6853590296653347`*^9}, 3.685359148315501*^9, 3.6853598281764526`*^9, { 3.6853683109000263`*^9, 3.685368382250126*^9}, {3.685368420160179*^9, 3.6853684704302497`*^9}, {3.6853685194503183`*^9, 3.685368742860631*^9}, { 3.685369008901004*^9, 3.68536902061102*^9}, {3.6853690791611023`*^9, 3.685369132301176*^9}, {3.6853693219914417`*^9, 3.6853693304114532`*^9}, 3.6853696089118433`*^9, {3.6858758911429157`*^9, 3.685875951793*^9}, { 3.6859484099082212`*^9, 3.6859484970032024`*^9}, {3.686052829875022*^9, 3.686052906242383*^9}, {3.6860535326822133`*^9, 3.686053598029951*^9}, { 3.68605365168902*^9, 3.6860541446091995`*^9}, {3.6860541846064873`*^9, 3.68605440393201*^9}, {3.686054713802734*^9, 3.6860547858298535`*^9}, { 3.6860548280202665`*^9, 3.686054837219793*^9}, {3.686054874127904*^9, 3.686054892139934*^9}, {3.686055136014883*^9, 3.6860551460584574`*^9}, { 3.686055211281188*^9, 3.6860552301962633`*^9}, {3.6860553465409174`*^9, 3.6860553998749685`*^9}, {3.6860556017188663`*^9, 3.6860556050188704`*^9}, {3.6862923512707715`*^9, 3.686292363600789*^9}, { 3.686292409650853*^9, 3.6862924109708548`*^9}, {3.6862924536109147`*^9, 3.6862924596309233`*^9}, {3.686292542221039*^9, 3.6862925430110397`*^9}, { 3.686292988803664*^9, 3.686293001033681*^9}, {3.6866504529025555`*^9, 3.686650526682659*^9}, {3.686650671852862*^9, 3.6866507242929354`*^9}, { 3.6866507657529936`*^9, 3.6866507887630253`*^9}, {3.6866508208230705`*^9, 3.6866509100531955`*^9}, {3.6866509593932643`*^9, 3.686650971113281*^9}, { 3.686651007793332*^9, 3.6866511595335445`*^9}, {3.686651223513634*^9, 3.686651234033649*^9}, {3.686651304763748*^9, 3.6866513363837924`*^9}, { 3.6866514102038956`*^9, 3.686651429943923*^9}, {3.686652993837468*^9, 3.6866530046274834`*^9}, {3.686804398511652*^9, 3.6868044081516657`*^9}, { 3.6868046315619783`*^9, 3.686804631801979*^9}, {3.686804685872054*^9, 3.686804707092084*^9}, {3.6868047382021275`*^9, 3.686804767812169*^9}, { 3.686804824012248*^9, 3.6868048404922705`*^9}, {3.686804942142413*^9, 3.6868049633424425`*^9}, {3.6868050765526013`*^9, 3.686805101092636*^9}, { 3.6868051463526993`*^9, 3.6868052234228067`*^9}, {3.686805307602925*^9, 3.686805311682931*^9}, {3.68680577547358*^9, 3.686805788923599*^9}, { 3.686821702197342*^9, 3.6868217282873783`*^9}, {3.6868225192884855`*^9, 3.686822538368512*^9}, {3.6868226306886415`*^9, 3.6868226683086944`*^9}, { 3.6868227318887835`*^9, 3.6868227627088265`*^9}, {3.686822801638881*^9, 3.6868230490692277`*^9}, {3.686823122979331*^9, 3.6868231833294153`*^9}, { 3.6868232450595016`*^9, 3.6868233753996844`*^9}, {3.6868234153897405`*^9, 3.686823451379791*^9}, {3.6868236736101017`*^9, 3.6868236786601086`*^9}, { 3.6868237164601617`*^9, 3.68682375072021*^9}, {3.68682389396041*^9, 3.68682390087042*^9}, {3.686823940790476*^9, 3.6868239416904774`*^9}, { 3.6868239808805323`*^9, 3.6868239872905407`*^9}, {3.686824051540631*^9, 3.6868240519006314`*^9}, {3.686824360861064*^9, 3.6868243761510854`*^9}, { 3.6868245440213203`*^9, 3.686824577221367*^9}, {3.686824685841519*^9, 3.6868246979115357`*^9}, 3.6868248012716804`*^9, 3.6868253582724605`*^9, { 3.6868255183026843`*^9, 3.686825518932685*^9}, {3.6868264466639843`*^9, 3.6868264497139883`*^9}, {3.6868267792744493`*^9, 3.6868268152945004`*^9}, {3.686827100164899*^9, 3.6868271210549283`*^9}, 3.686827162004986*^9, {3.6868272414950967`*^9, 3.686827327475217*^9}, { 3.686827953126093*^9, 3.686827976506126*^9}, {3.686829128577739*^9, 3.686829138957753*^9}, 3.6868292410978966`*^9, {3.6868292768379464`*^9, 3.686829282727955*^9}, {3.6868293820380936`*^9, 3.686829418138144*^9}, { 3.686829846748744*^9, 3.686829848298746*^9}, {3.6868313063207874`*^9, 3.686831307180789*^9}, {3.6868331276633377`*^9, 3.68683328653356*^9}, { 3.6868394697195063`*^9, 3.6868394933895392`*^9}, 3.686839530999592*^9, { 3.686839582829664*^9, 3.68683963686974*^9}, {3.6868397551199055`*^9, 3.68683979365996*^9}, {3.6868398344600167`*^9, 3.686839866200061*^9}, { 3.687092084401948*^9, 3.687092117031994*^9}, {3.6870922598621936`*^9, 3.6870922645422*^9}, {3.6870962086478376`*^9, 3.6870962658779182`*^9}, 3.687096444838168*^9, {3.687096500978247*^9, 3.687096501638248*^9}, { 3.6870965809883595`*^9, 3.687096592708376*^9}, 3.687096837948719*^9, { 3.68709688890879*^9, 3.687096985798926*^9}, {3.6870971015990877`*^9, 3.6870972179192505`*^9}, {3.6870972618993125`*^9, 3.687097305639374*^9}, { 3.6870973356794157`*^9, 3.6870975186496716`*^9}, {3.6870975796097574`*^9, 3.6870975953197794`*^9}, {3.6870976531898603`*^9, 3.6870976848899045`*^9}, 3.6870977782500353`*^9, {3.687413757687042*^9, 3.6874137834070783`*^9}, { 3.6874140542074575`*^9, 3.687414094417514*^9}, {3.6874143478878684`*^9, 3.687414485538061*^9}, {3.6874146116082373`*^9, 3.68741464894829*^9}, { 3.6874147451084247`*^9, 3.687414766118454*^9}, 3.6874149094486547`*^9, { 3.6874150416688395`*^9, 3.6874150634888706`*^9}, {3.6874152437091227`*^9, 3.687415268869158*^9}, 3.6874153442892637`*^9, {3.687415449879411*^9, 3.687415469659439*^9}, 3.687415529739523*^9, 3.687415564789572*^9, 3.687415645529685*^9, {3.6874168016913037`*^9, 3.687416803441306*^9}, { 3.687421022677213*^9, 3.6874212686075573`*^9}, {3.68742948209425*^9, 3.6874294906842623`*^9}, {3.687844340668378*^9, 3.6878443698084188`*^9}, { 3.6886534778571014`*^9, 3.6886534911571198`*^9}, {3.688906380162199*^9, 3.6889064680223217`*^9}, {3.688906514222396*^9, 3.6889065193925257`*^9}, { 3.688908192623024*^9, 3.6889082006430354`*^9}, {3.688908261823121*^9, 3.688908271653135*^9}, {3.6889083776232834`*^9, 3.6889083922733035`*^9}, { 3.688908466073407*^9, 3.6889084993734536`*^9}, 3.688908533623502*^9, { 3.688908616683618*^9, 3.6889086271336327`*^9}, {3.6889086885637183`*^9, 3.6889087063437433`*^9}, {3.6889091647443852`*^9, 3.6889092012544365`*^9}, {3.6889093019045773`*^9, 3.6889093406746316`*^9}, 3.6889101071957045`*^9, {3.689905940063133*^9, 3.689905972983179*^9}, { 3.692530981927737*^9, 3.6925310416778207`*^9}, {3.692531099797902*^9, 3.6925311384779563`*^9}, {3.692531192258032*^9, 3.692531244668105*^9}, { 3.6925312919881716`*^9, 3.692531425418358*^9}, {3.6925315270885005`*^9, 3.692531643928664*^9}, {3.692535489534048*^9, 3.6925356485142703`*^9}, { 3.692535753564418*^9, 3.6925357992544813`*^9}, {3.6925358831745987`*^9, 3.692535899604622*^9}, {3.692536042584822*^9, 3.692536159384986*^9}, { 3.6925366121156197`*^9, 3.6925366207256317`*^9}, {3.6925367265057793`*^9, 3.69253672683578*^9}, {3.6925368590559654`*^9, 3.6925368636559715`*^9}, { 3.6925370880062857`*^9, 3.692537177856412*^9}, {3.692537322456614*^9, 3.6925373869767046`*^9}, {3.6925390913352747`*^9, 3.6925390925252767`*^9}, {3.692539644430175*^9, 3.6925396711502123`*^9}, { 3.692539727510291*^9, 3.692539730440295*^9}, {3.69253993367058*^9, 3.692539963780622*^9}, {3.6925400018406754`*^9, 3.692540003630678*^9}, { 3.6925401743409166`*^9, 3.6925401747509174`*^9}, {3.692540399111232*^9, 3.692540407981244*^9}, {3.69254047647134*^9, 3.6925404886113567`*^9}, { 3.6925406039715185`*^9, 3.69254060531152*^9}, {3.6925414948727655`*^9, 3.6925414953427663`*^9}, {3.6925415478528395`*^9, 3.692541613062931*^9}, 3.692541649332982*^9, {3.692541727633092*^9, 3.6925418840133104`*^9}, { 3.692541924473367*^9, 3.692542041693531*^9}, {3.6925421488836813`*^9, 3.6925422549438295`*^9}, {3.6925422976938896`*^9, 3.692542521444203*^9}, { 3.6925426221843443`*^9, 3.6925426357343626`*^9}, 3.692542739374508*^9, 3.692599799510878*^9, {3.692599834884901*^9, 3.6925998954663663`*^9}, { 3.692599925635092*^9, 3.6926000095928946`*^9}, {3.692600108929576*^9, 3.6926001456386757`*^9}, {3.6926001874800687`*^9, 3.692600454421337*^9}, { 3.692600503149027*^9, 3.6926006000391626`*^9}, {3.692600680251275*^9, 3.6926006814012766`*^9}, {3.6926009000215826`*^9, 3.6926009410816402`*^9}, 3.692601280532116*^9, {3.6926044914726114`*^9, 3.69260449774262*^9}, 3.6926045660127153`*^9, 3.6926046690228596`*^9, {3.69296647863291*^9, 3.6929664798829117`*^9}, {3.6929665643330297`*^9, 3.6929666141830997`*^9}, {3.6929670390036945`*^9, 3.6929670405536966`*^9}, {3.6929670861037607`*^9, 3.6929670952937737`*^9}, {3.6929671302538223`*^9, 3.6929671549438567`*^9}, {3.6929671904739065`*^9, 3.69296722137395*^9}, { 3.6929672596240034`*^9, 3.6929673352541094`*^9}, 3.6929678909232683`*^9, { 3.6930146982034283`*^9, 3.693014722713463*^9}, {3.6930148540136466`*^9, 3.693014857023651*^9}, {3.6930148913836985`*^9, 3.693014894823704*^9}, { 3.693014930903754*^9, 3.6930151942541227`*^9}, {3.693015247824198*^9, 3.693015430554454*^9}, {3.693015673794794*^9, 3.69301579223496*^9}, { 3.6930163123576884`*^9, 3.693016326897709*^9}, {3.6930164225678425`*^9, 3.693016429727853*^9}, {3.693016686718212*^9, 3.693016698128228*^9}, { 3.693016737038283*^9, 3.693016755068308*^9}, {3.6930168429225607`*^9, 3.6930168719926014`*^9}, {3.6930172049430676`*^9, 3.693017284063178*^9}, { 3.693017336433252*^9, 3.6930173662532935`*^9}, {3.6930180949163136`*^9, 3.6930180975563173`*^9}, {3.6930181870764427`*^9, 3.693018199956461*^9}, { 3.6930182954065943`*^9, 3.693018305996609*^9}, {3.693139886141657*^9, 3.6931399045016823`*^9}, {3.6931402916003532`*^9, 3.693140295770359*^9}, { 3.693140426020541*^9, 3.693140426530542*^9}, {3.6931410492237864`*^9, 3.6931410888738413`*^9}, {3.6931411194438844`*^9, 3.693141126553894*^9}, { 3.693141412004294*^9, 3.693141454164353*^9}, {3.6931415979955544`*^9, 3.6931417931758275`*^9}, {3.6932199559445915`*^9, 3.6932199772046213`*^9}, {3.6932201435748544`*^9, 3.693220170284892*^9}, { 3.693220713855653*^9, 3.693220721825664*^9}, {3.693625124589745*^9, 3.693625153729786*^9}, {3.6940907995669713`*^9, 3.6940909688872085`*^9}, { 3.6940913675677667`*^9, 3.6940914223978434`*^9}, {3.694091508037963*^9, 3.694091572118053*^9}, 3.694092009628666*^9, {3.6940920553287296`*^9, 3.694092229168973*^9}, {3.6940923053990793`*^9, 3.694092374419176*^9}, { 3.6940924537392874`*^9, 3.694092457789293*^9}, 3.694092642849552*^9, { 3.6940928573598523`*^9, 3.694092862379859*^9}, {3.6940945886222763`*^9, 3.694094601932295*^9}, 3.694094849542641*^9, {3.694095764293922*^9, 3.6940957644739223`*^9}, {3.6940960602743363`*^9, 3.6940960732243547`*^9}, {3.6940961211044216`*^9, 3.694096124194426*^9}, { 3.694665030960044*^9, 3.6946650634500895`*^9}, {3.6946652071402903`*^9, 3.6946653490404887`*^9}, {3.6946658702212186`*^9, 3.6946658881212435`*^9}, {3.694665923041292*^9, 3.694665953561335*^9}, { 3.694665995981395*^9, 3.6946660149414215`*^9}, {3.694666050571471*^9, 3.6946660547214766`*^9}, {3.694666169991638*^9, 3.694666292151809*^9}, { 3.6946663456618843`*^9, 3.6946663943919525`*^9}, 3.6946667526224537`*^9, 3.69466680700253*^9, 3.694687076625702*^9, {3.6946874316161985`*^9, 3.6946874621962414`*^9}, 3.694687499496294*^9, {3.694687567516389*^9, 3.694687642816495*^9}, {3.694687679006545*^9, 3.6946877198966026`*^9}, { 3.6946877714966745`*^9, 3.694687931746899*^9}, {3.723798739728607*^9, 3.723798744014243*^9}, {3.7237990126446104`*^9, 3.723799023974499*^9}, { 3.7244116671877546`*^9, 3.7244116733393917`*^9}, {3.724411761793063*^9, 3.7244117718753977`*^9}, {3.724411928386671*^9, 3.7244119682966137`*^9}, { 3.724412131847311*^9, 3.724412188341254*^9}, {3.729414981357122*^9, 3.7294149861075096`*^9}, {3.749817651293678*^9, 3.749817653108206*^9}, { 3.7498176831919456`*^9, 3.7498176846222315`*^9}, 3.7498177601545563`*^9, { 3.749817859674735*^9, 3.749817861044999*^9}, {3.7498179561547127`*^9, 3.749817964489929*^9}, {3.749818149334386*^9, 3.749818237397959*^9}, 3.749818617867873*^9, {3.7505621848002787`*^9, 3.7505622174085107`*^9}, { 3.75056238761455*^9, 3.750562431347901*^9}, {3.7505626332829456`*^9, 3.7505627331565337`*^9}, {3.7505627632642183`*^9, 3.7505627635859113`*^9}, {3.7515359581577415`*^9, 3.7515359614850826`*^9}, {3.751536071974715*^9, 3.7515360961721487`*^9}, 3.7515362040373974`*^9, {3.751536256080162*^9, 3.7515365099108534`*^9}, { 3.751549231137398*^9, 3.7515493334258356`*^9}, {3.7515496891619573`*^9, 3.751549689458767*^9}, {3.763384318028655*^9, 3.763384321230183*^9}, 3.7633844800900145`*^9, {3.7650666220235834`*^9, 3.765066676848461*^9}, { 3.7650667705927696`*^9, 3.765066781277461*^9}, {3.7650668220493402`*^9, 3.7650670769609847`*^9}, {3.765075343296377*^9, 3.765075345014902*^9}, { 3.765075479631569*^9, 3.7650755114191623`*^9}, {3.765075617307859*^9, 3.7650756180851874`*^9}, {3.76507585422694*^9, 3.765075872425325*^9}, { 3.7650760811750383`*^9, 3.7650762635610576`*^9}, {3.7650763100785646`*^9, 3.765076323109063*^9}, {3.7650763765120716`*^9, 3.765076385469493*^9}, { 3.7650764317497897`*^9, 3.7650764864127855`*^9}, 3.765076672990033*^9, { 3.7650767604139767`*^9, 3.7650767965644426`*^9}, {3.765076849411788*^9, 3.76507688334435*^9}, {3.765076928656023*^9, 3.7650769388747053`*^9}, 3.76507697239373*^9, {3.7650770147173185`*^9, 3.7650770820420313`*^9}, { 3.765077138264634*^9, 3.765077175747029*^9}, {3.765077340035742*^9, 3.765077493212038*^9}, {3.7650775254837503`*^9, 3.765077573524544*^9}, { 3.765077619369755*^9, 3.7650776808294816`*^9}, {3.765088266857733*^9, 3.765088281236836*^9}, {3.76508836959641*^9, 3.765088394392946*^9}, { 3.7650900504082956`*^9, 3.765090052695187*^9}, {3.7650900911122713`*^9, 3.765090094160341*^9}, {3.765090519594511*^9, 3.7650905411898503`*^9}, { 3.7885193337832556`*^9, 3.788519339935099*^9}, {3.788519391172593*^9, 3.7885194472501445`*^9}, {3.7885195529105897`*^9, 3.788519558251149*^9}, { 3.7885305232444134`*^9, 3.788530576893549*^9}, 3.788530695024667*^9, { 3.7885307280202837`*^9, 3.788530769626217*^9}, {3.7963483332994423`*^9, 3.796348466639106*^9}, {3.820027614612806*^9, 3.8200276304022093`*^9}, 3.8200276853924747`*^9, {3.829884589354769*^9, 3.8298846124571314`*^9}, { 3.8520843315211163`*^9, 3.8520844713778353`*^9}, {3.852084551874168*^9, 3.852084660898754*^9}}, CellLabel-> "In[162]:=",ExpressionUUID->"952ad393-ea79-4d42-b527-7582ac977961"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE", ",", "GG", ",", "\[Rho]\[Rho]", ",", "\[Kappa]\[Kappa]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE_", ",", "GG_", ",", "\[Rho]\[Rho]_", ",", "\[Kappa]\[Kappa]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "ix0", ",", "iz0", ",", "ux", ",", "uy", " ", ",", "uz", " ", ",", "\[Theta]x", " ", ",", "\[Theta]y", " ", ",", "\[Theta]z", " ", ",", "\[Delta]ux", " ", ",", "\[Delta]uy", ",", "\[Delta]uz", ",", "\[Delta]\[Theta]x", ",", "\[Delta]\[Theta]y", ",", "\[Delta]\[Theta]z", ",", "fx", ",", "fy", ",", "fz", ",", "mx", ",", "my", ",", "mz"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "mapping", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", " ", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz0", "=", RowBox[{"ix0", "\[Cross]", "iy0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"2", ",", "2"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"fx", "=", RowBox[{"ix0", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"fy", "=", RowBox[{"iy0", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"fz", "=", RowBox[{"iz0", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"mx", "=", RowBox[{"ix0", ".", RowBox[{"{", RowBox[{"mX", ",", "mY", ",", "mZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"my", "=", RowBox[{"iy0", ".", RowBox[{"{", RowBox[{"mX", ",", "mY", ",", "mZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"mz", "=", RowBox[{"iz0", ".", RowBox[{"{", RowBox[{"mX", ",", "mY", ",", "mZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"-", FractionBox["1", RowBox[{"420", " ", SuperscriptBox["h0", "3"]}]]}], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "210"}], " ", "fx", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"7", " ", RowBox[{"(", RowBox[{ RowBox[{"720", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"5", " ", "fz", " ", SuperscriptBox["h0", "5"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{"5", " ", "fy", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"6", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"h0", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"h0", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}], "-", RowBox[{"360", " ", "EE", " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"12", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], "-", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"5", " ", "GG", " ", "\[Kappa]\[Kappa]", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"10", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], "-", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"5", " ", "GG", " ", "\[Kappa]\[Kappa]", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"10", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"2", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"15", " ", "fz", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"15", " ", "mx", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{"\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"5", " ", "Izz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"5", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"5", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"4", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"4", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{"Izz", " ", "\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"4", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{"6", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "Iyy"}], " ", RowBox[{"(", RowBox[{ RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], "-", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], "-", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"10", " ", "my"}], "+", RowBox[{"Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}], "+", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"10", " ", "mz"}], "+", RowBox[{"Izz", " ", "\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}], "+", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"AA", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"420", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["h0", "2"], " ", "\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"70", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"ux", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{ RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"156", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"54", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"22", " ", "h0", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"13", " ", "h0", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}], "+", RowBox[{ RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"54", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"156", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"13", " ", "h0", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"22", " ", "h0", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}], "+", RowBox[{ RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"54", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"156", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"13", " ", "h0", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"22", " ", "h0", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}], "+", RowBox[{ RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"156", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"54", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"22", " ", "h0", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"13", " ", "h0", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}], "+", RowBox[{"h0", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "22"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"13", " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "13"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"22", " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"13", " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"22", " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"22", " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"13", " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{"h0", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"3", " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"4", " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"3", " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"4", " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}]}], "]"}]}], ";"}]}]], "Input", CellChangeTimes->{{3.4430689313272*^9, 3.4430690080792*^9}, { 3.4430690869528*^9, 3.4430691077320004`*^9}, {3.4430691700116*^9, 3.4430691708072*^9}, {3.4430692071717997`*^9, 3.443069246359*^9}, { 3.4430772782732*^9, 3.4430773623416*^9}, {3.4430773978316*^9, 3.4430774104676*^9}, {3.4430775053780003`*^9, 3.4430776180598*^9}, { 3.4434109099524*^9, 3.4434109159584*^9}, {3.4438800815346003`*^9, 3.4438802689304*^9}, {3.443880362624*^9, 3.4438803824516*^9}, { 3.443929565615374*^9, 3.443929570232974*^9}, {3.443935321321974*^9, 3.443935335705174*^9}, {3.443935419945174*^9, 3.443935421489574*^9}, { 3.443935494013974*^9, 3.443935494715974*^9}, {3.443935617565974*^9, 3.4439357217895737`*^9}, {3.443935755360774*^9, 3.443935816107174*^9}, { 3.443942155230774*^9, 3.443942209939974*^9}, {3.443942305710374*^9, 3.4439423142123737`*^9}, {3.4439442908131742`*^9, 3.443944441181574*^9}, { 3.4439447830065737`*^9, 3.4439447917425737`*^9}, {3.443944908541774*^9, 3.443944916060974*^9}, {3.4442731097938004`*^9, 3.4442731115254*^9}, { 3.444273189229*^9, 3.4442732700526*^9}, {3.4442748430004*^9, 3.4442748605036*^9}, {3.4442748977438*^9, 3.4442748989762*^9}, { 3.4442749340762*^9, 3.4442749351057997`*^9}, 3.4442752313382*^9, { 3.4442919702026*^9, 3.4442919911846*^9}, {3.4442921151577997`*^9, 3.4442921271074*^9}, {3.4443811023684*^9, 3.4443811036632*^9}, { 3.4443814073171997`*^9, 3.4443814402956*^9}, {3.4443815036316*^9, 3.4443815147855997`*^9}, {3.4443815537232*^9, 3.4443815747676*^9}, { 3.4443816138143997`*^9, 3.444381633174*^9}, {3.4443816850439997`*^9, 3.4443817801728*^9}, 3.4443853618688*^9, {3.4443855607376003`*^9, 3.4443856337924*^9}, {3.4443861200444*^9, 3.4443861523676*^9}, { 3.4443862280495996`*^9, 3.444386291448*^9}, {3.4443864047352*^9, 3.4443864135336*^9}, {3.4443870026832*^9, 3.4443870095316*^9}, { 3.4444082055056*^9, 3.4444082437412*^9}, {3.4444082797148*^9, 3.4444084583816*^9}, {3.4444084889108*^9, 3.4444085087539997`*^9}, { 3.444408942517*^9, 3.4444089563386*^9}, {3.4444091419564*^9, 3.4444091647167997`*^9}, {3.4444092206428003`*^9, 3.4444092944463997`*^9}, {3.4444093856284*^9, 3.4444094281071997`*^9}, { 3.4444094976988*^9, 3.4444095275104*^9}, {3.444409611064*^9, 3.4444096125772*^9}, 3.4444098504616003`*^9, {3.444409913392*^9, 3.4444099166056004`*^9}, 3.4444100178496*^9, {3.4444103063248*^9, 3.4444103358712*^9}, {3.4444103868208*^9, 3.4444104432460003`*^9}, { 3.4444921219564*^9, 3.4444921256224003`*^9}, {3.444492194824*^9, 3.4444921973668003`*^9}, {3.4444922814351997`*^9, 3.4444922853508*^9}, { 3.4444923330868*^9, 3.4444923345844*^9}, {3.444492366424*^9, 3.4444923855808*^9}, {3.4453153475226*^9, 3.445315360689*^9}, { 3.4465518166373653`*^9, 3.446551863016165*^9}, {3.446551894231765*^9, 3.446552159384965*^9}, {3.446552232377365*^9, 3.4465522555589647`*^9}, { 3.446553347388365*^9, 3.4465533616155653`*^9}, {3.4466058525769997`*^9, 3.4466058529046*^9}, {3.4466064371219997`*^9, 3.4466065097244*^9}, { 3.4466127725788*^9, 3.4466127766036*^9}, {3.4466128124835997`*^9, 3.4466130037864*^9}, {3.4466131532696*^9, 3.4466131761703997`*^9}, { 3.4466133992192*^9, 3.4466134478756*^9}, {3.446613483584*^9, 3.4466134932092*^9}, {3.4466135740952*^9, 3.4466135794927998`*^9}, { 3.4466137283948*^9, 3.4466137341356*^9}, {3.4466138994342003`*^9, 3.4466139023826*^9}, {3.4466139549858*^9, 3.4466139579653997`*^9}, { 3.4466142109818*^9, 3.4466142245226*^9}, {3.4466142793878*^9, 3.4466143652033997`*^9}, {3.4466144712834*^9, 3.4466145978929996`*^9}, { 3.4466146992618*^9, 3.4466147509914*^9}, {3.4466151283086*^9, 3.4466152768986*^9}, {3.4466153107506*^9, 3.4466153406558*^9}, { 3.4466194331976*^9, 3.4466194377528*^9}, {3.4466194847712*^9, 3.446619488718*^9}, {3.4466389495861998`*^9, 3.4466389768238*^9}, { 3.4466391218414*^9, 3.446639306561*^9}, {3.4466393990222*^9, 3.4466394004886*^9}, {3.4466394475694*^9, 3.4466394487706003`*^9}, { 3.4466395034174*^9, 3.4466395049462*^9}, 3.4466395515755997`*^9, { 3.4466396000176*^9, 3.4466396190808*^9}, {3.4466397459088*^9, 3.446639748826*^9}, {3.4466397974356003`*^9, 3.446639798668*^9}, 3.4466398447816*^9, {3.446639894218*^9, 3.4466399201556*^9}, { 3.4466399570964003`*^9, 3.4466399583288*^9}, {3.446639994006*^9, 3.4466400056904*^9}, {3.4466400383568*^9, 3.4466400395892*^9}, { 3.4466400745643997`*^9, 3.4466401025976*^9}, {3.4466401660834*^9, 3.4466401806070004`*^9}, {3.4466402251294003`*^9, 3.446640227407*^9}, { 3.446640260479*^9, 3.4466402657674*^9}, {3.4466404133122*^9, 3.4466405185654*^9}, 3.4466405830462*^9, {3.4467273294214*^9, 3.4467273777813997`*^9}, {3.4467274366558*^9, 3.4467275620954*^9}, { 3.446727593311*^9, 3.4467277412614*^9}, {3.4467283334639997`*^9, 3.4467283356012*^9}, {3.4467283707636003`*^9, 3.4467283727604*^9}, { 3.4467289882664003`*^9, 3.4467291276836*^9}, {3.446778464322*^9, 3.4467786797424*^9}, {3.4467801953803997`*^9, 3.4467802409792*^9}, { 3.4467802998691998`*^9, 3.4467804023456*^9}, 3.4467804345596*^9, { 3.4467808656344*^9, 3.4467808670852003`*^9}, 3.4467818107525997`*^9, { 3.446781855509*^9, 3.446781874385*^9}, {3.4467826737914*^9, 3.4467827381726*^9}, {3.4467828623018*^9, 3.4467831045386*^9}, { 3.4470344113984003`*^9, 3.4470344123344*^9}, {3.4470344628316*^9, 3.4470345343108*^9}, {3.447043591118539*^9, 3.447043642192939*^9}, { 3.447045649625739*^9, 3.447045718437339*^9}, {3.447054774023939*^9, 3.447054834198939*^9}, {3.4470549103449388`*^9, 3.4470549116169386`*^9}, { 3.447054943902939*^9, 3.4470553027109385`*^9}, {3.447055334559939*^9, 3.447055353684939*^9}, {3.447057311918539*^9, 3.447057369747739*^9}, { 3.4470575058577385`*^9, 3.4470575951365385`*^9}, {3.4470581848789387`*^9, 3.4470582040825386`*^9}, {3.451276121243*^9, 3.4512761425838003`*^9}, { 3.4512762022382*^9, 3.4512762064346*^9}, {3.4512762476966*^9, 3.4512762827654*^9}, {3.451276489091*^9, 3.451276541975*^9}, { 3.4512765853118*^9, 3.4512766132046003`*^9}, {3.4512773470306*^9, 3.4512773766082*^9}, {3.4512776069110003`*^9, 3.4512777499318*^9}, 3.4512777831286*^9, {3.4512778785538*^9, 3.451277881627*^9}, { 3.4512780242734003`*^9, 3.4512780302794*^9}, 3.4512780737878*^9, { 3.4512781866226*^9, 3.4512781930810003`*^9}, {3.4512863325078*^9, 3.4512863539266*^9}, {3.4568019250434*^9, 3.4568022712698*^9}, { 3.4568023177422*^9, 3.4568024125278*^9}, {3.4568024694365997`*^9, 3.4568024750369997`*^9}, {3.4568026914402*^9, 3.4568028101094*^9}, { 3.4568028406698*^9, 3.4568028564726*^9}, 3.4568028886085997`*^9, { 3.4568030489454*^9, 3.4568030800986*^9}, 3.4568032004128*^9, { 3.4568035073698*^9, 3.4568035176034*^9}, {3.4568040146596003`*^9, 3.4568040844852*^9}, {3.4568043016684*^9, 3.4568043154744*^9}, { 3.4568045482264*^9, 3.4568045486632*^9}, {3.4568048944996*^9, 3.4568049806116*^9}, {3.4660560628582*^9, 3.4660560753538*^9}, { 3.4660676729379997`*^9, 3.4660676735931997`*^9}, {3.4660677244024*^9, 3.4660677277251997`*^9}, {3.4742646771287394`*^9, 3.47426469439174*^9}, { 3.47426489921974*^9, 3.4742649800437393`*^9}, {3.4801246373348*^9, 3.4801246860536003`*^9}, {3.4801247748176003`*^9, 3.4801247821028*^9}, { 3.4801248161264*^9, 3.4801248295736*^9}, {3.4801248810692*^9, 3.4801248964508*^9}, {3.4801249330484*^9, 3.480124947884*^9}, 3.4801249886468*^9, {3.4801251139147997`*^9, 3.48012512588*^9}, { 3.4838339444988003`*^9, 3.4838339567448*^9}, 3.4838341692012*^9, { 3.4838344350408*^9, 3.4838344353684*^9}, {3.4938987575920324`*^9, 3.4938987586840324`*^9}, {3.4941630624049997`*^9, 3.4941631381274*^9}, { 3.4941632311345997`*^9, 3.4941632492306004`*^9}, 3.4941633249217997`*^9, { 3.4941633940922003`*^9, 3.4941634063538*^9}, {3.4941634538402*^9, 3.4941635051642*^9}, {3.494163565115*^9, 3.4941636341762*^9}, { 3.4941636853442*^9, 3.4941639323234*^9}, {3.4941640277798*^9, 3.4941641455754004`*^9}, {3.4941641790374002`*^9, 3.4941641803789997`*^9}, {3.4941642676142*^9, 3.4941643277678003`*^9}, 3.4941644677018003`*^9, {3.4941646208938*^9, 3.4941646322349997`*^9}, { 3.4941652592693996`*^9, 3.4941652807194*^9}, {3.4941653119038*^9, 3.494165416299*^9}, {3.494165453895*^9, 3.4941654544722*^9}, { 3.4950990979779997`*^9, 3.495099142701*^9}, {3.495099172958*^9, 3.4950991806289997`*^9}, {3.495099227097*^9, 3.495099238113*^9}, 3.495099290797*^9, {3.495099346084*^9, 3.495099359507*^9}, { 3.495099456308*^9, 3.495099464091*^9}, 3.495099683108*^9, { 3.495100428112*^9, 3.495100434958*^9}, {3.4951006496219997`*^9, 3.495100649992*^9}, {3.4987235265018*^9, 3.4987235939094*^9}, { 3.4987236420666*^9, 3.4987236530646*^9}, {3.4987237305341997`*^9, 3.4987237396914*^9}, {3.498733136159*^9, 3.4987332972446003`*^9}, { 3.4987364783094*^9, 3.4987364860626*^9}, {3.4987366201134*^9, 3.4987366236078*^9}, {3.4987367272386*^9, 3.4987367464890003`*^9}, { 3.4987369428462*^9, 3.4987369670886*^9}, {3.4987370134518003`*^9, 3.4987370259941998`*^9}, {3.4987370944002*^9, 3.4987371027618*^9}, { 3.4987371921029997`*^9, 3.498737193663*^9}, {3.4987372660938*^9, 3.4987372935498*^9}, {3.4987373290554*^9, 3.4987377176202*^9}, { 3.4987377520182*^9, 3.4987379139462*^9}, {3.4987382030216*^9, 3.4987382667078*^9}, {3.4987888391818*^9, 3.4987888608346*^9}, { 3.4988785131146*^9, 3.4988785160162*^9}, {3.5007170967096*^9, 3.5007170999076*^9}, 3.5007182237316*^9, {3.5007182772864*^9, 3.5007182987832003`*^9}, {3.5009573226744003`*^9, 3.5009573940444*^9}, 3.5009574358710003`*^9, 3.5009604278482*^9, {3.5009897246173353`*^9, 3.5009898480289354`*^9}, {3.5009901464413357`*^9, 3.5009901475333357`*^9}, {3.5009901801997356`*^9, 3.500990274096135*^9}, { 3.5010475253292*^9, 3.5010475852332*^9}, {3.5010605722018003`*^9, 3.5010606739762*^9}, {3.5010607202146*^9, 3.5010607323358*^9}, { 3.5010607920526*^9, 3.501061118467*^9}, {3.5010612022078*^9, 3.5010612277138*^9}, {3.5010616467766*^9, 3.5010617938534*^9}, { 3.5010618406222*^9, 3.5010619950778*^9}, {3.5010621500638*^9, 3.5010622514014*^9}, {3.5010625292218*^9, 3.5010625409374*^9}, { 3.5010626043046*^9, 3.5010626313862*^9}, {3.5010626787166*^9, 3.5010626790754004`*^9}, {3.501074457561*^9, 3.5010744671082*^9}, 3.5010763029458*^9, {3.5032210899309998`*^9, 3.5032212413900003`*^9}, { 3.557658203404973*^9, 3.557658219644601*^9}, {3.5576584433801947`*^9, 3.557658496030287*^9}, {3.5576585501779823`*^9, 3.5576586046064777`*^9}, { 3.557658648910555*^9, 3.557658754600741*^9}, {3.557658963945511*^9, 3.5576589782507353`*^9}, {3.557659009949991*^9, 3.5576591437514267`*^9}, { 3.557659182221094*^9, 3.5576592187719584`*^9}, 3.557659413865901*^9, { 3.557659921100792*^9, 3.5576599556392527`*^9}, {3.557660706920972*^9, 3.5576607248454037`*^9}, {3.557661209085854*^9, 3.557661209413454*^9}, { 3.5577526651911488`*^9, 3.5577526932087984`*^9}, {3.5577527272480583`*^9, 3.557752747122493*^9}, {3.5577528374934516`*^9, 3.557752838523053*^9}, { 3.557752881204728*^9, 3.557752891313546*^9}, {3.557752938612829*^9, 3.5577529469120436`*^9}, {3.557753060714244*^9, 3.557753062633047*^9}, { 3.5577536609544907`*^9, 3.5577536637936954`*^9}, {3.5577537824631042`*^9, 3.557753810184353*^9}, {3.557753841025607*^9, 3.5577540648392*^9}, 3.5577541920574236`*^9, {3.5577547033327217`*^9, 3.557754716967146*^9}, { 3.5577547716296415`*^9, 3.557754802112095*^9}, {3.5577549509363565`*^9, 3.5577549771444025`*^9}, 3.5577551382302856`*^9, {3.55775527184452*^9, 3.557755272858522*^9}, {3.557755881555991*^9, 3.557755886548*^9}, { 3.557756158316077*^9, 3.557756231885806*^9}, {3.5577572408487787`*^9, 3.557757248835993*^9}, {3.5577572834368534`*^9, 3.5577575888229895`*^9}, { 3.5577578129641833`*^9, 3.557757862837471*^9}, {3.557758025514557*^9, 3.557758079272251*^9}, 3.557810586960072*^9, {3.5578240262005973`*^9, 3.5578240345360737`*^9}, {3.557824091429328*^9, 3.5578241008156557`*^9}, { 3.557831525255726*^9, 3.5578315319793377`*^9}, 3.5578315716190076`*^9, { 3.557831606079468*^9, 3.557831629432709*^9}, {3.5578316663267736`*^9, 3.5578317569473333`*^9}, {3.5578322144181366`*^9, 3.557832218084143*^9}, { 3.557836356693412*^9, 3.557836473771618*^9}, {3.5578365201660995`*^9, 3.5578365974018345`*^9}, {3.5578366426731143`*^9, 3.557836658865943*^9}, { 3.557836691017599*^9, 3.5578367924957776`*^9}, {3.5578368305442443`*^9, 3.557836888279946*^9}, {3.5578369382156334`*^9, 3.5578370776642785`*^9}, { 3.5578383536061196`*^9, 3.5578383735117545`*^9}, {3.5578385892445335`*^9, 3.5578385978869486`*^9}, {3.5578386713006773`*^9, 3.557838700113928*^9}, { 3.5578387451200075`*^9, 3.5578387467892103`*^9}, {3.5578388951454706`*^9, 3.5578389248635225`*^9}, {3.5578389679351983`*^9, 3.557838983535226*^9}, { 3.5578390227692947`*^9, 3.557839023143696*^9}, {3.557839097696226*^9, 3.5578391125162525`*^9}, {3.5578391553539276`*^9, 3.557839199892006*^9}, { 3.55783924184048*^9, 3.557839294490572*^9}, {3.5578393285922318`*^9, 3.557839398683155*^9}, {3.557839430522811*^9, 3.557839470162481*^9}, { 3.5578395370865984`*^9, 3.5578395446994114`*^9}, {3.5578396068499207`*^9, 3.5578396118575296`*^9}, 3.5578943518105097`*^9, {3.557894388361374*^9, 3.5578944029629993`*^9}, {3.5578944607611012`*^9, 3.5578944989499683`*^9}, {3.5578945393696394`*^9, 3.557894561537278*^9}, { 3.5578946028617506`*^9, 3.5578946188985786`*^9}, {3.557894650894235*^9, 3.5578947812636642`*^9}, {3.55789481884413*^9, 3.5578948191249304`*^9}, { 3.5578949768100076`*^9, 3.5578949836272197`*^9}, {3.5578967386805477`*^9, 3.55789678549623*^9}, {3.5578968804691963`*^9, 3.557896888643611*^9}, { 3.557897022491846*^9, 3.5578970341450663`*^9}, {3.557897620940097*^9, 3.55789765120415*^9}, {3.5579218072271147`*^9, 3.5579218263059483`*^9}, { 3.557922095312821*^9, 3.557922116965659*^9}, {3.557922178086566*^9, 3.557922188616585*^9}, {3.5579223258812256`*^9, 3.557922327066828*^9}, { 3.5579224596046605`*^9, 3.557922461804264*^9}, 3.5579805928465395`*^9, { 3.5579815200581703`*^9, 3.557981541711009*^9}, 3.557985544779242*^9, { 3.5579863164793987`*^9, 3.5579863339514294`*^9}, {3.557986523210962*^9, 3.557986568841042*^9}, 3.5579866122559185`*^9, 3.557986993536188*^9, { 3.5579871244716187`*^9, 3.5579871290580263`*^9}, 3.557987173486905*^9, 3.5579872166989803`*^9, {3.5599618621582537`*^9, 3.5599618642486577`*^9}, { 3.559961969720443*^9, 3.5599619894700775`*^9}, 3.559963611089726*^9, { 3.5601298891258235`*^9, 3.560129889422224*^9}, {3.560132445157113*^9, 3.5601324458591146`*^9}, {3.561978472080926*^9, 3.561978472392926*^9}, { 3.6297802564412937`*^9, 3.6297802957377625`*^9}, {3.62978033369263*^9, 3.629780429741998*^9}, {3.6297805790030603`*^9, 3.6297809429048996`*^9}, { 3.629780987957779*^9, 3.629781197575347*^9}, {3.629781240397422*^9, 3.629781337663593*^9}, {3.6297813946972933`*^9, 3.6297814529165955`*^9}, { 3.6297814952550697`*^9, 3.629781527578326*^9}, {3.62978162025529*^9, 3.629781647633338*^9}, {3.629781678833393*^9, 3.629781763120341*^9}, 3.6297818028224106`*^9, {3.6297818432108817`*^9, 3.629781872570133*^9}, { 3.629782355765382*^9, 3.629782427603508*^9}, {3.6297824692243814`*^9, 3.629782674863942*^9}, {3.629782707218399*^9, 3.6297829295343895`*^9}, { 3.629783005631323*^9, 3.6297830574702144`*^9}, {3.6297831098551064`*^9, 3.629783142786764*^9}, {3.629783433711675*^9, 3.629783442619291*^9}, { 3.6297834942397814`*^9, 3.6297835175930223`*^9}, 3.6297835794939313`*^9, { 3.6297836160291953`*^9, 3.6297837668970604`*^9}, {3.6297842042438283`*^9, 3.6297842697483435`*^9}, {3.6297843514456873`*^9, 3.629784370742921*^9}, { 3.629784443829049*^9, 3.6297844678842916`*^9}, {3.6297845252611923`*^9, 3.629784525588793*^9}, {3.6297846136821475`*^9, 3.629784629235375*^9}, { 3.629784814797701*^9, 3.629784927648299*^9}, {3.629785259960083*^9, 3.6297852602096834`*^9}, {3.6297858780175686`*^9, 3.629785917282837*^9}, { 3.629786048057867*^9, 3.629786048681868*^9}, 3.6297863278755584`*^9, { 3.6297867047133856`*^9, 3.629786748533863*^9}, {3.6297867791567163`*^9, 3.6297868491540394`*^9}, {3.6297875320748396`*^9, 3.629787569795706*^9}, { 3.6297876247234025`*^9, 3.6297877281983843`*^9}, {3.6297877681812544`*^9, 3.629787774015665*^9}, {3.629787831408166*^9, 3.6297878355265727`*^9}, { 3.6297878775686464`*^9, 3.6297878861174617`*^9}, {3.6297879185343184`*^9, 3.629787919064719*^9}, {3.6297880043032694`*^9, 3.62978800470887*^9}, 3.6297880488257475`*^9, {3.6297882100052304`*^9, 3.6297882174776435`*^9}, { 3.6297882697533355`*^9, 3.6297882948381796`*^9}, {3.6297883467550707`*^9, 3.6297883991087627`*^9}, {3.6297887361785545`*^9, 3.629788783961438*^9}, 3.629788825395111*^9, {3.629789006152629*^9, 3.6297890321266747`*^9}, { 3.6297891133248167`*^9, 3.629789145336073*^9}, {3.6297891926821566`*^9, 3.629789194257759*^9}, {3.629789255316266*^9, 3.6297892556282673`*^9}, { 3.629869102295367*^9, 3.629869160124668*^9}, {3.6298691942887287`*^9, 3.6298696149902673`*^9}, {3.6298696993864155`*^9, 3.62986975897852*^9}, { 3.6298698387726603`*^9, 3.629869912030389*^9}, {3.6298700722270703`*^9, 3.629870234560955*^9}, {3.629870580429163*^9, 3.629870630458451*^9}, { 3.630556081081209*^9, 3.630556104902451*^9}, {3.6305562643503313`*^9, 3.6305562763935523`*^9}, {3.6305563415080667`*^9, 3.630556480956712*^9}, { 3.630556692851884*^9, 3.630556695347888*^9}, {3.630556730042349*^9, 3.630556914528273*^9}, {3.6305653725974936`*^9, 3.6305656807121167`*^9}, { 3.630565758760581*^9, 3.6305657739024467`*^9}, {3.630565858170267*^9, 3.63056596644846*^9}, {3.6305661502619734`*^9, 3.6305661523230915`*^9}, { 3.6305662653385553`*^9, 3.630566370352562*^9}, {3.6305667786019125`*^9, 3.630566790535595*^9}, {3.6305668214773645`*^9, 3.630567044691132*^9}, { 3.6305670772499943`*^9, 3.6305670783710585`*^9}, 3.630567272031135*^9, { 3.630567303902958*^9, 3.630567409875019*^9}, {3.630568671196477*^9, 3.6305687195002403`*^9}, {3.6305687542132254`*^9, 3.630568758623478*^9}, { 3.630568855671028*^9, 3.630568859250233*^9}, {3.630569706514694*^9, 3.630569775526641*^9}, 3.630569982346471*^9, {3.6305701679130845`*^9, 3.630570205199217*^9}, {3.6305703751399374`*^9, 3.630570526177576*^9}, { 3.630587657039589*^9, 3.630587688367381*^9}, {3.6305880733027773`*^9, 3.6305883365376396`*^9}, {3.6305886689118233`*^9, 3.6305886717978287`*^9}, 3.6305889776831656`*^9, {3.6305890389444733`*^9, 3.6305890437180815`*^9}, { 3.630589093248169*^9, 3.6305891296430326`*^9}, 3.630589181700324*^9, { 3.6305892509956455`*^9, 3.6305892594820604`*^9}, {3.630589318949365*^9, 3.6305893334729905`*^9}, {3.630589630294712*^9, 3.6305896376267247`*^9}, { 3.630589683288005*^9, 3.630589684988408*^9}, {3.630597310538067*^9, 3.630597340080757*^9}, {3.630597391446695*^9, 3.630597400596218*^9}, { 3.6305974350611897`*^9, 3.6305974605306463`*^9}, {3.630633997622449*^9, 3.630634003125764*^9}, {3.630659322217756*^9, 3.63065932438616*^9}, { 3.6306611578252783`*^9, 3.6306611625988865`*^9}, {3.6306612541554475`*^9, 3.630661257587454*^9}, {3.6306613001287284`*^9, 3.6306613026715326`*^9}, { 3.6306613920752897`*^9, 3.6306613949768953`*^9}, {3.6306706377509866`*^9, 3.630670654957817*^9}, {3.6306749981919994`*^9, 3.630675005793434*^9}, { 3.6306751229631357`*^9, 3.630675150017683*^9}, {3.6306752035287437`*^9, 3.6306752096180925`*^9}, {3.630675315921172*^9, 3.6306753201514144`*^9}, { 3.6306757793287754`*^9, 3.6306757796257925`*^9}, {3.630675814406262*^9, 3.6306758147026625`*^9}, {3.6306760107574763`*^9, 3.6306760154417443`*^9}, {3.6306789722320743`*^9, 3.6306789870309205`*^9}, {3.6306790257051325`*^9, 3.630679028076268*^9}, { 3.6306800259177256`*^9, 3.6306800406129513`*^9}, {3.6306801239326982`*^9, 3.6306801300167084`*^9}, {3.630680769261832*^9, 3.6306807806186523`*^9}, { 3.630681157468514*^9, 3.6306811577649145`*^9}, {3.6306812744219193`*^9, 3.63068127471832*^9}, {3.6306817187418995`*^9, 3.6306817919060287`*^9}, { 3.630681879188182*^9, 3.6306819111526375`*^9}, {3.6306821191790032`*^9, 3.6306821283050194`*^9}, {3.630720543651497*^9, 3.6307205534300566`*^9}, { 3.630721035525631*^9, 3.630721092774905*^9}, {3.6307212510439577`*^9, 3.6307213064777765`*^9}, {3.6307477437169704`*^9, 3.6307478284095197`*^9}, {3.6307478614971776`*^9, 3.6307478785948076`*^9}, {3.6307479884814005`*^9, 3.630748002880226*^9}, { 3.630748045624301*^9, 3.630748063876333*^9}, {3.630748111596817*^9, 3.6307481498324842`*^9}, {3.6307489182430334`*^9, 3.6307489447786803`*^9}, {3.630749037427243*^9, 3.6307490443848553`*^9}, { 3.6307491041485605`*^9, 3.6307491384218206`*^9}, {3.6307491914151134`*^9, 3.630749196890723*^9}, {3.6307492445800066`*^9, 3.6307493439989815`*^9}, { 3.630749396212273*^9, 3.6307494766304145`*^9}, {3.6307495333989143`*^9, 3.6307495547241516`*^9}, {3.6307496525831237`*^9, 3.630749669571553*^9}, { 3.630750220602922*^9, 3.6307502881822405`*^9}, {3.6307510631916018`*^9, 3.630751068292811*^9}, {3.6307511226589065`*^9, 3.630751137962533*^9}, { 3.6307512555243397`*^9, 3.630751282777588*^9}, {3.630752266971757*^9, 3.630752414599744*^9}, {3.630752446407563*^9, 3.630752457388191*^9}, { 3.6307589380050273`*^9, 3.6307590266300964`*^9}, {3.6307591666721067`*^9, 3.63075923229886*^9}, 3.630760288282259*^9, {3.6307603547370596`*^9, 3.630760557414652*^9}, {3.630760654134184*^9, 3.63076065510824*^9}, { 3.6307606911683025`*^9, 3.6307606919283457`*^9}, {3.6307607642334814`*^9, 3.6307607648645177`*^9}, {3.630761455000991*^9, 3.6307614616743727`*^9}, { 3.630761507825012*^9, 3.630761605776615*^9}, {3.630761652999316*^9, 3.630761695865768*^9}, {3.630761771278081*^9, 3.6307617792215357`*^9}, 3.6307629478424797`*^9, {3.632205207880766*^9, 3.6322052561155243`*^9}, { 3.6322052892474194`*^9, 3.6322052915745525`*^9}, 3.6322053746993074`*^9, { 3.6322062705415463`*^9, 3.6322062726016645`*^9}, {3.6322063396935015`*^9, 3.63220636484194*^9}, {3.6322064410612993`*^9, 3.6322064491667633`*^9}, { 3.632206580308264*^9, 3.6322066373275256`*^9}, {3.6322066736436024`*^9, 3.6322067467737856`*^9}, {3.632206782260815*^9, 3.6322071351279984`*^9}, 3.6322071989226465`*^9, {3.632207270393735*^9, 3.6322073359894867`*^9}, { 3.6322073997741346`*^9, 3.6322074126708727`*^9}, {3.632207491777397*^9, 3.632207682289294*^9}, {3.632207809621577*^9, 3.632207827973626*^9}, { 3.6322079043859973`*^9, 3.6322079279443445`*^9}, {3.6322080916397076`*^9, 3.6322081666649985`*^9}, 3.634905258940913*^9, {3.634905370524296*^9, 3.6349054089004903`*^9}, {3.6349054472556844`*^9, 3.63490544787272*^9}, { 3.634905483492757*^9, 3.6349055164646425`*^9}, {3.634905574352954*^9, 3.634905628121029*^9}, {3.6349057012822137`*^9, 3.6349057207913294`*^9}, { 3.6349061371061416`*^9, 3.634906354438572*^9}, {3.6349063890455513`*^9, 3.6349064369332905`*^9}, {3.634906537696054*^9, 3.634906601859724*^9}, 3.634906706128688*^9, {3.6349069249442034`*^9, 3.6349069328326545`*^9}, { 3.6349070151973653`*^9, 3.6349070242298822`*^9}, {3.6349070817921743`*^9, 3.6349070822111983`*^9}, {3.634907723288866*^9, 3.634907739005765*^9}, { 3.6349079580732946`*^9, 3.6349079868219395`*^9}, {3.634908200284148*^9, 3.634908315195721*^9}, {3.6349083774582825`*^9, 3.6349084027997313`*^9}, { 3.63490844507615*^9, 3.634908448843365*^9}, {3.634914956333157*^9, 3.634915020054802*^9}, {3.634915050572547*^9, 3.6349150956171236`*^9}, { 3.6349539785771523`*^9, 3.634953978975175*^9}, {3.6349540728785458`*^9, 3.6349541681829967`*^9}, {3.634954211263461*^9, 3.6349542495746527`*^9}, { 3.6349543251259737`*^9, 3.634954355882733*^9}, {3.6349543892536416`*^9, 3.6349544742835045`*^9}, {3.634954547519694*^9, 3.6349545640246377`*^9}, { 3.6349547051657104`*^9, 3.6349547107930326`*^9}, {3.634954745355009*^9, 3.634954752101395*^9}, {3.6349547948858423`*^9, 3.6349548053894434`*^9}, { 3.634954904907135*^9, 3.6349549451084347`*^9}, {3.634955219605135*^9, 3.6349552640926795`*^9}, {3.634955320189888*^9, 3.634955348763522*^9}, { 3.634955386393675*^9, 3.6349555039273973`*^9}, {3.6349557669644423`*^9, 3.6349557672004557`*^9}, {3.634955894841756*^9, 3.634955902578199*^9}, { 3.6349559513739896`*^9, 3.6349560216320086`*^9}, {3.634956120144643*^9, 3.634956128996149*^9}, {3.6349561700724983`*^9, 3.6349561978900895`*^9}, { 3.6349562480719595`*^9, 3.634956254326318*^9}, {3.634956331684742*^9, 3.6349563460575643`*^9}, {3.634956379242462*^9, 3.63495642676418*^9}, 3.6349564696636343`*^9, {3.6351524116477795`*^9, 3.6351524153379908`*^9}, { 3.6352134400282927`*^9, 3.635213442148414*^9}, {3.6352134745862694`*^9, 3.635213495869487*^9}, {3.6352135383409157`*^9, 3.6352137157160616`*^9}, { 3.6352137493569856`*^9, 3.635213764522853*^9}, {3.635214215036621*^9, 3.635214227593339*^9}, {3.635214407257615*^9, 3.63521441713218*^9}, { 3.635215297101512*^9, 3.635215303964904*^9}, {3.6352154111120324`*^9, 3.635215431504199*^9}, {3.635216346055508*^9, 3.635216494371991*^9}, { 3.635216631050809*^9, 3.6352166603244834`*^9}, {3.635216763034358*^9, 3.635216764164423*^9}, {3.6352168771938877`*^9, 3.635216888828553*^9}, 3.6352169832479534`*^9, 3.635217037668066*^9, {3.6352172024924936`*^9, 3.6352172054526625`*^9}, {3.635217344025589*^9, 3.635217346898753*^9}, 3.6352173863770113`*^9, {3.635217519639633*^9, 3.6352175507014103`*^9}, 3.635217615445113*^9, {3.6352178715087595`*^9, 3.635217880460271*^9}, { 3.6352185912849283`*^9, 3.635218598444338*^9}, {3.6352186995721216`*^9, 3.635218714955002*^9}, {3.6352189761749425`*^9, 3.6352189789341*^9}, { 3.6352195060322485`*^9, 3.635219509972474*^9}, 3.6352195673477554`*^9, 3.6352195994635925`*^9, {3.6352197336482677`*^9, 3.635219737452485*^9}, { 3.6352197706093817`*^9, 3.6352197723214793`*^9}, {3.635219941784172*^9, 3.6352199485115566`*^9}, {3.6352200714185867`*^9, 3.6352200854323883`*^9}, {3.6352202085694313`*^9, 3.635220235849992*^9}, { 3.6352202816336107`*^9, 3.6352203110962954`*^9}, {3.6352204980449886`*^9, 3.6352205276526823`*^9}, {3.6352253191447396`*^9, 3.6352253299913597`*^9}, {3.6352253611111403`*^9, 3.6352253637572913`*^9}, {3.635225409322898*^9, 3.6352255965196047`*^9}, { 3.6352260914249115`*^9, 3.6352261698393965`*^9}, {3.63522638233055*^9, 3.6352264188036366`*^9}, {3.635227493469104*^9, 3.635227556935734*^9}, { 3.6352276745764627`*^9, 3.635227730116639*^9}, {3.6352287979917183`*^9, 3.6352288587651944`*^9}, {3.635228894237223*^9, 3.635228948324317*^9}, { 3.635229365252164*^9, 3.6352293902275925`*^9}, {3.63522947690555*^9, 3.6352294807837715`*^9}, {3.6352492831123204`*^9, 3.6352492983621926`*^9}, 3.6356569054520617`*^9, {3.6363778004499054`*^9, 3.636377802787039*^9}, { 3.6363778414932528`*^9, 3.6363778525308843`*^9}, {3.636384436335312*^9, 3.6363846409950175`*^9}, {3.636384971250907*^9, 3.6363849738080535`*^9}, { 3.6363850170465264`*^9, 3.636385030729309*^9}, {3.6363851286779118`*^9, 3.636385138359465*^9}, {3.6363851699712734`*^9, 3.636385223111313*^9}, { 3.656076172452749*^9, 3.656076182171566*^9}, {3.6560765578514256`*^9, 3.656076619019133*^9}, 3.6560772545486493`*^9, {3.6630719749029694`*^9, 3.6630719878027077`*^9}, {3.6630720702554235`*^9, 3.6630720807290225`*^9}, {3.6630721155740156`*^9, 3.6630721713712068`*^9}, {3.663072270834896*^9, 3.6630722882218904`*^9}, 3.6630724099968557`*^9, {3.685234767958906*^9, 3.685234768480936*^9}, { 3.685252204033695*^9, 3.6852522340537376`*^9}, {3.6852522757137957`*^9, 3.6852523115138454`*^9}, {3.68525376314359*^9, 3.6852537725041256`*^9}, { 3.6852539763277836`*^9, 3.6852539861693463`*^9}, 3.6852540682470407`*^9, 3.6852541660656357`*^9, {3.6852604801645336`*^9, 3.6852605060345697`*^9}, { 3.6852605373446136`*^9, 3.6852605977846985`*^9}, 3.685260655254779*^9, { 3.6853280002218475`*^9, 3.685328019561875*^9}, 3.685328064721938*^9, { 3.6853280953119807`*^9, 3.6853282636022167`*^9}, {3.685328356242346*^9, 3.685328598671985*^9}, {3.6853286682069626`*^9, 3.6853287982524004`*^9}, { 3.6853288753368096`*^9, 3.6853289367033195`*^9}, {3.685328968274125*^9, 3.685328978713722*^9}, {3.685329033941881*^9, 3.685329044950511*^9}, { 3.685329173522865*^9, 3.6853294420842257`*^9}, {3.6853296024223967`*^9, 3.6853296124319687`*^9}, {3.6853297221712456`*^9, 3.685329733349885*^9}, { 3.6853298076291337`*^9, 3.6853298739599276`*^9}, {3.685330038474337*^9, 3.685330051652091*^9}, {3.6853311309428225`*^9, 3.685331168378964*^9}, { 3.685340142134763*^9, 3.685340180544817*^9}, {3.6853583292043543`*^9, 3.685358334834362*^9}, {3.685358366084406*^9, 3.685358366954407*^9}, { 3.685358408404465*^9, 3.685358518294619*^9}, 3.685358620174762*^9, 3.6853586578748145`*^9, {3.6853588750151186`*^9, 3.6853588857151337`*^9}, { 3.6853589302051954`*^9, 3.685358938995208*^9}, {3.685359014715314*^9, 3.6853590296653347`*^9}, 3.685359148315501*^9, 3.6853598281764526`*^9, { 3.6853683109000263`*^9, 3.685368382250126*^9}, {3.685368420160179*^9, 3.6853684704302497`*^9}, {3.6853685194503183`*^9, 3.685368742860631*^9}, { 3.685369008901004*^9, 3.68536902061102*^9}, {3.6853690791611023`*^9, 3.685369132301176*^9}, {3.6853693219914417`*^9, 3.6853693304114532`*^9}, 3.6853696089118433`*^9, {3.6858758911429157`*^9, 3.685875951793*^9}, { 3.6859484099082212`*^9, 3.6859484970032024`*^9}, {3.686052829875022*^9, 3.686052906242383*^9}, {3.6860535326822133`*^9, 3.686053598029951*^9}, { 3.68605365168902*^9, 3.6860541446091995`*^9}, {3.6860541846064873`*^9, 3.68605440393201*^9}, {3.686054713802734*^9, 3.6860547858298535`*^9}, { 3.6860548280202665`*^9, 3.686054837219793*^9}, {3.686054874127904*^9, 3.686054892139934*^9}, {3.686055136014883*^9, 3.6860551460584574`*^9}, { 3.686055211281188*^9, 3.6860552301962633`*^9}, {3.6860553465409174`*^9, 3.6860553998749685`*^9}, {3.6860556017188663`*^9, 3.6860556050188704`*^9}, {3.6862923512707715`*^9, 3.686292363600789*^9}, { 3.686292409650853*^9, 3.6862924109708548`*^9}, {3.6862924536109147`*^9, 3.6862924596309233`*^9}, {3.686292542221039*^9, 3.6862925430110397`*^9}, { 3.686292988803664*^9, 3.686293001033681*^9}, {3.6866504529025555`*^9, 3.686650526682659*^9}, {3.686650671852862*^9, 3.6866507242929354`*^9}, { 3.6866507657529936`*^9, 3.6866507887630253`*^9}, {3.6866508208230705`*^9, 3.6866509100531955`*^9}, {3.6866509593932643`*^9, 3.686650971113281*^9}, { 3.686651007793332*^9, 3.6866511595335445`*^9}, {3.686651223513634*^9, 3.686651234033649*^9}, {3.686651304763748*^9, 3.6866513363837924`*^9}, { 3.6866514102038956`*^9, 3.686651429943923*^9}, {3.686652993837468*^9, 3.6866530046274834`*^9}, {3.686804398511652*^9, 3.6868044081516657`*^9}, { 3.6868046315619783`*^9, 3.686804631801979*^9}, {3.686804685872054*^9, 3.686804707092084*^9}, {3.6868047382021275`*^9, 3.686804767812169*^9}, { 3.686804824012248*^9, 3.6868048404922705`*^9}, {3.686804942142413*^9, 3.6868049633424425`*^9}, {3.6868050765526013`*^9, 3.686805101092636*^9}, { 3.6868051463526993`*^9, 3.6868052234228067`*^9}, {3.686805307602925*^9, 3.686805311682931*^9}, {3.68680577547358*^9, 3.686805788923599*^9}, { 3.686821702197342*^9, 3.6868217282873783`*^9}, {3.6868225192884855`*^9, 3.686822538368512*^9}, {3.6868226306886415`*^9, 3.6868226683086944`*^9}, { 3.6868227318887835`*^9, 3.6868227627088265`*^9}, {3.686822801638881*^9, 3.6868230490692277`*^9}, {3.686823122979331*^9, 3.6868231833294153`*^9}, { 3.6868232450595016`*^9, 3.6868233753996844`*^9}, {3.6868234153897405`*^9, 3.686823451379791*^9}, {3.6868236736101017`*^9, 3.6868236786601086`*^9}, { 3.6868237164601617`*^9, 3.68682375072021*^9}, {3.68682389396041*^9, 3.68682390087042*^9}, {3.686823940790476*^9, 3.6868239416904774`*^9}, { 3.6868239808805323`*^9, 3.6868239872905407`*^9}, {3.686824051540631*^9, 3.6868240519006314`*^9}, {3.686824360861064*^9, 3.6868243761510854`*^9}, { 3.6868245440213203`*^9, 3.686824577221367*^9}, {3.686824685841519*^9, 3.6868246979115357`*^9}, 3.6868248012716804`*^9, 3.6868253582724605`*^9, { 3.6868255183026843`*^9, 3.686825518932685*^9}, {3.6868264466639843`*^9, 3.6868264497139883`*^9}, {3.6868267792744493`*^9, 3.6868268152945004`*^9}, {3.686827100164899*^9, 3.6868271210549283`*^9}, 3.686827162004986*^9, {3.6868272414950967`*^9, 3.686827327475217*^9}, { 3.686827953126093*^9, 3.686827976506126*^9}, {3.686829128577739*^9, 3.686829138957753*^9}, 3.6868292410978966`*^9, {3.6868292768379464`*^9, 3.686829282727955*^9}, {3.6868293820380936`*^9, 3.686829418138144*^9}, { 3.686829846748744*^9, 3.686829848298746*^9}, {3.6868313063207874`*^9, 3.686831307180789*^9}, {3.6868331276633377`*^9, 3.68683328653356*^9}, { 3.6868394697195063`*^9, 3.6868394933895392`*^9}, 3.686839530999592*^9, { 3.686839582829664*^9, 3.68683963686974*^9}, {3.6868397551199055`*^9, 3.68683979365996*^9}, {3.6868398344600167`*^9, 3.686839866200061*^9}, { 3.687092084401948*^9, 3.687092117031994*^9}, {3.6870922598621936`*^9, 3.6870922645422*^9}, {3.6870962086478376`*^9, 3.6870962658779182`*^9}, 3.687096444838168*^9, {3.687096500978247*^9, 3.687096501638248*^9}, { 3.6870965809883595`*^9, 3.687096592708376*^9}, 3.687096837948719*^9, { 3.68709688890879*^9, 3.687096985798926*^9}, {3.6870971015990877`*^9, 3.6870972179192505`*^9}, {3.6870972618993125`*^9, 3.687097305639374*^9}, { 3.6870973356794157`*^9, 3.6870975186496716`*^9}, {3.6870975796097574`*^9, 3.6870975953197794`*^9}, {3.6870976531898603`*^9, 3.6870976848899045`*^9}, 3.6870977782500353`*^9, {3.687413757687042*^9, 3.6874137834070783`*^9}, { 3.6874140542074575`*^9, 3.687414094417514*^9}, {3.6874143478878684`*^9, 3.687414485538061*^9}, {3.6874146116082373`*^9, 3.68741464894829*^9}, { 3.6874147451084247`*^9, 3.687414766118454*^9}, 3.6874149094486547`*^9, { 3.6874150416688395`*^9, 3.6874150634888706`*^9}, {3.6874152437091227`*^9, 3.687415268869158*^9}, 3.6874153442892637`*^9, {3.687415449879411*^9, 3.687415469659439*^9}, 3.687415529739523*^9, 3.687415564789572*^9, 3.687415645529685*^9, {3.6874168016913037`*^9, 3.687416803441306*^9}, { 3.687421022677213*^9, 3.6874212686075573`*^9}, {3.68742948209425*^9, 3.6874294906842623`*^9}, {3.687844340668378*^9, 3.6878443698084188`*^9}, { 3.6886534778571014`*^9, 3.6886534911571198`*^9}, {3.688906380162199*^9, 3.6889064680223217`*^9}, {3.688906514222396*^9, 3.6889065193925257`*^9}, { 3.688908192623024*^9, 3.6889082006430354`*^9}, {3.688908261823121*^9, 3.688908271653135*^9}, {3.6889083776232834`*^9, 3.6889083922733035`*^9}, { 3.688908466073407*^9, 3.6889084993734536`*^9}, 3.688908533623502*^9, { 3.688908616683618*^9, 3.6889086271336327`*^9}, {3.6889086885637183`*^9, 3.6889087063437433`*^9}, {3.6889091647443852`*^9, 3.6889092012544365`*^9}, {3.6889093019045773`*^9, 3.6889093406746316`*^9}, 3.6889101071957045`*^9, {3.689905940063133*^9, 3.689905972983179*^9}, { 3.692530981927737*^9, 3.6925310416778207`*^9}, {3.692531099797902*^9, 3.6925311384779563`*^9}, {3.692531192258032*^9, 3.692531244668105*^9}, { 3.6925312919881716`*^9, 3.692531425418358*^9}, {3.6925315270885005`*^9, 3.692531643928664*^9}, {3.692535489534048*^9, 3.6925356485142703`*^9}, { 3.692535753564418*^9, 3.6925357992544813`*^9}, {3.6925358831745987`*^9, 3.692535899604622*^9}, {3.692536042584822*^9, 3.692536159384986*^9}, { 3.6925366121156197`*^9, 3.6925366207256317`*^9}, {3.6925367265057793`*^9, 3.69253672683578*^9}, {3.6925368590559654`*^9, 3.6925368636559715`*^9}, { 3.6925370880062857`*^9, 3.692537177856412*^9}, {3.692537322456614*^9, 3.6925373869767046`*^9}, {3.6925390913352747`*^9, 3.6925390925252767`*^9}, {3.692539644430175*^9, 3.6925396711502123`*^9}, { 3.692539727510291*^9, 3.692539730440295*^9}, {3.69253993367058*^9, 3.692539963780622*^9}, {3.6925400018406754`*^9, 3.692540003630678*^9}, { 3.6925401743409166`*^9, 3.6925401747509174`*^9}, {3.692540399111232*^9, 3.692540407981244*^9}, {3.69254047647134*^9, 3.6925404886113567`*^9}, { 3.6925406039715185`*^9, 3.69254060531152*^9}, {3.6925414948727655`*^9, 3.6925414953427663`*^9}, {3.6925415478528395`*^9, 3.692541613062931*^9}, 3.692541649332982*^9, {3.692541727633092*^9, 3.6925418840133104`*^9}, { 3.692541924473367*^9, 3.692542041693531*^9}, {3.6925421488836813`*^9, 3.6925422549438295`*^9}, {3.6925422976938896`*^9, 3.692542521444203*^9}, { 3.6925426221843443`*^9, 3.6925426357343626`*^9}, 3.692542739374508*^9, 3.692599799510878*^9, {3.692599834884901*^9, 3.6925998954663663`*^9}, { 3.692599925635092*^9, 3.6926000095928946`*^9}, {3.692600108929576*^9, 3.6926001456386757`*^9}, {3.6926001874800687`*^9, 3.692600454421337*^9}, { 3.692600503149027*^9, 3.6926006000391626`*^9}, {3.692600680251275*^9, 3.6926006814012766`*^9}, {3.6926009000215826`*^9, 3.6926009410816402`*^9}, 3.692601280532116*^9, {3.6926044914726114`*^9, 3.69260449774262*^9}, 3.6926045660127153`*^9, 3.6926046690228596`*^9, {3.69296647863291*^9, 3.6929664798829117`*^9}, {3.6929665643330297`*^9, 3.6929666141830997`*^9}, {3.6929670390036945`*^9, 3.6929670405536966`*^9}, {3.6929670861037607`*^9, 3.6929670952937737`*^9}, {3.6929671302538223`*^9, 3.6929671549438567`*^9}, {3.6929671904739065`*^9, 3.69296722137395*^9}, { 3.6929672596240034`*^9, 3.6929673352541094`*^9}, 3.6929678909232683`*^9, { 3.6930146982034283`*^9, 3.693014722713463*^9}, {3.6930148540136466`*^9, 3.693014857023651*^9}, {3.6930148913836985`*^9, 3.693014894823704*^9}, { 3.693014930903754*^9, 3.6930151942541227`*^9}, {3.693015247824198*^9, 3.693015430554454*^9}, {3.693015673794794*^9, 3.69301579223496*^9}, { 3.6930163123576884`*^9, 3.693016326897709*^9}, {3.6930164225678425`*^9, 3.693016429727853*^9}, {3.693016686718212*^9, 3.693016698128228*^9}, { 3.693016737038283*^9, 3.693016755068308*^9}, {3.6930168429225607`*^9, 3.6930168719926014`*^9}, {3.6930172049430676`*^9, 3.693017284063178*^9}, { 3.693017336433252*^9, 3.6930173662532935`*^9}, {3.6930180949163136`*^9, 3.6930180975563173`*^9}, {3.6930181870764427`*^9, 3.693018199956461*^9}, { 3.6930182954065943`*^9, 3.693018305996609*^9}, {3.693139886141657*^9, 3.6931399045016823`*^9}, {3.6931402916003532`*^9, 3.693140295770359*^9}, { 3.693140426020541*^9, 3.693140426530542*^9}, {3.6931410492237864`*^9, 3.6931410888738413`*^9}, {3.6931411194438844`*^9, 3.693141126553894*^9}, { 3.693141412004294*^9, 3.693141454164353*^9}, {3.6931415979955544`*^9, 3.6931417931758275`*^9}, {3.6932199559445915`*^9, 3.6932199772046213`*^9}, {3.6932201435748544`*^9, 3.693220170284892*^9}, { 3.693220713855653*^9, 3.693220721825664*^9}, {3.693625124589745*^9, 3.693625153729786*^9}, {3.6940907995669713`*^9, 3.6940909688872085`*^9}, { 3.6940913675677667`*^9, 3.6940914223978434`*^9}, {3.694091508037963*^9, 3.694091572118053*^9}, 3.694092009628666*^9, {3.6940920553287296`*^9, 3.694092229168973*^9}, {3.6940923053990793`*^9, 3.694092374419176*^9}, { 3.6940924537392874`*^9, 3.694092457789293*^9}, 3.694092642849552*^9, { 3.6940928573598523`*^9, 3.694092862379859*^9}, {3.6940945886222763`*^9, 3.694094601932295*^9}, 3.694094849542641*^9, {3.694095764293922*^9, 3.6940957644739223`*^9}, {3.6940960602743363`*^9, 3.6940960732243547`*^9}, {3.6940961211044216`*^9, 3.694096124194426*^9}, { 3.694665030960044*^9, 3.6946650634500895`*^9}, {3.6946652071402903`*^9, 3.6946653490404887`*^9}, {3.6946658702212186`*^9, 3.6946658881212435`*^9}, {3.694665923041292*^9, 3.694665953561335*^9}, { 3.694665995981395*^9, 3.6946660149414215`*^9}, {3.694666050571471*^9, 3.6946660547214766`*^9}, {3.694666169991638*^9, 3.694666292151809*^9}, { 3.6946663456618843`*^9, 3.6946663943919525`*^9}, 3.6946667526224537`*^9, 3.69466680700253*^9, 3.694687076625702*^9, {3.6946874316161985`*^9, 3.6946874621962414`*^9}, 3.694687499496294*^9, {3.694687567516389*^9, 3.694687642816495*^9}, {3.694687679006545*^9, 3.6946877198966026`*^9}, { 3.6946877714966745`*^9, 3.694687931746899*^9}, {3.723798739728607*^9, 3.723798744014243*^9}, {3.7237990126446104`*^9, 3.723799023974499*^9}, { 3.7244116671877546`*^9, 3.7244116733393917`*^9}, {3.724411761793063*^9, 3.7244117718753977`*^9}, {3.724411928386671*^9, 3.7244119682966137`*^9}, { 3.724412131847311*^9, 3.724412188341254*^9}, {3.729414981357122*^9, 3.7294149861075096`*^9}, {3.749817651293678*^9, 3.749817653108206*^9}, { 3.7498176831919456`*^9, 3.7498176846222315`*^9}, 3.7498177601545563`*^9, { 3.749817859674735*^9, 3.749817861044999*^9}, {3.7498179561547127`*^9, 3.749817964489929*^9}, {3.749818149334386*^9, 3.749818237397959*^9}, 3.749818617867873*^9, {3.7505621848002787`*^9, 3.7505622174085107`*^9}, { 3.75056238761455*^9, 3.750562431347901*^9}, {3.7505626332829456`*^9, 3.7505627331565337`*^9}, {3.7505627632642183`*^9, 3.7505627635859113`*^9}, {3.7515359581577415`*^9, 3.7515359614850826`*^9}, {3.751536071974715*^9, 3.7515360961721487`*^9}, 3.7515362040373974`*^9, {3.751536256080162*^9, 3.7515365099108534`*^9}, { 3.751549231137398*^9, 3.7515493334258356`*^9}, {3.7515496891619573`*^9, 3.751549689458767*^9}, {3.763384318028655*^9, 3.763384321230183*^9}, 3.7633844800900145`*^9, {3.7650666220235834`*^9, 3.765066676848461*^9}, { 3.7650667705927696`*^9, 3.765066781277461*^9}, {3.7650668220493402`*^9, 3.7650670769609847`*^9}, {3.765075343296377*^9, 3.765075345014902*^9}, { 3.765075479631569*^9, 3.7650755114191623`*^9}, {3.765075617307859*^9, 3.7650756180851874`*^9}, {3.76507585422694*^9, 3.765075872425325*^9}, { 3.7650760811750383`*^9, 3.7650762635610576`*^9}, {3.7650763100785646`*^9, 3.765076323109063*^9}, {3.7650763765120716`*^9, 3.765076385469493*^9}, { 3.7650764317497897`*^9, 3.7650764864127855`*^9}, 3.765076672990033*^9, { 3.7650767604139767`*^9, 3.7650767965644426`*^9}, {3.765076849411788*^9, 3.76507688334435*^9}, {3.765076928656023*^9, 3.7650769388747053`*^9}, 3.76507697239373*^9, {3.7650770147173185`*^9, 3.7650770820420313`*^9}, { 3.765077138264634*^9, 3.765077175747029*^9}, {3.765077340035742*^9, 3.765077493212038*^9}, {3.7650775254837503`*^9, 3.765077573524544*^9}, { 3.765077619369755*^9, 3.7650776808294816`*^9}, {3.765088266857733*^9, 3.765088281236836*^9}, {3.76508836959641*^9, 3.765088394392946*^9}, { 3.7650900504082956`*^9, 3.765090052695187*^9}, {3.7650900911122713`*^9, 3.765090094160341*^9}, {3.765090519594511*^9, 3.7650905411898503`*^9}, { 3.7885193337832556`*^9, 3.788519339935099*^9}, {3.788519391172593*^9, 3.7885194472501445`*^9}, {3.7885195529105897`*^9, 3.788519558251149*^9}, { 3.7885305232444134`*^9, 3.7885305903888035`*^9}, {3.7885308807721663`*^9, 3.78853088502055*^9}, {3.8200276995553846`*^9, 3.82002773164934*^9}, 3.829884585166191*^9, {3.8298846167331247`*^9, 3.82988461691162*^9}},ExpressionUUID->"fd362622-c1e3-4356-b6fc-\ a24956b44459"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"GENERICBEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE_", ",", "GG_", ",", "\[Rho]\[Rho]_", ",", "\[Kappa]\[Kappa]_"}], "}"}], ",", RowBox[{"{", RowBox[{ "AA_", ",", "Sy_", ",", "Sz_", ",", "Iyy_", ",", "Izz_", ",", "Iyz_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fx_", ",", "fy_", ",", "fz_", ",", "mx_", ",", "my_", ",", "mz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Xi]", ",", "r0", ",", "r\[Alpha]0", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "ix0", ",", "iz0", ",", "s", ",", "x", ",", "jac", ",", "NL", ",", "NQ", ",", "FF", ",", "FFINV", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "u0", ",", "v0", ",", "w0", ",", "\[Phi]0", ",", "\[Theta]0", ",", "\[Psi]0", ",", "u2", ",", "v2", ",", "w2", ",", "\[Phi]2", ",", "\[Theta]2", ",", "\[Psi]2", ",", "EEEE", ",", "AE", ",", "CE", ",", "BE", ",", "\[Epsilon]", ",", "\[Kappa]", ",", "Irr", ",", "F", ",", "M", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wine", ",", "\[Delta]wbrn", ",", "\[Delta]WW", ",", "equ", ",", "sol", ",", "bl", ",", "EEE", ",", "GGG", ",", "\[Rho]\[Rho]\[Rho]", ",", "\[Kappa]\[Kappa]\[Kappa]", ",", "AAA", ",", "SSz", ",", "SSy", ",", "IIyy", ",", "IIzz", ",", "IIyz", ",", "JJp", ",", "ffx", ",", "ffy", ",", "ffz", ",", "mmx", ",", "mmy", ",", "mmz", ",", "A\[Rho]", ",", "B\[Rho]", ",", "C\[Rho]", ",", "\[Epsilon]0", ",", "\[Kappa]0"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"mapping", " ", "to", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{"\[Xi]", "*", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]0", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "r0"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Alpha]0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r\[Alpha]0", ".", "r\[Alpha]0"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"L", ">", "0"}], ",", RowBox[{"h", ">", "0"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"i\[Alpha]0", " ", "=", RowBox[{"r\[Alpha]0", "/", "h\[Alpha]0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"iz0", "=", RowBox[{"ix0", "\[Cross]", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"s", "=", RowBox[{"i\[Alpha]0", ".", "r0"}]}], ";", "\[IndentingNewLine]", RowBox[{"x", "=", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], ".", "ix0"}], "+", "s"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"jac", " ", "=", "h\[Alpha]0"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"simple", " ", "metrics"}], "*)"}], "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"use", " ", "simple"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NL", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Xi]"}], ",", "\[Xi]"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NQ", "=", " ", RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "\[Xi]"}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", "\[Xi]"}]}], ")"}]}], ",", RowBox[{"h\[Alpha]0", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "\[Xi]"}], ")"}], "2"], " ", "\[Xi]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{"2", " ", "\[Xi]"}]}], ")"}], " ", SuperscriptBox["\[Xi]", "2"]}], ",", RowBox[{"h\[Alpha]0", " ", SuperscriptBox["\[Xi]", "2"], " ", RowBox[{"(", " ", RowBox[{"\[Xi]", "-", "1"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2", ",", "1"}], "]"}], "]"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2", ",", "1"}], "]"}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3", ",", "1"}], "]"}], "]"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3", ",", "1"}], "]"}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2", ",", "2"}], "]"}], "]"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3", ",", "3"}], "]"}], "]"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2", ",", "2"}], "]"}], "]"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3", ",", "3"}], "]"}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2", ",", "3"}], "]"}], "]"}], ",", RowBox[{"-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2", ",", "3"}], "]"}], "]"}], ",", RowBox[{"-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3", ",", "2"}], "]"}], "]"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "v"}], "/", "h\[Alpha]0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "w"}]}], "/", "h\[Alpha]0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"transform", " ", "to", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], ".", "FFINV"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], ".", "FFINV"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u0", ",", "v0", ",", "w0"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]0", ",", "\[Theta]0", ",", "\[Psi]0"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u2", ",", "v2", ",", "w2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]2", ",", "\[Theta]2", ",", "\[Psi]2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"elasticity", " ", "dyad", " ", "and", " ", "cross"}], "-", RowBox[{ "section", " ", "properties", " ", "are", " ", "known", " ", "in", " ", "the", " ", "material", " ", "system"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"EEE", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "EE", "]"}], "===", "Function"}], ",", RowBox[{"EE", "[", "x", "]"}], ",", "EE"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GGG", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "GG", "]"}], "===", "Function"}], ",", RowBox[{"GG", "[", "x", "]"}], ",", "GG"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Rho]\[Rho]\[Rho]", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "\[Rho]\[Rho]", "]"}], "===", "Function"}], ",", RowBox[{"\[Rho]\[Rho]", "[", "x", "]"}], ",", "\[Rho]\[Rho]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]\[Kappa]\[Kappa]", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "\[Kappa]\[Kappa]", "]"}], "===", "Function"}], ",", RowBox[{"\[Kappa]\[Kappa]", "[", "x", "]"}], ",", "\[Kappa]\[Kappa]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"AAA", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "AA", "]"}], "===", "Function"}], ",", RowBox[{"AA", "[", "x", "]"}], ",", "AA"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"SSz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Sz", "]"}], "===", "Function"}], ",", RowBox[{"Sz", "[", "x", "]"}], ",", "Sz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"SSy", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Sy", "]"}], "===", "Function"}], ",", RowBox[{"Sy", "[", "x", "]"}], ",", "Sy"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIyy", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Iyy", "]"}], "===", "Function"}], ",", RowBox[{"Iyy", "[", "x", "]"}], ",", "Iyy"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIzz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Izz", "]"}], "===", "Function"}], ",", RowBox[{"Izz", "[", "x", "]"}], ",", "Izz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIyz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Iyz", "]"}], "===", "Function"}], ",", RowBox[{"Iyz", "[", "x", "]"}], ",", "Iyz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ffx", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "fx", "]"}], "===", "Function"}], ",", RowBox[{"fx", "[", "x", "]"}], ",", "fx"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ffy", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "fy", "]"}], "===", "Function"}], ",", RowBox[{"fy", "[", "x", "]"}], ",", "fy"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ffz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "fz", "]"}], "===", "Function"}], ",", RowBox[{"fz", "[", "x", "]"}], ",", "fz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"mmx", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "mx", "]"}], "===", "Function"}], ",", RowBox[{"mx", "[", "x", "]"}], ",", "mx"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"mmy", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "my", "]"}], "===", "Function"}], ",", RowBox[{"my", "[", "x", "]"}], ",", "my"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"mmz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "mz", "]"}], "===", "Function"}], ",", RowBox[{"mz", "[", "x", "]"}], ",", "mz"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"elasticity", " ", "dyad", " ", "and", " ", "cross"}], "-", RowBox[{ "section", " ", "properties", " ", "are", " ", "known", " ", "in", " ", "the", " ", "material", " ", "system"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"AE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EEE", " ", "AAA"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"GGG", " ", "AAA"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"GGG", " ", "AAA"}]}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"CE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"EEE", " ", "SSy"}], ",", RowBox[{ RowBox[{"-", "EEE"}], " ", "SSz"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "GGG"}], " ", "SSy"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"GGG", " ", "SSz"}], ",", "0", ",", "0"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"BE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"GGG", " ", "\[Kappa]\[Kappa]\[Kappa]", " ", RowBox[{"(", RowBox[{"IIyy", "+", "IIzz"}], ")"}]}], " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"EEE", " ", "IIyy"}], ",", RowBox[{ RowBox[{"-", "EEE"}], " ", "IIyz"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"-", "EEE"}], " ", "IIyz"}], ",", RowBox[{"EEE", " ", "IIzz"}]}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"inertia", " ", "properties"}], "*)"}], "\[IndentingNewLine]", RowBox[{"A\[Rho]", "=", RowBox[{"\[Rho]\[Rho]\[Rho]", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"AAA", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "AAA", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "AAA"}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"C\[Rho]", "=", RowBox[{"\[Rho]\[Rho]\[Rho]", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "SSy", ",", RowBox[{"-", "SSz"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "SSy"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"SSz", ",", "0", ",", "0"}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"B\[Rho]", "=", RowBox[{"\[Rho]\[Rho]\[Rho]", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"IIyy", "+", "IIzz"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "IIyy", ",", RowBox[{"-", "IIyz"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "IIyz"}], ",", "IIzz"}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"strain", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]0", "=", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], RowBox[{"{", RowBox[{"u0", ",", "v0", ",", "w0"}], "}"}]}], "/", "h\[Alpha]0"}], "+", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], "\[Cross]", RowBox[{"{", RowBox[{"\[Phi]0", ",", "\[Theta]0", ",", "\[Psi]0"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]0", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], RowBox[{"{", RowBox[{"\[Phi]0", ",", "\[Theta]0", ",", "\[Psi]0"}], "}"}]}], "/", "h\[Alpha]0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "resultants"}], "*)"}], "\[IndentingNewLine]", RowBox[{"F", "=", RowBox[{ RowBox[{"AE", ".", "\[Epsilon]0"}], "+", RowBox[{"CE", ".", "\[Kappa]0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M", "=", RowBox[{ RowBox[{ RowBox[{"Transpose", "[", "CE", "]"}], ".", "\[Epsilon]0"}], "+", RowBox[{"BE", ".", "\[Kappa]0"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expressions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", "\[Epsilon]0", "]"}], ".", "F"}]}], "-", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", "\[Kappa]0", "]"}], ".", "M"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", RowBox[{"{", RowBox[{"u0", ",", "v0", ",", "w0"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"ffx", ",", "ffy", ",", "ffz"}], "}"}]}], "+", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", RowBox[{"{", RowBox[{"\[Phi]0", ",", "\[Theta]0", ",", "\[Psi]0"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"mmx", ",", "mmy", ",", "mmz"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wine", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", RowBox[{"{", RowBox[{"u0", ",", "v0", ",", "w0"}], "}"}], "]"}], ".", RowBox[{"(", RowBox[{ RowBox[{"A\[Rho]", ".", RowBox[{"{", RowBox[{"u2", ",", "v2", ",", "w2"}], "}"}]}], "+", RowBox[{"C\[Rho]", ".", RowBox[{"{", RowBox[{"\[Phi]2", ",", "\[Theta]2", ",", "\[Psi]2"}], "}"}]}]}], ")"}]}]}], "-", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", RowBox[{"{", RowBox[{"\[Phi]0", ",", "\[Theta]0", ",", "\[Psi]0"}], "}"}], "]"}], ".", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"C\[Rho]", ".", RowBox[{"{", RowBox[{"u2", ",", "v2", ",", "w2"}], "}"}]}]}], "+", RowBox[{"B\[Rho]", ".", RowBox[{"{", RowBox[{"\[Phi]2", ",", "\[Theta]2", ",", "\[Psi]2"}], "}"}]}]}], ")"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wine"}], ")"}], "*", "jac"}], ",", RowBox[{"{", "\[Xi]", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wine"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Xi]", ",", "0", ",", "1"}], "}"}]}], "]"}]}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAMB", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{ "AA", ",", "0", ",", "0", ",", "Iyy", ",", "Izz", ",", "0", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fz", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAMV", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{ "AA_", ",", "Sy_", ",", "Sz_", ",", "Iyy_", ",", "Izz_", ",", "Iyz_", ",", "Jp_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fx_", ",", "fy_", ",", "fz_", ",", "mx_", ",", "my_", ",", "mz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "r\[Alpha]0", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "ix0", ",", "iz0", ",", "s", ",", "x", ",", "jac", ",", "NL", ",", "NQ", ",", "FF", ",", "FFINV", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "u0", ",", "v0", ",", "w0", ",", "\[Phi]0", ",", "\[Theta]0", ",", "\[Psi]0", ",", "u2", ",", "v2", ",", "w2", ",", "\[Phi]2", ",", "\[Theta]2", ",", "\[Psi]2", ",", "EEEE", ",", "AE", ",", "CE", ",", "BE", ",", "\[Epsilon]", ",", "\[Kappa]", ",", "Irr", ",", "F", ",", "M", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wine", ",", "\[Delta]wbrn", ",", "\[Delta]WW", ",", "equ", ",", "sol", ",", "bl", ",", "EEE", ",", "GGG", ",", "\[Rho]\[Rho]\[Rho]", ",", "\[Kappa]\[Kappa]\[Kappa]", ",", "AAA", ",", "SSz", ",", "SSy", ",", "IIyy", ",", "IIzz", ",", "IIyz", ",", "JJp", ",", "ffx", ",", "ffy", ",", "ffz", ",", "mmx", ",", "mmy", ",", "mmz", ",", "A\[Rho]", ",", "B\[Rho]", ",", "C\[Rho]", ",", "\[Epsilon]0", ",", "\[Kappa]0"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"mapping", " ", "to", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{"\[Xi]", "*", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]0", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "r0"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Alpha]0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r\[Alpha]0", ".", "r\[Alpha]0"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"L", ">", "0"}], ",", RowBox[{"h", ">", "0"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"i\[Alpha]0", " ", "=", RowBox[{"r\[Alpha]0", "/", "h\[Alpha]0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"iz0", "=", RowBox[{"ix0", "\[Cross]", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"s", "=", RowBox[{"i\[Alpha]0", ".", "r0"}]}], ";", "\[IndentingNewLine]", RowBox[{"x", "=", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], ".", "ix0"}], "+", "s"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"jac", " ", "=", "h\[Alpha]0"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"simple", " ", "metrics"}], "*)"}], "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"use", " ", "simple"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NL", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Xi]"}], ",", "\[Xi]"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NQ", "=", " ", RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "\[Xi]"}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", "\[Xi]"}]}], ")"}]}], ",", RowBox[{"h\[Alpha]0", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "\[Xi]"}], ")"}], "2"], " ", "\[Xi]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{"2", " ", "\[Xi]"}]}], ")"}], " ", SuperscriptBox["\[Xi]", "2"]}], ",", RowBox[{"h\[Alpha]0", " ", SuperscriptBox["\[Xi]", "2"], " ", RowBox[{"(", " ", RowBox[{"\[Xi]", "-", "1"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2", ",", "1"}], "]"}], "]"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2", ",", "1"}], "]"}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3", ",", "1"}], "]"}], "]"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3", ",", "1"}], "]"}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2", ",", "2"}], "]"}], "]"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3", ",", "3"}], "]"}], "]"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2", ",", "2"}], "]"}], "]"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3", ",", "3"}], "]"}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2", ",", "3"}], "]"}], "]"}], ",", RowBox[{"-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2", ",", "3"}], "]"}], "]"}], ",", RowBox[{"-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3", ",", "2"}], "]"}], "]"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "v"}], "/", "h\[Alpha]0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "w"}]}], "/", "h\[Alpha]0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"transform", " ", "to", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], ".", "FFINV"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], ".", "FFINV"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u0", ",", "v0", ",", "w0"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], " ", "/.", RowBox[{"rule", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]0", ",", "\[Theta]0", ",", "\[Psi]0"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], " ", "/.", RowBox[{"rule", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u2", ",", "v2", ",", "w2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "/.", RowBox[{"rule", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]2", ",", "\[Theta]2", ",", "\[Psi]2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], " ", "/.", RowBox[{"rule", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"elasticity", " ", "dyad", " ", "and", " ", "cross"}], "-", RowBox[{ "section", " ", "properties", " ", "are", " ", "known", " ", "in", " ", "the", " ", "material", " ", "system"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"EEE", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "EE", "]"}], "===", "Function"}], ",", RowBox[{"EE", "[", "x", "]"}], ",", "EE"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GGG", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "GG", "]"}], "===", "Function"}], ",", RowBox[{"GG", "[", "x", "]"}], ",", "GG"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Rho]\[Rho]\[Rho]", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "\[Rho]\[Rho]", "]"}], "===", "Function"}], ",", RowBox[{"\[Rho]\[Rho]", "[", "x", "]"}], ",", "\[Rho]\[Rho]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"AAA", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "AA", "]"}], "===", "Function"}], ",", RowBox[{"AA", "[", "x", "]"}], ",", "AA"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"SSz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Sz", "]"}], "===", "Function"}], ",", RowBox[{"Sz", "[", "x", "]"}], ",", "Sz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"SSy", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Sy", "]"}], "===", "Function"}], ",", RowBox[{"Sy", "[", "x", "]"}], ",", "Sy"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIyy", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Iyy", "]"}], "===", "Function"}], ",", RowBox[{"Iyy", "[", "x", "]"}], ",", "Iyy"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIzz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Izz", "]"}], "===", "Function"}], ",", RowBox[{"Izz", "[", "x", "]"}], ",", "Izz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIyz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Iyz", "]"}], "===", "Function"}], ",", RowBox[{"Iyz", "[", "x", "]"}], ",", "Iyz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"JJp", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Jp", "]"}], "===", "Function"}], ",", RowBox[{"Jp", "[", "x", "]"}], ",", "Jp"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ffx", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "fx", "]"}], "===", "Function"}], ",", RowBox[{"fx", "[", "x", "]"}], ",", "fx"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ffy", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "fy", "]"}], "===", "Function"}], ",", RowBox[{"fy", "[", "x", "]"}], ",", "fy"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ffz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "fz", "]"}], "===", "Function"}], ",", RowBox[{"fz", "[", "x", "]"}], ",", "fz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"mmx", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "mx", "]"}], "===", "Function"}], ",", RowBox[{"mx", "[", "x", "]"}], ",", "mx"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"mmy", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "my", "]"}], "===", "Function"}], ",", RowBox[{"my", "[", "x", "]"}], ",", "my"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"mmz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "mz", "]"}], "===", "Function"}], ",", RowBox[{"mz", "[", "x", "]"}], ",", "mz"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"elasticity", " ", "dyad", " ", "and", " ", "cross"}], "-", RowBox[{ "section", " ", "properties", " ", "are", " ", "known", " ", "in", " ", "the", " ", "material", " ", "system"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"AE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EEE", " ", "AAA"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"GGG", " ", "AAA"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"GGG", " ", "AAA"}]}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"CE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"EEE", " ", "SSy"}], ",", RowBox[{ RowBox[{"-", "EEE"}], " ", "SSz"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "GGG"}], " ", "SSy"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"GGG", " ", "SSz"}], ",", "0", ",", "0"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"BE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"GGG", " ", "JJp"}], " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"EEE", " ", "IIyy"}], ",", RowBox[{ RowBox[{"-", "EEE"}], " ", "IIyz"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"-", "EEE"}], " ", "IIyz"}], ",", RowBox[{"EEE", " ", "IIzz"}]}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"inertia", " ", "properties"}], "*)"}], "\[IndentingNewLine]", RowBox[{"A\[Rho]", "=", RowBox[{"\[Rho]\[Rho]\[Rho]", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"AAA", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "AAA", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "AAA"}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"C\[Rho]", "=", RowBox[{"\[Rho]\[Rho]\[Rho]", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "SSy", ",", RowBox[{"-", "SSz"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "SSy"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"SSz", ",", "0", ",", "0"}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"B\[Rho]", "=", RowBox[{"\[Rho]\[Rho]\[Rho]", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"IIyy", "+", "IIzz"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "IIyy", ",", RowBox[{"-", "IIyz"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "IIyz"}], ",", "IIzz"}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"strain", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]0", "=", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], RowBox[{"{", RowBox[{"u0", ",", "v0", ",", "w0"}], "}"}]}], "/", "h\[Alpha]0"}], "+", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], "\[Cross]", RowBox[{"{", RowBox[{"\[Phi]0", ",", "\[Theta]0", ",", "\[Psi]0"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]0", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], RowBox[{"{", RowBox[{"\[Phi]0", ",", "\[Theta]0", ",", "\[Psi]0"}], "}"}]}], "/", "h\[Alpha]0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "resultants"}], "*)"}], "\[IndentingNewLine]", RowBox[{"F", "=", RowBox[{ RowBox[{"AE", ".", "\[Epsilon]0"}], "+", RowBox[{"CE", ".", "\[Kappa]0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M", "=", RowBox[{ RowBox[{ RowBox[{"Transpose", "[", "CE", "]"}], ".", "\[Epsilon]0"}], "+", RowBox[{"BE", ".", "\[Kappa]0"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expressions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", "\[Epsilon]0", "]"}], ".", "F"}]}], "-", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", "\[Kappa]0", "]"}], ".", "M"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", RowBox[{"{", RowBox[{"u0", ",", "v0", ",", "w0"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"ffx", ",", "ffy", ",", "ffz"}], "}"}]}], "+", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", RowBox[{"{", RowBox[{"\[Phi]0", ",", "\[Theta]0", ",", "\[Psi]0"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"mmx", ",", "mmy", ",", "mmz"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wine", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", RowBox[{"{", RowBox[{"u0", ",", "v0", ",", "w0"}], "}"}], "]"}], ".", RowBox[{"(", RowBox[{ RowBox[{"A\[Rho]", ".", RowBox[{"{", RowBox[{"u2", ",", "v2", ",", "w2"}], "}"}]}], "+", RowBox[{"C\[Rho]", ".", RowBox[{"{", RowBox[{"\[Phi]2", ",", "\[Theta]2", ",", "\[Psi]2"}], "}"}]}]}], ")"}]}]}], "-", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", RowBox[{"{", RowBox[{"\[Phi]0", ",", "\[Theta]0", ",", "\[Psi]0"}], "}"}], "]"}], ".", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"C\[Rho]", ".", RowBox[{"{", RowBox[{"u2", ",", "v2", ",", "w2"}], "}"}]}]}], "+", RowBox[{"B\[Rho]", ".", RowBox[{"{", RowBox[{"\[Phi]2", ",", "\[Theta]2", ",", "\[Psi]2"}], "}"}]}]}], ")"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wine"}], ")"}], "*", "jac"}], ",", RowBox[{"{", "\[Xi]", "}"}]}], "]"}]}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_", ",", "Jp_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{ "AA", ",", "0", ",", "0", ",", "Iyy", ",", "Izz", ",", "0", ",", "Jp", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fz", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{ "AA_", ",", "Sy_", ",", "Sz_", ",", "Iyy_", ",", "Izz_", ",", "Ixy_", ",", "Jp_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fx_", ",", "fy_", ",", "fz_", ",", "mx_", ",", "my_", ",", "mz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "h", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "ix0", ",", "iz0", ",", "ux", ",", "uy", " ", ",", "uz", " ", ",", "\[Theta]x", " ", ",", "\[Theta]y", " ", ",", "\[Theta]z", " ", ",", "\[Delta]ux", " ", ",", "\[Delta]uy", ",", "\[Delta]uz", ",", "\[Delta]\[Theta]x", ",", "\[Delta]\[Theta]y", ",", "\[Delta]\[Theta]z"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "mapping", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"h", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz0", "=", RowBox[{"ix0", "\[Cross]", "iy0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"2", ",", "2"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ FractionBox["1", RowBox[{"420", " ", SuperscriptBox["h", "3"]}]], RowBox[{"(", RowBox[{ RowBox[{"210", " ", "fx", " ", SuperscriptBox["h", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{"AA", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"420", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", "\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"70", " ", RowBox[{"ux", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"70", " ", RowBox[{"ux", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}], "+", RowBox[{"156", " ", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"54", " ", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"54", " ", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"156", " ", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"156", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"54", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"54", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"156", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"22", " ", "h", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"13", " ", "h", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"13", " ", "h", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"22", " ", "h", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"22", " ", "h", " ", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"13", " ", "h", " ", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"13", " ", "h", " ", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"22", " ", "h", " ", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"22", " ", "h", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"13", " ", "h", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"4", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"3", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"13", " ", "h", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"22", " ", "h", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"3", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"4", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"22", " ", "h", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"13", " ", "h", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"4", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"3", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"13", " ", "h", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"22", " ", "h", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"3", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"4", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"7", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "720"}], " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"Ixy", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"360", " ", "EE", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{ RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"Ixy", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"uy", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{ RowBox[{"uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{ RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{ RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{ RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{ RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}], "+", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"uy", "[", RowBox[{"1", ",", "0"}], "]"}]}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"12", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"6", " ", "Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"6", " ", "Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"6", " ", "Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"5", " ", "EE", " ", "Sy", " ", RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"5", " ", "EE", " ", "Sy", " ", RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"5", " ", "EE", " ", "Sy", " ", RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"5", " ", "EE", " ", "Sy", " ", RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"5", " ", "EE", " ", "Sz", " ", RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"5", " ", "EE", " ", "Sz", " ", RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"5", " ", "EE", " ", "Sz", " ", RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"5", " ", "EE", " ", "Sz", " ", RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"5", " ", "GG", " ", "Jp", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"5", " ", "GG", " ", "Jp", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"5", " ", "GG", " ", "Jp", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"5", " ", "GG", " ", "Jp", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"5", " ", "EE", " ", "Sy", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"5", " ", "EE", " ", "Sy", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"20", " ", "EE", " ", "Iyy", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"10", " ", "EE", " ", "Iyy", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"5", " ", "EE", " ", "Sy", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"5", " ", "EE", " ", "Sy", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"10", " ", "EE", " ", "Iyy", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"20", " ", "EE", " ", "Iyy", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"5", " ", "EE", " ", "Sz", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"5", " ", "EE", " ", "Sz", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"5", " ", "EE", " ", "Sz", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"5", " ", "EE", " ", "Sz", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"2", " ", "Ixy", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", "\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], "-", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"5", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", "\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], "-", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"5", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"6", " ", SuperscriptBox["h", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"5", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"5", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"5", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"5", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"10", " ", "mz", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"5", " ", "Sz", " ", "\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{ RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "2"}], "]"}], "+", RowBox[{"ux", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"10", " ", "mz", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"10", " ", "my", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"5", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"ux", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"5", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"ux", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"10", " ", "my", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"5", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"ux", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"5", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"ux", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"Izz", " ", "\[Rho]\[Rho]", " ", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"Izz", " ", "\[Rho]\[Rho]", " ", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"Izz", " ", "\[Rho]\[Rho]", " ", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"Izz", " ", "\[Rho]\[Rho]", " ", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"Izz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"Izz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"Izz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"Izz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["h", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"30", " ", "fy", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"30", " ", "fz", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"30", " ", "mx", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"21", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"9", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"21", " ", "Sz", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"9", " ", "Sz", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"30", " ", "mx", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"9", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"21", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"9", " ", "Sz", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"21", " ", "Sz", " ", "\[Rho]\[Rho]", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"5", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"ux", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"5", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"ux", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"5", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"ux", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"5", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"ux", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"5", " ", "Sz", " ", "\[Rho]\[Rho]", " ", RowBox[{"ux", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"5", " ", "Sz", " ", "\[Rho]\[Rho]", " ", RowBox[{"ux", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"5", " ", "Sz", " ", "\[Rho]\[Rho]", " ", RowBox[{"ux", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"5", " ", "Sz", " ", "\[Rho]\[Rho]", " ", RowBox[{"ux", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"21", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"9", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"21", " ", "Sz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"9", " ", "Sz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"20", " ", "Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"20", " ", "Izz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"10", " ", "Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"10", " ", "Izz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"9", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"21", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"9", " ", "Sz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"21", " ", "Sz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"10", " ", "Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"10", " ", "Izz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"20", " ", "Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"20", " ", "Izz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"5", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"5", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"8", " ", "Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"2", " ", "Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"8", " ", "Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"2", " ", "Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"5", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"5", " ", "Sy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"2", " ", "Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"8", " ", "Iyy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"2", " ", "Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"8", " ", "Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"5", " ", "Sz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"5", " ", "Sz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"8", " ", "Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"2", " ", "Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"8", " ", "Izz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"2", " ", "Izz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"5", " ", "Sz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"5", " ", "Sz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"2", " ", "Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"8", " ", "Ixy", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"2", " ", "Izz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"8", " ", "Izz", " ", "\[Rho]\[Rho]", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["h", "5"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "5"}], " ", "fz", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"5", " ", "fy", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"Sz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"2", " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "-", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"3", " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{"3", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"3", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{"Sy", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"2", " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "-", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"3", " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{"3", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"3", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4430689313272*^9, 3.4430690080792*^9}, { 3.4430690869528*^9, 3.4430691077320004`*^9}, {3.4430691700116*^9, 3.4430691708072*^9}, {3.4430692071717997`*^9, 3.443069246359*^9}, { 3.4430772782732*^9, 3.4430773623416*^9}, {3.4430773978316*^9, 3.4430774104676*^9}, {3.4430775053780003`*^9, 3.4430776180598*^9}, { 3.4434109099524*^9, 3.4434109159584*^9}, {3.4438800815346003`*^9, 3.4438802689304*^9}, {3.443880362624*^9, 3.4438803824516*^9}, { 3.443929565615374*^9, 3.443929570232974*^9}, {3.443935321321974*^9, 3.443935335705174*^9}, {3.443935419945174*^9, 3.443935421489574*^9}, { 3.443935494013974*^9, 3.443935494715974*^9}, {3.443935617565974*^9, 3.4439357217895737`*^9}, {3.443935755360774*^9, 3.443935816107174*^9}, { 3.443942155230774*^9, 3.443942209939974*^9}, {3.443942305710374*^9, 3.4439423142123737`*^9}, {3.4439442908131742`*^9, 3.443944441181574*^9}, { 3.4439447830065737`*^9, 3.4439447917425737`*^9}, {3.443944908541774*^9, 3.443944916060974*^9}, {3.4442731097938004`*^9, 3.4442731115254*^9}, { 3.444273189229*^9, 3.4442732700526*^9}, {3.4442748430004*^9, 3.4442748605036*^9}, {3.4442748977438*^9, 3.4442748989762*^9}, { 3.4442749340762*^9, 3.4442749351057997`*^9}, 3.4442752313382*^9, { 3.4442919702026*^9, 3.4442919911846*^9}, {3.4442921151577997`*^9, 3.4442921271074*^9}, {3.4443811023684*^9, 3.4443811036632*^9}, { 3.4443814073171997`*^9, 3.4443814402956*^9}, {3.4443815036316*^9, 3.4443815147855997`*^9}, {3.4443815537232*^9, 3.4443815747676*^9}, { 3.4443816138143997`*^9, 3.444381633174*^9}, {3.4443816850439997`*^9, 3.4443817801728*^9}, 3.4443853618688*^9, {3.4443855607376003`*^9, 3.4443856337924*^9}, {3.4443861200444*^9, 3.4443861523676*^9}, { 3.4443862280495996`*^9, 3.444386291448*^9}, {3.4443864047352*^9, 3.4443864135336*^9}, {3.4443870026832*^9, 3.4443870095316*^9}, { 3.4444082055056*^9, 3.4444082437412*^9}, {3.4444082797148*^9, 3.4444084583816*^9}, {3.4444084889108*^9, 3.4444085087539997`*^9}, { 3.444408942517*^9, 3.4444089563386*^9}, {3.4444091419564*^9, 3.4444091647167997`*^9}, {3.4444092206428003`*^9, 3.4444092944463997`*^9}, {3.4444093856284*^9, 3.4444094281071997`*^9}, { 3.4444094976988*^9, 3.4444095275104*^9}, {3.444409611064*^9, 3.4444096125772*^9}, 3.4444098504616003`*^9, {3.444409913392*^9, 3.4444099166056004`*^9}, 3.4444100178496*^9, {3.4444103063248*^9, 3.4444103358712*^9}, {3.4444103868208*^9, 3.4444104432460003`*^9}, { 3.4444921219564*^9, 3.4444921256224003`*^9}, {3.444492194824*^9, 3.4444921973668003`*^9}, {3.4444922814351997`*^9, 3.4444922853508*^9}, { 3.4444923330868*^9, 3.4444923345844*^9}, {3.444492366424*^9, 3.4444923855808*^9}, {3.4453153475226*^9, 3.445315360689*^9}, { 3.4465518166373653`*^9, 3.446551863016165*^9}, {3.446551894231765*^9, 3.446552159384965*^9}, {3.446552232377365*^9, 3.4465522555589647`*^9}, { 3.446553347388365*^9, 3.4465533616155653`*^9}, {3.4466058525769997`*^9, 3.4466058529046*^9}, {3.4466064371219997`*^9, 3.4466065097244*^9}, { 3.4466127725788*^9, 3.4466127766036*^9}, {3.4466128124835997`*^9, 3.4466130037864*^9}, {3.4466131532696*^9, 3.4466131761703997`*^9}, { 3.4466133992192*^9, 3.4466134478756*^9}, {3.446613483584*^9, 3.4466134932092*^9}, {3.4466135740952*^9, 3.4466135794927998`*^9}, { 3.4466137283948*^9, 3.4466137341356*^9}, {3.4466138994342003`*^9, 3.4466139023826*^9}, {3.4466139549858*^9, 3.4466139579653997`*^9}, { 3.4466142109818*^9, 3.4466142245226*^9}, {3.4466142793878*^9, 3.4466143652033997`*^9}, {3.4466144712834*^9, 3.4466145978929996`*^9}, { 3.4466146992618*^9, 3.4466147509914*^9}, {3.4466151283086*^9, 3.4466152768986*^9}, {3.4466153107506*^9, 3.4466153406558*^9}, { 3.4466194331976*^9, 3.4466194377528*^9}, {3.4466194847712*^9, 3.446619488718*^9}, {3.4466389495861998`*^9, 3.4466389768238*^9}, { 3.4466391218414*^9, 3.446639306561*^9}, {3.4466393990222*^9, 3.4466394004886*^9}, {3.4466394475694*^9, 3.4466394487706003`*^9}, { 3.4466395034174*^9, 3.4466395049462*^9}, 3.4466395515755997`*^9, { 3.4466396000176*^9, 3.4466396190808*^9}, {3.4466397459088*^9, 3.446639748826*^9}, {3.4466397974356003`*^9, 3.446639798668*^9}, 3.4466398447816*^9, {3.446639894218*^9, 3.4466399201556*^9}, { 3.4466399570964003`*^9, 3.4466399583288*^9}, {3.446639994006*^9, 3.4466400056904*^9}, {3.4466400383568*^9, 3.4466400395892*^9}, { 3.4466400745643997`*^9, 3.4466401025976*^9}, {3.4466401660834*^9, 3.4466401806070004`*^9}, {3.4466402251294003`*^9, 3.446640227407*^9}, { 3.446640260479*^9, 3.4466402657674*^9}, {3.4466404133122*^9, 3.4466405185654*^9}, 3.4466405830462*^9, {3.4467273294214*^9, 3.4467273777813997`*^9}, {3.4467274366558*^9, 3.4467275620954*^9}, { 3.446727593311*^9, 3.4467277412614*^9}, {3.4467283334639997`*^9, 3.4467283356012*^9}, {3.4467283707636003`*^9, 3.4467283727604*^9}, { 3.4467289882664003`*^9, 3.4467291276836*^9}, {3.446778464322*^9, 3.4467786797424*^9}, {3.4467801953803997`*^9, 3.4467802409792*^9}, { 3.4467802998691998`*^9, 3.4467804023456*^9}, 3.4467804345596*^9, { 3.4467808656344*^9, 3.4467808670852003`*^9}, 3.4467818107525997`*^9, { 3.446781855509*^9, 3.446781874385*^9}, {3.4467826737914*^9, 3.4467827381726*^9}, {3.4467828623018*^9, 3.4467831045386*^9}, { 3.4470344113984003`*^9, 3.4470344123344*^9}, {3.4470344628316*^9, 3.4470345343108*^9}, {3.447043591118539*^9, 3.447043642192939*^9}, { 3.447045649625739*^9, 3.447045718437339*^9}, {3.447054774023939*^9, 3.447054834198939*^9}, {3.4470549103449388`*^9, 3.4470549116169386`*^9}, { 3.447054943902939*^9, 3.4470553027109385`*^9}, {3.447055334559939*^9, 3.447055353684939*^9}, {3.447057311918539*^9, 3.447057369747739*^9}, { 3.4470575058577385`*^9, 3.4470575951365385`*^9}, {3.4470581848789387`*^9, 3.4470582040825386`*^9}, {3.451276121243*^9, 3.4512761425838003`*^9}, { 3.4512762022382*^9, 3.4512762064346*^9}, {3.4512762476966*^9, 3.4512762827654*^9}, {3.451276489091*^9, 3.451276541975*^9}, { 3.4512765853118*^9, 3.4512766132046003`*^9}, {3.4512773470306*^9, 3.4512773766082*^9}, {3.4512776069110003`*^9, 3.4512777499318*^9}, 3.4512777831286*^9, {3.4512778785538*^9, 3.451277881627*^9}, { 3.4512780242734003`*^9, 3.4512780302794*^9}, 3.4512780737878*^9, { 3.4512781866226*^9, 3.4512781930810003`*^9}, {3.4512863325078*^9, 3.4512863539266*^9}, {3.4568019250434*^9, 3.4568022712698*^9}, { 3.4568023177422*^9, 3.4568024125278*^9}, {3.4568024694365997`*^9, 3.4568024750369997`*^9}, {3.4568026914402*^9, 3.4568028101094*^9}, { 3.4568028406698*^9, 3.4568028564726*^9}, 3.4568028886085997`*^9, { 3.4568030489454*^9, 3.4568030800986*^9}, 3.4568032004128*^9, { 3.4568035073698*^9, 3.4568035176034*^9}, {3.4568040146596003`*^9, 3.4568040844852*^9}, {3.4568043016684*^9, 3.4568043154744*^9}, { 3.4568045482264*^9, 3.4568045486632*^9}, {3.4568048944996*^9, 3.4568049806116*^9}, {3.4660560628582*^9, 3.4660560753538*^9}, { 3.4660676729379997`*^9, 3.4660676735931997`*^9}, {3.4660677244024*^9, 3.4660677277251997`*^9}, {3.4742646771287394`*^9, 3.47426469439174*^9}, { 3.47426489921974*^9, 3.4742649800437393`*^9}, {3.4801246373348*^9, 3.4801246860536003`*^9}, {3.4801247748176003`*^9, 3.4801247821028*^9}, { 3.4801248161264*^9, 3.4801248295736*^9}, {3.4801248810692*^9, 3.4801248964508*^9}, {3.4801249330484*^9, 3.480124947884*^9}, 3.4801249886468*^9, {3.4801251139147997`*^9, 3.48012512588*^9}, { 3.4838339444988003`*^9, 3.4838339567448*^9}, 3.4838341692012*^9, { 3.4838344350408*^9, 3.4838344353684*^9}, {3.4938987575920324`*^9, 3.4938987586840324`*^9}, {3.4941630624049997`*^9, 3.4941631381274*^9}, { 3.4941632311345997`*^9, 3.4941632492306004`*^9}, 3.4941633249217997`*^9, { 3.4941633940922003`*^9, 3.4941634063538*^9}, {3.4941634538402*^9, 3.4941635051642*^9}, {3.494163565115*^9, 3.4941636341762*^9}, { 3.4941636853442*^9, 3.4941639323234*^9}, {3.4941640277798*^9, 3.4941641455754004`*^9}, {3.4941641790374002`*^9, 3.4941641803789997`*^9}, {3.4941642676142*^9, 3.4941643277678003`*^9}, 3.4941644677018003`*^9, {3.4941646208938*^9, 3.4941646322349997`*^9}, { 3.4941652592693996`*^9, 3.4941652807194*^9}, {3.4941653119038*^9, 3.494165416299*^9}, {3.494165453895*^9, 3.4941654544722*^9}, { 3.4950990979779997`*^9, 3.495099142701*^9}, {3.495099172958*^9, 3.4950991806289997`*^9}, {3.495099227097*^9, 3.495099238113*^9}, 3.495099290797*^9, {3.495099346084*^9, 3.495099359507*^9}, { 3.495099456308*^9, 3.495099464091*^9}, 3.495099683108*^9, { 3.495100428112*^9, 3.495100434958*^9}, {3.4951006496219997`*^9, 3.495100649992*^9}, {3.4987235265018*^9, 3.4987235939094*^9}, { 3.4987236420666*^9, 3.4987236530646*^9}, {3.4987237305341997`*^9, 3.4987237396914*^9}, {3.498733136159*^9, 3.4987332972446003`*^9}, { 3.4987364783094*^9, 3.4987364860626*^9}, {3.4987366201134*^9, 3.4987366236078*^9}, {3.4987367272386*^9, 3.4987367464890003`*^9}, { 3.4987369428462*^9, 3.4987369670886*^9}, {3.4987370134518003`*^9, 3.4987370259941998`*^9}, {3.4987370944002*^9, 3.4987371027618*^9}, { 3.4987371921029997`*^9, 3.498737193663*^9}, {3.4987372660938*^9, 3.4987372935498*^9}, {3.4987373290554*^9, 3.4987377176202*^9}, { 3.4987377520182*^9, 3.4987379139462*^9}, {3.4987382030216*^9, 3.4987382667078*^9}, {3.4987888391818*^9, 3.4987888608346*^9}, { 3.4988785131146*^9, 3.4988785160162*^9}, {3.5007170967096*^9, 3.5007170999076*^9}, 3.5007182237316*^9, {3.5007182772864*^9, 3.5007182987832003`*^9}, {3.5009573226744003`*^9, 3.5009573940444*^9}, 3.5009574358710003`*^9, 3.5009604278482*^9, {3.5009897246173353`*^9, 3.5009898480289354`*^9}, {3.5009901464413357`*^9, 3.5009901475333357`*^9}, {3.5009901801997356`*^9, 3.500990274096135*^9}, { 3.5010475253292*^9, 3.5010475852332*^9}, {3.5010605722018003`*^9, 3.5010606739762*^9}, {3.5010607202146*^9, 3.5010607323358*^9}, { 3.5010607920526*^9, 3.501061118467*^9}, {3.5010612022078*^9, 3.5010612277138*^9}, {3.5010616467766*^9, 3.5010617938534*^9}, { 3.5010618406222*^9, 3.5010619950778*^9}, {3.5010621500638*^9, 3.5010622514014*^9}, {3.5010625292218*^9, 3.5010625409374*^9}, { 3.5010626043046*^9, 3.5010626313862*^9}, {3.5010626787166*^9, 3.5010626790754004`*^9}, {3.501074457561*^9, 3.5010744671082*^9}, 3.5010763029458*^9, {3.5032210899309998`*^9, 3.5032212413900003`*^9}, { 3.557658203404973*^9, 3.557658219644601*^9}, {3.5576584433801947`*^9, 3.557658496030287*^9}, {3.5576585501779823`*^9, 3.5576586046064777`*^9}, { 3.557658648910555*^9, 3.557658754600741*^9}, {3.557658963945511*^9, 3.5576589782507353`*^9}, {3.557659009949991*^9, 3.5576591437514267`*^9}, { 3.557659182221094*^9, 3.5576592187719584`*^9}, 3.557659413865901*^9, { 3.557659921100792*^9, 3.5576599556392527`*^9}, {3.557660706920972*^9, 3.5576607248454037`*^9}, {3.557661209085854*^9, 3.557661209413454*^9}, { 3.5577526651911488`*^9, 3.5577526932087984`*^9}, {3.5577527272480583`*^9, 3.557752747122493*^9}, {3.5577528374934516`*^9, 3.557752838523053*^9}, { 3.557752881204728*^9, 3.557752891313546*^9}, {3.557752938612829*^9, 3.5577529469120436`*^9}, {3.557753060714244*^9, 3.557753062633047*^9}, { 3.5577536609544907`*^9, 3.5577536637936954`*^9}, {3.5577537824631042`*^9, 3.557753810184353*^9}, {3.557753841025607*^9, 3.5577540648392*^9}, 3.5577541920574236`*^9, {3.5577547033327217`*^9, 3.557754716967146*^9}, { 3.5577547716296415`*^9, 3.557754802112095*^9}, {3.5577549509363565`*^9, 3.5577549771444025`*^9}, 3.5577551382302856`*^9, {3.55775527184452*^9, 3.557755272858522*^9}, {3.557755881555991*^9, 3.557755886548*^9}, { 3.557756158316077*^9, 3.557756231885806*^9}, {3.5577572408487787`*^9, 3.557757248835993*^9}, {3.5577572834368534`*^9, 3.5577575888229895`*^9}, { 3.5577578129641833`*^9, 3.557757862837471*^9}, {3.557758025514557*^9, 3.557758079272251*^9}, 3.557810586960072*^9, {3.5578240262005973`*^9, 3.5578240345360737`*^9}, {3.557824091429328*^9, 3.5578241008156557`*^9}, { 3.557831525255726*^9, 3.5578315319793377`*^9}, 3.5578315716190076`*^9, { 3.557831606079468*^9, 3.557831629432709*^9}, {3.5578316663267736`*^9, 3.5578317569473333`*^9}, {3.5578322144181366`*^9, 3.557832218084143*^9}, { 3.557836356693412*^9, 3.557836473771618*^9}, {3.5578365201660995`*^9, 3.5578365974018345`*^9}, {3.5578366426731143`*^9, 3.557836658865943*^9}, { 3.557836691017599*^9, 3.5578367924957776`*^9}, {3.5578368305442443`*^9, 3.557836888279946*^9}, {3.5578369382156334`*^9, 3.5578370776642785`*^9}, { 3.5578383536061196`*^9, 3.5578383735117545`*^9}, {3.5578385892445335`*^9, 3.5578385978869486`*^9}, {3.5578386713006773`*^9, 3.557838700113928*^9}, { 3.5578387451200075`*^9, 3.5578387467892103`*^9}, {3.5578388951454706`*^9, 3.5578389248635225`*^9}, {3.5578389679351983`*^9, 3.557838983535226*^9}, { 3.5578390227692947`*^9, 3.557839023143696*^9}, {3.557839097696226*^9, 3.5578391125162525`*^9}, {3.5578391553539276`*^9, 3.557839199892006*^9}, { 3.55783924184048*^9, 3.557839294490572*^9}, {3.5578393285922318`*^9, 3.557839398683155*^9}, {3.557839430522811*^9, 3.557839470162481*^9}, { 3.5578395370865984`*^9, 3.5578395446994114`*^9}, {3.5578396068499207`*^9, 3.5578396118575296`*^9}, 3.5578943518105097`*^9, {3.557894388361374*^9, 3.5578944029629993`*^9}, {3.5578944607611012`*^9, 3.5578944989499683`*^9}, {3.5578945393696394`*^9, 3.557894561537278*^9}, { 3.5578946028617506`*^9, 3.5578946188985786`*^9}, {3.557894650894235*^9, 3.5578947812636642`*^9}, {3.55789481884413*^9, 3.5578948191249304`*^9}, { 3.5578949768100076`*^9, 3.5578949836272197`*^9}, {3.5578967386805477`*^9, 3.55789678549623*^9}, {3.5578968804691963`*^9, 3.557896888643611*^9}, { 3.557897022491846*^9, 3.5578970341450663`*^9}, {3.557897620940097*^9, 3.55789765120415*^9}, {3.5579218072271147`*^9, 3.5579218263059483`*^9}, { 3.557922095312821*^9, 3.557922116965659*^9}, {3.557922178086566*^9, 3.557922188616585*^9}, {3.5579223258812256`*^9, 3.557922327066828*^9}, { 3.5579224596046605`*^9, 3.557922461804264*^9}, 3.5579805928465395`*^9, { 3.5579815200581703`*^9, 3.557981541711009*^9}, 3.557985544779242*^9, { 3.5579863164793987`*^9, 3.5579863339514294`*^9}, {3.557986523210962*^9, 3.557986568841042*^9}, 3.5579866122559185`*^9, 3.557986993536188*^9, { 3.5579871244716187`*^9, 3.5579871290580263`*^9}, 3.557987173486905*^9, 3.5579872166989803`*^9, {3.5599618621582537`*^9, 3.5599618642486577`*^9}, { 3.559961969720443*^9, 3.5599619894700775`*^9}, 3.559963611089726*^9, { 3.5601298891258235`*^9, 3.560129889422224*^9}, {3.560132445157113*^9, 3.5601324458591146`*^9}, {3.561978472080926*^9, 3.561978472392926*^9}, { 3.6297802564412937`*^9, 3.6297802957377625`*^9}, {3.62978033369263*^9, 3.629780429741998*^9}, {3.6297805790030603`*^9, 3.6297809429048996`*^9}, { 3.629780987957779*^9, 3.629781197575347*^9}, {3.629781240397422*^9, 3.629781337663593*^9}, {3.6297813946972933`*^9, 3.6297814529165955`*^9}, { 3.6297814952550697`*^9, 3.629781527578326*^9}, {3.62978162025529*^9, 3.629781647633338*^9}, {3.629781678833393*^9, 3.629781763120341*^9}, 3.6297818028224106`*^9, {3.6297818432108817`*^9, 3.629781872570133*^9}, { 3.629782355765382*^9, 3.629782427603508*^9}, {3.6297824692243814`*^9, 3.629782674863942*^9}, {3.629782707218399*^9, 3.6297829295343895`*^9}, { 3.629783005631323*^9, 3.6297830574702144`*^9}, {3.6297831098551064`*^9, 3.629783142786764*^9}, {3.629783433711675*^9, 3.629783442619291*^9}, { 3.6297834942397814`*^9, 3.6297835175930223`*^9}, 3.6297835794939313`*^9, { 3.6297836160291953`*^9, 3.6297837668970604`*^9}, {3.6297842042438283`*^9, 3.6297842697483435`*^9}, {3.6297843514456873`*^9, 3.629784370742921*^9}, { 3.629784443829049*^9, 3.6297844678842916`*^9}, {3.6297845252611923`*^9, 3.629784525588793*^9}, {3.6297846136821475`*^9, 3.629784629235375*^9}, { 3.629784814797701*^9, 3.629784927648299*^9}, {3.629785259960083*^9, 3.6297852602096834`*^9}, {3.6297858780175686`*^9, 3.629785917282837*^9}, { 3.629786048057867*^9, 3.629786048681868*^9}, 3.6297863278755584`*^9, { 3.6297867047133856`*^9, 3.629786748533863*^9}, {3.6297867791567163`*^9, 3.6297868491540394`*^9}, {3.6297875320748396`*^9, 3.629787569795706*^9}, { 3.6297876247234025`*^9, 3.6297877281983843`*^9}, {3.6297877681812544`*^9, 3.629787774015665*^9}, {3.629787831408166*^9, 3.6297878355265727`*^9}, { 3.6297878775686464`*^9, 3.6297878861174617`*^9}, {3.6297879185343184`*^9, 3.629787919064719*^9}, {3.6297880043032694`*^9, 3.62978800470887*^9}, 3.6297880488257475`*^9, {3.6297882100052304`*^9, 3.6297882174776435`*^9}, { 3.6297882697533355`*^9, 3.6297882948381796`*^9}, {3.6297883467550707`*^9, 3.6297883991087627`*^9}, {3.6297887361785545`*^9, 3.629788783961438*^9}, 3.629788825395111*^9, {3.629789006152629*^9, 3.6297890321266747`*^9}, { 3.6297891133248167`*^9, 3.629789145336073*^9}, {3.6297891926821566`*^9, 3.629789194257759*^9}, {3.629789255316266*^9, 3.6297892556282673`*^9}, { 3.629869102295367*^9, 3.629869160124668*^9}, {3.6298691942887287`*^9, 3.6298696149902673`*^9}, {3.6298696993864155`*^9, 3.62986975897852*^9}, { 3.6298698387726603`*^9, 3.629869912030389*^9}, {3.6298700722270703`*^9, 3.629870234560955*^9}, {3.629870580429163*^9, 3.629870630458451*^9}, { 3.630556081081209*^9, 3.630556104902451*^9}, {3.6305562643503313`*^9, 3.6305562763935523`*^9}, {3.6305563415080667`*^9, 3.630556480956712*^9}, { 3.630556692851884*^9, 3.630556695347888*^9}, {3.630556730042349*^9, 3.630556914528273*^9}, {3.6305653725974936`*^9, 3.6305656807121167`*^9}, { 3.630565758760581*^9, 3.6305657739024467`*^9}, {3.630565858170267*^9, 3.63056596644846*^9}, {3.6305661502619734`*^9, 3.6305661523230915`*^9}, { 3.6305662653385553`*^9, 3.630566370352562*^9}, {3.6305667786019125`*^9, 3.630566790535595*^9}, {3.6305668214773645`*^9, 3.630567044691132*^9}, { 3.6305670772499943`*^9, 3.6305670783710585`*^9}, 3.630567272031135*^9, { 3.630567303902958*^9, 3.630567409875019*^9}, {3.630568671196477*^9, 3.6305687195002403`*^9}, {3.6305687542132254`*^9, 3.630568758623478*^9}, { 3.630568855671028*^9, 3.630568859250233*^9}, {3.630569706514694*^9, 3.630569775526641*^9}, 3.630569982346471*^9, {3.6305701679130845`*^9, 3.630570205199217*^9}, {3.6305703751399374`*^9, 3.630570526177576*^9}, { 3.630587657039589*^9, 3.630587688367381*^9}, {3.6305880733027773`*^9, 3.6305883365376396`*^9}, {3.6305886689118233`*^9, 3.6305886717978287`*^9}, 3.6305889776831656`*^9, {3.6305890389444733`*^9, 3.6305890437180815`*^9}, { 3.630589093248169*^9, 3.6305891296430326`*^9}, 3.630589181700324*^9, { 3.6305892509956455`*^9, 3.6305892594820604`*^9}, {3.630589318949365*^9, 3.6305893334729905`*^9}, {3.630589630294712*^9, 3.6305896376267247`*^9}, { 3.630589683288005*^9, 3.630589684988408*^9}, {3.630597310538067*^9, 3.630597340080757*^9}, {3.630597391446695*^9, 3.630597400596218*^9}, { 3.6305974350611897`*^9, 3.6305974605306463`*^9}, {3.630633997622449*^9, 3.630634003125764*^9}, {3.630659322217756*^9, 3.63065932438616*^9}, { 3.6306611578252783`*^9, 3.6306611625988865`*^9}, {3.6306612541554475`*^9, 3.630661257587454*^9}, {3.6306613001287284`*^9, 3.6306613026715326`*^9}, { 3.6306613920752897`*^9, 3.6306613949768953`*^9}, {3.6306706377509866`*^9, 3.630670654957817*^9}, {3.6306749981919994`*^9, 3.630675005793434*^9}, { 3.6306751229631357`*^9, 3.630675150017683*^9}, {3.6306752035287437`*^9, 3.6306752096180925`*^9}, {3.630675315921172*^9, 3.6306753201514144`*^9}, { 3.6306757793287754`*^9, 3.6306757796257925`*^9}, {3.630675814406262*^9, 3.6306758147026625`*^9}, {3.6306760107574763`*^9, 3.6306760154417443`*^9}, {3.6306789722320743`*^9, 3.6306789870309205`*^9}, {3.6306790257051325`*^9, 3.630679028076268*^9}, { 3.6306800259177256`*^9, 3.6306800406129513`*^9}, {3.6306801239326982`*^9, 3.6306801300167084`*^9}, {3.630680769261832*^9, 3.6306807806186523`*^9}, { 3.630681157468514*^9, 3.6306811577649145`*^9}, {3.6306812744219193`*^9, 3.63068127471832*^9}, {3.6306817187418995`*^9, 3.6306817919060287`*^9}, { 3.630681879188182*^9, 3.6306819111526375`*^9}, {3.6306821191790032`*^9, 3.6306821283050194`*^9}, {3.630720543651497*^9, 3.6307205534300566`*^9}, { 3.630721035525631*^9, 3.630721092774905*^9}, {3.6307212510439577`*^9, 3.6307213064777765`*^9}, {3.6307477437169704`*^9, 3.6307478284095197`*^9}, {3.6307478614971776`*^9, 3.6307478785948076`*^9}, {3.6307479884814005`*^9, 3.630748002880226*^9}, { 3.630748045624301*^9, 3.630748063876333*^9}, {3.630748111596817*^9, 3.6307481498324842`*^9}, {3.6307489182430334`*^9, 3.6307489447786803`*^9}, {3.630749037427243*^9, 3.6307490443848553`*^9}, { 3.6307491041485605`*^9, 3.6307491384218206`*^9}, {3.6307491914151134`*^9, 3.630749196890723*^9}, {3.6307492445800066`*^9, 3.6307493439989815`*^9}, { 3.630749396212273*^9, 3.6307494766304145`*^9}, {3.6307495333989143`*^9, 3.6307495547241516`*^9}, {3.6307496525831237`*^9, 3.630749669571553*^9}, { 3.630750220602922*^9, 3.6307502881822405`*^9}, {3.6307510631916018`*^9, 3.630751068292811*^9}, {3.6307511226589065`*^9, 3.630751137962533*^9}, { 3.6307512555243397`*^9, 3.630751282777588*^9}, {3.630752266971757*^9, 3.630752414599744*^9}, {3.630752446407563*^9, 3.630752457388191*^9}, { 3.6307589380050273`*^9, 3.6307590266300964`*^9}, {3.6307591666721067`*^9, 3.63075923229886*^9}, 3.630760288282259*^9, {3.6307603547370596`*^9, 3.630760557414652*^9}, {3.630760654134184*^9, 3.63076065510824*^9}, { 3.6307606911683025`*^9, 3.6307606919283457`*^9}, {3.6307607642334814`*^9, 3.6307607648645177`*^9}, {3.630761455000991*^9, 3.6307614616743727`*^9}, { 3.630761507825012*^9, 3.630761605776615*^9}, {3.630761652999316*^9, 3.630761695865768*^9}, {3.630761771278081*^9, 3.6307617792215357`*^9}, 3.6307629478424797`*^9, {3.632205207880766*^9, 3.6322052561155243`*^9}, { 3.6322052892474194`*^9, 3.6322052915745525`*^9}, 3.6322053746993074`*^9, { 3.6322062705415463`*^9, 3.6322062726016645`*^9}, {3.6322063396935015`*^9, 3.63220636484194*^9}, {3.6322064410612993`*^9, 3.6322064491667633`*^9}, { 3.632206580308264*^9, 3.6322066373275256`*^9}, {3.6322066736436024`*^9, 3.6322067467737856`*^9}, {3.632206782260815*^9, 3.6322071351279984`*^9}, 3.6322071989226465`*^9, {3.632207270393735*^9, 3.6322073359894867`*^9}, { 3.6322073997741346`*^9, 3.6322074126708727`*^9}, {3.632207491777397*^9, 3.632207682289294*^9}, {3.632207809621577*^9, 3.632207827973626*^9}, { 3.6322079043859973`*^9, 3.6322079279443445`*^9}, {3.6322080916397076`*^9, 3.6322081666649985`*^9}, 3.634905258940913*^9, {3.634905370524296*^9, 3.6349054089004903`*^9}, {3.6349054472556844`*^9, 3.63490544787272*^9}, { 3.634905483492757*^9, 3.6349055164646425`*^9}, {3.634905574352954*^9, 3.634905628121029*^9}, {3.6349057012822137`*^9, 3.6349057207913294`*^9}, { 3.6349061371061416`*^9, 3.634906354438572*^9}, {3.6349063890455513`*^9, 3.6349064369332905`*^9}, {3.634906537696054*^9, 3.634906601859724*^9}, 3.634906706128688*^9, {3.6349069249442034`*^9, 3.6349069328326545`*^9}, { 3.6349070151973653`*^9, 3.6349070242298822`*^9}, {3.6349070817921743`*^9, 3.6349070822111983`*^9}, {3.634907723288866*^9, 3.634907739005765*^9}, { 3.6349079580732946`*^9, 3.6349079868219395`*^9}, {3.634908200284148*^9, 3.634908315195721*^9}, {3.6349083774582825`*^9, 3.6349084027997313`*^9}, { 3.63490844507615*^9, 3.634908448843365*^9}, {3.634914956333157*^9, 3.634915020054802*^9}, {3.634915050572547*^9, 3.6349150956171236`*^9}, { 3.6349539785771523`*^9, 3.634953978975175*^9}, {3.6349540728785458`*^9, 3.6349541681829967`*^9}, {3.634954211263461*^9, 3.6349542495746527`*^9}, { 3.6349543251259737`*^9, 3.634954355882733*^9}, {3.6349543892536416`*^9, 3.6349544742835045`*^9}, {3.634954547519694*^9, 3.6349545640246377`*^9}, { 3.6349547051657104`*^9, 3.6349547107930326`*^9}, {3.634954745355009*^9, 3.634954752101395*^9}, {3.6349547948858423`*^9, 3.6349548053894434`*^9}, { 3.634954904907135*^9, 3.6349549451084347`*^9}, {3.634955219605135*^9, 3.6349552640926795`*^9}, {3.634955320189888*^9, 3.634955348763522*^9}, { 3.634955386393675*^9, 3.6349555039273973`*^9}, {3.6349557669644423`*^9, 3.6349557672004557`*^9}, {3.634955894841756*^9, 3.634955902578199*^9}, { 3.6349559513739896`*^9, 3.6349560216320086`*^9}, {3.634956120144643*^9, 3.634956128996149*^9}, {3.6349561700724983`*^9, 3.6349561978900895`*^9}, { 3.6349562480719595`*^9, 3.634956254326318*^9}, {3.634956331684742*^9, 3.6349563460575643`*^9}, {3.634956379242462*^9, 3.63495642676418*^9}, 3.6349564696636343`*^9, {3.6351524116477795`*^9, 3.6351524153379908`*^9}, { 3.6352134400282927`*^9, 3.635213442148414*^9}, {3.6352134745862694`*^9, 3.635213495869487*^9}, {3.6352135383409157`*^9, 3.6352137157160616`*^9}, { 3.6352137493569856`*^9, 3.635213764522853*^9}, {3.635214215036621*^9, 3.635214227593339*^9}, {3.635214407257615*^9, 3.63521441713218*^9}, { 3.635215297101512*^9, 3.635215303964904*^9}, {3.6352154111120324`*^9, 3.635215431504199*^9}, {3.635216346055508*^9, 3.635216494371991*^9}, { 3.635216631050809*^9, 3.6352166603244834`*^9}, {3.635216763034358*^9, 3.635216764164423*^9}, {3.6352168771938877`*^9, 3.635216888828553*^9}, 3.6352169832479534`*^9, 3.635217037668066*^9, {3.6352172024924936`*^9, 3.6352172054526625`*^9}, {3.635217344025589*^9, 3.635217346898753*^9}, 3.6352173863770113`*^9, {3.635217519639633*^9, 3.6352175507014103`*^9}, 3.635217615445113*^9, {3.6352178715087595`*^9, 3.635217880460271*^9}, { 3.6352185912849283`*^9, 3.635218598444338*^9}, {3.6352186995721216`*^9, 3.635218714955002*^9}, {3.6352189761749425`*^9, 3.6352189789341*^9}, { 3.6352195060322485`*^9, 3.635219509972474*^9}, 3.6352195673477554`*^9, 3.6352195994635925`*^9, {3.6352197336482677`*^9, 3.635219737452485*^9}, { 3.6352197706093817`*^9, 3.6352197723214793`*^9}, {3.635219941784172*^9, 3.6352199485115566`*^9}, {3.6352200714185867`*^9, 3.6352200854323883`*^9}, {3.6352202085694313`*^9, 3.635220235849992*^9}, { 3.6352202816336107`*^9, 3.6352203110962954`*^9}, {3.6352204980449886`*^9, 3.6352205276526823`*^9}, {3.6352253191447396`*^9, 3.6352253299913597`*^9}, {3.6352253611111403`*^9, 3.6352253637572913`*^9}, {3.635225409322898*^9, 3.6352255965196047`*^9}, { 3.6352260914249115`*^9, 3.6352261698393965`*^9}, {3.63522638233055*^9, 3.6352264188036366`*^9}, {3.635227493469104*^9, 3.635227556935734*^9}, { 3.6352276745764627`*^9, 3.635227730116639*^9}, {3.6352287979917183`*^9, 3.6352288587651944`*^9}, {3.635228894237223*^9, 3.635228948324317*^9}, { 3.635229365252164*^9, 3.6352293902275925`*^9}, {3.63522947690555*^9, 3.6352294807837715`*^9}, {3.6352492831123204`*^9, 3.6352492983621926`*^9}, 3.6356569054520617`*^9, {3.6363778004499054`*^9, 3.636377802787039*^9}, { 3.6363778414932528`*^9, 3.6363778525308843`*^9}, {3.636384436335312*^9, 3.6363846409950175`*^9}, {3.636384971250907*^9, 3.6363849738080535`*^9}, { 3.6363850170465264`*^9, 3.636385030729309*^9}, {3.6363851286779118`*^9, 3.636385138359465*^9}, {3.6363851699712734`*^9, 3.636385223111313*^9}, { 3.656076172452749*^9, 3.656076182171566*^9}, {3.6560765578514256`*^9, 3.656076619019133*^9}, 3.6560772545486493`*^9, {3.6630719749029694`*^9, 3.6630719878027077`*^9}, {3.6630720702554235`*^9, 3.6630720807290225`*^9}, {3.6630721155740156`*^9, 3.6630721713712068`*^9}, {3.663072270834896*^9, 3.6630722882218904`*^9}, 3.6630724099968557`*^9, {3.685234767958906*^9, 3.685234768480936*^9}, { 3.685252204033695*^9, 3.6852522340537376`*^9}, {3.6852522757137957`*^9, 3.6852523115138454`*^9}, {3.68525376314359*^9, 3.6852537725041256`*^9}, { 3.6852539763277836`*^9, 3.6852539861693463`*^9}, 3.6852540682470407`*^9, 3.6852541660656357`*^9, {3.6852604801645336`*^9, 3.6852605060345697`*^9}, { 3.6852605373446136`*^9, 3.6852605977846985`*^9}, 3.685260655254779*^9, { 3.6853280002218475`*^9, 3.685328019561875*^9}, 3.685328064721938*^9, { 3.6853280953119807`*^9, 3.6853282636022167`*^9}, {3.685328356242346*^9, 3.685328598671985*^9}, {3.6853286682069626`*^9, 3.6853287982524004`*^9}, { 3.6853288753368096`*^9, 3.6853289367033195`*^9}, {3.685328968274125*^9, 3.685328978713722*^9}, {3.685329033941881*^9, 3.685329044950511*^9}, { 3.685329173522865*^9, 3.6853294420842257`*^9}, {3.6853296024223967`*^9, 3.6853296124319687`*^9}, {3.6853297221712456`*^9, 3.685329733349885*^9}, { 3.6853298076291337`*^9, 3.6853298739599276`*^9}, {3.685330038474337*^9, 3.685330051652091*^9}, {3.6853311309428225`*^9, 3.685331168378964*^9}, { 3.685340142134763*^9, 3.685340180544817*^9}, {3.6853583292043543`*^9, 3.685358334834362*^9}, {3.685358366084406*^9, 3.685358366954407*^9}, { 3.685358408404465*^9, 3.685358518294619*^9}, 3.685358620174762*^9, 3.6853586578748145`*^9, {3.6853588750151186`*^9, 3.6853588857151337`*^9}, { 3.6853589302051954`*^9, 3.685358938995208*^9}, {3.685359014715314*^9, 3.6853590296653347`*^9}, 3.685359148315501*^9, 3.6853598281764526`*^9, { 3.6853683109000263`*^9, 3.685368382250126*^9}, {3.685368420160179*^9, 3.6853684704302497`*^9}, {3.6853685194503183`*^9, 3.685368742860631*^9}, { 3.685369008901004*^9, 3.68536902061102*^9}, {3.6853690791611023`*^9, 3.685369132301176*^9}, {3.6853693219914417`*^9, 3.6853693304114532`*^9}, 3.6853696089118433`*^9, {3.6858758911429157`*^9, 3.685875951793*^9}, { 3.6859484099082212`*^9, 3.6859484970032024`*^9}, {3.686052829875022*^9, 3.686052906242383*^9}, {3.6860535326822133`*^9, 3.686053598029951*^9}, { 3.68605365168902*^9, 3.6860541446091995`*^9}, {3.6860541846064873`*^9, 3.68605440393201*^9}, {3.686054713802734*^9, 3.6860547858298535`*^9}, { 3.6860548280202665`*^9, 3.686054837219793*^9}, {3.686054874127904*^9, 3.686054892139934*^9}, {3.686055136014883*^9, 3.6860551460584574`*^9}, { 3.686055211281188*^9, 3.6860552301962633`*^9}, {3.6860553465409174`*^9, 3.6860553998749685`*^9}, {3.6860556017188663`*^9, 3.6860556050188704`*^9}, {3.6862923512707715`*^9, 3.686292363600789*^9}, { 3.686292409650853*^9, 3.6862924109708548`*^9}, {3.6862924536109147`*^9, 3.6862924596309233`*^9}, {3.686292542221039*^9, 3.6862925430110397`*^9}, { 3.686292988803664*^9, 3.686293001033681*^9}, {3.6866504529025555`*^9, 3.686650526682659*^9}, {3.686650671852862*^9, 3.6866507242929354`*^9}, { 3.6866507657529936`*^9, 3.6866507887630253`*^9}, {3.6866508208230705`*^9, 3.6866509100531955`*^9}, {3.6866509593932643`*^9, 3.686650971113281*^9}, { 3.686651007793332*^9, 3.6866511595335445`*^9}, {3.686651223513634*^9, 3.686651234033649*^9}, {3.686651304763748*^9, 3.6866513363837924`*^9}, { 3.6866514102038956`*^9, 3.686651429943923*^9}, {3.686652993837468*^9, 3.6866530046274834`*^9}, {3.686804398511652*^9, 3.6868044081516657`*^9}, { 3.6868046315619783`*^9, 3.686804631801979*^9}, {3.686804685872054*^9, 3.686804707092084*^9}, {3.6868047382021275`*^9, 3.686804767812169*^9}, { 3.686804824012248*^9, 3.6868048404922705`*^9}, {3.686804942142413*^9, 3.6868049633424425`*^9}, {3.6868050765526013`*^9, 3.686805101092636*^9}, { 3.6868051463526993`*^9, 3.6868052234228067`*^9}, {3.686805307602925*^9, 3.686805311682931*^9}, {3.68680577547358*^9, 3.686805788923599*^9}, { 3.686821702197342*^9, 3.6868217282873783`*^9}, {3.6868225192884855`*^9, 3.686822538368512*^9}, {3.6868226306886415`*^9, 3.6868226683086944`*^9}, { 3.6868227318887835`*^9, 3.6868227627088265`*^9}, {3.686822801638881*^9, 3.6868230490692277`*^9}, {3.686823122979331*^9, 3.6868231833294153`*^9}, { 3.6868232450595016`*^9, 3.6868233753996844`*^9}, {3.6868234153897405`*^9, 3.686823451379791*^9}, {3.6868236736101017`*^9, 3.6868236786601086`*^9}, { 3.6868237164601617`*^9, 3.68682375072021*^9}, {3.68682389396041*^9, 3.68682390087042*^9}, {3.686823940790476*^9, 3.6868239416904774`*^9}, { 3.6868239808805323`*^9, 3.6868239872905407`*^9}, {3.686824051540631*^9, 3.6868240519006314`*^9}, {3.686824360861064*^9, 3.6868243761510854`*^9}, { 3.6868245440213203`*^9, 3.686824577221367*^9}, {3.686824685841519*^9, 3.6868246979115357`*^9}, 3.6868248012716804`*^9, 3.6868253582724605`*^9, { 3.6868255183026843`*^9, 3.686825518932685*^9}, {3.6868264466639843`*^9, 3.6868264497139883`*^9}, {3.6868267792744493`*^9, 3.6868268152945004`*^9}, {3.686827100164899*^9, 3.6868271210549283`*^9}, 3.686827162004986*^9, {3.6868272414950967`*^9, 3.686827327475217*^9}, { 3.686827953126093*^9, 3.686827976506126*^9}, {3.686829128577739*^9, 3.686829138957753*^9}, 3.6868292410978966`*^9, {3.6868292768379464`*^9, 3.686829282727955*^9}, {3.6868293820380936`*^9, 3.686829418138144*^9}, { 3.686829846748744*^9, 3.686829848298746*^9}, {3.6868313063207874`*^9, 3.686831307180789*^9}, {3.6868331276633377`*^9, 3.68683328653356*^9}, { 3.6868394697195063`*^9, 3.6868394933895392`*^9}, 3.686839530999592*^9, { 3.686839582829664*^9, 3.68683963686974*^9}, {3.6868397551199055`*^9, 3.68683979365996*^9}, {3.6868398344600167`*^9, 3.686839866200061*^9}, { 3.687092084401948*^9, 3.687092117031994*^9}, {3.6870922598621936`*^9, 3.6870922645422*^9}, {3.6870962086478376`*^9, 3.6870962658779182`*^9}, 3.687096444838168*^9, {3.687096500978247*^9, 3.687096501638248*^9}, { 3.6870965809883595`*^9, 3.687096592708376*^9}, 3.687096837948719*^9, { 3.68709688890879*^9, 3.687096985798926*^9}, {3.6870971015990877`*^9, 3.6870972179192505`*^9}, {3.6870972618993125`*^9, 3.687097305639374*^9}, { 3.6870973356794157`*^9, 3.6870975186496716`*^9}, {3.6870975796097574`*^9, 3.6870975953197794`*^9}, {3.6870976531898603`*^9, 3.6870976848899045`*^9}, 3.6870977782500353`*^9, {3.687413757687042*^9, 3.6874137834070783`*^9}, { 3.6874140542074575`*^9, 3.687414094417514*^9}, {3.6874143478878684`*^9, 3.687414485538061*^9}, {3.6874146116082373`*^9, 3.68741464894829*^9}, { 3.6874147451084247`*^9, 3.687414766118454*^9}, 3.6874149094486547`*^9, { 3.6874150416688395`*^9, 3.6874150634888706`*^9}, {3.6874152437091227`*^9, 3.687415268869158*^9}, 3.6874153442892637`*^9, {3.687415449879411*^9, 3.687415469659439*^9}, 3.687415529739523*^9, 3.687415564789572*^9, 3.687415645529685*^9, {3.6874168016913037`*^9, 3.687416803441306*^9}, { 3.687421022677213*^9, 3.6874212686075573`*^9}, {3.68742948209425*^9, 3.6874294906842623`*^9}, {3.687844340668378*^9, 3.6878443698084188`*^9}, { 3.6886534778571014`*^9, 3.6886534911571198`*^9}, {3.688906380162199*^9, 3.6889064680223217`*^9}, {3.688906514222396*^9, 3.6889065193925257`*^9}, { 3.688908192623024*^9, 3.6889082006430354`*^9}, {3.688908261823121*^9, 3.688908271653135*^9}, {3.6889083776232834`*^9, 3.6889083922733035`*^9}, { 3.688908466073407*^9, 3.6889084993734536`*^9}, 3.688908533623502*^9, { 3.688908616683618*^9, 3.6889086271336327`*^9}, {3.6889086885637183`*^9, 3.6889087063437433`*^9}, {3.6889091647443852`*^9, 3.6889092012544365`*^9}, {3.6889093019045773`*^9, 3.6889093406746316`*^9}, 3.6889101071957045`*^9, {3.689905940063133*^9, 3.689905972983179*^9}, { 3.692530981927737*^9, 3.6925310416778207`*^9}, {3.692531099797902*^9, 3.6925311384779563`*^9}, {3.692531192258032*^9, 3.692531244668105*^9}, { 3.6925312919881716`*^9, 3.692531425418358*^9}, {3.6925315270885005`*^9, 3.692531643928664*^9}, {3.692535489534048*^9, 3.6925356485142703`*^9}, { 3.692535753564418*^9, 3.6925357992544813`*^9}, {3.6925358831745987`*^9, 3.692535899604622*^9}, {3.692536042584822*^9, 3.692536159384986*^9}, { 3.6925366121156197`*^9, 3.6925366207256317`*^9}, {3.6925367265057793`*^9, 3.69253672683578*^9}, {3.6925368590559654`*^9, 3.6925368636559715`*^9}, { 3.6925370880062857`*^9, 3.692537177856412*^9}, {3.692537322456614*^9, 3.6925373869767046`*^9}, {3.6925390913352747`*^9, 3.6925390925252767`*^9}, {3.692539644430175*^9, 3.6925396711502123`*^9}, { 3.692539727510291*^9, 3.692539730440295*^9}, {3.69253993367058*^9, 3.692539963780622*^9}, {3.6925400018406754`*^9, 3.692540003630678*^9}, { 3.6925401743409166`*^9, 3.6925401747509174`*^9}, {3.692540399111232*^9, 3.692540407981244*^9}, {3.69254047647134*^9, 3.6925404886113567`*^9}, { 3.6925406039715185`*^9, 3.69254060531152*^9}, {3.6925414948727655`*^9, 3.6925414953427663`*^9}, {3.6925415478528395`*^9, 3.692541613062931*^9}, 3.692541649332982*^9, {3.692541727633092*^9, 3.6925418840133104`*^9}, { 3.692541924473367*^9, 3.692542041693531*^9}, {3.6925421488836813`*^9, 3.6925422549438295`*^9}, {3.6925422976938896`*^9, 3.692542521444203*^9}, { 3.6925426221843443`*^9, 3.6925426357343626`*^9}, 3.692542739374508*^9, 3.692599799510878*^9, {3.692599834884901*^9, 3.6925998954663663`*^9}, { 3.692599925635092*^9, 3.6926000095928946`*^9}, {3.692600108929576*^9, 3.6926001456386757`*^9}, {3.6926001874800687`*^9, 3.692600454421337*^9}, { 3.692600503149027*^9, 3.6926006000391626`*^9}, {3.692600680251275*^9, 3.6926006814012766`*^9}, {3.6926009000215826`*^9, 3.6926009410816402`*^9}, 3.692601280532116*^9, {3.6926044914726114`*^9, 3.69260449774262*^9}, 3.6926045660127153`*^9, 3.6926046690228596`*^9, {3.69296647863291*^9, 3.6929664798829117`*^9}, {3.6929665643330297`*^9, 3.6929666141830997`*^9}, {3.6929670390036945`*^9, 3.6929670405536966`*^9}, {3.6929670861037607`*^9, 3.6929670952937737`*^9}, {3.6929671302538223`*^9, 3.6929671549438567`*^9}, {3.6929671904739065`*^9, 3.69296722137395*^9}, { 3.6929672596240034`*^9, 3.6929673352541094`*^9}, 3.6929678909232683`*^9, { 3.6930146982034283`*^9, 3.693014722713463*^9}, {3.6930148540136466`*^9, 3.693014857023651*^9}, {3.6930148913836985`*^9, 3.693014894823704*^9}, { 3.693014930903754*^9, 3.6930151942541227`*^9}, {3.693015247824198*^9, 3.693015430554454*^9}, {3.693015673794794*^9, 3.69301579223496*^9}, { 3.6930163123576884`*^9, 3.693016326897709*^9}, {3.6930164225678425`*^9, 3.693016429727853*^9}, {3.693016686718212*^9, 3.693016698128228*^9}, { 3.693016737038283*^9, 3.693016755068308*^9}, {3.6930168429225607`*^9, 3.6930168719926014`*^9}, {3.6930172049430676`*^9, 3.693017284063178*^9}, { 3.693017336433252*^9, 3.6930173662532935`*^9}, {3.6930180949163136`*^9, 3.6930180975563173`*^9}, {3.6930181870764427`*^9, 3.693018199956461*^9}, { 3.6930182954065943`*^9, 3.693018305996609*^9}, {3.693139886141657*^9, 3.6931399045016823`*^9}, {3.6931402916003532`*^9, 3.693140295770359*^9}, { 3.693140426020541*^9, 3.693140426530542*^9}, {3.6931410492237864`*^9, 3.6931410888738413`*^9}, {3.6931411194438844`*^9, 3.693141126553894*^9}, { 3.693141412004294*^9, 3.693141454164353*^9}, {3.6931415979955544`*^9, 3.6931417931758275`*^9}, {3.6932199559445915`*^9, 3.6932199772046213`*^9}, {3.6932201435748544`*^9, 3.693220170284892*^9}, { 3.693220713855653*^9, 3.693220721825664*^9}, {3.693625124589745*^9, 3.693625153729786*^9}, {3.6940907995669713`*^9, 3.6940909688872085`*^9}, { 3.6940913675677667`*^9, 3.6940914223978434`*^9}, {3.694091508037963*^9, 3.694091572118053*^9}, 3.694092009628666*^9, {3.6940920553287296`*^9, 3.694092229168973*^9}, {3.6940923053990793`*^9, 3.694092374419176*^9}, { 3.6940924537392874`*^9, 3.694092457789293*^9}, 3.694092642849552*^9, { 3.6940928573598523`*^9, 3.694092862379859*^9}, {3.6940945886222763`*^9, 3.694094601932295*^9}, 3.694094849542641*^9, {3.694095764293922*^9, 3.6940957644739223`*^9}, {3.6940960602743363`*^9, 3.6940960732243547`*^9}, {3.6940961211044216`*^9, 3.694096124194426*^9}, { 3.694665030960044*^9, 3.6946650634500895`*^9}, {3.6946652071402903`*^9, 3.6946653490404887`*^9}, {3.6946658702212186`*^9, 3.6946658881212435`*^9}, {3.694665923041292*^9, 3.694665953561335*^9}, { 3.694665995981395*^9, 3.6946660149414215`*^9}, {3.694666050571471*^9, 3.6946660547214766`*^9}, {3.694666169991638*^9, 3.694666292151809*^9}, { 3.6946663456618843`*^9, 3.6946663943919525`*^9}, 3.6946667526224537`*^9, 3.69466680700253*^9, 3.694687076625702*^9, {3.6946874316161985`*^9, 3.6946874621962414`*^9}, 3.694687499496294*^9, {3.694687567516389*^9, 3.694687642816495*^9}, {3.694687679006545*^9, 3.6946877198966026`*^9}, { 3.6946877714966745`*^9, 3.694687931746899*^9}, {3.723798739728607*^9, 3.723798744014243*^9}, {3.7237990126446104`*^9, 3.723799023974499*^9}, { 3.7244116671877546`*^9, 3.7244116733393917`*^9}, {3.724411761793063*^9, 3.7244117718753977`*^9}, {3.724411928386671*^9, 3.7244119682966137`*^9}, { 3.724412131847311*^9, 3.724412188341254*^9}, {3.729414981357122*^9, 3.7294149861075096`*^9}, {3.749817651293678*^9, 3.749817653108206*^9}, { 3.7498176831919456`*^9, 3.7498176846222315`*^9}, 3.7498177601545563`*^9, { 3.749817859674735*^9, 3.749817861044999*^9}, {3.7498179561547127`*^9, 3.749817964489929*^9}, {3.749818149334386*^9, 3.749818237397959*^9}, 3.749818617867873*^9, {3.7505621848002787`*^9, 3.7505622174085107`*^9}, { 3.75056238761455*^9, 3.750562431347901*^9}, {3.7505626332829456`*^9, 3.7505627331565337`*^9}, {3.7505627632642183`*^9, 3.7505627635859113`*^9}, {3.7515359581577415`*^9, 3.7515359614850826`*^9}, {3.751536071974715*^9, 3.7515360961721487`*^9}, 3.7515362040373974`*^9, {3.751536256080162*^9, 3.7515365099108534`*^9}, { 3.751549231137398*^9, 3.7515493334258356`*^9}, {3.7515496891619573`*^9, 3.751549689458767*^9}, {3.763384318028655*^9, 3.763384321230183*^9}, 3.7633844800900145`*^9, {3.7650666220235834`*^9, 3.765066676848461*^9}, { 3.7650667705927696`*^9, 3.765066781277461*^9}, {3.7650668220493402`*^9, 3.7650670769609847`*^9}, {3.765075343296377*^9, 3.765075345014902*^9}, { 3.765075479631569*^9, 3.7650755114191623`*^9}, {3.765075617307859*^9, 3.7650756180851874`*^9}, {3.76507585422694*^9, 3.765075872425325*^9}, { 3.7650760811750383`*^9, 3.7650762635610576`*^9}, {3.7650763100785646`*^9, 3.765076323109063*^9}, {3.7650763765120716`*^9, 3.765076385469493*^9}, { 3.7650764317497897`*^9, 3.7650764864127855`*^9}, 3.765076672990033*^9, { 3.7650767604139767`*^9, 3.7650767965644426`*^9}, {3.765076849411788*^9, 3.76507688334435*^9}, {3.765076928656023*^9, 3.7650769388747053`*^9}, 3.76507697239373*^9, {3.7650770147173185`*^9, 3.7650770820420313`*^9}, { 3.765077138264634*^9, 3.765077175747029*^9}, {3.765077340035742*^9, 3.765077493212038*^9}, {3.7650775254837503`*^9, 3.765077573524544*^9}, { 3.765077619369755*^9, 3.7650776808294816`*^9}, {3.765088266857733*^9, 3.765088281236836*^9}, {3.76508836959641*^9, 3.765088394392946*^9}, { 3.7650900504082956`*^9, 3.765090052695187*^9}, {3.7650900911122713`*^9, 3.765090094160341*^9}, {3.765090519594511*^9, 3.7650905411898503`*^9}, { 3.7885193337832556`*^9, 3.788519339935099*^9}, {3.788519391172593*^9, 3.7885194472501445`*^9}, {3.7885195529105897`*^9, 3.788519558251149*^9}, { 3.7885305232444134`*^9, 3.7885305903888035`*^9}, {3.7885308807721663`*^9, 3.78853088502055*^9}, {3.8200276995553846`*^9, 3.82002773164934*^9}},ExpressionUUID->"f502c001-f09d-4c09-854f-\ 2f76074bffa3"] }, Closed]], Cell[CellGroupData[{ Cell["BEAM ELEMENT (evnt) defs", "Subsection", InitializationCell->True, CellChangeTimes->{{3.753018875511382*^9, 3.7530188786265306`*^9}, { 3.781589886623744*^9, 3.7815898932426767`*^9}, {3.7878947601549573`*^9, 3.787894760728943*^9}, 3.7878948945295725`*^9, {3.817439343565061*^9, 3.8174393448082724`*^9}, {3.817439544553817*^9, 3.8174395452236648`*^9}, 3.8431828716661205`*^9},ExpressionUUID->"57e3c84a-fd55-4b4e-bae5-\ 1a516add187a"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"EVNT", ",", RowBox[{"{", RowBox[{"s0_", ",", "sol0_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, { 3.7530189177531705`*^9, 3.753018918350237*^9}, {3.753018991800671*^9, 3.753019041865839*^9}, {3.7530191095313196`*^9, 3.7530191100576744`*^9}, 3.753019155952956*^9, {3.7530192458219423`*^9, 3.753019353286773*^9}, { 3.773986323215969*^9, 3.7739864366876383`*^9}, {3.7739864700193005`*^9, 3.7739865885966825`*^9}, {3.7739869332783327`*^9, 3.7739870501829805`*^9}, 3.773987085528166*^9, {3.7739872536160583`*^9, 3.773987270466986*^9}, { 3.773987482712697*^9, 3.7739875221812735`*^9}, {3.773987740298462*^9, 3.7739877466065903`*^9}, {3.7739878599976892`*^9, 3.7739878861137896`*^9}, {3.773987965425336*^9, 3.7739879715632877`*^9}, 3.773988098774023*^9, 3.7739883193781385`*^9, {3.7739884099852057`*^9, 3.7739885862960095`*^9}, {3.773988628922502*^9, 3.773988632767228*^9}, { 3.7739891227568517`*^9, 3.77398915009042*^9}, {3.7739892774900556`*^9, 3.773989291800435*^9}, {3.7739896060525217`*^9, 3.773989635013425*^9}, { 3.7751890832095585`*^9, 3.7751890882413054`*^9}, {3.7751894923762302`*^9, 3.7751895008441906`*^9}, {3.7751911834227276`*^9, 3.775191222686661*^9}, 3.7751912606478214`*^9, {3.7751943412188396`*^9, 3.775194461553982*^9}, { 3.775194496052539*^9, 3.7751945353727713`*^9}, {3.7751945737174063`*^9, 3.775194621343042*^9}, {3.775194667862669*^9, 3.7751947598351893`*^9}, { 3.7751948235734253`*^9, 3.7751949415953684`*^9}, {3.775195100078847*^9, 3.77519512113822*^9}, {3.7751954506873007`*^9, 3.775195467864645*^9}, { 3.775270786870551*^9, 3.775270796325161*^9}, {3.7752708274391947`*^9, 3.775270839737406*^9}, {3.7752709283091574`*^9, 3.7752709474534383`*^9}, { 3.7752710502850266`*^9, 3.7752711744130797`*^9}, {3.7752712273079033`*^9, 3.7752713060364757`*^9}, {3.775271448825513*^9, 3.7752714699277525`*^9}, { 3.775271509321142*^9, 3.775271585609558*^9}, {3.775271620653377*^9, 3.77527180192237*^9}, {3.781589928213842*^9, 3.781590052438653*^9}, { 3.7815900898176003`*^9, 3.781590109307678*^9}, {3.781590201383393*^9, 3.7815902433873234`*^9}, {3.7815905445265956`*^9, 3.781590569573782*^9}, { 3.7815906952864275`*^9, 3.781590715680611*^9}, {3.7815908323678637`*^9, 3.781590881239719*^9}, {3.7815911048122363`*^9, 3.781591119274813*^9}, { 3.817439386305109*^9, 3.8174394287787733`*^9}, {3.8174395552770724`*^9, 3.8174395603447847`*^9}, 3.817521302738725*^9, 3.8431828676201057`*^9}, CellLabel-> "In[167]:=",ExpressionUUID->"9f4e35d3-8759-444d-af8a-37d96abffa12"] }, Closed]], Cell[CellGroupData[{ Cell["BEAM ELEMENT (stab) defs ", "Subsection", CellChangeTimes->{{3.7530187996679964`*^9, 3.753018818586525*^9}, { 3.7633844046177063`*^9, 3.7633844068273706`*^9}, {3.787894828329872*^9, 3.787894876950384*^9}, 3.788519172464745*^9},ExpressionUUID->"0dcc77b2-81d9-45bf-913d-\ 861264d462d9"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iyy", ",", "Izz", ",", "iy0"}], "}"}], ",", RowBox[{"{", RowBox[{ "fx", ",", "fy", ",", "fz", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iyy", ",", "Izz", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iyy", ",", "Izz", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ "fx", ",", "fy", ",", "fz", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fx_", ",", "fy_", ",", "fz_", ",", "mx_", ",", "my_", ",", "mz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iyy", ",", "Izz", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ "fx", ",", "fy", ",", "fz", ",", "mx", ",", "my", ",", "mz"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fx_", ",", "fy_", ",", "fz_", ",", "mx_", ",", "my_", ",", "mz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "ix0", ",", "iz0", ",", "ux", ",", "uy", " ", ",", "uz", " ", ",", "\[Theta]x", " ", ",", "\[Theta]y", " ", ",", "\[Theta]z", " ", ",", "\[Delta]ux", " ", ",", "\[Delta]uy", ",", "\[Delta]uz", ",", "\[Delta]\[Theta]x", ",", "\[Delta]\[Theta]y", ",", "\[Delta]\[Theta]z"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "mapping", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz0", "=", RowBox[{"ix0", "\[Cross]", "iy0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", "1", "]"}], ",", RowBox[{"uy", "[", "1", "]"}], ",", RowBox[{"uz", "[", "1", "]"}]}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", "2", "]"}], ",", RowBox[{"uy", "[", "2", "]"}], ",", RowBox[{"uz", "[", "2", "]"}]}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", "1", "]"}], ",", RowBox[{"\[Theta]y", "[", "1", "]"}], ",", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", "2", "]"}], ",", RowBox[{"\[Theta]y", "[", "2", "]"}], ",", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], ",", RowBox[{"\[Delta]uy", "[", "1", "]"}], ",", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", "1", "]"}], ",", RowBox[{"uy", "[", "1", "]"}], ",", RowBox[{"uz", "[", "1", "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]ux", "[", "2", "]"}], ",", RowBox[{"\[Delta]uy", "[", "2", "]"}], ",", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", "2", "]"}], ",", RowBox[{"uy", "[", "2", "]"}], ",", RowBox[{"uz", "[", "2", "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], ",", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], ",", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", "1", "]"}], ",", RowBox[{"\[Theta]y", "[", "1", "]"}], ",", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], ",", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}], ",", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", "2", "]"}], ",", RowBox[{"\[Theta]y", "[", "2", "]"}], ",", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ FractionBox["1", RowBox[{"60", " ", SuperscriptBox["h0", "3"]}]], RowBox[{"(", RowBox[{ RowBox[{"30", " ", "fx", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "-", RowBox[{"5", " ", RowBox[{"(", RowBox[{ RowBox[{"144", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"uy", "[", "1", "]"}], "-", RowBox[{"uy", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", "1", "]"}], "-", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"uz", "[", "1", "]"}], "-", RowBox[{"uz", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", "1", "]"}], "-", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"12", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"mz", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", "1", "]"}], "-", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"my", " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"6", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"fz", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", "1", "]"}], "+", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"mx", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"fz", " ", SuperscriptBox["h0", "5"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], "-", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], ")"}]}], "-", RowBox[{"fy", " ", SuperscriptBox["h0", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "+", RowBox[{"6", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"h0", " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"h0", " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}]}], ")"}]}], "-", RowBox[{"72", " ", "EE", " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"uz", "[", "1", "]"}], "-", RowBox[{"uz", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], ")"}]}], "-", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"uy", "[", "1", "]"}], "-", RowBox[{"uy", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", "1", "]"}], "-", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]y", "[", "1", "]"}], "+", RowBox[{"\[Theta]y", "[", "2", "]"}]}], ")"}]}], "-", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", "1", "]"}], "-", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]z", "[", "1", "]"}], "+", RowBox[{"\[Theta]z", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"12", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"GG", " ", RowBox[{"(", RowBox[{"Iyy", "+", "Izz"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], "-", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]x", "[", "1", "]"}], "-", RowBox[{"\[Theta]x", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"2", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], ")"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}]}], ")"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], ")"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}]}], ")"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "AA", " ", "EE", " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{"36", " ", RowBox[{"(", RowBox[{ RowBox[{"ux", "[", "1", "]"}], "-", RowBox[{"ux", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"uy", "[", "1", "]"}], "-", RowBox[{"uy", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", "1", "]"}], "-", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"uz", "[", "1", "]"}], "-", RowBox[{"uz", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", "1", "]"}], "-", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"h0", " ", RowBox[{"(", RowBox[{ RowBox[{"30", " ", RowBox[{"(", RowBox[{ RowBox[{"ux", "[", "1", "]"}], "-", RowBox[{"ux", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"ux", "[", "1", "]"}], "-", RowBox[{"ux", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", RowBox[{"uz", "[", "1", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], ")"}]}], "-", RowBox[{"3", " ", RowBox[{"uz", "[", "2", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"h0", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]y", "[", "1", "]"}], "-", RowBox[{"4", " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}]}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"\[Theta]y", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]z", "[", "1", "]"}], "-", RowBox[{"4", " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}]}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"\[Theta]z", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"3", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"uy", "[", "1", "]"}], "-", RowBox[{"uy", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", "1", "]"}], "-", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]y", "[", "1", "]"}], "+", RowBox[{"\[Theta]y", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", "1", "]"}], "-", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]z", "[", "1", "]"}], "+", RowBox[{"\[Theta]z", "[", "2", "]"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4430689313272*^9, 3.4430690080792*^9}, { 3.4430690869528*^9, 3.4430691077320004`*^9}, {3.4430691700116*^9, 3.4430691708072*^9}, {3.4430692071717997`*^9, 3.443069246359*^9}, { 3.4430772782732*^9, 3.4430773623416*^9}, {3.4430773978316*^9, 3.4430774104676*^9}, {3.4430775053780003`*^9, 3.4430776180598*^9}, { 3.4434109099524*^9, 3.4434109159584*^9}, {3.4438800815346003`*^9, 3.4438802689304*^9}, {3.443880362624*^9, 3.4438803824516*^9}, { 3.443929565615374*^9, 3.443929570232974*^9}, {3.443935321321974*^9, 3.443935335705174*^9}, {3.443935419945174*^9, 3.443935421489574*^9}, { 3.443935494013974*^9, 3.443935494715974*^9}, {3.443935617565974*^9, 3.4439357217895737`*^9}, {3.443935755360774*^9, 3.443935816107174*^9}, { 3.443942155230774*^9, 3.443942209939974*^9}, {3.443942305710374*^9, 3.4439423142123737`*^9}, {3.4439442908131742`*^9, 3.443944441181574*^9}, { 3.4439447830065737`*^9, 3.4439447917425737`*^9}, {3.443944908541774*^9, 3.443944916060974*^9}, {3.4442731097938004`*^9, 3.4442731115254*^9}, { 3.444273189229*^9, 3.4442732700526*^9}, {3.4442748430004*^9, 3.4442748605036*^9}, {3.4442748977438*^9, 3.4442748989762*^9}, { 3.4442749340762*^9, 3.4442749351057997`*^9}, 3.4442752313382*^9, { 3.4442919702026*^9, 3.4442919911846*^9}, {3.4442921151577997`*^9, 3.4442921271074*^9}, {3.4443811023684*^9, 3.4443811036632*^9}, { 3.4443814073171997`*^9, 3.4443814402956*^9}, {3.4443815036316*^9, 3.4443815147855997`*^9}, {3.4443815537232*^9, 3.4443815747676*^9}, { 3.4443816138143997`*^9, 3.444381633174*^9}, {3.4443816850439997`*^9, 3.4443817801728*^9}, 3.4443853618688*^9, {3.4443855607376003`*^9, 3.4443856337924*^9}, {3.4443861200444*^9, 3.4443861523676*^9}, { 3.4443862280495996`*^9, 3.444386291448*^9}, {3.4443864047352*^9, 3.4443864135336*^9}, {3.4443870026832*^9, 3.4443870095316*^9}, { 3.4444082055056*^9, 3.4444082437412*^9}, {3.4444082797148*^9, 3.4444084583816*^9}, {3.4444084889108*^9, 3.4444085087539997`*^9}, { 3.444408942517*^9, 3.4444089563386*^9}, {3.4444091419564*^9, 3.4444091647167997`*^9}, {3.4444092206428003`*^9, 3.4444092944463997`*^9}, {3.4444093856284*^9, 3.4444094281071997`*^9}, { 3.4444094976988*^9, 3.4444095275104*^9}, {3.444409611064*^9, 3.4444096125772*^9}, 3.4444098504616003`*^9, {3.444409913392*^9, 3.4444099166056004`*^9}, 3.4444100178496*^9, {3.4444103063248*^9, 3.4444103358712*^9}, {3.4444103868208*^9, 3.4444104432460003`*^9}, { 3.4444921219564*^9, 3.4444921256224003`*^9}, {3.444492194824*^9, 3.4444921973668003`*^9}, {3.4444922814351997`*^9, 3.4444922853508*^9}, { 3.4444923330868*^9, 3.4444923345844*^9}, {3.444492366424*^9, 3.4444923855808*^9}, {3.4453153475226*^9, 3.445315360689*^9}, { 3.4465518166373653`*^9, 3.446551863016165*^9}, {3.446551894231765*^9, 3.446552159384965*^9}, {3.446552232377365*^9, 3.4465522555589647`*^9}, { 3.446553347388365*^9, 3.4465533616155653`*^9}, {3.4466058525769997`*^9, 3.4466058529046*^9}, {3.4466064371219997`*^9, 3.4466065097244*^9}, { 3.4466127725788*^9, 3.4466127766036*^9}, {3.4466128124835997`*^9, 3.4466130037864*^9}, {3.4466131532696*^9, 3.4466131761703997`*^9}, { 3.4466133992192*^9, 3.4466134478756*^9}, {3.446613483584*^9, 3.4466134932092*^9}, {3.4466135740952*^9, 3.4466135794927998`*^9}, { 3.4466137283948*^9, 3.4466137341356*^9}, {3.4466138994342003`*^9, 3.4466139023826*^9}, {3.4466139549858*^9, 3.4466139579653997`*^9}, { 3.4466142109818*^9, 3.4466142245226*^9}, {3.4466142793878*^9, 3.4466143652033997`*^9}, {3.4466144712834*^9, 3.4466145978929996`*^9}, { 3.4466146992618*^9, 3.4466147509914*^9}, {3.4466151283086*^9, 3.4466152768986*^9}, {3.4466153107506*^9, 3.4466153406558*^9}, { 3.4466194331976*^9, 3.4466194377528*^9}, {3.4466194847712*^9, 3.446619488718*^9}, {3.4466389495861998`*^9, 3.4466389768238*^9}, { 3.4466391218414*^9, 3.446639306561*^9}, {3.4466393990222*^9, 3.4466394004886*^9}, {3.4466394475694*^9, 3.4466394487706003`*^9}, { 3.4466395034174*^9, 3.4466395049462*^9}, 3.4466395515755997`*^9, { 3.4466396000176*^9, 3.4466396190808*^9}, {3.4466397459088*^9, 3.446639748826*^9}, {3.4466397974356003`*^9, 3.446639798668*^9}, 3.4466398447816*^9, {3.446639894218*^9, 3.4466399201556*^9}, { 3.4466399570964003`*^9, 3.4466399583288*^9}, {3.446639994006*^9, 3.4466400056904*^9}, {3.4466400383568*^9, 3.4466400395892*^9}, { 3.4466400745643997`*^9, 3.4466401025976*^9}, {3.4466401660834*^9, 3.4466401806070004`*^9}, {3.4466402251294003`*^9, 3.446640227407*^9}, { 3.446640260479*^9, 3.4466402657674*^9}, {3.4466404133122*^9, 3.4466405185654*^9}, 3.4466405830462*^9, {3.4467273294214*^9, 3.4467273777813997`*^9}, {3.4467274366558*^9, 3.4467275620954*^9}, { 3.446727593311*^9, 3.4467277412614*^9}, {3.4467283334639997`*^9, 3.4467283356012*^9}, {3.4467283707636003`*^9, 3.4467283727604*^9}, { 3.4467289882664003`*^9, 3.4467291276836*^9}, {3.446778464322*^9, 3.4467786797424*^9}, {3.4467801953803997`*^9, 3.4467802409792*^9}, { 3.4467802998691998`*^9, 3.4467804023456*^9}, 3.4467804345596*^9, { 3.4467808656344*^9, 3.4467808670852003`*^9}, 3.4467818107525997`*^9, { 3.446781855509*^9, 3.446781874385*^9}, {3.4467826737914*^9, 3.4467827381726*^9}, {3.4467828623018*^9, 3.4467831045386*^9}, { 3.4470344113984003`*^9, 3.4470344123344*^9}, {3.4470344628316*^9, 3.4470345343108*^9}, {3.447043591118539*^9, 3.447043642192939*^9}, { 3.447045649625739*^9, 3.447045718437339*^9}, {3.447054774023939*^9, 3.447054834198939*^9}, {3.4470549103449388`*^9, 3.4470549116169386`*^9}, { 3.447054943902939*^9, 3.4470553027109385`*^9}, {3.447055334559939*^9, 3.447055353684939*^9}, {3.447057311918539*^9, 3.447057369747739*^9}, { 3.4470575058577385`*^9, 3.4470575951365385`*^9}, {3.4470581848789387`*^9, 3.4470582040825386`*^9}, {3.451276121243*^9, 3.4512761425838003`*^9}, { 3.4512762022382*^9, 3.4512762064346*^9}, {3.4512762476966*^9, 3.4512762827654*^9}, {3.451276489091*^9, 3.451276541975*^9}, { 3.4512765853118*^9, 3.4512766132046003`*^9}, {3.4512773470306*^9, 3.4512773766082*^9}, {3.4512776069110003`*^9, 3.4512777499318*^9}, 3.4512777831286*^9, {3.4512778785538*^9, 3.451277881627*^9}, { 3.4512780242734003`*^9, 3.4512780302794*^9}, 3.4512780737878*^9, { 3.4512781866226*^9, 3.4512781930810003`*^9}, {3.4512863325078*^9, 3.4512863539266*^9}, {3.4568019250434*^9, 3.4568022712698*^9}, { 3.4568023177422*^9, 3.4568024125278*^9}, {3.4568024694365997`*^9, 3.4568024750369997`*^9}, {3.4568026914402*^9, 3.4568028101094*^9}, { 3.4568028406698*^9, 3.4568028564726*^9}, 3.4568028886085997`*^9, { 3.4568030489454*^9, 3.4568030800986*^9}, 3.4568032004128*^9, { 3.4568035073698*^9, 3.4568035176034*^9}, {3.4568040146596003`*^9, 3.4568040844852*^9}, {3.4568043016684*^9, 3.4568043154744*^9}, { 3.4568045482264*^9, 3.4568045486632*^9}, {3.4568048944996*^9, 3.4568049806116*^9}, {3.4660560628582*^9, 3.4660560753538*^9}, { 3.4660676729379997`*^9, 3.4660676735931997`*^9}, {3.4660677244024*^9, 3.4660677277251997`*^9}, {3.4742646771287394`*^9, 3.47426469439174*^9}, { 3.47426489921974*^9, 3.4742649800437393`*^9}, {3.4801246373348*^9, 3.4801246860536003`*^9}, {3.4801247748176003`*^9, 3.4801247821028*^9}, { 3.4801248161264*^9, 3.4801248295736*^9}, {3.4801248810692*^9, 3.4801248964508*^9}, {3.4801249330484*^9, 3.480124947884*^9}, 3.4801249886468*^9, {3.4801251139147997`*^9, 3.48012512588*^9}, { 3.4838339444988003`*^9, 3.4838339567448*^9}, 3.4838341692012*^9, { 3.4838344350408*^9, 3.4838344353684*^9}, {3.4938987575920324`*^9, 3.4938987586840324`*^9}, {3.4941630624049997`*^9, 3.4941631381274*^9}, { 3.4941632311345997`*^9, 3.4941632492306004`*^9}, 3.4941633249217997`*^9, { 3.4941633940922003`*^9, 3.4941634063538*^9}, {3.4941634538402*^9, 3.4941635051642*^9}, {3.494163565115*^9, 3.4941636341762*^9}, { 3.4941636853442*^9, 3.4941639323234*^9}, {3.4941640277798*^9, 3.4941641455754004`*^9}, {3.4941641790374002`*^9, 3.4941641803789997`*^9}, {3.4941642676142*^9, 3.4941643277678003`*^9}, 3.4941644677018003`*^9, {3.4941646208938*^9, 3.4941646322349997`*^9}, { 3.4941652592693996`*^9, 3.4941652807194*^9}, {3.4941653119038*^9, 3.494165416299*^9}, {3.494165453895*^9, 3.4941654544722*^9}, { 3.4950990979779997`*^9, 3.495099142701*^9}, {3.495099172958*^9, 3.4950991806289997`*^9}, {3.495099227097*^9, 3.495099238113*^9}, 3.495099290797*^9, {3.495099346084*^9, 3.495099359507*^9}, { 3.495099456308*^9, 3.495099464091*^9}, 3.495099683108*^9, { 3.495100428112*^9, 3.495100434958*^9}, {3.4951006496219997`*^9, 3.495100649992*^9}, {3.4987235265018*^9, 3.4987235939094*^9}, { 3.4987236420666*^9, 3.4987236530646*^9}, {3.4987237305341997`*^9, 3.4987237396914*^9}, {3.498733136159*^9, 3.4987332972446003`*^9}, { 3.4987364783094*^9, 3.4987364860626*^9}, {3.4987366201134*^9, 3.4987366236078*^9}, {3.4987367272386*^9, 3.4987367464890003`*^9}, { 3.4987369428462*^9, 3.4987369670886*^9}, {3.4987370134518003`*^9, 3.4987370259941998`*^9}, {3.4987370944002*^9, 3.4987371027618*^9}, { 3.4987371921029997`*^9, 3.498737193663*^9}, {3.4987372660938*^9, 3.4987372935498*^9}, {3.4987373290554*^9, 3.4987377176202*^9}, { 3.4987377520182*^9, 3.4987379139462*^9}, {3.4987382030216*^9, 3.4987382667078*^9}, {3.4987888391818*^9, 3.4987888608346*^9}, { 3.4988785131146*^9, 3.4988785160162*^9}, {3.5007170967096*^9, 3.5007170999076*^9}, 3.5007182237316*^9, {3.5007182772864*^9, 3.5007182987832003`*^9}, {3.5009573226744003`*^9, 3.5009573940444*^9}, 3.5009574358710003`*^9, 3.5009604278482*^9, {3.5009897246173353`*^9, 3.5009898480289354`*^9}, {3.5009901464413357`*^9, 3.5009901475333357`*^9}, {3.5009901801997356`*^9, 3.500990274096135*^9}, { 3.5010475253292*^9, 3.5010475852332*^9}, {3.5010605722018003`*^9, 3.5010606739762*^9}, {3.5010607202146*^9, 3.5010607323358*^9}, { 3.5010607920526*^9, 3.501061118467*^9}, {3.5010612022078*^9, 3.5010612277138*^9}, {3.5010616467766*^9, 3.5010617938534*^9}, { 3.5010618406222*^9, 3.5010619950778*^9}, {3.5010621500638*^9, 3.5010622514014*^9}, {3.5010625292218*^9, 3.5010625409374*^9}, { 3.5010626043046*^9, 3.5010626313862*^9}, {3.5010626787166*^9, 3.5010626790754004`*^9}, {3.501074457561*^9, 3.5010744671082*^9}, 3.5010763029458*^9, {3.5032210899309998`*^9, 3.5032212413900003`*^9}, { 3.557658203404973*^9, 3.557658219644601*^9}, {3.5576584433801947`*^9, 3.557658496030287*^9}, {3.5576585501779823`*^9, 3.5576586046064777`*^9}, { 3.557658648910555*^9, 3.557658754600741*^9}, {3.557658963945511*^9, 3.5576589782507353`*^9}, {3.557659009949991*^9, 3.5576591437514267`*^9}, { 3.557659182221094*^9, 3.5576592187719584`*^9}, 3.557659413865901*^9, { 3.557659921100792*^9, 3.5576599556392527`*^9}, {3.557660706920972*^9, 3.5576607248454037`*^9}, {3.557661209085854*^9, 3.557661209413454*^9}, { 3.5577526651911488`*^9, 3.5577526932087984`*^9}, {3.5577527272480583`*^9, 3.557752747122493*^9}, {3.5577528374934516`*^9, 3.557752838523053*^9}, { 3.557752881204728*^9, 3.557752891313546*^9}, {3.557752938612829*^9, 3.5577529469120436`*^9}, {3.557753060714244*^9, 3.557753062633047*^9}, { 3.5577536609544907`*^9, 3.5577536637936954`*^9}, {3.5577537824631042`*^9, 3.557753810184353*^9}, {3.557753841025607*^9, 3.5577540648392*^9}, 3.5577541920574236`*^9, {3.5577547033327217`*^9, 3.557754716967146*^9}, { 3.5577547716296415`*^9, 3.557754802112095*^9}, {3.5577549509363565`*^9, 3.5577549771444025`*^9}, 3.5577551382302856`*^9, {3.55775527184452*^9, 3.557755272858522*^9}, {3.557755881555991*^9, 3.557755886548*^9}, { 3.557756158316077*^9, 3.557756231885806*^9}, {3.5577572408487787`*^9, 3.557757248835993*^9}, {3.5577572834368534`*^9, 3.5577575888229895`*^9}, { 3.5577578129641833`*^9, 3.557757862837471*^9}, {3.557758025514557*^9, 3.557758079272251*^9}, 3.557810586960072*^9, {3.5578240262005973`*^9, 3.5578240345360737`*^9}, {3.557824091429328*^9, 3.5578241008156557`*^9}, { 3.557831525255726*^9, 3.5578315319793377`*^9}, 3.5578315716190076`*^9, { 3.557831606079468*^9, 3.557831629432709*^9}, {3.5578316663267736`*^9, 3.5578317569473333`*^9}, {3.5578322144181366`*^9, 3.557832218084143*^9}, { 3.557836356693412*^9, 3.557836473771618*^9}, {3.5578365201660995`*^9, 3.5578365974018345`*^9}, {3.5578366426731143`*^9, 3.557836658865943*^9}, { 3.557836691017599*^9, 3.5578367924957776`*^9}, {3.5578368305442443`*^9, 3.557836888279946*^9}, {3.5578369382156334`*^9, 3.5578370776642785`*^9}, { 3.5578383536061196`*^9, 3.5578383735117545`*^9}, {3.5578385892445335`*^9, 3.5578385978869486`*^9}, {3.5578386713006773`*^9, 3.557838700113928*^9}, { 3.5578387451200075`*^9, 3.5578387467892103`*^9}, {3.5578388951454706`*^9, 3.5578389248635225`*^9}, {3.5578389679351983`*^9, 3.557838983535226*^9}, { 3.5578390227692947`*^9, 3.557839023143696*^9}, {3.557839097696226*^9, 3.5578391125162525`*^9}, {3.5578391553539276`*^9, 3.557839199892006*^9}, { 3.55783924184048*^9, 3.557839294490572*^9}, {3.5578393285922318`*^9, 3.557839398683155*^9}, {3.557839430522811*^9, 3.557839470162481*^9}, { 3.5578395370865984`*^9, 3.5578395446994114`*^9}, {3.5578396068499207`*^9, 3.5578396118575296`*^9}, 3.5578943518105097`*^9, {3.557894388361374*^9, 3.5578944029629993`*^9}, {3.5578944607611012`*^9, 3.5578944989499683`*^9}, {3.5578945393696394`*^9, 3.557894561537278*^9}, { 3.5578946028617506`*^9, 3.5578946188985786`*^9}, {3.557894650894235*^9, 3.5578947812636642`*^9}, {3.55789481884413*^9, 3.5578948191249304`*^9}, { 3.5578949768100076`*^9, 3.5578949836272197`*^9}, {3.5578967386805477`*^9, 3.55789678549623*^9}, {3.5578968804691963`*^9, 3.557896888643611*^9}, { 3.557897022491846*^9, 3.5578970341450663`*^9}, {3.557897620940097*^9, 3.55789765120415*^9}, {3.5579218072271147`*^9, 3.5579218263059483`*^9}, { 3.557922095312821*^9, 3.557922116965659*^9}, {3.557922178086566*^9, 3.557922188616585*^9}, {3.5579223258812256`*^9, 3.557922327066828*^9}, { 3.5579224596046605`*^9, 3.557922461804264*^9}, 3.5579805928465395`*^9, { 3.5579815200581703`*^9, 3.557981541711009*^9}, 3.557985544779242*^9, { 3.5579863164793987`*^9, 3.5579863339514294`*^9}, {3.557986523210962*^9, 3.557986568841042*^9}, 3.5579866122559185`*^9, 3.557986993536188*^9, { 3.5579871244716187`*^9, 3.5579871290580263`*^9}, 3.557987173486905*^9, 3.5579872166989803`*^9, {3.5599618621582537`*^9, 3.5599618642486577`*^9}, { 3.559961969720443*^9, 3.5599619894700775`*^9}, 3.559963611089726*^9, { 3.5601298891258235`*^9, 3.560129889422224*^9}, {3.560132445157113*^9, 3.5601324458591146`*^9}, {3.561978472080926*^9, 3.561978472392926*^9}, { 3.6297802564412937`*^9, 3.6297802957377625`*^9}, {3.62978033369263*^9, 3.629780429741998*^9}, {3.6297805790030603`*^9, 3.6297809429048996`*^9}, { 3.629780987957779*^9, 3.629781197575347*^9}, {3.629781240397422*^9, 3.629781337663593*^9}, {3.6297813946972933`*^9, 3.6297814529165955`*^9}, { 3.6297814952550697`*^9, 3.629781527578326*^9}, {3.62978162025529*^9, 3.629781647633338*^9}, {3.629781678833393*^9, 3.629781763120341*^9}, 3.6297818028224106`*^9, {3.6297818432108817`*^9, 3.629781872570133*^9}, { 3.629782355765382*^9, 3.629782427603508*^9}, {3.6297824692243814`*^9, 3.629782674863942*^9}, {3.629782707218399*^9, 3.6297829295343895`*^9}, { 3.629783005631323*^9, 3.6297830574702144`*^9}, {3.6297831098551064`*^9, 3.629783142786764*^9}, {3.629783433711675*^9, 3.629783442619291*^9}, { 3.6297834942397814`*^9, 3.6297835175930223`*^9}, 3.6297835794939313`*^9, { 3.6297836160291953`*^9, 3.6297837668970604`*^9}, {3.6297842042438283`*^9, 3.6297842697483435`*^9}, {3.6297843514456873`*^9, 3.629784370742921*^9}, { 3.629784443829049*^9, 3.6297844678842916`*^9}, {3.6297845252611923`*^9, 3.629784525588793*^9}, {3.6297846136821475`*^9, 3.629784629235375*^9}, { 3.629784814797701*^9, 3.629784927648299*^9}, {3.629785259960083*^9, 3.6297852602096834`*^9}, {3.6297858780175686`*^9, 3.629785917282837*^9}, { 3.629786048057867*^9, 3.629786048681868*^9}, 3.6297863278755584`*^9, { 3.6297867047133856`*^9, 3.629786748533863*^9}, {3.6297867791567163`*^9, 3.6297868491540394`*^9}, {3.6297875320748396`*^9, 3.629787569795706*^9}, { 3.6297876247234025`*^9, 3.6297877281983843`*^9}, {3.6297877681812544`*^9, 3.629787774015665*^9}, {3.629787831408166*^9, 3.6297878355265727`*^9}, { 3.6297878775686464`*^9, 3.6297878861174617`*^9}, {3.6297879185343184`*^9, 3.629787919064719*^9}, {3.6297880043032694`*^9, 3.62978800470887*^9}, 3.6297880488257475`*^9, {3.6297882100052304`*^9, 3.6297882174776435`*^9}, { 3.6297882697533355`*^9, 3.6297882948381796`*^9}, {3.6297883467550707`*^9, 3.6297883991087627`*^9}, {3.6297887361785545`*^9, 3.629788783961438*^9}, 3.629788825395111*^9, {3.629789006152629*^9, 3.6297890321266747`*^9}, { 3.6297891133248167`*^9, 3.629789145336073*^9}, {3.6297891926821566`*^9, 3.629789194257759*^9}, {3.629789255316266*^9, 3.6297892556282673`*^9}, { 3.629869102295367*^9, 3.629869160124668*^9}, {3.6298691942887287`*^9, 3.6298696149902673`*^9}, {3.6298696993864155`*^9, 3.62986975897852*^9}, { 3.6298698387726603`*^9, 3.629869912030389*^9}, {3.6298700722270703`*^9, 3.629870234560955*^9}, {3.629870580429163*^9, 3.629870630458451*^9}, { 3.630556081081209*^9, 3.630556104902451*^9}, {3.6305562643503313`*^9, 3.6305562763935523`*^9}, {3.6305563415080667`*^9, 3.630556480956712*^9}, { 3.630556692851884*^9, 3.630556695347888*^9}, {3.630556730042349*^9, 3.630556914528273*^9}, {3.6305653725974936`*^9, 3.6305656807121167`*^9}, { 3.630565758760581*^9, 3.6305657739024467`*^9}, {3.630565858170267*^9, 3.63056596644846*^9}, {3.6305661502619734`*^9, 3.6305661523230915`*^9}, { 3.6305662653385553`*^9, 3.630566370352562*^9}, {3.6305667786019125`*^9, 3.630566790535595*^9}, {3.6305668214773645`*^9, 3.630567044691132*^9}, { 3.6305670772499943`*^9, 3.6305670783710585`*^9}, 3.630567272031135*^9, { 3.630567303902958*^9, 3.630567409875019*^9}, {3.630568671196477*^9, 3.6305687195002403`*^9}, {3.6305687542132254`*^9, 3.630568758623478*^9}, { 3.630568855671028*^9, 3.630568859250233*^9}, {3.630569706514694*^9, 3.630569775526641*^9}, 3.630569982346471*^9, {3.6305701679130845`*^9, 3.630570205199217*^9}, {3.6305703751399374`*^9, 3.630570526177576*^9}, { 3.630587657039589*^9, 3.630587688367381*^9}, {3.6305880733027773`*^9, 3.6305883365376396`*^9}, {3.6305886689118233`*^9, 3.6305886717978287`*^9}, 3.6305889776831656`*^9, {3.6305890389444733`*^9, 3.6305890437180815`*^9}, { 3.630589093248169*^9, 3.6305891296430326`*^9}, 3.630589181700324*^9, { 3.6305892509956455`*^9, 3.6305892594820604`*^9}, {3.630589318949365*^9, 3.6305893334729905`*^9}, {3.630589630294712*^9, 3.6305896376267247`*^9}, { 3.630589683288005*^9, 3.630589684988408*^9}, {3.630597310538067*^9, 3.630597340080757*^9}, {3.630597391446695*^9, 3.630597400596218*^9}, { 3.6305974350611897`*^9, 3.6305974605306463`*^9}, {3.630633997622449*^9, 3.630634003125764*^9}, {3.630659322217756*^9, 3.63065932438616*^9}, { 3.6306611578252783`*^9, 3.6306611625988865`*^9}, {3.6306612541554475`*^9, 3.630661257587454*^9}, {3.6306613001287284`*^9, 3.6306613026715326`*^9}, { 3.6306613920752897`*^9, 3.6306613949768953`*^9}, {3.6306706377509866`*^9, 3.630670654957817*^9}, {3.6306749981919994`*^9, 3.630675005793434*^9}, { 3.6306751229631357`*^9, 3.630675150017683*^9}, {3.6306752035287437`*^9, 3.6306752096180925`*^9}, {3.630675315921172*^9, 3.6306753201514144`*^9}, { 3.6306757793287754`*^9, 3.6306757796257925`*^9}, {3.630675814406262*^9, 3.6306758147026625`*^9}, {3.6306760107574763`*^9, 3.6306760154417443`*^9}, {3.6306789722320743`*^9, 3.6306789870309205`*^9}, {3.6306790257051325`*^9, 3.630679028076268*^9}, { 3.6306800259177256`*^9, 3.6306800406129513`*^9}, {3.6306801239326982`*^9, 3.6306801300167084`*^9}, {3.630680769261832*^9, 3.6306807806186523`*^9}, { 3.630681157468514*^9, 3.6306811577649145`*^9}, {3.6306812744219193`*^9, 3.63068127471832*^9}, {3.6306817187418995`*^9, 3.6306817919060287`*^9}, { 3.630681879188182*^9, 3.6306819111526375`*^9}, {3.6306821191790032`*^9, 3.6306821283050194`*^9}, {3.630720543651497*^9, 3.6307205534300566`*^9}, { 3.630721035525631*^9, 3.630721092774905*^9}, {3.6307212510439577`*^9, 3.6307213064777765`*^9}, {3.6307477437169704`*^9, 3.6307478284095197`*^9}, {3.6307478614971776`*^9, 3.6307478785948076`*^9}, {3.6307479884814005`*^9, 3.630748002880226*^9}, { 3.630748045624301*^9, 3.630748063876333*^9}, {3.630748111596817*^9, 3.6307481498324842`*^9}, {3.6307489182430334`*^9, 3.6307489447786803`*^9}, {3.630749037427243*^9, 3.6307490443848553`*^9}, { 3.6307491041485605`*^9, 3.6307491384218206`*^9}, {3.6307491914151134`*^9, 3.630749196890723*^9}, {3.6307492445800066`*^9, 3.6307493439989815`*^9}, { 3.630749396212273*^9, 3.6307494766304145`*^9}, {3.6307495333989143`*^9, 3.6307495547241516`*^9}, {3.6307496525831237`*^9, 3.630749669571553*^9}, { 3.630750220602922*^9, 3.6307502881822405`*^9}, {3.6307510631916018`*^9, 3.630751068292811*^9}, {3.6307511226589065`*^9, 3.630751137962533*^9}, { 3.6307512555243397`*^9, 3.630751282777588*^9}, {3.630752266971757*^9, 3.630752414599744*^9}, {3.630752446407563*^9, 3.630752457388191*^9}, { 3.6307589380050273`*^9, 3.6307590266300964`*^9}, {3.6307591666721067`*^9, 3.63075923229886*^9}, 3.630760288282259*^9, {3.6307603547370596`*^9, 3.630760557414652*^9}, {3.630760654134184*^9, 3.63076065510824*^9}, { 3.6307606911683025`*^9, 3.6307606919283457`*^9}, {3.6307607642334814`*^9, 3.6307607648645177`*^9}, {3.630761455000991*^9, 3.6307614616743727`*^9}, { 3.630761507825012*^9, 3.630761605776615*^9}, {3.630761652999316*^9, 3.630761695865768*^9}, {3.630761771278081*^9, 3.6307617792215357`*^9}, 3.6307629478424797`*^9, {3.632205207880766*^9, 3.6322052561155243`*^9}, { 3.6322052892474194`*^9, 3.6322052915745525`*^9}, 3.6322053746993074`*^9, { 3.6322062705415463`*^9, 3.6322062726016645`*^9}, {3.6322063396935015`*^9, 3.63220636484194*^9}, {3.6322064410612993`*^9, 3.6322064491667633`*^9}, { 3.632206580308264*^9, 3.6322066373275256`*^9}, {3.6322066736436024`*^9, 3.6322067467737856`*^9}, {3.632206782260815*^9, 3.6322071351279984`*^9}, 3.6322071989226465`*^9, {3.632207270393735*^9, 3.6322073359894867`*^9}, { 3.6322073997741346`*^9, 3.6322074126708727`*^9}, {3.632207491777397*^9, 3.632207682289294*^9}, {3.632207809621577*^9, 3.632207827973626*^9}, { 3.6322079043859973`*^9, 3.6322079279443445`*^9}, {3.6322080916397076`*^9, 3.6322081666649985`*^9}, 3.634905258940913*^9, {3.634905370524296*^9, 3.6349054089004903`*^9}, {3.6349054472556844`*^9, 3.63490544787272*^9}, { 3.634905483492757*^9, 3.6349055164646425`*^9}, {3.634905574352954*^9, 3.634905628121029*^9}, {3.6349057012822137`*^9, 3.6349057207913294`*^9}, { 3.6349061371061416`*^9, 3.634906354438572*^9}, {3.6349063890455513`*^9, 3.6349064369332905`*^9}, {3.634906537696054*^9, 3.634906601859724*^9}, 3.634906706128688*^9, {3.6349069249442034`*^9, 3.6349069328326545`*^9}, { 3.6349070151973653`*^9, 3.6349070242298822`*^9}, {3.6349070817921743`*^9, 3.6349070822111983`*^9}, {3.634907723288866*^9, 3.634907739005765*^9}, { 3.6349079580732946`*^9, 3.6349079868219395`*^9}, {3.634908200284148*^9, 3.634908315195721*^9}, {3.6349083774582825`*^9, 3.6349084027997313`*^9}, { 3.63490844507615*^9, 3.634908448843365*^9}, {3.634914956333157*^9, 3.634915020054802*^9}, {3.634915050572547*^9, 3.6349150956171236`*^9}, { 3.6349539785771523`*^9, 3.634953978975175*^9}, {3.6349540728785458`*^9, 3.6349541681829967`*^9}, {3.634954211263461*^9, 3.6349542495746527`*^9}, { 3.6349543251259737`*^9, 3.634954355882733*^9}, {3.6349543892536416`*^9, 3.6349544742835045`*^9}, {3.634954547519694*^9, 3.6349545640246377`*^9}, { 3.6349547051657104`*^9, 3.6349547107930326`*^9}, {3.634954745355009*^9, 3.634954752101395*^9}, {3.6349547948858423`*^9, 3.6349548053894434`*^9}, { 3.634954904907135*^9, 3.6349549451084347`*^9}, {3.634955219605135*^9, 3.6349552640926795`*^9}, {3.634955320189888*^9, 3.634955348763522*^9}, { 3.634955386393675*^9, 3.6349555039273973`*^9}, {3.6349557669644423`*^9, 3.6349557672004557`*^9}, {3.634955894841756*^9, 3.634955902578199*^9}, { 3.6349559513739896`*^9, 3.6349560216320086`*^9}, {3.634956120144643*^9, 3.634956128996149*^9}, {3.6349561700724983`*^9, 3.6349561978900895`*^9}, { 3.6349562480719595`*^9, 3.634956254326318*^9}, {3.634956331684742*^9, 3.6349563460575643`*^9}, {3.634956379242462*^9, 3.63495642676418*^9}, 3.6349564696636343`*^9, {3.6351524116477795`*^9, 3.6351524153379908`*^9}, { 3.6352134400282927`*^9, 3.635213442148414*^9}, {3.6352134745862694`*^9, 3.635213495869487*^9}, {3.6352135383409157`*^9, 3.6352137157160616`*^9}, { 3.6352137493569856`*^9, 3.635213764522853*^9}, {3.635214215036621*^9, 3.635214227593339*^9}, {3.635214407257615*^9, 3.63521441713218*^9}, { 3.635215297101512*^9, 3.635215303964904*^9}, {3.6352154111120324`*^9, 3.635215431504199*^9}, {3.635216346055508*^9, 3.635216494371991*^9}, { 3.635216631050809*^9, 3.6352166603244834`*^9}, {3.635216763034358*^9, 3.635216764164423*^9}, {3.6352168771938877`*^9, 3.635216888828553*^9}, 3.6352169832479534`*^9, 3.635217037668066*^9, {3.6352172024924936`*^9, 3.6352172054526625`*^9}, {3.635217344025589*^9, 3.635217346898753*^9}, 3.6352173863770113`*^9, {3.635217519639633*^9, 3.6352175507014103`*^9}, 3.635217615445113*^9, {3.6352178715087595`*^9, 3.635217880460271*^9}, { 3.6352185912849283`*^9, 3.635218598444338*^9}, {3.6352186995721216`*^9, 3.635218714955002*^9}, {3.6352189761749425`*^9, 3.6352189789341*^9}, { 3.6352195060322485`*^9, 3.635219509972474*^9}, 3.6352195673477554`*^9, 3.6352195994635925`*^9, {3.6352197336482677`*^9, 3.635219737452485*^9}, { 3.6352197706093817`*^9, 3.6352197723214793`*^9}, {3.635219941784172*^9, 3.6352199485115566`*^9}, {3.6352200714185867`*^9, 3.6352200854323883`*^9}, {3.6352202085694313`*^9, 3.635220235849992*^9}, { 3.6352202816336107`*^9, 3.6352203110962954`*^9}, {3.6352204980449886`*^9, 3.6352205276526823`*^9}, {3.6352253191447396`*^9, 3.6352253299913597`*^9}, {3.6352253611111403`*^9, 3.6352253637572913`*^9}, {3.635225409322898*^9, 3.6352255965196047`*^9}, { 3.6352260914249115`*^9, 3.6352261698393965`*^9}, {3.63522638233055*^9, 3.6352264188036366`*^9}, {3.635227493469104*^9, 3.635227556935734*^9}, { 3.6352276745764627`*^9, 3.635227730116639*^9}, {3.6352287979917183`*^9, 3.6352288587651944`*^9}, {3.635228894237223*^9, 3.635228948324317*^9}, { 3.635229365252164*^9, 3.6352293902275925`*^9}, {3.63522947690555*^9, 3.6352294807837715`*^9}, {3.6352492831123204`*^9, 3.6352492983621926`*^9}, 3.6356569054520617`*^9, {3.6363778004499054`*^9, 3.636377802787039*^9}, { 3.6363778414932528`*^9, 3.6363778525308843`*^9}, {3.636384436335312*^9, 3.6363846409950175`*^9}, {3.636384971250907*^9, 3.6363849738080535`*^9}, { 3.6363850170465264`*^9, 3.636385030729309*^9}, {3.6363851286779118`*^9, 3.636385138359465*^9}, {3.6363851699712734`*^9, 3.636385223111313*^9}, { 3.656076172452749*^9, 3.656076182171566*^9}, {3.6560765578514256`*^9, 3.656076619019133*^9}, 3.6560772545486493`*^9, {3.6630719749029694`*^9, 3.6630719878027077`*^9}, {3.6630720702554235`*^9, 3.6630720807290225`*^9}, {3.6630721155740156`*^9, 3.6630721713712068`*^9}, {3.663072270834896*^9, 3.6630722882218904`*^9}, 3.6630724099968557`*^9, {3.685234767958906*^9, 3.685234768480936*^9}, { 3.685252204033695*^9, 3.6852522340537376`*^9}, {3.6852522757137957`*^9, 3.6852523115138454`*^9}, {3.68525376314359*^9, 3.6852537725041256`*^9}, { 3.6852539763277836`*^9, 3.6852539861693463`*^9}, 3.6852540682470407`*^9, 3.6852541660656357`*^9, {3.6852604801645336`*^9, 3.6852605060345697`*^9}, { 3.6852605373446136`*^9, 3.6852605977846985`*^9}, 3.685260655254779*^9, { 3.6853280002218475`*^9, 3.685328019561875*^9}, 3.685328064721938*^9, { 3.6853280953119807`*^9, 3.6853282636022167`*^9}, {3.685328356242346*^9, 3.685328598671985*^9}, {3.6853286682069626`*^9, 3.6853287982524004`*^9}, { 3.6853288753368096`*^9, 3.6853289367033195`*^9}, {3.685328968274125*^9, 3.685328978713722*^9}, {3.685329033941881*^9, 3.685329044950511*^9}, { 3.685329173522865*^9, 3.6853294420842257`*^9}, {3.6853296024223967`*^9, 3.6853296124319687`*^9}, {3.6853297221712456`*^9, 3.685329733349885*^9}, { 3.6853298076291337`*^9, 3.6853298739599276`*^9}, {3.685330038474337*^9, 3.685330051652091*^9}, {3.6853311309428225`*^9, 3.685331168378964*^9}, { 3.685340142134763*^9, 3.685340180544817*^9}, {3.6853583292043543`*^9, 3.685358334834362*^9}, {3.685358366084406*^9, 3.685358366954407*^9}, { 3.685358408404465*^9, 3.685358518294619*^9}, 3.685358620174762*^9, 3.6853586578748145`*^9, {3.6853588750151186`*^9, 3.6853588857151337`*^9}, { 3.6853589302051954`*^9, 3.685358938995208*^9}, {3.685359014715314*^9, 3.6853590296653347`*^9}, 3.685359148315501*^9, 3.6853598281764526`*^9, { 3.6853683109000263`*^9, 3.685368382250126*^9}, {3.685368420160179*^9, 3.6853684704302497`*^9}, {3.6853685194503183`*^9, 3.685368742860631*^9}, { 3.685369008901004*^9, 3.68536902061102*^9}, {3.6853690791611023`*^9, 3.685369132301176*^9}, {3.6853693219914417`*^9, 3.6853693304114532`*^9}, 3.6853696089118433`*^9, {3.6858758911429157`*^9, 3.685875951793*^9}, { 3.6859484099082212`*^9, 3.6859484970032024`*^9}, {3.686052829875022*^9, 3.686052906242383*^9}, {3.6860535326822133`*^9, 3.686053598029951*^9}, { 3.68605365168902*^9, 3.6860541446091995`*^9}, {3.6860541846064873`*^9, 3.68605440393201*^9}, {3.686054713802734*^9, 3.6860547858298535`*^9}, { 3.6860548280202665`*^9, 3.686054837219793*^9}, {3.686054874127904*^9, 3.686054892139934*^9}, {3.686055136014883*^9, 3.6860551460584574`*^9}, { 3.686055211281188*^9, 3.6860552301962633`*^9}, {3.6860553465409174`*^9, 3.6860553998749685`*^9}, {3.6860556017188663`*^9, 3.6860556050188704`*^9}, {3.6862923512707715`*^9, 3.686292363600789*^9}, { 3.686292409650853*^9, 3.6862924109708548`*^9}, {3.6862924536109147`*^9, 3.6862924596309233`*^9}, {3.686292542221039*^9, 3.6862925430110397`*^9}, { 3.686292988803664*^9, 3.686293001033681*^9}, {3.6866504529025555`*^9, 3.686650526682659*^9}, {3.686650671852862*^9, 3.6866507242929354`*^9}, { 3.6866507657529936`*^9, 3.6866507887630253`*^9}, {3.6866508208230705`*^9, 3.6866509100531955`*^9}, {3.6866509593932643`*^9, 3.686650971113281*^9}, { 3.686651007793332*^9, 3.6866511595335445`*^9}, {3.686651223513634*^9, 3.686651234033649*^9}, {3.686651304763748*^9, 3.6866513363837924`*^9}, { 3.6866514102038956`*^9, 3.686651429943923*^9}, {3.686652993837468*^9, 3.6866530046274834`*^9}, {3.686804398511652*^9, 3.6868044081516657`*^9}, { 3.6868046315619783`*^9, 3.686804631801979*^9}, {3.686804685872054*^9, 3.686804707092084*^9}, {3.6868047382021275`*^9, 3.686804767812169*^9}, { 3.686804824012248*^9, 3.6868048404922705`*^9}, {3.686804942142413*^9, 3.6868049633424425`*^9}, {3.6868050765526013`*^9, 3.686805101092636*^9}, { 3.6868051463526993`*^9, 3.6868052234228067`*^9}, {3.686805307602925*^9, 3.686805311682931*^9}, {3.68680577547358*^9, 3.686805788923599*^9}, { 3.686821702197342*^9, 3.6868217282873783`*^9}, {3.6868225192884855`*^9, 3.686822538368512*^9}, {3.6868226306886415`*^9, 3.6868226683086944`*^9}, { 3.6868227318887835`*^9, 3.6868227627088265`*^9}, {3.686822801638881*^9, 3.6868230490692277`*^9}, {3.686823122979331*^9, 3.6868231833294153`*^9}, { 3.6868232450595016`*^9, 3.6868233753996844`*^9}, {3.6868234153897405`*^9, 3.686823451379791*^9}, {3.6868236736101017`*^9, 3.6868236786601086`*^9}, { 3.6868237164601617`*^9, 3.68682375072021*^9}, {3.68682389396041*^9, 3.68682390087042*^9}, {3.686823940790476*^9, 3.6868239416904774`*^9}, { 3.6868239808805323`*^9, 3.6868239872905407`*^9}, {3.686824051540631*^9, 3.6868240519006314`*^9}, {3.686824360861064*^9, 3.6868243761510854`*^9}, { 3.6868245440213203`*^9, 3.686824577221367*^9}, {3.686824685841519*^9, 3.6868246979115357`*^9}, 3.6868248012716804`*^9, 3.6868253582724605`*^9, { 3.6868255183026843`*^9, 3.686825518932685*^9}, {3.6868264466639843`*^9, 3.6868264497139883`*^9}, {3.6868267792744493`*^9, 3.6868268152945004`*^9}, {3.686827100164899*^9, 3.6868271210549283`*^9}, 3.686827162004986*^9, {3.6868272414950967`*^9, 3.686827327475217*^9}, { 3.686827953126093*^9, 3.686827976506126*^9}, {3.686829128577739*^9, 3.686829138957753*^9}, 3.6868292410978966`*^9, {3.6868292768379464`*^9, 3.686829282727955*^9}, {3.6868293820380936`*^9, 3.686829418138144*^9}, { 3.686829846748744*^9, 3.686829848298746*^9}, {3.6868313063207874`*^9, 3.686831307180789*^9}, {3.6868331276633377`*^9, 3.68683328653356*^9}, { 3.6868394697195063`*^9, 3.6868394933895392`*^9}, 3.686839530999592*^9, { 3.686839582829664*^9, 3.68683963686974*^9}, {3.6868397551199055`*^9, 3.68683979365996*^9}, {3.6868398344600167`*^9, 3.686839866200061*^9}, { 3.687092084401948*^9, 3.687092117031994*^9}, {3.6870922598621936`*^9, 3.6870922645422*^9}, {3.6870962086478376`*^9, 3.6870962658779182`*^9}, 3.687096444838168*^9, {3.687096500978247*^9, 3.687096501638248*^9}, { 3.6870965809883595`*^9, 3.687096592708376*^9}, 3.687096837948719*^9, { 3.68709688890879*^9, 3.687096985798926*^9}, {3.6870971015990877`*^9, 3.6870972179192505`*^9}, {3.6870972618993125`*^9, 3.687097305639374*^9}, { 3.6870973356794157`*^9, 3.6870975186496716`*^9}, {3.6870975796097574`*^9, 3.6870975953197794`*^9}, {3.6870976531898603`*^9, 3.6870976848899045`*^9}, 3.6870977782500353`*^9, {3.687413757687042*^9, 3.6874137834070783`*^9}, { 3.6874140542074575`*^9, 3.687414094417514*^9}, {3.6874143478878684`*^9, 3.687414485538061*^9}, {3.6874146116082373`*^9, 3.68741464894829*^9}, { 3.6874147451084247`*^9, 3.687414766118454*^9}, 3.6874149094486547`*^9, { 3.6874150416688395`*^9, 3.6874150634888706`*^9}, {3.6874152437091227`*^9, 3.687415268869158*^9}, 3.6874153442892637`*^9, {3.687415449879411*^9, 3.687415469659439*^9}, 3.687415529739523*^9, 3.687415564789572*^9, 3.687415645529685*^9, {3.6874168016913037`*^9, 3.687416803441306*^9}, { 3.687421022677213*^9, 3.6874212686075573`*^9}, {3.68742948209425*^9, 3.6874294906842623`*^9}, {3.687844340668378*^9, 3.6878443698084188`*^9}, { 3.6886534778571014`*^9, 3.6886534911571198`*^9}, {3.688906380162199*^9, 3.6889064680223217`*^9}, {3.688906514222396*^9, 3.6889065193925257`*^9}, { 3.688908192623024*^9, 3.6889082006430354`*^9}, {3.688908261823121*^9, 3.688908271653135*^9}, {3.6889083776232834`*^9, 3.6889083922733035`*^9}, { 3.688908466073407*^9, 3.6889084993734536`*^9}, 3.688908533623502*^9, { 3.688908616683618*^9, 3.6889086271336327`*^9}, {3.6889086885637183`*^9, 3.6889087063437433`*^9}, {3.6889091647443852`*^9, 3.6889092012544365`*^9}, {3.6889093019045773`*^9, 3.6889093406746316`*^9}, 3.6889101071957045`*^9, {3.689905940063133*^9, 3.689905972983179*^9}, { 3.692530981927737*^9, 3.6925310416778207`*^9}, {3.692531099797902*^9, 3.6925311384779563`*^9}, {3.692531192258032*^9, 3.692531244668105*^9}, { 3.6925312919881716`*^9, 3.692531425418358*^9}, {3.6925315270885005`*^9, 3.692531643928664*^9}, {3.692535489534048*^9, 3.6925356485142703`*^9}, { 3.692535753564418*^9, 3.6925357992544813`*^9}, {3.6925358831745987`*^9, 3.692535899604622*^9}, {3.692536042584822*^9, 3.692536159384986*^9}, { 3.6925366121156197`*^9, 3.6925366207256317`*^9}, {3.6925367265057793`*^9, 3.69253672683578*^9}, {3.6925368590559654`*^9, 3.6925368636559715`*^9}, { 3.6925370880062857`*^9, 3.692537177856412*^9}, {3.692537322456614*^9, 3.6925373869767046`*^9}, {3.6925390913352747`*^9, 3.6925390925252767`*^9}, {3.692539644430175*^9, 3.6925396711502123`*^9}, { 3.692539727510291*^9, 3.692539730440295*^9}, {3.69253993367058*^9, 3.692539963780622*^9}, {3.6925400018406754`*^9, 3.692540003630678*^9}, { 3.6925401743409166`*^9, 3.6925401747509174`*^9}, {3.692540399111232*^9, 3.692540407981244*^9}, {3.69254047647134*^9, 3.6925404886113567`*^9}, { 3.6925406039715185`*^9, 3.69254060531152*^9}, {3.6925414948727655`*^9, 3.6925414953427663`*^9}, {3.6925415478528395`*^9, 3.692541613062931*^9}, 3.692541649332982*^9, {3.692541727633092*^9, 3.6925418840133104`*^9}, { 3.692541924473367*^9, 3.692542041693531*^9}, {3.6925421488836813`*^9, 3.6925422549438295`*^9}, {3.6925422976938896`*^9, 3.692542521444203*^9}, { 3.6925426221843443`*^9, 3.6925426357343626`*^9}, 3.692542739374508*^9, 3.692599799510878*^9, {3.692599834884901*^9, 3.6925998954663663`*^9}, { 3.692599925635092*^9, 3.6926000095928946`*^9}, {3.692600108929576*^9, 3.6926001456386757`*^9}, {3.6926001874800687`*^9, 3.692600454421337*^9}, { 3.692600503149027*^9, 3.6926006000391626`*^9}, {3.692600680251275*^9, 3.6926006814012766`*^9}, {3.6926009000215826`*^9, 3.6926009410816402`*^9}, 3.692601280532116*^9, {3.6926044914726114`*^9, 3.69260449774262*^9}, 3.6926045660127153`*^9, 3.6926046690228596`*^9, {3.69296647863291*^9, 3.6929664798829117`*^9}, {3.6929665643330297`*^9, 3.6929666141830997`*^9}, {3.6929670390036945`*^9, 3.6929670405536966`*^9}, {3.6929670861037607`*^9, 3.6929670952937737`*^9}, {3.6929671302538223`*^9, 3.6929671549438567`*^9}, {3.6929671904739065`*^9, 3.69296722137395*^9}, { 3.6929672596240034`*^9, 3.6929673352541094`*^9}, 3.6929678909232683`*^9, { 3.6930146982034283`*^9, 3.693014722713463*^9}, {3.6930148540136466`*^9, 3.693014857023651*^9}, {3.6930148913836985`*^9, 3.693014894823704*^9}, { 3.693014930903754*^9, 3.6930151942541227`*^9}, {3.693015247824198*^9, 3.693015430554454*^9}, {3.693015673794794*^9, 3.69301579223496*^9}, { 3.6930163123576884`*^9, 3.693016326897709*^9}, {3.6930164225678425`*^9, 3.693016429727853*^9}, {3.693016686718212*^9, 3.693016698128228*^9}, { 3.693016737038283*^9, 3.693016755068308*^9}, {3.6930168429225607`*^9, 3.6930168719926014`*^9}, {3.6930172049430676`*^9, 3.693017284063178*^9}, { 3.693017336433252*^9, 3.6930173662532935`*^9}, {3.6930180949163136`*^9, 3.6930180975563173`*^9}, {3.6930181870764427`*^9, 3.693018199956461*^9}, { 3.6930182954065943`*^9, 3.693018305996609*^9}, {3.693139886141657*^9, 3.6931399045016823`*^9}, {3.6931402916003532`*^9, 3.693140295770359*^9}, { 3.693140426020541*^9, 3.693140426530542*^9}, {3.6931410492237864`*^9, 3.6931410888738413`*^9}, {3.6931411194438844`*^9, 3.693141126553894*^9}, { 3.693141412004294*^9, 3.693141454164353*^9}, {3.6931415979955544`*^9, 3.6931417931758275`*^9}, {3.6932199559445915`*^9, 3.6932199772046213`*^9}, {3.6932201435748544`*^9, 3.693220170284892*^9}, { 3.693220713855653*^9, 3.693220721825664*^9}, {3.693625124589745*^9, 3.693625153729786*^9}, {3.6940907995669713`*^9, 3.6940909688872085`*^9}, { 3.6940913675677667`*^9, 3.6940914223978434`*^9}, {3.694091508037963*^9, 3.694091572118053*^9}, 3.694092009628666*^9, {3.6940920553287296`*^9, 3.694092229168973*^9}, {3.6940923053990793`*^9, 3.694092374419176*^9}, { 3.6940924537392874`*^9, 3.694092457789293*^9}, 3.694092642849552*^9, { 3.6940928573598523`*^9, 3.694092862379859*^9}, {3.6940945886222763`*^9, 3.694094601932295*^9}, 3.694094849542641*^9, {3.694095764293922*^9, 3.6940957644739223`*^9}, {3.6940960602743363`*^9, 3.6940960732243547`*^9}, {3.6940961211044216`*^9, 3.694096124194426*^9}, { 3.694665030960044*^9, 3.6946650634500895`*^9}, {3.6946652071402903`*^9, 3.6946653490404887`*^9}, {3.6946658702212186`*^9, 3.6946658881212435`*^9}, {3.694665923041292*^9, 3.694665953561335*^9}, { 3.694665995981395*^9, 3.6946660149414215`*^9}, {3.694666050571471*^9, 3.6946660547214766`*^9}, {3.694666169991638*^9, 3.694666292151809*^9}, { 3.6946663456618843`*^9, 3.6946663943919525`*^9}, 3.6946667526224537`*^9, 3.69466680700253*^9, 3.694687076625702*^9, {3.6946874316161985`*^9, 3.6946874621962414`*^9}, 3.694687499496294*^9, {3.694687567516389*^9, 3.694687642816495*^9}, {3.694687679006545*^9, 3.6946877198966026`*^9}, { 3.6946877714966745`*^9, 3.694687931746899*^9}, {3.723798739728607*^9, 3.723798744014243*^9}, {3.7237990126446104`*^9, 3.723799023974499*^9}, { 3.7244116671877546`*^9, 3.7244116733393917`*^9}, {3.724411761793063*^9, 3.7244117718753977`*^9}, {3.724411928386671*^9, 3.7244119682966137`*^9}, { 3.724412131847311*^9, 3.724412188341254*^9}, {3.729414981357122*^9, 3.7294149861075096`*^9}, {3.749817651293678*^9, 3.749817653108206*^9}, { 3.7498176831919456`*^9, 3.7498176846222315`*^9}, 3.7498177601545563`*^9, { 3.749817859674735*^9, 3.749817861044999*^9}, {3.7498179561547127`*^9, 3.749817964489929*^9}, {3.749818149334386*^9, 3.749818237397959*^9}, 3.749818617867873*^9, {3.7505621848002787`*^9, 3.7505622174085107`*^9}, { 3.75056238761455*^9, 3.750562431347901*^9}, {3.7505626332829456`*^9, 3.7505627331565337`*^9}, {3.7505627632642183`*^9, 3.7505627635859113`*^9}, {3.7515359581577415`*^9, 3.7515359614850826`*^9}, {3.751536071974715*^9, 3.7515360961721487`*^9}, 3.7515362040373974`*^9, {3.751536256080162*^9, 3.7515365099108534`*^9}, { 3.751549231137398*^9, 3.7515493334258356`*^9}, {3.7515496891619573`*^9, 3.751549689458767*^9}, {3.763384318028655*^9, 3.763384321230183*^9}, { 3.788530117667017*^9, 3.788530117980694*^9}, 3.7885303696209583`*^9, 3.788530509305438*^9, {3.78853083351016*^9, 3.788530862892729*^9}, { 3.788530925928982*^9, 3.7885309671960435`*^9}, {3.788533054135647*^9, 3.78853306391253*^9}, {3.788533559801361*^9, 3.7885336574548807`*^9}, { 3.788533916375413*^9, 3.7885339589240637`*^9}, {3.788535764582915*^9, 3.788535775009864*^9}, {3.788571051580041*^9, 3.788571053084015*^9}, 3.7885714852753925`*^9, {3.7885715554496107`*^9, 3.7885715772004504`*^9}, { 3.788571696555899*^9, 3.7885717388241262`*^9}, {3.788571794677034*^9, 3.7885718099292316`*^9}, 3.7885718526796875`*^9, {3.7885719048201413`*^9, 3.788571938458513*^9}, {3.7885720197107735`*^9, 3.7885720203433733`*^9}, { 3.7885721579483404`*^9, 3.788572246745886*^9}, {3.788572406392971*^9, 3.7885724747998886`*^9}, {3.7885725451809406`*^9, 3.7885725476052*^9}, { 3.788572796561078*^9, 3.7885727975057955`*^9}, 3.788572839094982*^9, { 3.788572904602244*^9, 3.788572917919137*^9}, {3.788573100895812*^9, 3.7885731714659753`*^9}, {3.7885733915788927`*^9, 3.788573436414242*^9}, 3.788573551866688*^9, 3.788573615961852*^9, {3.7885736607323666`*^9, 3.7885736628162546`*^9}, {3.788573695779252*^9, 3.788573697977635*^9}, { 3.788573733478549*^9, 3.7885737372812753`*^9}, 3.788573918957203*^9, { 3.7885742166825914`*^9, 3.788574217920394*^9}, {3.7888329679101725`*^9, 3.788833009852073*^9}, {3.788833043135027*^9, 3.7888330914074025`*^9}, { 3.7888332335219045`*^9, 3.7888332629628363`*^9}, 3.7890212989633403`*^9, { 3.818906513404701*^9, 3.818906542445839*^9}, {3.852337533659197*^9, 3.8523375850504904`*^9}}, CellLabel-> "In[168]:=",ExpressionUUID->"444b167e-bccb-4ea5-b199-ec19bc9c80b5"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"GENERICBEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fx_", ",", "fy_", ",", "fz_", ",", "mx_", ",", "my_", ",", "mz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "NL", ",", "NQ", ",", "r0", ",", "r\[Alpha]0", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "ix0", ",", "iz0", ",", "s", ",", "x", ",", "jac", ",", "FF", ",", "FFINV", ",", "ns", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "EEEE", ",", "AE", ",", "CE", ",", "BE", ",", "\[Epsilon]", ",", "\[Kappa]", ",", "up", ",", "F", ",", "M", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wstb", ",", "\[Delta]W", ",", "ux", ",", "upx", ",", "uy", ",", "uz", ",", "\[Theta]x", ",", "\[Theta]y", ",", "\[Theta]z"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"mapping", " ", "to", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{"\[Alpha]", "*", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]0", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r0"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Alpha]0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r\[Alpha]0", ".", "r\[Alpha]0"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"L", ">", "0"}], ",", RowBox[{"h", ">", "0"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"i\[Alpha]0", " ", "=", RowBox[{"r\[Alpha]0", "/", "h\[Alpha]0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"iz0", "=", RowBox[{"ix0", "\[Cross]", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{"s", "=", RowBox[{"i\[Alpha]0", ".", "r0"}]}], ";", "\[IndentingNewLine]", RowBox[{"x", "=", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], ".", "ix0"}], "+", "s"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"jac", " ", "=", "h\[Alpha]0"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"simple", " ", "metrics"}], "*)"}], "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NL", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]"}], ",", "\[Alpha]"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NQ", "=", " ", RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}]}], ",", RowBox[{"h\[Alpha]0", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "2"], " ", "\[Alpha]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", SuperscriptBox["\[Alpha]", "2"]}], ",", RowBox[{"h\[Alpha]0", " ", SuperscriptBox["\[Alpha]", "2"], " ", RowBox[{"(", " ", RowBox[{"\[Alpha]", "-", "1"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"transform", " ", "to", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ux", "[", "1", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "ix0"}]}], ";", " ", RowBox[{ RowBox[{"ux", "[", "2", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"uy", "[", "1", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iy0"}]}], ";", " ", RowBox[{ RowBox[{"uy", "[", "2", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"uz", "[", "1", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iz0"}]}], ";", " ", RowBox[{ RowBox[{"uz", "[", "2", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Theta]x", "[", "1", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "ix0"}]}], ";", " ", RowBox[{ RowBox[{"\[Theta]x", "[", "2", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Theta]y", "[", "1", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iy0"}]}], ";", " ", RowBox[{ RowBox[{"\[Theta]y", "[", "2", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Theta]z", "[", "1", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iz0"}]}], ";", " ", RowBox[{ RowBox[{"\[Theta]z", "[", "2", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"upx", "[", "1", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "ix0"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"upx", "[", "2", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "ix0"}]}], " ", ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", "1", "]"}], ",", RowBox[{"ux", "[", "2", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"up", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"upx", "[", "1", "]"}], ",", RowBox[{"upx", "[", "2", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", "1", "]"}], ",", RowBox[{"\[Theta]x", "[", "2", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{ RowBox[{"uy", "[", "1", "]"}], ",", RowBox[{"\[Theta]z", "[", "1", "]"}], ",", RowBox[{"uy", "[", "2", "]"}], ",", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{ RowBox[{"uz", "[", "1", "]"}], ",", RowBox[{"-", RowBox[{"\[Theta]y", "[", "1", "]"}]}], ",", RowBox[{"uz", "[", "2", "]"}], ",", RowBox[{"-", RowBox[{"\[Theta]y", "[", "2", "]"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], "/", "h\[Alpha]0"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}]}], "/", "h\[Alpha]0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"elasticity", " ", "dyad", " ", "and", " ", "cross"}], "-", RowBox[{ "section", " ", "properties", " ", "are", " ", "known", " ", "in", " ", "the", " ", "material", " ", "system"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"AE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EE", " ", "AA"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"GG", " ", "AA"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"GG", " ", "AA"}]}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"BE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"GG", " ", "Iyy"}], "+", RowBox[{"GG", " ", "Izz"}]}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"EE", " ", "Iyy"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"EE", " ", "Izz"}]}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"strain", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}]}], "/", "h\[Alpha]0"}], "+", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], "\[Cross]", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}]}], "/", "h\[Alpha]0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "resultants"}], "*)"}], "\[IndentingNewLine]", RowBox[{"F", "=", RowBox[{"AE", ".", "\[Epsilon]"}]}], ";", "\[IndentingNewLine]", RowBox[{"M", "=", RowBox[{"BE", ".", "\[Kappa]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expressions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], ".", "F"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Kappa]", "]"}], ".", "M"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fz"}], "}"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"mx", ",", "my", ",", "mz"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wstb", "=", RowBox[{ RowBox[{"-", "AA"}], " ", "EE", " ", RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "up"}], ")"}], " ", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], RowBox[{"\[Delta]", "[", "v", "]"}]}], " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}]}], "+", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], RowBox[{"\[Delta]", "[", "w", "]"}]}], " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}]}]}], ")"}], "/", RowBox[{ RowBox[{"(", "h\[Alpha]0", ")"}], "^", "3"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]W", " ", "=", RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wstb"}], ")"}], " ", "jac"}], ",", RowBox[{"{", "\[Alpha]", "}"}]}], "]"}]}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}]}]], "Input", CellChangeTimes->{{3.4430689313272*^9, 3.4430690080792*^9}, { 3.4430690869528*^9, 3.4430691077320004`*^9}, {3.4430691700116*^9, 3.4430691708072*^9}, {3.4430692071717997`*^9, 3.443069246359*^9}, { 3.4430772782732*^9, 3.4430773623416*^9}, {3.4430773978316*^9, 3.4430774104676*^9}, {3.4430775053780003`*^9, 3.4430776180598*^9}, { 3.4434109099524*^9, 3.4434109159584*^9}, {3.4438800815346003`*^9, 3.4438802689304*^9}, {3.443880362624*^9, 3.4438803824516*^9}, { 3.443929565615374*^9, 3.443929570232974*^9}, {3.443935321321974*^9, 3.443935335705174*^9}, {3.443935419945174*^9, 3.443935421489574*^9}, { 3.443935494013974*^9, 3.443935494715974*^9}, {3.443935617565974*^9, 3.4439357217895737`*^9}, {3.443935755360774*^9, 3.443935816107174*^9}, { 3.443942155230774*^9, 3.443942209939974*^9}, {3.443942305710374*^9, 3.4439423142123737`*^9}, {3.4439442908131742`*^9, 3.443944441181574*^9}, { 3.4439447830065737`*^9, 3.4439447917425737`*^9}, {3.443944908541774*^9, 3.443944916060974*^9}, {3.4442731097938004`*^9, 3.4442731115254*^9}, { 3.444273189229*^9, 3.4442732700526*^9}, {3.4442748430004*^9, 3.4442748605036*^9}, {3.4442748977438*^9, 3.4442748989762*^9}, { 3.4442749340762*^9, 3.4442749351057997`*^9}, 3.4442752313382*^9, { 3.4442919702026*^9, 3.4442919911846*^9}, {3.4442921151577997`*^9, 3.4442921271074*^9}, {3.4443811023684*^9, 3.4443811036632*^9}, { 3.4443814073171997`*^9, 3.4443814402956*^9}, {3.4443815036316*^9, 3.4443815147855997`*^9}, {3.4443815537232*^9, 3.4443815747676*^9}, { 3.4443816138143997`*^9, 3.444381633174*^9}, {3.4443816850439997`*^9, 3.4443817801728*^9}, 3.4443853618688*^9, {3.4443855607376003`*^9, 3.4443856337924*^9}, {3.4443861200444*^9, 3.4443861523676*^9}, { 3.4443862280495996`*^9, 3.444386291448*^9}, {3.4443864047352*^9, 3.4443864135336*^9}, {3.4443870026832*^9, 3.4443870095316*^9}, { 3.4444082055056*^9, 3.4444082437412*^9}, {3.4444082797148*^9, 3.4444084583816*^9}, {3.4444084889108*^9, 3.4444085087539997`*^9}, { 3.444408942517*^9, 3.4444089563386*^9}, {3.4444091419564*^9, 3.4444091647167997`*^9}, {3.4444092206428003`*^9, 3.4444092944463997`*^9}, {3.4444093856284*^9, 3.4444094281071997`*^9}, { 3.4444094976988*^9, 3.4444095275104*^9}, {3.444409611064*^9, 3.4444096125772*^9}, 3.4444098504616003`*^9, {3.444409913392*^9, 3.4444099166056004`*^9}, 3.4444100178496*^9, {3.4444103063248*^9, 3.4444103358712*^9}, {3.4444103868208*^9, 3.4444104432460003`*^9}, { 3.4444921219564*^9, 3.4444921256224003`*^9}, {3.444492194824*^9, 3.4444921973668003`*^9}, {3.4444922814351997`*^9, 3.4444922853508*^9}, { 3.4444923330868*^9, 3.4444923345844*^9}, {3.444492366424*^9, 3.4444923855808*^9}, {3.4453153475226*^9, 3.445315360689*^9}, { 3.4465518166373653`*^9, 3.446551863016165*^9}, {3.446551894231765*^9, 3.446552159384965*^9}, {3.446552232377365*^9, 3.4465522555589647`*^9}, { 3.446553347388365*^9, 3.4465533616155653`*^9}, {3.4466058525769997`*^9, 3.4466058529046*^9}, {3.4466064371219997`*^9, 3.4466065097244*^9}, { 3.4466127725788*^9, 3.4466127766036*^9}, {3.4466128124835997`*^9, 3.4466130037864*^9}, {3.4466131532696*^9, 3.4466131761703997`*^9}, { 3.4466133992192*^9, 3.4466134478756*^9}, {3.446613483584*^9, 3.4466134932092*^9}, {3.4466135740952*^9, 3.4466135794927998`*^9}, { 3.4466137283948*^9, 3.4466137341356*^9}, {3.4466138994342003`*^9, 3.4466139023826*^9}, {3.4466139549858*^9, 3.4466139579653997`*^9}, { 3.4466142109818*^9, 3.4466142245226*^9}, {3.4466142793878*^9, 3.4466143652033997`*^9}, {3.4466144712834*^9, 3.4466145978929996`*^9}, { 3.4466146992618*^9, 3.4466147509914*^9}, {3.4466151283086*^9, 3.4466152768986*^9}, {3.4466153107506*^9, 3.4466153406558*^9}, { 3.4466194331976*^9, 3.4466194377528*^9}, {3.4466194847712*^9, 3.446619488718*^9}, {3.4466389495861998`*^9, 3.4466389768238*^9}, { 3.4466391218414*^9, 3.446639306561*^9}, {3.4466393990222*^9, 3.4466394004886*^9}, {3.4466394475694*^9, 3.4466394487706003`*^9}, { 3.4466395034174*^9, 3.4466395049462*^9}, 3.4466395515755997`*^9, { 3.4466396000176*^9, 3.4466396190808*^9}, {3.4466397459088*^9, 3.446639748826*^9}, {3.4466397974356003`*^9, 3.446639798668*^9}, 3.4466398447816*^9, {3.446639894218*^9, 3.4466399201556*^9}, { 3.4466399570964003`*^9, 3.4466399583288*^9}, {3.446639994006*^9, 3.4466400056904*^9}, {3.4466400383568*^9, 3.4466400395892*^9}, { 3.4466400745643997`*^9, 3.4466401025976*^9}, {3.4466401660834*^9, 3.4466401806070004`*^9}, {3.4466402251294003`*^9, 3.446640227407*^9}, { 3.446640260479*^9, 3.4466402657674*^9}, {3.4466404133122*^9, 3.4466405185654*^9}, 3.4466405830462*^9, {3.4467273294214*^9, 3.4467273777813997`*^9}, {3.4467274366558*^9, 3.4467275620954*^9}, { 3.446727593311*^9, 3.4467277412614*^9}, {3.4467283334639997`*^9, 3.4467283356012*^9}, {3.4467283707636003`*^9, 3.4467283727604*^9}, { 3.4467289882664003`*^9, 3.4467291276836*^9}, {3.446778464322*^9, 3.4467786797424*^9}, {3.4467801953803997`*^9, 3.4467802409792*^9}, { 3.4467802998691998`*^9, 3.4467804023456*^9}, 3.4467804345596*^9, { 3.4467808656344*^9, 3.4467808670852003`*^9}, 3.4467818107525997`*^9, { 3.446781855509*^9, 3.446781874385*^9}, {3.4467826737914*^9, 3.4467827381726*^9}, {3.4467828623018*^9, 3.4467831045386*^9}, { 3.4470344113984003`*^9, 3.4470344123344*^9}, {3.4470344628316*^9, 3.4470345343108*^9}, {3.447043591118539*^9, 3.447043642192939*^9}, { 3.447045649625739*^9, 3.447045718437339*^9}, {3.447054774023939*^9, 3.447054834198939*^9}, {3.4470549103449388`*^9, 3.4470549116169386`*^9}, { 3.447054943902939*^9, 3.4470553027109385`*^9}, {3.447055334559939*^9, 3.447055353684939*^9}, {3.447057311918539*^9, 3.447057369747739*^9}, { 3.4470575058577385`*^9, 3.4470575951365385`*^9}, {3.4470581848789387`*^9, 3.4470582040825386`*^9}, {3.451276121243*^9, 3.4512761425838003`*^9}, { 3.4512762022382*^9, 3.4512762064346*^9}, {3.4512762476966*^9, 3.4512762827654*^9}, {3.451276489091*^9, 3.451276541975*^9}, { 3.4512765853118*^9, 3.4512766132046003`*^9}, {3.4512773470306*^9, 3.4512773766082*^9}, {3.4512776069110003`*^9, 3.4512777499318*^9}, 3.4512777831286*^9, {3.4512778785538*^9, 3.451277881627*^9}, { 3.4512780242734003`*^9, 3.4512780302794*^9}, 3.4512780737878*^9, { 3.4512781866226*^9, 3.4512781930810003`*^9}, {3.4512863325078*^9, 3.4512863539266*^9}, {3.4568019250434*^9, 3.4568022712698*^9}, { 3.4568023177422*^9, 3.4568024125278*^9}, {3.4568024694365997`*^9, 3.4568024750369997`*^9}, {3.4568026914402*^9, 3.4568028101094*^9}, { 3.4568028406698*^9, 3.4568028564726*^9}, 3.4568028886085997`*^9, { 3.4568030489454*^9, 3.4568030800986*^9}, 3.4568032004128*^9, { 3.4568035073698*^9, 3.4568035176034*^9}, {3.4568040146596003`*^9, 3.4568040844852*^9}, {3.4568043016684*^9, 3.4568043154744*^9}, { 3.4568045482264*^9, 3.4568045486632*^9}, {3.4568048944996*^9, 3.4568049806116*^9}, {3.4660560628582*^9, 3.4660560753538*^9}, { 3.4660676729379997`*^9, 3.4660676735931997`*^9}, {3.4660677244024*^9, 3.4660677277251997`*^9}, {3.4742646771287394`*^9, 3.47426469439174*^9}, { 3.47426489921974*^9, 3.4742649800437393`*^9}, {3.4801246373348*^9, 3.4801246860536003`*^9}, {3.4801247748176003`*^9, 3.4801247821028*^9}, { 3.4801248161264*^9, 3.4801248295736*^9}, {3.4801248810692*^9, 3.4801248964508*^9}, {3.4801249330484*^9, 3.480124947884*^9}, 3.4801249886468*^9, {3.4801251139147997`*^9, 3.48012512588*^9}, { 3.4838339444988003`*^9, 3.4838339567448*^9}, 3.4838341692012*^9, { 3.4838344350408*^9, 3.4838344353684*^9}, {3.4938987575920324`*^9, 3.4938987586840324`*^9}, {3.4941630624049997`*^9, 3.4941631381274*^9}, { 3.4941632311345997`*^9, 3.4941632492306004`*^9}, 3.4941633249217997`*^9, { 3.4941633940922003`*^9, 3.4941634063538*^9}, {3.4941634538402*^9, 3.4941635051642*^9}, {3.494163565115*^9, 3.4941636341762*^9}, { 3.4941636853442*^9, 3.4941639323234*^9}, {3.4941640277798*^9, 3.4941641455754004`*^9}, {3.4941641790374002`*^9, 3.4941641803789997`*^9}, {3.4941642676142*^9, 3.4941643277678003`*^9}, 3.4941644677018003`*^9, {3.4941646208938*^9, 3.4941646322349997`*^9}, { 3.4941652592693996`*^9, 3.4941652807194*^9}, {3.4941653119038*^9, 3.494165416299*^9}, {3.494165453895*^9, 3.4941654544722*^9}, { 3.4950990979779997`*^9, 3.495099142701*^9}, {3.495099172958*^9, 3.4950991806289997`*^9}, {3.495099227097*^9, 3.495099238113*^9}, 3.495099290797*^9, {3.495099346084*^9, 3.495099359507*^9}, { 3.495099456308*^9, 3.495099464091*^9}, 3.495099683108*^9, { 3.495100428112*^9, 3.495100434958*^9}, {3.4951006496219997`*^9, 3.495100649992*^9}, {3.4987235265018*^9, 3.4987235939094*^9}, { 3.4987236420666*^9, 3.4987236530646*^9}, {3.4987237305341997`*^9, 3.4987237396914*^9}, {3.498733136159*^9, 3.4987332972446003`*^9}, { 3.4987364783094*^9, 3.4987364860626*^9}, {3.4987366201134*^9, 3.4987366236078*^9}, {3.4987367272386*^9, 3.4987367464890003`*^9}, { 3.4987369428462*^9, 3.4987369670886*^9}, {3.4987370134518003`*^9, 3.4987370259941998`*^9}, {3.4987370944002*^9, 3.4987371027618*^9}, { 3.4987371921029997`*^9, 3.498737193663*^9}, {3.4987372660938*^9, 3.4987372935498*^9}, {3.4987373290554*^9, 3.4987377176202*^9}, { 3.4987377520182*^9, 3.4987379139462*^9}, {3.4987382030216*^9, 3.4987382667078*^9}, {3.4987888391818*^9, 3.4987888608346*^9}, { 3.4988785131146*^9, 3.4988785160162*^9}, {3.5007170967096*^9, 3.5007170999076*^9}, 3.5007182237316*^9, {3.5007182772864*^9, 3.5007182987832003`*^9}, {3.5009573226744003`*^9, 3.5009573940444*^9}, 3.5009574358710003`*^9, 3.5009604278482*^9, {3.5009897246173353`*^9, 3.5009898480289354`*^9}, {3.5009901464413357`*^9, 3.5009901475333357`*^9}, {3.5009901801997356`*^9, 3.500990274096135*^9}, { 3.5010475253292*^9, 3.5010475852332*^9}, {3.5010605722018003`*^9, 3.5010606739762*^9}, {3.5010607202146*^9, 3.5010607323358*^9}, { 3.5010607920526*^9, 3.501061118467*^9}, {3.5010612022078*^9, 3.5010612277138*^9}, {3.5010616467766*^9, 3.5010617938534*^9}, { 3.5010618406222*^9, 3.5010619950778*^9}, {3.5010621500638*^9, 3.5010622514014*^9}, {3.5010625292218*^9, 3.5010625409374*^9}, { 3.5010626043046*^9, 3.5010626313862*^9}, {3.5010626787166*^9, 3.5010626790754004`*^9}, {3.501074457561*^9, 3.5010744671082*^9}, 3.5010763029458*^9, {3.5032210899309998`*^9, 3.5032212413900003`*^9}, { 3.557658203404973*^9, 3.557658219644601*^9}, {3.5576584433801947`*^9, 3.557658496030287*^9}, {3.5576585501779823`*^9, 3.5576586046064777`*^9}, { 3.557658648910555*^9, 3.557658754600741*^9}, {3.557658963945511*^9, 3.5576589782507353`*^9}, {3.557659009949991*^9, 3.5576591437514267`*^9}, { 3.557659182221094*^9, 3.5576592187719584`*^9}, 3.557659413865901*^9, { 3.557659921100792*^9, 3.5576599556392527`*^9}, {3.557660706920972*^9, 3.5576607248454037`*^9}, {3.557661209085854*^9, 3.557661209413454*^9}, { 3.5577526651911488`*^9, 3.5577526932087984`*^9}, {3.5577527272480583`*^9, 3.557752747122493*^9}, {3.5577528374934516`*^9, 3.557752838523053*^9}, { 3.557752881204728*^9, 3.557752891313546*^9}, {3.557752938612829*^9, 3.5577529469120436`*^9}, {3.557753060714244*^9, 3.557753062633047*^9}, { 3.5577536609544907`*^9, 3.5577536637936954`*^9}, {3.5577537824631042`*^9, 3.557753810184353*^9}, {3.557753841025607*^9, 3.5577540648392*^9}, 3.5577541920574236`*^9, {3.5577547033327217`*^9, 3.557754716967146*^9}, { 3.5577547716296415`*^9, 3.557754802112095*^9}, {3.5577549509363565`*^9, 3.5577549771444025`*^9}, 3.5577551382302856`*^9, {3.55775527184452*^9, 3.557755272858522*^9}, {3.557755881555991*^9, 3.557755886548*^9}, { 3.557756158316077*^9, 3.557756231885806*^9}, {3.5577572408487787`*^9, 3.557757248835993*^9}, {3.5577572834368534`*^9, 3.5577575888229895`*^9}, { 3.5577578129641833`*^9, 3.557757862837471*^9}, {3.557758025514557*^9, 3.557758079272251*^9}, 3.557810586960072*^9, {3.5578240262005973`*^9, 3.5578240345360737`*^9}, {3.557824091429328*^9, 3.5578241008156557`*^9}, { 3.557831525255726*^9, 3.5578315319793377`*^9}, 3.5578315716190076`*^9, { 3.557831606079468*^9, 3.557831629432709*^9}, {3.5578316663267736`*^9, 3.5578317569473333`*^9}, {3.5578322144181366`*^9, 3.557832218084143*^9}, { 3.557836356693412*^9, 3.557836473771618*^9}, {3.5578365201660995`*^9, 3.5578365974018345`*^9}, {3.5578366426731143`*^9, 3.557836658865943*^9}, { 3.557836691017599*^9, 3.5578367924957776`*^9}, {3.5578368305442443`*^9, 3.557836888279946*^9}, {3.5578369382156334`*^9, 3.5578370776642785`*^9}, { 3.5578383536061196`*^9, 3.5578383735117545`*^9}, {3.5578385892445335`*^9, 3.5578385978869486`*^9}, {3.5578386713006773`*^9, 3.557838700113928*^9}, { 3.5578387451200075`*^9, 3.5578387467892103`*^9}, {3.5578388951454706`*^9, 3.5578389248635225`*^9}, {3.5578389679351983`*^9, 3.557838983535226*^9}, { 3.5578390227692947`*^9, 3.557839023143696*^9}, {3.557839097696226*^9, 3.5578391125162525`*^9}, {3.5578391553539276`*^9, 3.557839199892006*^9}, { 3.55783924184048*^9, 3.557839294490572*^9}, {3.5578393285922318`*^9, 3.557839398683155*^9}, {3.557839430522811*^9, 3.557839470162481*^9}, { 3.5578395370865984`*^9, 3.5578395446994114`*^9}, {3.5578396068499207`*^9, 3.5578396118575296`*^9}, 3.5578943518105097`*^9, {3.557894388361374*^9, 3.5578944029629993`*^9}, {3.5578944607611012`*^9, 3.5578944989499683`*^9}, {3.5578945393696394`*^9, 3.557894561537278*^9}, { 3.5578946028617506`*^9, 3.5578946188985786`*^9}, {3.557894650894235*^9, 3.5578947812636642`*^9}, {3.55789481884413*^9, 3.5578948191249304`*^9}, { 3.5578949768100076`*^9, 3.5578949836272197`*^9}, {3.5578967386805477`*^9, 3.55789678549623*^9}, {3.5578968804691963`*^9, 3.557896888643611*^9}, { 3.557897022491846*^9, 3.5578970341450663`*^9}, {3.557897620940097*^9, 3.55789765120415*^9}, {3.5579218072271147`*^9, 3.5579218263059483`*^9}, { 3.557922095312821*^9, 3.557922116965659*^9}, {3.557922178086566*^9, 3.557922188616585*^9}, {3.5579223258812256`*^9, 3.557922327066828*^9}, { 3.5579224596046605`*^9, 3.557922461804264*^9}, 3.5579805928465395`*^9, { 3.5579815200581703`*^9, 3.557981541711009*^9}, 3.557985544779242*^9, { 3.5579863164793987`*^9, 3.5579863339514294`*^9}, {3.557986523210962*^9, 3.557986568841042*^9}, 3.5579866122559185`*^9, 3.557986993536188*^9, { 3.5579871244716187`*^9, 3.5579871290580263`*^9}, 3.557987173486905*^9, 3.5579872166989803`*^9, {3.5599618621582537`*^9, 3.5599618642486577`*^9}, { 3.559961969720443*^9, 3.5599619894700775`*^9}, 3.559963611089726*^9, { 3.5601298891258235`*^9, 3.560129889422224*^9}, {3.560132445157113*^9, 3.5601324458591146`*^9}, {3.561978472080926*^9, 3.561978472392926*^9}, { 3.6297802564412937`*^9, 3.6297802957377625`*^9}, {3.62978033369263*^9, 3.629780429741998*^9}, {3.6297805790030603`*^9, 3.6297809429048996`*^9}, { 3.629780987957779*^9, 3.629781197575347*^9}, {3.629781240397422*^9, 3.629781337663593*^9}, {3.6297813946972933`*^9, 3.6297814529165955`*^9}, { 3.6297814952550697`*^9, 3.629781527578326*^9}, {3.62978162025529*^9, 3.629781647633338*^9}, {3.629781678833393*^9, 3.629781763120341*^9}, 3.6297818028224106`*^9, {3.6297818432108817`*^9, 3.629781872570133*^9}, { 3.629782355765382*^9, 3.629782427603508*^9}, {3.6297824692243814`*^9, 3.629782674863942*^9}, {3.629782707218399*^9, 3.6297829295343895`*^9}, { 3.629783005631323*^9, 3.6297830574702144`*^9}, {3.6297831098551064`*^9, 3.629783142786764*^9}, {3.629783433711675*^9, 3.629783442619291*^9}, { 3.6297834942397814`*^9, 3.6297835175930223`*^9}, 3.6297835794939313`*^9, { 3.6297836160291953`*^9, 3.6297837668970604`*^9}, {3.6297842042438283`*^9, 3.6297842697483435`*^9}, {3.6297843514456873`*^9, 3.629784370742921*^9}, { 3.629784443829049*^9, 3.6297844678842916`*^9}, {3.6297845252611923`*^9, 3.629784525588793*^9}, {3.6297846136821475`*^9, 3.629784629235375*^9}, { 3.629784814797701*^9, 3.629784927648299*^9}, {3.629785259960083*^9, 3.6297852602096834`*^9}, {3.6297858780175686`*^9, 3.629785917282837*^9}, { 3.629786048057867*^9, 3.629786048681868*^9}, 3.6297863278755584`*^9, { 3.6297867047133856`*^9, 3.629786748533863*^9}, {3.6297867791567163`*^9, 3.6297868491540394`*^9}, {3.6297875320748396`*^9, 3.629787569795706*^9}, { 3.6297876247234025`*^9, 3.6297877281983843`*^9}, {3.6297877681812544`*^9, 3.629787774015665*^9}, {3.629787831408166*^9, 3.6297878355265727`*^9}, { 3.6297878775686464`*^9, 3.6297878861174617`*^9}, {3.6297879185343184`*^9, 3.629787919064719*^9}, {3.6297880043032694`*^9, 3.62978800470887*^9}, 3.6297880488257475`*^9, {3.6297882100052304`*^9, 3.6297882174776435`*^9}, { 3.6297882697533355`*^9, 3.6297882948381796`*^9}, {3.6297883467550707`*^9, 3.6297883991087627`*^9}, {3.6297887361785545`*^9, 3.629788783961438*^9}, 3.629788825395111*^9, {3.629789006152629*^9, 3.6297890321266747`*^9}, { 3.6297891133248167`*^9, 3.629789145336073*^9}, {3.6297891926821566`*^9, 3.629789194257759*^9}, {3.629789255316266*^9, 3.6297892556282673`*^9}, { 3.629869102295367*^9, 3.629869160124668*^9}, {3.6298691942887287`*^9, 3.6298696149902673`*^9}, {3.6298696993864155`*^9, 3.62986975897852*^9}, { 3.6298698387726603`*^9, 3.629869912030389*^9}, {3.6298700722270703`*^9, 3.629870234560955*^9}, {3.629870580429163*^9, 3.629870630458451*^9}, { 3.630556081081209*^9, 3.630556104902451*^9}, {3.6305562643503313`*^9, 3.6305562763935523`*^9}, {3.6305563415080667`*^9, 3.630556480956712*^9}, { 3.630556692851884*^9, 3.630556695347888*^9}, {3.630556730042349*^9, 3.630556914528273*^9}, {3.6305653725974936`*^9, 3.6305656807121167`*^9}, { 3.630565758760581*^9, 3.6305657739024467`*^9}, {3.630565858170267*^9, 3.63056596644846*^9}, {3.6305661502619734`*^9, 3.6305661523230915`*^9}, { 3.6305662653385553`*^9, 3.630566370352562*^9}, {3.6305667786019125`*^9, 3.630566790535595*^9}, {3.6305668214773645`*^9, 3.630567044691132*^9}, { 3.6305670772499943`*^9, 3.6305670783710585`*^9}, 3.630567272031135*^9, { 3.630567303902958*^9, 3.630567409875019*^9}, {3.630568671196477*^9, 3.6305687195002403`*^9}, {3.6305687542132254`*^9, 3.630568758623478*^9}, { 3.630568855671028*^9, 3.630568859250233*^9}, {3.630569706514694*^9, 3.630569775526641*^9}, 3.630569982346471*^9, {3.6305701679130845`*^9, 3.630570205199217*^9}, {3.6305703751399374`*^9, 3.630570526177576*^9}, { 3.630587657039589*^9, 3.630587688367381*^9}, {3.6305880733027773`*^9, 3.6305883365376396`*^9}, {3.6305886689118233`*^9, 3.6305886717978287`*^9}, 3.6305889776831656`*^9, {3.6305890389444733`*^9, 3.6305890437180815`*^9}, { 3.630589093248169*^9, 3.6305891296430326`*^9}, 3.630589181700324*^9, { 3.6305892509956455`*^9, 3.6305892594820604`*^9}, {3.630589318949365*^9, 3.6305893334729905`*^9}, {3.630589630294712*^9, 3.6305896376267247`*^9}, { 3.630589683288005*^9, 3.630589684988408*^9}, {3.630597310538067*^9, 3.630597340080757*^9}, {3.630597391446695*^9, 3.630597400596218*^9}, { 3.6305974350611897`*^9, 3.6305974605306463`*^9}, {3.630633997622449*^9, 3.630634003125764*^9}, {3.630659322217756*^9, 3.63065932438616*^9}, { 3.6306611578252783`*^9, 3.6306611625988865`*^9}, {3.6306612541554475`*^9, 3.630661257587454*^9}, {3.6306613001287284`*^9, 3.6306613026715326`*^9}, { 3.6306613920752897`*^9, 3.6306613949768953`*^9}, {3.6306706377509866`*^9, 3.630670654957817*^9}, {3.6306749981919994`*^9, 3.630675005793434*^9}, { 3.6306751229631357`*^9, 3.630675150017683*^9}, {3.6306752035287437`*^9, 3.6306752096180925`*^9}, {3.630675315921172*^9, 3.6306753201514144`*^9}, { 3.6306757793287754`*^9, 3.6306757796257925`*^9}, {3.630675814406262*^9, 3.6306758147026625`*^9}, {3.6306760107574763`*^9, 3.6306760154417443`*^9}, {3.6306789722320743`*^9, 3.6306789870309205`*^9}, {3.6306790257051325`*^9, 3.630679028076268*^9}, { 3.6306800259177256`*^9, 3.6306800406129513`*^9}, {3.6306801239326982`*^9, 3.6306801300167084`*^9}, {3.630680769261832*^9, 3.6306807806186523`*^9}, { 3.630681157468514*^9, 3.6306811577649145`*^9}, {3.6306812744219193`*^9, 3.63068127471832*^9}, {3.6306817187418995`*^9, 3.6306817919060287`*^9}, { 3.630681879188182*^9, 3.6306819111526375`*^9}, {3.6306821191790032`*^9, 3.6306821283050194`*^9}, {3.630720543651497*^9, 3.6307205534300566`*^9}, { 3.630721035525631*^9, 3.630721092774905*^9}, {3.6307212510439577`*^9, 3.6307213064777765`*^9}, {3.6307477437169704`*^9, 3.6307478284095197`*^9}, {3.6307478614971776`*^9, 3.6307478785948076`*^9}, {3.6307479884814005`*^9, 3.630748002880226*^9}, { 3.630748045624301*^9, 3.630748063876333*^9}, {3.630748111596817*^9, 3.6307481498324842`*^9}, {3.6307489182430334`*^9, 3.6307489447786803`*^9}, {3.630749037427243*^9, 3.6307490443848553`*^9}, { 3.6307491041485605`*^9, 3.6307491384218206`*^9}, {3.6307491914151134`*^9, 3.630749196890723*^9}, {3.6307492445800066`*^9, 3.6307493439989815`*^9}, { 3.630749396212273*^9, 3.6307494766304145`*^9}, {3.6307495333989143`*^9, 3.6307495547241516`*^9}, {3.6307496525831237`*^9, 3.630749669571553*^9}, { 3.630750220602922*^9, 3.6307502881822405`*^9}, {3.6307510631916018`*^9, 3.630751068292811*^9}, {3.6307511226589065`*^9, 3.630751137962533*^9}, { 3.6307512555243397`*^9, 3.630751282777588*^9}, {3.630752266971757*^9, 3.630752414599744*^9}, {3.630752446407563*^9, 3.630752457388191*^9}, { 3.6307589380050273`*^9, 3.6307590266300964`*^9}, {3.6307591666721067`*^9, 3.63075923229886*^9}, 3.630760288282259*^9, {3.6307603547370596`*^9, 3.630760557414652*^9}, {3.630760654134184*^9, 3.63076065510824*^9}, { 3.6307606911683025`*^9, 3.6307606919283457`*^9}, {3.6307607642334814`*^9, 3.6307607648645177`*^9}, {3.630761455000991*^9, 3.6307614616743727`*^9}, { 3.630761507825012*^9, 3.630761605776615*^9}, {3.630761652999316*^9, 3.630761695865768*^9}, {3.630761771278081*^9, 3.6307617792215357`*^9}, 3.6307629478424797`*^9, {3.632205207880766*^9, 3.6322052561155243`*^9}, { 3.6322052892474194`*^9, 3.6322052915745525`*^9}, 3.6322053746993074`*^9, { 3.6322062705415463`*^9, 3.6322062726016645`*^9}, {3.6322063396935015`*^9, 3.63220636484194*^9}, {3.6322064410612993`*^9, 3.6322064491667633`*^9}, { 3.632206580308264*^9, 3.6322066373275256`*^9}, {3.6322066736436024`*^9, 3.6322067467737856`*^9}, {3.632206782260815*^9, 3.6322071351279984`*^9}, 3.6322071989226465`*^9, {3.632207270393735*^9, 3.6322073359894867`*^9}, { 3.6322073997741346`*^9, 3.6322074126708727`*^9}, {3.632207491777397*^9, 3.632207682289294*^9}, {3.632207809621577*^9, 3.632207827973626*^9}, { 3.6322079043859973`*^9, 3.6322079279443445`*^9}, {3.6322080916397076`*^9, 3.6322081666649985`*^9}, 3.634905258940913*^9, {3.634905370524296*^9, 3.6349054089004903`*^9}, {3.6349054472556844`*^9, 3.63490544787272*^9}, { 3.634905483492757*^9, 3.6349055164646425`*^9}, {3.634905574352954*^9, 3.634905628121029*^9}, {3.6349057012822137`*^9, 3.6349057207913294`*^9}, { 3.6349061371061416`*^9, 3.634906354438572*^9}, {3.6349063890455513`*^9, 3.6349064369332905`*^9}, {3.634906537696054*^9, 3.634906601859724*^9}, 3.634906706128688*^9, {3.6349069249442034`*^9, 3.6349069328326545`*^9}, { 3.6349070151973653`*^9, 3.6349070242298822`*^9}, {3.6349070817921743`*^9, 3.6349070822111983`*^9}, {3.634907723288866*^9, 3.634907739005765*^9}, { 3.6349079580732946`*^9, 3.6349079868219395`*^9}, {3.634908200284148*^9, 3.634908315195721*^9}, {3.6349083774582825`*^9, 3.6349084027997313`*^9}, { 3.63490844507615*^9, 3.634908448843365*^9}, {3.634914956333157*^9, 3.634915020054802*^9}, {3.634915050572547*^9, 3.6349150956171236`*^9}, { 3.6349539785771523`*^9, 3.634953978975175*^9}, {3.6349540728785458`*^9, 3.6349541681829967`*^9}, {3.634954211263461*^9, 3.6349542495746527`*^9}, { 3.6349543251259737`*^9, 3.634954355882733*^9}, {3.6349543892536416`*^9, 3.6349544742835045`*^9}, {3.634954547519694*^9, 3.6349545640246377`*^9}, { 3.6349547051657104`*^9, 3.6349547107930326`*^9}, {3.634954745355009*^9, 3.634954752101395*^9}, {3.6349547948858423`*^9, 3.6349548053894434`*^9}, { 3.634954904907135*^9, 3.6349549451084347`*^9}, {3.634955219605135*^9, 3.6349552640926795`*^9}, {3.634955320189888*^9, 3.634955348763522*^9}, { 3.634955386393675*^9, 3.6349555039273973`*^9}, {3.6349557669644423`*^9, 3.6349557672004557`*^9}, {3.634955894841756*^9, 3.634955902578199*^9}, { 3.6349559513739896`*^9, 3.6349560216320086`*^9}, {3.634956120144643*^9, 3.634956128996149*^9}, {3.6349561700724983`*^9, 3.6349561978900895`*^9}, { 3.6349562480719595`*^9, 3.634956254326318*^9}, {3.634956331684742*^9, 3.6349563460575643`*^9}, {3.634956379242462*^9, 3.63495642676418*^9}, 3.6349564696636343`*^9, {3.6351524116477795`*^9, 3.6351524153379908`*^9}, { 3.6352134400282927`*^9, 3.635213442148414*^9}, {3.6352134745862694`*^9, 3.635213495869487*^9}, {3.6352135383409157`*^9, 3.6352137157160616`*^9}, { 3.6352137493569856`*^9, 3.635213764522853*^9}, {3.635214215036621*^9, 3.635214227593339*^9}, {3.635214407257615*^9, 3.63521441713218*^9}, { 3.635215297101512*^9, 3.635215303964904*^9}, {3.6352154111120324`*^9, 3.635215431504199*^9}, {3.635216346055508*^9, 3.635216494371991*^9}, { 3.635216631050809*^9, 3.6352166603244834`*^9}, {3.635216763034358*^9, 3.635216764164423*^9}, {3.6352168771938877`*^9, 3.635216888828553*^9}, 3.6352169832479534`*^9, 3.635217037668066*^9, {3.6352172024924936`*^9, 3.6352172054526625`*^9}, {3.635217344025589*^9, 3.635217346898753*^9}, 3.6352173863770113`*^9, {3.635217519639633*^9, 3.6352175507014103`*^9}, 3.635217615445113*^9, {3.6352178715087595`*^9, 3.635217880460271*^9}, { 3.6352185912849283`*^9, 3.635218598444338*^9}, {3.6352186995721216`*^9, 3.635218714955002*^9}, {3.6352189761749425`*^9, 3.6352189789341*^9}, { 3.6352195060322485`*^9, 3.635219509972474*^9}, 3.6352195673477554`*^9, 3.6352195994635925`*^9, {3.6352197336482677`*^9, 3.635219737452485*^9}, { 3.6352197706093817`*^9, 3.6352197723214793`*^9}, {3.635219941784172*^9, 3.6352199485115566`*^9}, {3.6352200714185867`*^9, 3.6352200854323883`*^9}, {3.6352202085694313`*^9, 3.635220235849992*^9}, { 3.6352202816336107`*^9, 3.6352203110962954`*^9}, {3.6352204980449886`*^9, 3.6352205276526823`*^9}, {3.6352253191447396`*^9, 3.6352253299913597`*^9}, {3.6352253611111403`*^9, 3.6352253637572913`*^9}, {3.635225409322898*^9, 3.6352255965196047`*^9}, { 3.6352260914249115`*^9, 3.6352261698393965`*^9}, {3.63522638233055*^9, 3.6352264188036366`*^9}, {3.635227493469104*^9, 3.635227556935734*^9}, { 3.6352276745764627`*^9, 3.635227730116639*^9}, {3.6352287979917183`*^9, 3.6352288587651944`*^9}, {3.635228894237223*^9, 3.635228948324317*^9}, { 3.635229365252164*^9, 3.6352293902275925`*^9}, {3.63522947690555*^9, 3.6352294807837715`*^9}, {3.6352492831123204`*^9, 3.6352492983621926`*^9}, 3.6356569054520617`*^9, {3.6363778004499054`*^9, 3.636377802787039*^9}, { 3.6363778414932528`*^9, 3.6363778525308843`*^9}, {3.636384436335312*^9, 3.6363846409950175`*^9}, {3.636384971250907*^9, 3.6363849738080535`*^9}, { 3.6363850170465264`*^9, 3.636385030729309*^9}, {3.6363851286779118`*^9, 3.636385138359465*^9}, {3.6363851699712734`*^9, 3.636385223111313*^9}, { 3.656076172452749*^9, 3.656076182171566*^9}, {3.6560765578514256`*^9, 3.656076619019133*^9}, 3.6560772545486493`*^9, {3.6630719749029694`*^9, 3.6630719878027077`*^9}, {3.6630720702554235`*^9, 3.6630720807290225`*^9}, {3.6630721155740156`*^9, 3.6630721713712068`*^9}, {3.663072270834896*^9, 3.6630722882218904`*^9}, 3.6630724099968557`*^9, {3.685234767958906*^9, 3.685234768480936*^9}, { 3.685252204033695*^9, 3.6852522340537376`*^9}, {3.6852522757137957`*^9, 3.6852523115138454`*^9}, {3.68525376314359*^9, 3.6852537725041256`*^9}, { 3.6852539763277836`*^9, 3.6852539861693463`*^9}, 3.6852540682470407`*^9, 3.6852541660656357`*^9, {3.6852604801645336`*^9, 3.6852605060345697`*^9}, { 3.6852605373446136`*^9, 3.6852605977846985`*^9}, 3.685260655254779*^9, { 3.6853280002218475`*^9, 3.685328019561875*^9}, 3.685328064721938*^9, { 3.6853280953119807`*^9, 3.6853282636022167`*^9}, {3.685328356242346*^9, 3.685328598671985*^9}, {3.6853286682069626`*^9, 3.6853287982524004`*^9}, { 3.6853288753368096`*^9, 3.6853289367033195`*^9}, {3.685328968274125*^9, 3.685328978713722*^9}, {3.685329033941881*^9, 3.685329044950511*^9}, { 3.685329173522865*^9, 3.6853294420842257`*^9}, {3.6853296024223967`*^9, 3.6853296124319687`*^9}, {3.6853297221712456`*^9, 3.685329733349885*^9}, { 3.6853298076291337`*^9, 3.6853298739599276`*^9}, {3.685330038474337*^9, 3.685330051652091*^9}, {3.6853311309428225`*^9, 3.685331168378964*^9}, { 3.685340142134763*^9, 3.685340180544817*^9}, {3.6853583292043543`*^9, 3.685358334834362*^9}, {3.685358366084406*^9, 3.685358366954407*^9}, { 3.685358408404465*^9, 3.685358518294619*^9}, 3.685358620174762*^9, 3.6853586578748145`*^9, {3.6853588750151186`*^9, 3.6853588857151337`*^9}, { 3.6853589302051954`*^9, 3.685358938995208*^9}, {3.685359014715314*^9, 3.6853590296653347`*^9}, 3.685359148315501*^9, 3.6853598281764526`*^9, { 3.6853683109000263`*^9, 3.685368382250126*^9}, {3.685368420160179*^9, 3.6853684704302497`*^9}, {3.6853685194503183`*^9, 3.685368742860631*^9}, { 3.685369008901004*^9, 3.68536902061102*^9}, {3.6853690791611023`*^9, 3.685369132301176*^9}, {3.6853693219914417`*^9, 3.6853693304114532`*^9}, 3.6853696089118433`*^9, {3.6858758911429157`*^9, 3.685875951793*^9}, { 3.6859484099082212`*^9, 3.6859484970032024`*^9}, {3.686052829875022*^9, 3.686052906242383*^9}, {3.6860535326822133`*^9, 3.686053598029951*^9}, { 3.68605365168902*^9, 3.6860541446091995`*^9}, {3.6860541846064873`*^9, 3.68605440393201*^9}, {3.686054713802734*^9, 3.6860547858298535`*^9}, { 3.6860548280202665`*^9, 3.686054837219793*^9}, {3.686054874127904*^9, 3.686054892139934*^9}, {3.686055136014883*^9, 3.6860551460584574`*^9}, { 3.686055211281188*^9, 3.6860552301962633`*^9}, {3.6860553465409174`*^9, 3.6860553998749685`*^9}, {3.6860556017188663`*^9, 3.6860556050188704`*^9}, {3.6862923512707715`*^9, 3.686292363600789*^9}, { 3.686292409650853*^9, 3.6862924109708548`*^9}, {3.6862924536109147`*^9, 3.6862924596309233`*^9}, {3.686292542221039*^9, 3.6862925430110397`*^9}, { 3.686292988803664*^9, 3.686293001033681*^9}, {3.6866504529025555`*^9, 3.686650526682659*^9}, {3.686650671852862*^9, 3.6866507242929354`*^9}, { 3.6866507657529936`*^9, 3.6866507887630253`*^9}, {3.6866508208230705`*^9, 3.6866509100531955`*^9}, {3.6866509593932643`*^9, 3.686650971113281*^9}, { 3.686651007793332*^9, 3.6866511595335445`*^9}, {3.686651223513634*^9, 3.686651234033649*^9}, {3.686651304763748*^9, 3.6866513363837924`*^9}, { 3.6866514102038956`*^9, 3.686651429943923*^9}, {3.686652993837468*^9, 3.6866530046274834`*^9}, {3.686804398511652*^9, 3.6868044081516657`*^9}, { 3.6868046315619783`*^9, 3.686804631801979*^9}, {3.686804685872054*^9, 3.686804707092084*^9}, {3.6868047382021275`*^9, 3.686804767812169*^9}, { 3.686804824012248*^9, 3.6868048404922705`*^9}, {3.686804942142413*^9, 3.6868049633424425`*^9}, {3.6868050765526013`*^9, 3.686805101092636*^9}, { 3.6868051463526993`*^9, 3.6868052234228067`*^9}, {3.686805307602925*^9, 3.686805311682931*^9}, {3.68680577547358*^9, 3.686805788923599*^9}, { 3.686821702197342*^9, 3.6868217282873783`*^9}, {3.6868225192884855`*^9, 3.686822538368512*^9}, {3.6868226306886415`*^9, 3.6868226683086944`*^9}, { 3.6868227318887835`*^9, 3.6868227627088265`*^9}, {3.686822801638881*^9, 3.6868230490692277`*^9}, {3.686823122979331*^9, 3.6868231833294153`*^9}, { 3.6868232450595016`*^9, 3.6868233753996844`*^9}, {3.6868234153897405`*^9, 3.686823451379791*^9}, {3.6868236736101017`*^9, 3.6868236786601086`*^9}, { 3.6868237164601617`*^9, 3.68682375072021*^9}, {3.68682389396041*^9, 3.68682390087042*^9}, {3.686823940790476*^9, 3.6868239416904774`*^9}, { 3.6868239808805323`*^9, 3.6868239872905407`*^9}, {3.686824051540631*^9, 3.6868240519006314`*^9}, {3.686824360861064*^9, 3.6868243761510854`*^9}, { 3.6868245440213203`*^9, 3.686824577221367*^9}, {3.686824685841519*^9, 3.6868246979115357`*^9}, 3.6868248012716804`*^9, 3.6868253582724605`*^9, { 3.6868255183026843`*^9, 3.686825518932685*^9}, {3.6868264466639843`*^9, 3.6868264497139883`*^9}, {3.6868267792744493`*^9, 3.6868268152945004`*^9}, {3.686827100164899*^9, 3.6868271210549283`*^9}, 3.686827162004986*^9, {3.6868272414950967`*^9, 3.686827327475217*^9}, { 3.686827953126093*^9, 3.686827976506126*^9}, {3.686829128577739*^9, 3.686829138957753*^9}, 3.6868292410978966`*^9, {3.6868292768379464`*^9, 3.686829282727955*^9}, {3.6868293820380936`*^9, 3.686829418138144*^9}, { 3.686829846748744*^9, 3.686829848298746*^9}, {3.6868313063207874`*^9, 3.686831307180789*^9}, {3.6868331276633377`*^9, 3.68683328653356*^9}, { 3.6868394697195063`*^9, 3.6868394933895392`*^9}, 3.686839530999592*^9, { 3.686839582829664*^9, 3.68683963686974*^9}, {3.6868397551199055`*^9, 3.68683979365996*^9}, {3.6868398344600167`*^9, 3.686839866200061*^9}, { 3.687092084401948*^9, 3.687092117031994*^9}, {3.6870922598621936`*^9, 3.6870922645422*^9}, {3.6870962086478376`*^9, 3.6870962658779182`*^9}, 3.687096444838168*^9, {3.687096500978247*^9, 3.687096501638248*^9}, { 3.6870965809883595`*^9, 3.687096592708376*^9}, 3.687096837948719*^9, { 3.68709688890879*^9, 3.687096985798926*^9}, {3.6870971015990877`*^9, 3.6870972179192505`*^9}, {3.6870972618993125`*^9, 3.687097305639374*^9}, { 3.6870973356794157`*^9, 3.6870975186496716`*^9}, {3.6870975796097574`*^9, 3.6870975953197794`*^9}, {3.6870976531898603`*^9, 3.6870976848899045`*^9}, 3.6870977782500353`*^9, {3.687413757687042*^9, 3.6874137834070783`*^9}, { 3.6874140542074575`*^9, 3.687414094417514*^9}, {3.6874143478878684`*^9, 3.687414485538061*^9}, {3.6874146116082373`*^9, 3.68741464894829*^9}, { 3.6874147451084247`*^9, 3.687414766118454*^9}, 3.6874149094486547`*^9, { 3.6874150416688395`*^9, 3.6874150634888706`*^9}, {3.6874152437091227`*^9, 3.687415268869158*^9}, 3.6874153442892637`*^9, {3.687415449879411*^9, 3.687415469659439*^9}, 3.687415529739523*^9, 3.687415564789572*^9, 3.687415645529685*^9, {3.6874168016913037`*^9, 3.687416803441306*^9}, { 3.687421022677213*^9, 3.6874212686075573`*^9}, {3.68742948209425*^9, 3.6874294906842623`*^9}, {3.687844340668378*^9, 3.6878443698084188`*^9}, { 3.6886534778571014`*^9, 3.6886534911571198`*^9}, {3.688906380162199*^9, 3.6889064680223217`*^9}, {3.688906514222396*^9, 3.6889065193925257`*^9}, { 3.688908192623024*^9, 3.6889082006430354`*^9}, {3.688908261823121*^9, 3.688908271653135*^9}, {3.6889083776232834`*^9, 3.6889083922733035`*^9}, { 3.688908466073407*^9, 3.6889084993734536`*^9}, 3.688908533623502*^9, { 3.688908616683618*^9, 3.6889086271336327`*^9}, {3.6889086885637183`*^9, 3.6889087063437433`*^9}, {3.6889091647443852`*^9, 3.6889092012544365`*^9}, {3.6889093019045773`*^9, 3.6889093406746316`*^9}, 3.6889101071957045`*^9, {3.689905940063133*^9, 3.689905972983179*^9}, { 3.692530981927737*^9, 3.6925310416778207`*^9}, {3.692531099797902*^9, 3.6925311384779563`*^9}, {3.692531192258032*^9, 3.692531244668105*^9}, { 3.6925312919881716`*^9, 3.692531425418358*^9}, {3.6925315270885005`*^9, 3.692531643928664*^9}, {3.692535489534048*^9, 3.6925356485142703`*^9}, { 3.692535753564418*^9, 3.6925357992544813`*^9}, {3.6925358831745987`*^9, 3.692535899604622*^9}, {3.692536042584822*^9, 3.692536159384986*^9}, { 3.6925366121156197`*^9, 3.6925366207256317`*^9}, {3.6925367265057793`*^9, 3.69253672683578*^9}, {3.6925368590559654`*^9, 3.6925368636559715`*^9}, { 3.6925370880062857`*^9, 3.692537177856412*^9}, {3.692537322456614*^9, 3.6925373869767046`*^9}, {3.6925390913352747`*^9, 3.6925390925252767`*^9}, {3.692539644430175*^9, 3.6925396711502123`*^9}, { 3.692539727510291*^9, 3.692539730440295*^9}, {3.69253993367058*^9, 3.692539963780622*^9}, {3.6925400018406754`*^9, 3.692540003630678*^9}, { 3.6925401743409166`*^9, 3.6925401747509174`*^9}, {3.692540399111232*^9, 3.692540407981244*^9}, {3.69254047647134*^9, 3.6925404886113567`*^9}, { 3.6925406039715185`*^9, 3.69254060531152*^9}, {3.6925414948727655`*^9, 3.6925414953427663`*^9}, {3.6925415478528395`*^9, 3.692541613062931*^9}, 3.692541649332982*^9, {3.692541727633092*^9, 3.6925418840133104`*^9}, { 3.692541924473367*^9, 3.692542041693531*^9}, {3.6925421488836813`*^9, 3.6925422549438295`*^9}, {3.6925422976938896`*^9, 3.692542521444203*^9}, { 3.6925426221843443`*^9, 3.6925426357343626`*^9}, 3.692542739374508*^9, 3.692599799510878*^9, {3.692599834884901*^9, 3.6925998954663663`*^9}, { 3.692599925635092*^9, 3.6926000095928946`*^9}, {3.692600108929576*^9, 3.6926001456386757`*^9}, {3.6926001874800687`*^9, 3.692600454421337*^9}, { 3.692600503149027*^9, 3.6926006000391626`*^9}, {3.692600680251275*^9, 3.6926006814012766`*^9}, {3.6926009000215826`*^9, 3.6926009410816402`*^9}, 3.692601280532116*^9, {3.6926044914726114`*^9, 3.69260449774262*^9}, 3.6926045660127153`*^9, 3.6926046690228596`*^9, {3.69296647863291*^9, 3.6929664798829117`*^9}, {3.6929665643330297`*^9, 3.6929666141830997`*^9}, {3.6929670390036945`*^9, 3.6929670405536966`*^9}, {3.6929670861037607`*^9, 3.6929670952937737`*^9}, {3.6929671302538223`*^9, 3.6929671549438567`*^9}, {3.6929671904739065`*^9, 3.69296722137395*^9}, { 3.6929672596240034`*^9, 3.6929673352541094`*^9}, 3.6929678909232683`*^9, { 3.6930146982034283`*^9, 3.693014722713463*^9}, {3.6930148540136466`*^9, 3.693014857023651*^9}, {3.6930148913836985`*^9, 3.693014894823704*^9}, { 3.693014930903754*^9, 3.6930151942541227`*^9}, {3.693015247824198*^9, 3.693015430554454*^9}, {3.693015673794794*^9, 3.69301579223496*^9}, { 3.6930163123576884`*^9, 3.693016326897709*^9}, {3.6930164225678425`*^9, 3.693016429727853*^9}, {3.693016686718212*^9, 3.693016698128228*^9}, { 3.693016737038283*^9, 3.693016755068308*^9}, {3.6930168429225607`*^9, 3.6930168719926014`*^9}, {3.6930172049430676`*^9, 3.693017284063178*^9}, { 3.693017336433252*^9, 3.6930173662532935`*^9}, {3.6930180949163136`*^9, 3.6930180975563173`*^9}, {3.6930181870764427`*^9, 3.693018199956461*^9}, { 3.6930182954065943`*^9, 3.693018305996609*^9}, {3.693139886141657*^9, 3.6931399045016823`*^9}, {3.6931402916003532`*^9, 3.693140295770359*^9}, { 3.693140426020541*^9, 3.693140426530542*^9}, {3.6931410492237864`*^9, 3.6931410888738413`*^9}, {3.6931411194438844`*^9, 3.693141126553894*^9}, { 3.693141412004294*^9, 3.693141454164353*^9}, {3.6931415979955544`*^9, 3.6931417931758275`*^9}, {3.6932199559445915`*^9, 3.6932199772046213`*^9}, {3.6932201435748544`*^9, 3.693220170284892*^9}, { 3.693220713855653*^9, 3.693220721825664*^9}, {3.693625124589745*^9, 3.693625153729786*^9}, {3.6940907995669713`*^9, 3.6940909688872085`*^9}, { 3.6940913675677667`*^9, 3.6940914223978434`*^9}, {3.694091508037963*^9, 3.694091572118053*^9}, 3.694092009628666*^9, {3.6940920553287296`*^9, 3.694092229168973*^9}, {3.6940923053990793`*^9, 3.694092374419176*^9}, { 3.6940924537392874`*^9, 3.694092457789293*^9}, 3.694092642849552*^9, { 3.6940928573598523`*^9, 3.694092862379859*^9}, {3.6940945886222763`*^9, 3.694094601932295*^9}, 3.694094849542641*^9, {3.694095764293922*^9, 3.6940957644739223`*^9}, {3.6940960602743363`*^9, 3.6940960732243547`*^9}, {3.6940961211044216`*^9, 3.694096124194426*^9}, { 3.694665030960044*^9, 3.6946650634500895`*^9}, {3.6946652071402903`*^9, 3.6946653490404887`*^9}, {3.6946658702212186`*^9, 3.6946658881212435`*^9}, {3.694665923041292*^9, 3.694665953561335*^9}, { 3.694665995981395*^9, 3.6946660149414215`*^9}, {3.694666050571471*^9, 3.6946660547214766`*^9}, {3.694666169991638*^9, 3.694666292151809*^9}, { 3.6946663456618843`*^9, 3.6946663943919525`*^9}, 3.6946667526224537`*^9, 3.69466680700253*^9, 3.694687076625702*^9, {3.6946874316161985`*^9, 3.6946874621962414`*^9}, 3.694687499496294*^9, {3.694687567516389*^9, 3.694687642816495*^9}, {3.694687679006545*^9, 3.6946877198966026`*^9}, { 3.6946877714966745`*^9, 3.694687931746899*^9}, {3.723798739728607*^9, 3.723798744014243*^9}, {3.7237990126446104`*^9, 3.723799023974499*^9}, { 3.7244116671877546`*^9, 3.7244116733393917`*^9}, {3.724411761793063*^9, 3.7244117718753977`*^9}, {3.724411928386671*^9, 3.7244119682966137`*^9}, { 3.724412131847311*^9, 3.724412188341254*^9}, {3.729414981357122*^9, 3.7294149861075096`*^9}, {3.749817651293678*^9, 3.749817653108206*^9}, { 3.7498176831919456`*^9, 3.7498176846222315`*^9}, 3.7498177601545563`*^9, { 3.749817859674735*^9, 3.749817861044999*^9}, {3.7498179561547127`*^9, 3.749817964489929*^9}, {3.749818149334386*^9, 3.749818237397959*^9}, 3.749818617867873*^9, {3.7505621848002787`*^9, 3.7505622174085107`*^9}, { 3.75056238761455*^9, 3.750562431347901*^9}, {3.7505626332829456`*^9, 3.7505627331565337`*^9}, {3.7505627632642183`*^9, 3.7505627635859113`*^9}, {3.7515359581577415`*^9, 3.7515359614850826`*^9}, {3.751536071974715*^9, 3.7515360961721487`*^9}, 3.7515362040373974`*^9, {3.751536256080162*^9, 3.7515365099108534`*^9}, { 3.751549231137398*^9, 3.7515493334258356`*^9}, {3.7515496891619573`*^9, 3.751549689458767*^9}, {3.763384318028655*^9, 3.763384321230183*^9}, { 3.788530117667017*^9, 3.788530117980694*^9}, 3.7885303696209583`*^9, 3.788530509305438*^9, {3.78853083351016*^9, 3.788530862892729*^9}, { 3.788530925928982*^9, 3.7885309671960435`*^9}, {3.788533054135647*^9, 3.78853306391253*^9}, {3.788533559801361*^9, 3.7885336574548807`*^9}, { 3.788533916375413*^9, 3.7885339589240637`*^9}, {3.788535764582915*^9, 3.788535775009864*^9}, {3.788571051580041*^9, 3.788571053084015*^9}, 3.7885714852753925`*^9, {3.7885715554496107`*^9, 3.7885715772004504`*^9}, { 3.788571696555899*^9, 3.7885717388241262`*^9}, {3.788571794677034*^9, 3.7885718099292316`*^9}, 3.7885718526796875`*^9, {3.7885719048201413`*^9, 3.788571938458513*^9}, {3.7885720197107735`*^9, 3.7885720203433733`*^9}, { 3.7885721579483404`*^9, 3.788572246745886*^9}, {3.788572406392971*^9, 3.7885724747998886`*^9}, {3.7885725451809406`*^9, 3.7885725476052*^9}, { 3.788572796561078*^9, 3.7885727975057955`*^9}, 3.788572839094982*^9, { 3.788572904602244*^9, 3.788572917919137*^9}, {3.788573100895812*^9, 3.7885731714659753`*^9}, {3.7885733915788927`*^9, 3.788573436414242*^9}, 3.788573551866688*^9, 3.788573615961852*^9, {3.7885736607323666`*^9, 3.7885736628162546`*^9}, {3.788573695779252*^9, 3.788573697977635*^9}, { 3.788573733478549*^9, 3.7885738111703186`*^9}, {3.7888332726117997`*^9, 3.788833305367669*^9}},ExpressionUUID->"54be39e6-3c82-4e0b-b05a-\ 59ff1239990b"] }, Closed]], Cell[CellGroupData[{ Cell["BEAM ELEMENT (nonl xz) defs ", "Subsection", CellChangeTimes->{{3.7530187996679964`*^9, 3.753018803413909*^9}, { 3.7633629633672647`*^9, 3.763362967100765*^9}, {3.787894773214689*^9, 3.7878947881941814`*^9}, {3.78789485671918*^9, 3.78789488217928*^9}, 3.7885197052606735`*^9, {3.788530025907043*^9, 3.7885300287809105`*^9}, 3.7885306781716957`*^9, {3.8200271989371843`*^9, 3.8200272016625395`*^9}, { 3.8200274346181693`*^9, 3.8200274405428553`*^9}, {3.8216146694524984`*^9, 3.8216146730659995`*^9}, {3.852092974762933*^9, 3.8520929752366495`*^9}, { 3.8524280520829296`*^9, 3.8524280542544956`*^9}, {3.852428196459839*^9, 3.8524281972980237`*^9}},ExpressionUUID->"593b153a-85e3-4705-8251-\ 1376e04cb34a"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "rotations", " ", "are", " ", "replaced", " ", "by", " ", "first", " ", "derivatives", " ", "of", " ", "approximation"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iy_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE", "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", "Iy"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iy_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[CapitalDelta]h", ",", "h0", ",", "ix", ",", "iz", ",", "NN", ",", "\[Xi]", ",", "u", ",", "w", ",", "\[Epsilon]", ",", "\[Kappa]", ",", "fx", ",", "fz", ",", "\[Delta]wint", ",", "\[Delta]wext"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[CapitalDelta]h", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"\[CapitalDelta]h", ".", "\[CapitalDelta]h"}], "]"}], ",", " ", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix", "=", RowBox[{"\[CapitalDelta]h", "/", "h0"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz", "=", RowBox[{"ix", StyleBox["\[Cross]", "OperatorCharacter"], StyleBox[ RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], "OperatorCharacter"]}]}], StyleBox[";", "OperatorCharacter"], StyleBox["\[IndentingNewLine]", "OperatorCharacter"], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "\[Xi]"}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", "\[Xi]"}]}], ")"}]}], ",", RowBox[{"h0", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "\[Xi]"}], ")"}], "2"], " ", "\[Xi]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{"2", " ", "\[Xi]"}]}], ")"}], " ", SuperscriptBox["\[Xi]", "2"]}], ",", RowBox[{"h0", " ", SuperscriptBox["\[Xi]", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Xi]"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NN", ".", RowBox[{"Flatten", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", RowBox[{"2", ";;", "3"}], ",", "1"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"NN", ".", RowBox[{"Flatten", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", RowBox[{"2", ";;", "3"}], ",", "3"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"ix", ".", RowBox[{"{", RowBox[{"u", ",", "0", ",", "w"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"iz", ".", RowBox[{"{", RowBox[{"u", ",", "0", ",", "w"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "strain", " ", "measures", " ", "for", " ", "a", " ", "planar", " ", "problem"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "u"}], "/", "h0"}], "+", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "u"}], "/", "h0"}], ")"}], "2"], "/", "2"}], "+", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "w"}], "/", "h0"}], ")"}], "2"], "/", "2"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "w"}], "/", "h0"}], "*", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"\[Xi]", ",", "\[Xi]"}]], "u"}], "/", RowBox[{"h0", "^", "2"}]}]}], "-", RowBox[{ RowBox[{"(", RowBox[{"1", "+", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "u"}], "/", "h0"}]}], ")"}], RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"\[Xi]", ",", "\[Xi]"}]], "w"}], "/", RowBox[{"h0", "^", "2"}]}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]", "=", RowBox[{"\[Kappa]", "/", RowBox[{ RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", "\[Epsilon]"}]}], ")"}], "^", RowBox[{"(", RowBox[{"3", "/", "2"}], ")"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"\[Kappa]", "=", RowBox[{ RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"\[Xi]", ",", "\[Xi]"}]], "w"}]}], "/", RowBox[{"h0", "^", "2"}]}]}], ";"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"fx", " ", "=", RowBox[{"ix", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"fz", " ", "=", RowBox[{"iz", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "density"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"\[Delta]\[Delta]", "[", "\[Kappa]", "]"}]}], "*", "EE", "*", "Iy", "*", "\[Kappa]"}], "-", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", "\[Epsilon]", "]"}], "*", "EE", "*", "AA", "*", "\[Epsilon]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", "u", "]"}], "*", "fx"}], "+", RowBox[{ RowBox[{"\[Delta]", "[", "w", "]"}], "*", "fz"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ",", "\[Xi]"}], "]"}], "*", "h0"}]}]}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4430689313272*^9, 3.4430690080792*^9}, { 3.4430690869528*^9, 3.4430691077320004`*^9}, {3.4430691700116*^9, 3.4430691708072*^9}, {3.4430692071717997`*^9, 3.443069246359*^9}, { 3.4430772782732*^9, 3.4430773623416*^9}, {3.4430773978316*^9, 3.4430774104676*^9}, {3.4430775053780003`*^9, 3.4430776180598*^9}, { 3.4434109099524*^9, 3.4434109159584*^9}, {3.4438800815346003`*^9, 3.4438802689304*^9}, {3.443880362624*^9, 3.4438803824516*^9}, { 3.443929565615374*^9, 3.443929570232974*^9}, {3.443935321321974*^9, 3.443935335705174*^9}, {3.443935419945174*^9, 3.443935421489574*^9}, { 3.443935494013974*^9, 3.443935494715974*^9}, {3.443935617565974*^9, 3.4439357217895737`*^9}, {3.443935755360774*^9, 3.443935816107174*^9}, { 3.443942155230774*^9, 3.443942209939974*^9}, {3.443942305710374*^9, 3.4439423142123737`*^9}, {3.4439442908131742`*^9, 3.443944441181574*^9}, { 3.4439447830065737`*^9, 3.4439447917425737`*^9}, {3.443944908541774*^9, 3.443944916060974*^9}, {3.4442731097938004`*^9, 3.4442731115254*^9}, { 3.444273189229*^9, 3.4442732700526*^9}, {3.4442748430004*^9, 3.4442748605036*^9}, {3.4442748977438*^9, 3.4442748989762*^9}, { 3.4442749340762*^9, 3.4442749351057997`*^9}, 3.4442752313382*^9, { 3.4442919702026*^9, 3.4442919911846*^9}, {3.4442921151577997`*^9, 3.4442921271074*^9}, {3.4443811023684*^9, 3.4443811036632*^9}, { 3.4443814073171997`*^9, 3.4443814402956*^9}, {3.4443815036316*^9, 3.4443815147855997`*^9}, {3.4443815537232*^9, 3.4443815747676*^9}, { 3.4443816138143997`*^9, 3.444381633174*^9}, {3.4443816850439997`*^9, 3.4443817801728*^9}, 3.4443853618688*^9, {3.4443855607376003`*^9, 3.4443856337924*^9}, {3.4443861200444*^9, 3.4443861523676*^9}, { 3.4443862280495996`*^9, 3.444386291448*^9}, {3.4443864047352*^9, 3.4443864135336*^9}, {3.4443870026832*^9, 3.4443870095316*^9}, { 3.4444082055056*^9, 3.4444082437412*^9}, {3.4444082797148*^9, 3.4444084583816*^9}, {3.4444084889108*^9, 3.4444085087539997`*^9}, { 3.444408942517*^9, 3.4444089563386*^9}, {3.4444091419564*^9, 3.4444091647167997`*^9}, {3.4444092206428003`*^9, 3.4444092944463997`*^9}, {3.4444093856284*^9, 3.4444094281071997`*^9}, { 3.4444094976988*^9, 3.4444095275104*^9}, {3.444409611064*^9, 3.4444096125772*^9}, 3.4444098504616003`*^9, {3.444409913392*^9, 3.4444099166056004`*^9}, 3.4444100178496*^9, {3.4444103063248*^9, 3.4444103358712*^9}, {3.4444103868208*^9, 3.4444104432460003`*^9}, { 3.4444921219564*^9, 3.4444921256224003`*^9}, {3.444492194824*^9, 3.4444921973668003`*^9}, {3.4444922814351997`*^9, 3.4444922853508*^9}, { 3.4444923330868*^9, 3.4444923345844*^9}, {3.444492366424*^9, 3.4444923855808*^9}, {3.4453153475226*^9, 3.445315360689*^9}, { 3.4465518166373653`*^9, 3.446551863016165*^9}, {3.446551894231765*^9, 3.446552159384965*^9}, {3.446552232377365*^9, 3.4465522555589647`*^9}, { 3.446553347388365*^9, 3.4465533616155653`*^9}, {3.4466058525769997`*^9, 3.4466058529046*^9}, {3.4466064371219997`*^9, 3.4466065097244*^9}, { 3.4466127725788*^9, 3.4466127766036*^9}, {3.4466128124835997`*^9, 3.4466130037864*^9}, {3.4466131532696*^9, 3.4466131761703997`*^9}, { 3.4466133992192*^9, 3.4466134478756*^9}, {3.446613483584*^9, 3.4466134932092*^9}, {3.4466135740952*^9, 3.4466135794927998`*^9}, { 3.4466137283948*^9, 3.4466137341356*^9}, {3.4466138994342003`*^9, 3.4466139023826*^9}, {3.4466139549858*^9, 3.4466139579653997`*^9}, { 3.4466142109818*^9, 3.4466142245226*^9}, {3.4466142793878*^9, 3.4466143652033997`*^9}, {3.4466144712834*^9, 3.4466145978929996`*^9}, { 3.4466146992618*^9, 3.4466147509914*^9}, {3.4466151283086*^9, 3.4466152768986*^9}, {3.4466153107506*^9, 3.4466153406558*^9}, { 3.4466194331976*^9, 3.4466194377528*^9}, {3.4466194847712*^9, 3.446619488718*^9}, {3.4466389495861998`*^9, 3.4466389768238*^9}, { 3.4466391218414*^9, 3.446639306561*^9}, {3.4466393990222*^9, 3.4466394004886*^9}, {3.4466394475694*^9, 3.4466394487706003`*^9}, { 3.4466395034174*^9, 3.4466395049462*^9}, 3.4466395515755997`*^9, { 3.4466396000176*^9, 3.4466396190808*^9}, {3.4466397459088*^9, 3.446639748826*^9}, {3.4466397974356003`*^9, 3.446639798668*^9}, 3.4466398447816*^9, {3.446639894218*^9, 3.4466399201556*^9}, { 3.4466399570964003`*^9, 3.4466399583288*^9}, {3.446639994006*^9, 3.4466400056904*^9}, {3.4466400383568*^9, 3.4466400395892*^9}, { 3.4466400745643997`*^9, 3.4466401025976*^9}, {3.4466401660834*^9, 3.4466401806070004`*^9}, {3.4466402251294003`*^9, 3.446640227407*^9}, { 3.446640260479*^9, 3.4466402657674*^9}, {3.4466404133122*^9, 3.4466405185654*^9}, 3.4466405830462*^9, {3.4467273294214*^9, 3.4467273777813997`*^9}, {3.4467274366558*^9, 3.4467275620954*^9}, { 3.446727593311*^9, 3.4467277412614*^9}, {3.4467283334639997`*^9, 3.4467283356012*^9}, {3.4467283707636003`*^9, 3.4467283727604*^9}, { 3.4467289882664003`*^9, 3.4467291276836*^9}, {3.446778464322*^9, 3.4467786797424*^9}, {3.4467801953803997`*^9, 3.4467802409792*^9}, { 3.4467802998691998`*^9, 3.4467804023456*^9}, 3.4467804345596*^9, { 3.4467808656344*^9, 3.4467808670852003`*^9}, 3.4467818107525997`*^9, { 3.446781855509*^9, 3.446781874385*^9}, {3.4467826737914*^9, 3.4467827381726*^9}, {3.4467828623018*^9, 3.4467831045386*^9}, { 3.4470344113984003`*^9, 3.4470344123344*^9}, {3.4470344628316*^9, 3.4470345343108*^9}, {3.447043591118539*^9, 3.447043642192939*^9}, { 3.447045649625739*^9, 3.447045718437339*^9}, {3.447054774023939*^9, 3.447054834198939*^9}, {3.4470549103449388`*^9, 3.4470549116169386`*^9}, { 3.447054943902939*^9, 3.4470553027109385`*^9}, {3.447055334559939*^9, 3.447055353684939*^9}, {3.447057311918539*^9, 3.447057369747739*^9}, { 3.4470575058577385`*^9, 3.4470575951365385`*^9}, {3.4470581848789387`*^9, 3.4470582040825386`*^9}, {3.451276121243*^9, 3.4512761425838003`*^9}, { 3.4512762022382*^9, 3.4512762064346*^9}, {3.4512762476966*^9, 3.4512762827654*^9}, {3.451276489091*^9, 3.451276541975*^9}, { 3.4512765853118*^9, 3.4512766132046003`*^9}, {3.4512773470306*^9, 3.4512773766082*^9}, {3.4512776069110003`*^9, 3.4512777499318*^9}, 3.4512777831286*^9, {3.4512778785538*^9, 3.451277881627*^9}, { 3.4512780242734003`*^9, 3.4512780302794*^9}, 3.4512780737878*^9, { 3.4512781866226*^9, 3.4512781930810003`*^9}, {3.4512863325078*^9, 3.4512863539266*^9}, {3.4568019250434*^9, 3.4568022712698*^9}, { 3.4568023177422*^9, 3.4568024125278*^9}, {3.4568024694365997`*^9, 3.4568024750369997`*^9}, {3.4568026914402*^9, 3.4568028101094*^9}, { 3.4568028406698*^9, 3.4568028564726*^9}, 3.4568028886085997`*^9, { 3.4568030489454*^9, 3.4568030800986*^9}, 3.4568032004128*^9, { 3.4568035073698*^9, 3.4568035176034*^9}, {3.4568040146596003`*^9, 3.4568040844852*^9}, {3.4568043016684*^9, 3.4568043154744*^9}, { 3.4568045482264*^9, 3.4568045486632*^9}, {3.4568048944996*^9, 3.4568049806116*^9}, {3.4660560628582*^9, 3.4660560753538*^9}, { 3.4660676729379997`*^9, 3.4660676735931997`*^9}, {3.4660677244024*^9, 3.4660677277251997`*^9}, {3.4742646771287394`*^9, 3.47426469439174*^9}, { 3.47426489921974*^9, 3.4742649800437393`*^9}, {3.4801246373348*^9, 3.4801246860536003`*^9}, {3.4801247748176003`*^9, 3.4801247821028*^9}, { 3.4801248161264*^9, 3.4801248295736*^9}, {3.4801248810692*^9, 3.4801248964508*^9}, {3.4801249330484*^9, 3.480124947884*^9}, 3.4801249886468*^9, {3.4801251139147997`*^9, 3.48012512588*^9}, { 3.4838339444988003`*^9, 3.4838339567448*^9}, 3.4838341692012*^9, { 3.4838344350408*^9, 3.4838344353684*^9}, {3.4938987575920324`*^9, 3.4938987586840324`*^9}, {3.4941630624049997`*^9, 3.4941631381274*^9}, { 3.4941632311345997`*^9, 3.4941632492306004`*^9}, 3.4941633249217997`*^9, { 3.4941633940922003`*^9, 3.4941634063538*^9}, {3.4941634538402*^9, 3.4941635051642*^9}, {3.494163565115*^9, 3.4941636341762*^9}, { 3.4941636853442*^9, 3.4941639323234*^9}, {3.4941640277798*^9, 3.4941641455754004`*^9}, {3.4941641790374002`*^9, 3.4941641803789997`*^9}, {3.4941642676142*^9, 3.4941643277678003`*^9}, 3.4941644677018003`*^9, {3.4941646208938*^9, 3.4941646322349997`*^9}, { 3.4941652592693996`*^9, 3.4941652807194*^9}, {3.4941653119038*^9, 3.494165416299*^9}, {3.494165453895*^9, 3.4941654544722*^9}, { 3.4950990979779997`*^9, 3.495099142701*^9}, {3.495099172958*^9, 3.4950991806289997`*^9}, {3.495099227097*^9, 3.495099238113*^9}, 3.495099290797*^9, {3.495099346084*^9, 3.495099359507*^9}, { 3.495099456308*^9, 3.495099464091*^9}, 3.495099683108*^9, { 3.495100428112*^9, 3.495100434958*^9}, {3.4951006496219997`*^9, 3.495100649992*^9}, {3.4987235265018*^9, 3.4987235939094*^9}, { 3.4987236420666*^9, 3.4987236530646*^9}, {3.4987237305341997`*^9, 3.4987237396914*^9}, {3.498733136159*^9, 3.4987332972446003`*^9}, { 3.4987364783094*^9, 3.4987364860626*^9}, {3.4987366201134*^9, 3.4987366236078*^9}, {3.4987367272386*^9, 3.4987367464890003`*^9}, { 3.4987369428462*^9, 3.4987369670886*^9}, {3.4987370134518003`*^9, 3.4987370259941998`*^9}, {3.4987370944002*^9, 3.4987371027618*^9}, { 3.4987371921029997`*^9, 3.498737193663*^9}, {3.4987372660938*^9, 3.4987372935498*^9}, {3.4987373290554*^9, 3.4987377176202*^9}, { 3.4987377520182*^9, 3.4987379139462*^9}, {3.4987382030216*^9, 3.4987382667078*^9}, {3.4987888391818*^9, 3.4987888608346*^9}, { 3.4988785131146*^9, 3.4988785160162*^9}, {3.5007170967096*^9, 3.5007170999076*^9}, 3.5007182237316*^9, {3.5007182772864*^9, 3.5007182987832003`*^9}, {3.5009573226744003`*^9, 3.5009573940444*^9}, 3.5009574358710003`*^9, 3.5009604278482*^9, {3.5009897246173353`*^9, 3.5009898480289354`*^9}, {3.5009901464413357`*^9, 3.5009901475333357`*^9}, {3.5009901801997356`*^9, 3.500990274096135*^9}, { 3.5010475253292*^9, 3.5010475852332*^9}, {3.5010605722018003`*^9, 3.5010606739762*^9}, {3.5010607202146*^9, 3.5010607323358*^9}, { 3.5010607920526*^9, 3.501061118467*^9}, {3.5010612022078*^9, 3.5010612277138*^9}, {3.5010616467766*^9, 3.5010617938534*^9}, { 3.5010618406222*^9, 3.5010619950778*^9}, {3.5010621500638*^9, 3.5010622514014*^9}, {3.5010625292218*^9, 3.5010625409374*^9}, { 3.5010626043046*^9, 3.5010626313862*^9}, {3.5010626787166*^9, 3.5010626790754004`*^9}, {3.501074457561*^9, 3.5010744671082*^9}, 3.5010763029458*^9, {3.5032210899309998`*^9, 3.5032212413900003`*^9}, { 3.557658203404973*^9, 3.557658219644601*^9}, {3.5576584433801947`*^9, 3.557658496030287*^9}, {3.5576585501779823`*^9, 3.5576586046064777`*^9}, { 3.557658648910555*^9, 3.557658754600741*^9}, {3.557658963945511*^9, 3.5576589782507353`*^9}, {3.557659009949991*^9, 3.5576591437514267`*^9}, { 3.557659182221094*^9, 3.5576592187719584`*^9}, 3.557659413865901*^9, { 3.557659921100792*^9, 3.5576599556392527`*^9}, {3.557660706920972*^9, 3.5576607248454037`*^9}, {3.557661209085854*^9, 3.557661209413454*^9}, { 3.5577526651911488`*^9, 3.5577526932087984`*^9}, {3.5577527272480583`*^9, 3.557752747122493*^9}, {3.5577528374934516`*^9, 3.557752838523053*^9}, { 3.557752881204728*^9, 3.557752891313546*^9}, {3.557752938612829*^9, 3.5577529469120436`*^9}, {3.557753060714244*^9, 3.557753062633047*^9}, { 3.5577536609544907`*^9, 3.5577536637936954`*^9}, {3.5577537824631042`*^9, 3.557753810184353*^9}, {3.557753841025607*^9, 3.5577540648392*^9}, 3.5577541920574236`*^9, {3.5577547033327217`*^9, 3.557754716967146*^9}, { 3.5577547716296415`*^9, 3.557754802112095*^9}, {3.5577549509363565`*^9, 3.5577549771444025`*^9}, 3.5577551382302856`*^9, {3.55775527184452*^9, 3.557755272858522*^9}, {3.557755881555991*^9, 3.557755886548*^9}, { 3.557756158316077*^9, 3.557756231885806*^9}, {3.5577572408487787`*^9, 3.557757248835993*^9}, {3.5577572834368534`*^9, 3.5577575888229895`*^9}, { 3.5577578129641833`*^9, 3.557757862837471*^9}, {3.557758025514557*^9, 3.557758079272251*^9}, 3.557810586960072*^9, {3.5578240262005973`*^9, 3.5578240345360737`*^9}, {3.557824091429328*^9, 3.5578241008156557`*^9}, { 3.557831525255726*^9, 3.5578315319793377`*^9}, 3.5578315716190076`*^9, { 3.557831606079468*^9, 3.557831629432709*^9}, {3.5578316663267736`*^9, 3.5578317569473333`*^9}, {3.5578322144181366`*^9, 3.557832218084143*^9}, { 3.557836356693412*^9, 3.557836473771618*^9}, {3.5578365201660995`*^9, 3.5578365974018345`*^9}, {3.5578366426731143`*^9, 3.557836658865943*^9}, { 3.557836691017599*^9, 3.5578367924957776`*^9}, {3.5578368305442443`*^9, 3.557836888279946*^9}, {3.5578369382156334`*^9, 3.5578370776642785`*^9}, { 3.5578383536061196`*^9, 3.5578383735117545`*^9}, {3.5578385892445335`*^9, 3.5578385978869486`*^9}, {3.5578386713006773`*^9, 3.557838700113928*^9}, { 3.5578387451200075`*^9, 3.5578387467892103`*^9}, {3.5578388951454706`*^9, 3.5578389248635225`*^9}, {3.5578389679351983`*^9, 3.557838983535226*^9}, { 3.5578390227692947`*^9, 3.557839023143696*^9}, {3.557839097696226*^9, 3.5578391125162525`*^9}, {3.5578391553539276`*^9, 3.557839199892006*^9}, { 3.55783924184048*^9, 3.557839294490572*^9}, {3.5578393285922318`*^9, 3.557839398683155*^9}, {3.557839430522811*^9, 3.557839470162481*^9}, { 3.5578395370865984`*^9, 3.5578395446994114`*^9}, {3.5578396068499207`*^9, 3.5578396118575296`*^9}, 3.5578943518105097`*^9, {3.557894388361374*^9, 3.5578944029629993`*^9}, {3.5578944607611012`*^9, 3.5578944989499683`*^9}, {3.5578945393696394`*^9, 3.557894561537278*^9}, { 3.5578946028617506`*^9, 3.5578946188985786`*^9}, {3.557894650894235*^9, 3.5578947812636642`*^9}, {3.55789481884413*^9, 3.5578948191249304`*^9}, { 3.5578949768100076`*^9, 3.5578949836272197`*^9}, {3.5578967386805477`*^9, 3.55789678549623*^9}, {3.5578968804691963`*^9, 3.557896888643611*^9}, { 3.557897022491846*^9, 3.5578970341450663`*^9}, {3.557897620940097*^9, 3.55789765120415*^9}, {3.5579218072271147`*^9, 3.5579218263059483`*^9}, { 3.557922095312821*^9, 3.557922116965659*^9}, {3.557922178086566*^9, 3.557922188616585*^9}, {3.5579223258812256`*^9, 3.557922327066828*^9}, { 3.5579224596046605`*^9, 3.557922461804264*^9}, 3.5579805928465395`*^9, { 3.5579815200581703`*^9, 3.557981541711009*^9}, 3.557985544779242*^9, { 3.5579863164793987`*^9, 3.5579863339514294`*^9}, {3.557986523210962*^9, 3.557986568841042*^9}, 3.5579866122559185`*^9, 3.557986993536188*^9, { 3.5579871244716187`*^9, 3.5579871290580263`*^9}, 3.557987173486905*^9, 3.5579872166989803`*^9, {3.5599618621582537`*^9, 3.5599618642486577`*^9}, { 3.559961969720443*^9, 3.5599619894700775`*^9}, 3.559963611089726*^9, { 3.5601298891258235`*^9, 3.560129889422224*^9}, {3.560132445157113*^9, 3.5601324458591146`*^9}, {3.561978472080926*^9, 3.561978472392926*^9}, { 3.6297802564412937`*^9, 3.6297802957377625`*^9}, {3.62978033369263*^9, 3.629780429741998*^9}, {3.6297805790030603`*^9, 3.6297809429048996`*^9}, { 3.629780987957779*^9, 3.629781197575347*^9}, {3.629781240397422*^9, 3.629781337663593*^9}, {3.6297813946972933`*^9, 3.6297814529165955`*^9}, { 3.6297814952550697`*^9, 3.629781527578326*^9}, {3.62978162025529*^9, 3.629781647633338*^9}, {3.629781678833393*^9, 3.629781763120341*^9}, 3.6297818028224106`*^9, {3.6297818432108817`*^9, 3.629781872570133*^9}, { 3.629782355765382*^9, 3.629782427603508*^9}, {3.6297824692243814`*^9, 3.629782674863942*^9}, {3.629782707218399*^9, 3.6297829295343895`*^9}, { 3.629783005631323*^9, 3.6297830574702144`*^9}, {3.6297831098551064`*^9, 3.629783142786764*^9}, {3.629783433711675*^9, 3.629783442619291*^9}, { 3.6297834942397814`*^9, 3.6297835175930223`*^9}, 3.6297835794939313`*^9, { 3.6297836160291953`*^9, 3.6297837668970604`*^9}, {3.6297842042438283`*^9, 3.6297842697483435`*^9}, {3.6297843514456873`*^9, 3.629784370742921*^9}, { 3.629784443829049*^9, 3.6297844678842916`*^9}, {3.6297845252611923`*^9, 3.629784525588793*^9}, {3.6297846136821475`*^9, 3.629784629235375*^9}, { 3.629784814797701*^9, 3.629784927648299*^9}, {3.629785259960083*^9, 3.6297852602096834`*^9}, {3.6297858780175686`*^9, 3.629785917282837*^9}, { 3.629786048057867*^9, 3.629786048681868*^9}, 3.6297863278755584`*^9, { 3.6297867047133856`*^9, 3.629786748533863*^9}, {3.6297867791567163`*^9, 3.6297868491540394`*^9}, {3.6297875320748396`*^9, 3.629787569795706*^9}, { 3.6297876247234025`*^9, 3.6297877281983843`*^9}, {3.6297877681812544`*^9, 3.629787774015665*^9}, {3.629787831408166*^9, 3.6297878355265727`*^9}, { 3.6297878775686464`*^9, 3.6297878861174617`*^9}, {3.6297879185343184`*^9, 3.629787919064719*^9}, {3.6297880043032694`*^9, 3.62978800470887*^9}, 3.6297880488257475`*^9, {3.6297882100052304`*^9, 3.6297882174776435`*^9}, { 3.6297882697533355`*^9, 3.6297882948381796`*^9}, {3.6297883467550707`*^9, 3.6297883991087627`*^9}, {3.6297887361785545`*^9, 3.629788783961438*^9}, 3.629788825395111*^9, {3.629789006152629*^9, 3.6297890321266747`*^9}, { 3.6297891133248167`*^9, 3.629789145336073*^9}, {3.6297891926821566`*^9, 3.629789194257759*^9}, {3.629789255316266*^9, 3.6297892556282673`*^9}, { 3.629869102295367*^9, 3.629869160124668*^9}, {3.6298691942887287`*^9, 3.6298696149902673`*^9}, {3.6298696993864155`*^9, 3.62986975897852*^9}, { 3.6298698387726603`*^9, 3.629869912030389*^9}, {3.6298700722270703`*^9, 3.629870234560955*^9}, {3.629870580429163*^9, 3.629870630458451*^9}, { 3.630556081081209*^9, 3.630556104902451*^9}, {3.6305562643503313`*^9, 3.6305562763935523`*^9}, {3.6305563415080667`*^9, 3.630556480956712*^9}, { 3.630556692851884*^9, 3.630556695347888*^9}, {3.630556730042349*^9, 3.630556914528273*^9}, {3.6305653725974936`*^9, 3.6305656807121167`*^9}, { 3.630565758760581*^9, 3.6305657739024467`*^9}, {3.630565858170267*^9, 3.63056596644846*^9}, {3.6305661502619734`*^9, 3.6305661523230915`*^9}, { 3.6305662653385553`*^9, 3.630566370352562*^9}, {3.6305667786019125`*^9, 3.630566790535595*^9}, {3.6305668214773645`*^9, 3.630567044691132*^9}, { 3.6305670772499943`*^9, 3.6305670783710585`*^9}, 3.630567272031135*^9, { 3.630567303902958*^9, 3.630567409875019*^9}, {3.630568671196477*^9, 3.6305687195002403`*^9}, {3.6305687542132254`*^9, 3.630568758623478*^9}, { 3.630568855671028*^9, 3.630568859250233*^9}, {3.630569706514694*^9, 3.630569775526641*^9}, 3.630569982346471*^9, {3.6305701679130845`*^9, 3.630570205199217*^9}, {3.6305703751399374`*^9, 3.630570526177576*^9}, { 3.630587657039589*^9, 3.630587688367381*^9}, {3.6305880733027773`*^9, 3.6305883365376396`*^9}, {3.6305886689118233`*^9, 3.6305886717978287`*^9}, 3.6305889776831656`*^9, {3.6305890389444733`*^9, 3.6305890437180815`*^9}, { 3.630589093248169*^9, 3.6305891296430326`*^9}, 3.630589181700324*^9, { 3.6305892509956455`*^9, 3.6305892594820604`*^9}, {3.630589318949365*^9, 3.6305893334729905`*^9}, {3.630589630294712*^9, 3.6305896376267247`*^9}, { 3.630589683288005*^9, 3.630589684988408*^9}, {3.630597310538067*^9, 3.630597340080757*^9}, {3.630597391446695*^9, 3.630597400596218*^9}, { 3.6305974350611897`*^9, 3.6305974605306463`*^9}, {3.630633997622449*^9, 3.630634003125764*^9}, {3.630659322217756*^9, 3.63065932438616*^9}, { 3.6306611578252783`*^9, 3.6306611625988865`*^9}, {3.6306612541554475`*^9, 3.630661257587454*^9}, {3.6306613001287284`*^9, 3.6306613026715326`*^9}, { 3.6306613920752897`*^9, 3.6306613949768953`*^9}, {3.6306706377509866`*^9, 3.630670654957817*^9}, {3.6306749981919994`*^9, 3.630675005793434*^9}, { 3.6306751229631357`*^9, 3.630675150017683*^9}, {3.6306752035287437`*^9, 3.6306752096180925`*^9}, {3.630675315921172*^9, 3.6306753201514144`*^9}, { 3.6306757793287754`*^9, 3.6306757796257925`*^9}, {3.630675814406262*^9, 3.6306758147026625`*^9}, {3.6306760107574763`*^9, 3.6306760154417443`*^9}, {3.6306789722320743`*^9, 3.6306789870309205`*^9}, {3.6306790257051325`*^9, 3.630679028076268*^9}, { 3.6306800259177256`*^9, 3.6306800406129513`*^9}, {3.6306801239326982`*^9, 3.6306801300167084`*^9}, {3.630680769261832*^9, 3.6306807806186523`*^9}, { 3.630681157468514*^9, 3.6306811577649145`*^9}, {3.6306812744219193`*^9, 3.63068127471832*^9}, {3.6306817187418995`*^9, 3.6306817919060287`*^9}, { 3.630681879188182*^9, 3.6306819111526375`*^9}, {3.6306821191790032`*^9, 3.6306821283050194`*^9}, {3.630720543651497*^9, 3.6307205534300566`*^9}, { 3.630721035525631*^9, 3.630721092774905*^9}, {3.6307212510439577`*^9, 3.6307213064777765`*^9}, {3.6307477437169704`*^9, 3.6307478284095197`*^9}, {3.6307478614971776`*^9, 3.6307478785948076`*^9}, {3.6307479884814005`*^9, 3.630748002880226*^9}, { 3.630748045624301*^9, 3.630748063876333*^9}, {3.630748111596817*^9, 3.6307481498324842`*^9}, {3.6307489182430334`*^9, 3.6307489447786803`*^9}, {3.630749037427243*^9, 3.6307490443848553`*^9}, { 3.6307491041485605`*^9, 3.6307491384218206`*^9}, {3.6307491914151134`*^9, 3.630749196890723*^9}, {3.6307492445800066`*^9, 3.6307493439989815`*^9}, { 3.630749396212273*^9, 3.6307494766304145`*^9}, {3.6307495333989143`*^9, 3.6307495547241516`*^9}, {3.6307496525831237`*^9, 3.630749669571553*^9}, { 3.630750220602922*^9, 3.6307502881822405`*^9}, {3.6307510631916018`*^9, 3.630751068292811*^9}, {3.6307511226589065`*^9, 3.630751137962533*^9}, { 3.6307512555243397`*^9, 3.630751282777588*^9}, {3.630752266971757*^9, 3.630752414599744*^9}, {3.630752446407563*^9, 3.630752457388191*^9}, { 3.6307589380050273`*^9, 3.6307590266300964`*^9}, {3.6307591666721067`*^9, 3.63075923229886*^9}, 3.630760288282259*^9, {3.6307603547370596`*^9, 3.630760557414652*^9}, {3.630760654134184*^9, 3.63076065510824*^9}, { 3.6307606911683025`*^9, 3.6307606919283457`*^9}, {3.6307607642334814`*^9, 3.6307607648645177`*^9}, {3.630761455000991*^9, 3.6307614616743727`*^9}, { 3.630761507825012*^9, 3.630761605776615*^9}, {3.630761652999316*^9, 3.630761695865768*^9}, {3.630761771278081*^9, 3.6307617792215357`*^9}, 3.6307629478424797`*^9, {3.632205207880766*^9, 3.6322052561155243`*^9}, { 3.6322052892474194`*^9, 3.6322052915745525`*^9}, 3.6322053746993074`*^9, { 3.6322062705415463`*^9, 3.6322062726016645`*^9}, {3.6322063396935015`*^9, 3.63220636484194*^9}, {3.6322064410612993`*^9, 3.6322064491667633`*^9}, { 3.632206580308264*^9, 3.6322066373275256`*^9}, {3.6322066736436024`*^9, 3.6322067467737856`*^9}, {3.632206782260815*^9, 3.6322071351279984`*^9}, 3.6322071989226465`*^9, {3.632207270393735*^9, 3.6322073359894867`*^9}, { 3.6322073997741346`*^9, 3.6322074126708727`*^9}, {3.632207491777397*^9, 3.632207682289294*^9}, {3.632207809621577*^9, 3.632207827973626*^9}, { 3.6322079043859973`*^9, 3.6322079279443445`*^9}, {3.6322080916397076`*^9, 3.6322081666649985`*^9}, 3.634905258940913*^9, {3.634905370524296*^9, 3.6349054089004903`*^9}, {3.6349054472556844`*^9, 3.63490544787272*^9}, { 3.634905483492757*^9, 3.6349055164646425`*^9}, {3.634905574352954*^9, 3.634905628121029*^9}, {3.6349057012822137`*^9, 3.6349057207913294`*^9}, { 3.6349061371061416`*^9, 3.634906354438572*^9}, {3.6349063890455513`*^9, 3.6349064369332905`*^9}, {3.634906537696054*^9, 3.634906601859724*^9}, 3.634906706128688*^9, {3.6349069249442034`*^9, 3.6349069328326545`*^9}, { 3.6349070151973653`*^9, 3.6349070242298822`*^9}, {3.6349070817921743`*^9, 3.6349070822111983`*^9}, {3.634907723288866*^9, 3.634907739005765*^9}, { 3.6349079580732946`*^9, 3.6349079868219395`*^9}, {3.634908200284148*^9, 3.634908315195721*^9}, {3.6349083774582825`*^9, 3.6349084027997313`*^9}, { 3.63490844507615*^9, 3.634908448843365*^9}, {3.634914956333157*^9, 3.634915020054802*^9}, {3.634915050572547*^9, 3.6349150956171236`*^9}, { 3.6349539785771523`*^9, 3.634953978975175*^9}, {3.6349540728785458`*^9, 3.6349541681829967`*^9}, {3.634954211263461*^9, 3.6349542495746527`*^9}, { 3.6349543251259737`*^9, 3.634954355882733*^9}, {3.6349543892536416`*^9, 3.6349544742835045`*^9}, {3.634954547519694*^9, 3.6349545640246377`*^9}, { 3.6349547051657104`*^9, 3.6349547107930326`*^9}, {3.634954745355009*^9, 3.634954752101395*^9}, {3.6349547948858423`*^9, 3.6349548053894434`*^9}, { 3.634954904907135*^9, 3.6349549451084347`*^9}, {3.634955219605135*^9, 3.6349552640926795`*^9}, {3.634955320189888*^9, 3.634955348763522*^9}, { 3.634955386393675*^9, 3.6349555039273973`*^9}, {3.6349557669644423`*^9, 3.6349557672004557`*^9}, {3.634955894841756*^9, 3.634955902578199*^9}, { 3.6349559513739896`*^9, 3.6349560216320086`*^9}, {3.634956120144643*^9, 3.634956128996149*^9}, {3.6349561700724983`*^9, 3.6349561978900895`*^9}, { 3.6349562480719595`*^9, 3.634956254326318*^9}, {3.634956331684742*^9, 3.6349563460575643`*^9}, {3.634956379242462*^9, 3.63495642676418*^9}, 3.6349564696636343`*^9, {3.6351524116477795`*^9, 3.6351524153379908`*^9}, { 3.6352134400282927`*^9, 3.635213442148414*^9}, {3.6352134745862694`*^9, 3.635213495869487*^9}, {3.6352135383409157`*^9, 3.6352137157160616`*^9}, { 3.6352137493569856`*^9, 3.635213764522853*^9}, {3.635214215036621*^9, 3.635214227593339*^9}, {3.635214407257615*^9, 3.63521441713218*^9}, { 3.635215297101512*^9, 3.635215303964904*^9}, {3.6352154111120324`*^9, 3.635215431504199*^9}, {3.635216346055508*^9, 3.635216494371991*^9}, { 3.635216631050809*^9, 3.6352166603244834`*^9}, {3.635216763034358*^9, 3.635216764164423*^9}, {3.6352168771938877`*^9, 3.635216888828553*^9}, 3.6352169832479534`*^9, 3.635217037668066*^9, {3.6352172024924936`*^9, 3.6352172054526625`*^9}, {3.635217344025589*^9, 3.635217346898753*^9}, 3.6352173863770113`*^9, {3.635217519639633*^9, 3.6352175507014103`*^9}, 3.635217615445113*^9, {3.6352178715087595`*^9, 3.635217880460271*^9}, { 3.6352185912849283`*^9, 3.635218598444338*^9}, {3.6352186995721216`*^9, 3.635218714955002*^9}, {3.6352189761749425`*^9, 3.6352189789341*^9}, { 3.6352195060322485`*^9, 3.635219509972474*^9}, 3.6352195673477554`*^9, 3.6352195994635925`*^9, {3.6352197336482677`*^9, 3.635219737452485*^9}, { 3.6352197706093817`*^9, 3.6352197723214793`*^9}, {3.635219941784172*^9, 3.6352199485115566`*^9}, {3.6352200714185867`*^9, 3.6352200854323883`*^9}, {3.6352202085694313`*^9, 3.635220235849992*^9}, { 3.6352202816336107`*^9, 3.6352203110962954`*^9}, {3.6352204980449886`*^9, 3.6352205276526823`*^9}, {3.6352253191447396`*^9, 3.6352253299913597`*^9}, {3.6352253611111403`*^9, 3.6352253637572913`*^9}, {3.635225409322898*^9, 3.6352255965196047`*^9}, { 3.6352260914249115`*^9, 3.6352261698393965`*^9}, {3.63522638233055*^9, 3.6352264188036366`*^9}, {3.635227493469104*^9, 3.635227556935734*^9}, { 3.6352276745764627`*^9, 3.635227730116639*^9}, {3.6352287979917183`*^9, 3.6352288587651944`*^9}, {3.635228894237223*^9, 3.635228948324317*^9}, { 3.635229365252164*^9, 3.6352293902275925`*^9}, {3.63522947690555*^9, 3.6352294807837715`*^9}, {3.6352492831123204`*^9, 3.6352492983621926`*^9}, 3.6356569054520617`*^9, {3.6363778004499054`*^9, 3.636377802787039*^9}, { 3.6363778414932528`*^9, 3.6363778525308843`*^9}, {3.636384436335312*^9, 3.6363846409950175`*^9}, {3.636384971250907*^9, 3.6363849738080535`*^9}, { 3.6363850170465264`*^9, 3.636385030729309*^9}, {3.6363851286779118`*^9, 3.636385138359465*^9}, {3.6363851699712734`*^9, 3.636385223111313*^9}, { 3.656076172452749*^9, 3.656076182171566*^9}, {3.6560765578514256`*^9, 3.656076619019133*^9}, 3.6560772545486493`*^9, {3.6630719749029694`*^9, 3.6630719878027077`*^9}, {3.6630720702554235`*^9, 3.6630720807290225`*^9}, {3.6630721155740156`*^9, 3.6630721713712068`*^9}, {3.663072270834896*^9, 3.6630722882218904`*^9}, 3.6630724099968557`*^9, {3.685234767958906*^9, 3.685234768480936*^9}, { 3.685252204033695*^9, 3.6852522340537376`*^9}, {3.6852522757137957`*^9, 3.6852523115138454`*^9}, {3.68525376314359*^9, 3.6852537725041256`*^9}, { 3.6852539763277836`*^9, 3.6852539861693463`*^9}, 3.6852540682470407`*^9, 3.6852541660656357`*^9, {3.6852604801645336`*^9, 3.6852605060345697`*^9}, { 3.6852605373446136`*^9, 3.6852605977846985`*^9}, 3.685260655254779*^9, { 3.6853280002218475`*^9, 3.685328019561875*^9}, 3.685328064721938*^9, { 3.6853280953119807`*^9, 3.6853282636022167`*^9}, {3.685328356242346*^9, 3.685328598671985*^9}, {3.6853286682069626`*^9, 3.6853287982524004`*^9}, { 3.6853288753368096`*^9, 3.6853289367033195`*^9}, {3.685328968274125*^9, 3.685328978713722*^9}, {3.685329033941881*^9, 3.685329044950511*^9}, { 3.685329173522865*^9, 3.6853294420842257`*^9}, {3.6853296024223967`*^9, 3.6853296124319687`*^9}, {3.6853297221712456`*^9, 3.685329733349885*^9}, { 3.6853298076291337`*^9, 3.6853298739599276`*^9}, {3.685330038474337*^9, 3.685330051652091*^9}, {3.6853311309428225`*^9, 3.685331168378964*^9}, { 3.685340142134763*^9, 3.685340180544817*^9}, {3.6853583292043543`*^9, 3.685358334834362*^9}, {3.685358366084406*^9, 3.685358366954407*^9}, { 3.685358408404465*^9, 3.685358518294619*^9}, 3.685358620174762*^9, 3.6853586578748145`*^9, {3.6853588750151186`*^9, 3.6853588857151337`*^9}, { 3.6853589302051954`*^9, 3.685358938995208*^9}, {3.685359014715314*^9, 3.6853590296653347`*^9}, 3.685359148315501*^9, 3.6853598281764526`*^9, { 3.6853683109000263`*^9, 3.685368382250126*^9}, {3.685368420160179*^9, 3.6853684704302497`*^9}, {3.6853685194503183`*^9, 3.685368742860631*^9}, { 3.685369008901004*^9, 3.68536902061102*^9}, {3.6853690791611023`*^9, 3.685369132301176*^9}, {3.6853693219914417`*^9, 3.6853693304114532`*^9}, 3.6853696089118433`*^9, {3.6858758911429157`*^9, 3.685875951793*^9}, { 3.6859484099082212`*^9, 3.6859484970032024`*^9}, {3.686052829875022*^9, 3.686052906242383*^9}, {3.6860535326822133`*^9, 3.686053598029951*^9}, { 3.68605365168902*^9, 3.6860541446091995`*^9}, {3.6860541846064873`*^9, 3.68605440393201*^9}, {3.686054713802734*^9, 3.6860547858298535`*^9}, { 3.6860548280202665`*^9, 3.686054837219793*^9}, {3.686054874127904*^9, 3.686054892139934*^9}, {3.686055136014883*^9, 3.6860551460584574`*^9}, { 3.686055211281188*^9, 3.6860552301962633`*^9}, {3.6860553465409174`*^9, 3.6860553998749685`*^9}, {3.6860556017188663`*^9, 3.6860556050188704`*^9}, {3.6862923512707715`*^9, 3.686292363600789*^9}, { 3.686292409650853*^9, 3.6862924109708548`*^9}, {3.6862924536109147`*^9, 3.6862924596309233`*^9}, {3.686292542221039*^9, 3.6862925430110397`*^9}, { 3.686292988803664*^9, 3.686293001033681*^9}, {3.6866504529025555`*^9, 3.686650526682659*^9}, {3.686650671852862*^9, 3.6866507242929354`*^9}, { 3.6866507657529936`*^9, 3.6866507887630253`*^9}, {3.6866508208230705`*^9, 3.6866509100531955`*^9}, {3.6866509593932643`*^9, 3.686650971113281*^9}, { 3.686651007793332*^9, 3.6866511595335445`*^9}, {3.686651223513634*^9, 3.686651234033649*^9}, {3.686651304763748*^9, 3.6866513363837924`*^9}, { 3.6866514102038956`*^9, 3.686651429943923*^9}, {3.686652993837468*^9, 3.6866530046274834`*^9}, {3.686804398511652*^9, 3.6868044081516657`*^9}, { 3.6868046315619783`*^9, 3.686804631801979*^9}, {3.686804685872054*^9, 3.686804707092084*^9}, {3.6868047382021275`*^9, 3.686804767812169*^9}, { 3.686804824012248*^9, 3.6868048404922705`*^9}, {3.686804942142413*^9, 3.6868049633424425`*^9}, {3.6868050765526013`*^9, 3.686805101092636*^9}, { 3.6868051463526993`*^9, 3.6868052234228067`*^9}, {3.686805307602925*^9, 3.686805311682931*^9}, {3.68680577547358*^9, 3.686805788923599*^9}, { 3.686821702197342*^9, 3.6868217282873783`*^9}, {3.6868225192884855`*^9, 3.686822538368512*^9}, {3.6868226306886415`*^9, 3.6868226683086944`*^9}, { 3.6868227318887835`*^9, 3.6868227627088265`*^9}, {3.686822801638881*^9, 3.6868230490692277`*^9}, {3.686823122979331*^9, 3.6868231833294153`*^9}, { 3.6868232450595016`*^9, 3.6868233753996844`*^9}, {3.6868234153897405`*^9, 3.686823451379791*^9}, {3.6868236736101017`*^9, 3.6868236786601086`*^9}, { 3.6868237164601617`*^9, 3.68682375072021*^9}, {3.68682389396041*^9, 3.68682390087042*^9}, {3.686823940790476*^9, 3.6868239416904774`*^9}, { 3.6868239808805323`*^9, 3.6868239872905407`*^9}, {3.686824051540631*^9, 3.6868240519006314`*^9}, {3.686824360861064*^9, 3.6868243761510854`*^9}, { 3.6868245440213203`*^9, 3.686824577221367*^9}, {3.686824685841519*^9, 3.6868246979115357`*^9}, 3.6868248012716804`*^9, 3.6868253582724605`*^9, { 3.6868255183026843`*^9, 3.686825518932685*^9}, {3.6868264466639843`*^9, 3.6868264497139883`*^9}, {3.6868267792744493`*^9, 3.6868268152945004`*^9}, {3.686827100164899*^9, 3.6868271210549283`*^9}, 3.686827162004986*^9, {3.6868272414950967`*^9, 3.686827327475217*^9}, { 3.686827953126093*^9, 3.686827976506126*^9}, {3.686829128577739*^9, 3.686829138957753*^9}, 3.6868292410978966`*^9, {3.6868292768379464`*^9, 3.686829282727955*^9}, {3.6868293820380936`*^9, 3.686829418138144*^9}, { 3.686829846748744*^9, 3.686829848298746*^9}, {3.6868313063207874`*^9, 3.686831307180789*^9}, {3.6868331276633377`*^9, 3.68683328653356*^9}, { 3.6868394697195063`*^9, 3.6868394933895392`*^9}, 3.686839530999592*^9, { 3.686839582829664*^9, 3.68683963686974*^9}, {3.6868397551199055`*^9, 3.68683979365996*^9}, {3.6868398344600167`*^9, 3.686839866200061*^9}, { 3.687092084401948*^9, 3.687092117031994*^9}, {3.6870922598621936`*^9, 3.6870922645422*^9}, {3.6870962086478376`*^9, 3.6870962658779182`*^9}, 3.687096444838168*^9, {3.687096500978247*^9, 3.687096501638248*^9}, { 3.6870965809883595`*^9, 3.687096592708376*^9}, 3.687096837948719*^9, { 3.68709688890879*^9, 3.687096985798926*^9}, {3.6870971015990877`*^9, 3.6870972179192505`*^9}, {3.6870972618993125`*^9, 3.687097305639374*^9}, { 3.6870973356794157`*^9, 3.6870975186496716`*^9}, {3.6870975796097574`*^9, 3.6870975953197794`*^9}, {3.6870976531898603`*^9, 3.6870976848899045`*^9}, 3.6870977782500353`*^9, {3.687413757687042*^9, 3.6874137834070783`*^9}, { 3.6874140542074575`*^9, 3.687414094417514*^9}, {3.6874143478878684`*^9, 3.687414485538061*^9}, {3.6874146116082373`*^9, 3.68741464894829*^9}, { 3.6874147451084247`*^9, 3.687414766118454*^9}, 3.6874149094486547`*^9, { 3.6874150416688395`*^9, 3.6874150634888706`*^9}, {3.6874152437091227`*^9, 3.687415268869158*^9}, 3.6874153442892637`*^9, {3.687415449879411*^9, 3.687415469659439*^9}, 3.687415529739523*^9, 3.687415564789572*^9, 3.687415645529685*^9, {3.6874168016913037`*^9, 3.687416803441306*^9}, { 3.687421022677213*^9, 3.6874212686075573`*^9}, {3.68742948209425*^9, 3.6874294906842623`*^9}, {3.687844340668378*^9, 3.6878443698084188`*^9}, { 3.6886534778571014`*^9, 3.6886534911571198`*^9}, {3.688906380162199*^9, 3.6889064680223217`*^9}, {3.688906514222396*^9, 3.6889065193925257`*^9}, { 3.688908192623024*^9, 3.6889082006430354`*^9}, {3.688908261823121*^9, 3.688908271653135*^9}, {3.6889083776232834`*^9, 3.6889083922733035`*^9}, { 3.688908466073407*^9, 3.6889084993734536`*^9}, 3.688908533623502*^9, { 3.688908616683618*^9, 3.6889086271336327`*^9}, {3.6889086885637183`*^9, 3.6889087063437433`*^9}, {3.6889091647443852`*^9, 3.6889092012544365`*^9}, {3.6889093019045773`*^9, 3.6889093406746316`*^9}, 3.6889101071957045`*^9, {3.689905940063133*^9, 3.689905972983179*^9}, { 3.692530981927737*^9, 3.6925310416778207`*^9}, {3.692531099797902*^9, 3.6925311384779563`*^9}, {3.692531192258032*^9, 3.692531244668105*^9}, { 3.6925312919881716`*^9, 3.692531425418358*^9}, {3.6925315270885005`*^9, 3.692531643928664*^9}, {3.692535489534048*^9, 3.6925356485142703`*^9}, { 3.692535753564418*^9, 3.6925357992544813`*^9}, {3.6925358831745987`*^9, 3.692535899604622*^9}, {3.692536042584822*^9, 3.692536159384986*^9}, { 3.6925366121156197`*^9, 3.6925366207256317`*^9}, {3.6925367265057793`*^9, 3.69253672683578*^9}, {3.6925368590559654`*^9, 3.6925368636559715`*^9}, { 3.6925370880062857`*^9, 3.692537177856412*^9}, {3.692537322456614*^9, 3.6925373869767046`*^9}, {3.6925390913352747`*^9, 3.6925390925252767`*^9}, {3.692539644430175*^9, 3.6925396711502123`*^9}, { 3.692539727510291*^9, 3.692539730440295*^9}, {3.69253993367058*^9, 3.692539963780622*^9}, {3.6925400018406754`*^9, 3.692540003630678*^9}, { 3.6925401743409166`*^9, 3.6925401747509174`*^9}, {3.692540399111232*^9, 3.692540407981244*^9}, {3.69254047647134*^9, 3.6925404886113567`*^9}, { 3.6925406039715185`*^9, 3.69254060531152*^9}, {3.6925414948727655`*^9, 3.6925414953427663`*^9}, {3.6925415478528395`*^9, 3.692541613062931*^9}, 3.692541649332982*^9, {3.692541727633092*^9, 3.6925418840133104`*^9}, { 3.692541924473367*^9, 3.692542041693531*^9}, {3.6925421488836813`*^9, 3.6925422549438295`*^9}, {3.6925422976938896`*^9, 3.692542521444203*^9}, { 3.6925426221843443`*^9, 3.6925426357343626`*^9}, 3.692542739374508*^9, 3.692599799510878*^9, {3.692599834884901*^9, 3.6925998954663663`*^9}, { 3.692599925635092*^9, 3.6926000095928946`*^9}, {3.692600108929576*^9, 3.6926001456386757`*^9}, {3.6926001874800687`*^9, 3.692600454421337*^9}, { 3.692600503149027*^9, 3.6926006000391626`*^9}, {3.692600680251275*^9, 3.6926006814012766`*^9}, {3.6926009000215826`*^9, 3.6926009410816402`*^9}, 3.692601280532116*^9, {3.6926044914726114`*^9, 3.69260449774262*^9}, 3.6926045660127153`*^9, 3.6926046690228596`*^9, {3.69296647863291*^9, 3.6929664798829117`*^9}, {3.6929665643330297`*^9, 3.6929666141830997`*^9}, {3.6929670390036945`*^9, 3.6929670405536966`*^9}, {3.6929670861037607`*^9, 3.6929670952937737`*^9}, {3.6929671302538223`*^9, 3.6929671549438567`*^9}, {3.6929671904739065`*^9, 3.69296722137395*^9}, { 3.6929672596240034`*^9, 3.6929673352541094`*^9}, 3.6929678909232683`*^9, { 3.6930146982034283`*^9, 3.693014722713463*^9}, {3.6930148540136466`*^9, 3.693014857023651*^9}, {3.6930148913836985`*^9, 3.693014894823704*^9}, { 3.693014930903754*^9, 3.6930151942541227`*^9}, {3.693015247824198*^9, 3.693015430554454*^9}, {3.693015673794794*^9, 3.69301579223496*^9}, { 3.6930163123576884`*^9, 3.693016326897709*^9}, {3.6930164225678425`*^9, 3.693016429727853*^9}, {3.693016686718212*^9, 3.693016698128228*^9}, { 3.693016737038283*^9, 3.693016755068308*^9}, {3.6930168429225607`*^9, 3.6930168719926014`*^9}, {3.6930172049430676`*^9, 3.693017284063178*^9}, { 3.693017336433252*^9, 3.6930173662532935`*^9}, {3.6930180949163136`*^9, 3.6930180975563173`*^9}, {3.6930181870764427`*^9, 3.693018199956461*^9}, { 3.6930182954065943`*^9, 3.693018305996609*^9}, {3.693139886141657*^9, 3.6931399045016823`*^9}, {3.6931402916003532`*^9, 3.693140295770359*^9}, { 3.693140426020541*^9, 3.693140426530542*^9}, {3.6931410492237864`*^9, 3.6931410888738413`*^9}, {3.6931411194438844`*^9, 3.693141126553894*^9}, { 3.693141412004294*^9, 3.693141454164353*^9}, {3.6931415979955544`*^9, 3.6931417931758275`*^9}, {3.6932199559445915`*^9, 3.6932199772046213`*^9}, {3.6932201435748544`*^9, 3.693220170284892*^9}, { 3.693220713855653*^9, 3.693220721825664*^9}, {3.693625124589745*^9, 3.693625153729786*^9}, {3.6940907995669713`*^9, 3.6940909688872085`*^9}, { 3.6940913675677667`*^9, 3.6940914223978434`*^9}, {3.694091508037963*^9, 3.694091572118053*^9}, 3.694092009628666*^9, {3.6940920553287296`*^9, 3.694092229168973*^9}, {3.6940923053990793`*^9, 3.694092374419176*^9}, { 3.6940924537392874`*^9, 3.694092457789293*^9}, 3.694092642849552*^9, { 3.6940928573598523`*^9, 3.694092862379859*^9}, {3.6940945886222763`*^9, 3.694094601932295*^9}, 3.694094849542641*^9, {3.694095764293922*^9, 3.6940957644739223`*^9}, {3.6940960602743363`*^9, 3.6940960732243547`*^9}, {3.6940961211044216`*^9, 3.694096124194426*^9}, { 3.694665030960044*^9, 3.6946650634500895`*^9}, {3.6946652071402903`*^9, 3.6946653490404887`*^9}, {3.6946658702212186`*^9, 3.6946658881212435`*^9}, {3.694665923041292*^9, 3.694665953561335*^9}, { 3.694665995981395*^9, 3.6946660149414215`*^9}, {3.694666050571471*^9, 3.6946660547214766`*^9}, {3.694666169991638*^9, 3.694666292151809*^9}, { 3.6946663456618843`*^9, 3.6946663943919525`*^9}, 3.6946667526224537`*^9, 3.69466680700253*^9, 3.694687076625702*^9, {3.6946874316161985`*^9, 3.6946874621962414`*^9}, 3.694687499496294*^9, {3.694687567516389*^9, 3.694687642816495*^9}, {3.694687679006545*^9, 3.6946877198966026`*^9}, { 3.6946877714966745`*^9, 3.694687931746899*^9}, {3.723798739728607*^9, 3.723798744014243*^9}, {3.7237990126446104`*^9, 3.723799023974499*^9}, { 3.7244116671877546`*^9, 3.7244116733393917`*^9}, {3.724411761793063*^9, 3.7244117718753977`*^9}, {3.724411928386671*^9, 3.7244119682966137`*^9}, { 3.724412131847311*^9, 3.724412188341254*^9}, {3.729414981357122*^9, 3.7294149861075096`*^9}, {3.749817651293678*^9, 3.749817653108206*^9}, { 3.7498176831919456`*^9, 3.7498176846222315`*^9}, 3.7498177601545563`*^9, { 3.749817859674735*^9, 3.749817861044999*^9}, {3.7498179561547127`*^9, 3.749817964489929*^9}, {3.749818149334386*^9, 3.749818237397959*^9}, 3.749818617867873*^9, {3.7505621848002787`*^9, 3.7505622174085107`*^9}, { 3.75056238761455*^9, 3.750562431347901*^9}, {3.7505626332829456`*^9, 3.7505627331565337`*^9}, {3.7505627632642183`*^9, 3.7505627635859113`*^9}, {3.7515359581577415`*^9, 3.7515359614850826`*^9}, {3.751536071974715*^9, 3.7515360961721487`*^9}, 3.7515362040373974`*^9, {3.751536256080162*^9, 3.7515365099108534`*^9}, { 3.751549231137398*^9, 3.7515493334258356`*^9}, {3.7515496891619573`*^9, 3.751549689458767*^9}, 3.753020403650548*^9, {3.7530205114189386`*^9, 3.753020525224822*^9}, {3.753021995594639*^9, 3.753022011512741*^9}, { 3.760634689749445*^9, 3.7606348247488756`*^9}, {3.7606349119783344`*^9, 3.7606349350197754`*^9}, {3.76063496856853*^9, 3.7606349922504683`*^9}, { 3.760667269592998*^9, 3.760667271545692*^9}, 3.7606679283912125`*^9, 3.760668039709257*^9, {3.763302716900259*^9, 3.763302749083943*^9}, { 3.763304867499642*^9, 3.7633048681948185`*^9}, {3.763337978730939*^9, 3.763338014197137*^9}, {3.763338054806819*^9, 3.7633381289118147`*^9}, { 3.763338224472745*^9, 3.7633382447254143`*^9}, 3.763338501519575*^9, { 3.7633387342733064`*^9, 3.763338775483101*^9}, {3.7633388525735607`*^9, 3.7633390131554184`*^9}, {3.763360596353942*^9, 3.7633606328922167`*^9}, { 3.7633606638773637`*^9, 3.763360724941125*^9}, {3.763360812068123*^9, 3.763360863571327*^9}, {3.763361217769263*^9, 3.763361243271195*^9}, { 3.763361578316657*^9, 3.7633615820345063`*^9}, {3.763362291476118*^9, 3.763362301380039*^9}, {3.763362505004878*^9, 3.763362606421646*^9}, { 3.763362742167684*^9, 3.7633627524126663`*^9}, {3.7633628090243473`*^9, 3.763362931819517*^9}, 3.7633630680313087`*^9, {3.76336360941794*^9, 3.7633636782369685`*^9}, {3.763363813698273*^9, 3.763363822992702*^9}, { 3.7633837714269123`*^9, 3.763383775708086*^9}, {3.7633839861442327`*^9, 3.7633839966350546`*^9}, {3.7633846907375526`*^9, 3.76338471098131*^9}, 3.763426089635152*^9, {3.7634262143520336`*^9, 3.7634262475470448`*^9}, { 3.7634276458524485`*^9, 3.7634276705117846`*^9}, {3.7634292721860075`*^9, 3.7634292840439587`*^9}, {3.76352820463631*^9, 3.7635282147939873`*^9}, { 3.763528430960533*^9, 3.7635284413250494`*^9}, {3.7635285114344244`*^9, 3.763528537124817*^9}, {3.763528653934307*^9, 3.7635286747218256`*^9}, { 3.7635486952594075`*^9, 3.763548696007099*^9}, {3.7639579130072594`*^9, 3.7639579464687676`*^9}, {3.763957980699315*^9, 3.7639580928074217`*^9}, { 3.763959813173403*^9, 3.7639598134702053`*^9}, {3.7639608015345135`*^9, 3.7639608287155933`*^9}, {3.7645603385872726`*^9, 3.764560365934222*^9}, { 3.76456061596602*^9, 3.76456062636983*^9}, {3.7647257988231063`*^9, 3.7647258025896564`*^9}, {3.765077713031946*^9, 3.7650777913378534`*^9}, { 3.7740698865922914`*^9, 3.774069989744633*^9}, {3.7740700982535834`*^9, 3.774070098487667*^9}, {3.7740701415628414`*^9, 3.7740702370647106`*^9}, { 3.77407029325229*^9, 3.7740703348543596`*^9}, {3.774070397587008*^9, 3.774070454974152*^9}, {3.7740709929610343`*^9, 3.7740710067172923`*^9}, { 3.775190474681038*^9, 3.7751904884151363`*^9}, {3.7751905901325903`*^9, 3.775190642609686*^9}, 3.775190717712206*^9, {3.7751956728394384`*^9, 3.7751957010601625`*^9}, 3.7751957418100777`*^9, {3.7751958741450567`*^9, 3.775195882844048*^9}, {3.7751959530858574`*^9, 3.775196055684782*^9}, { 3.7836566506037264`*^9, 3.783656699859296*^9}, {3.783834162184903*^9, 3.7838342075157394`*^9}, {3.7838342453955064`*^9, 3.7838342564437876`*^9}, {3.783834288539219*^9, 3.783834289188504*^9}, { 3.783834319888338*^9, 3.783834404011998*^9}, {3.783835274452033*^9, 3.783835643262226*^9}, 3.783835673435833*^9, {3.783837186915415*^9, 3.783837252940491*^9}, 3.783838076793089*^9, {3.7838387026691084`*^9, 3.7838387106794033`*^9}, {3.7838387751330376`*^9, 3.78383877586726*^9}, 3.7885184612710266`*^9, {3.7885197610115976`*^9, 3.788519761667694*^9}, { 3.788519815581788*^9, 3.788519877459923*^9}, {3.788519910619506*^9, 3.7885199214314795`*^9}, {3.78852990807364*^9, 3.78852991935472*^9}, { 3.788529949778452*^9, 3.7885299511123505`*^9}, 3.7885729856546545`*^9, { 3.795769635061987*^9, 3.7957696738473544`*^9}, {3.7957698528454103`*^9, 3.795769867081932*^9}, {3.7963499268904905`*^9, 3.796349974573367*^9}, { 3.8116565658363085`*^9, 3.811656579625844*^9}, {3.8116566792733173`*^9, 3.811656696847624*^9}, {3.819778974172573*^9, 3.819778996370713*^9}, { 3.819779237456471*^9, 3.819779375493654*^9}, {3.819779556474127*^9, 3.8197797185600586`*^9}, 3.8200272939729*^9, 3.8200273875005593`*^9, 3.820027421880412*^9, {3.8200275035350485`*^9, 3.8200275049354267`*^9}, { 3.8216146854806337`*^9, 3.8216146951363287`*^9}, {3.8216147521969256`*^9, 3.8216148295973682`*^9}, {3.852428110418418*^9, 3.8524282580965376`*^9}, { 3.8524282926566954`*^9, 3.8524283525785737`*^9}, {3.8524418028142138`*^9, 3.852441835111664*^9}, {3.8526155162841244`*^9, 3.852615518838768*^9}, { 3.852618384835059*^9, 3.8526183854788876`*^9}, {3.8526185653384037`*^9, 3.8526185655779724`*^9}, {3.852952260237672*^9, 3.8529522878415303`*^9}, { 3.8529525793242254`*^9, 3.8529525856490264`*^9}, {3.852959535316224*^9, 3.8529595898176904`*^9}, {3.8529665599131017`*^9, 3.852966564916722*^9}, { 3.852966693544965*^9, 3.852966727285118*^9}, {3.8529678456095867`*^9, 3.8529678780810432`*^9}}, CellLabel-> "In[173]:=",ExpressionUUID->"d9156204-3b55-401d-92de-546075f23b33"] }, Open ]], Cell[CellGroupData[{ Cell["BEAM ELEMENT (disp ++) defs ", "Subsection", CellChangeTimes->{{3.5579867801590133`*^9, 3.557986782249417*^9}, { 3.7530188279461737`*^9, 3.75301883733206*^9}, {3.7878948627741256`*^9, 3.787894875357033*^9}, {3.8216145697031803`*^9, 3.821614594102014*^9}},ExpressionUUID->"22fd3af4-820c-4389-83ac-\ d39e8e057331"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"CURVEDBEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "II_"}], "}"}], ",", RowBox[{"{", RowBox[{"fs_", ",", "fn_", ",", "fb_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"I1_", ",", "I2_", ",", "I3_"}], "}"}]}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r", ",", "dr", ",", "h", ",", "es", ",", "en", ",", "eb", ",", "\[Delta]W", ",", "rule", ",", "KK", ",", "FF", ",", "R"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "needs", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Zeta]"}], ")"}], "*", RowBox[{"(", RowBox[{"1", "-", RowBox[{"2", "\[Zeta]"}]}], ")"}]}], ",", RowBox[{"4", RowBox[{"(", RowBox[{"1", "-", "\[Zeta]"}], ")"}], "*", "\[Zeta]"}], ",", RowBox[{"\[Zeta]", "*", RowBox[{"(", RowBox[{ RowBox[{"2", "\[Zeta]"}], "-", "1"}], ")"}]}]}], "}"}], ".", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "1"}], "]"}], "]"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I2", ",", "1"}], "]"}], "]"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I3", ",", "1"}], "]"}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dr", "=", RowBox[{"D", "[", RowBox[{"r", ",", "\[Zeta]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"hh", "=", RowBox[{"Sqrt", "[", RowBox[{"dr", ".", "dr"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"h", "=", RowBox[{"Abs", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"hh", " ", "/.", RowBox[{"\[Zeta]", "\[Rule]", "0"}]}], ")"}], "+", RowBox[{"4", RowBox[{"(", RowBox[{"hh", " ", "/.", RowBox[{"\[Zeta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], ")"}]}], "+", RowBox[{"(", RowBox[{"hh", " ", "/.", RowBox[{"\[Zeta]", "\[Rule]", "1."}]}], ")"}]}], ")"}], "/", "6"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"es", " ", "=", RowBox[{"dr", "/", "hh"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", " ", "=", RowBox[{ RowBox[{"D", "[", RowBox[{"es", ",", "\[Zeta]"}], "]"}], "/", "hh"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]b", "=", RowBox[{"Sqrt", "[", RowBox[{"en", ".", "en"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{"en", "/", "\[Kappa]b"}]}], ";", "\[IndentingNewLine]", RowBox[{"eb", " ", "=", " ", RowBox[{"es", "\[Cross]", "en"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"basis", "=", RowBox[{ RowBox[{"{", RowBox[{"es", ",", "en", ",", "eb"}], "}"}], " ", "/.", RowBox[{"\[Zeta]", "\[Rule]", RowBox[{"1", "/", "2."}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"basis1", "=", RowBox[{ RowBox[{"{", RowBox[{"es", ",", "en", ",", "eb"}], "}"}], " ", "/.", RowBox[{"\[Zeta]", "\[Rule]", "0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"basis2", "=", RowBox[{ RowBox[{"{", RowBox[{"es", ",", "en", ",", "eb"}], "}"}], " ", "/.", RowBox[{"\[Zeta]", "\[Rule]", "1"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"R", "=", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"1", "/", "\[Kappa]b"}], ")"}], "/.", " ", RowBox[{"\[Zeta]", "\[Rule]", RowBox[{"1", "/", "2."}]}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "needs", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]rule", " ", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"a", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]a", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"b", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]b", "[", "any", "]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"us", "[", "1", "]"}], ",", RowBox[{"un", "[", "1", "]"}], ",", RowBox[{"ub", "[", "1", "]"}]}], "}"}], "=", RowBox[{"basis1", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"us", "[", "2", "]"}], ",", RowBox[{"un", "[", "2", "]"}], ",", RowBox[{"ub", "[", "2", "]"}]}], "}"}], "=", RowBox[{"basis2", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I3", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[CapitalTheta]s", "[", "1", "]"}], ",", RowBox[{"\[CapitalTheta]n", "[", "1", "]"}], ",", RowBox[{"\[CapitalTheta]b", "[", "1", "]"}]}], "}"}], "=", RowBox[{"basis1", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[CapitalTheta]s", "[", "2", "]"}], ",", RowBox[{"\[CapitalTheta]n", "[", "2", "]"}], ",", RowBox[{"\[CapitalTheta]b", "[", "2", "]"}]}], "}"}], "=", RowBox[{"basis2", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I3", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"aa", "=", RowBox[{"{", RowBox[{ RowBox[{"us", "[", "1", "]"}], ",", RowBox[{"un", "[", "1", "]"}], ",", RowBox[{"ub", "[", "1", "]"}], ",", RowBox[{"\[CapitalTheta]s", "[", "1", "]"}], ",", RowBox[{"\[CapitalTheta]n", "[", "1", "]"}], ",", RowBox[{"\[CapitalTheta]b", "[", "1", "]"}], ",", RowBox[{"us", "[", "2", "]"}], ",", RowBox[{"un", "[", "2", "]"}], ",", RowBox[{"ub", "[", "2", "]"}], ",", RowBox[{"\[CapitalTheta]s", "[", "2", "]"}], ",", RowBox[{"\[CapitalTheta]n", "[", "2", "]"}], ",", RowBox[{"\[CapitalTheta]b", "[", "2", "]"}]}], "}"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]aa", "=", RowBox[{"aa", " ", "/.", "\[Delta]rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"ELEMENT", " ", "CONTRIBUTION"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], " ", "\[IndentingNewLine]", RowBox[{"KK", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"2", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"6", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"EE", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"GG", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{ "16", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", RowBox[{"Cos", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{ "2", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "-", RowBox[{"2", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "-", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"EE", " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"GG", " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"5", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"8", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"3", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"2", " ", "EE", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"2", " ", "GG", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"EE", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"GG", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", "AA", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "3"]}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"2", " ", "AA", " ", SuperscriptBox["R", "4"]}]}], ")"}]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"AA", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", "AA", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II", " ", "R"}], "+", RowBox[{"GG", " ", "II", " ", "R"}], "+", RowBox[{"7", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "3"]}], "+", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "GG", " ", "h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ "32", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", RowBox[{"Cos", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "h", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", "\[ImaginaryI]", " ", "AA", " ", SuperscriptBox["R", "3"]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{"h", "-", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}]}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"h", "+", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"]}], "-", SuperscriptBox["R", "2"]}], ")"}]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{"II", "-", RowBox[{"3", " ", "AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["GG", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "-", RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"9", " ", "AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{"h", "+", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}]}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"h", "-", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"3", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"3", " ", "h"}], "R"], "]"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "h", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", "\[ImaginaryI]", " ", "AA", " ", SuperscriptBox["R", "3"]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"4", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"4", " ", "h"}], "R"], "]"}]}]}], ")"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "AA"}], " ", SuperscriptBox["R", "4"]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "h", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", "\[ImaginaryI]", " ", "AA", " ", SuperscriptBox["R", "3"]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{"h", "-", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}]}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"h", "+", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"]}], "-", SuperscriptBox["R", "2"]}], ")"}]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{"II", "-", RowBox[{"3", " ", "AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["GG", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "-", RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"9", " ", "AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{"h", "+", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}]}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"h", "-", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"3", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"3", " ", "h"}], "R"], "]"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "h", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", "\[ImaginaryI]", " ", "AA", " ", SuperscriptBox["R", "3"]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"4", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"4", " ", "h"}], "R"], "]"}]}]}], ")"}]}]}], ")"}]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "GG", " ", "h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II", " ", "R"}], "+", RowBox[{"GG", " ", "II", " ", "R"}], "+", RowBox[{"3", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "3"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"2", " ", "AA", " ", SuperscriptBox["R", "4"]}]}], ")"}]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "-", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{ "2", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"]}], "-", SuperscriptBox["R", "2"]}], ")"}]}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{"II", "-", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}], "+", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"3", " ", "h"}], RowBox[{"2", " ", "R"}]], "]"}]}], "-", RowBox[{"2", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", " ", "AA", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"2", " ", "AA", " ", "GG", " ", RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "II", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "h"}], "+", RowBox[{"R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"2", " ", "AA", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"2", " ", "AA", " ", "GG", " ", RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "II", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "h"}], "+", RowBox[{"R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"2", " ", "AA", " ", "GG", " ", RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "II", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "h"}], "+", RowBox[{"R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"8", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"16", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"6", " ", "AA", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"16", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"9", " ", "AA", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"16", " ", "AA", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"AA", " ", RowBox[{"(", RowBox[{ RowBox[{"7", " ", SuperscriptBox["EE", "2"]}], "-", RowBox[{"4", " ", "EE", " ", "GG"}], "-", RowBox[{"4", " ", SuperscriptBox["GG", "2"]}]}], ")"}], " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{ "16", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["EE", "2"], " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{ "8", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"2", " ", "AA", " ", SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "-", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"8", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"2", " ", "GG", " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"AA", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", "EE"}], "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "-", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", " ", "AA", " ", "GG", " ", RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "II", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "h"}], "+", RowBox[{"R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "GG", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{"EE", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", "AA", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{"AA", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "GG", " ", RowBox[{"(", RowBox[{ RowBox[{"8", " ", SuperscriptBox["h", "2"]}], "-", RowBox[{"4", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{"4", " ", SuperscriptBox["GG", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"]}], "-", SuperscriptBox["R", "2"]}], ")"}]}], "+", RowBox[{ SuperscriptBox["EE", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"]}], "+", RowBox[{"15", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"AA", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], "2"], " ", SuperscriptBox["R", "3"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "EE", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", "II"}], "-", RowBox[{"4", " ", "GG", " ", "II"}], "+", RowBox[{"3", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "-", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"4", " ", "EE", " ", "GG", " ", RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "II", " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "AA"}], " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"R", " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"3", " ", "h"}], RowBox[{"2", " ", "R"}]], "]"}]}], "-", RowBox[{"2", " ", "h", " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "-", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"8", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"2", " ", "GG", " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"AA", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", "EE"}], "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "-", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"2", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"8", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"2", " ", "AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"2", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"2", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "-", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"4", " ", "EE", " ", "GG", " ", RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "II", " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "AA"}], " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"R", " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"3", " ", "h"}], RowBox[{"2", " ", "R"}]], "]"}]}], "-", RowBox[{"2", " ", "h", " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "-", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"4", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "-", RowBox[{"2", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "-", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ "2", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "-", RowBox[{"2", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "-", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"EE", " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"GG", " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"5", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"8", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"3", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"2", " ", "EE", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"2", " ", "GG", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"EE", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"GG", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "GG", " ", "h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II", " ", "R"}], "+", RowBox[{"GG", " ", "II", " ", "R"}], "+", RowBox[{"3", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "3"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "2"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"6", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "2", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"2", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"16", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "6"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"]}], "-", RowBox[{"2", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{"II", "-", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["GG", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["II", "2"], "-", RowBox[{"2", " ", "AA", " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"7", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["R", "4"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{ "8", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ "2", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"2", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{ "2", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", "AA", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II", " ", "R"}], "+", RowBox[{"GG", " ", "II", " ", "R"}], "+", RowBox[{"7", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "3"]}], "+", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "GG", " ", "h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ "8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"]}], "-", SuperscriptBox["R", "2"]}], ")"}]}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{"II", "-", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}], "+", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"3", " ", "h"}], RowBox[{"2", " ", "R"}]], "]"}]}], "-", RowBox[{"2", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "h", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", "\[ImaginaryI]", " ", "AA", " ", SuperscriptBox["R", "3"]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{"h", "-", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}]}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"h", "+", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"]}], "-", SuperscriptBox["R", "2"]}], ")"}]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{"II", "-", RowBox[{"3", " ", "AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["GG", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "-", RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"9", " ", "AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{"h", "+", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}]}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"h", "-", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"3", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"3", " ", "h"}], "R"], "]"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "h", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", "\[ImaginaryI]", " ", "AA", " ", SuperscriptBox["R", "3"]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"4", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"4", " ", "h"}], "R"], "]"}]}]}], ")"}]}]}], ")"}]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "2"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "2", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"2", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"15", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"4", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", "AA", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{ "4", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"12", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"12", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", "AA", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "3"]}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"2", " ", "AA", " ", SuperscriptBox["R", "4"]}]}], ")"}]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{ "2", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", "AA", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II", " ", "R"}], "+", RowBox[{"GG", " ", "II", " ", "R"}], "+", RowBox[{"7", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "3"]}], "+", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "GG", " ", "h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"2", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"2", " ", "\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"2", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"6", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"EE", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"GG", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "h", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", "\[ImaginaryI]", " ", "AA", " ", SuperscriptBox["R", "3"]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{"h", "-", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}]}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"h", "+", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"]}], "-", SuperscriptBox["R", "2"]}], ")"}]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{"II", "-", RowBox[{"3", " ", "AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["GG", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "-", RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"9", " ", "AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{"h", "+", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}]}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"h", "-", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"3", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"3", " ", "h"}], "R"], "]"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "h", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", "\[ImaginaryI]", " ", "AA", " ", SuperscriptBox["R", "3"]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"4", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"4", " ", "h"}], "R"], "]"}]}]}], ")"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ "16", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", RowBox[{"Cos", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"AA", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "-", RowBox[{"2", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "-", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"EE", " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"GG", " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"5", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"8", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"3", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"2", " ", "EE", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"2", " ", "GG", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"EE", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"GG", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"2", " ", "AA", " ", SuperscriptBox["R", "4"]}]}], ")"}]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "-", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{ "4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", SuperscriptBox["h", "2"]}], "+", SuperscriptBox["R", "2"]}], ")"}]}], "-", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{"II", "-", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}], "+", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "R"}], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"3", " ", "h"}], RowBox[{"2", " ", "R"}]], "]"}]}], "+", RowBox[{"2", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ "32", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", RowBox[{"Cos", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "h", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", "\[ImaginaryI]", " ", "AA", " ", SuperscriptBox["R", "3"]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{"h", "-", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}]}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"h", "+", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"]}], "-", SuperscriptBox["R", "2"]}], ")"}]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{"II", "-", RowBox[{"3", " ", "AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["GG", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "-", RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"9", " ", "AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{"h", "+", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}]}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"h", "-", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"3", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"3", " ", "h"}], "R"], "]"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "h", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", "\[ImaginaryI]", " ", "AA", " ", SuperscriptBox["R", "3"]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"4", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"4", " ", "h"}], "R"], "]"}]}]}], ")"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "AA"}], " ", SuperscriptBox["R", "4"]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "h", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", "\[ImaginaryI]", " ", "AA", " ", SuperscriptBox["R", "3"]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{"h", "-", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}]}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"h", "+", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"]}], "-", SuperscriptBox["R", "2"]}], ")"}]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{"II", "-", RowBox[{"3", " ", "AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["GG", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "-", RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"9", " ", "AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{"h", "+", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}]}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"h", "-", RowBox[{"\[ImaginaryI]", " ", "R"}]}], ")"}], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"3", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"3", " ", "h"}], "R"], "]"}]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "h", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", "\[ImaginaryI]", " ", "AA", " ", SuperscriptBox["R", "3"]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"4", " ", "h"}], "R"], "]"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"4", " ", "h"}], "R"], "]"}]}]}], ")"}]}]}], ")"}]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "GG", " ", "h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II", " ", "R"}], "+", RowBox[{"GG", " ", "II", " ", "R"}], "+", RowBox[{"3", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "3"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"2", " ", "AA", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"2", " ", "AA", " ", "GG", " ", RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "II", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "h"}], "+", RowBox[{"R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", " ", "AA", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"2", " ", "AA", " ", "GG", " ", RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "II", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "h"}], "+", RowBox[{"R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", " ", "AA", " ", "GG", " ", RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "II", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "h"}], "+", RowBox[{"R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "GG", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{"EE", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", "AA", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{"AA", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "GG", " ", RowBox[{"(", RowBox[{ RowBox[{"8", " ", SuperscriptBox["h", "2"]}], "-", RowBox[{"4", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{"4", " ", SuperscriptBox["GG", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"]}], "-", SuperscriptBox["R", "2"]}], ")"}]}], "+", RowBox[{ SuperscriptBox["EE", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"]}], "+", RowBox[{"15", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"AA", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], "2"], " ", SuperscriptBox["R", "3"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "EE", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", "II"}], "-", RowBox[{"4", " ", "GG", " ", "II"}], "+", RowBox[{"3", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "-", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"4", " ", "EE", " ", "GG", " ", RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "II", " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "AA"}], " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"R", " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"3", " ", "h"}], RowBox[{"2", " ", "R"}]], "]"}]}], "-", RowBox[{"2", " ", "h", " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "-", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", " ", "AA", " ", "GG", " ", RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "II", " ", "R", " ", RowBox[{"(", RowBox[{"h", "-", RowBox[{"R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"8", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"16", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"6", " ", "AA", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"16", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"9", " ", "AA", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"16", " ", "AA", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"AA", " ", RowBox[{"(", RowBox[{ RowBox[{"7", " ", SuperscriptBox["EE", "2"]}], "-", RowBox[{"4", " ", "EE", " ", "GG"}], "-", RowBox[{"4", " ", SuperscriptBox["GG", "2"]}]}], ")"}], " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{ "16", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["EE", "2"], " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{ "8", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"2", " ", "AA", " ", SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "-", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"8", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"2", " ", "GG", " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"AA", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", "EE"}], "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "-", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"4", " ", "EE", " ", "GG", " ", RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "II", " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "AA"}], " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"R", " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"3", " ", "h"}], RowBox[{"2", " ", "R"}]], "]"}]}], "-", RowBox[{"2", " ", "h", " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "-", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"4", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "-", RowBox[{"2", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "-", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"8", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"2", " ", "GG", " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"AA", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", "EE"}], "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "-", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"2", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"8", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"2", " ", "AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"2", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"2", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"EE", "+", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h"}], "-", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"4", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "EE", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EE", "-", RowBox[{"2", " ", "GG"}]}], ")"}], " ", "h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "II"}], "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ "2", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", "AA", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II", " ", "R"}], "+", RowBox[{"GG", " ", "II", " ", "R"}], "+", RowBox[{"7", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "3"]}], "+", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "GG", " ", "h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{ "4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["h", "2"]}], "-", SuperscriptBox["R", "2"]}], ")"}]}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{"II", "-", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}], "+", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"3", " ", "h"}], RowBox[{"2", " ", "R"}]], "]"}]}], "-", RowBox[{"2", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}]}]}], ")"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "2"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "2", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"2", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"15", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"4", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", "AA", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{ "4", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"12", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"12", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{ "2", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "-", RowBox[{"2", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "-", RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"EE", " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"GG", " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"5", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"8", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"3", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"2", " ", "EE", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"2", " ", "GG", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"EE", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"GG", " ", "h", " ", "II", " ", "R", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "+", RowBox[{"AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"Sin", "[", FractionBox["h", RowBox[{"2", " ", "R"}]], "]"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "GG", " ", "h", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "-", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II", " ", "R"}], "+", RowBox[{"GG", " ", "II", " ", "R"}], "+", RowBox[{"3", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "3"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "3"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"10", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"8", " ", "AA", " ", "GG", " ", "h", " ", SuperscriptBox["R", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", SuperscriptBox["R", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], "2"], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"4", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"4", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "7"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"EE", " ", "II", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"4", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["II", "2"]}], "+", RowBox[{"8", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II", " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "2"], " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"2", " ", "EE", " ", "GG", " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{ SuperscriptBox["GG", "2"], " ", SuperscriptBox["II", "2"], " ", SuperscriptBox["R", "2"]}], "+", RowBox[{"6", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "4"]}], "-", RowBox[{ "2", " ", "AA", " ", "EE", " ", "GG", " ", "II", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"2", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "II", " ", SuperscriptBox["R", "4"]}], "-", RowBox[{"9", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "6"]}], "+", RowBox[{"16", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["R", "6"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ SuperscriptBox["R", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"]}], "-", RowBox[{"2", " ", "EE", " ", "GG", " ", "II", " ", RowBox[{"(", RowBox[{"II", "-", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["GG", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["II", "2"], "-", RowBox[{"2", " ", "AA", " ", "II", " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"7", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["R", "4"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{ "8", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"8", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "-", RowBox[{"8", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{ "2", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"2", " ", "AA", " ", SuperscriptBox["GG", "2"], " ", "h", " ", "II", " ", SuperscriptBox["R", "3"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}], "-", RowBox[{"2", " ", SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", "h", " ", SuperscriptBox["R", "5"], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "h"}], "R"], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", SuperscriptBox["R", "2"]}], "-", RowBox[{"4", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"]}], "+", RowBox[{"4", " ", "AA", " ", "GG", " ", SuperscriptBox["R", "4"], " ", RowBox[{"Cos", "[", FractionBox["h", "R"], "]"}]}], "+", RowBox[{"h", " ", "R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", "II"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["R", "2"]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"EE", " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"R", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "EE"}], " ", "II"}], "+", RowBox[{"GG", " ", RowBox[{"(", RowBox[{"II", "+", RowBox[{"AA", " ", SuperscriptBox["R", "2"]}]}], ")"}]}]}], ")"}], " ", RowBox[{"Sin", "[", FractionBox["h", "R"], "]"}]}]}], ")"}]}], ")"}]}]}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{ RowBox[{ FractionBox[ RowBox[{"fs", " ", "h"}], "2"], "-", FractionBox[ RowBox[{"fn", " ", RowBox[{"(", RowBox[{"EE", "+", "GG"}], ")"}], " ", SuperscriptBox["h", "2"]}], RowBox[{"12", " ", "GG", " ", "R"}]]}], ",", RowBox[{ FractionBox[ RowBox[{"fn", " ", "h"}], "2"], "+", FractionBox[ RowBox[{"fs", " ", RowBox[{"(", RowBox[{"EE", "+", "GG"}], ")"}], " ", SuperscriptBox["h", "2"]}], RowBox[{"12", " ", "EE", " ", "R"}]]}], ",", FractionBox[ RowBox[{"fb", " ", "h"}], "2"], ",", "0", ",", RowBox[{"-", FractionBox[ RowBox[{"fb", " ", SuperscriptBox["h", "2"]}], "12"]}], ",", FractionBox[ RowBox[{"fn", " ", SuperscriptBox["h", "2"]}], "12"], ",", RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"fs", " ", "h"}], "2"]}], "-", FractionBox[ RowBox[{"fn", " ", RowBox[{"(", RowBox[{"EE", "+", "GG"}], ")"}], " ", SuperscriptBox["h", "2"]}], RowBox[{"12", " ", "GG", " ", "R"}]]}], ",", RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"fn", " ", "h"}], "2"]}], "+", FractionBox[ RowBox[{"fs", " ", RowBox[{"(", RowBox[{"EE", "+", "GG"}], ")"}], " ", SuperscriptBox["h", "2"]}], RowBox[{"12", " ", "EE", " ", "R"}]]}], ",", RowBox[{"-", FractionBox[ RowBox[{"fb", " ", "h"}], "2"]}], ",", "0", ",", RowBox[{"-", FractionBox[ RowBox[{"fb", " ", SuperscriptBox["h", "2"]}], "12"]}], ",", FractionBox[ RowBox[{"fn", " ", SuperscriptBox["h", "2"]}], "12"]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"-", RowBox[{"\[Delta]aa", ".", RowBox[{"(", RowBox[{ RowBox[{"KK", ".", "aa"}], "-", "FF"}], ")"}]}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"CURVEDBEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "II_", ",", "iy_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"I1_", ",", "I2_"}], "}"}]}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"h", ",", "\[Delta]W", ",", "rule", ",", "KK", ",", "FF"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "needs", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]rule", " ", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"a", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]a", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"b", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]b", "[", "any", "]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rule", " ", "=", RowBox[{"RULE", "[", RowBox[{ RowBox[{"{", "iy", "}"}], ",", RowBox[{"{", RowBox[{"I1", ",", "I2"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"h", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"x", "[", "2", "]"}], "-", RowBox[{"x", "[", "1", "]"}]}], ")"}], " ", "/.", " ", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"aa", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", "1", "]"}], ",", RowBox[{"uy", "[", "1", "]"}], ",", RowBox[{"uz", "[", "1", "]"}], ",", RowBox[{"\[CapitalTheta]x", "[", "1", "]"}], ",", RowBox[{"\[CapitalTheta]y", "[", "1", "]"}], ",", RowBox[{"\[CapitalTheta]z", "[", "1", "]"}], ",", RowBox[{"ux", "[", "2", "]"}], ",", RowBox[{"uy", "[", "2", "]"}], ",", RowBox[{"uz", "[", "2", "]"}], ",", RowBox[{"\[CapitalTheta]x", "[", "2", "]"}], ",", RowBox[{"\[CapitalTheta]y", "[", "2", "]"}], ",", RowBox[{"\[CapitalTheta]z", "[", "2", "]"}]}], "}"}], " ", "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]aa", "=", RowBox[{"aa", " ", "/.", "\[Delta]rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"ELEMENT", " ", "CONTRIBUTION"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], " ", "\[IndentingNewLine]", RowBox[{"KK", "=", RowBox[{"-", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"AA", " ", "EE"}], "h"]}], ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", RowBox[{"-", FractionBox[ RowBox[{"AA", " ", "EE"}], "h"]}], ",", "0", ",", "0", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", FractionBox[ RowBox[{"24", " ", "AA", " ", "EE", " ", "GG", " ", "II"}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]]}], ",", "0", ",", "0", ",", "0", ",", RowBox[{"-", FractionBox[ RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II"}], RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}]]}], ",", "0", ",", RowBox[{"-", FractionBox[ RowBox[{"24", " ", "AA", " ", "EE", " ", "GG", " ", "II"}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]]}], ",", "0", ",", "0", ",", "0", ",", FractionBox[ RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II"}], RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}]]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"-", FractionBox[ RowBox[{"24", " ", "AA", " ", "EE", " ", "GG", " ", "II"}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]]}], ",", "0", ",", FractionBox[ RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II"}], RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}]], ",", "0", ",", "0", ",", "0", ",", RowBox[{"-", FractionBox[ RowBox[{"24", " ", "AA", " ", "EE", " ", "GG", " ", "II"}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]]}], ",", "0", ",", RowBox[{"-", FractionBox[ RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II"}], RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}]]}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", RowBox[{"-", FractionBox[ RowBox[{"2", " ", "GG", " ", "II"}], "h"]}], ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", RowBox[{"-", FractionBox[ RowBox[{"2", " ", "GG", " ", "II"}], "h"]}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", FractionBox[ RowBox[{ "12", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II"}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]], ",", "0", ",", RowBox[{"-", FractionBox[ RowBox[{ RowBox[{"48", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"]}]}], RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}], ")"}]}]]}], ",", "0", ",", "0", ",", "0", ",", FractionBox[ RowBox[{ "12", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II"}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]], ",", "0", ",", FractionBox[ RowBox[{ RowBox[{"24", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"]}]}], RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}], ")"}]}]], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", FractionBox[ RowBox[{ "12", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II"}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]]}], ",", "0", ",", "0", ",", "0", ",", FractionBox[ RowBox[{ RowBox[{ RowBox[{"-", "48"}], " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"]}]}], RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}], ")"}]}]], ",", "0", ",", RowBox[{"-", FractionBox[ RowBox[{ "12", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II"}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]]}], ",", "0", ",", "0", ",", "0", ",", FractionBox[ RowBox[{ RowBox[{"24", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"]}]}], RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}], ")"}]}]]}], "}"}], ",", RowBox[{"{", RowBox[{ FractionBox[ RowBox[{"AA", " ", "EE"}], "h"], ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", FractionBox[ RowBox[{"AA", " ", "EE"}], "h"], ",", "0", ",", "0", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", FractionBox[ RowBox[{"24", " ", "AA", " ", "EE", " ", "GG", " ", "II"}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]], ",", "0", ",", "0", ",", "0", ",", FractionBox[ RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II"}], RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}]], ",", "0", ",", FractionBox[ RowBox[{"24", " ", "AA", " ", "EE", " ", "GG", " ", "II"}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]], ",", "0", ",", "0", ",", "0", ",", RowBox[{"-", FractionBox[ RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II"}], RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}]]}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", FractionBox[ RowBox[{"24", " ", "AA", " ", "EE", " ", "GG", " ", "II"}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]], ",", "0", ",", RowBox[{"-", FractionBox[ RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II"}], RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}]]}], ",", "0", ",", "0", ",", "0", ",", FractionBox[ RowBox[{"24", " ", "AA", " ", "EE", " ", "GG", " ", "II"}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]], ",", "0", ",", FractionBox[ RowBox[{ "6", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II"}], RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}]], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", FractionBox[ RowBox[{"2", " ", "GG", " ", "II"}], "h"], ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", FractionBox[ RowBox[{"2", " ", "GG", " ", "II"}], "h"], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", FractionBox[ RowBox[{ "12", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II"}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]], ",", "0", ",", RowBox[{"-", FractionBox[ RowBox[{ RowBox[{"24", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "-", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"]}]}], RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}], ")"}]}]]}], ",", "0", ",", "0", ",", "0", ",", FractionBox[ RowBox[{ "12", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II"}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]], ",", "0", ",", FractionBox[ RowBox[{ RowBox[{"48", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"]}]}], RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}], ")"}]}]], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", FractionBox[ RowBox[{ "12", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II"}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]]}], ",", "0", ",", "0", ",", "0", ",", FractionBox[ RowBox[{ RowBox[{ RowBox[{"-", "24"}], " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"]}]}], RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}], ")"}]}]], ",", "0", ",", RowBox[{"-", FractionBox[ RowBox[{ "12", " ", "AA", " ", "EE", " ", "GG", " ", "h", " ", "II"}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]]}], ",", "0", ",", "0", ",", "0", ",", FractionBox[ RowBox[{ RowBox[{"48", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "II"}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", SuperscriptBox["II", "2"]}]}], RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}], ")"}]}]]}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"KK", " ", "=", " ", RowBox[{"Re", "[", "KK", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{ FractionBox[ RowBox[{"fx", " ", "h"}], "2"], ",", FractionBox[ RowBox[{ RowBox[{"AA", " ", "fy", " ", "GG", " ", SuperscriptBox["h", "4"]}], "+", RowBox[{"12", " ", "EE", " ", "fy", " ", SuperscriptBox["h", "2"], " ", "II"}]}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]], ",", FractionBox[ RowBox[{ RowBox[{"AA", " ", "fz", " ", "GG", " ", SuperscriptBox["h", "4"]}], "+", RowBox[{"12", " ", "EE", " ", "fz", " ", SuperscriptBox["h", "2"], " ", "II"}]}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]], ",", "0", ",", RowBox[{"-", FractionBox[ RowBox[{ RowBox[{"AA", " ", "fz", " ", "GG", " ", SuperscriptBox["h", "5"]}], "+", RowBox[{"12", " ", "EE", " ", "fz", " ", SuperscriptBox["h", "3"], " ", "II"}]}], RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}], ")"}]}]]}], ",", FractionBox[ RowBox[{ RowBox[{"AA", " ", "fy", " ", "GG", " ", SuperscriptBox["h", "5"]}], "+", RowBox[{"12", " ", "EE", " ", "fy", " ", SuperscriptBox["h", "3"], " ", "II"}]}], RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}], ")"}]}]], ",", RowBox[{"-", FractionBox[ RowBox[{"fx", " ", "h"}], "2"]}], ",", RowBox[{"-", FractionBox[ RowBox[{ RowBox[{"AA", " ", "fy", " ", "GG", " ", SuperscriptBox["h", "4"]}], "+", RowBox[{"12", " ", "EE", " ", "fy", " ", SuperscriptBox["h", "2"], " ", "II"}]}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]]}], ",", FractionBox[ RowBox[{ RowBox[{ RowBox[{"-", "AA"}], " ", "fz", " ", "GG", " ", SuperscriptBox["h", "4"]}], "-", RowBox[{"12", " ", "EE", " ", "fz", " ", SuperscriptBox["h", "2"], " ", "II"}]}], RowBox[{ RowBox[{"2", " ", "AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"24", " ", "EE", " ", "h", " ", "II"}]}]], ",", "0", ",", FractionBox[ RowBox[{ RowBox[{ RowBox[{"-", "AA"}], " ", "fz", " ", "GG", " ", SuperscriptBox["h", "5"]}], "-", RowBox[{"12", " ", "EE", " ", "fz", " ", SuperscriptBox["h", "3"], " ", "II"}]}], RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}], ")"}]}]], ",", FractionBox[ RowBox[{ RowBox[{"AA", " ", "fy", " ", "GG", " ", SuperscriptBox["h", "5"]}], "+", RowBox[{"12", " ", "EE", " ", "fy", " ", SuperscriptBox["h", "3"], " ", "II"}]}], RowBox[{"12", " ", RowBox[{"(", RowBox[{ RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "3"]}], "+", RowBox[{"12", " ", "EE", " ", "h", " ", "II"}]}], ")"}]}]]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"-", RowBox[{"\[Delta]aa", ".", RowBox[{"(", RowBox[{ RowBox[{"KK", ".", "aa"}], "-", "FF"}], ")"}]}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.4430689313272*^9, 3.4430690080792*^9}, { 3.4430690869528*^9, 3.4430691077320004`*^9}, {3.4430691700116*^9, 3.4430691708072*^9}, {3.4430692071717997`*^9, 3.443069246359*^9}, { 3.4430772782732*^9, 3.4430773623416*^9}, {3.4430773978316*^9, 3.4430774104676*^9}, {3.4430775053780003`*^9, 3.4430776180598*^9}, { 3.4434109099524*^9, 3.4434109159584*^9}, {3.4438800815346003`*^9, 3.4438802689304*^9}, {3.443880362624*^9, 3.4438803824516*^9}, { 3.443929565615374*^9, 3.443929570232974*^9}, {3.443935321321974*^9, 3.443935335705174*^9}, {3.443935419945174*^9, 3.443935421489574*^9}, { 3.443935494013974*^9, 3.443935494715974*^9}, {3.443935617565974*^9, 3.4439357217895737`*^9}, {3.443935755360774*^9, 3.443935816107174*^9}, { 3.443942155230774*^9, 3.443942209939974*^9}, {3.443942305710374*^9, 3.4439423142123737`*^9}, {3.4439442908131742`*^9, 3.443944441181574*^9}, { 3.4439447830065737`*^9, 3.4439447917425737`*^9}, {3.443944908541774*^9, 3.443944916060974*^9}, {3.4442731097938004`*^9, 3.4442731115254*^9}, { 3.444273189229*^9, 3.4442732700526*^9}, {3.4442748430004*^9, 3.4442748605036*^9}, {3.4442748977438*^9, 3.4442748989762*^9}, { 3.4442749340762*^9, 3.4442749351057997`*^9}, 3.4442752313382*^9, { 3.4442919702026*^9, 3.4442919911846*^9}, {3.4442921151577997`*^9, 3.4442921271074*^9}, {3.4443811023684*^9, 3.4443811036632*^9}, { 3.4443814073171997`*^9, 3.4443814402956*^9}, {3.4443815036316*^9, 3.4443815147855997`*^9}, {3.4443815537232*^9, 3.4443815747676*^9}, { 3.4443816138143997`*^9, 3.444381633174*^9}, {3.4443816850439997`*^9, 3.4443817801728*^9}, 3.4443853618688*^9, {3.4443855607376003`*^9, 3.4443856337924*^9}, {3.4443861200444*^9, 3.4443861523676*^9}, { 3.4443862280495996`*^9, 3.444386291448*^9}, {3.4443864047352*^9, 3.4443864135336*^9}, {3.4443870026832*^9, 3.4443870095316*^9}, { 3.4444082055056*^9, 3.4444082437412*^9}, {3.4444082797148*^9, 3.4444084583816*^9}, {3.4444084889108*^9, 3.4444085087539997`*^9}, { 3.444408942517*^9, 3.4444089563386*^9}, {3.4444091419564*^9, 3.4444091647167997`*^9}, {3.4444092206428003`*^9, 3.4444092944463997`*^9}, {3.4444093856284*^9, 3.4444094281071997`*^9}, { 3.4444094976988*^9, 3.4444095275104*^9}, {3.444409611064*^9, 3.4444096125772*^9}, 3.4444098504616003`*^9, {3.444409913392*^9, 3.4444099166056004`*^9}, 3.4444100178496*^9, {3.4444103063248*^9, 3.4444103358712*^9}, {3.4444103868208*^9, 3.4444104432460003`*^9}, { 3.4444921219564*^9, 3.4444921256224003`*^9}, {3.444492194824*^9, 3.4444921973668003`*^9}, {3.4444922814351997`*^9, 3.4444922853508*^9}, { 3.4444923330868*^9, 3.4444923345844*^9}, {3.444492366424*^9, 3.4444923855808*^9}, {3.4453153475226*^9, 3.445315360689*^9}, { 3.4465518166373653`*^9, 3.446551863016165*^9}, {3.446551894231765*^9, 3.446552159384965*^9}, {3.446552232377365*^9, 3.4465522555589647`*^9}, { 3.446553347388365*^9, 3.4465533616155653`*^9}, {3.4466058525769997`*^9, 3.4466058529046*^9}, {3.4466064371219997`*^9, 3.4466065097244*^9}, { 3.4466127725788*^9, 3.4466127766036*^9}, {3.4466128124835997`*^9, 3.4466130037864*^9}, {3.4466131532696*^9, 3.4466131761703997`*^9}, { 3.4466133992192*^9, 3.4466134478756*^9}, {3.446613483584*^9, 3.4466134932092*^9}, {3.4466135740952*^9, 3.4466135794927998`*^9}, { 3.4466137283948*^9, 3.4466137341356*^9}, {3.4466138994342003`*^9, 3.4466139023826*^9}, {3.4466139549858*^9, 3.4466139579653997`*^9}, { 3.4466142109818*^9, 3.4466142245226*^9}, {3.4466142793878*^9, 3.4466143652033997`*^9}, {3.4466144712834*^9, 3.4466145978929996`*^9}, { 3.4466146992618*^9, 3.4466147509914*^9}, {3.4466151283086*^9, 3.4466152768986*^9}, {3.4466153107506*^9, 3.4466153406558*^9}, { 3.4466194331976*^9, 3.4466194377528*^9}, {3.4466194847712*^9, 3.446619488718*^9}, {3.4466389495861998`*^9, 3.4466389768238*^9}, { 3.4466391218414*^9, 3.446639306561*^9}, {3.4466393990222*^9, 3.4466394004886*^9}, {3.4466394475694*^9, 3.4466394487706003`*^9}, { 3.4466395034174*^9, 3.4466395049462*^9}, 3.4466395515755997`*^9, { 3.4466396000176*^9, 3.4466396190808*^9}, {3.4466397459088*^9, 3.446639748826*^9}, {3.4466397974356003`*^9, 3.446639798668*^9}, 3.4466398447816*^9, {3.446639894218*^9, 3.4466399201556*^9}, { 3.4466399570964003`*^9, 3.4466399583288*^9}, {3.446639994006*^9, 3.4466400056904*^9}, {3.4466400383568*^9, 3.4466400395892*^9}, { 3.4466400745643997`*^9, 3.4466401025976*^9}, {3.4466401660834*^9, 3.4466401806070004`*^9}, {3.4466402251294003`*^9, 3.446640227407*^9}, { 3.446640260479*^9, 3.4466402657674*^9}, {3.4466404133122*^9, 3.4466405185654*^9}, 3.4466405830462*^9, {3.4467273294214*^9, 3.4467273777813997`*^9}, {3.4467274366558*^9, 3.4467275620954*^9}, { 3.446727593311*^9, 3.4467277412614*^9}, {3.4467283334639997`*^9, 3.4467283356012*^9}, {3.4467283707636003`*^9, 3.4467283727604*^9}, { 3.4467289882664003`*^9, 3.4467291276836*^9}, {3.446778464322*^9, 3.4467786797424*^9}, {3.4467801953803997`*^9, 3.4467802409792*^9}, { 3.4467802998691998`*^9, 3.4467804023456*^9}, 3.4467804345596*^9, { 3.4467808656344*^9, 3.4467808670852003`*^9}, 3.4467818107525997`*^9, { 3.446781855509*^9, 3.446781874385*^9}, {3.4467826737914*^9, 3.4467827381726*^9}, {3.4467828623018*^9, 3.4467831045386*^9}, { 3.4470344113984003`*^9, 3.4470344123344*^9}, {3.4470344628316*^9, 3.4470345343108*^9}, {3.447043591118539*^9, 3.447043642192939*^9}, { 3.447045649625739*^9, 3.447045718437339*^9}, {3.447054774023939*^9, 3.447054834198939*^9}, {3.4470549103449388`*^9, 3.4470549116169386`*^9}, { 3.447054943902939*^9, 3.4470553027109385`*^9}, {3.447055334559939*^9, 3.447055353684939*^9}, {3.447057311918539*^9, 3.447057369747739*^9}, { 3.4470575058577385`*^9, 3.4470575951365385`*^9}, {3.4470581848789387`*^9, 3.4470582040825386`*^9}, {3.451276121243*^9, 3.4512761425838003`*^9}, { 3.4512762022382*^9, 3.4512762064346*^9}, {3.4512762476966*^9, 3.4512762827654*^9}, {3.451276489091*^9, 3.451276541975*^9}, { 3.4512765853118*^9, 3.4512766132046003`*^9}, {3.4512773470306*^9, 3.4512773766082*^9}, {3.4512776069110003`*^9, 3.4512777499318*^9}, 3.4512777831286*^9, {3.4512778785538*^9, 3.451277881627*^9}, { 3.4512780242734003`*^9, 3.4512780302794*^9}, 3.4512780737878*^9, { 3.4512781866226*^9, 3.4512781930810003`*^9}, {3.4512863325078*^9, 3.4512863539266*^9}, {3.4568019250434*^9, 3.4568022712698*^9}, { 3.4568023177422*^9, 3.4568024125278*^9}, {3.4568024694365997`*^9, 3.4568024750369997`*^9}, {3.4568026914402*^9, 3.4568028101094*^9}, { 3.4568028406698*^9, 3.4568028564726*^9}, 3.4568028886085997`*^9, { 3.4568030489454*^9, 3.4568030800986*^9}, 3.4568032004128*^9, { 3.4568035073698*^9, 3.4568035176034*^9}, {3.4568040146596003`*^9, 3.4568040844852*^9}, {3.4568043016684*^9, 3.4568043154744*^9}, { 3.4568045482264*^9, 3.4568045486632*^9}, {3.4568048944996*^9, 3.4568049806116*^9}, {3.4660560628582*^9, 3.4660560753538*^9}, { 3.4660676729379997`*^9, 3.4660676735931997`*^9}, {3.4660677244024*^9, 3.4660677277251997`*^9}, {3.4742646771287394`*^9, 3.47426469439174*^9}, { 3.47426489921974*^9, 3.4742649800437393`*^9}, {3.4801246373348*^9, 3.4801246860536003`*^9}, {3.4801247748176003`*^9, 3.4801247821028*^9}, { 3.4801248161264*^9, 3.4801248295736*^9}, {3.4801248810692*^9, 3.4801248964508*^9}, {3.4801249330484*^9, 3.480124947884*^9}, 3.4801249886468*^9, {3.4801251139147997`*^9, 3.48012512588*^9}, { 3.4838339444988003`*^9, 3.4838339567448*^9}, 3.4838341692012*^9, { 3.4838344350408*^9, 3.4838344353684*^9}, {3.4938987575920324`*^9, 3.4938987586840324`*^9}, {3.4941630624049997`*^9, 3.4941631381274*^9}, { 3.4941632311345997`*^9, 3.4941632492306004`*^9}, 3.4941633249217997`*^9, { 3.4941633940922003`*^9, 3.4941634063538*^9}, {3.4941634538402*^9, 3.4941635051642*^9}, {3.494163565115*^9, 3.4941636341762*^9}, { 3.4941636853442*^9, 3.4941639323234*^9}, {3.4941640277798*^9, 3.4941641455754004`*^9}, {3.4941641790374002`*^9, 3.4941641803789997`*^9}, {3.4941642676142*^9, 3.4941643277678003`*^9}, 3.4941644677018003`*^9, {3.4941646208938*^9, 3.4941646322349997`*^9}, { 3.4941652592693996`*^9, 3.4941652807194*^9}, {3.4941653119038*^9, 3.494165416299*^9}, {3.494165453895*^9, 3.4941654544722*^9}, { 3.4950990979779997`*^9, 3.495099142701*^9}, {3.495099172958*^9, 3.4950991806289997`*^9}, {3.495099227097*^9, 3.495099238113*^9}, 3.495099290797*^9, {3.495099346084*^9, 3.495099359507*^9}, { 3.495099456308*^9, 3.495099464091*^9}, 3.495099683108*^9, { 3.495100428112*^9, 3.495100434958*^9}, {3.4951006496219997`*^9, 3.495100649992*^9}, {3.4987235265018*^9, 3.4987235939094*^9}, { 3.4987236420666*^9, 3.4987236530646*^9}, {3.4987237305341997`*^9, 3.4987237396914*^9}, {3.498733136159*^9, 3.4987332972446003`*^9}, { 3.4987364783094*^9, 3.4987364860626*^9}, {3.4987366201134*^9, 3.4987366236078*^9}, {3.4987367272386*^9, 3.4987367464890003`*^9}, { 3.4987369428462*^9, 3.4987369670886*^9}, {3.4987370134518003`*^9, 3.4987370259941998`*^9}, {3.4987370944002*^9, 3.4987371027618*^9}, { 3.4987371921029997`*^9, 3.498737193663*^9}, {3.4987372660938*^9, 3.4987372935498*^9}, {3.4987373290554*^9, 3.4987377176202*^9}, { 3.4987377520182*^9, 3.4987379139462*^9}, {3.4987382030216*^9, 3.4987382667078*^9}, {3.4987888391818*^9, 3.4987888608346*^9}, { 3.4988785131146*^9, 3.4988785160162*^9}, {3.5007170967096*^9, 3.5007170999076*^9}, 3.5007182237316*^9, {3.5007182772864*^9, 3.5007182987832003`*^9}, {3.5009573226744003`*^9, 3.5009573940444*^9}, 3.5009574358710003`*^9, 3.5009604278482*^9, {3.5009897246173353`*^9, 3.5009898480289354`*^9}, {3.5009901464413357`*^9, 3.5009901475333357`*^9}, {3.5009901801997356`*^9, 3.500990274096135*^9}, { 3.5010475253292*^9, 3.5010475852332*^9}, {3.5010605722018003`*^9, 3.5010606739762*^9}, {3.5010607202146*^9, 3.5010607323358*^9}, { 3.5010607920526*^9, 3.501061118467*^9}, {3.5010612022078*^9, 3.5010612277138*^9}, {3.5010616467766*^9, 3.5010617938534*^9}, { 3.5010618406222*^9, 3.5010619950778*^9}, {3.5010621500638*^9, 3.5010622514014*^9}, {3.5010625292218*^9, 3.5010625409374*^9}, { 3.5010626043046*^9, 3.5010626313862*^9}, {3.5010626787166*^9, 3.5010626790754004`*^9}, {3.501074457561*^9, 3.5010744671082*^9}, 3.5010763029458*^9, {3.5032210899309998`*^9, 3.5032212413900003`*^9}, { 3.557658203404973*^9, 3.557658219644601*^9}, {3.5576584433801947`*^9, 3.557658496030287*^9}, {3.5576585501779823`*^9, 3.5576586046064777`*^9}, { 3.557658648910555*^9, 3.557658754600741*^9}, {3.557658963945511*^9, 3.5576589782507353`*^9}, {3.557659009949991*^9, 3.5576591437514267`*^9}, { 3.557659182221094*^9, 3.5576592187719584`*^9}, 3.557659413865901*^9, { 3.557659921100792*^9, 3.5576599556392527`*^9}, {3.557660706920972*^9, 3.5576607248454037`*^9}, {3.557661209085854*^9, 3.557661209413454*^9}, { 3.5577526651911488`*^9, 3.5577526932087984`*^9}, {3.5577527272480583`*^9, 3.557752747122493*^9}, {3.5577528374934516`*^9, 3.557752838523053*^9}, { 3.557752881204728*^9, 3.557752891313546*^9}, {3.557752938612829*^9, 3.5577529469120436`*^9}, {3.557753060714244*^9, 3.557753062633047*^9}, { 3.5577536609544907`*^9, 3.5577536637936954`*^9}, {3.5577537824631042`*^9, 3.557753810184353*^9}, {3.557753841025607*^9, 3.5577540648392*^9}, 3.5577541920574236`*^9, {3.5577547033327217`*^9, 3.557754716967146*^9}, { 3.5577547716296415`*^9, 3.557754802112095*^9}, {3.5577549509363565`*^9, 3.5577549771444025`*^9}, 3.5577551382302856`*^9, {3.55775527184452*^9, 3.557755272858522*^9}, {3.557755881555991*^9, 3.557755886548*^9}, { 3.557756158316077*^9, 3.557756231885806*^9}, {3.5577572408487787`*^9, 3.557757248835993*^9}, {3.5577572834368534`*^9, 3.5577575888229895`*^9}, { 3.5577578129641833`*^9, 3.557757862837471*^9}, {3.557758025514557*^9, 3.557758079272251*^9}, 3.557810586960072*^9, {3.5578240262005973`*^9, 3.5578240345360737`*^9}, {3.557824091429328*^9, 3.5578241008156557`*^9}, { 3.557831525255726*^9, 3.5578315319793377`*^9}, 3.5578315716190076`*^9, { 3.557831606079468*^9, 3.557831629432709*^9}, {3.5578316663267736`*^9, 3.5578317569473333`*^9}, {3.5578322144181366`*^9, 3.557832218084143*^9}, { 3.557836356693412*^9, 3.557836473771618*^9}, {3.5578365201660995`*^9, 3.5578365974018345`*^9}, {3.5578366426731143`*^9, 3.557836658865943*^9}, { 3.557836691017599*^9, 3.5578367924957776`*^9}, {3.5578368305442443`*^9, 3.557836888279946*^9}, {3.5578369382156334`*^9, 3.5578370776642785`*^9}, { 3.5578383536061196`*^9, 3.5578383735117545`*^9}, {3.5578385892445335`*^9, 3.5578385978869486`*^9}, {3.5578386713006773`*^9, 3.557838700113928*^9}, { 3.5578387451200075`*^9, 3.5578387467892103`*^9}, {3.5578388951454706`*^9, 3.5578389248635225`*^9}, {3.5578389679351983`*^9, 3.557838983535226*^9}, { 3.5578390227692947`*^9, 3.557839023143696*^9}, {3.557839097696226*^9, 3.5578391125162525`*^9}, {3.5578391553539276`*^9, 3.557839199892006*^9}, { 3.55783924184048*^9, 3.557839294490572*^9}, {3.5578393285922318`*^9, 3.557839398683155*^9}, {3.557839430522811*^9, 3.557839470162481*^9}, { 3.5578395370865984`*^9, 3.5578395446994114`*^9}, {3.5578396068499207`*^9, 3.5578396118575296`*^9}, 3.5578943518105097`*^9, {3.557894388361374*^9, 3.5578944029629993`*^9}, {3.5578944607611012`*^9, 3.5578944989499683`*^9}, {3.5578945393696394`*^9, 3.557894561537278*^9}, { 3.5578946028617506`*^9, 3.5578946188985786`*^9}, {3.557894650894235*^9, 3.5578947812636642`*^9}, {3.55789481884413*^9, 3.5578948191249304`*^9}, { 3.5578949768100076`*^9, 3.5578949836272197`*^9}, {3.5578967386805477`*^9, 3.55789678549623*^9}, {3.5578968804691963`*^9, 3.557896888643611*^9}, { 3.557897022491846*^9, 3.5578970341450663`*^9}, {3.557897620940097*^9, 3.55789765120415*^9}, {3.5579218072271147`*^9, 3.5579218263059483`*^9}, { 3.557922095312821*^9, 3.557922116965659*^9}, {3.557922178086566*^9, 3.557922188616585*^9}, {3.5579223258812256`*^9, 3.557922327066828*^9}, { 3.5579224596046605`*^9, 3.557922461804264*^9}, 3.5579805928465395`*^9, { 3.5579815200581703`*^9, 3.557981541711009*^9}, 3.557985544779242*^9, { 3.5579863164793987`*^9, 3.5579863339514294`*^9}, {3.557986523210962*^9, 3.557986568841042*^9}, 3.5579866122559185`*^9, 3.557986797646644*^9, 3.55798683514911*^9, {3.557987389828085*^9, 3.5579873922616887`*^9}, { 3.5579875133023014`*^9, 3.5579875144099035`*^9}, {3.557997154019827*^9, 3.5579971543474274`*^9}, {3.5579990909992294`*^9, 3.5579990915764303`*^9}, {3.7515496219127665`*^9, 3.7515496234124207`*^9}, {3.7515496694634647`*^9, 3.751549670619442*^9}}, CellLabel-> "In[138]:=",ExpressionUUID->"baeab370-f64d-49f1-a4ea-3223fb21e390"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["PLATE MODEL", "Section", CellChangeTimes->{ 3.4430806364968*^9, {3.4453166713873997`*^9, 3.4453166747414*^9}, { 3.447462264275*^9, 3.4474622644154*^9}, {3.4695731321116*^9, 3.4695731359491997`*^9}, 3.473055186341*^9, {3.4730552472860003`*^9, 3.47305524884*^9}, {3.473055399782*^9, 3.473055419801*^9}, { 3.4734696760778*^9, 3.4734697047349997`*^9}, {3.4770537891542*^9, 3.4770537950354*^9}, {3.4932799754514*^9, 3.4932799779161997`*^9}, { 3.4945558951644*^9, 3.4945558957416*^9}, {3.4957646303032*^9, 3.4957646329084*^9}, {3.497581602118*^9, 3.4975816042552*^9}, { 3.500960505817*^9, 3.5009605094206*^9}, {3.556623836083009*^9, 3.5566238462386265`*^9}, {3.5568725055395393`*^9, 3.5568725163821597`*^9}, {3.556872678728445*^9, 3.5568726810485783`*^9}, { 3.7323376045620503`*^9, 3.7323376086812124`*^9}, {3.7335630623483887`*^9, 3.733563072583865*^9}, {3.733563130246215*^9, 3.733563131355714*^9}, { 3.817531574263208*^9, 3.8175315898614454`*^9}},ExpressionUUID->"53e88fa2-3263-4b89-af46-\ d70dc8c83236"], Cell[CellGroupData[{ Cell["PLANE ELEMENT (disp) defs ", "Subsection", CellChangeTimes->{{3.766140428784856*^9, 3.7661404367673664`*^9}, { 3.78824987025541*^9, 3.788249871040884*^9}},ExpressionUUID->"1f5e47b0-f670-4db4-ad2c-\ 9e4ef3bda787"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"MEC", "-", "E1050"}], "|", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"MODE", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "NN", ",", "r", ",", "e\[Alpha]", ",", "e\[Beta]", ",", "en", ",", "FF", ",", "FFINV", ",", "jac", ",", "uvw", ",", "\[Epsilon]", ",", "\[Sigma]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "EEEE", ",", "\[Delta]wint", ",", "\[Delta]wext"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", " ", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"e\[Alpha]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}]}], ";", " ", RowBox[{"e\[Beta]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], ";", " ", RowBox[{"en", "=", RowBox[{"e\[Alpha]", StyleBox["\[Cross]", "OperatorCharacter"], "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"en", "/", RowBox[{"Sqrt", "[", RowBox[{"en", ".", "en"}], "]"}]}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"Lx", ">", "0"}], "&&", RowBox[{"Ly", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", " ", "e\[Beta]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"Lx", ">", "0"}], "&&", RowBox[{"Ly", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"Lx", ">", "0"}], "&&", RowBox[{"Ly", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "displacement", " ", "gradient", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{"FFINV", ".", RowBox[{"Transpose", "[", RowBox[{"D", "[", RowBox[{"uvw", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}], "}"}]}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Plane", " ", "stress", " ", "elasticity", " ", "tensor"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"IdentityMatrix", "[", "3", "]"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{"EEEE", "-", RowBox[{ RowBox[{"(", RowBox[{"EEEE", ".", "en"}], ")"}], ".", RowBox[{"Inverse", "[", RowBox[{"en", ".", "EEEE", ".", "en"}], "]"}], ".", RowBox[{"(", RowBox[{"en", ".", "EEEE"}], ")"}]}]}], "]"}]}], ";", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}], "*", "tt"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"MODE", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "node", ",", "NN", ",", "r", ",", "e\[Alpha]", ",", "e\[Beta]", ",", "en", ",", "FF", ",", "FFINV", ",", "jac", ",", "uvw", ",", "\[Epsilon]", ",", "\[Sigma]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "EEEE", ",", "\[Delta]wint", ",", "\[Delta]wext"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions", " ", "etc"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"node", " ", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"e\[Alpha]", ",", "e\[Beta]"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], "}"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{"e\[Alpha]", StyleBox["\[Cross]", "OperatorCharacter"], "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"en", "/", RowBox[{"Sqrt", "[", " ", RowBox[{"en", ".", " ", "en"}], "]"}]}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", "e\[Beta]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "displacement", " ", "gradient", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "uvw"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Plane", " ", "stress", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{"EEEE", "-", RowBox[{ RowBox[{"(", RowBox[{"EEEE", ".", "en"}], ")"}], ".", RowBox[{"Inverse", "[", RowBox[{"en", ".", "EEEE", ".", "en"}], "]"}], ".", RowBox[{"(", RowBox[{"en", ".", "EEEE"}], ")"}]}]}], "]"}]}], ";", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}], "*", "tt"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"REC9", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"TWODIM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"MODE", ",", RowBox[{"{", RowBox[{"TWODIM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"TWODIM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "NN", ",", "r", ",", "e1", ",", "e2", ",", "nn", ",", "FF", ",", "FFINV", ",", "jac", ",", "uvw", ",", "\[Epsilon]", ",", "\[Sigma]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "EEEE", ",", "\[Delta]wint", ",", "\[Delta]wext"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", " ", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"e1", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}]}], ";", " ", RowBox[{"e2", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], ";", " ", RowBox[{"e3", "=", RowBox[{"e1", StyleBox["\[Cross]", "OperatorCharacter"], "e2"}]}], ";", "\[IndentingNewLine]", RowBox[{"nn", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"e3", "/", RowBox[{"Sqrt", "[", RowBox[{"e3", ".", "e3"}], "]"}]}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e1", ",", " ", "e2", ",", "nn"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "displacement", " ", "gradient", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "uvw"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Plane", " ", "stress", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"MODE", "===", "DISP"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}], "*", "tt"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"Simplify", "[", RowBox[{"\[Sigma]", " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "3"}]}]}], "}"}]}], "]"}], "]"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426473093646455`*^9, 3.4426474078630457`*^9}, { 3.4426597184894*^9, 3.4426597783310003`*^9}, {3.442659859139*^9, 3.4426599679021997`*^9}, {3.4426601154852*^9, 3.442660125282*^9}, 3.4426603153866*^9, {3.4426606694491997`*^9, 3.442660676984*^9}, { 3.4426607660341997`*^9, 3.442660767017*^9}, {3.4426607970782003`*^9, 3.4426609236566*^9}, {3.4426609993859997`*^9, 3.442661000946*^9}, { 3.4426611720156*^9, 3.4426611866796*^9}, {3.4426612192836*^9, 3.4426612396104*^9}, {3.4426613536776*^9, 3.4426613563764*^9}, { 3.4426613962188*^9, 3.4426613966556*^9}, {3.443184440921*^9, 3.4431845165186*^9}, {3.4431848052298*^9, 3.4431848237002*^9}, { 3.4431849834618*^9, 3.4431849851934*^9}, {3.4431850342574*^9, 3.4431850385318003`*^9}, {3.4444402127514*^9, 3.4444402360889997`*^9}, { 3.44509636787*^9, 3.445096458974*^9}, {3.4450965569264*^9, 3.4450965855056*^9}, {3.4450966736612*^9, 3.4450967018348*^9}, 3.4450967876972*^9, {3.4451000792358*^9, 3.4451001019962*^9}, { 3.445132280975*^9, 3.4451322867782*^9}, 3.4451325631488*^9, 3.4451346101028*^9, {3.4455261966926003`*^9, 3.4455262691078*^9}, { 3.4455263543462*^9, 3.445526490113*^9}, {3.4455265305794*^9, 3.4455265347602*^9}, {3.4455267552349997`*^9, 3.4455267826754*^9}, 3.445526922233*^9, {3.445527218711*^9, 3.4455272895818*^9}, { 3.4455273640094*^9, 3.445527481259*^9}, 3.4455276192202*^9, { 3.4455278074376*^9, 3.4455278187164*^9}, {3.4455279660896*^9, 3.4455279742016*^9}, 3.4455280249016*^9, 3.4455285464407997`*^9, { 3.4461837560238*^9, 3.4461837697986*^9}, {3.446183892165*^9, 3.4461839004486*^9}, {3.4461839570142*^9, 3.4461841265550003`*^9}, 3.4461841729182*^9, {3.4461842101398*^9, 3.4461842206074*^9}, { 3.4461845241088*^9, 3.4461845410972*^9}, {3.4461845879440002`*^9, 3.4461847021516*^9}, {3.4461848428032*^9, 3.4461848544096003`*^9}, { 3.4461849111956*^9, 3.4461849123344*^9}, {3.4461850134868*^9, 3.446185058608*^9}, {3.4461852067616*^9, 3.446185223282*^9}, { 3.4461852548876*^9, 3.4461852626408*^9}, {3.4461853186604*^9, 3.446185320392*^9}, {3.4512642010481997`*^9, 3.451264207413*^9}, { 3.4512642788766003`*^9, 3.4512643136334*^9}, {3.4512643770006*^9, 3.4512644269362*^9}, {3.4512646983138*^9, 3.4512647384994*^9}, { 3.4512647823354*^9, 3.4512647868126*^9}, {3.4939932066616*^9, 3.4939932082060003`*^9}, {3.4939932399988003`*^9, 3.4939932614955997`*^9}, {3.493993300014*^9, 3.4939933073304*^9}, { 3.4939933992174*^9, 3.4939934078129997`*^9}, {3.4939934932314*^9, 3.493993515009*^9}, {3.4939935468556004`*^9, 3.493993568543*^9}, { 3.4939936486404*^9, 3.4939936621812*^9}, {3.4940328887262*^9, 3.4940328895218*^9}, {3.499487154582*^9, 3.49948716324*^9}, { 3.4994872083708*^9, 3.499487247324*^9}, {3.4994872822368*^9, 3.4994873816244*^9}, 3.499487417676*^9, {3.4994878504918003`*^9, 3.4994879045458*^9}, {3.4994879529370003`*^9, 3.4994879707794*^9}, { 3.4994880482042*^9, 3.4994880616826*^9}, {3.4994881084202003`*^9, 3.4994881177334003`*^9}, {3.4994884740218*^9, 3.4994884920554*^9}, { 3.4994885948282003`*^9, 3.4994886477434*^9}, {3.4994886790369997`*^9, 3.4994886860257998`*^9}, {3.4994887712953997`*^9, 3.4994887717478*^9}, { 3.6305517490219865`*^9, 3.6305518383945436`*^9}, 3.6305519329151096`*^9, { 3.6305521477354264`*^9, 3.6305521796235647`*^9}, {3.630552211063363*^9, 3.630552234159684*^9}, {3.6305523097380066`*^9, 3.6305523261429453`*^9}, { 3.630552400293186*^9, 3.630552443246643*^9}, {3.6305524899713154`*^9, 3.630552532581753*^9}, {3.630552564078554*^9, 3.630552660703081*^9}, { 3.6308069732471952`*^9, 3.6308070226836824`*^9}, {3.630831568112257*^9, 3.630831577359786*^9}, {3.632037136188613*^9, 3.6320372275628395`*^9}, { 3.632037282822*^9, 3.6320372864142056`*^9}, {3.632037326777514*^9, 3.6320373338819203`*^9}, {3.6320374068820953`*^9, 3.632037461262206*^9}, { 3.632037495368157*^9, 3.6320375996761227`*^9}, {3.632037657282418*^9, 3.6320377668306837`*^9}, {3.6320377993975463`*^9, 3.6320378258790607`*^9}, {3.6320379375314474`*^9, 3.632037944011818*^9}, { 3.632037974774577*^9, 3.63203804108137*^9}, {3.632038115937651*^9, 3.6320381168477035`*^9}, {3.632038171547832*^9, 3.6320381721648674`*^9}, { 3.6320382092969913`*^9, 3.6320382642141323`*^9}, 3.632038311238822*^9, { 3.6320383438376865`*^9, 3.6320384084533825`*^9}, {3.632038502612768*^9, 3.632038536966733*^9}, {3.6320386355663724`*^9, 3.632038663028943*^9}, { 3.6320387578143644`*^9, 3.632038876049127*^9}, {3.632038925681966*^9, 3.6320390116098804`*^9}, {3.6320390559574175`*^9, 3.632039057440502*^9}, { 3.6320390909984217`*^9, 3.6320392794842024`*^9}, {3.6320393098219376`*^9, 3.6320393228646836`*^9}, {3.6320393691423306`*^9, 3.632039469157051*^9}, { 3.6320395408921537`*^9, 3.6320395753041224`*^9}, {3.632039607865985*^9, 3.6320396287681804`*^9}, {3.632039834419943*^9, 3.6320399635053263`*^9}, { 3.632040008307889*^9, 3.632040011081047*^9}, {3.632040111200774*^9, 3.6320401709411907`*^9}, {3.6320402797014112`*^9, 3.6320403974661474`*^9}, {3.6320411172793183`*^9, 3.6320411297080293`*^9}, 3.632041280201637*^9, {3.632041357828077*^9, 3.632041361657296*^9}, { 3.632041402765647*^9, 3.632041437279621*^9}, 3.632041474164731*^9, { 3.6320415074596353`*^9, 3.632041548877004*^9}, {3.6320415931405363`*^9, 3.632041610919553*^9}, {3.632041656484159*^9, 3.6320416691688843`*^9}, { 3.6320420632294235`*^9, 3.6320420791513343`*^9}, {3.6320424482774467`*^9, 3.632042550289282*^9}, {3.632042803353756*^9, 3.632042928840934*^9}, { 3.632042961566806*^9, 3.63204301077662*^9}, {3.632043063037609*^9, 3.6320430712580795`*^9}, {3.632043120691907*^9, 3.632043161148221*^9}, { 3.6320432062678013`*^9, 3.6320432094549837`*^9}, 3.632043258394783*^9, { 3.632043351071084*^9, 3.632043352668175*^9}, {3.6345677461009674`*^9, 3.634568027044036*^9}, 3.634568059784909*^9, {3.6345686692177663`*^9, 3.6345687304812703`*^9}, {3.634568765543276*^9, 3.634568827443816*^9}, { 3.6346120324026976`*^9, 3.6346120417672334`*^9}, {3.6346121382917542`*^9, 3.6346122118989644`*^9}, {3.6346122814849443`*^9, 3.634612333070895*^9}, { 3.634612471677823*^9, 3.634612552263432*^9}, {3.6346125863993845`*^9, 3.6346126554953365`*^9}, {3.634612698763811*^9, 3.634612702163006*^9}, { 3.6348726356017313`*^9, 3.634872755937614*^9}, {3.634877631123617*^9, 3.6348776427762833`*^9}, {3.6348782474488688`*^9, 3.6348782744724145`*^9}, {3.63487832072106*^9, 3.634878440448908*^9}, { 3.6852817264030714`*^9, 3.6852817834531507`*^9}, {3.68794462572165*^9, 3.687944776911862*^9}, {3.6879451060223227`*^9, 3.6879451445423765`*^9}, { 3.6879452810225677`*^9, 3.6879452918025827`*^9}, {3.6879455589529567`*^9, 3.687945567592969*^9}, {3.6879456213830442`*^9, 3.6879456613631*^9}, { 3.6879457292931952`*^9, 3.6879457736132574`*^9}, {3.688022923252344*^9, 3.688023002982456*^9}, {3.6880230753425574`*^9, 3.688023230782775*^9}, 3.688023348002939*^9, {3.688023553833227*^9, 3.6880235620032387`*^9}, { 3.6880236295333333`*^9, 3.6880236382433453`*^9}, 3.6880237756035376`*^9, { 3.688031422416407*^9, 3.688031557816597*^9}, {3.6881117497443466`*^9, 3.688111797854414*^9}, {3.6881166477118034`*^9, 3.688116649471806*^9}, { 3.688118444084318*^9, 3.6881185798545084`*^9}, {3.688118642824597*^9, 3.688118799384816*^9}, {3.688118855204894*^9, 3.688118917084981*^9}, { 3.6881194959182944`*^9, 3.688119497718297*^9}, {3.6881196404384966`*^9, 3.688119655048517*^9}, {3.688119702888584*^9, 3.688119727678619*^9}, { 3.6881200919291286`*^9, 3.6881201295191813`*^9}, {3.6881202044892864`*^9, 3.688120237039332*^9}, {3.688120497669697*^9, 3.688120502989704*^9}, { 3.688120738340034*^9, 3.6881207493700495`*^9}, {3.6882745101002936`*^9, 3.6882745118602962`*^9}, {3.6883042728760366`*^9, 3.688304806616784*^9}, { 3.6883051027271986`*^9, 3.6883051086172066`*^9}, {3.6883054642977047`*^9, 3.6883054716377153`*^9}, {3.688306465909107*^9, 3.6883064729091167`*^9}, { 3.6883066024792986`*^9, 3.6883066550893717`*^9}, {3.6883071311300383`*^9, 3.688307145950059*^9}, 3.6883073798003864`*^9, {3.6887815904603148`*^9, 3.6887816040203333`*^9}, 3.6887816433103886`*^9, {3.6887816741004314`*^9, 3.688781699230467*^9}, {3.6887817847405863`*^9, 3.688781813880627*^9}, { 3.688781885830728*^9, 3.6887819020407505`*^9}, {3.6889574605581684`*^9, 3.688957501788226*^9}, {3.688960184803222*^9, 3.6889601992032423`*^9}, { 3.692771817740493*^9, 3.692771905640616*^9}, {3.6927726676816826`*^9, 3.6927727032617326`*^9}, {3.6927727333717747`*^9, 3.692772736561779*^9}, { 3.692772826191905*^9, 3.692772844901931*^9}, {3.692772893741999*^9, 3.6927728997420073`*^9}, {3.6927729636420975`*^9, 3.692773125862324*^9}, { 3.6927731981924257`*^9, 3.692773236352479*^9}, {3.6927732729025297`*^9, 3.692773282242543*^9}, {3.6927733353526173`*^9, 3.6927734137827272`*^9}, 3.6927736473730545`*^9, {3.6934868115444183`*^9, 3.693486813494421*^9}, { 3.6934868553944798`*^9, 3.693486917754567*^9}, {3.6934869973946786`*^9, 3.693487001174684*^9}, {3.6934870442947445`*^9, 3.6934870479747496`*^9}, { 3.693487349135171*^9, 3.6934873994352417`*^9}, {3.693487456975322*^9, 3.6934874585553246`*^9}, {3.6939897066669016`*^9, 3.6939897907970195`*^9}, {3.6939898244170666`*^9, 3.693989829937074*^9}, { 3.6939901042074585`*^9, 3.693990124237486*^9}, {3.69399018398757*^9, 3.6939902403476486`*^9}, {3.6939902781277018`*^9, 3.69399032732777*^9}, { 3.6939903908278594`*^9, 3.693990609328165*^9}, {3.693990640658209*^9, 3.693990673878256*^9}, {3.693990761178378*^9, 3.6939907769384003`*^9}, { 3.6939908128884506`*^9, 3.6939908380384855`*^9}, {3.6939908895785575`*^9, 3.6939908941885643`*^9}, {3.6939909859386926`*^9, 3.693991001898715*^9}, { 3.6939910395887675`*^9, 3.6939910643988028`*^9}, {3.693991107098862*^9, 3.6939911407889094`*^9}, {3.6939911957989864`*^9, 3.6939913838692493`*^9}, {3.6939918465598974`*^9, 3.693991856479911*^9}, { 3.6939919173699965`*^9, 3.6939919296100135`*^9}, {3.693991979330083*^9, 3.693992022780144*^9}, {3.6939921266502895`*^9, 3.6939921416103106`*^9}, { 3.6939921886903763`*^9, 3.693992235260442*^9}, {3.6939924451107354`*^9, 3.6939924757207785`*^9}, {3.6939925308708553`*^9, 3.693992535490862*^9}, { 3.69408137357989*^9, 3.6940813990399256`*^9}, {3.694081492270056*^9, 3.694081500430067*^9}, 3.694085807686309*^9, 3.694336369074993*^9, { 3.694336447585103*^9, 3.694336534165224*^9}, {3.6943365695452733`*^9, 3.694336572935278*^9}, {3.6943366355853662`*^9, 3.694336663395405*^9}, { 3.694336707865467*^9, 3.694336813505615*^9}, {3.6943368708856955`*^9, 3.694336972645838*^9}, {3.694337005795884*^9, 3.69433752400661*^9}, { 3.694337943297197*^9, 3.6943379730472383`*^9}, {3.694338096757412*^9, 3.694338100087416*^9}, {3.6943381564174953`*^9, 3.694338172057517*^9}, { 3.6943382111375713`*^9, 3.6943382179975815`*^9}, {3.694338370357795*^9, 3.694338415207857*^9}, {3.694338519908004*^9, 3.694338533448023*^9}, { 3.694338742738316*^9, 3.6943387845683746`*^9}, {3.6943388672484903`*^9, 3.694338909398549*^9}, {3.6943394389592905`*^9, 3.694339477079344*^9}, { 3.6943395685694723`*^9, 3.6943395881794996`*^9}, 3.6943396627096043`*^9, { 3.694339797119792*^9, 3.6943398030098004`*^9}, {3.6943398885999203`*^9, 3.6943400438301373`*^9}, {3.6943517756956816`*^9, 3.694351778765686*^9}, { 3.694351814965737*^9, 3.694351920335884*^9}, {3.6943520375260487`*^9, 3.694352038046049*^9}, {3.6943546301696777`*^9, 3.694354641489694*^9}, { 3.6943547065797853`*^9, 3.694354780889889*^9}, {3.694415922397947*^9, 3.694415933787963*^9}, {3.6944160021080585`*^9, 3.6944160163480783`*^9}, { 3.6944161612482815`*^9, 3.694416186218316*^9}, {3.6944162181183605`*^9, 3.694416241358393*^9}, {3.694416776009142*^9, 3.694416778289145*^9}, { 3.694417304849882*^9, 3.694417340579932*^9}, {3.6944179310727587`*^9, 3.6944179657728076`*^9}, {3.6944182927132654`*^9, 3.694418302313279*^9}, { 3.6944316170705633`*^9, 3.6944316923568697`*^9}, {3.6944318163219357`*^9, 3.694431820105152*^9}, {3.6965609549111967`*^9, 3.696560966061212*^9}, { 3.696560998851258*^9, 3.6965610020812626`*^9}, {3.6965611422314587`*^9, 3.696561159171482*^9}, 3.696563445644683*^9, {3.6965635186347857`*^9, 3.6965635322048044`*^9}, {3.696563569074856*^9, 3.6965635745148635`*^9}, { 3.696563720555068*^9, 3.69656372185507*^9}, {3.6965637807551527`*^9, 3.696563824135213*^9}, {3.6965639935254507`*^9, 3.696564031985504*^9}, { 3.696596096992402*^9, 3.696596186502527*^9}, {3.696596234252594*^9, 3.696596260452631*^9}, {3.6965963110027018`*^9, 3.69659632407272*^9}, 3.6965963803627987`*^9, {3.7244123642779827`*^9, 3.7244123648119507`*^9}, { 3.7255912428848085`*^9, 3.7255912492295227`*^9}, {3.725591466627203*^9, 3.725591704636403*^9}, {3.7255917405776634`*^9, 3.7255917613142586`*^9}, { 3.7255980783777914`*^9, 3.7255980873943977`*^9}, {3.725598135321295*^9, 3.7255981566673255`*^9}, {3.7255985463958807`*^9, 3.7255985750395555`*^9}, {3.725598660297285*^9, 3.725598669548276*^9}, { 3.7255989613446465`*^9, 3.7255989963014574`*^9}, {3.7255990922803245`*^9, 3.725599092624111*^9}, {3.7255991287997694`*^9, 3.7255991802271013`*^9}, 3.7255992673973975`*^9, {3.725599302619891*^9, 3.725599630275236*^9}, { 3.7255996917974653`*^9, 3.725600173598138*^9}, {3.72560026574846*^9, 3.7256002767652473`*^9}, 3.7256003308803263`*^9, {3.7256003995281887`*^9, 3.72560041238892*^9}, {3.725600503405278*^9, 3.725600537768276*^9}, { 3.72560062249599*^9, 3.725600660390954*^9}, {3.7256015423497496`*^9, 3.725601551460086*^9}, {3.725602674641403*^9, 3.725602676188448*^9}, { 3.725606737765007*^9, 3.7256067379681726`*^9}, {3.7259411263577843`*^9, 3.725941161974596*^9}, {3.7259413328141994`*^9, 3.7259413530325947`*^9}, { 3.725948620999795*^9, 3.7259486419857845`*^9}, 3.7259487502361426`*^9, { 3.725948801316684*^9, 3.7259488049789305`*^9}, {3.7259488747343755`*^9, 3.7259488880408845`*^9}, {3.7262144247900543`*^9, 3.7262144477456355`*^9}, {3.7574170493225684`*^9, 3.757417053184463*^9}, { 3.7831421588326306`*^9, 3.783142170925208*^9}, {3.783142395749114*^9, 3.7831425154306135`*^9}, {3.7831425557309313`*^9, 3.783142564092332*^9}, { 3.7831427526814885`*^9, 3.783142754255293*^9}, {3.7831428098757677`*^9, 3.7831428571042147`*^9}, {3.7834087348068304`*^9, 3.783408793037257*^9}, { 3.7834095081721888`*^9, 3.783409552999109*^9}, {3.783409588525758*^9, 3.7834095907684803`*^9}, {3.783409662061564*^9, 3.7834096810274954`*^9}, { 3.7834097163188562`*^9, 3.7834098893742294`*^9}, {3.7834100221449327`*^9, 3.783410060241215*^9}, {3.7834101051335173`*^9, 3.7834101131745987`*^9}, { 3.783410606354042*^9, 3.783410612361685*^9}, {3.783410755716464*^9, 3.7834107918890605`*^9}, {3.7834108581708117`*^9, 3.7834108764020586`*^9}, {3.783656780899205*^9, 3.783656816754212*^9}, { 3.783656906347945*^9, 3.783656914312093*^9}, {3.783657051037856*^9, 3.7836572912656827`*^9}, {3.783657346545521*^9, 3.7836573583072553`*^9}, { 3.783657399653203*^9, 3.783657405924858*^9}, {3.78365743635863*^9, 3.783657444445655*^9}, {3.783657544607131*^9, 3.7836575974442415`*^9}, { 3.784785690868435*^9, 3.7847857118559847`*^9}, {3.7847931085113173`*^9, 3.7847931143650365`*^9}, {3.784793162925936*^9, 3.784793168863771*^9}, { 3.788250819548458*^9, 3.7882508340994453`*^9}, {3.788250923421962*^9, 3.788250985225994*^9}, {3.789021541724124*^9, 3.789021542741435*^9}, { 3.814675243788579*^9, 3.81467524657043*^9}, {3.814675296484918*^9, 3.8146753026102443`*^9}, 3.8146767508872194`*^9, {3.8146767833631124`*^9, 3.8146768340288363`*^9}, {3.8146768678429646`*^9, 3.814676881416951*^9}, { 3.819778869762148*^9, 3.8197788819676495`*^9}, {3.8200281551494493`*^9, 3.8200282443038893`*^9}, 3.820028306018581*^9, {3.820028830464693*^9, 3.820028898308877*^9}, {3.8436188654069076`*^9, 3.843618871317108*^9}, { 3.8469114507424884`*^9, 3.8469114924591775`*^9}, {3.846911710003416*^9, 3.846911730341361*^9}, {3.846912038982461*^9, 3.846912051966134*^9}, { 3.8469120857716913`*^9, 3.8469120984335556`*^9}, 3.846912467488207*^9, { 3.846912605028914*^9, 3.8469126582335243`*^9}, {3.846912823206394*^9, 3.8469128572750063`*^9}, {3.8469129263437014`*^9, 3.8469129533099966`*^9}, 3.846913299667283*^9, {3.8469133963598742`*^9, 3.8469134147191906`*^9}, { 3.8469134714459963`*^9, 3.8469134727490387`*^9}, {3.846913563275012*^9, 3.8469135761291294`*^9}, {3.847105214587804*^9, 3.847105223753584*^9}, { 3.8471055237950907`*^9, 3.8471055304047117`*^9}, {3.847105638827262*^9, 3.8471056537154665`*^9}, {3.847106253534446*^9, 3.8471062610359097`*^9}, { 3.8471075005414257`*^9, 3.8471075008503447`*^9}}, CellLabel-> "In[175]:=",ExpressionUUID->"2d2dcd52-3c40-4702-a04b-d68350cdb23b"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Alpha]", ",", "\[Beta]", ",", "xg", ",", "yg", ",", "jac", ",", "x3", ",", "y3", ",", "x6", ",", "y6", ",", "x", ",", "y", ",", "K3", ",", "N3", ",", "N6", ",", "u", ",", "v", ",", "\[Psi]", ",", "E\[Sigma]", ",", "\[Delta]w", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wmap", ",", "NN", ",", "FF", ",", "\[Epsilon]\[Epsilon]", ",", "tri"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"mapping", " ", "for", " ", "the", " ", "geometry"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"x3", "=", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "1", ",", "1"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"y3", "=", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "1", ",", "2"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"K3", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"xg", "=", RowBox[{"K3", ".", "x3"}]}], ";", "\[IndentingNewLine]", RowBox[{"yg", "=", RowBox[{"K3", ".", "y3"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "xg"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "xg"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "yg"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "yg"}]}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"x6", "=", RowBox[{"Join", "[", RowBox[{"x3", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Mean", "[", "#", "]"}], "&"}], ",", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{"x3", ",", RowBox[{"RotateLeft", "[", "x3", "]"}]}], "}"}], "]"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"y6", " ", "=", RowBox[{"Join", "[", RowBox[{"y3", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Mean", "[", "#", "]"}], "&"}], ",", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{"y3", ",", RowBox[{"RotateLeft", "[", "y3", "]"}]}], "}"}], "]"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"N3", "=", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", "1"}], "}"}], ",", "x3", ",", "y3"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"1", ",", "x", ",", "y"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N6", "=", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", "1", ",", "1", ",", "1", ",", "1"}], "}"}], ",", "x6", ",", "y6", ",", RowBox[{"x6", "*", "y6"}], ",", RowBox[{"x6", "^", "2"}], ",", RowBox[{"y6", "^", "2"}]}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"1", ",", "x", ",", "y", ",", RowBox[{"x", "*", "y"}], ",", RowBox[{"x", "^", "2"}], ",", RowBox[{"y", "^", "2"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"N6", ".", RowBox[{"Join", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"uX", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"uX", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"uX", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}], "]"}]}], "}"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"N6", ".", RowBox[{"Join", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"uY", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"uY", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"uY", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}], "]"}]}], "}"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{"N3", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "3", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Epsilon]\[Epsilon]", "=", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], "-", "\[Psi]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}], "+", "\[Psi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"E\[Sigma]", "=", RowBox[{ RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "\[Nu]\[Nu]", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Nu]\[Nu]", ",", "1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}]}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"tt", "*", RowBox[{"E\[Sigma]", ".", "\[Epsilon]\[Epsilon]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"(", RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Epsilon]\[Epsilon]", "]"}], ".", "NN"}]}], ")"}], " ", "/.", " ", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "xg"}], ",", RowBox[{"y", "\[Rule]", "yg"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", "u", "]"}], "*", "fX"}], "+", RowBox[{ RowBox[{"\[Delta]", "[", "v", "]"}], "*", "fY"}]}], ")"}], "/.", " ", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "xg"}], ",", RowBox[{"y", "\[Rule]", "yg"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"{", RowBox[{"TWODIM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Triangle", "[", "node_", "]"}]}], "}"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"TWODIM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "}"}], ",", RowBox[{"Triangle", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"TWODIM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"I1_", ",", "I2_", ",", "I3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "NN", ",", "r", ",", "e1", ",", "e2", ",", "nn", ",", "FF", ",", "FFINV", ",", "jac", ",", "uvw", ",", "\[Epsilon]", ",", "\[Sigma]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "EEEE", ",", "\[Delta]wint", ",", "\[Delta]wext"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", " ", "=", RowBox[{"{", RowBox[{"I1", ",", "I2", ",", "I3"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"e1", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}]}], ";", " ", RowBox[{"e2", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], ";", " ", RowBox[{"e3", "=", RowBox[{"e1", StyleBox["\[Cross]", "OperatorCharacter"], "e2"}]}], ";", "\[IndentingNewLine]", RowBox[{"nn", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"e3", "/", RowBox[{"Sqrt", "[", RowBox[{"e3", ".", "e3"}], "]"}]}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e1", ",", " ", "e2", ",", "nn"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "displacement", " ", "gradient", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "uvw"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Plane", " ", "stress", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"MODE", "===", "DISP"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}], "*", "tt"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"Simplify", "[", RowBox[{"\[Sigma]", " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "3"}]}]}], "}"}]}], "]"}], "]"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Triangle", "[", "node_", "]"}]}], "}"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "mX", ",", "mY", ",", "mZ"}], "}"}]}], "}"}], ",", RowBox[{"Triangle", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"I1_", ",", "I2_", ",", "I3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "NN", ",", "r", ",", "e1", ",", "e2", ",", "e3", ",", "nn", ",", "PP", ",", "FF", ",", "FFINV", ",", "jac", ",", "uvw", ",", "\[Phi]\[Theta]\[Psi]", ",", "\[Epsilon]", ",", "\[Sigma]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "EEEE", ",", "EECC", ",", "CCEE", ",", "CCCC", ",", "\[Delta]wint", ",", "\[Delta]wext"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", " ", "=", RowBox[{"{", RowBox[{"I1", ",", "I2", ",", "I3"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"e1", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}]}], ";", " ", RowBox[{"e2", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], ";", " ", RowBox[{"e3", "=", RowBox[{"e1", StyleBox["\[Cross]", "OperatorCharacter"], "e2"}]}], ";", "\[IndentingNewLine]", RowBox[{"nn", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"e3", "/", RowBox[{"Sqrt", "[", RowBox[{"e3", ".", "e3"}], "]"}]}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e1", ",", " ", "e2", ",", "nn"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"PP", "=", RowBox[{"LeviCivitaTensor", "[", "3", "]"}]}], ";", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]\[Theta]\[Psi]", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "displacement", " ", "gradient", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{ RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "uvw"}]}], "}"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{"PP", ".", "nn"}], ")"}], "*", RowBox[{"(", RowBox[{"nn", ".", "\[Phi]\[Theta]\[Psi]"}], ")"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Plane", " ", "stress", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], "]"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}]}], "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EECC", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{"i", ",", "j", ",", "l", ",", "k"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"l", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"CCEE", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{"j", ",", "i", ",", "k", ",", "l"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"l", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"CCCC", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{"j", ",", "i", ",", "l", ",", "k"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"l", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"tt", "*", RowBox[{"Simplify", "[", RowBox[{"EEEE", "-", RowBox[{ RowBox[{"(", RowBox[{"EEEE", ".", "nn"}], ")"}], ".", RowBox[{"Inverse", "[", RowBox[{"nn", ".", "EEEE", ".", "nn"}], "]"}], ".", RowBox[{"(", RowBox[{"nn", ".", "EEEE"}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{"EECC", ".", "nn"}], ")"}], ".", RowBox[{"Inverse", "[", RowBox[{"nn", ".", "CCCC", ".", "nn"}], "]"}], ".", RowBox[{"(", RowBox[{"nn", ".", "CCEE"}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EEEE", ".", "nn"}], ")"}], ".", RowBox[{"(", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "nn", ",", "nn"}], "]"}], "*", RowBox[{"1", "/", RowBox[{"(", RowBox[{"nn", ".", RowBox[{"(", RowBox[{"nn", ".", "EEEE", ".", "nn"}], ")"}], ".", "nn"}], ")"}]}]}], ")"}], ".", RowBox[{"(", RowBox[{"nn", ".", "EEEE"}], ")"}]}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", "\[Phi]\[Theta]\[Psi]", "]"}], ".", RowBox[{"{", RowBox[{"mX", ",", "mY", ",", "mZ"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"EMS", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "Mz_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "nodes_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "NN", ",", "r", ",", "e1", ",", "e2", ",", "e3", ",", "nn", ",", "PP", ",", "FF", ",", "FFINV", ",", "jac", ",", "uvw", ",", "\[Phi]\[Theta]\[Psi]", ",", "\[Epsilon]", ",", "\[Sigma]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "EEEE", ",", "EECC", ",", "CCEE", ",", "CCCC", ",", "\[Delta]wint", ",", "\[Delta]wext"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"Length", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "[", "3", "]"}], "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}]}], "}"}]}], ";", RowBox[{ RowBox[{"NN", "[", "4", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"INT", "[", "3", "]"}], "=", "TRI7"}], ";", RowBox[{ RowBox[{"INT", "[", "4", "]"}], "=", "REC9"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"MID", "[", "3", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "3"}]}]}], "}"}]}], ";", " ", RowBox[{ RowBox[{"MID", "[", "4", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{ RowBox[{"NN", "[", "nl", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"e1", ",", "e2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], "}"}], " ", "/.", RowBox[{"MID", "[", "nl", "]"}]}]}], ";", "\[IndentingNewLine]", " ", RowBox[{"e3", "=", RowBox[{"e1", StyleBox["\[Cross]", "OperatorCharacter"], "e2"}]}], ";", "\[IndentingNewLine]", RowBox[{"nn", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"e3", "/", RowBox[{"Sqrt", "[", RowBox[{"e3", ".", "e3"}], "]"}]}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e1", ",", " ", "e2", ",", "nn"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"PP", "=", RowBox[{"LeviCivitaTensor", "[", "3", "]"}]}], ";", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]\[Theta]\[Psi]", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "displacement", " ", "gradient", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{ RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "uvw"}]}], "}"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{"PP", ".", "nn"}], ")"}], "*", RowBox[{"(", RowBox[{"nn", ".", "\[Phi]\[Theta]\[Psi]"}], ")"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Plane", " ", "stress", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], "]"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}]}], "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EECC", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{"i", ",", "j", ",", "l", ",", "k"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"l", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"CCEE", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{"j", ",", "i", ",", "k", ",", "l"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"l", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"CCCC", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{"j", ",", "i", ",", "l", ",", "k"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"l", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"tt", "*", RowBox[{"Simplify", "[", RowBox[{"EEEE", "-", RowBox[{ RowBox[{"(", RowBox[{"EEEE", ".", "nn"}], ")"}], ".", RowBox[{"Inverse", "[", RowBox[{"nn", ".", "EEEE", ".", "nn"}], "]"}], ".", RowBox[{"(", RowBox[{"nn", ".", "EEEE"}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{"EECC", ".", "nn"}], ")"}], ".", RowBox[{"Inverse", "[", RowBox[{"nn", ".", "CCCC", ".", "nn"}], "]"}], ".", RowBox[{"(", RowBox[{"nn", ".", "CCEE"}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"EEEE", ".", "nn"}], ")"}], ".", RowBox[{"(", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "nn", ",", "nn"}], "]"}], "*", RowBox[{"1", "/", RowBox[{"(", RowBox[{"nn", ".", RowBox[{"(", RowBox[{"nn", ".", "EEEE", ".", "nn"}], ")"}], ".", "nn"}], ")"}]}]}], ")"}], ".", RowBox[{"(", RowBox[{"nn", ".", "EEEE"}], ")"}]}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"non", "-", RowBox[{"symmetric", " ", "stress"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", "\[Phi]\[Theta]\[Psi]", "]"}], ".", RowBox[{"{", RowBox[{"mX", ",", "mY", ",", "mZ"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", "model_"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"\[Epsilon]0_", ",", "\[Lambda]\[Lambda]_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}]}], "]"}], ":=", RowBox[{ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "ns", ",", "enode", " ", ",", "NN", ",", "\[Alpha]", ",", "\[Beta]", ",", "X", ",", "Y", ",", "r", ",", "FF", ",", "FFINV", ",", "PP", ",", "jac", ",", "uv", ",", "\[Epsilon]", ",", "\[Sigma]", ",", "\[Rho]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "EEEE", ",", "IIII", ",", "II", ",", "IIII1", ",", "IIII2", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wlag"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ns", " ", "=", RowBox[{"Dimensions", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"enode", " ", "=", RowBox[{"Flatten", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "[", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}], "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "*", RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", "*", RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "*", "\[Beta]"}], ",", RowBox[{"\[Alpha]", "*", "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"assuming", " ", "a", " ", "linear", " ", "mapping"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"X", ",", "Y"}], "}"}], "=", RowBox[{"r", "=", RowBox[{ RowBox[{"NN", "[", "ns", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "1", ",", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}]}], "]"}], "]"}]}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], "}"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uv", "=", RowBox[{ RowBox[{"NN", "[", "ns", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "2", ",", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}]}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "displacement", " ", "gradient", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "uv"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "uv"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"plane", "-", RowBox[{ "stress", " ", "or", " ", "strain", " ", "symmetric", " ", "elasticity", " ", "dyad"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"II", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIII1", "=", RowBox[{"Outer", "[", RowBox[{"Times", ",", "II", ",", "II"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIII", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "i", ",", "j", ",", "j", ",", "i"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "II"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "II"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIII2", "=", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"IIII", "[", RowBox[{"[", RowBox[{"i", ",", "j", ",", "k", ",", "l"}], "]"}], "]"}], "+", RowBox[{"IIII", "[", RowBox[{"[", RowBox[{"j", ",", "i", ",", "k", ",", "l"}], "]"}], "]"}], "+", RowBox[{"IIII", "[", RowBox[{"[", RowBox[{"i", ",", "j", ",", "l", ",", "k"}], "]"}], "]"}], "+", RowBox[{"IIII", "[", RowBox[{"[", RowBox[{"j", ",", "i", ",", "l", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"l", ",", "1", ",", "2"}], "}"}]}], "]"}], "/", "4"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{ RowBox[{"tt", "[", RowBox[{"X", ",", "Y"}], "]"}], "*", RowBox[{ RowBox[{"EE", "[", RowBox[{"X", ",", "Y"}], "]"}], "/", RowBox[{"(", RowBox[{"1", "+", RowBox[{"\[Nu]\[Nu]", "[", RowBox[{"X", ",", "Y"}], "]"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Nu]\[Nu]", "[", RowBox[{"X", ",", "Y"}], "]"}], "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "[", RowBox[{"X", ",", "Y"}], "]"}]}], ")"}]}], "*", "IIII1"}], "+", "IIII2"}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"model", "===", "strain"}], ",", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{ RowBox[{"tt", "[", RowBox[{"X", ",", "Y"}], "]"}], "*", RowBox[{ RowBox[{"EE", "[", RowBox[{"X", ",", "Y"}], "]"}], "/", RowBox[{"(", RowBox[{"1", "+", RowBox[{"\[Nu]\[Nu]", "[", RowBox[{"X", ",", "Y"}], "]"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Nu]\[Nu]", "[", RowBox[{"X", ",", "Y"}], "]"}], "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"2", "*", RowBox[{"\[Nu]\[Nu]", "[", RowBox[{"X", ",", "Y"}], "]"}]}]}], ")"}]}], "*", "IIII1"}], "+", "IIII2"}], ")"}]}]}]}], "]"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Epsilon]0", "[", RowBox[{"X", ",", "Y"}], "]"}], "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}], "+", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ")"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"MODE", "\[Equal]", "DISP"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wext", "=", RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uv", "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"fX", "[", RowBox[{"X", ",", "Y"}], "]"}], ",", RowBox[{"fY", "[", RowBox[{"X", ",", "Y"}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wlag", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Lambda]\[Lambda]", "[", RowBox[{"X", ",", "Y"}], "]"}], "]"}], ".", "uv"}], "+", RowBox[{ RowBox[{"\[Lambda]\[Lambda]", "[", RowBox[{"X", ",", "Y"}], "]"}], ".", RowBox[{"\[Delta]", "[", "uv", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"LIN3", ",", RowBox[{"QUAD", "[", RowBox[{"LIN3", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wext", "+", "\[Delta]wint", "+", "\[Delta]wlag"}], ")"}], "*", "jac"}], ",", RowBox[{"{", "\[Alpha]", "}"}]}], "]"}], ",", RowBox[{"{", "\[Beta]", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", "\[Delta]WW", "]"}]}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"MODE", "\[Equal]", "POSTP"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"LIN3", ",", RowBox[{"QUAD", "[", RowBox[{"LIN3", ",", RowBox[{"\[Sigma]", "*", "jac"}], ",", RowBox[{"{", "\[Alpha]", "}"}]}], "]"}], ",", RowBox[{"{", "\[Beta]", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", "\[Delta]WW", "]"}]}]}], "]"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "at", " ", "the", " ", "centerpoint"}], "*)"}], "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"MODE", "\[Equal]", "STRESS"}], ",", RowBox[{"Return", "[", RowBox[{"\[Sigma]", " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "3"}]}]}], "}"}]}], "]"}]}], "]"}]}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", "]"}], "/;", " ", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}]}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"computational", " ", "homogenization", " ", "element"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", RowBox[{"tt_", ",", "\[Epsilon]0_", ",", "\[Lambda]\[Lambda]_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}]}], "]"}], ":=", RowBox[{ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "ns", ",", "NN", ",", "\[Alpha]", ",", "\[Beta]", ",", "X", ",", "Y", ",", "r", ",", "FF", ",", "FFINV", ",", "PP", ",", "jac", ",", "uv", ",", "\[Epsilon]", ",", "\[Sigma]", ",", "s", ",", "\[Rho]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "EEEE", ",", "IIII", ",", "II", ",", "IIII1", ",", "IIII2", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wlag"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ns", " ", "=", RowBox[{"Length", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "[", "3", "]"}], "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "[", "6", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"1", "+", RowBox[{"2", " ", SuperscriptBox["\[Beta]", "2"]}], "-", RowBox[{"3", " ", "\[Alpha]"}], "+", RowBox[{"2", " ", SuperscriptBox["\[Alpha]", "2"]}], "+", RowBox[{"\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"4", " ", "\[Alpha]"}]}], ")"}]}]}], ",", RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}]}], ",", RowBox[{"\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", "4"}], " ", "\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]", "+", "\[Alpha]"}], ")"}]}], ",", RowBox[{"4", " ", "\[Beta]", " ", "\[Alpha]"}], ",", RowBox[{ RowBox[{"-", "4"}], " ", "\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]", "+", "\[Alpha]"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"assuming", " ", "a", " ", "linear", " ", "mapping"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"X", ",", "Y"}], "}"}], "=", RowBox[{"r", "=", RowBox[{ RowBox[{"NN", "[", "ns", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "1", ",", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}]}], "]"}], "]"}]}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], "}"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "3"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uv", "=", RowBox[{ RowBox[{"NN", "[", "ns", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "2", ",", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}]}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "displacement", " ", "gradient", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "uv"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "uv"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"plane", "-", RowBox[{ "stress", " ", "or", " ", "strain", " ", "symmetric", " ", "elasticity", " ", "dyad"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"II", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIII1", "=", RowBox[{"Outer", "[", RowBox[{"Times", ",", "II", ",", "II"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIII", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "i", ",", "j", ",", "j", ",", "i"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "II"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "II"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIII2", "=", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"IIII", "[", RowBox[{"[", RowBox[{"i", ",", "j", ",", "k", ",", "l"}], "]"}], "]"}], "+", RowBox[{"IIII", "[", RowBox[{"[", RowBox[{"j", ",", "i", ",", "k", ",", "l"}], "]"}], "]"}], "+", RowBox[{"IIII", "[", RowBox[{"[", RowBox[{"i", ",", "j", ",", "l", ",", "k"}], "]"}], "]"}], "+", RowBox[{"IIII", "[", RowBox[{"[", RowBox[{"j", ",", "i", ",", "l", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"l", ",", "1", ",", "2"}], "}"}]}], "]"}], "/", "4"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{ RowBox[{"tt", "[", RowBox[{"X", ",", "Y"}], "]"}], "*", RowBox[{ RowBox[{"EE", "[", RowBox[{"X", ",", "Y"}], "]"}], "/", RowBox[{"(", RowBox[{"1", "+", RowBox[{"\[Nu]\[Nu]", "[", RowBox[{"X", ",", "Y"}], "]"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Nu]\[Nu]", "[", RowBox[{"X", ",", "Y"}], "]"}], "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "[", RowBox[{"X", ",", "Y"}], "]"}]}], ")"}]}], "*", "IIII1"}], "+", "IIII2"}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"model", "===", "strain"}], ",", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{ RowBox[{"tt", "[", RowBox[{"X", ",", "Y"}], "]"}], "*", RowBox[{ RowBox[{"EE", "[", RowBox[{"X", ",", "Y"}], "]"}], "/", RowBox[{"(", RowBox[{"1", "+", RowBox[{"\[Nu]\[Nu]", "[", RowBox[{"X", ",", "Y"}], "]"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Nu]\[Nu]", "[", RowBox[{"X", ",", "Y"}], "]"}], "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"2", "*", RowBox[{"\[Nu]\[Nu]", "[", RowBox[{"X", ",", "Y"}], "]"}]}]}], ")"}]}], "*", "IIII1"}], "+", "IIII2"}], ")"}]}]}]}], "]"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Epsilon]0", "[", RowBox[{"X", ",", "Y"}], "]"}], "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}], "+", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ")"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"MODE", "\[Equal]", "DISP"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wext", "=", RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uv", "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"fX", "[", RowBox[{"X", ",", "Y"}], "]"}], ",", RowBox[{"fY", "[", RowBox[{"X", ",", "Y"}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wlag", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Lambda]\[Lambda]", "[", RowBox[{"X", ",", "Y"}], "]"}], "]"}], ".", "uv"}], "+", RowBox[{ RowBox[{"\[Lambda]\[Lambda]", "[", RowBox[{"X", ",", "Y"}], "]"}], ".", RowBox[{"\[Delta]", "[", "uv", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wext", "+", "\[Delta]wint", "+", "\[Delta]wlag"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", "\[Delta]WW", "]"}]}]}], "]"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"MODE", "\[Equal]", "POSTP"}], ",", RowBox[{ RowBox[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{"\[Sigma]", "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}], ";", RowBox[{"Return", "[", "\[Delta]WW", "]"}]}]}], "]"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "at", " ", "the", " ", "centerpoint"}], "*)"}], "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"MODE", "\[Equal]", "STRESS"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"s", "=", RowBox[{"\[Sigma]", " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "3"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{ RowBox[{"s", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], ",", RowBox[{"s", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"s", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"s", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ")"}], "/", "2"}]}], "}"}], "]"}]}]}], "]"}]}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", "]"}], "/;", " ", RowBox[{ RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", "3", "}"}]}], " ", "||", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", "6", "}"}]}]}]}]}], " ", ";"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.4426473093646455`*^9, 3.4426474078630457`*^9}, { 3.4426597184894*^9, 3.4426597783310003`*^9}, {3.442659859139*^9, 3.4426599679021997`*^9}, {3.4426601154852*^9, 3.442660125282*^9}, 3.4426603153866*^9, {3.4426606694491997`*^9, 3.442660676984*^9}, { 3.4426607660341997`*^9, 3.442660767017*^9}, {3.4426607970782003`*^9, 3.4426609236566*^9}, {3.4426609993859997`*^9, 3.442661000946*^9}, { 3.4426611720156*^9, 3.4426611866796*^9}, {3.4426612192836*^9, 3.4426612396104*^9}, {3.4426613536776*^9, 3.4426613563764*^9}, { 3.4426613962188*^9, 3.4426613966556*^9}, {3.443184440921*^9, 3.4431845165186*^9}, {3.4431848052298*^9, 3.4431848237002*^9}, { 3.4431849834618*^9, 3.4431849851934*^9}, {3.4431850342574*^9, 3.4431850385318003`*^9}, {3.4444402127514*^9, 3.4444402360889997`*^9}, { 3.44509636787*^9, 3.445096458974*^9}, {3.4450965569264*^9, 3.4450965855056*^9}, {3.4450966736612*^9, 3.4450967018348*^9}, 3.4450967876972*^9, {3.4451000792358*^9, 3.4451001019962*^9}, { 3.445132280975*^9, 3.4451322867782*^9}, 3.4451325631488*^9, 3.4451346101028*^9, {3.4455261966926003`*^9, 3.4455262691078*^9}, { 3.4455263543462*^9, 3.445526490113*^9}, {3.4455265305794*^9, 3.4455265347602*^9}, {3.4455267552349997`*^9, 3.4455267826754*^9}, 3.445526922233*^9, {3.445527218711*^9, 3.4455272895818*^9}, { 3.4455273640094*^9, 3.445527481259*^9}, 3.4455276192202*^9, { 3.4455278074376*^9, 3.4455278187164*^9}, {3.4455279660896*^9, 3.4455279742016*^9}, 3.4455280249016*^9, 3.4455285464407997`*^9, { 3.4461837560238*^9, 3.4461837697986*^9}, {3.446183892165*^9, 3.4461839004486*^9}, {3.4461839570142*^9, 3.4461841265550003`*^9}, 3.4461841729182*^9, {3.4461842101398*^9, 3.4461842206074*^9}, { 3.4461845241088*^9, 3.4461845410972*^9}, {3.4461845879440002`*^9, 3.4461847021516*^9}, {3.4461848428032*^9, 3.4461848544096003`*^9}, { 3.4461849111956*^9, 3.4461849123344*^9}, {3.4461850134868*^9, 3.446185058608*^9}, {3.4461852067616*^9, 3.446185223282*^9}, { 3.4461852548876*^9, 3.4461852626408*^9}, {3.4461853186604*^9, 3.446185320392*^9}, {3.4512642010481997`*^9, 3.451264207413*^9}, { 3.4512642788766003`*^9, 3.4512643136334*^9}, {3.4512643770006*^9, 3.4512644269362*^9}, {3.4512646983138*^9, 3.4512647384994*^9}, { 3.4512647823354*^9, 3.4512647868126*^9}, {3.4939932066616*^9, 3.4939932082060003`*^9}, {3.4939932399988003`*^9, 3.4939932614955997`*^9}, {3.493993300014*^9, 3.4939933073304*^9}, { 3.4939933992174*^9, 3.4939934078129997`*^9}, {3.4939934932314*^9, 3.493993515009*^9}, {3.4939935468556004`*^9, 3.493993568543*^9}, { 3.4939936486404*^9, 3.4939936621812*^9}, {3.4940328887262*^9, 3.4940328895218*^9}, {3.499487154582*^9, 3.49948716324*^9}, { 3.4994872083708*^9, 3.499487247324*^9}, {3.4994872822368*^9, 3.4994873816244*^9}, 3.499487417676*^9, {3.4994878504918003`*^9, 3.4994879045458*^9}, {3.4994879529370003`*^9, 3.4994879707794*^9}, { 3.4994880482042*^9, 3.4994880616826*^9}, {3.4994881084202003`*^9, 3.4994881177334003`*^9}, {3.4994884740218*^9, 3.4994884920554*^9}, { 3.4994885948282003`*^9, 3.4994886477434*^9}, {3.4994886790369997`*^9, 3.4994886860257998`*^9}, {3.4994887712953997`*^9, 3.4994887717478*^9}, { 3.6305517490219865`*^9, 3.6305518383945436`*^9}, 3.6305519329151096`*^9, { 3.6305521477354264`*^9, 3.6305521796235647`*^9}, {3.630552211063363*^9, 3.630552234159684*^9}, {3.6305523097380066`*^9, 3.6305523261429453`*^9}, { 3.630552400293186*^9, 3.630552443246643*^9}, {3.6305524899713154`*^9, 3.630552532581753*^9}, {3.630552564078554*^9, 3.630552660703081*^9}, { 3.6308069732471952`*^9, 3.6308070226836824`*^9}, {3.630831568112257*^9, 3.630831577359786*^9}, {3.632037136188613*^9, 3.6320372275628395`*^9}, { 3.632037282822*^9, 3.6320372864142056`*^9}, {3.632037326777514*^9, 3.6320373338819203`*^9}, {3.6320374068820953`*^9, 3.632037461262206*^9}, { 3.632037495368157*^9, 3.6320375996761227`*^9}, {3.632037657282418*^9, 3.6320377668306837`*^9}, {3.6320377993975463`*^9, 3.6320378258790607`*^9}, {3.6320379375314474`*^9, 3.632037944011818*^9}, { 3.632037974774577*^9, 3.63203804108137*^9}, {3.632038115937651*^9, 3.6320381168477035`*^9}, {3.632038171547832*^9, 3.6320381721648674`*^9}, { 3.6320382092969913`*^9, 3.6320382642141323`*^9}, 3.632038311238822*^9, { 3.6320383438376865`*^9, 3.6320384084533825`*^9}, {3.632038502612768*^9, 3.632038536966733*^9}, {3.6320386355663724`*^9, 3.632038663028943*^9}, { 3.6320387578143644`*^9, 3.632038876049127*^9}, {3.632038925681966*^9, 3.6320390116098804`*^9}, {3.6320390559574175`*^9, 3.632039057440502*^9}, { 3.6320390909984217`*^9, 3.6320392794842024`*^9}, {3.6320393098219376`*^9, 3.6320393228646836`*^9}, {3.6320393691423306`*^9, 3.632039469157051*^9}, { 3.6320395408921537`*^9, 3.6320395753041224`*^9}, {3.632039607865985*^9, 3.6320396287681804`*^9}, {3.632039834419943*^9, 3.6320399635053263`*^9}, { 3.632040008307889*^9, 3.632040011081047*^9}, {3.632040111200774*^9, 3.6320401709411907`*^9}, {3.6320402797014112`*^9, 3.6320403974661474`*^9}, {3.6320411172793183`*^9, 3.6320411297080293`*^9}, 3.632041280201637*^9, {3.632041357828077*^9, 3.632041361657296*^9}, { 3.632041402765647*^9, 3.632041437279621*^9}, 3.632041474164731*^9, { 3.6320415074596353`*^9, 3.632041548877004*^9}, {3.6320415931405363`*^9, 3.632041610919553*^9}, {3.632041656484159*^9, 3.6320416691688843`*^9}, { 3.6320420632294235`*^9, 3.6320420791513343`*^9}, {3.6320424482774467`*^9, 3.632042550289282*^9}, {3.632042803353756*^9, 3.632042928840934*^9}, { 3.632042961566806*^9, 3.63204301077662*^9}, {3.632043063037609*^9, 3.6320430712580795`*^9}, {3.632043120691907*^9, 3.632043161148221*^9}, { 3.6320432062678013`*^9, 3.6320432094549837`*^9}, 3.632043258394783*^9, { 3.632043351071084*^9, 3.632043352668175*^9}, {3.6345677461009674`*^9, 3.634568027044036*^9}, 3.634568059784909*^9, {3.6345686692177663`*^9, 3.6345687304812703`*^9}, {3.634568765543276*^9, 3.634568827443816*^9}, { 3.6346120324026976`*^9, 3.6346120417672334`*^9}, {3.6346121382917542`*^9, 3.6346122118989644`*^9}, {3.6346122814849443`*^9, 3.634612333070895*^9}, { 3.634612471677823*^9, 3.634612552263432*^9}, {3.6346125863993845`*^9, 3.6346126554953365`*^9}, {3.634612698763811*^9, 3.634612702163006*^9}, { 3.6348726356017313`*^9, 3.634872755937614*^9}, {3.634877631123617*^9, 3.6348776427762833`*^9}, {3.6348782474488688`*^9, 3.6348782744724145`*^9}, {3.63487832072106*^9, 3.634878440448908*^9}, { 3.6852817264030714`*^9, 3.6852817834531507`*^9}, {3.68794462572165*^9, 3.687944776911862*^9}, {3.6879451060223227`*^9, 3.6879451445423765`*^9}, { 3.6879452810225677`*^9, 3.6879452918025827`*^9}, {3.6879455589529567`*^9, 3.687945567592969*^9}, {3.6879456213830442`*^9, 3.6879456613631*^9}, { 3.6879457292931952`*^9, 3.6879457736132574`*^9}, {3.688022923252344*^9, 3.688023002982456*^9}, {3.6880230753425574`*^9, 3.688023230782775*^9}, 3.688023348002939*^9, {3.688023553833227*^9, 3.6880235620032387`*^9}, { 3.6880236295333333`*^9, 3.6880236382433453`*^9}, 3.6880237756035376`*^9, { 3.688031422416407*^9, 3.688031557816597*^9}, {3.6881117497443466`*^9, 3.688111797854414*^9}, {3.6881166477118034`*^9, 3.688116649471806*^9}, { 3.688118444084318*^9, 3.6881185798545084`*^9}, {3.688118642824597*^9, 3.688118799384816*^9}, {3.688118855204894*^9, 3.688118917084981*^9}, { 3.6881194959182944`*^9, 3.688119497718297*^9}, {3.6881196404384966`*^9, 3.688119655048517*^9}, {3.688119702888584*^9, 3.688119727678619*^9}, { 3.6881200919291286`*^9, 3.6881201295191813`*^9}, {3.6881202044892864`*^9, 3.688120237039332*^9}, {3.688120497669697*^9, 3.688120502989704*^9}, { 3.688120738340034*^9, 3.6881207493700495`*^9}, {3.6882745101002936`*^9, 3.6882745118602962`*^9}, {3.6883042728760366`*^9, 3.688304806616784*^9}, { 3.6883051027271986`*^9, 3.6883051086172066`*^9}, {3.6883054642977047`*^9, 3.6883054716377153`*^9}, {3.688306465909107*^9, 3.6883064729091167`*^9}, { 3.6883066024792986`*^9, 3.6883066550893717`*^9}, {3.6883071311300383`*^9, 3.688307145950059*^9}, 3.6883073798003864`*^9, {3.6887815904603148`*^9, 3.6887816040203333`*^9}, 3.6887816433103886`*^9, {3.6887816741004314`*^9, 3.688781699230467*^9}, {3.6887817847405863`*^9, 3.688781813880627*^9}, { 3.688781885830728*^9, 3.6887819020407505`*^9}, {3.6889574605581684`*^9, 3.688957501788226*^9}, {3.688960184803222*^9, 3.6889601992032423`*^9}, { 3.692771817740493*^9, 3.692771905640616*^9}, {3.6927726676816826`*^9, 3.6927727032617326`*^9}, {3.6927727333717747`*^9, 3.692772736561779*^9}, { 3.692772826191905*^9, 3.692772844901931*^9}, {3.692772893741999*^9, 3.6927728997420073`*^9}, {3.6927729636420975`*^9, 3.692773125862324*^9}, { 3.6927731981924257`*^9, 3.692773236352479*^9}, {3.6927732729025297`*^9, 3.692773282242543*^9}, {3.6927733353526173`*^9, 3.6927734137827272`*^9}, 3.6927736473730545`*^9, {3.6934868115444183`*^9, 3.693486813494421*^9}, { 3.6934868553944798`*^9, 3.693486917754567*^9}, {3.6934869973946786`*^9, 3.693487001174684*^9}, {3.6934870442947445`*^9, 3.6934870479747496`*^9}, { 3.693487349135171*^9, 3.6934873994352417`*^9}, {3.693487456975322*^9, 3.6934874585553246`*^9}, {3.6939897066669016`*^9, 3.6939897907970195`*^9}, {3.6939898244170666`*^9, 3.693989829937074*^9}, { 3.6939901042074585`*^9, 3.693990124237486*^9}, {3.69399018398757*^9, 3.6939902403476486`*^9}, {3.6939902781277018`*^9, 3.69399032732777*^9}, { 3.6939903908278594`*^9, 3.693990609328165*^9}, {3.693990640658209*^9, 3.693990673878256*^9}, {3.693990761178378*^9, 3.6939907769384003`*^9}, { 3.6939908128884506`*^9, 3.6939908380384855`*^9}, {3.6939908895785575`*^9, 3.6939908941885643`*^9}, {3.6939909859386926`*^9, 3.693991001898715*^9}, { 3.6939910395887675`*^9, 3.6939910643988028`*^9}, {3.693991107098862*^9, 3.6939911407889094`*^9}, {3.6939911957989864`*^9, 3.6939913838692493`*^9}, {3.6939918465598974`*^9, 3.693991856479911*^9}, { 3.6939919173699965`*^9, 3.6939919296100135`*^9}, {3.693991979330083*^9, 3.693992022780144*^9}, {3.6939921266502895`*^9, 3.6939921416103106`*^9}, { 3.6939921886903763`*^9, 3.693992235260442*^9}, {3.6939924451107354`*^9, 3.6939924757207785`*^9}, {3.6939925308708553`*^9, 3.693992535490862*^9}, { 3.69408137357989*^9, 3.6940813990399256`*^9}, {3.694081492270056*^9, 3.694081500430067*^9}, 3.694085807686309*^9, 3.694336369074993*^9, { 3.694336447585103*^9, 3.694336534165224*^9}, {3.6943365695452733`*^9, 3.694336572935278*^9}, {3.6943366355853662`*^9, 3.694336663395405*^9}, { 3.694336707865467*^9, 3.694336813505615*^9}, {3.6943368708856955`*^9, 3.694336972645838*^9}, {3.694337005795884*^9, 3.69433752400661*^9}, { 3.694337943297197*^9, 3.6943379730472383`*^9}, {3.694338096757412*^9, 3.694338100087416*^9}, {3.6943381564174953`*^9, 3.694338172057517*^9}, { 3.6943382111375713`*^9, 3.6943382179975815`*^9}, {3.694338370357795*^9, 3.694338415207857*^9}, {3.694338519908004*^9, 3.694338533448023*^9}, { 3.694338742738316*^9, 3.6943387845683746`*^9}, {3.6943388672484903`*^9, 3.694338909398549*^9}, {3.6943394389592905`*^9, 3.694339477079344*^9}, { 3.6943395685694723`*^9, 3.6943395881794996`*^9}, 3.6943396627096043`*^9, { 3.694339797119792*^9, 3.6943398030098004`*^9}, {3.6943398885999203`*^9, 3.6943400438301373`*^9}, {3.6943517756956816`*^9, 3.694351778765686*^9}, { 3.694351814965737*^9, 3.694351920335884*^9}, {3.6943520375260487`*^9, 3.694352038046049*^9}, {3.6943546301696777`*^9, 3.694354641489694*^9}, { 3.6943547065797853`*^9, 3.694354780889889*^9}, {3.694415922397947*^9, 3.694415933787963*^9}, {3.6944160021080585`*^9, 3.6944160163480783`*^9}, { 3.6944161612482815`*^9, 3.694416186218316*^9}, {3.6944162181183605`*^9, 3.694416241358393*^9}, {3.694416776009142*^9, 3.694416778289145*^9}, { 3.694417304849882*^9, 3.694417340579932*^9}, {3.6944179310727587`*^9, 3.6944179657728076`*^9}, {3.6944182927132654`*^9, 3.694418302313279*^9}, { 3.6944316170705633`*^9, 3.6944316923568697`*^9}, {3.6944318163219357`*^9, 3.694431820105152*^9}, {3.6965609549111967`*^9, 3.696560966061212*^9}, { 3.696560998851258*^9, 3.6965610020812626`*^9}, {3.6965611422314587`*^9, 3.696561159171482*^9}, 3.696563445644683*^9, {3.6965635186347857`*^9, 3.6965635322048044`*^9}, {3.696563569074856*^9, 3.6965635745148635`*^9}, { 3.696563720555068*^9, 3.69656372185507*^9}, {3.6965637807551527`*^9, 3.696563824135213*^9}, {3.6965639935254507`*^9, 3.696564031985504*^9}, { 3.696596096992402*^9, 3.696596186502527*^9}, {3.696596234252594*^9, 3.696596260452631*^9}, {3.6965963110027018`*^9, 3.69659632407272*^9}, 3.6965963803627987`*^9, {3.7244123642779827`*^9, 3.7244123648119507`*^9}, { 3.7255912428848085`*^9, 3.7255912492295227`*^9}, {3.725591466627203*^9, 3.725591704636403*^9}, {3.7255917405776634`*^9, 3.7255917613142586`*^9}, { 3.7255980783777914`*^9, 3.7255980873943977`*^9}, {3.725598135321295*^9, 3.7255981566673255`*^9}, {3.7255985463958807`*^9, 3.7255985750395555`*^9}, {3.725598660297285*^9, 3.725598669548276*^9}, { 3.7255989613446465`*^9, 3.7255989963014574`*^9}, {3.7255990922803245`*^9, 3.725599092624111*^9}, {3.7255991287997694`*^9, 3.7255991802271013`*^9}, 3.7255992673973975`*^9, {3.725599302619891*^9, 3.725599630275236*^9}, { 3.7255996917974653`*^9, 3.725600173598138*^9}, {3.72560026574846*^9, 3.7256002767652473`*^9}, 3.7256003308803263`*^9, {3.7256003995281887`*^9, 3.72560041238892*^9}, {3.725600503405278*^9, 3.725600537768276*^9}, { 3.72560062249599*^9, 3.725600660390954*^9}, {3.7256015423497496`*^9, 3.725601551460086*^9}, {3.725602674641403*^9, 3.725602676188448*^9}, { 3.725606737765007*^9, 3.7256067379681726`*^9}, {3.7259411263577843`*^9, 3.725941161974596*^9}, {3.7259413328141994`*^9, 3.7259413530325947`*^9}, { 3.725948620999795*^9, 3.7259486419857845`*^9}, 3.7259487502361426`*^9, { 3.725948801316684*^9, 3.7259488049789305`*^9}, {3.7259488747343755`*^9, 3.7259488880408845`*^9}, {3.7262144247900543`*^9, 3.7262144477456355`*^9}, {3.7574170493225684`*^9, 3.757417053184463*^9}, { 3.7831421588326306`*^9, 3.783142170925208*^9}, {3.783142395749114*^9, 3.7831425154306135`*^9}, {3.7831425557309313`*^9, 3.783142564092332*^9}, { 3.7831427526814885`*^9, 3.783142754255293*^9}, {3.7831428098757677`*^9, 3.7831428571042147`*^9}, {3.7834087348068304`*^9, 3.783408793037257*^9}, { 3.7834095081721888`*^9, 3.783409552999109*^9}, {3.783409588525758*^9, 3.7834095907684803`*^9}, {3.783409662061564*^9, 3.7834096810274954`*^9}, { 3.7834097163188562`*^9, 3.7834098893742294`*^9}, {3.7834100221449327`*^9, 3.783410060241215*^9}, {3.7834101051335173`*^9, 3.7834101131745987`*^9}, { 3.783410606354042*^9, 3.783410612361685*^9}, {3.783410755716464*^9, 3.7834107918890605`*^9}, {3.7834108581708117`*^9, 3.7834108764020586`*^9}, {3.783656780899205*^9, 3.783656816754212*^9}, { 3.783656906347945*^9, 3.783656914312093*^9}, {3.783657051037856*^9, 3.7836572912656827`*^9}, {3.783657346545521*^9, 3.7836573583072553`*^9}, { 3.783657399653203*^9, 3.783657405924858*^9}, {3.78365743635863*^9, 3.783657444445655*^9}, {3.783657544607131*^9, 3.7836575974442415`*^9}, { 3.784785690868435*^9, 3.7847857118559847`*^9}, {3.7847931085113173`*^9, 3.7847931143650365`*^9}, {3.784793162925936*^9, 3.784793168863771*^9}, { 3.788250819548458*^9, 3.7882508340994453`*^9}, {3.788250923421962*^9, 3.788250985225994*^9}, {3.789021541724124*^9, 3.789021542741435*^9}, { 3.814675243788579*^9, 3.81467524657043*^9}, {3.814675296484918*^9, 3.8146753026102443`*^9}, 3.8146767508872194`*^9, {3.8146767833631124`*^9, 3.8146768340288363`*^9}, {3.8146768678429646`*^9, 3.814676881416951*^9}, { 3.819778869762148*^9, 3.8197788819676495`*^9}, {3.8200281551494493`*^9, 3.8200282443038893`*^9}, 3.820028306018581*^9},ExpressionUUID->"011777fb-5213-41bb-a29f-\ 4836f1a5efd3"] }, Closed]], Cell[CellGroupData[{ Cell["PLANE ELEMENT (evnt) defs", "Subsection", InitializationCell->True, CellChangeTimes->{{3.753018875511382*^9, 3.7530188786265306`*^9}, { 3.781589886623744*^9, 3.7815898932426767`*^9}, {3.7878947601549573`*^9, 3.787894760728943*^9}, 3.7878948945295725`*^9, {3.817439343565061*^9, 3.8174393448082724`*^9}, {3.817439544553817*^9, 3.8174395452236648`*^9}, { 3.817439659219601*^9, 3.8174396600345135`*^9}, 3.843182883058161*^9},ExpressionUUID->"ea12c303-fa8b-4684-9abb-\ f0e78137131f"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"EVNT", ",", RowBox[{"{", RowBox[{"s0_", ",", "sol0_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"PLANE", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLANE", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, { 3.7530189177531705`*^9, 3.753018918350237*^9}, {3.753018991800671*^9, 3.753019041865839*^9}, {3.7530191095313196`*^9, 3.7530191100576744`*^9}, 3.753019155952956*^9, {3.7530192458219423`*^9, 3.753019353286773*^9}, { 3.773986323215969*^9, 3.7739864366876383`*^9}, {3.7739864700193005`*^9, 3.7739865885966825`*^9}, {3.7739869332783327`*^9, 3.7739870501829805`*^9}, 3.773987085528166*^9, {3.7739872536160583`*^9, 3.773987270466986*^9}, { 3.773987482712697*^9, 3.7739875221812735`*^9}, {3.773987740298462*^9, 3.7739877466065903`*^9}, {3.7739878599976892`*^9, 3.7739878861137896`*^9}, {3.773987965425336*^9, 3.7739879715632877`*^9}, 3.773988098774023*^9, 3.7739883193781385`*^9, {3.7739884099852057`*^9, 3.7739885862960095`*^9}, {3.773988628922502*^9, 3.773988632767228*^9}, { 3.7739891227568517`*^9, 3.77398915009042*^9}, {3.7739892774900556`*^9, 3.773989291800435*^9}, {3.7739896060525217`*^9, 3.773989635013425*^9}, { 3.7751890832095585`*^9, 3.7751890882413054`*^9}, {3.7751894923762302`*^9, 3.7751895008441906`*^9}, {3.7751911834227276`*^9, 3.775191222686661*^9}, 3.7751912606478214`*^9, {3.7751943412188396`*^9, 3.775194461553982*^9}, { 3.775194496052539*^9, 3.7751945353727713`*^9}, {3.7751945737174063`*^9, 3.775194621343042*^9}, {3.775194667862669*^9, 3.7751947598351893`*^9}, { 3.7751948235734253`*^9, 3.7751949415953684`*^9}, {3.775195100078847*^9, 3.77519512113822*^9}, {3.7751954506873007`*^9, 3.775195467864645*^9}, { 3.775270786870551*^9, 3.775270796325161*^9}, {3.7752708274391947`*^9, 3.775270839737406*^9}, {3.7752709283091574`*^9, 3.7752709474534383`*^9}, { 3.7752710502850266`*^9, 3.7752711744130797`*^9}, {3.7752712273079033`*^9, 3.7752713060364757`*^9}, {3.775271448825513*^9, 3.7752714699277525`*^9}, { 3.775271509321142*^9, 3.775271585609558*^9}, {3.775271620653377*^9, 3.77527180192237*^9}, {3.781589928213842*^9, 3.781590052438653*^9}, { 3.7815900898176003`*^9, 3.781590109307678*^9}, {3.781590201383393*^9, 3.7815902433873234`*^9}, {3.7815905445265956`*^9, 3.781590569573782*^9}, { 3.7815906952864275`*^9, 3.781590715680611*^9}, {3.7815908323678637`*^9, 3.781590881239719*^9}, {3.7815911048122363`*^9, 3.781591119274813*^9}, { 3.817439386305109*^9, 3.8174394287787733`*^9}, {3.8174395552770724`*^9, 3.8174395603447847`*^9}, {3.8174396709099665`*^9, 3.817439676294123*^9}, 3.8175213211484346`*^9, 3.8431828885395837`*^9}, CellLabel-> "In[181]:=",ExpressionUUID->"7bf9157a-5288-4830-ac6a-ed9a8a1f8b82"] }, Closed]], Cell[CellGroupData[{ Cell["PLANE ELEMENT (stre) defs ", "Subsection", CellChangeTimes->{{3.766140428784856*^9, 3.7661404367673664`*^9}, { 3.7834159393565364`*^9, 3.783415939864867*^9}, {3.790129829798637*^9, 3.7901298377928085`*^9}},ExpressionUUID->"5ae82b95-f0fd-43fb-a5f1-\ 353de1edd4c4"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STRES", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", "anya_", ",", "anyb_"}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "NN", ",", "r", ",", "e\[Alpha]", ",", "e\[Beta]", ",", "en", ",", "FF", ",", "FFINV", ",", "jac", ",", "uvw", ",", "\[Epsilon]", ",", "\[Sigma]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "EEEE", ",", "\[Delta]wint", ",", "\[Delta]wext"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"Length", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "[", "3", "]"}], "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "[", "4", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{ RowBox[{"NN", "[", "nl", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"e\[Alpha]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}]}], ";", " ", RowBox[{"e\[Beta]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], ";", " ", RowBox[{"en", "=", RowBox[{"e\[Alpha]", StyleBox["\[Cross]", "OperatorCharacter"], "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"en", "/", RowBox[{"Sqrt", "[", RowBox[{"en", ".", "en"}], "]"}]}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"Lx", ">", "0"}], "&&", RowBox[{"Ly", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", " ", "e\[Beta]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"Lx", ">", "0"}], "&&", RowBox[{"Ly", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"Lx", ">", "0"}], "&&", RowBox[{"Ly", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{ RowBox[{"NN", "[", "nl", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "displacement", " ", "gradient", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{"FFINV", ".", RowBox[{"Transpose", "[", RowBox[{"D", "[", RowBox[{"uvw", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}], "}"}]}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Plane", " ", "stress", " ", "elasticity", " ", "tensor"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"IdentityMatrix", "[", "3", "]"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{"EEEE", "-", RowBox[{ RowBox[{"(", RowBox[{"EEEE", ".", "en"}], ")"}], ".", RowBox[{"Inverse", "[", RowBox[{"en", ".", "EEEE", ".", "en"}], "]"}], ".", RowBox[{"(", RowBox[{"en", ".", "EEEE"}], ")"}]}]}], "]"}]}], ";", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"Thread", "[", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[Sigma]XX", ",", "\[Sigma]XY", ",", "\[Sigma]XZ"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Sigma]YX", ",", "\[Sigma]YY", ",", "\[Sigma]YZ"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Sigma]ZX", ",", "\[Sigma]ZY", ",", "\[Sigma]ZZ"}], "}"}]}], "}"}], "]"}], "\[Rule]", " ", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}], "]"}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STRES", ",", RowBox[{"{", RowBox[{"TWODIM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", "anya_", ",", "anyb_"}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "NN", ",", "r", ",", "e\[Alpha]", ",", "e\[Beta]", ",", "en", ",", "FF", ",", "FFINV", ",", "jac", ",", "uvw", ",", "\[Epsilon]", ",", "\[Sigma]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "EEEE", ",", "\[Delta]wint", ",", "\[Delta]wext"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"Length", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "[", "3", "]"}], "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "[", "4", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{ RowBox[{"NN", "[", "nl", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"e\[Alpha]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}]}], ";", " ", RowBox[{"e\[Beta]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], ";", " ", RowBox[{"en", "=", RowBox[{"e\[Alpha]", StyleBox["\[Cross]", "OperatorCharacter"], "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"en", "/", RowBox[{"Sqrt", "[", RowBox[{"en", ".", "en"}], "]"}]}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"Lx", ">", "0"}], "&&", RowBox[{"Ly", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", " ", "e\[Beta]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"Lx", ">", "0"}], "&&", RowBox[{"Ly", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"Lx", ">", "0"}], "&&", RowBox[{"Ly", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{ RowBox[{"NN", "[", "nl", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "displacement", " ", "gradient", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{"FFINV", ".", RowBox[{"Transpose", "[", RowBox[{"D", "[", RowBox[{"uvw", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}], "}"}]}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Plane", " ", "stress", " ", "elasticity", " ", "tensor"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"IdentityMatrix", "[", "3", "]"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"Thread", "[", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[Sigma]XX", ",", "\[Sigma]XY", ",", "\[Sigma]XZ"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Sigma]YX", ",", "\[Sigma]YY", ",", "\[Sigma]YZ"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Sigma]ZX", ",", "\[Sigma]ZY", ",", "\[Sigma]ZZ"}], "}"}]}], "}"}], "]"}], "\[Rule]", " ", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}], "]"}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426473093646455`*^9, 3.4426474078630457`*^9}, { 3.4426597184894*^9, 3.4426597783310003`*^9}, {3.442659859139*^9, 3.4426599679021997`*^9}, {3.4426601154852*^9, 3.442660125282*^9}, 3.4426603153866*^9, {3.4426606694491997`*^9, 3.442660676984*^9}, { 3.4426607660341997`*^9, 3.442660767017*^9}, {3.4426607970782003`*^9, 3.4426609236566*^9}, {3.4426609993859997`*^9, 3.442661000946*^9}, { 3.4426611720156*^9, 3.4426611866796*^9}, {3.4426612192836*^9, 3.4426612396104*^9}, {3.4426613536776*^9, 3.4426613563764*^9}, { 3.4426613962188*^9, 3.4426613966556*^9}, {3.443184440921*^9, 3.4431845165186*^9}, {3.4431848052298*^9, 3.4431848237002*^9}, { 3.4431849834618*^9, 3.4431849851934*^9}, {3.4431850342574*^9, 3.4431850385318003`*^9}, {3.4444402127514*^9, 3.4444402360889997`*^9}, { 3.44509636787*^9, 3.445096458974*^9}, {3.4450965569264*^9, 3.4450965855056*^9}, {3.4450966736612*^9, 3.4450967018348*^9}, 3.4450967876972*^9, {3.4451000792358*^9, 3.4451001019962*^9}, { 3.445132280975*^9, 3.4451322867782*^9}, 3.4451325631488*^9, 3.4451346101028*^9, {3.4455261966926003`*^9, 3.4455262691078*^9}, { 3.4455263543462*^9, 3.445526490113*^9}, {3.4455265305794*^9, 3.4455265347602*^9}, {3.4455267552349997`*^9, 3.4455267826754*^9}, 3.445526922233*^9, {3.445527218711*^9, 3.4455272895818*^9}, { 3.4455273640094*^9, 3.445527481259*^9}, 3.4455276192202*^9, { 3.4455278074376*^9, 3.4455278187164*^9}, {3.4455279660896*^9, 3.4455279742016*^9}, 3.4455280249016*^9, 3.4455285464407997`*^9, { 3.4461837560238*^9, 3.4461837697986*^9}, {3.446183892165*^9, 3.4461839004486*^9}, {3.4461839570142*^9, 3.4461841265550003`*^9}, 3.4461841729182*^9, {3.4461842101398*^9, 3.4461842206074*^9}, { 3.4461845241088*^9, 3.4461845410972*^9}, {3.4461845879440002`*^9, 3.4461847021516*^9}, {3.4461848428032*^9, 3.4461848544096003`*^9}, { 3.4461849111956*^9, 3.4461849123344*^9}, {3.4461850134868*^9, 3.446185058608*^9}, {3.4461852067616*^9, 3.446185223282*^9}, { 3.4461852548876*^9, 3.4461852626408*^9}, {3.4461853186604*^9, 3.446185320392*^9}, {3.4512642010481997`*^9, 3.451264207413*^9}, { 3.4512642788766003`*^9, 3.4512643136334*^9}, {3.4512643770006*^9, 3.4512644269362*^9}, {3.4512646983138*^9, 3.4512647384994*^9}, { 3.4512647823354*^9, 3.4512647868126*^9}, {3.4939932066616*^9, 3.4939932082060003`*^9}, {3.4939932399988003`*^9, 3.4939932614955997`*^9}, {3.493993300014*^9, 3.4939933073304*^9}, { 3.4939933992174*^9, 3.4939934078129997`*^9}, {3.4939934932314*^9, 3.493993515009*^9}, {3.4939935468556004`*^9, 3.493993568543*^9}, { 3.4939936486404*^9, 3.4939936621812*^9}, {3.4940328887262*^9, 3.4940328895218*^9}, {3.499487154582*^9, 3.49948716324*^9}, { 3.4994872083708*^9, 3.499487247324*^9}, {3.4994872822368*^9, 3.4994873816244*^9}, 3.499487417676*^9, {3.4994878504918003`*^9, 3.4994879045458*^9}, {3.4994879529370003`*^9, 3.4994879707794*^9}, { 3.4994880482042*^9, 3.4994880616826*^9}, {3.4994881084202003`*^9, 3.4994881177334003`*^9}, {3.4994884740218*^9, 3.4994884920554*^9}, { 3.4994885948282003`*^9, 3.4994886477434*^9}, {3.4994886790369997`*^9, 3.4994886860257998`*^9}, {3.4994887712953997`*^9, 3.4994887717478*^9}, { 3.6305517490219865`*^9, 3.6305518383945436`*^9}, 3.6305519329151096`*^9, { 3.6305521477354264`*^9, 3.6305521796235647`*^9}, {3.630552211063363*^9, 3.630552234159684*^9}, {3.6305523097380066`*^9, 3.6305523261429453`*^9}, { 3.630552400293186*^9, 3.630552443246643*^9}, {3.6305524899713154`*^9, 3.630552532581753*^9}, {3.630552564078554*^9, 3.630552660703081*^9}, { 3.6308069732471952`*^9, 3.6308070226836824`*^9}, {3.630831568112257*^9, 3.630831577359786*^9}, {3.632037136188613*^9, 3.6320372275628395`*^9}, { 3.632037282822*^9, 3.6320372864142056`*^9}, {3.632037326777514*^9, 3.6320373338819203`*^9}, {3.6320374068820953`*^9, 3.632037461262206*^9}, { 3.632037495368157*^9, 3.6320375996761227`*^9}, {3.632037657282418*^9, 3.6320377668306837`*^9}, {3.6320377993975463`*^9, 3.6320378258790607`*^9}, {3.6320379375314474`*^9, 3.632037944011818*^9}, { 3.632037974774577*^9, 3.63203804108137*^9}, {3.632038115937651*^9, 3.6320381168477035`*^9}, {3.632038171547832*^9, 3.6320381721648674`*^9}, { 3.6320382092969913`*^9, 3.6320382642141323`*^9}, 3.632038311238822*^9, { 3.6320383438376865`*^9, 3.6320384084533825`*^9}, {3.632038502612768*^9, 3.632038536966733*^9}, {3.6320386355663724`*^9, 3.632038663028943*^9}, { 3.6320387578143644`*^9, 3.632038876049127*^9}, {3.632038925681966*^9, 3.6320390116098804`*^9}, {3.6320390559574175`*^9, 3.632039057440502*^9}, { 3.6320390909984217`*^9, 3.6320392794842024`*^9}, {3.6320393098219376`*^9, 3.6320393228646836`*^9}, {3.6320393691423306`*^9, 3.632039469157051*^9}, { 3.6320395408921537`*^9, 3.6320395753041224`*^9}, {3.632039607865985*^9, 3.6320396287681804`*^9}, {3.632039834419943*^9, 3.6320399635053263`*^9}, { 3.632040008307889*^9, 3.632040011081047*^9}, {3.632040111200774*^9, 3.6320401709411907`*^9}, {3.6320402797014112`*^9, 3.6320403974661474`*^9}, {3.6320411172793183`*^9, 3.6320411297080293`*^9}, 3.632041280201637*^9, {3.632041357828077*^9, 3.632041361657296*^9}, { 3.632041402765647*^9, 3.632041437279621*^9}, 3.632041474164731*^9, { 3.6320415074596353`*^9, 3.632041548877004*^9}, {3.6320415931405363`*^9, 3.632041610919553*^9}, {3.632041656484159*^9, 3.6320416691688843`*^9}, { 3.6320420632294235`*^9, 3.6320420791513343`*^9}, {3.6320424482774467`*^9, 3.632042550289282*^9}, {3.632042803353756*^9, 3.632042928840934*^9}, { 3.632042961566806*^9, 3.63204301077662*^9}, {3.632043063037609*^9, 3.6320430712580795`*^9}, {3.632043120691907*^9, 3.632043161148221*^9}, { 3.6320432062678013`*^9, 3.6320432094549837`*^9}, 3.632043258394783*^9, { 3.632043351071084*^9, 3.632043352668175*^9}, {3.6345677461009674`*^9, 3.634568027044036*^9}, 3.634568059784909*^9, {3.6345686692177663`*^9, 3.6345687304812703`*^9}, {3.634568765543276*^9, 3.634568827443816*^9}, { 3.6346120324026976`*^9, 3.6346120417672334`*^9}, {3.6346121382917542`*^9, 3.6346122118989644`*^9}, {3.6346122814849443`*^9, 3.634612333070895*^9}, { 3.634612471677823*^9, 3.634612552263432*^9}, {3.6346125863993845`*^9, 3.6346126554953365`*^9}, {3.634612698763811*^9, 3.634612702163006*^9}, { 3.6348726356017313`*^9, 3.634872755937614*^9}, {3.634877631123617*^9, 3.6348776427762833`*^9}, {3.6348782474488688`*^9, 3.6348782744724145`*^9}, {3.63487832072106*^9, 3.634878440448908*^9}, { 3.6852817264030714`*^9, 3.6852817834531507`*^9}, {3.68794462572165*^9, 3.687944776911862*^9}, {3.6879451060223227`*^9, 3.6879451445423765`*^9}, { 3.6879452810225677`*^9, 3.6879452918025827`*^9}, {3.6879455589529567`*^9, 3.687945567592969*^9}, {3.6879456213830442`*^9, 3.6879456613631*^9}, { 3.6879457292931952`*^9, 3.6879457736132574`*^9}, {3.688022923252344*^9, 3.688023002982456*^9}, {3.6880230753425574`*^9, 3.688023230782775*^9}, 3.688023348002939*^9, {3.688023553833227*^9, 3.6880235620032387`*^9}, { 3.6880236295333333`*^9, 3.6880236382433453`*^9}, 3.6880237756035376`*^9, { 3.688031422416407*^9, 3.688031557816597*^9}, {3.6881117497443466`*^9, 3.688111797854414*^9}, {3.6881166477118034`*^9, 3.688116649471806*^9}, { 3.688118444084318*^9, 3.6881185798545084`*^9}, {3.688118642824597*^9, 3.688118799384816*^9}, {3.688118855204894*^9, 3.688118917084981*^9}, { 3.6881194959182944`*^9, 3.688119497718297*^9}, {3.6881196404384966`*^9, 3.688119655048517*^9}, {3.688119702888584*^9, 3.688119727678619*^9}, { 3.6881200919291286`*^9, 3.6881201295191813`*^9}, {3.6881202044892864`*^9, 3.688120237039332*^9}, {3.688120497669697*^9, 3.688120502989704*^9}, { 3.688120738340034*^9, 3.6881207493700495`*^9}, {3.6882745101002936`*^9, 3.6882745118602962`*^9}, {3.6883042728760366`*^9, 3.688304806616784*^9}, { 3.6883051027271986`*^9, 3.6883051086172066`*^9}, {3.6883054642977047`*^9, 3.6883054716377153`*^9}, {3.688306465909107*^9, 3.6883064729091167`*^9}, { 3.6883066024792986`*^9, 3.6883066550893717`*^9}, {3.6883071311300383`*^9, 3.688307145950059*^9}, 3.6883073798003864`*^9, {3.6887815904603148`*^9, 3.6887816040203333`*^9}, 3.6887816433103886`*^9, {3.6887816741004314`*^9, 3.688781699230467*^9}, {3.6887817847405863`*^9, 3.688781813880627*^9}, { 3.688781885830728*^9, 3.6887819020407505`*^9}, {3.6889574605581684`*^9, 3.688957501788226*^9}, {3.688960184803222*^9, 3.6889601992032423`*^9}, { 3.692771817740493*^9, 3.692771905640616*^9}, {3.6927726676816826`*^9, 3.6927727032617326`*^9}, {3.6927727333717747`*^9, 3.692772736561779*^9}, { 3.692772826191905*^9, 3.692772844901931*^9}, {3.692772893741999*^9, 3.6927728997420073`*^9}, {3.6927729636420975`*^9, 3.692773125862324*^9}, { 3.6927731981924257`*^9, 3.692773236352479*^9}, {3.6927732729025297`*^9, 3.692773282242543*^9}, {3.6927733353526173`*^9, 3.6927734137827272`*^9}, 3.6927736473730545`*^9, {3.6934868115444183`*^9, 3.693486813494421*^9}, { 3.6934868553944798`*^9, 3.693486917754567*^9}, {3.6934869973946786`*^9, 3.693487001174684*^9}, {3.6934870442947445`*^9, 3.6934870479747496`*^9}, { 3.693487349135171*^9, 3.6934873994352417`*^9}, {3.693487456975322*^9, 3.6934874585553246`*^9}, {3.6939897066669016`*^9, 3.6939897907970195`*^9}, {3.6939898244170666`*^9, 3.693989829937074*^9}, { 3.6939901042074585`*^9, 3.693990124237486*^9}, {3.69399018398757*^9, 3.6939902403476486`*^9}, {3.6939902781277018`*^9, 3.69399032732777*^9}, { 3.6939903908278594`*^9, 3.693990609328165*^9}, {3.693990640658209*^9, 3.693990673878256*^9}, {3.693990761178378*^9, 3.6939907769384003`*^9}, { 3.6939908128884506`*^9, 3.6939908380384855`*^9}, {3.6939908895785575`*^9, 3.6939908941885643`*^9}, {3.6939909859386926`*^9, 3.693991001898715*^9}, { 3.6939910395887675`*^9, 3.6939910643988028`*^9}, {3.693991107098862*^9, 3.6939911407889094`*^9}, {3.6939911957989864`*^9, 3.6939913838692493`*^9}, {3.6939918465598974`*^9, 3.693991856479911*^9}, { 3.6939919173699965`*^9, 3.6939919296100135`*^9}, {3.693991979330083*^9, 3.693992022780144*^9}, {3.6939921266502895`*^9, 3.6939921416103106`*^9}, { 3.6939921886903763`*^9, 3.693992235260442*^9}, {3.6939924451107354`*^9, 3.6939924757207785`*^9}, {3.6939925308708553`*^9, 3.693992535490862*^9}, { 3.69408137357989*^9, 3.6940813990399256`*^9}, {3.694081492270056*^9, 3.694081500430067*^9}, 3.694085807686309*^9, 3.694336369074993*^9, { 3.694336447585103*^9, 3.694336534165224*^9}, {3.6943365695452733`*^9, 3.694336572935278*^9}, {3.6943366355853662`*^9, 3.694336663395405*^9}, { 3.694336707865467*^9, 3.694336813505615*^9}, {3.6943368708856955`*^9, 3.694336972645838*^9}, {3.694337005795884*^9, 3.69433752400661*^9}, { 3.694337943297197*^9, 3.6943379730472383`*^9}, {3.694338096757412*^9, 3.694338100087416*^9}, {3.6943381564174953`*^9, 3.694338172057517*^9}, { 3.6943382111375713`*^9, 3.6943382179975815`*^9}, {3.694338370357795*^9, 3.694338415207857*^9}, {3.694338519908004*^9, 3.694338533448023*^9}, { 3.694338742738316*^9, 3.6943387845683746`*^9}, {3.6943388672484903`*^9, 3.694338909398549*^9}, {3.6943394389592905`*^9, 3.694339477079344*^9}, { 3.6943395685694723`*^9, 3.6943395881794996`*^9}, 3.6943396627096043`*^9, { 3.694339797119792*^9, 3.6943398030098004`*^9}, {3.6943398885999203`*^9, 3.6943400438301373`*^9}, {3.6943517756956816`*^9, 3.694351778765686*^9}, { 3.694351814965737*^9, 3.694351920335884*^9}, {3.6943520375260487`*^9, 3.694352038046049*^9}, {3.6943546301696777`*^9, 3.694354641489694*^9}, { 3.6943547065797853`*^9, 3.694354780889889*^9}, {3.694415922397947*^9, 3.694415933787963*^9}, {3.6944160021080585`*^9, 3.6944160163480783`*^9}, { 3.6944161612482815`*^9, 3.694416186218316*^9}, {3.6944162181183605`*^9, 3.694416241358393*^9}, {3.694416776009142*^9, 3.694416778289145*^9}, { 3.694417304849882*^9, 3.694417340579932*^9}, {3.6944179310727587`*^9, 3.6944179657728076`*^9}, {3.6944182927132654`*^9, 3.694418302313279*^9}, { 3.6944316170705633`*^9, 3.6944316923568697`*^9}, {3.6944318163219357`*^9, 3.694431820105152*^9}, {3.6965609549111967`*^9, 3.696560966061212*^9}, { 3.696560998851258*^9, 3.6965610020812626`*^9}, {3.6965611422314587`*^9, 3.696561159171482*^9}, 3.696563445644683*^9, {3.6965635186347857`*^9, 3.6965635322048044`*^9}, {3.696563569074856*^9, 3.6965635745148635`*^9}, { 3.696563720555068*^9, 3.69656372185507*^9}, {3.6965637807551527`*^9, 3.696563824135213*^9}, {3.6965639935254507`*^9, 3.696564031985504*^9}, { 3.696596096992402*^9, 3.696596186502527*^9}, {3.696596234252594*^9, 3.696596260452631*^9}, {3.6965963110027018`*^9, 3.69659632407272*^9}, 3.6965963803627987`*^9, {3.7244123642779827`*^9, 3.7244123648119507`*^9}, { 3.7255912428848085`*^9, 3.7255912492295227`*^9}, {3.725591466627203*^9, 3.725591704636403*^9}, {3.7255917405776634`*^9, 3.7255917613142586`*^9}, { 3.7255980783777914`*^9, 3.7255980873943977`*^9}, {3.725598135321295*^9, 3.7255981566673255`*^9}, {3.7255985463958807`*^9, 3.7255985750395555`*^9}, {3.725598660297285*^9, 3.725598669548276*^9}, { 3.7255989613446465`*^9, 3.7255989963014574`*^9}, {3.7255990922803245`*^9, 3.725599092624111*^9}, {3.7255991287997694`*^9, 3.7255991802271013`*^9}, 3.7255992673973975`*^9, {3.725599302619891*^9, 3.725599630275236*^9}, { 3.7255996917974653`*^9, 3.725600173598138*^9}, {3.72560026574846*^9, 3.7256002767652473`*^9}, 3.7256003308803263`*^9, {3.7256003995281887`*^9, 3.72560041238892*^9}, {3.725600503405278*^9, 3.725600537768276*^9}, { 3.72560062249599*^9, 3.725600660390954*^9}, {3.7256015423497496`*^9, 3.725601551460086*^9}, {3.725602674641403*^9, 3.725602676188448*^9}, { 3.725606737765007*^9, 3.7256067379681726`*^9}, {3.7259411263577843`*^9, 3.725941161974596*^9}, {3.7259413328141994`*^9, 3.7259413530325947`*^9}, { 3.725948620999795*^9, 3.7259486419857845`*^9}, 3.7259487502361426`*^9, { 3.725948801316684*^9, 3.7259488049789305`*^9}, {3.7259488747343755`*^9, 3.7259488880408845`*^9}, {3.7262144247900543`*^9, 3.7262144477456355`*^9}, {3.7574170493225684`*^9, 3.757417053184463*^9}, { 3.7831421588326306`*^9, 3.783142170925208*^9}, {3.783142395749114*^9, 3.7831425154306135`*^9}, {3.7831425557309313`*^9, 3.783142564092332*^9}, { 3.7831427526814885`*^9, 3.783142754255293*^9}, {3.7831428098757677`*^9, 3.7831428571042147`*^9}, {3.7834087348068304`*^9, 3.783408793037257*^9}, { 3.7834095081721888`*^9, 3.783409552999109*^9}, {3.783409588525758*^9, 3.7834095907684803`*^9}, {3.783409662061564*^9, 3.7834096810274954`*^9}, { 3.7834097163188562`*^9, 3.7834098893742294`*^9}, {3.7834100221449327`*^9, 3.783410060241215*^9}, {3.7834101051335173`*^9, 3.7834101131745987`*^9}, { 3.783410606354042*^9, 3.783410612361685*^9}, {3.783410755716464*^9, 3.7834107918890605`*^9}, {3.7834108581708117`*^9, 3.7834108764020586`*^9}, {3.7834159554758463`*^9, 3.7834161146811748`*^9}, {3.7834161647621775`*^9, 3.783416208755393*^9}, { 3.7834163179588566`*^9, 3.7834163817031116`*^9}, {3.7834164360783715`*^9, 3.7834164850567703`*^9}, {3.7834166132894554`*^9, 3.7834166233562546`*^9}, 3.783416674821188*^9, {3.783417354030015*^9, 3.7834173639170065`*^9}, 3.783417417707629*^9, {3.8146751632720823`*^9, 3.814675196666747*^9}, { 3.847249940282611*^9, 3.8472499529957237`*^9}}, CellLabel-> "In[182]:=",ExpressionUUID->"f67fddb7-31f7-4f35-a9f0-7e763617fabc"] }, Closed]], Cell[CellGroupData[{ Cell["PLANE ELEMENT (vibr) defs ", "Subsection", CellChangeTimes->{{3.7574178626155615`*^9, 3.757417866610338*^9}, { 3.7882369565320654`*^9, 3.788236957825534*^9}},ExpressionUUID->"27e33fef-e1d9-482f-ae22-\ 13ba3c4b5aa6"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "NN", ",", "INT", ",", "MID", ",", "r", ",", "e1", ",", "e2", ",", "e3", ",", "nn", ",", "FF", ",", "FFINV", ",", "jac", ",", "uvw", ",", "uvw0", ",", "uvw2", ",", "\[Epsilon]", ",", "\[Sigma]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "EEEE", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wine"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"Length", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "[", "3", "]"}], "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}]}], "}"}]}], ";", " ", RowBox[{ RowBox[{"NN", "[", "4", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"INT", "[", "3", "]"}], "=", "TRI7"}], ";", RowBox[{ RowBox[{"INT", "[", "4", "]"}], "=", "REC9"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"MID", "[", "3", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "3"}]}]}], "}"}]}], ";", " ", RowBox[{ RowBox[{"MID", "[", "4", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"element", " ", "plane"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{ RowBox[{"NN", "[", "nl", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"e1", ",", "e2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], "}"}], " ", "/.", RowBox[{"MID", "[", "nl", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"e3", "=", RowBox[{"e1", StyleBox["\[Cross]", "OperatorCharacter"], "e2"}]}], ";", "\[IndentingNewLine]", RowBox[{"nn", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"e3", "/", RowBox[{"Sqrt", "[", RowBox[{"e3", ".", "e3"}], "]"}]}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e1", ",", " ", "e2", ",", "nn"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{ RowBox[{"NN", "[", "nl", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"uvw", " ", "=", RowBox[{"uvw", "-", RowBox[{"e3", RowBox[{"(", RowBox[{"e3", ".", "uvw"}], ")"}]}]}]}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{"uvw0", "=", RowBox[{"uvw", "/.", " ", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"uvw2", "=", RowBox[{"uvw", "/.", " ", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "displacement", " ", "gradient", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "uvw0"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "uvw0"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "uvw0"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Plane", " ", "stress", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{"EEEE", "-", RowBox[{ RowBox[{"(", RowBox[{"EEEE", ".", "nn"}], ")"}], ".", RowBox[{"Inverse", "[", RowBox[{"nn", ".", "EEEE", ".", "nn"}], "]"}], ".", RowBox[{"(", RowBox[{"nn", ".", "EEEE"}], ")"}]}]}], "]"}]}], ";", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}], "*", "tt"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uvw0", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wine", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "uvw0", "]"}], ".", "uvw2"}]}], "*", "\[Rho]\[Rho]", "*", "tt"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"QUAD", "[", RowBox[{ RowBox[{"INT", "[", "nl", "]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wext", "+", "\[Delta]wint", "+", "\[Delta]wine"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426473093646455`*^9, 3.4426474078630457`*^9}, { 3.4426597184894*^9, 3.4426597783310003`*^9}, {3.442659859139*^9, 3.4426599679021997`*^9}, {3.4426601154852*^9, 3.442660125282*^9}, 3.4426603153866*^9, {3.4426606694491997`*^9, 3.442660676984*^9}, { 3.4426607660341997`*^9, 3.442660767017*^9}, {3.4426607970782003`*^9, 3.4426609236566*^9}, {3.4426609993859997`*^9, 3.442661000946*^9}, { 3.4426611720156*^9, 3.4426611866796*^9}, {3.4426612192836*^9, 3.4426612396104*^9}, {3.4426613536776*^9, 3.4426613563764*^9}, { 3.4426613962188*^9, 3.4426613966556*^9}, {3.443184440921*^9, 3.4431845165186*^9}, {3.4431848052298*^9, 3.4431848237002*^9}, { 3.4431849834618*^9, 3.4431849851934*^9}, {3.4431850342574*^9, 3.4431850385318003`*^9}, {3.4444402127514*^9, 3.4444402360889997`*^9}, { 3.44509636787*^9, 3.445096458974*^9}, {3.4450965569264*^9, 3.4450965855056*^9}, {3.4450966736612*^9, 3.4450967018348*^9}, 3.4450967876972*^9, {3.4451000792358*^9, 3.4451001019962*^9}, { 3.445132280975*^9, 3.4451322867782*^9}, 3.4451325631488*^9, 3.4451346101028*^9, {3.4455261966926003`*^9, 3.4455262691078*^9}, { 3.4455263543462*^9, 3.445526490113*^9}, {3.4455265305794*^9, 3.4455265347602*^9}, {3.4455267552349997`*^9, 3.4455267826754*^9}, 3.445526922233*^9, {3.445527218711*^9, 3.4455272895818*^9}, { 3.4455273640094*^9, 3.445527481259*^9}, 3.4455276192202*^9, { 3.4455278074376*^9, 3.4455278187164*^9}, {3.4455279660896*^9, 3.4455279742016*^9}, 3.4455280249016*^9, 3.4455285464407997`*^9, { 3.4461837560238*^9, 3.4461837697986*^9}, {3.446183892165*^9, 3.4461839004486*^9}, {3.4461839570142*^9, 3.4461841265550003`*^9}, 3.4461841729182*^9, {3.4461842101398*^9, 3.4461842206074*^9}, { 3.4461845241088*^9, 3.4461845410972*^9}, {3.4461845879440002`*^9, 3.4461847021516*^9}, {3.4461848428032*^9, 3.4461848544096003`*^9}, { 3.4461849111956*^9, 3.4461849123344*^9}, {3.4461850134868*^9, 3.446185058608*^9}, {3.4461852067616*^9, 3.446185223282*^9}, { 3.4461852548876*^9, 3.4461852626408*^9}, {3.4461853186604*^9, 3.446185320392*^9}, {3.4512642010481997`*^9, 3.451264207413*^9}, { 3.4512642788766003`*^9, 3.4512643136334*^9}, {3.4512643770006*^9, 3.4512644269362*^9}, {3.4512646983138*^9, 3.4512647384994*^9}, { 3.4512647823354*^9, 3.4512647868126*^9}, {3.4939932066616*^9, 3.4939932082060003`*^9}, {3.4939932399988003`*^9, 3.4939932614955997`*^9}, {3.493993300014*^9, 3.4939933073304*^9}, { 3.4939933992174*^9, 3.4939934078129997`*^9}, {3.4939934932314*^9, 3.493993515009*^9}, {3.4939935468556004`*^9, 3.493993568543*^9}, { 3.4939936486404*^9, 3.4939936621812*^9}, {3.4940328887262*^9, 3.4940328895218*^9}, {3.499487154582*^9, 3.49948716324*^9}, { 3.4994872083708*^9, 3.499487247324*^9}, {3.4994872822368*^9, 3.4994873816244*^9}, 3.499487417676*^9, {3.4994878504918003`*^9, 3.4994879045458*^9}, {3.4994879529370003`*^9, 3.4994879707794*^9}, { 3.4994880482042*^9, 3.4994880616826*^9}, {3.4994881084202003`*^9, 3.4994881177334003`*^9}, {3.4994884740218*^9, 3.4994884920554*^9}, { 3.4994885948282003`*^9, 3.4994886477434*^9}, {3.4994886790369997`*^9, 3.4994886860257998`*^9}, {3.4994887712953997`*^9, 3.4994887717478*^9}, { 3.6305517490219865`*^9, 3.6305518383945436`*^9}, 3.6305519329151096`*^9, { 3.6305521477354264`*^9, 3.6305521796235647`*^9}, {3.630552211063363*^9, 3.630552234159684*^9}, {3.6305523097380066`*^9, 3.6305523261429453`*^9}, { 3.630552400293186*^9, 3.630552443246643*^9}, {3.6305524899713154`*^9, 3.630552532581753*^9}, {3.630552564078554*^9, 3.630552660703081*^9}, { 3.6308069732471952`*^9, 3.6308070226836824`*^9}, {3.630831568112257*^9, 3.630831577359786*^9}, {3.632037136188613*^9, 3.6320372275628395`*^9}, { 3.632037282822*^9, 3.6320372864142056`*^9}, {3.632037326777514*^9, 3.6320373338819203`*^9}, {3.6320374068820953`*^9, 3.632037461262206*^9}, { 3.632037495368157*^9, 3.6320375996761227`*^9}, {3.632037657282418*^9, 3.6320377668306837`*^9}, {3.6320377993975463`*^9, 3.6320378258790607`*^9}, {3.6320379375314474`*^9, 3.632037944011818*^9}, { 3.632037974774577*^9, 3.63203804108137*^9}, {3.632038115937651*^9, 3.6320381168477035`*^9}, {3.632038171547832*^9, 3.6320381721648674`*^9}, { 3.6320382092969913`*^9, 3.6320382642141323`*^9}, 3.632038311238822*^9, { 3.6320383438376865`*^9, 3.6320384084533825`*^9}, {3.632038502612768*^9, 3.632038536966733*^9}, {3.6320386355663724`*^9, 3.632038663028943*^9}, { 3.6320387578143644`*^9, 3.632038876049127*^9}, {3.632038925681966*^9, 3.6320390116098804`*^9}, {3.6320390559574175`*^9, 3.632039057440502*^9}, { 3.6320390909984217`*^9, 3.6320392794842024`*^9}, {3.6320393098219376`*^9, 3.6320393228646836`*^9}, {3.6320393691423306`*^9, 3.632039469157051*^9}, { 3.6320395408921537`*^9, 3.6320395753041224`*^9}, {3.632039607865985*^9, 3.6320396287681804`*^9}, {3.632039834419943*^9, 3.6320399635053263`*^9}, { 3.632040008307889*^9, 3.632040011081047*^9}, {3.632040111200774*^9, 3.6320401709411907`*^9}, {3.6320402797014112`*^9, 3.6320403974661474`*^9}, {3.6320411172793183`*^9, 3.6320411297080293`*^9}, 3.632041280201637*^9, {3.632041357828077*^9, 3.632041361657296*^9}, { 3.632041402765647*^9, 3.632041437279621*^9}, 3.632041474164731*^9, { 3.6320415074596353`*^9, 3.632041548877004*^9}, {3.6320415931405363`*^9, 3.632041610919553*^9}, {3.632041656484159*^9, 3.6320416691688843`*^9}, { 3.6320420632294235`*^9, 3.6320420791513343`*^9}, {3.6320424482774467`*^9, 3.632042550289282*^9}, {3.632042803353756*^9, 3.632042928840934*^9}, { 3.632042961566806*^9, 3.63204301077662*^9}, {3.632043063037609*^9, 3.6320430712580795`*^9}, {3.632043120691907*^9, 3.632043161148221*^9}, { 3.6320432062678013`*^9, 3.6320432094549837`*^9}, 3.632043258394783*^9, { 3.632043351071084*^9, 3.632043352668175*^9}, {3.6345677461009674`*^9, 3.634568027044036*^9}, 3.634568059784909*^9, {3.6345686692177663`*^9, 3.6345687304812703`*^9}, {3.634568765543276*^9, 3.634568827443816*^9}, { 3.6346120324026976`*^9, 3.6346120417672334`*^9}, {3.6346121382917542`*^9, 3.6346122118989644`*^9}, {3.6346122814849443`*^9, 3.634612333070895*^9}, { 3.634612471677823*^9, 3.634612552263432*^9}, {3.6346125863993845`*^9, 3.6346126554953365`*^9}, {3.634612698763811*^9, 3.634612702163006*^9}, { 3.6348726356017313`*^9, 3.634872755937614*^9}, {3.634877631123617*^9, 3.6348776427762833`*^9}, {3.6348782474488688`*^9, 3.6348782744724145`*^9}, {3.63487832072106*^9, 3.634878440448908*^9}, { 3.6852817264030714`*^9, 3.6852817834531507`*^9}, {3.68794462572165*^9, 3.687944776911862*^9}, {3.6879451060223227`*^9, 3.6879451445423765`*^9}, { 3.6879452810225677`*^9, 3.6879452918025827`*^9}, {3.6879455589529567`*^9, 3.687945567592969*^9}, {3.6879456213830442`*^9, 3.6879456613631*^9}, { 3.6879457292931952`*^9, 3.6879457736132574`*^9}, {3.688022923252344*^9, 3.688023002982456*^9}, {3.6880230753425574`*^9, 3.688023230782775*^9}, 3.688023348002939*^9, {3.688023553833227*^9, 3.6880235620032387`*^9}, { 3.6880236295333333`*^9, 3.6880236382433453`*^9}, 3.6880237756035376`*^9, { 3.688031422416407*^9, 3.688031557816597*^9}, {3.6881117497443466`*^9, 3.688111797854414*^9}, {3.6881166477118034`*^9, 3.688116649471806*^9}, { 3.688118444084318*^9, 3.6881185798545084`*^9}, {3.688118642824597*^9, 3.688118799384816*^9}, {3.688118855204894*^9, 3.688118917084981*^9}, { 3.6881194959182944`*^9, 3.688119497718297*^9}, {3.6881196404384966`*^9, 3.688119655048517*^9}, {3.688119702888584*^9, 3.688119727678619*^9}, { 3.6881200919291286`*^9, 3.6881201295191813`*^9}, {3.6881202044892864`*^9, 3.688120237039332*^9}, {3.688120497669697*^9, 3.688120502989704*^9}, { 3.688120738340034*^9, 3.6881207493700495`*^9}, {3.6882745101002936`*^9, 3.6882745118602962`*^9}, {3.6883042728760366`*^9, 3.688304806616784*^9}, { 3.6883051027271986`*^9, 3.6883051086172066`*^9}, {3.6883054642977047`*^9, 3.6883054716377153`*^9}, {3.688306465909107*^9, 3.6883064729091167`*^9}, { 3.6883066024792986`*^9, 3.6883066550893717`*^9}, {3.6883071311300383`*^9, 3.688307145950059*^9}, 3.6883073798003864`*^9, {3.6887815904603148`*^9, 3.6887816040203333`*^9}, 3.6887816433103886`*^9, {3.6887816741004314`*^9, 3.688781699230467*^9}, {3.6887817847405863`*^9, 3.688781813880627*^9}, { 3.688781885830728*^9, 3.6887819020407505`*^9}, {3.6889574605581684`*^9, 3.688957501788226*^9}, {3.688960184803222*^9, 3.6889601992032423`*^9}, { 3.692771817740493*^9, 3.692771905640616*^9}, {3.6927726676816826`*^9, 3.6927727032617326`*^9}, {3.6927727333717747`*^9, 3.692772736561779*^9}, { 3.692772826191905*^9, 3.692772844901931*^9}, {3.692772893741999*^9, 3.6927728997420073`*^9}, {3.6927729636420975`*^9, 3.692773125862324*^9}, { 3.6927731981924257`*^9, 3.692773236352479*^9}, {3.6927732729025297`*^9, 3.692773282242543*^9}, {3.6927733353526173`*^9, 3.6927734137827272`*^9}, 3.6927736473730545`*^9, {3.6934868115444183`*^9, 3.693486813494421*^9}, { 3.6934868553944798`*^9, 3.693486917754567*^9}, {3.6934869973946786`*^9, 3.693487001174684*^9}, {3.6934870442947445`*^9, 3.6934870479747496`*^9}, { 3.693487349135171*^9, 3.6934873994352417`*^9}, {3.693487456975322*^9, 3.6934874585553246`*^9}, {3.6939897066669016`*^9, 3.6939897907970195`*^9}, {3.6939898244170666`*^9, 3.693989829937074*^9}, { 3.6939901042074585`*^9, 3.693990124237486*^9}, {3.69399018398757*^9, 3.6939902403476486`*^9}, {3.6939902781277018`*^9, 3.69399032732777*^9}, { 3.6939903908278594`*^9, 3.693990609328165*^9}, {3.693990640658209*^9, 3.693990673878256*^9}, {3.693990761178378*^9, 3.6939907769384003`*^9}, { 3.6939908128884506`*^9, 3.6939908380384855`*^9}, {3.6939908895785575`*^9, 3.6939908941885643`*^9}, {3.6939909859386926`*^9, 3.693991001898715*^9}, { 3.6939910395887675`*^9, 3.6939910643988028`*^9}, {3.693991107098862*^9, 3.6939911407889094`*^9}, {3.6939911957989864`*^9, 3.6939913838692493`*^9}, {3.6939918465598974`*^9, 3.693991856479911*^9}, { 3.6939919173699965`*^9, 3.6939919296100135`*^9}, {3.693991979330083*^9, 3.693992022780144*^9}, {3.6939921266502895`*^9, 3.6939921416103106`*^9}, { 3.6939921886903763`*^9, 3.693992235260442*^9}, {3.6939924451107354`*^9, 3.6939924757207785`*^9}, {3.6939925308708553`*^9, 3.693992535490862*^9}, { 3.69408137357989*^9, 3.6940813990399256`*^9}, {3.694081492270056*^9, 3.694081500430067*^9}, 3.694085807686309*^9, 3.694336369074993*^9, { 3.694336447585103*^9, 3.694336534165224*^9}, {3.6943365695452733`*^9, 3.694336572935278*^9}, {3.6943366355853662`*^9, 3.694336663395405*^9}, { 3.694336707865467*^9, 3.694336813505615*^9}, {3.6943368708856955`*^9, 3.694336972645838*^9}, {3.694337005795884*^9, 3.69433752400661*^9}, { 3.694337943297197*^9, 3.6943379730472383`*^9}, {3.694338096757412*^9, 3.694338100087416*^9}, {3.6943381564174953`*^9, 3.694338172057517*^9}, { 3.6943382111375713`*^9, 3.6943382179975815`*^9}, {3.694338370357795*^9, 3.694338415207857*^9}, {3.694338519908004*^9, 3.694338533448023*^9}, { 3.694338742738316*^9, 3.6943387845683746`*^9}, {3.6943388672484903`*^9, 3.694338909398549*^9}, {3.6943394389592905`*^9, 3.694339477079344*^9}, { 3.6943395685694723`*^9, 3.6943395881794996`*^9}, 3.6943396627096043`*^9, { 3.694339797119792*^9, 3.6943398030098004`*^9}, {3.6943398885999203`*^9, 3.6943400438301373`*^9}, {3.6943517756956816`*^9, 3.694351778765686*^9}, { 3.694351814965737*^9, 3.694351920335884*^9}, {3.6943520375260487`*^9, 3.694352038046049*^9}, {3.6943546301696777`*^9, 3.694354641489694*^9}, { 3.6943547065797853`*^9, 3.694354780889889*^9}, {3.694415922397947*^9, 3.694415933787963*^9}, {3.6944160021080585`*^9, 3.6944160163480783`*^9}, { 3.6944161612482815`*^9, 3.694416186218316*^9}, {3.6944162181183605`*^9, 3.694416241358393*^9}, {3.694416776009142*^9, 3.694416778289145*^9}, { 3.694417304849882*^9, 3.694417340579932*^9}, {3.6944179310727587`*^9, 3.6944179657728076`*^9}, {3.6944182927132654`*^9, 3.694418302313279*^9}, { 3.6944316170705633`*^9, 3.6944316923568697`*^9}, {3.6944318163219357`*^9, 3.694431820105152*^9}, {3.6965609549111967`*^9, 3.696560966061212*^9}, { 3.696560998851258*^9, 3.6965610020812626`*^9}, {3.6965611422314587`*^9, 3.696561159171482*^9}, 3.696563445644683*^9, {3.6965635186347857`*^9, 3.6965635322048044`*^9}, {3.696563569074856*^9, 3.6965635745148635`*^9}, { 3.696563720555068*^9, 3.69656372185507*^9}, {3.6965637807551527`*^9, 3.696563824135213*^9}, {3.6965639935254507`*^9, 3.696564031985504*^9}, { 3.696596096992402*^9, 3.696596186502527*^9}, {3.696596234252594*^9, 3.696596260452631*^9}, {3.6965963110027018`*^9, 3.69659632407272*^9}, 3.6965963803627987`*^9, {3.7244123642779827`*^9, 3.7244123648119507`*^9}, { 3.7255912428848085`*^9, 3.7255912492295227`*^9}, {3.725591466627203*^9, 3.725591704636403*^9}, {3.7255917405776634`*^9, 3.7255917613142586`*^9}, { 3.7255980783777914`*^9, 3.7255980873943977`*^9}, {3.725598135321295*^9, 3.7255981566673255`*^9}, {3.7255985463958807`*^9, 3.7255985750395555`*^9}, {3.725598660297285*^9, 3.725598669548276*^9}, { 3.7255989613446465`*^9, 3.7255989963014574`*^9}, {3.7255990922803245`*^9, 3.725599092624111*^9}, {3.7255991287997694`*^9, 3.7255991802271013`*^9}, 3.7255992673973975`*^9, {3.725599302619891*^9, 3.725599630275236*^9}, { 3.7255996917974653`*^9, 3.725600173598138*^9}, {3.72560026574846*^9, 3.7256002767652473`*^9}, 3.7256003308803263`*^9, {3.7256003995281887`*^9, 3.72560041238892*^9}, {3.725600503405278*^9, 3.725600537768276*^9}, { 3.72560062249599*^9, 3.725600660390954*^9}, {3.7256015423497496`*^9, 3.725601551460086*^9}, {3.725602674641403*^9, 3.725602676188448*^9}, { 3.725606737765007*^9, 3.7256067379681726`*^9}, {3.7259411263577843`*^9, 3.725941161974596*^9}, {3.7259413328141994`*^9, 3.7259413530325947`*^9}, { 3.725948620999795*^9, 3.7259486419857845`*^9}, 3.7259487502361426`*^9, { 3.725948801316684*^9, 3.7259488049789305`*^9}, {3.7259488747343755`*^9, 3.7259488880408845`*^9}, {3.7262144247900543`*^9, 3.7262144477456355`*^9}, {3.7574170493225684`*^9, 3.757417053184463*^9}, 3.7574180050911236`*^9, {3.7882499486380305`*^9, 3.788249965805548*^9}, 3.788250180826583*^9, {3.7882504752171006`*^9, 3.788250476401018*^9}, { 3.788250589938117*^9, 3.788250591161209*^9}, {3.7882506821511555`*^9, 3.7882506894349337`*^9}, {3.8146753539411077`*^9, 3.814675358135168*^9}, { 3.8200284878289385`*^9, 3.8200284930218515`*^9}, {3.820028529332723*^9, 3.8200285764790335`*^9}}, CellLabel-> "In[184]:=",ExpressionUUID->"789ff18c-02c4-4c25-92e6-da4904f027bb"] }, Closed]], Cell[CellGroupData[{ Cell["PLANE ELEMENT (stab) defs ", "Subsection", CellChangeTimes->{{3.766140428784856*^9, 3.7661404367673664`*^9}, { 3.78824987025541*^9, 3.788249871040884*^9}, {3.7890213529026747`*^9, 3.7890213537383194`*^9}},ExpressionUUID->"40bab93a-cb0f-46ed-887b-\ 7b7a9234f336"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426473093646455`*^9, 3.4426474078630457`*^9}, { 3.4426597184894*^9, 3.4426597783310003`*^9}, {3.442659859139*^9, 3.4426599679021997`*^9}, {3.4426601154852*^9, 3.442660125282*^9}, 3.4426603153866*^9, {3.4426606694491997`*^9, 3.442660676984*^9}, { 3.4426607660341997`*^9, 3.442660767017*^9}, {3.4426607970782003`*^9, 3.4426609236566*^9}, {3.4426609993859997`*^9, 3.442661000946*^9}, { 3.4426611720156*^9, 3.4426611866796*^9}, {3.4426612192836*^9, 3.4426612396104*^9}, {3.4426613536776*^9, 3.4426613563764*^9}, { 3.4426613962188*^9, 3.4426613966556*^9}, {3.443184440921*^9, 3.4431845165186*^9}, {3.4431848052298*^9, 3.4431848237002*^9}, { 3.4431849834618*^9, 3.4431849851934*^9}, {3.4431850342574*^9, 3.4431850385318003`*^9}, {3.4444402127514*^9, 3.4444402360889997`*^9}, { 3.44509636787*^9, 3.445096458974*^9}, {3.4450965569264*^9, 3.4450965855056*^9}, {3.4450966736612*^9, 3.4450967018348*^9}, 3.4450967876972*^9, {3.4451000792358*^9, 3.4451001019962*^9}, { 3.445132280975*^9, 3.4451322867782*^9}, 3.4451325631488*^9, 3.4451346101028*^9, {3.4455261966926003`*^9, 3.4455262691078*^9}, { 3.4455263543462*^9, 3.445526490113*^9}, {3.4455265305794*^9, 3.4455265347602*^9}, {3.4455267552349997`*^9, 3.4455267826754*^9}, 3.445526922233*^9, {3.445527218711*^9, 3.4455272895818*^9}, { 3.4455273640094*^9, 3.445527481259*^9}, 3.4455276192202*^9, { 3.4455278074376*^9, 3.4455278187164*^9}, {3.4455279660896*^9, 3.4455279742016*^9}, 3.4455280249016*^9, 3.4455285464407997`*^9, { 3.4461837560238*^9, 3.4461837697986*^9}, {3.446183892165*^9, 3.4461839004486*^9}, {3.4461839570142*^9, 3.4461841265550003`*^9}, 3.4461841729182*^9, {3.4461842101398*^9, 3.4461842206074*^9}, { 3.4461845241088*^9, 3.4461845410972*^9}, {3.4461845879440002`*^9, 3.4461847021516*^9}, {3.4461848428032*^9, 3.4461848544096003`*^9}, { 3.4461849111956*^9, 3.4461849123344*^9}, {3.4461850134868*^9, 3.446185058608*^9}, {3.4461852067616*^9, 3.446185223282*^9}, { 3.4461852548876*^9, 3.4461852626408*^9}, {3.4461853186604*^9, 3.446185320392*^9}, {3.4512642010481997`*^9, 3.451264207413*^9}, { 3.4512642788766003`*^9, 3.4512643136334*^9}, {3.4512643770006*^9, 3.4512644269362*^9}, {3.4512646983138*^9, 3.4512647384994*^9}, { 3.4512647823354*^9, 3.4512647868126*^9}, {3.4939932066616*^9, 3.4939932082060003`*^9}, {3.4939932399988003`*^9, 3.4939932614955997`*^9}, {3.493993300014*^9, 3.4939933073304*^9}, { 3.4939933992174*^9, 3.4939934078129997`*^9}, {3.4939934932314*^9, 3.493993515009*^9}, {3.4939935468556004`*^9, 3.493993568543*^9}, { 3.4939936486404*^9, 3.4939936621812*^9}, {3.4940328887262*^9, 3.4940328895218*^9}, {3.499487154582*^9, 3.49948716324*^9}, { 3.4994872083708*^9, 3.499487247324*^9}, {3.4994872822368*^9, 3.4994873816244*^9}, 3.499487417676*^9, {3.4994878504918003`*^9, 3.4994879045458*^9}, {3.4994879529370003`*^9, 3.4994879707794*^9}, { 3.4994880482042*^9, 3.4994880616826*^9}, {3.4994881084202003`*^9, 3.4994881177334003`*^9}, {3.4994884740218*^9, 3.4994884920554*^9}, { 3.4994885948282003`*^9, 3.4994886477434*^9}, {3.4994886790369997`*^9, 3.4994886860257998`*^9}, {3.4994887712953997`*^9, 3.4994887717478*^9}, { 3.6305517490219865`*^9, 3.6305518383945436`*^9}, 3.6305519329151096`*^9, { 3.6305521477354264`*^9, 3.6305521796235647`*^9}, {3.630552211063363*^9, 3.630552234159684*^9}, {3.6305523097380066`*^9, 3.6305523261429453`*^9}, { 3.630552400293186*^9, 3.630552443246643*^9}, {3.6305524899713154`*^9, 3.630552532581753*^9}, {3.630552564078554*^9, 3.630552660703081*^9}, { 3.6308069732471952`*^9, 3.6308070226836824`*^9}, {3.630831568112257*^9, 3.630831577359786*^9}, {3.632037136188613*^9, 3.6320372275628395`*^9}, { 3.632037282822*^9, 3.6320372864142056`*^9}, {3.632037326777514*^9, 3.6320373338819203`*^9}, {3.6320374068820953`*^9, 3.632037461262206*^9}, { 3.632037495368157*^9, 3.6320375996761227`*^9}, {3.632037657282418*^9, 3.6320377668306837`*^9}, {3.6320377993975463`*^9, 3.6320378258790607`*^9}, {3.6320379375314474`*^9, 3.632037944011818*^9}, { 3.632037974774577*^9, 3.63203804108137*^9}, {3.632038115937651*^9, 3.6320381168477035`*^9}, {3.632038171547832*^9, 3.6320381721648674`*^9}, { 3.6320382092969913`*^9, 3.6320382642141323`*^9}, 3.632038311238822*^9, { 3.6320383438376865`*^9, 3.6320384084533825`*^9}, {3.632038502612768*^9, 3.632038536966733*^9}, {3.6320386355663724`*^9, 3.632038663028943*^9}, { 3.6320387578143644`*^9, 3.632038876049127*^9}, {3.632038925681966*^9, 3.6320390116098804`*^9}, {3.6320390559574175`*^9, 3.632039057440502*^9}, { 3.6320390909984217`*^9, 3.6320392794842024`*^9}, {3.6320393098219376`*^9, 3.6320393228646836`*^9}, {3.6320393691423306`*^9, 3.632039469157051*^9}, { 3.6320395408921537`*^9, 3.6320395753041224`*^9}, {3.632039607865985*^9, 3.6320396287681804`*^9}, {3.632039834419943*^9, 3.6320399635053263`*^9}, { 3.632040008307889*^9, 3.632040011081047*^9}, {3.632040111200774*^9, 3.6320401709411907`*^9}, {3.6320402797014112`*^9, 3.6320403974661474`*^9}, {3.6320411172793183`*^9, 3.6320411297080293`*^9}, 3.632041280201637*^9, {3.632041357828077*^9, 3.632041361657296*^9}, { 3.632041402765647*^9, 3.632041437279621*^9}, 3.632041474164731*^9, { 3.6320415074596353`*^9, 3.632041548877004*^9}, {3.6320415931405363`*^9, 3.632041610919553*^9}, {3.632041656484159*^9, 3.6320416691688843`*^9}, { 3.6320420632294235`*^9, 3.6320420791513343`*^9}, {3.6320424482774467`*^9, 3.632042550289282*^9}, {3.632042803353756*^9, 3.632042928840934*^9}, { 3.632042961566806*^9, 3.63204301077662*^9}, {3.632043063037609*^9, 3.6320430712580795`*^9}, {3.632043120691907*^9, 3.632043161148221*^9}, { 3.6320432062678013`*^9, 3.6320432094549837`*^9}, 3.632043258394783*^9, { 3.632043351071084*^9, 3.632043352668175*^9}, {3.6345677461009674`*^9, 3.634568027044036*^9}, 3.634568059784909*^9, {3.6345686692177663`*^9, 3.6345687304812703`*^9}, {3.634568765543276*^9, 3.634568827443816*^9}, { 3.6346120324026976`*^9, 3.6346120417672334`*^9}, {3.6346121382917542`*^9, 3.6346122118989644`*^9}, {3.6346122814849443`*^9, 3.634612333070895*^9}, { 3.634612471677823*^9, 3.634612552263432*^9}, {3.6346125863993845`*^9, 3.6346126554953365`*^9}, {3.634612698763811*^9, 3.634612702163006*^9}, { 3.6348726356017313`*^9, 3.634872755937614*^9}, {3.634877631123617*^9, 3.6348776427762833`*^9}, {3.6348782474488688`*^9, 3.6348782744724145`*^9}, {3.63487832072106*^9, 3.634878440448908*^9}, { 3.6852817264030714`*^9, 3.6852817834531507`*^9}, {3.68794462572165*^9, 3.687944776911862*^9}, {3.6879451060223227`*^9, 3.6879451445423765`*^9}, { 3.6879452810225677`*^9, 3.6879452918025827`*^9}, {3.6879455589529567`*^9, 3.687945567592969*^9}, {3.6879456213830442`*^9, 3.6879456613631*^9}, { 3.6879457292931952`*^9, 3.6879457736132574`*^9}, {3.688022923252344*^9, 3.688023002982456*^9}, {3.6880230753425574`*^9, 3.688023230782775*^9}, 3.688023348002939*^9, {3.688023553833227*^9, 3.6880235620032387`*^9}, { 3.6880236295333333`*^9, 3.6880236382433453`*^9}, 3.6880237756035376`*^9, { 3.688031422416407*^9, 3.688031557816597*^9}, {3.6881117497443466`*^9, 3.688111797854414*^9}, {3.6881166477118034`*^9, 3.688116649471806*^9}, { 3.688118444084318*^9, 3.6881185798545084`*^9}, {3.688118642824597*^9, 3.688118799384816*^9}, {3.688118855204894*^9, 3.688118917084981*^9}, { 3.6881194959182944`*^9, 3.688119497718297*^9}, {3.6881196404384966`*^9, 3.688119655048517*^9}, {3.688119702888584*^9, 3.688119727678619*^9}, { 3.6881200919291286`*^9, 3.6881201295191813`*^9}, {3.6881202044892864`*^9, 3.688120237039332*^9}, {3.688120497669697*^9, 3.688120502989704*^9}, { 3.688120738340034*^9, 3.6881207493700495`*^9}, {3.6882745101002936`*^9, 3.6882745118602962`*^9}, {3.6883042728760366`*^9, 3.688304806616784*^9}, { 3.6883051027271986`*^9, 3.6883051086172066`*^9}, {3.6883054642977047`*^9, 3.6883054716377153`*^9}, {3.688306465909107*^9, 3.6883064729091167`*^9}, { 3.6883066024792986`*^9, 3.6883066550893717`*^9}, {3.6883071311300383`*^9, 3.688307145950059*^9}, 3.6883073798003864`*^9, {3.6887815904603148`*^9, 3.6887816040203333`*^9}, 3.6887816433103886`*^9, {3.6887816741004314`*^9, 3.688781699230467*^9}, {3.6887817847405863`*^9, 3.688781813880627*^9}, { 3.688781885830728*^9, 3.6887819020407505`*^9}, {3.6889574605581684`*^9, 3.688957501788226*^9}, {3.688960184803222*^9, 3.6889601992032423`*^9}, { 3.692771817740493*^9, 3.692771905640616*^9}, {3.6927726676816826`*^9, 3.6927727032617326`*^9}, {3.6927727333717747`*^9, 3.692772736561779*^9}, { 3.692772826191905*^9, 3.692772844901931*^9}, {3.692772893741999*^9, 3.6927728997420073`*^9}, {3.6927729636420975`*^9, 3.692773125862324*^9}, { 3.6927731981924257`*^9, 3.692773236352479*^9}, {3.6927732729025297`*^9, 3.692773282242543*^9}, {3.6927733353526173`*^9, 3.6927734137827272`*^9}, 3.6927736473730545`*^9, {3.6934868115444183`*^9, 3.693486813494421*^9}, { 3.6934868553944798`*^9, 3.693486917754567*^9}, {3.6934869973946786`*^9, 3.693487001174684*^9}, {3.6934870442947445`*^9, 3.6934870479747496`*^9}, { 3.693487349135171*^9, 3.6934873994352417`*^9}, {3.693487456975322*^9, 3.6934874585553246`*^9}, {3.6939897066669016`*^9, 3.6939897907970195`*^9}, {3.6939898244170666`*^9, 3.693989829937074*^9}, { 3.6939901042074585`*^9, 3.693990124237486*^9}, {3.69399018398757*^9, 3.6939902403476486`*^9}, {3.6939902781277018`*^9, 3.69399032732777*^9}, { 3.6939903908278594`*^9, 3.693990609328165*^9}, {3.693990640658209*^9, 3.693990673878256*^9}, {3.693990761178378*^9, 3.6939907769384003`*^9}, { 3.6939908128884506`*^9, 3.6939908380384855`*^9}, {3.6939908895785575`*^9, 3.6939908941885643`*^9}, {3.6939909859386926`*^9, 3.693991001898715*^9}, { 3.6939910395887675`*^9, 3.6939910643988028`*^9}, {3.693991107098862*^9, 3.6939911407889094`*^9}, {3.6939911957989864`*^9, 3.6939913838692493`*^9}, {3.6939918465598974`*^9, 3.693991856479911*^9}, { 3.6939919173699965`*^9, 3.6939919296100135`*^9}, {3.693991979330083*^9, 3.693992022780144*^9}, {3.6939921266502895`*^9, 3.6939921416103106`*^9}, { 3.6939921886903763`*^9, 3.693992235260442*^9}, {3.6939924451107354`*^9, 3.6939924757207785`*^9}, {3.6939925308708553`*^9, 3.693992535490862*^9}, { 3.69408137357989*^9, 3.6940813990399256`*^9}, {3.694081492270056*^9, 3.694081500430067*^9}, 3.694085807686309*^9, 3.694336369074993*^9, { 3.694336447585103*^9, 3.694336534165224*^9}, {3.6943365695452733`*^9, 3.694336572935278*^9}, {3.6943366355853662`*^9, 3.694336663395405*^9}, { 3.694336707865467*^9, 3.694336813505615*^9}, {3.6943368708856955`*^9, 3.694336972645838*^9}, {3.694337005795884*^9, 3.69433752400661*^9}, { 3.694337943297197*^9, 3.6943379730472383`*^9}, {3.694338096757412*^9, 3.694338100087416*^9}, {3.6943381564174953`*^9, 3.694338172057517*^9}, { 3.6943382111375713`*^9, 3.6943382179975815`*^9}, {3.694338370357795*^9, 3.694338415207857*^9}, {3.694338519908004*^9, 3.694338533448023*^9}, { 3.694338742738316*^9, 3.6943387845683746`*^9}, {3.6943388672484903`*^9, 3.694338909398549*^9}, {3.6943394389592905`*^9, 3.694339477079344*^9}, { 3.6943395685694723`*^9, 3.6943395881794996`*^9}, 3.6943396627096043`*^9, { 3.694339797119792*^9, 3.6943398030098004`*^9}, {3.6943398885999203`*^9, 3.6943400438301373`*^9}, {3.6943517756956816`*^9, 3.694351778765686*^9}, { 3.694351814965737*^9, 3.694351920335884*^9}, {3.6943520375260487`*^9, 3.694352038046049*^9}, {3.6943546301696777`*^9, 3.694354641489694*^9}, { 3.6943547065797853`*^9, 3.694354780889889*^9}, {3.694415922397947*^9, 3.694415933787963*^9}, {3.6944160021080585`*^9, 3.6944160163480783`*^9}, { 3.6944161612482815`*^9, 3.694416186218316*^9}, {3.6944162181183605`*^9, 3.694416241358393*^9}, {3.694416776009142*^9, 3.694416778289145*^9}, { 3.694417304849882*^9, 3.694417340579932*^9}, {3.6944179310727587`*^9, 3.6944179657728076`*^9}, {3.6944182927132654`*^9, 3.694418302313279*^9}, { 3.6944316170705633`*^9, 3.6944316923568697`*^9}, {3.6944318163219357`*^9, 3.694431820105152*^9}, {3.6965609549111967`*^9, 3.696560966061212*^9}, { 3.696560998851258*^9, 3.6965610020812626`*^9}, {3.6965611422314587`*^9, 3.696561159171482*^9}, 3.696563445644683*^9, {3.6965635186347857`*^9, 3.6965635322048044`*^9}, {3.696563569074856*^9, 3.6965635745148635`*^9}, { 3.696563720555068*^9, 3.69656372185507*^9}, {3.6965637807551527`*^9, 3.696563824135213*^9}, {3.6965639935254507`*^9, 3.696564031985504*^9}, { 3.696596096992402*^9, 3.696596186502527*^9}, {3.696596234252594*^9, 3.696596260452631*^9}, {3.6965963110027018`*^9, 3.69659632407272*^9}, 3.6965963803627987`*^9, {3.7244123642779827`*^9, 3.7244123648119507`*^9}, { 3.7255912428848085`*^9, 3.7255912492295227`*^9}, {3.725591466627203*^9, 3.725591704636403*^9}, {3.7255917405776634`*^9, 3.7255917613142586`*^9}, { 3.7255980783777914`*^9, 3.7255980873943977`*^9}, {3.725598135321295*^9, 3.7255981566673255`*^9}, {3.7255985463958807`*^9, 3.7255985750395555`*^9}, {3.725598660297285*^9, 3.725598669548276*^9}, { 3.7255989613446465`*^9, 3.7255989963014574`*^9}, {3.7255990922803245`*^9, 3.725599092624111*^9}, {3.7255991287997694`*^9, 3.7255991802271013`*^9}, 3.7255992673973975`*^9, {3.725599302619891*^9, 3.725599630275236*^9}, { 3.7255996917974653`*^9, 3.725600173598138*^9}, {3.72560026574846*^9, 3.7256002767652473`*^9}, 3.7256003308803263`*^9, {3.7256003995281887`*^9, 3.72560041238892*^9}, {3.725600503405278*^9, 3.725600537768276*^9}, { 3.72560062249599*^9, 3.725600660390954*^9}, {3.7256015423497496`*^9, 3.725601551460086*^9}, {3.725602674641403*^9, 3.725602676188448*^9}, { 3.725606737765007*^9, 3.7256067379681726`*^9}, {3.7259411263577843`*^9, 3.725941161974596*^9}, {3.7259413328141994`*^9, 3.7259413530325947`*^9}, { 3.725948620999795*^9, 3.7259486419857845`*^9}, 3.7259487502361426`*^9, { 3.725948801316684*^9, 3.7259488049789305`*^9}, {3.7259488747343755`*^9, 3.7259488880408845`*^9}, {3.7262144247900543`*^9, 3.7262144477456355`*^9}, {3.7574170493225684`*^9, 3.757417053184463*^9}, { 3.7831421588326306`*^9, 3.783142170925208*^9}, {3.783142395749114*^9, 3.7831425154306135`*^9}, {3.7831425557309313`*^9, 3.783142564092332*^9}, { 3.7831427526814885`*^9, 3.783142754255293*^9}, {3.7831428098757677`*^9, 3.7831428571042147`*^9}, {3.7834087348068304`*^9, 3.783408793037257*^9}, { 3.7834095081721888`*^9, 3.783409552999109*^9}, {3.783409588525758*^9, 3.7834095907684803`*^9}, {3.783409662061564*^9, 3.7834096810274954`*^9}, { 3.7834097163188562`*^9, 3.7834098893742294`*^9}, {3.7834100221449327`*^9, 3.783410060241215*^9}, {3.7834101051335173`*^9, 3.7834101131745987`*^9}, { 3.783410606354042*^9, 3.783410612361685*^9}, {3.783410755716464*^9, 3.7834107918890605`*^9}, {3.7834108581708117`*^9, 3.7834108764020586`*^9}, {3.783656780899205*^9, 3.783656816754212*^9}, { 3.783656906347945*^9, 3.783656914312093*^9}, {3.783657051037856*^9, 3.7836572912656827`*^9}, {3.783657346545521*^9, 3.7836573583072553`*^9}, { 3.783657399653203*^9, 3.783657405924858*^9}, {3.78365743635863*^9, 3.783657444445655*^9}, {3.783657544607131*^9, 3.7836575974442415`*^9}, { 3.784785690868435*^9, 3.7847857118559847`*^9}, {3.7847931085113173`*^9, 3.7847931143650365`*^9}, {3.784793162925936*^9, 3.784793168863771*^9}, { 3.788250819548458*^9, 3.7882508340994453`*^9}, {3.788250923421962*^9, 3.788250985225994*^9}, 3.7890213628913355`*^9, {3.789021393201993*^9, 3.789021408295926*^9}, {3.7890214429674954`*^9, 3.7890214979516497`*^9}, { 3.7890215681110067`*^9, 3.7890215803212132`*^9}, {3.7890216445484834`*^9, 3.789021733239565*^9}, {3.7890218407693024`*^9, 3.789021950403524*^9}}, CellLabel-> "In[186]:=",ExpressionUUID->"e30b30d1-f4fc-4b90-b189-ecf785028196"] }, Closed]], Cell[CellGroupData[{ Cell["PLANE ELEMENT (nonl) defs ", "Subsection", CellChangeTimes->{{3.7574169773814163`*^9, 3.7574169848245335`*^9}, { 3.7574180750707226`*^9, 3.757418078890803*^9}, {3.7577456071227565`*^9, 3.7577456152773933`*^9}, 3.790129668121153*^9},ExpressionUUID->"71983723-34bb-49cc-83f5-\ d5537d96e557"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "NN", ",", "INT", ",", "MID", ",", "DOM", ",", "r", ",", "e1", ",", "e2", ",", "e3", ",", "nn", ",", "FF", ",", "FFINV", ",", "jac", ",", "uvw", ",", "\[Epsilon]", ",", "\[Sigma]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "EEEE", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "FG", ",", "\[Delta]EG", ",", "EG", ",", "SS"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"Length", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "[", "3", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", RowBox[{ RowBox[{"NN", "[", "4", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"INT", "[", "3", "]"}], "=", "TRI7"}], ";", RowBox[{ RowBox[{"INT", "[", "4", "]"}], "=", "REC9"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"MID", "[", "3", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "3"}]}]}], "}"}]}], ";", " ", RowBox[{ RowBox[{"MID", "[", "4", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"DOM", "[", "4", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"DOM", "[", "3", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "orthonomal", " ", "basis", " ", "defined", " ", "by", " ", "the", " ", "mapping"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{ RowBox[{"NN", "[", "nl", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"e1", ",", "e2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], "}"}], " ", "/.", RowBox[{"MID", "[", "nl", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"e3", "=", RowBox[{"e1", StyleBox["\[Cross]", "OperatorCharacter"], "e2"}]}], ";", "\[IndentingNewLine]", RowBox[{"nn", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"e3", "/", RowBox[{"Sqrt", "[", RowBox[{"e3", ".", "e3"}], "]"}]}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e1", ",", " ", "e2", ",", " ", "nn"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{ RowBox[{"NN", "[", "nl", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "displacement", " ", "gradient", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"FG", "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "uvw"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"EG", "=", RowBox[{ RowBox[{"(", RowBox[{"FG", "+", RowBox[{"Transpose", "[", "FG", "]"}], "+", RowBox[{"FG", ".", RowBox[{"Transpose", "[", "FG", "]"}]}]}], ")"}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]EG", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]", "[", "FG", "]"}], "+", RowBox[{"Transpose", "[", RowBox[{"\[Delta]", "[", "FG", "]"}], "]"}], "+", RowBox[{ RowBox[{"\[Delta]", "[", "FG", "]"}], ".", RowBox[{"Transpose", "[", "FG", "]"}]}], "+", RowBox[{"FG", ".", RowBox[{"Transpose", "[", RowBox[{"\[Delta]", "[", "FG", "]"}], "]"}]}]}], ")"}], "/", "2"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Plane", " ", "stress", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{"EEEE", "-", RowBox[{ RowBox[{"(", RowBox[{"EEEE", ".", "nn"}], ")"}], ".", RowBox[{"Inverse", "[", RowBox[{"nn", ".", "EEEE", ".", "nn"}], "]"}], ".", RowBox[{"(", RowBox[{"nn", ".", "EEEE"}], ")"}]}]}], "]"}]}], ";", " ", "\[IndentingNewLine]", " ", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"SS", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"EG", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", "\[Delta]EG", "]"}], ".", RowBox[{"Flatten", "[", "SS", "]"}]}]}], " ", "tt"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"nl", "\[Equal]", "3"}], ",", RowBox[{"Return", "[", RowBox[{"QUAD", "[", RowBox[{ RowBox[{"INT", "[", "nl", "]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "]"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"nl", "\[Equal]", "4"}], ",", RowBox[{"Return", "[", RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}], StyleBox["\[Element]", "OperatorCharacter"], RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}], "]"}]}]}], "]"}], "]"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426473093646455`*^9, 3.4426474078630457`*^9}, { 3.4426597184894*^9, 3.4426597783310003`*^9}, {3.442659859139*^9, 3.4426599679021997`*^9}, {3.4426601154852*^9, 3.442660125282*^9}, 3.4426603153866*^9, {3.4426606694491997`*^9, 3.442660676984*^9}, { 3.4426607660341997`*^9, 3.442660767017*^9}, {3.4426607970782003`*^9, 3.4426609236566*^9}, {3.4426609993859997`*^9, 3.442661000946*^9}, { 3.4426611720156*^9, 3.4426611866796*^9}, {3.4426612192836*^9, 3.4426612396104*^9}, {3.4426613536776*^9, 3.4426613563764*^9}, { 3.4426613962188*^9, 3.4426613966556*^9}, {3.443184440921*^9, 3.4431845165186*^9}, {3.4431848052298*^9, 3.4431848237002*^9}, { 3.4431849834618*^9, 3.4431849851934*^9}, {3.4431850342574*^9, 3.4431850385318003`*^9}, {3.4444402127514*^9, 3.4444402360889997`*^9}, { 3.44509636787*^9, 3.445096458974*^9}, {3.4450965569264*^9, 3.4450965855056*^9}, {3.4450966736612*^9, 3.4450967018348*^9}, 3.4450967876972*^9, {3.4451000792358*^9, 3.4451001019962*^9}, { 3.445132280975*^9, 3.4451322867782*^9}, 3.4451325631488*^9, 3.4451346101028*^9, {3.4455261966926003`*^9, 3.4455262691078*^9}, { 3.4455263543462*^9, 3.445526490113*^9}, {3.4455265305794*^9, 3.4455265347602*^9}, {3.4455267552349997`*^9, 3.4455267826754*^9}, 3.445526922233*^9, {3.445527218711*^9, 3.4455272895818*^9}, { 3.4455273640094*^9, 3.445527481259*^9}, 3.4455276192202*^9, { 3.4455278074376*^9, 3.4455278187164*^9}, {3.4455279660896*^9, 3.4455279742016*^9}, 3.4455280249016*^9, 3.4455285464407997`*^9, { 3.4461837560238*^9, 3.4461837697986*^9}, {3.446183892165*^9, 3.4461839004486*^9}, {3.4461839570142*^9, 3.4461841265550003`*^9}, 3.4461841729182*^9, {3.4461842101398*^9, 3.4461842206074*^9}, { 3.4461845241088*^9, 3.4461845410972*^9}, {3.4461845879440002`*^9, 3.4461847021516*^9}, {3.4461848428032*^9, 3.4461848544096003`*^9}, { 3.4461849111956*^9, 3.4461849123344*^9}, {3.4461850134868*^9, 3.446185058608*^9}, {3.4461852067616*^9, 3.446185223282*^9}, { 3.4461852548876*^9, 3.4461852626408*^9}, {3.4461853186604*^9, 3.446185320392*^9}, {3.4512642010481997`*^9, 3.451264207413*^9}, { 3.4512642788766003`*^9, 3.4512643136334*^9}, {3.4512643770006*^9, 3.4512644269362*^9}, {3.4512646983138*^9, 3.4512647384994*^9}, { 3.4512647823354*^9, 3.4512647868126*^9}, {3.4939932066616*^9, 3.4939932082060003`*^9}, {3.4939932399988003`*^9, 3.4939932614955997`*^9}, {3.493993300014*^9, 3.4939933073304*^9}, { 3.4939933992174*^9, 3.4939934078129997`*^9}, {3.4939934932314*^9, 3.493993515009*^9}, {3.4939935468556004`*^9, 3.493993568543*^9}, { 3.4939936486404*^9, 3.4939936621812*^9}, {3.4940328887262*^9, 3.4940328895218*^9}, {3.499487154582*^9, 3.49948716324*^9}, { 3.4994872083708*^9, 3.499487247324*^9}, {3.4994872822368*^9, 3.4994873816244*^9}, 3.499487417676*^9, {3.4994878504918003`*^9, 3.4994879045458*^9}, {3.4994879529370003`*^9, 3.4994879707794*^9}, { 3.4994880482042*^9, 3.4994880616826*^9}, {3.4994881084202003`*^9, 3.4994881177334003`*^9}, {3.4994884740218*^9, 3.4994884920554*^9}, { 3.4994885948282003`*^9, 3.4994886477434*^9}, {3.4994886790369997`*^9, 3.4994886860257998`*^9}, {3.4994887712953997`*^9, 3.4994887717478*^9}, { 3.6305517490219865`*^9, 3.6305518383945436`*^9}, 3.6305519329151096`*^9, { 3.6305521477354264`*^9, 3.6305521796235647`*^9}, {3.630552211063363*^9, 3.630552234159684*^9}, {3.6305523097380066`*^9, 3.6305523261429453`*^9}, { 3.630552400293186*^9, 3.630552443246643*^9}, {3.6305524899713154`*^9, 3.630552532581753*^9}, {3.630552564078554*^9, 3.630552660703081*^9}, { 3.6308069732471952`*^9, 3.6308070226836824`*^9}, {3.630831568112257*^9, 3.630831577359786*^9}, {3.632037136188613*^9, 3.6320372275628395`*^9}, { 3.632037282822*^9, 3.6320372864142056`*^9}, {3.632037326777514*^9, 3.6320373338819203`*^9}, {3.6320374068820953`*^9, 3.632037461262206*^9}, { 3.632037495368157*^9, 3.6320375996761227`*^9}, {3.632037657282418*^9, 3.6320377668306837`*^9}, {3.6320377993975463`*^9, 3.6320378258790607`*^9}, {3.6320379375314474`*^9, 3.632037944011818*^9}, { 3.632037974774577*^9, 3.63203804108137*^9}, {3.632038115937651*^9, 3.6320381168477035`*^9}, {3.632038171547832*^9, 3.6320381721648674`*^9}, { 3.6320382092969913`*^9, 3.6320382642141323`*^9}, 3.632038311238822*^9, { 3.6320383438376865`*^9, 3.6320384084533825`*^9}, {3.632038502612768*^9, 3.632038536966733*^9}, {3.6320386355663724`*^9, 3.632038663028943*^9}, { 3.6320387578143644`*^9, 3.632038876049127*^9}, {3.632038925681966*^9, 3.6320390116098804`*^9}, {3.6320390559574175`*^9, 3.632039057440502*^9}, { 3.6320390909984217`*^9, 3.6320392794842024`*^9}, {3.6320393098219376`*^9, 3.6320393228646836`*^9}, {3.6320393691423306`*^9, 3.632039469157051*^9}, { 3.6320395408921537`*^9, 3.6320395753041224`*^9}, {3.632039607865985*^9, 3.6320396287681804`*^9}, {3.632039834419943*^9, 3.6320399635053263`*^9}, { 3.632040008307889*^9, 3.632040011081047*^9}, {3.632040111200774*^9, 3.6320401709411907`*^9}, {3.6320402797014112`*^9, 3.6320403974661474`*^9}, {3.6320411172793183`*^9, 3.6320411297080293`*^9}, 3.632041280201637*^9, {3.632041357828077*^9, 3.632041361657296*^9}, { 3.632041402765647*^9, 3.632041437279621*^9}, 3.632041474164731*^9, { 3.6320415074596353`*^9, 3.632041548877004*^9}, {3.6320415931405363`*^9, 3.632041610919553*^9}, {3.632041656484159*^9, 3.6320416691688843`*^9}, { 3.6320420632294235`*^9, 3.6320420791513343`*^9}, {3.6320424482774467`*^9, 3.632042550289282*^9}, {3.632042803353756*^9, 3.632042928840934*^9}, { 3.632042961566806*^9, 3.63204301077662*^9}, {3.632043063037609*^9, 3.6320430712580795`*^9}, {3.632043120691907*^9, 3.632043161148221*^9}, { 3.6320432062678013`*^9, 3.6320432094549837`*^9}, 3.632043258394783*^9, { 3.632043351071084*^9, 3.632043352668175*^9}, {3.6345677461009674`*^9, 3.634568027044036*^9}, 3.634568059784909*^9, {3.6345686692177663`*^9, 3.6345687304812703`*^9}, {3.634568765543276*^9, 3.634568827443816*^9}, { 3.6346120324026976`*^9, 3.6346120417672334`*^9}, {3.6346121382917542`*^9, 3.6346122118989644`*^9}, {3.6346122814849443`*^9, 3.634612333070895*^9}, { 3.634612471677823*^9, 3.634612552263432*^9}, {3.6346125863993845`*^9, 3.6346126554953365`*^9}, {3.634612698763811*^9, 3.634612702163006*^9}, { 3.6348726356017313`*^9, 3.634872755937614*^9}, {3.634877631123617*^9, 3.6348776427762833`*^9}, {3.6348782474488688`*^9, 3.6348782744724145`*^9}, {3.63487832072106*^9, 3.634878440448908*^9}, { 3.6852817264030714`*^9, 3.6852817834531507`*^9}, {3.68794462572165*^9, 3.687944776911862*^9}, {3.6879451060223227`*^9, 3.6879451445423765`*^9}, { 3.6879452810225677`*^9, 3.6879452918025827`*^9}, {3.6879455589529567`*^9, 3.687945567592969*^9}, {3.6879456213830442`*^9, 3.6879456613631*^9}, { 3.6879457292931952`*^9, 3.6879457736132574`*^9}, {3.688022923252344*^9, 3.688023002982456*^9}, {3.6880230753425574`*^9, 3.688023230782775*^9}, 3.688023348002939*^9, {3.688023553833227*^9, 3.6880235620032387`*^9}, { 3.6880236295333333`*^9, 3.6880236382433453`*^9}, 3.6880237756035376`*^9, { 3.688031422416407*^9, 3.688031557816597*^9}, {3.6881117497443466`*^9, 3.688111797854414*^9}, {3.6881166477118034`*^9, 3.688116649471806*^9}, { 3.688118444084318*^9, 3.6881185798545084`*^9}, {3.688118642824597*^9, 3.688118799384816*^9}, {3.688118855204894*^9, 3.688118917084981*^9}, { 3.6881194959182944`*^9, 3.688119497718297*^9}, {3.6881196404384966`*^9, 3.688119655048517*^9}, {3.688119702888584*^9, 3.688119727678619*^9}, { 3.6881200919291286`*^9, 3.6881201295191813`*^9}, {3.6881202044892864`*^9, 3.688120237039332*^9}, {3.688120497669697*^9, 3.688120502989704*^9}, { 3.688120738340034*^9, 3.6881207493700495`*^9}, {3.6882745101002936`*^9, 3.6882745118602962`*^9}, {3.6883042728760366`*^9, 3.688304806616784*^9}, { 3.6883051027271986`*^9, 3.6883051086172066`*^9}, {3.6883054642977047`*^9, 3.6883054716377153`*^9}, {3.688306465909107*^9, 3.6883064729091167`*^9}, { 3.6883066024792986`*^9, 3.6883066550893717`*^9}, {3.6883071311300383`*^9, 3.688307145950059*^9}, 3.6883073798003864`*^9, {3.6887815904603148`*^9, 3.6887816040203333`*^9}, 3.6887816433103886`*^9, {3.6887816741004314`*^9, 3.688781699230467*^9}, {3.6887817847405863`*^9, 3.688781813880627*^9}, { 3.688781885830728*^9, 3.6887819020407505`*^9}, {3.6889574605581684`*^9, 3.688957501788226*^9}, {3.688960184803222*^9, 3.6889601992032423`*^9}, { 3.692771817740493*^9, 3.692771905640616*^9}, {3.6927726676816826`*^9, 3.6927727032617326`*^9}, {3.6927727333717747`*^9, 3.692772736561779*^9}, { 3.692772826191905*^9, 3.692772844901931*^9}, {3.692772893741999*^9, 3.6927728997420073`*^9}, {3.6927729636420975`*^9, 3.692773125862324*^9}, { 3.6927731981924257`*^9, 3.692773236352479*^9}, {3.6927732729025297`*^9, 3.692773282242543*^9}, {3.6927733353526173`*^9, 3.6927734137827272`*^9}, 3.6927736473730545`*^9, {3.6934868115444183`*^9, 3.693486813494421*^9}, { 3.6934868553944798`*^9, 3.693486917754567*^9}, {3.6934869973946786`*^9, 3.693487001174684*^9}, {3.6934870442947445`*^9, 3.6934870479747496`*^9}, { 3.693487349135171*^9, 3.6934873994352417`*^9}, {3.693487456975322*^9, 3.6934874585553246`*^9}, {3.6939897066669016`*^9, 3.6939897907970195`*^9}, {3.6939898244170666`*^9, 3.693989829937074*^9}, { 3.6939901042074585`*^9, 3.693990124237486*^9}, {3.69399018398757*^9, 3.6939902403476486`*^9}, {3.6939902781277018`*^9, 3.69399032732777*^9}, { 3.6939903908278594`*^9, 3.693990609328165*^9}, {3.693990640658209*^9, 3.693990673878256*^9}, {3.693990761178378*^9, 3.6939907769384003`*^9}, { 3.6939908128884506`*^9, 3.6939908380384855`*^9}, {3.6939908895785575`*^9, 3.6939908941885643`*^9}, {3.6939909859386926`*^9, 3.693991001898715*^9}, { 3.6939910395887675`*^9, 3.6939910643988028`*^9}, {3.693991107098862*^9, 3.6939911407889094`*^9}, {3.6939911957989864`*^9, 3.6939913838692493`*^9}, {3.6939918465598974`*^9, 3.693991856479911*^9}, { 3.6939919173699965`*^9, 3.6939919296100135`*^9}, {3.693991979330083*^9, 3.693992022780144*^9}, {3.6939921266502895`*^9, 3.6939921416103106`*^9}, { 3.6939921886903763`*^9, 3.693992235260442*^9}, {3.6939924451107354`*^9, 3.6939924757207785`*^9}, {3.6939925308708553`*^9, 3.693992535490862*^9}, { 3.69408137357989*^9, 3.6940813990399256`*^9}, {3.694081492270056*^9, 3.694081500430067*^9}, 3.694085807686309*^9, 3.694336369074993*^9, { 3.694336447585103*^9, 3.694336534165224*^9}, {3.6943365695452733`*^9, 3.694336572935278*^9}, {3.6943366355853662`*^9, 3.694336663395405*^9}, { 3.694336707865467*^9, 3.694336813505615*^9}, {3.6943368708856955`*^9, 3.694336972645838*^9}, {3.694337005795884*^9, 3.69433752400661*^9}, { 3.694337943297197*^9, 3.6943379730472383`*^9}, {3.694338096757412*^9, 3.694338100087416*^9}, {3.6943381564174953`*^9, 3.694338172057517*^9}, { 3.6943382111375713`*^9, 3.6943382179975815`*^9}, {3.694338370357795*^9, 3.694338415207857*^9}, {3.694338519908004*^9, 3.694338533448023*^9}, { 3.694338742738316*^9, 3.6943387845683746`*^9}, {3.6943388672484903`*^9, 3.694338909398549*^9}, {3.6943394389592905`*^9, 3.694339477079344*^9}, { 3.6943395685694723`*^9, 3.6943395881794996`*^9}, 3.6943396627096043`*^9, { 3.694339797119792*^9, 3.6943398030098004`*^9}, {3.6943398885999203`*^9, 3.6943400438301373`*^9}, {3.6943517756956816`*^9, 3.694351778765686*^9}, { 3.694351814965737*^9, 3.694351920335884*^9}, {3.6943520375260487`*^9, 3.694352038046049*^9}, {3.6943546301696777`*^9, 3.694354641489694*^9}, { 3.6943547065797853`*^9, 3.694354780889889*^9}, {3.694415922397947*^9, 3.694415933787963*^9}, {3.6944160021080585`*^9, 3.6944160163480783`*^9}, { 3.6944161612482815`*^9, 3.694416186218316*^9}, {3.6944162181183605`*^9, 3.694416241358393*^9}, {3.694416776009142*^9, 3.694416778289145*^9}, { 3.694417304849882*^9, 3.694417340579932*^9}, {3.6944179310727587`*^9, 3.6944179657728076`*^9}, {3.6944182927132654`*^9, 3.694418302313279*^9}, { 3.6944316170705633`*^9, 3.6944316923568697`*^9}, {3.6944318163219357`*^9, 3.694431820105152*^9}, {3.6965609549111967`*^9, 3.696560966061212*^9}, { 3.696560998851258*^9, 3.6965610020812626`*^9}, {3.6965611422314587`*^9, 3.696561159171482*^9}, 3.696563445644683*^9, {3.6965635186347857`*^9, 3.6965635322048044`*^9}, {3.696563569074856*^9, 3.6965635745148635`*^9}, { 3.696563720555068*^9, 3.69656372185507*^9}, {3.6965637807551527`*^9, 3.696563824135213*^9}, {3.6965639935254507`*^9, 3.696564031985504*^9}, { 3.696596096992402*^9, 3.696596186502527*^9}, {3.696596234252594*^9, 3.696596260452631*^9}, {3.6965963110027018`*^9, 3.69659632407272*^9}, 3.6965963803627987`*^9, {3.7244123642779827`*^9, 3.7244123648119507`*^9}, { 3.7255912428848085`*^9, 3.7255912492295227`*^9}, {3.725591466627203*^9, 3.725591704636403*^9}, {3.7255917405776634`*^9, 3.7255917613142586`*^9}, { 3.7255980783777914`*^9, 3.7255980873943977`*^9}, {3.725598135321295*^9, 3.7255981566673255`*^9}, {3.7255985463958807`*^9, 3.7255985750395555`*^9}, {3.725598660297285*^9, 3.725598669548276*^9}, { 3.7255989613446465`*^9, 3.7255989963014574`*^9}, {3.7255990922803245`*^9, 3.725599092624111*^9}, {3.7255991287997694`*^9, 3.7255991802271013`*^9}, 3.7255992673973975`*^9, {3.725599302619891*^9, 3.725599630275236*^9}, { 3.7255996917974653`*^9, 3.725600173598138*^9}, {3.72560026574846*^9, 3.7256002767652473`*^9}, 3.7256003308803263`*^9, {3.7256003995281887`*^9, 3.72560041238892*^9}, {3.725600503405278*^9, 3.725600537768276*^9}, { 3.72560062249599*^9, 3.725600660390954*^9}, {3.7256015423497496`*^9, 3.725601551460086*^9}, {3.725602674641403*^9, 3.725602676188448*^9}, { 3.725606737765007*^9, 3.7256067379681726`*^9}, {3.7259411263577843`*^9, 3.725941161974596*^9}, {3.7259413328141994`*^9, 3.7259413530325947`*^9}, { 3.725948620999795*^9, 3.7259486419857845`*^9}, 3.7259487502361426`*^9, { 3.725948801316684*^9, 3.7259488049789305`*^9}, {3.7259488747343755`*^9, 3.7259488880408845`*^9}, {3.7262144247900543`*^9, 3.7262144477456355`*^9}, {3.7574171303554697`*^9, 3.7574171843446183`*^9}, {3.7574172301540523`*^9, 3.757417230424534*^9}, { 3.7574172774582806`*^9, 3.757417279859251*^9}, {3.757418119406087*^9, 3.757418162231819*^9}, {3.790129674473545*^9, 3.79012968521891*^9}, { 3.814675393524129*^9, 3.8146753964039536`*^9}, {3.8216148844365788`*^9, 3.8216149206900663`*^9}, 3.8217798501935825`*^9}, CellLabel-> "In[189]:=",ExpressionUUID->"28d2293e-8a04-44d8-a288-643ade99678c"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]_", ",", "\[Nu]_"}], "}"}], ",", RowBox[{"{", "t_", "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "pol", ",", "sha", ",", "nod", ",", "x", ",", "y", ",", "NN", ",", "u", ",", "v", ",", "E\[Sigma]", ",", "EE", ",", "\[Delta]E", ",", "SS", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]WW"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nod", " ", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"sha", "=", RowBox[{"{", RowBox[{"1", ",", "x", ",", "y"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"pol", "=", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nod", ",", "1", ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"sha", " ", ".", RowBox[{"Inverse", "[", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"sha", " ", "/.", " ", RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], "\[Rule]", "#"}], "]"}]}], "&"}], ",", "pol"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "approximations", "*)"}], " ", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nod", ",", "2", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nod", ",", "2", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"plane", " ", "stress", " ", "elasticity"}], "*)"}], "\[IndentingNewLine]", RowBox[{"E\[Sigma]", "=", RowBox[{ RowBox[{"\[CapitalEpsilon]", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "\[Nu]", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Nu]", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]"}], ")"}], "/", "2"}]}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"strain", " ", "and", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"EE", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], ")"}], "^", "2"}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], ")"}], "^", "2"}]}], ")"}], "/", "2"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}], ")"}], "^", "2"}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}], ")"}], "^", "2"}]}], ")"}], "/", "2"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], "+", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}]}], ")"}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], ")"}], "*", RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], ")"}], "*", RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}], ")"}]}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]E", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], "]"}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], "]"}], RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], "]"}], RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}]}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}], "]"}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}], "]"}], RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}], "]"}], RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}]}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], "+", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}]}], "]"}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], "]"}], "*", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}]}], "+", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], "*", RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}], "]"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], "]"}], "*", RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}]}], "+", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], "*", RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}], "]"}]}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SS", "=", RowBox[{"t", " ", RowBox[{"E\[Sigma]", ".", "EE"}]}]}], " ", ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{"-", RowBox[{"\[Delta]E", ".", "SS"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "0"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fz"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"Integrate", "[", RowBox[{ RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], StyleBox["\[Element]", "OperatorCharacter"], RowBox[{"Polygon", "[", "pol", "]"}]}], ",", RowBox[{"Assumptions", "\[Rule]", RowBox[{"L", ">", "0"}]}]}], "]"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.4426473093646455`*^9, 3.4426474078630457`*^9}, { 3.4426597184894*^9, 3.4426597783310003`*^9}, {3.442659859139*^9, 3.4426599679021997`*^9}, {3.4426601154852*^9, 3.442660125282*^9}, 3.4426603153866*^9, {3.4426606694491997`*^9, 3.442660676984*^9}, { 3.4426607660341997`*^9, 3.442660767017*^9}, {3.4426607970782003`*^9, 3.4426609236566*^9}, {3.4426609993859997`*^9, 3.442661000946*^9}, { 3.4426611720156*^9, 3.4426611866796*^9}, {3.4426612192836*^9, 3.4426612396104*^9}, {3.4426613536776*^9, 3.4426613563764*^9}, { 3.4426613962188*^9, 3.4426613966556*^9}, {3.443184440921*^9, 3.4431845165186*^9}, {3.4431848052298*^9, 3.4431848237002*^9}, { 3.4431849834618*^9, 3.4431849851934*^9}, {3.4431850342574*^9, 3.4431850385318003`*^9}, {3.4444402127514*^9, 3.4444402360889997`*^9}, { 3.44509636787*^9, 3.445096458974*^9}, {3.4450965569264*^9, 3.4450965855056*^9}, {3.4450966736612*^9, 3.4450967018348*^9}, 3.4450967876972*^9, {3.4451000792358*^9, 3.4451001019962*^9}, { 3.445132280975*^9, 3.4451322867782*^9}, 3.4451325631488*^9, 3.4451346101028*^9, {3.4455261966926003`*^9, 3.4455262691078*^9}, { 3.4455263543462*^9, 3.445526490113*^9}, {3.4455265305794*^9, 3.4455265347602*^9}, {3.4455267552349997`*^9, 3.4455267826754*^9}, 3.445526922233*^9, {3.445527218711*^9, 3.4455272895818*^9}, { 3.4455273640094*^9, 3.445527481259*^9}, 3.4455276192202*^9, { 3.4455278074376*^9, 3.4455278187164*^9}, {3.4455279660896*^9, 3.4455279742016*^9}, 3.4455280249016*^9, 3.4455285464407997`*^9, { 3.4461837560238*^9, 3.4461837697986*^9}, {3.446183892165*^9, 3.4461839004486*^9}, {3.4461839570142*^9, 3.4461841265550003`*^9}, 3.4461841729182*^9, {3.4461842101398*^9, 3.4461842206074*^9}, { 3.4461845241088*^9, 3.4461845410972*^9}, {3.4461845879440002`*^9, 3.4461847021516*^9}, {3.4461848428032*^9, 3.4461848544096003`*^9}, { 3.4461849111956*^9, 3.4461849123344*^9}, {3.4461850134868*^9, 3.446185058608*^9}, {3.4461852067616*^9, 3.446185223282*^9}, { 3.4461852548876*^9, 3.4461852626408*^9}, {3.4461853186604*^9, 3.446185320392*^9}, {3.4512642010481997`*^9, 3.451264207413*^9}, { 3.4512642788766003`*^9, 3.4512643136334*^9}, {3.4512643770006*^9, 3.4512644269362*^9}, {3.4512646983138*^9, 3.4512647384994*^9}, { 3.4512647823354*^9, 3.4512647868126*^9}, {3.4939932066616*^9, 3.4939932082060003`*^9}, {3.4939932399988003`*^9, 3.4939932614955997`*^9}, {3.493993300014*^9, 3.4939933073304*^9}, { 3.4939933992174*^9, 3.4939934078129997`*^9}, {3.4939934932314*^9, 3.493993515009*^9}, {3.4939935468556004`*^9, 3.493993568543*^9}, { 3.4939936486404*^9, 3.4939936621812*^9}, {3.4940328887262*^9, 3.4940328895218*^9}, {3.499487154582*^9, 3.49948716324*^9}, { 3.4994872083708*^9, 3.499487247324*^9}, {3.4994872822368*^9, 3.4994873816244*^9}, 3.499487417676*^9, {3.4994878504918003`*^9, 3.4994879045458*^9}, {3.4994879529370003`*^9, 3.4994879707794*^9}, { 3.4994880482042*^9, 3.4994880616826*^9}, {3.4994881084202003`*^9, 3.4994881177334003`*^9}, {3.4994884740218*^9, 3.4994884920554*^9}, { 3.4994885948282003`*^9, 3.4994886477434*^9}, {3.4994886790369997`*^9, 3.4994886860257998`*^9}, {3.4994887712953997`*^9, 3.4994887717478*^9}, { 3.6305517490219865`*^9, 3.6305518383945436`*^9}, 3.6305519329151096`*^9, { 3.6305521477354264`*^9, 3.6305521796235647`*^9}, {3.630552211063363*^9, 3.630552234159684*^9}, {3.6305523097380066`*^9, 3.6305523261429453`*^9}, { 3.630552400293186*^9, 3.630552443246643*^9}, {3.6305524899713154`*^9, 3.630552532581753*^9}, {3.630552564078554*^9, 3.630552660703081*^9}, { 3.6308069732471952`*^9, 3.6308070226836824`*^9}, {3.630831568112257*^9, 3.630831577359786*^9}, {3.632037136188613*^9, 3.6320372275628395`*^9}, { 3.632037282822*^9, 3.6320372864142056`*^9}, {3.632037326777514*^9, 3.6320373338819203`*^9}, {3.6320374068820953`*^9, 3.632037461262206*^9}, { 3.632037495368157*^9, 3.6320375996761227`*^9}, {3.632037657282418*^9, 3.6320377668306837`*^9}, {3.6320377993975463`*^9, 3.6320378258790607`*^9}, {3.6320379375314474`*^9, 3.632037944011818*^9}, { 3.632037974774577*^9, 3.63203804108137*^9}, {3.632038115937651*^9, 3.6320381168477035`*^9}, {3.632038171547832*^9, 3.6320381721648674`*^9}, { 3.6320382092969913`*^9, 3.6320382642141323`*^9}, 3.632038311238822*^9, { 3.6320383438376865`*^9, 3.6320384084533825`*^9}, {3.632038502612768*^9, 3.632038536966733*^9}, {3.6320386355663724`*^9, 3.632038663028943*^9}, { 3.6320387578143644`*^9, 3.632038876049127*^9}, {3.632038925681966*^9, 3.6320390116098804`*^9}, {3.6320390559574175`*^9, 3.632039057440502*^9}, { 3.6320390909984217`*^9, 3.6320392794842024`*^9}, {3.6320393098219376`*^9, 3.6320393228646836`*^9}, {3.6320393691423306`*^9, 3.632039469157051*^9}, { 3.6320395408921537`*^9, 3.6320395753041224`*^9}, {3.632039607865985*^9, 3.6320396287681804`*^9}, {3.632039834419943*^9, 3.6320399635053263`*^9}, { 3.632040008307889*^9, 3.632040011081047*^9}, {3.632040111200774*^9, 3.6320401709411907`*^9}, {3.6320402797014112`*^9, 3.6320403974661474`*^9}, {3.6320411172793183`*^9, 3.6320411297080293`*^9}, 3.632041280201637*^9, {3.632041357828077*^9, 3.632041361657296*^9}, { 3.632041402765647*^9, 3.632041437279621*^9}, 3.632041474164731*^9, { 3.6320415074596353`*^9, 3.632041548877004*^9}, {3.6320415931405363`*^9, 3.632041610919553*^9}, {3.632041656484159*^9, 3.6320416691688843`*^9}, { 3.6320420632294235`*^9, 3.6320420791513343`*^9}, {3.6320424482774467`*^9, 3.632042550289282*^9}, {3.632042803353756*^9, 3.632042928840934*^9}, { 3.632042961566806*^9, 3.63204301077662*^9}, {3.632043063037609*^9, 3.6320430712580795`*^9}, {3.632043120691907*^9, 3.632043161148221*^9}, { 3.6320432062678013`*^9, 3.6320432094549837`*^9}, 3.632043258394783*^9, { 3.632043351071084*^9, 3.632043352668175*^9}, {3.6345677461009674`*^9, 3.634568027044036*^9}, 3.634568059784909*^9, {3.6345686692177663`*^9, 3.6345687304812703`*^9}, {3.634568765543276*^9, 3.634568827443816*^9}, { 3.6346120324026976`*^9, 3.6346120417672334`*^9}, {3.6346121382917542`*^9, 3.6346122118989644`*^9}, {3.6346122814849443`*^9, 3.634612333070895*^9}, { 3.634612471677823*^9, 3.634612552263432*^9}, {3.6346125863993845`*^9, 3.6346126554953365`*^9}, {3.634612698763811*^9, 3.634612702163006*^9}, { 3.6348726356017313`*^9, 3.634872755937614*^9}, {3.634877631123617*^9, 3.6348776427762833`*^9}, {3.6348782474488688`*^9, 3.6348782744724145`*^9}, {3.63487832072106*^9, 3.634878440448908*^9}, { 3.6852817264030714`*^9, 3.6852817834531507`*^9}, {3.68794462572165*^9, 3.687944776911862*^9}, {3.6879451060223227`*^9, 3.6879451445423765`*^9}, { 3.6879452810225677`*^9, 3.6879452918025827`*^9}, {3.6879455589529567`*^9, 3.687945567592969*^9}, {3.6879456213830442`*^9, 3.6879456613631*^9}, { 3.6879457292931952`*^9, 3.6879457736132574`*^9}, {3.688022923252344*^9, 3.688023002982456*^9}, {3.6880230753425574`*^9, 3.688023230782775*^9}, 3.688023348002939*^9, {3.688023553833227*^9, 3.6880235620032387`*^9}, { 3.6880236295333333`*^9, 3.6880236382433453`*^9}, 3.6880237756035376`*^9, { 3.688031422416407*^9, 3.688031557816597*^9}, {3.6881117497443466`*^9, 3.688111797854414*^9}, {3.6881166477118034`*^9, 3.688116649471806*^9}, { 3.688118444084318*^9, 3.6881185798545084`*^9}, {3.688118642824597*^9, 3.688118799384816*^9}, {3.688118855204894*^9, 3.688118917084981*^9}, { 3.6881194959182944`*^9, 3.688119497718297*^9}, {3.6881196404384966`*^9, 3.688119655048517*^9}, {3.688119702888584*^9, 3.688119727678619*^9}, { 3.6881200919291286`*^9, 3.6881201295191813`*^9}, {3.6881202044892864`*^9, 3.688120237039332*^9}, {3.688120497669697*^9, 3.688120502989704*^9}, { 3.688120738340034*^9, 3.6881207493700495`*^9}, {3.6882745101002936`*^9, 3.6882745118602962`*^9}, {3.6883042728760366`*^9, 3.688304806616784*^9}, { 3.6883051027271986`*^9, 3.6883051086172066`*^9}, {3.6883054642977047`*^9, 3.6883054716377153`*^9}, {3.688306465909107*^9, 3.6883064729091167`*^9}, { 3.6883066024792986`*^9, 3.6883066550893717`*^9}, {3.6883071311300383`*^9, 3.688307145950059*^9}, 3.6883073798003864`*^9, {3.6887815904603148`*^9, 3.6887816040203333`*^9}, 3.6887816433103886`*^9, {3.6887816741004314`*^9, 3.688781699230467*^9}, {3.6887817847405863`*^9, 3.688781813880627*^9}, { 3.688781885830728*^9, 3.6887819020407505`*^9}, {3.6889574605581684`*^9, 3.688957501788226*^9}, {3.688960184803222*^9, 3.6889601992032423`*^9}, { 3.692771817740493*^9, 3.692771905640616*^9}, {3.6927726676816826`*^9, 3.6927727032617326`*^9}, {3.6927727333717747`*^9, 3.692772736561779*^9}, { 3.692772826191905*^9, 3.692772844901931*^9}, {3.692772893741999*^9, 3.6927728997420073`*^9}, {3.6927729636420975`*^9, 3.692773125862324*^9}, { 3.6927731981924257`*^9, 3.692773236352479*^9}, {3.6927732729025297`*^9, 3.692773282242543*^9}, {3.6927733353526173`*^9, 3.6927734137827272`*^9}, 3.6927736473730545`*^9, {3.6934868115444183`*^9, 3.693486813494421*^9}, { 3.6934868553944798`*^9, 3.693486917754567*^9}, {3.6934869973946786`*^9, 3.693487001174684*^9}, {3.6934870442947445`*^9, 3.6934870479747496`*^9}, { 3.693487349135171*^9, 3.6934873994352417`*^9}, {3.693487456975322*^9, 3.6934874585553246`*^9}, {3.6939897066669016`*^9, 3.6939897907970195`*^9}, {3.6939898244170666`*^9, 3.693989829937074*^9}, { 3.6939901042074585`*^9, 3.693990124237486*^9}, {3.69399018398757*^9, 3.6939902403476486`*^9}, {3.6939902781277018`*^9, 3.69399032732777*^9}, { 3.6939903908278594`*^9, 3.693990609328165*^9}, {3.693990640658209*^9, 3.693990673878256*^9}, {3.693990761178378*^9, 3.6939907769384003`*^9}, { 3.6939908128884506`*^9, 3.6939908380384855`*^9}, {3.6939908895785575`*^9, 3.6939908941885643`*^9}, {3.6939909859386926`*^9, 3.693991001898715*^9}, { 3.6939910395887675`*^9, 3.6939910643988028`*^9}, {3.693991107098862*^9, 3.6939911407889094`*^9}, {3.6939911957989864`*^9, 3.6939913838692493`*^9}, {3.6939918465598974`*^9, 3.693991856479911*^9}, { 3.6939919173699965`*^9, 3.6939919296100135`*^9}, {3.693991979330083*^9, 3.693992022780144*^9}, {3.6939921266502895`*^9, 3.6939921416103106`*^9}, { 3.6939921886903763`*^9, 3.693992235260442*^9}, {3.6939924451107354`*^9, 3.6939924757207785`*^9}, {3.6939925308708553`*^9, 3.693992535490862*^9}, { 3.69408137357989*^9, 3.6940813990399256`*^9}, {3.694081492270056*^9, 3.694081500430067*^9}, 3.694085807686309*^9, 3.694336369074993*^9, { 3.694336447585103*^9, 3.694336534165224*^9}, {3.6943365695452733`*^9, 3.694336572935278*^9}, {3.6943366355853662`*^9, 3.694336663395405*^9}, { 3.694336707865467*^9, 3.694336813505615*^9}, {3.6943368708856955`*^9, 3.694336972645838*^9}, {3.694337005795884*^9, 3.69433752400661*^9}, { 3.694337943297197*^9, 3.6943379730472383`*^9}, {3.694338096757412*^9, 3.694338100087416*^9}, {3.6943381564174953`*^9, 3.694338172057517*^9}, { 3.6943382111375713`*^9, 3.6943382179975815`*^9}, {3.694338370357795*^9, 3.694338415207857*^9}, {3.694338519908004*^9, 3.694338533448023*^9}, { 3.694338742738316*^9, 3.6943387845683746`*^9}, {3.6943388672484903`*^9, 3.694338909398549*^9}, {3.6943394389592905`*^9, 3.694339477079344*^9}, { 3.6943395685694723`*^9, 3.6943395881794996`*^9}, 3.6943396627096043`*^9, { 3.694339797119792*^9, 3.6943398030098004`*^9}, {3.6943398885999203`*^9, 3.6943400438301373`*^9}, {3.6943517756956816`*^9, 3.694351778765686*^9}, { 3.694351814965737*^9, 3.694351920335884*^9}, {3.6943520375260487`*^9, 3.694352038046049*^9}, {3.6943546301696777`*^9, 3.694354641489694*^9}, { 3.6943547065797853`*^9, 3.694354780889889*^9}, {3.694415922397947*^9, 3.694415933787963*^9}, {3.6944160021080585`*^9, 3.6944160163480783`*^9}, { 3.6944161612482815`*^9, 3.694416186218316*^9}, {3.6944162181183605`*^9, 3.694416241358393*^9}, {3.694416776009142*^9, 3.694416778289145*^9}, { 3.694417304849882*^9, 3.694417340579932*^9}, {3.6944179310727587`*^9, 3.6944179657728076`*^9}, {3.6944182927132654`*^9, 3.694418302313279*^9}, { 3.6944316170705633`*^9, 3.6944316923568697`*^9}, {3.6944318163219357`*^9, 3.694431820105152*^9}, {3.6965609549111967`*^9, 3.696560966061212*^9}, { 3.696560998851258*^9, 3.6965610020812626`*^9}, {3.6965611422314587`*^9, 3.696561159171482*^9}, 3.696563445644683*^9, {3.6965635186347857`*^9, 3.6965635322048044`*^9}, {3.696563569074856*^9, 3.6965635745148635`*^9}, { 3.696563720555068*^9, 3.69656372185507*^9}, {3.6965637807551527`*^9, 3.696563824135213*^9}, {3.6965639935254507`*^9, 3.696564031985504*^9}, { 3.696596096992402*^9, 3.696596186502527*^9}, {3.696596234252594*^9, 3.696596260452631*^9}, {3.6965963110027018`*^9, 3.69659632407272*^9}, 3.6965963803627987`*^9, {3.7244123642779827`*^9, 3.7244123648119507`*^9}, { 3.7255912428848085`*^9, 3.7255912492295227`*^9}, {3.725591466627203*^9, 3.725591704636403*^9}, {3.7255917405776634`*^9, 3.7255917613142586`*^9}, { 3.7255980783777914`*^9, 3.7255980873943977`*^9}, {3.725598135321295*^9, 3.7255981566673255`*^9}, {3.7255985463958807`*^9, 3.7255985750395555`*^9}, {3.725598660297285*^9, 3.725598669548276*^9}, { 3.7255989613446465`*^9, 3.7255989963014574`*^9}, {3.7255990922803245`*^9, 3.725599092624111*^9}, {3.7255991287997694`*^9, 3.7255991802271013`*^9}, 3.7255992673973975`*^9, {3.725599302619891*^9, 3.725599630275236*^9}, { 3.7255996917974653`*^9, 3.725600173598138*^9}, {3.72560026574846*^9, 3.7256002767652473`*^9}, 3.7256003308803263`*^9, {3.7256003995281887`*^9, 3.72560041238892*^9}, {3.725600503405278*^9, 3.725600537768276*^9}, { 3.72560062249599*^9, 3.725600660390954*^9}, {3.7256015423497496`*^9, 3.725601551460086*^9}, {3.725602674641403*^9, 3.725602676188448*^9}, { 3.725606737765007*^9, 3.7256067379681726`*^9}, {3.7259411263577843`*^9, 3.725941161974596*^9}, {3.7259413328141994`*^9, 3.7259413530325947`*^9}, { 3.725948620999795*^9, 3.7259486419857845`*^9}, 3.7259487502361426`*^9, { 3.725948801316684*^9, 3.7259488049789305`*^9}, {3.7259488747343755`*^9, 3.7259488880408845`*^9}, {3.7262144247900543`*^9, 3.7262144477456355`*^9}, {3.7574171303554697`*^9, 3.7574171843446183`*^9}, {3.7574172301540523`*^9, 3.757417230424534*^9}, { 3.7574172774582806`*^9, 3.757417279859251*^9}, {3.757418119406087*^9, 3.757418162231819*^9}, {3.790129674473545*^9, 3.79012968521891*^9}, { 3.814675393524129*^9, 3.8146753964039536`*^9}, {3.8216148844365788`*^9, 3.8216149206900663`*^9}, 3.8217798501935825`*^9},ExpressionUUID->"9c3ae2e4-46f0-4717-b32c-\ 5c9d4baaa58c"] }, Closed]], Cell[CellGroupData[{ Cell["PLANE ELEMENT (tmec) defs ", "Subsection", CellChangeTimes->{{3.7577458100953183`*^9, 3.757745817919499*^9}, { 3.7901297746587725`*^9, 3.79012978895208*^9}},ExpressionUUID->"12fe72e9-7d6c-409c-888f-\ fd1cfd4e4141"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"TMEC", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE_", ",", "\[Nu]\[Nu]_", ",", "\[Alpha]\[Alpha]_", ",", "kk_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"ss_", ",", "\[CurlyTheta]0_"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"TMEC", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE", ",", "\[Nu]\[Nu]", ",", "\[Alpha]\[Alpha]", ",", "kk"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"ss", ",", "\[CurlyTheta]0"}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"TMEC", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE_", ",", "\[Nu]\[Nu]_", ",", "\[Alpha]\[Alpha]_", ",", "kk_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}], ",", RowBox[{"{", RowBox[{"ss_", ",", "\[CurlyTheta]0_"}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "NN", ",", "INT", ",", "MID", ",", "r", ",", "e1", ",", "e2", ",", "e3", ",", "nn", ",", "FF", ",", "FFINV", ",", "jac", ",", "uvw", ",", "du", ",", "d\[CurlyTheta]", ",", "\[Epsilon]", ",", "\[Sigma]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "EEEE", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]pint", ",", "\[Delta]pext", ",", "\[CurlyTheta]\[CurlyTheta]"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"Length", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "[", "3", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Xi]", "-", "\[Eta]"}], ",", "\[Xi]", ",", "\[Eta]"}], "}"}]}], ";", RowBox[{ RowBox[{"NN", "[", "4", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Xi]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Eta]"}], ")"}]}], ",", RowBox[{"\[Xi]", RowBox[{"(", RowBox[{"1", "-", "\[Eta]"}], ")"}]}], ",", RowBox[{"\[Xi]", " ", "\[Eta]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Xi]"}], ")"}], "\[Eta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"INT", "[", "3", "]"}], "=", "TRI7"}], ";", RowBox[{ RowBox[{"INT", "[", "4", "]"}], "=", "REC9"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"MID", "[", "3", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"\[Xi]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"\[Eta]", "\[Rule]", RowBox[{"1", "/", "3"}]}]}], "}"}]}], ";", " ", RowBox[{ RowBox[{"MID", "[", "4", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"\[Xi]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Eta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{ RowBox[{"NN", "[", "nl", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"e1", ",", "e2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Eta]"], "r"}]}], "}"}], " ", "/.", RowBox[{"MID", "[", "nl", "]"}]}]}], ";", "\[IndentingNewLine]", " ", RowBox[{"e3", "=", RowBox[{"e1", StyleBox["\[Cross]", "OperatorCharacter"], "e2"}]}], ";", "\[IndentingNewLine]", RowBox[{"nn", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"e3", "/", RowBox[{"Sqrt", "[", RowBox[{"e3", ".", "e3"}], "]"}]}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e1", ",", " ", "e2", ",", "nn"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{ RowBox[{"NN", "[", "nl", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CurlyTheta]\[CurlyTheta]", "=", RowBox[{ RowBox[{"NN", "[", "nl", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "4"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "displacement", " ", "gradient", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"du", "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Eta]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Zeta]"], "uvw"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"d\[CurlyTheta]", "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "\[CurlyTheta]\[CurlyTheta]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Eta]"], "\[CurlyTheta]\[CurlyTheta]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Zeta]"], "\[CurlyTheta]\[CurlyTheta]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Plane", " ", "stress", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", " ", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", " ", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", " ", "\[Nu]\[Nu]"}]}], ")"}], "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{"EEEE", "-", RowBox[{ RowBox[{"(", RowBox[{"EEEE", ".", "nn"}], ")"}], ".", RowBox[{"Inverse", "[", RowBox[{"nn", ".", "EEEE", ".", "nn"}], "]"}], ".", RowBox[{"(", RowBox[{"nn", ".", "EEEE"}], ")"}]}]}], "]"}]}], ";", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{"du", "-", RowBox[{ RowBox[{"IdentityMatrix", "[", "3", "]"}], "*", "\[Alpha]\[Alpha]", "*", RowBox[{"(", RowBox[{"\[CurlyTheta]\[CurlyTheta]", "-", "\[CurlyTheta]0"}], ")"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]\[Delta]", "[", "du", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}], "*", "tt"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]pint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", "d\[CurlyTheta]", "]"}], ".", "d\[CurlyTheta]"}]}], "*", "kk", "*", "tt"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]pext", "=", " ", RowBox[{ RowBox[{ "\[Delta]\[Delta]", "[", "\[CurlyTheta]\[CurlyTheta]", "]"}], "*", "ss"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"QUAD", "[", RowBox[{ RowBox[{"INT", "[", "nl", "]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wext", "+", "\[Delta]wint", "+", "\[Delta]pint", "+", "\[Delta]pext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Xi]", ",", "\[Eta]"}], "}"}]}], "]"}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426473093646455`*^9, 3.4426474078630457`*^9}, { 3.4426597184894*^9, 3.4426597783310003`*^9}, {3.442659859139*^9, 3.4426599679021997`*^9}, {3.4426601154852*^9, 3.442660125282*^9}, 3.4426603153866*^9, {3.4426606694491997`*^9, 3.442660676984*^9}, { 3.4426607660341997`*^9, 3.442660767017*^9}, {3.4426607970782003`*^9, 3.4426609236566*^9}, {3.4426609993859997`*^9, 3.442661000946*^9}, { 3.4426611720156*^9, 3.4426611866796*^9}, {3.4426612192836*^9, 3.4426612396104*^9}, {3.4426613536776*^9, 3.4426613563764*^9}, { 3.4426613962188*^9, 3.4426613966556*^9}, {3.443184440921*^9, 3.4431845165186*^9}, {3.4431848052298*^9, 3.4431848237002*^9}, { 3.4431849834618*^9, 3.4431849851934*^9}, {3.4431850342574*^9, 3.4431850385318003`*^9}, {3.4444402127514*^9, 3.4444402360889997`*^9}, { 3.44509636787*^9, 3.445096458974*^9}, {3.4450965569264*^9, 3.4450965855056*^9}, {3.4450966736612*^9, 3.4450967018348*^9}, 3.4450967876972*^9, {3.4451000792358*^9, 3.4451001019962*^9}, { 3.445132280975*^9, 3.4451322867782*^9}, 3.4451325631488*^9, 3.4451346101028*^9, {3.4455261966926003`*^9, 3.4455262691078*^9}, { 3.4455263543462*^9, 3.445526490113*^9}, {3.4455265305794*^9, 3.4455265347602*^9}, {3.4455267552349997`*^9, 3.4455267826754*^9}, 3.445526922233*^9, {3.445527218711*^9, 3.4455272895818*^9}, { 3.4455273640094*^9, 3.445527481259*^9}, 3.4455276192202*^9, { 3.4455278074376*^9, 3.4455278187164*^9}, {3.4455279660896*^9, 3.4455279742016*^9}, 3.4455280249016*^9, 3.4455285464407997`*^9, { 3.4461837560238*^9, 3.4461837697986*^9}, {3.446183892165*^9, 3.4461839004486*^9}, {3.4461839570142*^9, 3.4461841265550003`*^9}, 3.4461841729182*^9, {3.4461842101398*^9, 3.4461842206074*^9}, { 3.4461845241088*^9, 3.4461845410972*^9}, {3.4461845879440002`*^9, 3.4461847021516*^9}, {3.4461848428032*^9, 3.4461848544096003`*^9}, { 3.4461849111956*^9, 3.4461849123344*^9}, {3.4461850134868*^9, 3.446185058608*^9}, {3.4461852067616*^9, 3.446185223282*^9}, { 3.4461852548876*^9, 3.4461852626408*^9}, {3.4461853186604*^9, 3.446185320392*^9}, {3.4512642010481997`*^9, 3.451264207413*^9}, { 3.4512642788766003`*^9, 3.4512643136334*^9}, {3.4512643770006*^9, 3.4512644269362*^9}, {3.4512646983138*^9, 3.4512647384994*^9}, { 3.4512647823354*^9, 3.4512647868126*^9}, {3.4939932066616*^9, 3.4939932082060003`*^9}, {3.4939932399988003`*^9, 3.4939932614955997`*^9}, {3.493993300014*^9, 3.4939933073304*^9}, { 3.4939933992174*^9, 3.4939934078129997`*^9}, {3.4939934932314*^9, 3.493993515009*^9}, {3.4939935468556004`*^9, 3.493993568543*^9}, { 3.4939936486404*^9, 3.4939936621812*^9}, {3.4940328887262*^9, 3.4940328895218*^9}, {3.499487154582*^9, 3.49948716324*^9}, { 3.4994872083708*^9, 3.499487247324*^9}, {3.4994872822368*^9, 3.4994873816244*^9}, 3.499487417676*^9, {3.4994878504918003`*^9, 3.4994879045458*^9}, {3.4994879529370003`*^9, 3.4994879707794*^9}, { 3.4994880482042*^9, 3.4994880616826*^9}, {3.4994881084202003`*^9, 3.4994881177334003`*^9}, {3.4994884740218*^9, 3.4994884920554*^9}, { 3.4994885948282003`*^9, 3.4994886477434*^9}, {3.4994886790369997`*^9, 3.4994886860257998`*^9}, {3.4994887712953997`*^9, 3.4994887717478*^9}, { 3.6305517490219865`*^9, 3.6305518383945436`*^9}, 3.6305519329151096`*^9, { 3.6305521477354264`*^9, 3.6305521796235647`*^9}, {3.630552211063363*^9, 3.630552234159684*^9}, {3.6305523097380066`*^9, 3.6305523261429453`*^9}, { 3.630552400293186*^9, 3.630552443246643*^9}, {3.6305524899713154`*^9, 3.630552532581753*^9}, {3.630552564078554*^9, 3.630552660703081*^9}, { 3.6308069732471952`*^9, 3.6308070226836824`*^9}, {3.630831568112257*^9, 3.630831577359786*^9}, {3.632037136188613*^9, 3.6320372275628395`*^9}, { 3.632037282822*^9, 3.6320372864142056`*^9}, {3.632037326777514*^9, 3.6320373338819203`*^9}, {3.6320374068820953`*^9, 3.632037461262206*^9}, { 3.632037495368157*^9, 3.6320375996761227`*^9}, {3.632037657282418*^9, 3.6320377668306837`*^9}, {3.6320377993975463`*^9, 3.6320378258790607`*^9}, {3.6320379375314474`*^9, 3.632037944011818*^9}, { 3.632037974774577*^9, 3.63203804108137*^9}, {3.632038115937651*^9, 3.6320381168477035`*^9}, {3.632038171547832*^9, 3.6320381721648674`*^9}, { 3.6320382092969913`*^9, 3.6320382642141323`*^9}, 3.632038311238822*^9, { 3.6320383438376865`*^9, 3.6320384084533825`*^9}, {3.632038502612768*^9, 3.632038536966733*^9}, {3.6320386355663724`*^9, 3.632038663028943*^9}, { 3.6320387578143644`*^9, 3.632038876049127*^9}, {3.632038925681966*^9, 3.6320390116098804`*^9}, {3.6320390559574175`*^9, 3.632039057440502*^9}, { 3.6320390909984217`*^9, 3.6320392794842024`*^9}, {3.6320393098219376`*^9, 3.6320393228646836`*^9}, {3.6320393691423306`*^9, 3.632039469157051*^9}, { 3.6320395408921537`*^9, 3.6320395753041224`*^9}, {3.632039607865985*^9, 3.6320396287681804`*^9}, {3.632039834419943*^9, 3.6320399635053263`*^9}, { 3.632040008307889*^9, 3.632040011081047*^9}, {3.632040111200774*^9, 3.6320401709411907`*^9}, {3.6320402797014112`*^9, 3.6320403974661474`*^9}, {3.6320411172793183`*^9, 3.6320411297080293`*^9}, 3.632041280201637*^9, {3.632041357828077*^9, 3.632041361657296*^9}, { 3.632041402765647*^9, 3.632041437279621*^9}, 3.632041474164731*^9, { 3.6320415074596353`*^9, 3.632041548877004*^9}, {3.6320415931405363`*^9, 3.632041610919553*^9}, {3.632041656484159*^9, 3.6320416691688843`*^9}, { 3.6320420632294235`*^9, 3.6320420791513343`*^9}, {3.6320424482774467`*^9, 3.632042550289282*^9}, {3.632042803353756*^9, 3.632042928840934*^9}, { 3.632042961566806*^9, 3.63204301077662*^9}, {3.632043063037609*^9, 3.6320430712580795`*^9}, {3.632043120691907*^9, 3.632043161148221*^9}, { 3.6320432062678013`*^9, 3.6320432094549837`*^9}, 3.632043258394783*^9, { 3.632043351071084*^9, 3.632043352668175*^9}, {3.6345677461009674`*^9, 3.634568027044036*^9}, 3.634568059784909*^9, {3.6345686692177663`*^9, 3.6345687304812703`*^9}, {3.634568765543276*^9, 3.634568827443816*^9}, { 3.6346120324026976`*^9, 3.6346120417672334`*^9}, {3.6346121382917542`*^9, 3.6346122118989644`*^9}, {3.6346122814849443`*^9, 3.634612333070895*^9}, { 3.634612471677823*^9, 3.634612552263432*^9}, {3.6346125863993845`*^9, 3.6346126554953365`*^9}, {3.634612698763811*^9, 3.634612702163006*^9}, { 3.6348726356017313`*^9, 3.634872755937614*^9}, {3.634877631123617*^9, 3.6348776427762833`*^9}, {3.6348782474488688`*^9, 3.6348782744724145`*^9}, {3.63487832072106*^9, 3.634878440448908*^9}, { 3.6852817264030714`*^9, 3.6852817834531507`*^9}, {3.68794462572165*^9, 3.687944776911862*^9}, {3.6879451060223227`*^9, 3.6879451445423765`*^9}, { 3.6879452810225677`*^9, 3.6879452918025827`*^9}, {3.6879455589529567`*^9, 3.687945567592969*^9}, {3.6879456213830442`*^9, 3.6879456613631*^9}, { 3.6879457292931952`*^9, 3.6879457736132574`*^9}, {3.688022923252344*^9, 3.688023002982456*^9}, {3.6880230753425574`*^9, 3.688023230782775*^9}, 3.688023348002939*^9, {3.688023553833227*^9, 3.6880235620032387`*^9}, { 3.6880236295333333`*^9, 3.6880236382433453`*^9}, 3.6880237756035376`*^9, { 3.688031422416407*^9, 3.688031557816597*^9}, {3.6881117497443466`*^9, 3.688111797854414*^9}, {3.6881166477118034`*^9, 3.688116649471806*^9}, { 3.688118444084318*^9, 3.6881185798545084`*^9}, {3.688118642824597*^9, 3.688118799384816*^9}, {3.688118855204894*^9, 3.688118917084981*^9}, { 3.6881194959182944`*^9, 3.688119497718297*^9}, {3.6881196404384966`*^9, 3.688119655048517*^9}, {3.688119702888584*^9, 3.688119727678619*^9}, { 3.6881200919291286`*^9, 3.6881201295191813`*^9}, {3.6881202044892864`*^9, 3.688120237039332*^9}, {3.688120497669697*^9, 3.688120502989704*^9}, { 3.688120738340034*^9, 3.6881207493700495`*^9}, {3.6882745101002936`*^9, 3.6882745118602962`*^9}, {3.6883042728760366`*^9, 3.688304806616784*^9}, { 3.6883051027271986`*^9, 3.6883051086172066`*^9}, {3.6883054642977047`*^9, 3.6883054716377153`*^9}, {3.688306465909107*^9, 3.6883064729091167`*^9}, { 3.6883066024792986`*^9, 3.6883066550893717`*^9}, {3.6883071311300383`*^9, 3.688307145950059*^9}, 3.6883073798003864`*^9, {3.6887815904603148`*^9, 3.6887816040203333`*^9}, 3.6887816433103886`*^9, {3.6887816741004314`*^9, 3.688781699230467*^9}, {3.6887817847405863`*^9, 3.688781813880627*^9}, { 3.688781885830728*^9, 3.6887819020407505`*^9}, {3.6889574605581684`*^9, 3.688957501788226*^9}, {3.688960184803222*^9, 3.6889601992032423`*^9}, { 3.692771817740493*^9, 3.692771905640616*^9}, {3.6927726676816826`*^9, 3.6927727032617326`*^9}, {3.6927727333717747`*^9, 3.692772736561779*^9}, { 3.692772826191905*^9, 3.692772844901931*^9}, {3.692772893741999*^9, 3.6927728997420073`*^9}, {3.6927729636420975`*^9, 3.692773125862324*^9}, { 3.6927731981924257`*^9, 3.692773236352479*^9}, {3.6927732729025297`*^9, 3.692773282242543*^9}, {3.6927733353526173`*^9, 3.6927734137827272`*^9}, 3.6927736473730545`*^9, {3.6934868115444183`*^9, 3.693486813494421*^9}, { 3.6934868553944798`*^9, 3.693486917754567*^9}, {3.6934869973946786`*^9, 3.693487001174684*^9}, {3.6934870442947445`*^9, 3.6934870479747496`*^9}, { 3.693487349135171*^9, 3.6934873994352417`*^9}, {3.693487456975322*^9, 3.6934874585553246`*^9}, {3.6939897066669016`*^9, 3.6939897907970195`*^9}, {3.6939898244170666`*^9, 3.693989829937074*^9}, { 3.6939901042074585`*^9, 3.693990124237486*^9}, {3.69399018398757*^9, 3.6939902403476486`*^9}, {3.6939902781277018`*^9, 3.69399032732777*^9}, { 3.6939903908278594`*^9, 3.693990609328165*^9}, {3.693990640658209*^9, 3.693990673878256*^9}, {3.693990761178378*^9, 3.6939907769384003`*^9}, { 3.6939908128884506`*^9, 3.6939908380384855`*^9}, {3.6939908895785575`*^9, 3.6939908941885643`*^9}, {3.6939909859386926`*^9, 3.693991001898715*^9}, { 3.6939910395887675`*^9, 3.6939910643988028`*^9}, {3.693991107098862*^9, 3.6939911407889094`*^9}, {3.6939911957989864`*^9, 3.6939913838692493`*^9}, {3.6939918465598974`*^9, 3.693991856479911*^9}, { 3.6939919173699965`*^9, 3.6939919296100135`*^9}, {3.693991979330083*^9, 3.693992022780144*^9}, {3.6939921266502895`*^9, 3.6939921416103106`*^9}, { 3.6939921886903763`*^9, 3.693992235260442*^9}, {3.6939924451107354`*^9, 3.6939924757207785`*^9}, {3.6939925308708553`*^9, 3.693992535490862*^9}, { 3.69408137357989*^9, 3.6940813990399256`*^9}, {3.694081492270056*^9, 3.694081500430067*^9}, 3.694085807686309*^9, 3.694336369074993*^9, { 3.694336447585103*^9, 3.694336534165224*^9}, {3.6943365695452733`*^9, 3.694336572935278*^9}, {3.6943366355853662`*^9, 3.694336663395405*^9}, { 3.694336707865467*^9, 3.694336813505615*^9}, {3.6943368708856955`*^9, 3.694336972645838*^9}, {3.694337005795884*^9, 3.69433752400661*^9}, { 3.694337943297197*^9, 3.6943379730472383`*^9}, {3.694338096757412*^9, 3.694338100087416*^9}, {3.6943381564174953`*^9, 3.694338172057517*^9}, { 3.6943382111375713`*^9, 3.6943382179975815`*^9}, {3.694338370357795*^9, 3.694338415207857*^9}, {3.694338519908004*^9, 3.694338533448023*^9}, { 3.694338742738316*^9, 3.6943387845683746`*^9}, {3.6943388672484903`*^9, 3.694338909398549*^9}, {3.6943394389592905`*^9, 3.694339477079344*^9}, { 3.6943395685694723`*^9, 3.6943395881794996`*^9}, 3.6943396627096043`*^9, { 3.694339797119792*^9, 3.6943398030098004`*^9}, {3.6943398885999203`*^9, 3.6943400438301373`*^9}, {3.6943517756956816`*^9, 3.694351778765686*^9}, { 3.694351814965737*^9, 3.694351920335884*^9}, {3.6943520375260487`*^9, 3.694352038046049*^9}, {3.6943546301696777`*^9, 3.694354641489694*^9}, { 3.6943547065797853`*^9, 3.694354780889889*^9}, {3.694415922397947*^9, 3.694415933787963*^9}, {3.6944160021080585`*^9, 3.6944160163480783`*^9}, { 3.6944161612482815`*^9, 3.694416186218316*^9}, {3.6944162181183605`*^9, 3.694416241358393*^9}, {3.694416776009142*^9, 3.694416778289145*^9}, { 3.694417304849882*^9, 3.694417340579932*^9}, {3.6944179310727587`*^9, 3.6944179657728076`*^9}, {3.6944182927132654`*^9, 3.694418302313279*^9}, { 3.6944316170705633`*^9, 3.6944316923568697`*^9}, {3.6944318163219357`*^9, 3.694431820105152*^9}, {3.6965609549111967`*^9, 3.696560966061212*^9}, { 3.696560998851258*^9, 3.6965610020812626`*^9}, {3.6965611422314587`*^9, 3.696561159171482*^9}, 3.696563445644683*^9, {3.6965635186347857`*^9, 3.6965635322048044`*^9}, {3.696563569074856*^9, 3.6965635745148635`*^9}, { 3.696563720555068*^9, 3.69656372185507*^9}, {3.6965637807551527`*^9, 3.696563824135213*^9}, {3.6965639935254507`*^9, 3.696564031985504*^9}, { 3.696596096992402*^9, 3.696596186502527*^9}, {3.696596234252594*^9, 3.696596260452631*^9}, {3.6965963110027018`*^9, 3.69659632407272*^9}, 3.6965963803627987`*^9, {3.7244123642779827`*^9, 3.7244123648119507`*^9}, { 3.7255912428848085`*^9, 3.7255912492295227`*^9}, {3.725591466627203*^9, 3.725591704636403*^9}, {3.7255917405776634`*^9, 3.7255917613142586`*^9}, { 3.7255980783777914`*^9, 3.7255980873943977`*^9}, {3.725598135321295*^9, 3.7255981566673255`*^9}, {3.7255985463958807`*^9, 3.7255985750395555`*^9}, {3.725598660297285*^9, 3.725598669548276*^9}, { 3.7255989613446465`*^9, 3.7255989963014574`*^9}, {3.7255990922803245`*^9, 3.725599092624111*^9}, {3.7255991287997694`*^9, 3.7255991802271013`*^9}, 3.7255992673973975`*^9, {3.725599302619891*^9, 3.725599630275236*^9}, { 3.7255996917974653`*^9, 3.725600173598138*^9}, {3.72560026574846*^9, 3.7256002767652473`*^9}, 3.7256003308803263`*^9, {3.7256003995281887`*^9, 3.72560041238892*^9}, {3.725600503405278*^9, 3.725600537768276*^9}, { 3.72560062249599*^9, 3.725600660390954*^9}, {3.7256015423497496`*^9, 3.725601551460086*^9}, {3.725602674641403*^9, 3.725602676188448*^9}, { 3.725606737765007*^9, 3.7256067379681726`*^9}, {3.7259411263577843`*^9, 3.725941161974596*^9}, {3.7259413328141994`*^9, 3.7259413530325947`*^9}, { 3.725948620999795*^9, 3.7259486419857845`*^9}, 3.7259487502361426`*^9, { 3.725948801316684*^9, 3.7259488049789305`*^9}, {3.7259488747343755`*^9, 3.7259488880408845`*^9}, {3.7262144247900543`*^9, 3.7262144477456355`*^9}, {3.7574170493225684`*^9, 3.757417053184463*^9}, 3.757746126576226*^9, 3.7577461878004365`*^9, {3.7901299755504103`*^9, 3.7901299864607277`*^9}, {3.822369517016216*^9, 3.8223695503530917`*^9}, 3.853212126776141*^9, {3.8532121589674606`*^9, 3.85321225468412*^9}}, CellLabel-> "In[191]:=",ExpressionUUID->"6c5ea344-3532-48e2-8358-f6e53755c076"] }, Open ]], Cell[CellGroupData[{ Cell["PLATE ELEMENT (disp) defs ", "Subsection", CellChangeTimes->{{3.6302475626780834`*^9, 3.6302475636452847`*^9}, { 3.6303896204112215`*^9, 3.630389621175623*^9}, {3.7658855359334097`*^9, 3.7658855563942738`*^9}, {3.7882511594490995`*^9, 3.788251160663724*^9}},ExpressionUUID->"3eeb74f9-ff05-4e6e-bef9-\ 4948d2376dbf"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"MEC", "-", "E1050"}], "|", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "n\[Alpha]", ",", "n\[Beta]", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "NN", ",", "mat", ",", "MM", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "r\[Gamma]", ",", "rn", ",", "jac", ",", "h\[Alpha]", ",", "e\[Alpha]", ",", "h\[Beta]", ",", "h\[Gamma]", ",", "e\[Beta]", ",", "en", ",", "e\[Gamma]", ",", "FF", ",", "\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]", ",", "edg", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "\[Pi]u", ",", "\[Pi]v", ",", "\[Pi]w", ",", "\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]", ",", "f\[Alpha]", ",", "f\[Gamma]", ",", "fn", ",", "m\[Alpha]", ",", "m\[Gamma]", ",", "mn", ",", "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]", ",", "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]", ",", "\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]", ",", "GG", ",", "N\[Alpha]\[Alpha]", ",", "N\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Gamma]", ",", "N\[Gamma]\[Alpha]", ",", "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]", ",", "Q\[Alpha]", ",", "Q\[Gamma]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wmap", ",", "AA"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"mat", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]", "=", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}]}], ";", " ", RowBox[{"r\[Beta]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Norm", "[", "r\[Beta]", "]"}]}], ";", " ", RowBox[{"h\[Alpha]", "=", RowBox[{"Norm", "[", "r\[Alpha]", "]"}]}], ";", RowBox[{"jac", "=", RowBox[{"Norm", "[", RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Alpha]", "=", RowBox[{"r\[Alpha]", "/", "h\[Alpha]"}]}], ";", RowBox[{"e\[Beta]", "=", RowBox[{"r\[Beta]", "/", "h\[Beta]"}]}], ";", " ", RowBox[{"en", "=", RowBox[{ RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], " ", "/", "jac"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r\[Gamma]", "=", RowBox[{"r\[Beta]", "-", RowBox[{ RowBox[{"(", RowBox[{"r\[Beta]", ".", "e\[Alpha]"}], ")"}], " ", "e\[Alpha]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Gamma]", "=", RowBox[{"Norm", "[", "r\[Gamma]", "]"}]}], ";", RowBox[{"e\[Gamma]", "=", RowBox[{"r\[Gamma]", "/", "h\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", "e\[Gamma]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]"}], "}"}], "=", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Alpha]"}], ",", RowBox[{"r\[Alpha]", ".", "r\[Beta]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Beta]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Beta]"}]}], "}"}]}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Gamma]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Gamma]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"edg", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Sort", "[", "#", "]"}], "&"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "projection", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Pi]\[Phi]", "=", RowBox[{ RowBox[{ RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], "/", "60"}], "+", " ", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Theta]", "=", RowBox[{ RowBox[{ RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], "/", "60"}], "+", " ", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"continuous", " ", "displacement"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Pi]w", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]"}], "}"}], "=", RowBox[{ RowBox[{"FF", "[", RowBox[{"[", RowBox[{ RowBox[{"1", ";;", "2"}], ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]"}], "}"}], "=", RowBox[{ RowBox[{"FF", "[", RowBox[{"[", RowBox[{ RowBox[{"1", ";;", "2"}], ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"fn", "=", RowBox[{ RowBox[{"FF", "[", RowBox[{"[", "3", "]"}], "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"strain", " ", "measures", " ", "with", " ", "non"}], "-", RowBox[{"symmetric", " ", "\[Epsilon]"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}]}]}], ")"}]}], "/", "h\[Gamma]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", " ", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Theta]"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], "/", "h\[Alpha]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], "+", "\[Pi]\[Theta]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", "\[Pi]\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Alpha]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Gamma]\[Gamma]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Gamma]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Gamma]\[Gamma]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", " ", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}], "*", "\[Kappa]\[Alpha]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{ RowBox[{"5", "/", "6"}], " ", "*", "GG", "*", "tt", "*", "\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Gamma]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]"}], "}"}]}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Gamma]"}], "}"}]}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "w", "]"}], "*", "fn"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wmap", "=", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "/", "100000"}], "*", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]w", "-", "w"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]w", "-", "w"}], ")"}]}], ")"}], "*", "tt", "*", RowBox[{"EE", "/", "jac"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI3", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wmap"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "n\[Alpha]", ",", "n\[Beta]", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "NN", ",", "mat", ",", "MM", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "r\[Gamma]", ",", "rn", ",", "jac", ",", "h\[Alpha]", ",", "e\[Alpha]", ",", "h\[Beta]", ",", "h\[Gamma]", ",", "e\[Beta]", ",", "en", ",", "e\[Gamma]", ",", "FF", ",", "\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]", ",", "edg", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "\[Pi]u", ",", "\[Pi]v", ",", "\[Pi]w", ",", "\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]", ",", "f\[Alpha]", ",", "f\[Gamma]", ",", "fn", ",", "m\[Alpha]", ",", "m\[Gamma]", ",", "mn", ",", "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]", ",", "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]", ",", "\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Alpha]", ",", "N\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Gamma]", ",", "N\[Gamma]\[Alpha]", ",", "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]", ",", "Q\[Alpha]", ",", "Q\[Gamma]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wmap", ",", "AA"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "n1", ",", "n2", ",", "n3", ",", "n12", ",", "n23", ",", "n31"}], "*)"}], "\[IndentingNewLine]", RowBox[{"MM", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "+", RowBox[{"2", " ", SuperscriptBox["\[Alpha]", "2"]}], "-", RowBox[{"3", " ", "\[Beta]"}], "+", RowBox[{"2", " ", SuperscriptBox["\[Beta]", "2"]}], "+", RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"4", " ", "\[Beta]"}]}], ")"}]}]}], ",", RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}]}], ",", RowBox[{"\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"-", "4"}], " ", "\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}]}], ",", RowBox[{"4", " ", "\[Alpha]", " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"-", "4"}], " ", "\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]", "=", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}]}], ";", " ", RowBox[{"r\[Beta]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Norm", "[", "r\[Beta]", "]"}]}], ";", " ", RowBox[{"h\[Alpha]", "=", RowBox[{"Norm", "[", "r\[Alpha]", "]"}]}], ";", RowBox[{"jac", "=", RowBox[{"Norm", "[", RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Alpha]", "=", RowBox[{"r\[Alpha]", "/", "h\[Alpha]"}]}], ";", RowBox[{"e\[Beta]", "=", RowBox[{"r\[Beta]", "/", "h\[Beta]"}]}], ";", " ", RowBox[{"en", "=", RowBox[{ RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], " ", "/", "jac"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r\[Gamma]", "=", RowBox[{"r\[Beta]", "-", RowBox[{ RowBox[{"(", RowBox[{"r\[Beta]", ".", "e\[Alpha]"}], ")"}], " ", "e\[Alpha]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Gamma]", "=", RowBox[{"Norm", "[", "r\[Gamma]", "]"}]}], ";", RowBox[{"e\[Gamma]", "=", RowBox[{"r\[Gamma]", "/", "h\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", "e\[Gamma]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]"}], "}"}], "=", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Alpha]"}], ",", RowBox[{"r\[Alpha]", ".", "r\[Beta]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Beta]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Beta]"}]}], "}"}]}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Gamma]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Gamma]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"edg", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Sort", "[", "#", "]"}], "&"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"MM", ".", RowBox[{"Join", "[", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"{", RowBox[{ RowBox[{"uZ", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "2"}], "}"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}]}], "}"}]}], ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "2"}], "}"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}]}]}], ")"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "2"}], "}"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}]}]}], ")"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "projection", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Pi]\[Phi]", "=", RowBox[{"NN", ".", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"5", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "5", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "5"}], "}"}]}], "}"}], "/", "420"}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}], ",", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "2"}], "}"}], "]"}], ",", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}]}], "}"}]}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Theta]", "=", RowBox[{"NN", ".", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"5", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "5", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "5"}], "}"}]}], "}"}], "/", "420"}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "2"}], "}"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}]}], "}"}]}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"continuous", " ", "displacement"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Pi]w", "=", RowBox[{"MM", ".", RowBox[{"Join", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "3"}], "]"}], "]"}], ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]"}], "}"}], "=", RowBox[{ RowBox[{"FF", "[", RowBox[{"[", RowBox[{ RowBox[{"1", ";;", "2"}], ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]"}], "}"}], "=", RowBox[{ RowBox[{"FF", "[", RowBox[{"[", RowBox[{ RowBox[{"1", ";;", "2"}], ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"fn", "=", RowBox[{ RowBox[{"FF", "[", RowBox[{"[", "3", "]"}], "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"strain", " ", "measures", " ", "with", " ", "non"}], "-", RowBox[{"symmetric", " ", "\[Epsilon]"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}]}]}], ")"}]}], "/", "h\[Gamma]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", " ", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Theta]"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], "/", "h\[Alpha]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], "+", "\[Pi]\[Theta]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", "\[Pi]\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Alpha]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Gamma]\[Gamma]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Gamma]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Gamma]\[Gamma]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", " ", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}], "*", "\[Kappa]\[Alpha]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Gamma]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]"}], "}"}]}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Gamma]"}], "}"}]}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "w", "]"}], "*", "fn"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wmap", "=", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "/", "100000"}], "*", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]w", "-", "w"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]w", "-", "w"}], ")"}]}], ")"}], "*", "tt", "*", RowBox[{"EE", "/", "jac"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"exp", "=", RowBox[{"QUAD", "[", RowBox[{"TRI28", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wmap"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", "exp", "]"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"int", "=", RowBox[{"Join", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"uZ", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "2"}], "}"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}], ",", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "2"}], "}"}], "]"}], ",", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "2"}], "}"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"eqs", "=", RowBox[{"D", "[", RowBox[{"exp", ",", RowBox[{"{", RowBox[{"\[Delta]", "[", "int", "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", " ", "=", " ", RowBox[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"eqs", "==", "0"}], "]"}], ",", "int"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{ RowBox[{"exp", " ", "/.", "sol"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{ RowBox[{"\[Delta]", "[", "int", "]"}], "->", "0"}], "]"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.4426474258030453`*^9, {3.4444401255942*^9, 3.4444401388073997`*^9}, { 3.4444401803034*^9, 3.4444401844062*^9}, 3.4444402418922*^9, { 3.4444402805022*^9, 3.4444403134026003`*^9}, {3.4444403443062*^9, 3.4444404484049997`*^9}, {3.444483267101*^9, 3.444483267335*^9}, { 3.4444833136046*^9, 3.4444835622998*^9}, {3.4444836421094*^9, 3.4444837777981997`*^9}, {3.444483920429*^9, 3.4444839412237997`*^9}, 3.4444842905546*^9, {3.4444843207406*^9, 3.4444844162282*^9}, { 3.4444844465078*^9, 3.4444844624354*^9}, {3.4444845255998*^9, 3.4444845894505997`*^9}, {3.4444846290746*^9, 3.444484933025*^9}, { 3.4444849790917997`*^9, 3.4444851148742*^9}, {3.444534936054*^9, 3.4445349675348*^9}, {3.4445355821731997`*^9, 3.44453585174*^9}, { 3.4445372162198*^9, 3.4445372264378*^9}, 3.444537384731*^9, { 3.4445377585382*^9, 3.4445377605818*^9}, {3.4445379733658*^9, 3.4445379736934*^9}, {3.4445380176762*^9, 3.444538032777*^9}, { 3.4445381079222*^9, 3.4445381581386003`*^9}, {3.4445382726456003`*^9, 3.4445382910067997`*^9}, {3.4445383401312*^9, 3.4445383475880003`*^9}, { 3.444538438458*^9, 3.4445384464608*^9}, {3.4445385680783997`*^9, 3.4445385687648*^9}, {3.4445389411991997`*^9, 3.4445389431024*^9}, { 3.444539746605*^9, 3.4445397807846003`*^9}, {3.4445408839765997`*^9, 3.4445409234133997`*^9}, {3.4445409681698*^9, 3.4445409932702*^9}, { 3.4445415452906*^9, 3.4445415706717997`*^9}, {3.4445416647242002`*^9, 3.4445416909477997`*^9}, {3.4445417660150003`*^9, 3.444541788557*^9}, { 3.4445420906977997`*^9, 3.444542104847*^9}, {3.4445421885878*^9, 3.4445421941414003`*^9}, {3.4445422252166*^9, 3.4445422386014*^9}, { 3.444542280425*^9, 3.4445423014538*^9}, {3.444542455769*^9, 3.4445424578282003`*^9}, {3.4445431739214*^9, 3.444543175809*^9}, { 3.4445647020962*^9, 3.4445648405618*^9}, {3.4445648825414*^9, 3.4445648858486*^9}, {3.4445649382646*^9, 3.4445651882702*^9}, { 3.4446164822206*^9, 3.4446165344494*^9}, {3.4446166121842003`*^9, 3.4446166738822002`*^9}, {3.4446167223046*^9, 3.4446168047974*^9}, { 3.444616843033*^9, 3.444616906447*^9}, {3.4446444694708*^9, 3.4446444700948*^9}, {3.4446477738310003`*^9, 3.4446477939862003`*^9}, { 3.4446478467298*^9, 3.4446478681018*^9}, 3.4446480456142*^9, { 3.4446487557418003`*^9, 3.4446487636198*^9}, 3.4446488179974003`*^9, { 3.4446488971205997`*^9, 3.4446489152478*^9}, {3.4446490003458*^9, 3.4446490008294*^9}, {3.4447042728942003`*^9, 3.4447042751562*^9}, { 3.4447044703278*^9, 3.4447044865362*^9}, 3.4447046475282*^9, 3.4447047993786*^9, {3.444704908329*^9, 3.4447049292642*^9}, { 3.4447049861926003`*^9, 3.4447049877214003`*^9}, {3.4447050279296*^9, 3.4447050419695997`*^9}, {3.4447053486656*^9, 3.4447053739376*^9}, 3.4447054561963997`*^9, 3.44470561612*^9, {3.4472133996876*^9, 3.4472134108571997`*^9}, {3.4472134470179996`*^9, 3.4472134648332*^9}, { 3.4472135032872*^9, 3.4472135245344*^9}, {3.4472136963059998`*^9, 3.4472137794384003`*^9}, {3.4472138235708*^9, 3.4472138388900003`*^9}, { 3.4472139099792*^9, 3.4472141367096*^9}, {3.447214202682*^9, 3.4472142975924*^9}, {3.4472144187732*^9, 3.4472145910284*^9}, { 3.4472146560492*^9, 3.4472147023968*^9}, {3.447214803594*^9, 3.4472148728736*^9}, {3.4472149156956*^9, 3.447214940484*^9}, { 3.447216227284*^9, 3.4472162419948*^9}, {3.4472163068908*^9, 3.4472163720832*^9}, {3.4472164665880003`*^9, 3.447216530392*^9}, { 3.4472166237268*^9, 3.4472167058452*^9}, 3.4472167362808*^9, { 3.4472171394658003`*^9, 3.4472171532874002`*^9}, {3.4472172028993998`*^9, 3.4472172216661997`*^9}, {3.4472172524606*^9, 3.4472172690278*^9}, { 3.4472173209133997`*^9, 3.4472173334245996`*^9}, {3.4472173920846*^9, 3.447217404861*^9}, {3.4472179572548*^9, 3.4472180351456003`*^9}, { 3.4472509764091997`*^9, 3.4472511017396*^9}, {3.4473910422216*^9, 3.4473912901524*^9}, 3.4473918688344*^9, {3.447392021185*^9, 3.4473920346633997`*^9}, {3.4473921383304*^9, 3.4473921479088*^9}, { 3.4473923024112*^9, 3.4473923734379997`*^9}, {3.4473928098168*^9, 3.4473928648691998`*^9}, {3.4473931872432003`*^9, 3.4473932461800003`*^9}, {3.4473933026675997`*^9, 3.4473934579812*^9}, { 3.4473935755271997`*^9, 3.447393742572*^9}, {3.4473939032676*^9, 3.4473939384144*^9}, {3.447395257644*^9, 3.4473953141628*^9}, { 3.4473954231132*^9, 3.4473954756384*^9}, {3.4473955348716*^9, 3.4473955723272*^9}, {3.447395648502*^9, 3.4473957588876*^9}, { 3.4473957903996*^9, 3.4473958488372*^9}, 3.4473962894154*^9, { 3.447396350817*^9, 3.447396352611*^9}, {3.4474625379146*^9, 3.4474625637326*^9}, {3.558360651728078*^9, 3.558360652102478*^9}, { 3.5619791319820857`*^9, 3.561979135788492*^9}, 3.561979369382504*^9, { 3.5619794930439215`*^9, 3.5619795010155354`*^9}, {3.561979569218855*^9, 3.56197960614412*^9}, {3.5619797417551584`*^9, 3.5619797448751636`*^9}, { 3.618719065033702*^9, 3.618719075426296*^9}, {3.6187194011669273`*^9, 3.6187194449454317`*^9}, {3.6187196998040085`*^9, 3.6187197102436056`*^9}, {3.618719902254588*^9, 3.6187199711455283`*^9}, { 3.618722365406472*^9, 3.6187225412555304`*^9}, {3.6187226885009522`*^9, 3.6187227109872384`*^9}, {3.618722756922866*^9, 3.6187231317203026`*^9}, { 3.618723424250035*^9, 3.6187234267291765`*^9}, {3.6187235105259695`*^9, 3.6187236491028957`*^9}, {3.618723691580325*^9, 3.618723745975436*^9}, { 3.618723778837316*^9, 3.6187238310002995`*^9}, {3.6187239055875654`*^9, 3.618723940035536*^9}, {3.6187239782667227`*^9, 3.6187240219352207`*^9}, { 3.618724166762504*^9, 3.618724177411113*^9}, {3.618729321696159*^9, 3.618729328067523*^9}, 3.618729374058154*^9, {3.6187294379838104`*^9, 3.618729708464281*^9}, {3.6187297631904106`*^9, 3.618729773195983*^9}, { 3.618729822648812*^9, 3.6187299321490746`*^9}, {3.618729984399063*^9, 3.61873000654133*^9}, {3.6187300746012225`*^9, 3.6187300860458775`*^9}, { 3.618731390835507*^9, 3.6187315116174154`*^9}, {3.618731747324897*^9, 3.6187318214091344`*^9}, {3.6187318769243097`*^9, 3.618732065297084*^9}, { 3.6187321012351394`*^9, 3.618732157420353*^9}, {3.618732188384124*^9, 3.6187322435542793`*^9}, {3.6187322786112847`*^9, 3.6187325478446836`*^9}, {3.6187325819856367`*^9, 3.6187326817653437`*^9}, {3.618732810863728*^9, 3.61873282594359*^9}, { 3.6187336474335766`*^9, 3.618733754678711*^9}, {3.618733827497876*^9, 3.61873396201257*^9}, {3.6187342020362988`*^9, 3.618734236455267*^9}, 3.618734298201799*^9, {3.618734712498495*^9, 3.618734712716508*^9}, 3.6187347739640107`*^9, {3.618738817361748*^9, 3.6187388333816643`*^9}, { 3.6187391349349127`*^9, 3.6187391457955337`*^9}, {3.618739376900752*^9, 3.618739397023903*^9}, {3.618739528394417*^9, 3.618739534809784*^9}, { 3.618739972366811*^9, 3.61873997340687*^9}, {3.6187400416617737`*^9, 3.618740043022852*^9}, {3.6187400971579485`*^9, 3.618740107902563*^9}, { 3.6187401713671927`*^9, 3.6187401723312483`*^9}, {3.6187402613443394`*^9, 3.618740268819767*^9}, {3.6187403697625403`*^9, 3.6187404057615995`*^9}, { 3.618740488277319*^9, 3.618740516244919*^9}, {3.618740647782442*^9, 3.6187406551668644`*^9}, 3.6187407823021364`*^9, {3.6187418050786357`*^9, 3.618741805749674*^9}, {3.6187418557605343`*^9, 3.6187419895921893`*^9}, { 3.618742022944097*^9, 3.61874204379729*^9}, {3.6187420836395683`*^9, 3.618742103384698*^9}, {3.620462440882641*^9, 3.6204624460519366`*^9}, { 3.6204624990259666`*^9, 3.620462576450395*^9}, {3.620463682857678*^9, 3.620463713336421*^9}, 3.6204637901188126`*^9, {3.620464238835478*^9, 3.62046424411378*^9}, 3.628912429385081*^9, {3.6289135207155013`*^9, 3.6289135210805225`*^9}, 3.6289497746958513`*^9, 3.6289498371774254`*^9, { 3.62894988410911*^9, 3.6289500319795675`*^9}, {3.6289501333883677`*^9, 3.628950183744248*^9}, {3.6289503323017445`*^9, 3.628950390181055*^9}, { 3.6289505050536256`*^9, 3.6289505113579865`*^9}, {3.62895070863527*^9, 3.6289507095043197`*^9}, {3.628951013180689*^9, 3.62895101407374*^9}, { 3.629190743153632*^9, 3.629190816645361*^9}, {3.6291909709608326`*^9, 3.629190981678051*^9}, {3.629191034624544*^9, 3.6291910410049553`*^9}, { 3.6293846391370816`*^9, 3.629384641102685*^9}, {3.6294628543371735`*^9, 3.629462867097191*^9}, {3.629468063172048*^9, 3.6294681151669397`*^9}, { 3.6295205836757097`*^9, 3.6295206295085897`*^9}, {3.6295206788826766`*^9, 3.6295207067911253`*^9}, {3.6295207408927855`*^9, 3.629520753700408*^9}, { 3.629521020590745*^9, 3.6295210354395943`*^9}, {3.6295211107369013`*^9, 3.62952114882508*^9}, {3.6295212327348795`*^9, 3.6295212477237363`*^9}, { 3.6295213424816394`*^9, 3.629521343230441*^9}, {3.6295215363119802`*^9, 3.6295216753550243`*^9}, {3.629521922272258*^9, 3.6295219939855833`*^9}, { 3.6295220298188467`*^9, 3.629522446058778*^9}, {3.629522499348471*^9, 3.629522604352256*^9}, {3.629522755188921*^9, 3.62952288580795*^9}, { 3.629522918084407*^9, 3.6295233421087513`*^9}, {3.6295233808436193`*^9, 3.629523390936837*^9}, {3.629523424274096*^9, 3.6295234533369465`*^9}, { 3.6295235190130625`*^9, 3.629523521680667*^9}, 3.6295235894315863`*^9, { 3.6295237270706277`*^9, 3.629523799454755*^9}, {3.6295238514808464`*^9, 3.629523883460902*^9}, {3.6295239376085978`*^9, 3.6295239442386093`*^9}, { 3.6295241089904985`*^9, 3.629524177537019*^9}, 3.629524211888279*^9, { 3.629524277423994*^9, 3.629524396904604*^9}, {3.6295244794839497`*^9, 3.6295246248450055`*^9}, 3.629524657090262*^9, {3.6295259599109507`*^9, 3.629526013465844*^9}, {3.6295261092188125`*^9, 3.629526201414974*^9}, 3.6295263436092243`*^9, {3.6295263910333076`*^9, 3.629526583303645*^9}, { 3.629526616672104*^9, 3.629526647653758*^9}, {3.629526687558628*^9, 3.629526744888729*^9}, {3.629526804075233*^9, 3.6295268598453307`*^9}, { 3.6295269393898706`*^9, 3.6295269586559043`*^9}, {3.6295271490074387`*^9, 3.6295272149019547`*^9}, {3.6295272553684254`*^9, 3.6295272827620735`*^9}, {3.6295274137087035`*^9, 3.6295274761244135`*^9}, {3.6295275252801*^9, 3.6295279912529182`*^9}, { 3.6295281572216096`*^9, 3.629528160435215*^9}, {3.6295282905550437`*^9, 3.6295284308616905`*^9}, 3.6295285402022824`*^9, {3.629528582088356*^9, 3.629528616798417*^9}, {3.6295287666834803`*^9, 3.6295290316343455`*^9}, { 3.629529086515242*^9, 3.629529118432898*^9}, {3.6295291548121614`*^9, 3.629529292794404*^9}, {3.6295293426208916`*^9, 3.6295293491261034`*^9}, { 3.629529420699029*^9, 3.629529571535694*^9}, {3.6295296539506383`*^9, 3.629529656103442*^9}, {3.6295296894407005`*^9, 3.629529692295506*^9}, { 3.6295297445555973`*^9, 3.629529766426836*^9}, {3.6295298053333044`*^9, 3.6295298209489317`*^9}, {3.6295308380551186`*^9, 3.6295308386635194`*^9}, {3.629532377840223*^9, 3.6295323811630287`*^9}, { 3.629532480020402*^9, 3.629532482454006*^9}, {3.629532520720874*^9, 3.629532564619351*^9}, {3.62953259842461*^9, 3.6295326002654133`*^9}, { 3.6295326327758703`*^9, 3.6295326715107384`*^9}, {3.629532742428463*^9, 3.6295328288058147`*^9}, {3.6295329692184625`*^9, 3.6295330530062094`*^9}, {3.6295331824396367`*^9, 3.629533193562456*^9}, 3.6295350321720915`*^9, 3.629535158485513*^9, {3.629535245471266*^9, 3.6295352687465067`*^9}, {3.62953541293756*^9, 3.629535446384019*^9}, { 3.6295355043381205`*^9, 3.6295355262249594`*^9}, {3.629543790136781*^9, 3.629543791181983*^9}, {3.629543871350524*^9, 3.629544001673153*^9}, { 3.6295446682009234`*^9, 3.629544668466124*^9}, {3.6296010216162376`*^9, 3.6296010236442413`*^9}, {3.629601079336339*^9, 3.6296010902875586`*^9}, 3.6296011425476503`*^9, {3.6296043522397404`*^9, 3.629604399031022*^9}, { 3.629623884428093*^9, 3.629623914723346*^9}, {3.6296239662190366`*^9, 3.6296239738006496`*^9}, {3.6296240514731865`*^9, 3.6296240920176573`*^9}, {3.629624125947717*^9, 3.629624369432945*^9}, { 3.6296256512247963`*^9, 3.6296256817072496`*^9}, {3.6296260472626915`*^9, 3.629626047434292*^9}, {3.629628055568204*^9, 3.629628056098605*^9}, { 3.6296280911206665`*^9, 3.6296281088266973`*^9}, {3.6296281406819534`*^9, 3.629628273032586*^9}, {3.629628378831972*^9, 3.6296283814995766`*^9}, { 3.629628459562114*^9, 3.629628466379326*^9}, {3.629628519419419*^9, 3.6296285390754533`*^9}, {3.629633008133008*^9, 3.629633008835009*^9}, { 3.6296337764967575`*^9, 3.6296338344040594`*^9}, {3.6296342997684765`*^9, 3.629634432150309*^9}, {3.629634494035618*^9, 3.6296345320060844`*^9}, { 3.629634594499794*^9, 3.629634812182576*^9}, {3.6296348599810605`*^9, 3.6296348746918864`*^9}, {3.6296349071867433`*^9, 3.629635023172947*^9}, 3.6296350995818815`*^9, {3.6296363797201295`*^9, 3.6296363868961425`*^9}, { 3.629636462025874*^9, 3.6296364833355117`*^9}, {3.629636555922439*^9, 3.62963656780966*^9}, {3.629636770469616*^9, 3.629636774151222*^9}, { 3.6296369192782774`*^9, 3.6296369318830996`*^9}, {3.629637058539722*^9, 3.6296370719401455`*^9}, {3.629637278172508*^9, 3.629637286814923*^9}, { 3.6296376418091464`*^9, 3.629637662385583*^9}, {3.629637773551378*^9, 3.629637795360216*^9}, {3.6296390041751394`*^9, 3.629639039571602*^9}, 3.6296393829750047`*^9, {3.6296395546065063`*^9, 3.6296395649961243`*^9}, { 3.62964113386068*^9, 3.6296412507048855`*^9}, {3.629641303167777*^9, 3.629641313744596*^9}, {3.6296416285116315`*^9, 3.629641628886032*^9}, { 3.6296416658736973`*^9, 3.6296416815049243`*^9}, 3.6296417376338234`*^9, { 3.6296855551269727`*^9, 3.6296855804270077`*^9}, {3.6297079065796247`*^9, 3.6297079070476255`*^9}, {3.6297080850439377`*^9, 3.629708135728427*^9}, { 3.6297083496516027`*^9, 3.6297084025512953`*^9}, {3.629708781767563*^9, 3.629708790940379*^9}, {3.6297089402482414`*^9, 3.6297089618542795`*^9}, { 3.6297105345398417`*^9, 3.629710538580249*^9}, {3.6297107810514746`*^9, 3.6297107850138817`*^9}, {3.6297109100481014`*^9, 3.629710915710911*^9}, { 3.629711201534613*^9, 3.629711204311418*^9}, {3.629711236307074*^9, 3.6297115007275386`*^9}, {3.6297115377464037`*^9, 3.6297115441112146`*^9}, 3.6297116025645175`*^9, {3.6298716505389357`*^9, 3.629871851841689*^9}, { 3.62987837458679*^9, 3.629878383510006*^9}, {3.6298784402629056`*^9, 3.629878447345318*^9}, {3.6298785221786494`*^9, 3.6298786580236883`*^9}, { 3.629878689613744*^9, 3.629878737147027*^9}, 3.629878783853509*^9, { 3.629878832322794*^9, 3.6298789171723433`*^9}, {3.6298802128122005`*^9, 3.6298802929723125`*^9}, 3.6298813644148126`*^9, {3.629882428887303*^9, 3.629882435887313*^9}, {3.6298986251827383`*^9, 3.6298988530367384`*^9}, { 3.6298989036744275`*^9, 3.6298989486493063`*^9}, {3.629899016868226*^9, 3.6298991622448816`*^9}, {3.6298997154530535`*^9, 3.629899740147897*^9}, { 3.6298998248560457`*^9, 3.629899978048314*^9}, {3.6299000396372223`*^9, 3.6299001557638264`*^9}, {3.6299001966826982`*^9, 3.6299002595352087`*^9}, 3.6299005011236343`*^9, {3.6299005468317146`*^9, 3.629900567642151*^9}, { 3.629900887676713*^9, 3.629900990153293*^9}, {3.6299011689220085`*^9, 3.6299012295125146`*^9}, {3.6299013754039707`*^9, 3.6299014166036434`*^9}, 3.6299014589733176`*^9, {3.6299015096734066`*^9, 3.629901588765546*^9}, { 3.629901662569275*^9, 3.6299016974665365`*^9}, {3.629901952339784*^9, 3.6299019599057975`*^9}, 3.6299020306051216`*^9, {3.6299022330934772`*^9, 3.6299022682559395`*^9}, {3.6299023020455985`*^9, 3.629902332808852*^9}, { 3.6299024532566643`*^9, 3.629902462850681*^9}, {3.629949880225117*^9, 3.6299498807867184`*^9}, {3.6299503101150723`*^9, 3.6299503156998825`*^9}, {3.629950355058751*^9, 3.629950498937804*^9}, { 3.6299555415202007`*^9, 3.6299555507086167`*^9}, {3.6299556061667137`*^9, 3.6299557553497763`*^9}, {3.629955788499834*^9, 3.6299558948608212`*^9}, { 3.629956042764681*^9, 3.629956043809883*^9}, {3.6299560914211664`*^9, 3.6299561017327843`*^9}, 3.629956145849662*^9, {3.6299584813821354`*^9, 3.6299585082765827`*^9}, 3.6299585652946825`*^9, {3.629958616587573*^9, 3.6299586356508064`*^9}, {3.629958715073346*^9, 3.6299588186419287`*^9}, { 3.629958857454797*^9, 3.629958927249319*^9}, {3.629959427994599*^9, 3.629959494669116*^9}, {3.6299595293323765`*^9, 3.6299596037913074`*^9}, { 3.62995966795422*^9, 3.62995967360143*^9}, {3.6299597835972233`*^9, 3.6299597841120243`*^9}, {3.629959826622099*^9, 3.629959862533362*^9}, { 3.6299599051682367`*^9, 3.6299599235918694`*^9}, 3.629959979939168*^9, { 3.6299601345354395`*^9, 3.62996014612626*^9}, 3.6299601769831142`*^9, { 3.629960253142448*^9, 3.629960269538077*^9}, {3.6299603041701374`*^9, 3.6299603078205442`*^9}, {3.6299604300467587`*^9, 3.629960435491168*^9}, { 3.6299605300585346`*^9, 3.6299605636609936`*^9}, {3.6299606195870914`*^9, 3.6299606581971593`*^9}, {3.629960824228251*^9, 3.6299608755367413`*^9}, { 3.629960906658796*^9, 3.6299609978409557`*^9}, {3.6299610312250147`*^9, 3.629961070646284*^9}, {3.629961135698398*^9, 3.6299611643088484`*^9}, { 3.6299720458358483`*^9, 3.6299721791536827`*^9}, {3.6299722439717965`*^9, 3.629972300007095*^9}, {3.6299723670872126`*^9, 3.6299723937008595`*^9}, { 3.629972457801372*^9, 3.6299724710613956`*^9}, {3.629972740193068*^9, 3.6299728251196175`*^9}, {3.6299729203577843`*^9, 3.6299729350218105`*^9}, {3.6299729720874753`*^9, 3.6299730462188053`*^9}, {3.629973116044528*^9, 3.6299731230177402`*^9}, { 3.629973184310248*^9, 3.6299732090830917`*^9}, {3.629973349982539*^9, 3.6299734360166903`*^9}, 3.629973534562063*^9, {3.629973577446539*^9, 3.629973586104554*^9}, {3.6299740374133463`*^9, 3.629974083823428*^9}, { 3.6299742505565205`*^9, 3.629974337089873*^9}, {3.629974382907153*^9, 3.6299744466176653`*^9}, {3.629974589794717*^9, 3.629974590761918*^9}, { 3.629974776215044*^9, 3.6299747850134597`*^9}, {3.6299748226095257`*^9, 3.6299748237483273`*^9}, 3.6299748618435946`*^9, {3.629975198476586*^9, 3.6299752545898843`*^9}, {3.62997531475919*^9, 3.6299753175515947`*^9}, { 3.6299754601982455`*^9, 3.6299754625382495`*^9}, {3.629975592034077*^9, 3.629975592502078*^9}, {3.629983277446268*^9, 3.6299832946842985`*^9}, { 3.62998342081052*^9, 3.6299835439883366`*^9}, {3.629983615514462*^9, 3.629983931009416*^9}, {3.6299919807040443`*^9, 3.6299919808912444`*^9}, { 3.629992028330928*^9, 3.6299920922130404`*^9}, 3.629992198480427*^9, { 3.6299922299300823`*^9, 3.629992250506518*^9}, {3.629992292657792*^9, 3.6299923603151107`*^9}, {3.6299924387676487`*^9, 3.6299924398440504`*^9}, {3.6299925764846907`*^9, 3.6299926096347485`*^9}, {3.6299928122323046`*^9, 3.629992818768716*^9}, { 3.6299929049120674`*^9, 3.629992905411268*^9}, {3.6299929850338078`*^9, 3.6299929866250105`*^9}, {3.6299931061992207`*^9, 3.62999312270405*^9}, { 3.629993172312137*^9, 3.6299932618718944`*^9}, {3.6299933276572104`*^9, 3.6299933842073092`*^9}, {3.630287775665962*^9, 3.630287795852398*^9}, { 3.6303896387100534`*^9, 3.630389666774503*^9}, {3.6303896967889557`*^9, 3.6303897095341783`*^9}, {3.6303897587054644`*^9, 3.630389880448078*^9}, { 3.6303899127557354`*^9, 3.630390009444705*^9}, 3.630390057321189*^9, 3.630390443484267*^9, {3.63039095720877*^9, 3.6303909789240074`*^9}, { 3.6303910572205453`*^9, 3.6303911291054716`*^9}, {3.630391163035531*^9, 3.6303911740803504`*^9}, {3.630391240224467*^9, 3.6303912875081496`*^9}, { 3.6303913396902413`*^9, 3.630391404570755*^9}, {3.630391479513287*^9, 3.6303917572873745`*^9}, {3.630391868905571*^9, 3.6303920027226057`*^9}, { 3.630392064327114*^9, 3.630392219843787*^9}, {3.63039226121506*^9, 3.63039232943398*^9}, {3.6303924315985594`*^9, 3.6303924441097813`*^9}, { 3.6303926866122074`*^9, 3.6303927118530517`*^9}, {3.630392795671999*^9, 3.6303928006172075`*^9}, {3.6303986032190485`*^9, 3.6303986046230516`*^9}, {3.6303986654631586`*^9, 3.6303987936485834`*^9}, {3.63039889979117*^9, 3.6303989091199865`*^9}, { 3.630399006323757*^9, 3.630399007259759*^9}, {3.630399117224352*^9, 3.630399214771323*^9}, {3.6303992555185947`*^9, 3.6303993036758795`*^9}, { 3.630399467725767*^9, 3.630399502731636*^9}, {3.6303995748037624`*^9, 3.630399595614199*^9}, {3.6303996329294643`*^9, 3.630399658076709*^9}, { 3.630399711335202*^9, 3.6303997453120623`*^9}, {3.6303998546994543`*^9, 3.6303999880484886`*^9}, {3.6304000742074394`*^9, 3.630400123441126*^9}, { 3.6304001724564123`*^9, 3.630400251595351*^9}, {3.630400324166679*^9, 3.630400327052684*^9}, {3.630400358190338*^9, 3.6304003597503414`*^9}, { 3.6304004587481155`*^9, 3.6304004640521245`*^9}, {3.630400521975026*^9, 3.630400526124634*^9}, {3.630400567199506*^9, 3.630400593516752*^9}, { 3.6304012340070767`*^9, 3.6304013035207987`*^9}, {3.6304013614749007`*^9, 3.630401367933312*^9}, {3.630401686939398*^9, 3.6304017294598303`*^9}, { 3.630401794020523*^9, 3.6304018922061386`*^9}, {3.6304019687775183`*^9, 3.630401987153569*^9}, {3.630402072749465*^9, 3.63040208297405*^9}, { 3.6304022247881613`*^9, 3.630402255931943*^9}, 3.630402329306139*^9, { 3.6304023806970787`*^9, 3.6304024212403975`*^9}, {3.6304025002259154`*^9, 3.630402528595538*^9}, {3.6304025620694523`*^9, 3.630402575015193*^9}, { 3.6304026411829777`*^9, 3.630402649073429*^9}, {3.630402695548087*^9, 3.6304027128260756`*^9}, {3.630402783923142*^9, 3.6304027982389607`*^9}, { 3.6304028797236214`*^9, 3.6304030111811404`*^9}, {3.6304030562107162`*^9, 3.6304031598846455`*^9}, {3.630403236330018*^9, 3.6304032404072514`*^9}, { 3.630403373001835*^9, 3.6304033888147397`*^9}, {3.6304039420953856`*^9, 3.6304039512829113`*^9}, 3.6304039831437335`*^9, {3.630404015975611*^9, 3.6304040663624935`*^9}, {3.630404173614628*^9, 3.630404246945822*^9}, { 3.6304042891772375`*^9, 3.630404299595834*^9}, {3.630404391083066*^9, 3.630404392406142*^9}, {3.6304045301800222`*^9, 3.6304045579486103`*^9}, { 3.630404640215316*^9, 3.630404762796327*^9}, {3.630404877629895*^9, 3.630404883104208*^9}, {3.6304050364729805`*^9, 3.630405098270515*^9}, { 3.6304051736118245`*^9, 3.6304051965901384`*^9}, {3.6304053802536435`*^9, 3.63040539242334*^9}, {3.630406035965148*^9, 3.630406041998493*^9}, { 3.630406072049212*^9, 3.6304060962065935`*^9}, {3.630406264081196*^9, 3.6304062707025747`*^9}, {3.63040632219952*^9, 3.630406385461138*^9}, { 3.630406477200385*^9, 3.630406482095665*^9}, {3.6304066170883865`*^9, 3.6304066222256804`*^9}, {3.630406957868878*^9, 3.630406973411767*^9}, { 3.6304070081447535`*^9, 3.630407018199329*^9}, {3.630407411376817*^9, 3.630407412542884*^9}, {3.6304080609339695`*^9, 3.630408121202417*^9}, { 3.6304081585485525`*^9, 3.6304081832129636`*^9}, {3.63040821409673*^9, 3.630408421131572*^9}, 3.6304934333363276`*^9, {3.63049350751357*^9, 3.630493677593298*^9}, {3.630493716898546*^9, 3.6304937846684227`*^9}, 3.630493922944331*^9, {3.6304939556752033`*^9, 3.630494117430455*^9}, { 3.6304941486092386`*^9, 3.6304941767788496`*^9}, {3.6304942118648567`*^9, 3.6304942530272107`*^9}, {3.6304942838399734`*^9, 3.6304942845820155`*^9}, {3.6304943454054947`*^9, 3.6304944442451477`*^9}, {3.63080749995092*^9, 3.6308075480801234`*^9}, { 3.630807586536323*^9, 3.630807621440319*^9}, {3.630807680459695*^9, 3.630807682914836*^9}, {3.630807736889923*^9, 3.6308077644745007`*^9}, { 3.6308078081089964`*^9, 3.6308078670123653`*^9}, {3.630807991648494*^9, 3.630807997541831*^9}, {3.6308081080891542`*^9, 3.6308081919599514`*^9}, { 3.630808306368495*^9, 3.630808345060708*^9}, {3.6308087281906223`*^9, 3.6308087555171847`*^9}, {3.630809110815507*^9, 3.630809169033837*^9}, { 3.6308091998195972`*^9, 3.630809448512822*^9}, {3.6308095328996487`*^9, 3.6308095448223305`*^9}, {3.630809582269472*^9, 3.6308095873607635`*^9}, { 3.630809665529235*^9, 3.630809684808337*^9}, {3.6308316258485594`*^9, 3.6308318380886984`*^9}, {3.63083188164919*^9, 3.630831966930068*^9}, 3.6320400558356075`*^9, {3.6354749882908883`*^9, 3.635474989418953*^9}, { 3.635475084557395*^9, 3.6354750875145636`*^9}, {3.6354751334091887`*^9, 3.635475162315842*^9}, {3.6354754001974483`*^9, 3.6354754820331287`*^9}, 3.635475512931896*^9, {3.6354756222781506`*^9, 3.635475622861184*^9}, { 3.635475691642118*^9, 3.6354757057969275`*^9}, {3.6354757798291616`*^9, 3.635475797395167*^9}, {3.635475884848169*^9, 3.6354758981309285`*^9}, { 3.635475961488552*^9, 3.6354759738382587`*^9}, {3.6354760213729773`*^9, 3.6354760572050266`*^9}, {3.6354761282470903`*^9, 3.635476136040536*^9}, { 3.6354761719365892`*^9, 3.635476212217893*^9}, {3.6593346599546614`*^9, 3.659334660890663*^9}, {3.6593347077219453`*^9, 3.659334720701168*^9}, { 3.6593348752974396`*^9, 3.6593348758122406`*^9}, {3.6593349140947075`*^9, 3.6593350070240707`*^9}, {3.6593350466949406`*^9, 3.6593350543701544`*^9}, {3.659335103791041*^9, 3.6593351614487424`*^9}, 3.659335217686841*^9, {3.659335262084519*^9, 3.6593352995869846`*^9}, { 3.6593356899482727`*^9, 3.659335701819893*^9}, {3.659335964227954*^9, 3.659335964602355*^9}, {3.65933603594128*^9, 3.6593360629605274`*^9}, { 3.6593361352354546`*^9, 3.6593361504454813`*^9}, {3.6593363929479074`*^9, 3.6593364061611304`*^9}, 3.6593368946915884`*^9, {3.6884748265656157`*^9, 3.6884748268716326`*^9}, {3.6884748600075283`*^9, 3.688474861420609*^9}, { 3.6885242858240776`*^9, 3.6885243001140976`*^9}, {3.6888842911675606`*^9, 3.6888843311676164`*^9}, {3.688966242423658*^9, 3.688966263933688*^9}, { 3.6897393587897596`*^9, 3.6897393649897685`*^9}, 3.689739477049925*^9, { 3.6898595970621734`*^9, 3.689859597272174*^9}, {3.6898596707522764`*^9, 3.6898597190523443`*^9}, {3.689859768552414*^9, 3.6898597721424184`*^9}, { 3.689859855272535*^9, 3.689859859882541*^9}, {3.6898605078334484`*^9, 3.6898607266237545`*^9}, 3.6898608811139708`*^9, {3.6898609634740863`*^9, 3.689860974304102*^9}, 3.6898610140141573`*^9, {3.6898611496043468`*^9, 3.6898611683243732`*^9}, {3.689861462024784*^9, 3.6898615624849253`*^9}, { 3.6898616142149973`*^9, 3.6898616164350004`*^9}, 3.6898616657950697`*^9, { 3.689861716805141*^9, 3.689861749905187*^9}, {3.732677920575506*^9, 3.7326779208190203`*^9}, {3.7519672427004185`*^9, 3.7519672444968877`*^9}, {3.7519674022097683`*^9, 3.75196742976579*^9}, { 3.751967484127989*^9, 3.751967510853814*^9}, {3.7519675409404893`*^9, 3.751967541549782*^9}, {3.7519675797751045`*^9, 3.751967592209671*^9}, { 3.7519676829383273`*^9, 3.7519676841255474`*^9}, {3.7519677154775553`*^9, 3.7519677953499403`*^9}, 3.751967827811061*^9, {3.7519679545625095`*^9, 3.751967957999185*^9}, {3.751968003754015*^9, 3.7519681477513895`*^9}, { 3.751968264817631*^9, 3.751968270722477*^9}, {3.7519689618119907`*^9, 3.751968969888235*^9}, {3.7519691168917775`*^9, 3.7519691395895615`*^9}, { 3.751969242782174*^9, 3.7519692581691785`*^9}, {3.7519693625211954`*^9, 3.751969378579924*^9}, {3.751969409572627*^9, 3.751969438643936*^9}, { 3.7519695894526725`*^9, 3.751969614306203*^9}, {3.7523200108586655`*^9, 3.752320012354121*^9}, {3.7553831315619707`*^9, 3.755383134119626*^9}, { 3.7553831893197794`*^9, 3.755383241814331*^9}, {3.7553832736267967`*^9, 3.7553832810757113`*^9}, {3.7554336536222963`*^9, 3.755433684797229*^9}, { 3.7554337764737434`*^9, 3.7554338315300155`*^9}, {3.755433998047738*^9, 3.7554340265485487`*^9}, {3.755446573138784*^9, 3.755446636911299*^9}, { 3.75544667493072*^9, 3.755446753435521*^9}, {3.755446891541581*^9, 3.7554468921547422`*^9}, {3.7554469323588533`*^9, 3.755446936867403*^9}, { 3.7554470190332975`*^9, 3.7554472776872244`*^9}, {3.7555217323692026`*^9, 3.755521732847602*^9}, {3.755521767127169*^9, 3.7555217972041793`*^9}, { 3.755522561453134*^9, 3.755522564231819*^9}, {3.755522601885935*^9, 3.7555226037287407`*^9}, {3.7555226758687305`*^9, 3.755522678585092*^9}, { 3.7555234832604623`*^9, 3.7555235920444417`*^9}, {3.7555239506007543`*^9, 3.755524013893358*^9}, {3.755524076791689*^9, 3.7555240812793446`*^9}, { 3.7555241238138275`*^9, 3.7555241268985643`*^9}, {3.7555242930449886`*^9, 3.7555243378577013`*^9}, {3.7555256673767824`*^9, 3.7555256808205338`*^9}, {3.7555258588384123`*^9, 3.755525900317296*^9}, { 3.755525930708299*^9, 3.7555260436531134`*^9}, {3.755607147401991*^9, 3.7556071504143705`*^9}, {3.755607992884314*^9, 3.7556080025382996`*^9}, { 3.7556094344057455`*^9, 3.7556094348690443`*^9}, {3.7559613653116636`*^9, 3.755961445097105*^9}, 3.755961484246889*^9, {3.7559618979231987`*^9, 3.755961939470047*^9}, {3.7559620323724904`*^9, 3.7559620330864005`*^9}, { 3.755962155557907*^9, 3.7559621601593847`*^9}, {3.755962303755834*^9, 3.755962343830135*^9}, {3.7559624058018165`*^9, 3.7559624450501757`*^9}, 3.756002186674869*^9, 3.7560029626855392`*^9, {3.756003222110388*^9, 3.756003295034633*^9}, {3.7560056331492863`*^9, 3.7560056663855457`*^9}, { 3.7560057813555765`*^9, 3.7560057863836613`*^9}, {3.7560058917172394`*^9, 3.756005927847292*^9}, 3.756006092376186*^9, 3.756009112317705*^9, { 3.756091886039587*^9, 3.756091887764086*^9}, {3.756092005435152*^9, 3.7560920727337685`*^9}, {3.75609212911592*^9, 3.7560921293252516`*^9}, { 3.756092262958163*^9, 3.756092263157668*^9}, {3.756092342487877*^9, 3.756092347894502*^9}, {3.7560929036769304`*^9, 3.7560929278911004`*^9}, { 3.7560930741522417`*^9, 3.756093083420331*^9}, {3.7560932986236534`*^9, 3.7560933139459305`*^9}, {3.756093449985523*^9, 3.7560934874491863`*^9}, { 3.756093592694581*^9, 3.7560936019456573`*^9}, {3.756093634438078*^9, 3.756093673866626*^9}, {3.756093873069885*^9, 3.756093897964734*^9}, { 3.7560940650109406`*^9, 3.756094078056768*^9}, {3.756442536546026*^9, 3.756442607904289*^9}, {3.7564436397451363`*^9, 3.7564436403231254`*^9}, { 3.7636034984570236`*^9, 3.7636034989933815`*^9}, {3.763603551051456*^9, 3.7636035527617817`*^9}, {3.7636036049384193`*^9, 3.7636036392233057`*^9}, {3.7636036850937223`*^9, 3.763603692587598*^9}, { 3.7636037258272257`*^9, 3.7636037459031096`*^9}, {3.7636037792254367`*^9, 3.76360387572289*^9}, {3.763603971837229*^9, 3.7636040341423655`*^9}, { 3.763604066526084*^9, 3.7636040756798687`*^9}, {3.7636041452118535`*^9, 3.763604278007333*^9}, {3.763604317710966*^9, 3.7636043271387568`*^9}, { 3.7636043584877644`*^9, 3.763604415561053*^9}, {3.763604445680462*^9, 3.7636044504114943`*^9}, {3.763604615444647*^9, 3.7636048082554193`*^9}, 3.763604854904996*^9, {3.7636133594095488`*^9, 3.7636133618464766`*^9}, { 3.7636136063756704`*^9, 3.7636136315671196`*^9}, {3.7636990373827705`*^9, 3.7636990431157646`*^9}, {3.763699090332087*^9, 3.763699110952259*^9}, { 3.763699227420497*^9, 3.7636993642943506`*^9}, {3.763700085627533*^9, 3.763700088329999*^9}, {3.7637001721125274`*^9, 3.763700181422837*^9}, { 3.763700248063385*^9, 3.7637003918630466`*^9}, {3.763700591783223*^9, 3.7637006017496295`*^9}, {3.7637007583576717`*^9, 3.7637007603074865`*^9}, {3.7637137795793185`*^9, 3.7637137822587233`*^9}, {3.7637148704355187`*^9, 3.763714870624051*^9}, { 3.763727592158518*^9, 3.7637275933445053`*^9}, {3.7637276688363667`*^9, 3.7637276694756594`*^9}, 3.763803448896332*^9, {3.76380349501632*^9, 3.7638036835067654`*^9}, {3.763804829093463*^9, 3.7638048385675254`*^9}, 3.7638051033646154`*^9, 3.7638053924528885`*^9, {3.763805557684454*^9, 3.763805634255308*^9}, {3.763806843847647*^9, 3.763806847966059*^9}, { 3.763806942652097*^9, 3.7638071770752254`*^9}, {3.7638141184594107`*^9, 3.763814134133461*^9}, {3.7638146808628216`*^9, 3.7638146925645113`*^9}, { 3.7638147709278784`*^9, 3.7638147811883087`*^9}, {3.7638148155281043`*^9, 3.763814819843194*^9}, {3.7638150259647446`*^9, 3.763815028601293*^9}, { 3.7638151529595194`*^9, 3.763815155849978*^9}, {3.7638163770262136`*^9, 3.763816380851597*^9}, {3.7638164181856327`*^9, 3.7638164950537987`*^9}, 3.763816568304102*^9, {3.7638166173645625`*^9, 3.763816618808757*^9}, { 3.7638167204462805`*^9, 3.763816721012859*^9}, {3.763857602253485*^9, 3.7638579604183645`*^9}, {3.7638580038507566`*^9, 3.7638580060526443`*^9}, {3.763858082269992*^9, 3.7638581746835337`*^9}, { 3.7638582163351564`*^9, 3.7638582415275116`*^9}, {3.7638582983238*^9, 3.763858907503306*^9}, {3.763858941318697*^9, 3.763858956626134*^9}, { 3.7638602435602536`*^9, 3.763860245408451*^9}, {3.7638694636456347`*^9, 3.7638694647177277`*^9}, {3.7638708199536576`*^9, 3.763870829436488*^9}, { 3.763871287170555*^9, 3.7638712876184006`*^9}, {3.763943214376035*^9, 3.7639432984591475`*^9}, {3.763943418832348*^9, 3.7639434335508127`*^9}, { 3.76394347113767*^9, 3.7639435187320576`*^9}, {3.763943585908682*^9, 3.7639436125255404`*^9}, {3.763951722152746*^9, 3.76395172989299*^9}, { 3.7639517863423367`*^9, 3.7639519945900664`*^9}, {3.763952081515512*^9, 3.7639521530710773`*^9}, {3.763952353248129*^9, 3.763952357026309*^9}, { 3.7639524211903834`*^9, 3.7639524243979177`*^9}, {3.7639527174925117`*^9, 3.7639527180252266`*^9}, {3.7641265625745993`*^9, 3.7641265632314167`*^9}, {3.764126605555829*^9, 3.7641266075095396`*^9}, { 3.7641268313964133`*^9, 3.7641268543573804`*^9}, {3.764127044657903*^9, 3.7641270479422092`*^9}, {3.7641271442332697`*^9, 3.7641271469362774`*^9}, {3.764127227626192*^9, 3.7641272592640233`*^9}, { 3.764127335707515*^9, 3.7641273386484756`*^9}, {3.764127429843852*^9, 3.7641274364304185`*^9}, {3.7641275071859307`*^9, 3.764127516803895*^9}, 3.7641276043548007`*^9, {3.7641276925365753`*^9, 3.764127697080591*^9}, 3.764127798472331*^9, 3.764127853631323*^9, 3.764127908496078*^9, { 3.7641280050343323`*^9, 3.764128022046494*^9}, {3.764128128597419*^9, 3.764128154116727*^9}, {3.7641286864636617`*^9, 3.764128701643106*^9}, { 3.7641289910924444`*^9, 3.7641290126680794`*^9}, {3.7641290672285347`*^9, 3.7641290737798567`*^9}, {3.7641325425120363`*^9, 3.764132565390477*^9}, { 3.7641327425004654`*^9, 3.764132750040793*^9}, 3.7641327968340364`*^9, { 3.764133146776842*^9, 3.764133204874522*^9}, {3.7641333488187037`*^9, 3.7641333525577593`*^9}, {3.764413145593136*^9, 3.7644131471236105`*^9}, { 3.764413201645049*^9, 3.7644132349609704`*^9}, {3.764413325008136*^9, 3.7644133748980193`*^9}, {3.7644134113425665`*^9, 3.7644135151187*^9}, { 3.764413554409053*^9, 3.7644136160674934`*^9}, {3.76441371984758*^9, 3.764413730103909*^9}, 3.764419641962368*^9, {3.7644198522879405`*^9, 3.764419879249356*^9}, 3.764419909536559*^9, {3.764419991012162*^9, 3.764420000171088*^9}, {3.7644200798862047`*^9, 3.7644200950961914`*^9}, { 3.7644201529471693`*^9, 3.764420153715966*^9}, {3.764420210346301*^9, 3.764420255343707*^9}, {3.764420296178318*^9, 3.7644203000939393`*^9}, { 3.7644203803359275`*^9, 3.7644203931390867`*^9}, 3.7644204418727274`*^9, { 3.7647259720700207`*^9, 3.7647261047260523`*^9}, {3.7647263483375626`*^9, 3.76472635879602*^9}, 3.764726656736601*^9, {3.764727009127914*^9, 3.764727020100875*^9}, {3.7647270591828785`*^9, 3.7647270819631023`*^9}, { 3.7647272109090505`*^9, 3.764727227846332*^9}, {3.76473247809907*^9, 3.7647324813925114`*^9}, {3.7647349484962797`*^9, 3.7647349979358416`*^9}, {3.7647351097258167`*^9, 3.764735124772463*^9}, { 3.7647352810674453`*^9, 3.7647352901139917`*^9}, {3.7647353746429515`*^9, 3.764735379550926*^9}, {3.7647354596539807`*^9, 3.764735507677454*^9}, { 3.7647355546341*^9, 3.764735728811817*^9}, {3.764735837449795*^9, 3.76473584132898*^9}, {3.76473603649269*^9, 3.7647360592982664`*^9}, { 3.7647360998228803`*^9, 3.76473621551197*^9}, {3.7647362545599003`*^9, 3.764736286430997*^9}, {3.7647364592833533`*^9, 3.764736464019006*^9}, { 3.764736566167658*^9, 3.7647365918958225`*^9}, {3.764764761680134*^9, 3.7647648482473745`*^9}, 3.764764917763693*^9, {3.764764964821686*^9, 3.764765090741813*^9}, {3.7647651742140284`*^9, 3.7647652517335076`*^9}, { 3.764765341266399*^9, 3.7647653614173465`*^9}, 3.764765400284145*^9, { 3.764765691384389*^9, 3.764765708710143*^9}, 3.7647657454275875`*^9, { 3.76476578351686*^9, 3.764765871262255*^9}, {3.7647661045180917`*^9, 3.76476612822571*^9}, {3.7647661964223824`*^9, 3.764766239375331*^9}, { 3.764766330361228*^9, 3.764766338297905*^9}, {3.764767015060799*^9, 3.7647670193029037`*^9}, {3.764767076590926*^9, 3.7647671160277977`*^9}, { 3.7647671493139205`*^9, 3.7647672079236426`*^9}, {3.764767458938404*^9, 3.7647674608323865`*^9}, {3.764810938444873*^9, 3.7648109399353456`*^9}, { 3.7648118616019874`*^9, 3.7648118695079126`*^9}, {3.7648120589477816`*^9, 3.7648124600413237`*^9}, {3.76481250476682*^9, 3.7648125259602103`*^9}, { 3.764812601341893*^9, 3.7648126577763243`*^9}, {3.7648126944039307`*^9, 3.7648128855627623`*^9}, {3.764812924923909*^9, 3.764812926481821*^9}, { 3.764813041485982*^9, 3.764813131254232*^9}, {3.7648134679328885`*^9, 3.7648136479313235`*^9}, {3.7648136917777314`*^9, 3.764813697753367*^9}, { 3.7648137297570653`*^9, 3.764813747862262*^9}, 3.764813784221693*^9, { 3.7648138370678406`*^9, 3.7648141387969923`*^9}, {3.764814321050164*^9, 3.764814422489184*^9}, {3.764814461366684*^9, 3.7648145835728483`*^9}, { 3.764814614769511*^9, 3.7648147525825167`*^9}, {3.764815363375289*^9, 3.7648153644907384`*^9}, {3.764815451671169*^9, 3.7648154601533747`*^9}, { 3.7648175917802963`*^9, 3.7648176401910563`*^9}, {3.765885491237231*^9, 3.765885501131465*^9}, {3.766572999289345*^9, 3.7665729996020145`*^9}, { 3.7665730613126965`*^9, 3.7665730616706066`*^9}, {3.7840103262125545`*^9, 3.7840103546413517`*^9}, {3.784011309725755*^9, 3.7840113197719574`*^9}, { 3.784013374800973*^9, 3.7840133842981763`*^9}, {3.7840238533665447`*^9, 3.78402395932942*^9}, {3.784024091276659*^9, 3.784024112209529*^9}, { 3.7840242793219643`*^9, 3.784024296655184*^9}, {3.7840290670892677`*^9, 3.7840291348388853`*^9}, {3.784029222997594*^9, 3.784029542926179*^9}, { 3.784375172285057*^9, 3.784375319701829*^9}, {3.7843753678421807`*^9, 3.7843753788103914`*^9}, {3.7843754844339557`*^9, 3.784375827494117*^9}, { 3.784375862317687*^9, 3.7843759567563844`*^9}, {3.784376004941759*^9, 3.7843760080157185`*^9}, {3.784376101918992*^9, 3.7843761244332943`*^9}, { 3.784376181191763*^9, 3.7843762145091863`*^9}, {3.7843792489960337`*^9, 3.78437926273014*^9}, {3.7843793293934345`*^9, 3.784379368676588*^9}, { 3.7843796529835215`*^9, 3.7843796858862267`*^9}, {3.784450863324359*^9, 3.7844508986076546`*^9}, {3.7844510208392324`*^9, 3.784451027915551*^9}, { 3.7844511176315613`*^9, 3.7844511673791957`*^9}, {3.784451235055628*^9, 3.78445132575735*^9}, {3.784451995615477*^9, 3.7844520110330954`*^9}, { 3.7844522907551537`*^9, 3.7844523421551*^9}, {3.784700119490345*^9, 3.7847001627913013`*^9}, {3.7847004221290607`*^9, 3.7847004380767317`*^9}, 3.7847007913506136`*^9, {3.784781955129138*^9, 3.784781977787957*^9}, { 3.78488170216677*^9, 3.784881704210422*^9}, 3.784882130557441*^9, { 3.78488220347418*^9, 3.7848822064697027`*^9}, {3.784883393455822*^9, 3.784883458551924*^9}, 3.7848835306495824`*^9, {3.7848836822092113`*^9, 3.7848837303696923`*^9}, 3.7848838199009576`*^9, {3.7848842507527857`*^9, 3.7848842836585226`*^9}, 3.7848843847882996`*^9, {3.784884461405264*^9, 3.7848844645041113`*^9}, {3.784884559404122*^9, 3.7848845656634912`*^9}, { 3.7848852409944844`*^9, 3.7848852740337477`*^9}, {3.7848854548929386`*^9, 3.7848854893046365`*^9}, {3.7848856741783943`*^9, 3.784885691704702*^9}, { 3.784885809660874*^9, 3.784885811424426*^9}, {3.7848860031948376`*^9, 3.784886020570098*^9}, 3.7848861057105627`*^9, {3.7848861627726107`*^9, 3.7848862212876124`*^9}, {3.784886306497995*^9, 3.7848863509322224`*^9}, 3.784886472690192*^9, {3.7848866596243*^9, 3.784886664116289*^9}, { 3.7848866987282944`*^9, 3.7848867077911897`*^9}, {3.78488676128524*^9, 3.7848868667029366`*^9}, {3.7848869381224003`*^9, 3.7848869414281464`*^9}, {3.7848870104508753`*^9, 3.784887039889447*^9}, { 3.7848871795058794`*^9, 3.7848871976746817`*^9}, {3.7848872311446314`*^9, 3.78488724075662*^9}, 3.784887405188785*^9, {3.784887591926689*^9, 3.7848876119305134`*^9}, {3.784887676620901*^9, 3.7848876786672792`*^9}, { 3.78488771054331*^9, 3.784887714354906*^9}, {3.7848877625809546`*^9, 3.7848878103041153`*^9}, 3.7848878862881575`*^9, {3.787717235155089*^9, 3.787717269464238*^9}, {3.7877174592607603`*^9, 3.7877174674038067`*^9}, { 3.7877271032841845`*^9, 3.787727136247201*^9}, 3.787727355369296*^9, 3.7877274973278403`*^9, {3.787727855959008*^9, 3.78772792141208*^9}, 3.787728113487193*^9, {3.7877281704571557`*^9, 3.7877281735077004`*^9}, 3.7877282789827795`*^9, {3.7877286510229864`*^9, 3.787728665729192*^9}, { 3.7877287942225084`*^9, 3.787728807671986*^9}, {3.787729044867985*^9, 3.787729045536916*^9}, {3.787729589732438*^9, 3.7877296062090626`*^9}, { 3.787729794037467*^9, 3.7877297950347877`*^9}, {3.787729855548402*^9, 3.7877299039179935`*^9}, {3.7877300373241186`*^9, 3.787730068136018*^9}, { 3.7877301999859333`*^9, 3.7877302014150777`*^9}, {3.787732033225385*^9, 3.7877320471634016`*^9}, {3.787732077195259*^9, 3.7877320780358667`*^9}, 3.787732189759206*^9, {3.78773231889835*^9, 3.787732327710633*^9}, { 3.7877324857166643`*^9, 3.787732496655479*^9}, {3.7877325848303585`*^9, 3.78773258503596*^9}, {3.7877328504631166`*^9, 3.7877328625892415`*^9}, { 3.7877330254884944`*^9, 3.7877330271019044`*^9}, {3.787733136128061*^9, 3.7877331422258835`*^9}, {3.787733243513567*^9, 3.78773324558677*^9}, 3.787733310555999*^9, 3.7877334085329347`*^9, {3.7877337955932293`*^9, 3.7877337970498257`*^9}, {3.787733867727028*^9, 3.7877338687324905`*^9}, { 3.7877352224369583`*^9, 3.787735224161746*^9}, {3.787735343322833*^9, 3.787735348772827*^9}, {3.787735422704711*^9, 3.7877354268945775`*^9}, { 3.7877355100355635`*^9, 3.787735514671461*^9}, {3.7877356541994534`*^9, 3.7877356632141013`*^9}, 3.7877357913476543`*^9, 3.787736261837074*^9, { 3.7882542159043374`*^9, 3.7882542747998285`*^9}, {3.788254310967661*^9, 3.788254318430212*^9}, {3.788254585790197*^9, 3.7882545888318524`*^9}, { 3.7882547349987383`*^9, 3.788254735940298*^9}, 3.788254830063775*^9, 3.7882549155286837`*^9, {3.7882550121437798`*^9, 3.788255037735396*^9}, { 3.7882551764404287`*^9, 3.78825518352113*^9}, {3.7882552540030313`*^9, 3.788255290224329*^9}, {3.7882553843544893`*^9, 3.788255423248046*^9}, { 3.78825567982127*^9, 3.7882556852479534`*^9}, {3.7882557908576803`*^9, 3.7882558029800806`*^9}, {3.7882560240494256`*^9, 3.7882560388846164`*^9}, 3.788256102343512*^9, {3.788256161397396*^9, 3.7882561626372194`*^9}, { 3.7882562304311895`*^9, 3.78825629590362*^9}, {3.7882563614677362`*^9, 3.7882563620189795`*^9}, {3.7882564138122153`*^9, 3.7882564294158382`*^9}, {3.788256467457189*^9, 3.7882564889521217`*^9}, { 3.7882565883311844`*^9, 3.788256591497148*^9}, {3.7882568409513097`*^9, 3.7882568724526567`*^9}, {3.788256965258837*^9, 3.788256966444976*^9}, { 3.7882570073831463`*^9, 3.7882570497349973`*^9}, {3.7882570992487097`*^9, 3.788257144206352*^9}, {3.78825721252205*^9, 3.788257307277931*^9}, { 3.788257350410209*^9, 3.7882573617262745`*^9}, {3.788257424936472*^9, 3.788257434118204*^9}, {3.788276311330668*^9, 3.788276311647092*^9}, { 3.7882765465512347`*^9, 3.788276608568333*^9}, {3.7882767715851693`*^9, 3.7882768045752783`*^9}, {3.7882769342607436`*^9, 3.7882769409894867`*^9}, {3.7882770202208567`*^9, 3.7882770424485188`*^9}, {3.7882770760040703`*^9, 3.788277077341468*^9}, { 3.788277147336176*^9, 3.788277150397852*^9}, {3.7882772069909*^9, 3.7882772101572385`*^9}, {3.7882772503366175`*^9, 3.7882772773759403`*^9}, {3.7882773922958755`*^9, 3.7882773927832017`*^9}, {3.788277450684473*^9, 3.788277482126852*^9}, { 3.78827754293396*^9, 3.788277545027956*^9}, 3.7890961565048018`*^9, { 3.789096242941472*^9, 3.7890962452874937`*^9}, {3.789096286771101*^9, 3.789096287939043*^9}, {3.7890963300637918`*^9, 3.789096330454324*^9}, { 3.789096421623994*^9, 3.789096482010544*^9}, {3.789123616007924*^9, 3.7891236603119373`*^9}, {3.82004560462539*^9, 3.820045628865552*^9}, { 3.820045711583801*^9, 3.82004571444415*^9}, {3.82004574552601*^9, 3.8200458146656227`*^9}, {3.8200459471200194`*^9, 3.820045947496038*^9}, { 3.820113346283964*^9, 3.820113420687029*^9}, {3.843547853319944*^9, 3.8435478596811757`*^9}, {3.8435479019503555`*^9, 3.8435479743034277`*^9}, {3.843560932189252*^9, 3.8435609338416433`*^9}, { 3.8435611914261384`*^9, 3.8435611920632486`*^9}, {3.8435624320536933`*^9, 3.8435624411683536`*^9}, {3.8437295238924494`*^9, 3.843729569229367*^9}, { 3.8443920425579967`*^9, 3.844392043749901*^9}, {3.844392085066965*^9, 3.84439210220125*^9}, 3.8443921338951335`*^9, {3.8443921701680193`*^9, 3.8443921937971706`*^9}, {3.844513395563983*^9, 3.8445134085996456`*^9}, { 3.8447683674104347`*^9, 3.844768368670556*^9}, {3.8447684443309875`*^9, 3.8447684484900866`*^9}, 3.8447686520157948`*^9, {3.844768745687599*^9, 3.844768745855211*^9}, 3.845183304458513*^9, {3.8451835940010877`*^9, 3.845183594542489*^9}, {3.845184390302038*^9, 3.845184391945329*^9}, { 3.8451845184651327`*^9, 3.845184537503073*^9}, {3.845184725810747*^9, 3.845184727862517*^9}, 3.8451848085572977`*^9, {3.845255005543473*^9, 3.8452550701614428`*^9}, {3.845255116528925*^9, 3.845255130817441*^9}, { 3.8452553159491444`*^9, 3.845255398239421*^9}, {3.8452554316887584`*^9, 3.845255516323632*^9}, {3.845255572312236*^9, 3.84525558031181*^9}, { 3.8452556104383307`*^9, 3.845255693908064*^9}, {3.845527992682146*^9, 3.8455280119549503`*^9}, {3.8455280677849493`*^9, 3.8455282068632755`*^9}, 3.845528296510269*^9, {3.84552838544649*^9, 3.8455283972662654`*^9}, { 3.8455285111156416`*^9, 3.845528620724532*^9}, {3.8455286507394857`*^9, 3.8455286778537693`*^9}, {3.84552875397721*^9, 3.8455287832150126`*^9}, { 3.8455288134263644`*^9, 3.8455288242659492`*^9}, {3.845528882756366*^9, 3.845528933497317*^9}, {3.845529287839986*^9, 3.8455293012812443`*^9}, { 3.8455293978278055`*^9, 3.8455293981111383`*^9}, {3.845529499537836*^9, 3.8455295004065795`*^9}, {3.845609477072257*^9, 3.8456096065189395`*^9}, { 3.845609662788809*^9, 3.845609668689152*^9}, {3.845609712860342*^9, 3.8456097209108343`*^9}, {3.845609845478004*^9, 3.845609907655341*^9}, { 3.8456103094907556`*^9, 3.845610323020236*^9}, {3.845610368769788*^9, 3.845610376316151*^9}, {3.845610434176654*^9, 3.84561049090069*^9}, 3.845610522214707*^9, 3.8456107866420207`*^9, {3.8456108553684444`*^9, 3.845610855574578*^9}, {3.845611041459861*^9, 3.845611043810052*^9}, { 3.8456116165491714`*^9, 3.8456117283491564`*^9}, {3.8456117769969835`*^9, 3.8456118220363483`*^9}, {3.8456118703237553`*^9, 3.8456119831151495`*^9}, {3.8456124022981386`*^9, 3.8456124224583464`*^9}, {3.8456127164733524`*^9, 3.845612740344495*^9}, { 3.845780852075635*^9, 3.8457808657114325`*^9}, {3.8457821230286026`*^9, 3.845782123716519*^9}, {3.8457825521920204`*^9, 3.845782609179036*^9}, { 3.845782729323619*^9, 3.8457827515157847`*^9}, {3.845782785128273*^9, 3.845782803453997*^9}, {3.8457828344736314`*^9, 3.8457828358311925`*^9}, { 3.845783094796917*^9, 3.8457830991701584`*^9}, {3.8457833361542873`*^9, 3.845783501335464*^9}, {3.845783531957113*^9, 3.8457835680525503`*^9}, 3.845783764414663*^9, 3.84578597144022*^9, 3.8457864896793737`*^9, { 3.845787119546991*^9, 3.84578713411397*^9}, {3.845787696751997*^9, 3.8457877204318814`*^9}, 3.8457882983714895`*^9, {3.8457885986921697`*^9, 3.8457886169047403`*^9}, {3.8457887088707514`*^9, 3.8457887217894297`*^9}, {3.8457887909210815`*^9, 3.8457888144201937`*^9}, {3.8457888906519327`*^9, 3.8457889466368628`*^9}, {3.8457890416459827`*^9, 3.845789052312254*^9}, { 3.845789116545609*^9, 3.8457891180744157`*^9}, {3.845789226429738*^9, 3.8457892292024574`*^9}, {3.845790510151396*^9, 3.845790519684927*^9}, 3.8457906357570543`*^9, {3.8458635760826883`*^9, 3.845863582446103*^9}, { 3.8458636696732097`*^9, 3.845863680633752*^9}, {3.8458637198783617`*^9, 3.845863725217595*^9}, 3.8458643039964285`*^9, {3.845864896377093*^9, 3.8458649228570347`*^9}, 3.8458654592977276`*^9, {3.8458655305222178`*^9, 3.845865533812125*^9}, 3.8458656269752007`*^9, 3.8458662253983583`*^9, { 3.845866315341114*^9, 3.845866316735467*^9}, {3.8458664630238924`*^9, 3.845866520383334*^9}, {3.845866555205945*^9, 3.845866566614134*^9}, { 3.845866724894957*^9, 3.8458667295073595`*^9}, {3.8458670210920024`*^9, 3.8458670231028185`*^9}, 3.8458671129063563`*^9, 3.8458672295699835`*^9, 3.845867522574538*^9, {3.845867616322856*^9, 3.845867616819559*^9}, { 3.8458677144565196`*^9, 3.8458677161961637`*^9}, {3.845867821061138*^9, 3.845867825279958*^9}, 3.8458680066485095`*^9, {3.845868278532402*^9, 3.845868302364672*^9}, {3.8458688185729504`*^9, 3.845868834819693*^9}, { 3.845869294519817*^9, 3.845869295105886*^9}}, CellLabel-> "In[193]:=",ExpressionUUID->"01613799-7c68-4c0f-8663-961896f0ebdd"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", "fn_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Alpha]", ",", "\[Beta]", ",", "r", ",", "e1", ",", "e2", ",", "e3", ",", "en", ",", "FF", ",", "FFINV", ",", "jac", ",", "NN", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "AA", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Phi]", ",", "wc", ",", "E\[Sigma]", ",", "\[Delta]w", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wmap", ",", "\[Kappa]\[Kappa]", ",", "\[Gamma]\[Gamma]", ",", "MM", ",", "QQ", ",", "tri", ",", RowBox[{"mat", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}]}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"mapping", " ", "for", " ", "the", " ", "geometry"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"e1", ",", "e2"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"e3", "=", RowBox[{"e1", StyleBox["\[Cross]", "OperatorCharacter"], "e2"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{"e3", "/", RowBox[{"Sqrt", "[", RowBox[{"e3", ".", "e3"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "1", ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"D", "[", RowBox[{"r", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", " ", RowBox[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "approximations", "*)"}], "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"ind", "=", RowBox[{"{", RowBox[{ RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], ",", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], ",", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"wc", "=", RowBox[{"NN", ".", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2"}], "]"}], "]"}], ".", "en"}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "projection", "*)"}], "\[IndentingNewLine]", RowBox[{"AA", "=", RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", "jac", ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]"}], "}"}], "=", RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]"}], "}"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "/", "AA"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"strain", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Kappa]\[Kappa]", "=", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], ".", RowBox[{"Transpose", "[", "FFINV", "]"}], ".", RowBox[{"D", "[", RowBox[{"\[Phi]", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}], "}"}]}], "]"}]}], "-", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}], ".", RowBox[{"Transpose", "[", "FFINV", "]"}], ".", RowBox[{"D", "[", RowBox[{"\[Theta]", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}], "}"}]}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Gamma]\[Gamma]", "=", RowBox[{ RowBox[{ RowBox[{"Transpose", "[", "FFINV", "]"}], ".", RowBox[{"D", "[", RowBox[{"w", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}], "}"}]}], "]"}]}], "+", RowBox[{"{", RowBox[{"\[Pi]\[Theta]", ",", RowBox[{"-", "\[Pi]\[Phi]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"E\[Sigma]", "=", RowBox[{ RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "\[Nu]\[Nu]", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Nu]\[Nu]", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}]}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"MM", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", "E\[Sigma]"}], ")"}], ".", "\[Kappa]\[Kappa]"}]}], ";", "\[IndentingNewLine]", RowBox[{"QQ", "=", RowBox[{"tt", "*", "GG", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Kappa]\[Kappa]", "]"}], ".", "MM"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Gamma]\[Gamma]", "]"}], ".", "QQ"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "w", "]"}], "*", "fn"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wmap", "=", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", RowBox[{"wc", "-", "w"}], "]"}]}], "*", RowBox[{"(", RowBox[{"wc", "-", "w"}], ")"}], "*", RowBox[{"tt", "/", "AA"}], "*", "EE"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI1", ",", RowBox[{ RowBox[{"(", "\[Delta]wmap", ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Dohrmann", " ", "Bochev"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLATETEST", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", "fn_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Alpha]", ",", "\[Beta]", ",", "xg", ",", "yg", ",", "r", ",", "FF", ",", "FFINV", ",", "jac", ",", "NN", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "AA", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Phi]", ",", "wc", ",", "E\[Sigma]", ",", "\[Delta]w", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wmap", ",", "\[Kappa]\[Kappa]", ",", "\[Gamma]\[Gamma]", ",", "MM", ",", "QQ", ",", "tri"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"mapping", " ", "for", " ", "the", " ", "geometry"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "1", ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"D", "[", RowBox[{"r", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", " ", RowBox[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "approximations", "*)"}], "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]wx", "=", RowBox[{ RowBox[{"b", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "0"}], "}"}], "]"}], "+", RowBox[{ RowBox[{"b", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}], "*", "x"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]wy", "=", RowBox[{ RowBox[{"b", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}], "+", RowBox[{ RowBox[{"b", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "4"}], "}"}], "]"}], "*", "y"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"strain", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Kappa]\[Kappa]", "=", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], ".", RowBox[{"Transpose", "[", "FFINV", "]"}], ".", RowBox[{"D", "[", RowBox[{"\[Phi]", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}], "}"}]}], "]"}]}], "-", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}], ".", RowBox[{"Transpose", "[", "FFINV", "]"}], ".", RowBox[{"D", "[", RowBox[{"\[Theta]", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}], "}"}]}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Gamma]\[Gamma]", "=", RowBox[{ RowBox[{ RowBox[{"Transpose", "[", "FFINV", "]"}], ".", RowBox[{"D", "[", RowBox[{"\[Pi]w", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}], "}"}]}], "]"}]}], "+", RowBox[{"{", RowBox[{"\[Theta]", ",", RowBox[{"-", "\[Phi]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"E\[Sigma]", "=", RowBox[{ RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "\[Nu]\[Nu]", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Nu]\[Nu]", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}]}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"MM", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", "E\[Sigma]"}], ")"}], ".", "\[Kappa]\[Kappa]"}]}], ";", "\[IndentingNewLine]", RowBox[{"QQ", "=", RowBox[{"tt", "*", "GG", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Kappa]\[Kappa]", "]"}], ".", "MM"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Gamma]\[Gamma]", "]"}], ".", "QQ"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "w", "]"}], "*", "fn"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wmap", "=", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", RowBox[{"(", RowBox[{"\[Pi]w", "-", "w"}], ")"}], "]"}]}], "*", RowBox[{"(", RowBox[{"\[Pi]w", "-", "w"}], ")"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext", "+", RowBox[{"100", "*", "\[Delta]wmap"}]}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLATEBUILD", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", "fn_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "xn", ",", "yn", ",", "x", ",", "y", ",", "NN", ",", "MM", ",", "w", ",", "ww", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Phi]", ",", "E\[Sigma]", ",", "\[Delta]w", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Kappa]", ",", "\[Gamma]", ",", "M", ",", "Q", ",", "tri", ",", "Ae", ",", "asm"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"xn", "=", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "1", ",", "1"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"yn", "=", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "1", ",", "2"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", "1"}], "}"}], ",", "xn", ",", "yn"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"1", ",", "x", ",", "y"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"MM", "=", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "1"}], "}"}]}], "}"}], "]"}], ".", "NN"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"bending", " ", "mode", " ", "approximations"}], "*)"}], "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"MM", ".", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"ww", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]x", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "projection", "*)"}], "\[IndentingNewLine]", RowBox[{"asm", "=", RowBox[{ RowBox[{"h", ">", "0"}], "&&", RowBox[{"L", ">", "0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"tri", "=", RowBox[{"Polygon", "[", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{"xn", ",", "yn"}], "}"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Ae", "=", RowBox[{"Integrate", "[", RowBox[{"1", ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], StyleBox["\[Element]", "OperatorCharacter"], StyleBox["tri", "OperatorCharacter"]}], StyleBox[",", "OperatorCharacter"], RowBox[{ StyleBox["Assumptions", "OperatorCharacter"], StyleBox["\[Rule]", "OperatorCharacter"], "asm"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Phi]", "=", RowBox[{ RowBox[{"Integrate", "[", RowBox[{"\[Phi]", ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], StyleBox["\[Element]", "OperatorCharacter"], StyleBox["tri", "OperatorCharacter"]}], StyleBox[",", "OperatorCharacter"], RowBox[{ StyleBox["Assumptions", "OperatorCharacter"], StyleBox["\[Rule]", "OperatorCharacter"], "asm"}]}], "]"}], "/", "Ae"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Theta]", "=", RowBox[{ RowBox[{"Integrate", "[", RowBox[{"\[Theta]", ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], StyleBox["\[Element]", "OperatorCharacter"], StyleBox["tri", "OperatorCharacter"]}], StyleBox[",", "OperatorCharacter"], RowBox[{ StyleBox["Assumptions", "OperatorCharacter"], StyleBox["\[Rule]", "OperatorCharacter"], "asm"}]}], "]"}], "/", "Ae"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"strain", " ", "and", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Kappa]", "=", RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Theta]"}]}], ",", RowBox[{ SubscriptBox["\[PartialD]", "y"], "\[Phi]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Phi]"}], "-", RowBox[{ SubscriptBox["\[PartialD]", "y"], "\[Theta]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Gamma]", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}], "-", "\[Pi]\[Phi]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}], "+", "\[Pi]\[Theta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"E\[Sigma]", "=", RowBox[{ RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "\[Nu]\[Nu]", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Nu]\[Nu]", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}]}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M", "=", RowBox[{ RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", RowBox[{"(", RowBox[{"E\[Sigma]", ".", "\[Kappa]"}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Q", "=", RowBox[{"tt", "*", "GG", "*", "\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]w", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Kappa]", "]"}], ".", "M"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Gamma]", "]"}], ".", "Q"}], "+", RowBox[{ RowBox[{"\[Delta]", "[", "w", "]"}], "*", "fn"}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "ww", "]"}], "*", RowBox[{"(", RowBox[{"ww", "-", "w"}], ")"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Integrate", "[", RowBox[{"\[Delta]w", ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], StyleBox["\[Element]", "OperatorCharacter"], StyleBox["tri", "OperatorCharacter"]}], StyleBox[",", "OperatorCharacter"], RowBox[{ StyleBox["Assumptions", "OperatorCharacter"], StyleBox["\[Rule]", "OperatorCharacter"], "asm"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLATEBUILD", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", "fn_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Alpha]", ",", "\[Beta]", ",", "xg", ",", "yg", ",", "jac", ",", "xn", ",", "yn", ",", "xm", ",", "ym", ",", "x", ",", "y", ",", "N3", ",", "M3", ",", "K3", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "AA", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Phi]", ",", "wc", ",", "E\[Sigma]", ",", "\[Delta]w", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wmap", ",", "\[Kappa]\[Kappa]", ",", "\[Gamma]\[Gamma]", ",", "MM", ",", "QQ", ",", "tri"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"mapping", " ", "for", " ", "the", " ", "geometry"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"xn", ",", "yn"}], "}"}], "=", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "1", ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"K3", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"xg", "=", RowBox[{"K3", ".", "xn"}]}], ";", "\[IndentingNewLine]", RowBox[{"yg", "=", RowBox[{"K3", ".", "yn"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Abs", "[", RowBox[{"Det", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "xg"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "xg"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "yg"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "yg"}]}], "}"}]}], "}"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"xm", " ", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"xn", "[", RowBox[{"[", "1", "]"}], "]"}], "+", RowBox[{"xn", "[", RowBox[{"[", "2", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"xn", "[", RowBox[{"[", "2", "]"}], "]"}], "+", RowBox[{"xn", "[", RowBox[{"[", "3", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"xn", "[", RowBox[{"[", "3", "]"}], "]"}], "+", RowBox[{"xn", "[", RowBox[{"[", "1", "]"}], "]"}]}]}], "}"}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"ym", " ", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"yn", "[", RowBox[{"[", "1", "]"}], "]"}], "+", RowBox[{"yn", "[", RowBox[{"[", "2", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"yn", "[", RowBox[{"[", "2", "]"}], "]"}], "+", RowBox[{"yn", "[", RowBox[{"[", "3", "]"}], "]"}]}], ",", RowBox[{ RowBox[{"yn", "[", RowBox[{"[", "3", "]"}], "]"}], "+", RowBox[{"yn", "[", RowBox[{"[", "1", "]"}], "]"}]}]}], "}"}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"N3", "=", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", "1"}], "}"}], ",", "xn", ",", "yn"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"1", ",", "x", ",", "y"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M3", "=", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", "1"}], "}"}], ",", "xm", ",", "ym"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"1", ",", "x", ",", "y"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"M3", ".", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"wc", "=", RowBox[{"N3", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{ RowBox[{"N3", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"N3", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"N3", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"N3", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"N3", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"N3", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"N3", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"N3", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "projection", "*)"}], "\[IndentingNewLine]", RowBox[{"AA", "=", RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", "jac", ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Theta]", "=", RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Theta]", " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "xg"}], ",", RowBox[{"y", "\[Rule]", "yg"}]}], "}"}]}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "/", "AA"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Phi]", "=", RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Phi]", " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "xg"}], ",", RowBox[{"y", "\[Rule]", "yg"}]}], "}"}]}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "/", "AA"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Kappa]\[Kappa]", "=", RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Theta]"}]}], ",", RowBox[{ SubscriptBox["\[PartialD]", "y"], "\[Phi]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Phi]"}], "-", RowBox[{ SubscriptBox["\[PartialD]", "y"], "\[Theta]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Gamma]\[Gamma]", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}], "+", "\[Pi]\[Theta]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}], "-", "\[Pi]\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"E\[Sigma]", "=", RowBox[{ RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "\[Nu]\[Nu]", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Nu]\[Nu]", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}]}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"MM", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", "E\[Sigma]"}], ")"}], ".", "\[Kappa]\[Kappa]"}]}], ";", "\[IndentingNewLine]", RowBox[{"QQ", "=", RowBox[{"tt", "*", "GG", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Kappa]\[Kappa]", "]"}], ".", "MM"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Gamma]\[Gamma]", "]"}], ".", "QQ"}]}], ")"}], " ", "/.", " ", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "xg"}], ",", RowBox[{"y", "\[Rule]", "yg"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]", "[", "w", "]"}], "*", "fn"}], ")"}], "/.", " ", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "xg"}], ",", RowBox[{"y", "\[Rule]", "yg"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wmap", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]", "[", "wc", "]"}], "*", RowBox[{"(", RowBox[{"wc", "-", "w"}], ")"}]}], ")"}], " ", "/.", " ", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "xg"}], ",", RowBox[{"y", "\[Rule]", "yg"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wmap"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{"HETEROSIS", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ "n1_", ",", "n2_", ",", "n3_", ",", "n4_", ",", "n5_", ",", "n6_", ",", "n7_", ",", "n8_", ",", "n9_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}]}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "\[Alpha]", ",", "\[Beta]", ",", "\[IndentingNewLine]", "n", ",", "enode", ",", "N9", ",", "N8", ",", "r0", ",", "r0\[Alpha]", ",", "r0\[Beta]", ",", "e\[Alpha]", ",", "e\[Beta]", ",", "en", ",", "h\[Alpha]", ",", "h\[Beta]", ",", "FF", ",", "jac", ",", "x", ",", "y", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "E\[Sigma]", ",", "\[Epsilon]\[Epsilon]", ",", "\[Kappa]\[Kappa]", ",", "\[Gamma]\[Gamma]", ",", "M", ",", "Q", ",", "F", ",", "\[Delta]wint1", ",", "\[Delta]wint2", ",", "\[Delta]wext", ",", "f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{ "n1", ",", "n2", ",", "n3", ",", "n4", ",", "n5", ",", "n6", ",", "n7", ",", "n8", ",", "n9"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"N9", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", "4"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", "\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", "4"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", "\[Beta]"}], ",", RowBox[{"16", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", "\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"-", "4"}], " ", "\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", "\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", "4"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", "\[Alpha]", " ", "\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", "\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"N8", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", "4"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", "\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", "4"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", "\[Beta]"}], ",", "0", ",", RowBox[{ RowBox[{"-", "4"}], " ", "\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", "\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", "4"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", "\[Alpha]", " ", "\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", "\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "mapping", " ", "to", " ", "orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{"N9", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r0\[Alpha]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r0"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r0\[Beta]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r0"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Alpha]", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0\[Alpha]", ".", "r0\[Alpha]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0\[Beta]", ".", "r0\[Beta]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Alpha]", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"r0\[Alpha]", "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Beta]", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"r0\[Beta]", "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{"e\[Alpha]", StyleBox["\[Cross]", "OperatorCharacter"], "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"r0\[Alpha]", ",", "r0\[Beta]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", " ", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Det", "[", "FF", "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"f\[Alpha]", "=", RowBox[{"e\[Alpha]", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"f\[Beta]", "=", RowBox[{"e\[Beta]", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"fn", "=", RowBox[{"en", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "functions", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"N8", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}], ".", "e\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"N8", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}], ".", "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"N8", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}], ".", "en"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{"N9", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3"}], "]"}], "]"}], ".", "e\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{"N9", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3"}], "]"}], "]"}], ".", "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{"N9", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3"}], "]"}], "]"}], ".", "en"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"plane", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"E\[Sigma]", "=", RowBox[{ RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "\[Nu]\[Nu]", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Nu]\[Nu]", ",", "1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}]}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"plate", " ", "strain", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]\[Epsilon]", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}], "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], "/", "h\[Alpha]"}], "-", "\[Psi]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}], "/", "h\[Beta]"}], "+", "\[Psi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]\[Kappa]", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}]}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}], "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], "/", "h\[Alpha]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Theta]"}], "/", "h\[Beta]"}]}], ",", "0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Gamma]\[Gamma]", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}], "/", "h\[Beta]"}], "-", "\[Phi]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], "+", "\[Theta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"plate", " ", "stress", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"F", "=", RowBox[{"tt", "*", RowBox[{"E\[Sigma]", ".", "\[Epsilon]\[Epsilon]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M", "=", RowBox[{ RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", RowBox[{"E\[Sigma]", ".", "\[Kappa]\[Kappa]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Q", "=", RowBox[{"tt", "*", "GG", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint1", "=", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Kappa]\[Kappa]", "]"}], ".", "M"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Epsilon]\[Epsilon]", "]"}], ".", "F"}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint2", "=", RowBox[{"(", RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Gamma]\[Gamma]", "]"}], ".", "Q"}]}], " ", ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"QUAD", "[", RowBox[{"LIN2", ",", RowBox[{"QUAD", "[", RowBox[{"LIN2", ",", RowBox[{ RowBox[{"(", "\[Delta]wint2", ")"}], "*", "jac"}], ",", RowBox[{"{", "\[Alpha]", "}"}]}], "]"}], ",", RowBox[{"{", "\[Beta]", "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"LIN3", ",", RowBox[{"QUAD", "[", RowBox[{"LIN3", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint1", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", "\[Alpha]", "}"}]}], "]"}], ",", RowBox[{"{", "\[Beta]", "}"}]}], "]"}]}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "HETEROSIS", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLATEF", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ "n1_Integer", ",", "n2_Integer", ",", "n3_Integer", ",", "n4_Integer"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "enode", ",", "N4", ",", "N9", ",", "N8", ",", "r0", ",", "r0\[Alpha]", ",", "r0\[Beta]", ",", "e\[Alpha]", ",", "e\[Beta]", ",", "en", ",", "h\[Alpha]", ",", "h\[Beta]", ",", "FF", ",", "jac", ",", "x", ",", "y", ",", "dofu", ",", "dof\[Theta]", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "E\[Sigma]", ",", "\[Epsilon]\[Epsilon]", ",", "\[Kappa]\[Kappa]", ",", "\[Gamma]\[Gamma]", ",", "M", ",", "Q", ",", "F", ",", "\[Delta]wint1", ",", "\[Delta]wint2", ",", "\[Delta]wint3", ",", "\[Delta]wext", ",", "f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"N4", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"N9", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", "4"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", "\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", "4"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", "\[Beta]"}], ",", RowBox[{"16", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", "\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"-", "4"}], " ", "\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", "\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", "4"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", "\[Alpha]", " ", "\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", "\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"N8", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", "4"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", "\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", "4"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", "\[Beta]"}], ",", "0", ",", RowBox[{ RowBox[{"-", "4"}], " ", "\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Beta]"}], ")"}], " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", "\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", "4"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", "\[Alpha]", " ", "\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}], " ", "\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "mapping", " ", "to", " ", "orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{"N4", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r0\[Alpha]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r0"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r0\[Beta]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r0"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Alpha]", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0\[Alpha]", ".", "r0\[Alpha]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0\[Beta]", ".", "r0\[Beta]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Alpha]", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"r0\[Alpha]", "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Beta]", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"r0\[Beta]", "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{"e\[Alpha]", StyleBox["\[Cross]", "OperatorCharacter"], "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"r0\[Alpha]", ",", "r0\[Beta]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", " ", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Det", "[", "FF", "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"f\[Alpha]", "=", RowBox[{"e\[Alpha]", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"f\[Beta]", "=", RowBox[{"e\[Beta]", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"fn", "=", RowBox[{"en", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "functions", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"dofu", "=", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}], ",", RowBox[{"uY", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n4"}], "}"}], "]"}], "]"}], ",", RowBox[{"uY", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n4"}], "}"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n4"}], "}"}], "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}], "]"}], ",", RowBox[{"uY", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}], ",", RowBox[{"uY", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n4", ",", "2"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n4"}], "}"}], "]"}], "]"}], ",", RowBox[{"uY", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n4"}], "}"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n4"}], "}"}], "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n3", ",", "2"}], "]"}], "]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof\[Theta]", "=", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Z", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n4"}], "}"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n4"}], "}"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Z", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n4"}], "}"}], "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Z", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Z", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n4", ",", "3"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n4"}], "}"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n4"}], "}"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Z", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n4"}], "}"}], "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n3", ",", "3"}], "]"}], "]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"N8", ".", "dofu", ".", "e\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"N8", ".", "dofu", ".", "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"N8", ".", "dofu", ".", "en"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{"N9", ".", "dof\[Theta]", ".", "e\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{"N9", ".", "dof\[Theta]", ".", "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{"N9", ".", "dof\[Theta]", ".", "en"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"plane", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"E\[Sigma]", "=", RowBox[{ RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "\[Nu]\[Nu]", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Nu]\[Nu]", ",", "1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}]}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"plate", " ", "strain", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]\[Epsilon]", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}], "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], "/", "h\[Alpha]"}], "-", "\[Psi]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}], "/", "h\[Beta]"}], "+", "\[Psi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]\[Kappa]", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}]}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}], "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], "/", "h\[Alpha]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Theta]"}], "/", "h\[Beta]"}]}], ",", "0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Gamma]\[Gamma]", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}], "/", "h\[Beta]"}], "-", "\[Phi]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], "+", "\[Theta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"plate", " ", "stress", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"F", "=", RowBox[{"tt", "*", RowBox[{"E\[Sigma]", ".", "\[Epsilon]\[Epsilon]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M", "=", RowBox[{ RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", RowBox[{"E\[Sigma]", ".", "\[Kappa]\[Kappa]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Q", "=", RowBox[{"tt", "*", "GG", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint1", "=", RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Kappa]\[Kappa]", "]"}], ".", "M"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint2", "=", RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Epsilon]\[Epsilon]", "]"}], ".", "F"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint3", "=", RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Gamma]\[Gamma]", "]"}], ".", "Q"}]}]}], " ", ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}]}], ")"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"QUAD", "[", RowBox[{"LIN3", ",", RowBox[{"QUAD", "[", RowBox[{"LIN3", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint1", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", "\[Alpha]", "}"}]}], "]"}], ",", RowBox[{"{", "\[Beta]", "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"LIN2", ",", RowBox[{"QUAD", "[", RowBox[{"LIN2", ",", RowBox[{ RowBox[{"(", "\[Delta]wint2", ")"}], "*", "jac"}], ",", RowBox[{"{", "\[Alpha]", "}"}]}], "]"}], ",", RowBox[{"{", "\[Beta]", "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"LIN2", ",", RowBox[{"QUAD", "[", RowBox[{"LIN2", ",", RowBox[{ RowBox[{"(", "\[Delta]wint3", ")"}], "*", "jac"}], ",", RowBox[{"{", "\[Alpha]", "}"}]}], "]"}], ",", RowBox[{"{", "\[Beta]", "}"}]}], "]"}]}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"HUGHES", "-", "TEZDUAR"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ "n1_Integer", ",", "n2_Integer", ",", "n3_Integer", ",", "n4_Integer"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "\[Alpha]", ",", "\[Beta]", ",", "\[IndentingNewLine]", "n", ",", "enode", ",", "NN", ",", "r0", ",", "r0\[Alpha]", ",", "r0\[Beta]", ",", "e\[Alpha]", ",", "e\[Beta]", ",", "en", ",", "h\[Alpha]", ",", "h\[Beta]", ",", "FF", ",", "jac", ",", "x", ",", "y", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]\[Alpha]", ",", "\[Pi]\[Psi]\[Beta]", ",", "E\[Sigma]", ",", "\[Epsilon]\[Epsilon]", ",", "\[Kappa]\[Kappa]", ",", "\[Gamma]\[Gamma]", ",", "M", ",", "Q", ",", "F", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "f\[Alpha]", ",", "f\[Beta]", ",", "fn", ",", "int"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "mapping", " ", "to", " ", "orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r0\[Alpha]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r0"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r0\[Beta]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r0"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Alpha]", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0\[Alpha]", ".", "r0\[Alpha]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0\[Beta]", ".", "r0\[Beta]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Alpha]", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"r0\[Alpha]", "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Beta]", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"r0\[Beta]", "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{"e\[Alpha]", StyleBox["\[Cross]", "OperatorCharacter"], "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"r0\[Alpha]", ",", "r0\[Beta]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", " ", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Det", "[", "FF", "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"f\[Alpha]", "=", RowBox[{"e\[Alpha]", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"f\[Beta]", "=", RowBox[{"e\[Beta]", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"fn", "=", RowBox[{"en", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "functions", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}], ".", "e\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}], ".", "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}], ".", "en"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3"}], "]"}], "]"}], ".", "e\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3"}], "]"}], "]"}], ".", "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3"}], "]"}], "]"}], ".", "en"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "taylor", " ", "projections", " ", "onto", " ", "constants"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Pi]\[Phi]", "=", RowBox[{"\[Phi]", "/.", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Theta]", "=", RowBox[{"\[Theta]", "/.", RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Psi]\[Alpha]", "=", RowBox[{"\[Psi]", "/.", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Psi]\[Beta]", "=", RowBox[{"\[Psi]", "/.", RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"plane", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"E\[Sigma]", "=", RowBox[{ RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "\[Nu]\[Nu]", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Nu]\[Nu]", ",", "1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}]}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "plate", " ", "strain", " ", "and", " ", "stress", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]\[Epsilon]", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}], "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], "/", "h\[Alpha]"}], "-", "\[Pi]\[Psi]\[Beta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}], "/", "h\[Beta]"}], "+", "\[Pi]\[Psi]\[Alpha]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]\[Kappa]", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}]}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}], "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], "/", "h\[Alpha]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Theta]"}], "/", "h\[Beta]"}]}], ",", "0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Gamma]\[Gamma]", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}], "/", "h\[Beta]"}], "-", "\[Pi]\[Phi]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], "+", "\[Pi]\[Theta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"F", "=", RowBox[{"tt", "*", RowBox[{"E\[Sigma]", ".", "\[Epsilon]\[Epsilon]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M", "=", RowBox[{ RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", RowBox[{"E\[Sigma]", ".", "\[Kappa]\[Kappa]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Q", "=", RowBox[{"tt", "*", "GG", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Kappa]\[Kappa]", "]"}], ".", "M"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Gamma]\[Gamma]", "]"}], ".", "Q"}], " ", "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Epsilon]\[Epsilon]", "]"}], ".", "F"}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"LIN3", ",", RowBox[{"QUAD", "[", RowBox[{"LIN3", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", "\[Alpha]", "}"}]}], "]"}], ",", RowBox[{"{", "\[Beta]", "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"HUGHES", "-", "TEZDUAR"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLATEF", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ "n1_Integer", ",", "n2_Integer", ",", "n3_Integer", ",", "n4_Integer"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "\[Alpha]", ",", "\[Beta]", ",", "\[IndentingNewLine]", "n", ",", "enode", ",", "NN", ",", "MM", ",", "r0", ",", "r0\[Alpha]", ",", "r0\[Beta]", ",", "e\[Alpha]", ",", "e\[Beta]", ",", "en", ",", "h\[Alpha]", ",", "h\[Beta]", ",", "ex", ",", "ey", ",", "\[Rho]", ",", "FF", ",", "jac", ",", "x", ",", "y", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]x", ",", "\[Pi]\[Psi]y", ",", "E\[Sigma]", ",", "\[Epsilon]\[Epsilon]", ",", "\[Kappa]\[Kappa]", ",", "\[Gamma]\[Gamma]", ",", "M", ",", "Q", ",", "F", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "fx", ",", "fy", ",", "fn", ",", "int", ",", "xn", ",", "yn", ",", "xc", ",", "yc"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"MM", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"orthonormal", " ", "material", " ", "xyn"}], "-", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{"MM", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r0\[Alpha]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r0"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Alpha]", "=", RowBox[{"Sqrt", "[", RowBox[{"r0\[Alpha]", ".", "r0\[Alpha]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ex", "=", RowBox[{"r0\[Alpha]", "/", "h\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"r0\[Beta]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r0"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r0\[Beta]", "=", RowBox[{"r0\[Beta]", "-", RowBox[{ RowBox[{"(", RowBox[{"r0\[Beta]", ".", "ex"}], ")"}], "ex"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Sqrt", "[", RowBox[{"r0\[Beta]", ".", "r0\[Beta]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ey", "=", RowBox[{"r0\[Beta]", "/", "h\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{"ex", StyleBox["\[Cross]", "OperatorCharacter"], "ey"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"geometry", " ", "in", " ", "the", " ", "xyn"}], "-", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"rc", "=", RowBox[{"r0", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"xn", ",", "yn"}], "}"}], "=", RowBox[{"Transpose", "[", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"#", "-", "rc"}], ")"}], ".", "ex"}], ",", RowBox[{ RowBox[{"(", RowBox[{"#", "-", "rc"}], ")"}], ".", "ey"}]}], "}"}], "&"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", "1", ",", "1"}], "}"}], ",", "xn", ",", "yn", ",", RowBox[{"xn", "*", "yn"}]}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"1", ",", "x", ",", "y", ",", RowBox[{"x", " ", "y"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"xc", "=", RowBox[{"Mean", "[", "xn", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"yc", "=", RowBox[{"Mean", "[", "yn", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"x\[Alpha]\[Beta]", "=", RowBox[{"NN", ".", "xn"}]}], ";", "\[IndentingNewLine]", RowBox[{"y\[Alpha]\[Beta]", "=", RowBox[{"NN", ".", "yn"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"fx", "=", RowBox[{"ex", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"fy", "=", RowBox[{"ey", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"fn", "=", RowBox[{"en", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "functions", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}], ".", "ex"}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}], ".", "ey"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}], ".", "en"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3"}], "]"}], "]"}], ".", "ex"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3"}], "]"}], "]"}], ".", "ey"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3"}], "]"}], "]"}], ".", "en"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "taylor", " ", "projections", " ", "onto", " ", "constants"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Pi]\[Phi]", "=", RowBox[{"\[Phi]", "/.", RowBox[{"y", "\[Rule]", "yc"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Theta]", "=", RowBox[{"\[Theta]", "/.", RowBox[{"x", "\[Rule]", "xc"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Psi]x", "=", RowBox[{"\[Psi]", "/.", RowBox[{"y", "\[Rule]", "yc"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Psi]y", "=", RowBox[{"\[Psi]", "/.", RowBox[{"x", "\[Rule]", "xc"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"plane", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"E\[Sigma]", "=", RowBox[{ RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "\[Nu]\[Nu]", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Nu]\[Nu]", ",", "1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}]}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "plate", " ", "strain", " ", "and", " ", "stress", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]\[Epsilon]", "=", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], "-", "\[Pi]\[Psi]y"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}], "+", "\[Pi]\[Psi]x"}]}], "}"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]\[Kappa]", "=", RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Theta]"}]}], ",", RowBox[{ SubscriptBox["\[PartialD]", "y"], "\[Phi]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Phi]"}], "-", RowBox[{ SubscriptBox["\[PartialD]", "y"], "\[Theta]"}]}], ",", "0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Gamma]\[Gamma]", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}], "+", "\[Pi]\[Theta]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}], "-", "\[Pi]\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"F", "=", RowBox[{"tt", "*", RowBox[{"E\[Sigma]", ".", "\[Epsilon]\[Epsilon]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M", "=", RowBox[{ RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", RowBox[{"E\[Sigma]", ".", "\[Kappa]\[Kappa]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Q", "=", RowBox[{"tt", "*", "GG", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Kappa]\[Kappa]", "]"}], ".", "M"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Gamma]\[Gamma]", "]"}], ".", "Q"}], " ", "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Epsilon]\[Epsilon]", "]"}], ".", "F"}]}], ")"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"x", "->", RowBox[{"NN", ".", "xn"}]}], ",", RowBox[{"y", "->", RowBox[{"NN", ".", "yn"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fn"}], "}"}]}], ")"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"x", "->", RowBox[{"NN", ".", "xn"}]}], ",", RowBox[{"y", "->", RowBox[{"NN", ".", "yn"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"LIN3", ",", RowBox[{"QUAD", "[", RowBox[{"LIN3", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", "\[Alpha]", "}"}]}], "]"}], ",", RowBox[{"{", "\[Beta]", "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"PLATEF", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "\[Alpha]", ",", "\[Beta]", ",", "\[IndentingNewLine]", "n", ",", "n\[Alpha]", ",", "n\[Beta]", ",", "NN", ",", "r0", ",", "r0\[Alpha]", ",", "r0\[Beta]", ",", "e\[Alpha]", ",", "e\[Beta]", ",", "en", ",", "hx", ",", "hy", ",", "FF", ",", "jac", ",", "x", ",", "y", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]x", ",", "\[Pi]\[Psi]y", ",", "E\[Sigma]", ",", "\[Epsilon]\[Epsilon]", ",", "\[Kappa]\[Kappa]", ",", "\[Gamma]\[Gamma]", ",", "M", ",", "Q", ",", "F", ",", "\[Delta]wint", ",", "\[Delta]wext"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "nodes", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"n\[Alpha]", ",", "n\[Beta]"}], "}"}], "=", RowBox[{"Dimensions", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"nl", "=", RowBox[{"Flatten", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"Flatten", "[", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n\[Alpha]", ",", "\[Alpha]"}], "}"}], ",", RowBox[{"{", RowBox[{"n\[Beta]", ",", "\[Beta]"}], "}"}]}], "}"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "mapping", " ", "to", " ", "orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r0\[Alpha]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r0"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r0\[Beta]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r0"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"hx", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0\[Alpha]", ".", "r0\[Alpha]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"hy", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0\[Beta]", ".", "r0\[Beta]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Alpha]", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"r0\[Alpha]", "/", RowBox[{"Sqrt", "[", RowBox[{"r0\[Alpha]", ".", "r0\[Alpha]"}], "]"}]}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Beta]", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"r0\[Beta]", "/", RowBox[{"Sqrt", "[", RowBox[{"r0\[Beta]", ".", "r0\[Beta]"}], "]"}]}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{"e\[Alpha]", StyleBox["\[Cross]", "OperatorCharacter"], "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"r0\[Alpha]", ",", "r0\[Beta]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", " ", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Det", "[", "FF", "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "shape", " ", "function", " ", "in", " ", "material", " ", "coordinates"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"NN", " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"x", "/", "hx"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"y", "/", "hy"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "functions", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}], ".", "e\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}], ".", "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}], ".", "en"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3"}], "]"}], "]"}], ".", "e\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3"}], "]"}], "]"}], ".", "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3"}], "]"}], "]"}], ".", "en"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Print", "[", "\"\\"", "]"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"taylor", " ", "projections", " ", "onto", " ", "linears"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Pi]\[Phi]", "=", RowBox[{ RowBox[{"(", RowBox[{"\[Phi]", "/.", RowBox[{"y", "\[Rule]", RowBox[{"hy", "/", "2"}]}]}], ")"}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "y"], "\[Phi]"}], "/.", RowBox[{"y", "\[Rule]", RowBox[{"hy", "/", "2"}]}]}], ")"}], "*", RowBox[{"(", RowBox[{"y", "-", RowBox[{"hy", "/", "2"}]}], ")"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"+", RowBox[{"(", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "\[Phi]"}], "/.", RowBox[{"y", "\[Rule]", RowBox[{"hy", "/", "2"}]}]}], ")"}]}], "*", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"y", "-", RowBox[{"hy", "/", "2"}]}], ")"}], "^", "2"}], "/", "2"}], "*", "0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Theta]", "=", RowBox[{ RowBox[{"(", RowBox[{"\[Theta]", "/.", RowBox[{"x", "\[Rule]", RowBox[{"hx", "/", "2"}]}]}], ")"}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Theta]"}], "/.", RowBox[{"x", "\[Rule]", RowBox[{"hx", "/", "2"}]}]}], ")"}], "*", RowBox[{"(", RowBox[{"x", "-", RowBox[{"hx", "/", "2"}]}], ")"}], "*", RowBox[{"(", RowBox[{"9", "/", "4"}], ")"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"+", RowBox[{"(", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "\[Theta]"}], "/.", RowBox[{"x", "\[Rule]", RowBox[{"hx", "/", "2"}]}]}], ")"}]}], "*", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"x", "-", RowBox[{"hx", "/", "2"}]}], ")"}], "^", "2"}], "/", "2"}], "*", "0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Psi]x", "=", RowBox[{ RowBox[{"(", RowBox[{"\[Psi]", "/.", RowBox[{"y", "\[Rule]", RowBox[{"hy", "/", "2"}]}]}], ")"}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "y"], "\[Psi]"}], "/.", RowBox[{"y", "\[Rule]", RowBox[{"hy", "/", "2"}]}]}], ")"}], "*", RowBox[{"(", RowBox[{"y", "-", RowBox[{"hy", "/", "2"}]}], ")"}], "*", RowBox[{"(", RowBox[{"9", "/", "4"}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "\[Psi]"}], "/.", RowBox[{"y", "\[Rule]", RowBox[{"hy", "/", "2"}]}]}], ")"}], "*", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"y", "-", RowBox[{"hy", "/", "2"}]}], ")"}], "^", "2"}], "/", "2"}], "*", "0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Psi]y", "=", RowBox[{ RowBox[{"(", RowBox[{"\[Psi]", "/.", RowBox[{"x", "\[Rule]", RowBox[{"hx", "/", "2"}]}]}], ")"}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Psi]"}], "/.", RowBox[{"x", "\[Rule]", RowBox[{"hx", "/", "2"}]}]}], ")"}], "*", RowBox[{"(", RowBox[{"x", "-", RowBox[{"hx", "/", "2"}]}], ")"}], "*", "0"}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "\[Psi]"}], "/.", RowBox[{"x", "\[Rule]", RowBox[{"hx", "/", "2"}]}]}], ")"}], "*", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"x", "-", RowBox[{"hx", "/", "2"}]}], ")"}], "^", "2"}], "/", "2"}], "*", "0"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"plane", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"E\[Sigma]", "=", RowBox[{ RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "\[Nu]\[Nu]", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Nu]\[Nu]", ",", "1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}]}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "plate", " ", "strain", " ", "and", " ", "stress", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]\[Epsilon]", "=", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], "-", "\[Pi]\[Psi]y"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}], "+", "\[Pi]\[Psi]x"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]\[Kappa]", "=", RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Theta]"}]}], ",", RowBox[{ SubscriptBox["\[PartialD]", "y"], "\[Phi]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Phi]"}], "-", RowBox[{ SubscriptBox["\[PartialD]", "y"], "\[Theta]"}]}], ",", "0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Gamma]\[Gamma]", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}], "-", "\[Pi]\[Phi]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}], "+", "\[Pi]\[Theta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"F", "=", RowBox[{"tt", "*", RowBox[{"E\[Sigma]", ".", "\[Epsilon]\[Epsilon]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M", "=", RowBox[{ RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", RowBox[{"E\[Sigma]", ".", "\[Kappa]\[Kappa]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Q", "=", RowBox[{"tt", "*", "GG", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Kappa]\[Kappa]", "]"}], ".", "M"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Gamma]\[Gamma]", "]"}], ".", "Q"}], " ", "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Epsilon]\[Epsilon]", "]"}], ".", "F"}]}], ")"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"x", "->", RowBox[{"\[Alpha]", "*", "hx"}]}], ",", RowBox[{"y", "\[Rule]", RowBox[{"\[Beta]", "*", "hy"}]}]}], "}"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fz"}], "}"}]}], ")"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"x", "->", RowBox[{"\[Alpha]", "*", "hx"}]}], ",", RowBox[{"y", "\[Rule]", RowBox[{"\[Beta]", "*", "hy"}]}]}], "}"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", "\[Alpha]", "}"}]}], "]"}], ",", RowBox[{"{", "\[Beta]", "}"}]}], "]"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Kappa]\[Kappa]", "]"}], ".", "M"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Gamma]\[Gamma]", "]"}], ".", "Q"}], " ", "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Epsilon]\[Epsilon]", "]"}], ".", "F"}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fz"}], "}"}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"Integrate", "[", RowBox[{ RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "hx"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"y", ",", "0", ",", "hy"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"GENERICPLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"MODE", ",", RowBox[{"{", RowBox[{"GENERICPLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", RowBox[{"tt", ",", "0", ",", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}]}], "}"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"GENERICPLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", RowBox[{"tt_", ",", "st_", ",", "it_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "enode", ",", "n\[Alpha]", ",", "n\[Beta]", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "NN", ",", "r0", ",", "r\[Alpha]0", ",", "r\[Beta]0", ",", "rn0", ",", "h\[Alpha]0", ",", "h\[Beta]0", ",", "hn0", ",", "i\[Alpha]0", ",", "i\[Beta]0", ",", "in0", ",", "jac", ",", "FF", ",", "FFINV", ",", "GG", ",", "PP", ",", "u0", ",", "\[Theta]0", ",", "u00", ",", "\[Theta]00", ",", "\[Omega]00", ",", "f00", ",", "m00", ",", "F", ",", "M", ",", "\[Epsilon]", ",", "\[Kappa]", ",", "II0", ",", "III", ",", "IIII", ",", "IIII1", ",", "IIII2", ",", "EEEE", ",", "AE", ",", "BE", ",", "CE", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]WW"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "nodes", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"n\[Alpha]", ",", "n\[Beta]"}], "}"}], "=", RowBox[{"Dimensions", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"enode", "=", RowBox[{"Flatten", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"Flatten", "[", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n\[Alpha]", ",", "\[Alpha]"}], "}"}], ",", RowBox[{"{", RowBox[{"n\[Beta]", ",", "\[Beta]"}], "}"}]}], "}"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"generic", " ", "basis", " ", "vectors"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]0", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r0"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Beta]0", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r0"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"rn0", "=", RowBox[{ RowBox[{"r\[Alpha]0", "\[Cross]", "r\[Beta]0"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"hn0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Norm", "[", "rn0", "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"in0", "=", RowBox[{"rn0", "/", "hn0"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", " ", "=", "hn0"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "metric", " ", "dyad", " ", "and", " ", "permutation", " ", "symbol", " ", "of", " ", "generic", " ", "metrics"}], "*)"}], "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"r\[Alpha]0", ",", "r\[Beta]0", ",", "in0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], " ", "&&", " ", RowBox[{"h", ">", "0"}]}]}], " ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GG", " ", "=", RowBox[{"FF", ".", RowBox[{"Transpose", "[", "FF", "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"PP", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"FF", "[", RowBox[{"[", RowBox[{"a", ",", "i"}], "]"}], "]"}], "*", RowBox[{"FF", "[", RowBox[{"[", RowBox[{"b", ",", "j"}], "]"}], "]"}], "*", RowBox[{"FFINV", "[", RowBox[{"[", RowBox[{"k", ",", "c"}], "]"}], "]"}], "*", RowBox[{ RowBox[{"LeviCivitaTensor", "[", "3", "]"}], "[", RowBox[{"[", RowBox[{"i", ",", "j", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"a", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"b", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"c", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"displacement", " ", "and", " ", "rotation"}], "*)"}], "\[IndentingNewLine]", RowBox[{"u0", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]0", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"transform", " ", "to", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"u00", "=", RowBox[{"u0", ".", "FFINV"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]00", "=", RowBox[{"\[Theta]0", ".", "FFINV"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Omega]00", "=", RowBox[{"in0", ".", RowBox[{"(", RowBox[{"\[Theta]00", ".", "PP"}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"f00", "=", RowBox[{ RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}], ".", "FFINV"}]}], ";", "\[IndentingNewLine]", RowBox[{"m00", "=", RowBox[{ RowBox[{"{", RowBox[{"mX", ",", "mY", ",", "mZ"}], "}"}], ".", "FFINV"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "strain", " ", "measures", " ", "of", " ", "plate", " ", "model"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{ RowBox[{ RowBox[{"D", "[", RowBox[{"u00", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "n"}], "}"}], "}"}]}], "]"}], ".", RowBox[{"Transpose", "[", "FFINV", "]"}], ".", "FFINV"}], "+", RowBox[{"Outer", "[", RowBox[{"Times", ",", "in0", ",", "\[Omega]00"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]", "=", RowBox[{ RowBox[{"D", "[", RowBox[{"\[Omega]00", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "n"}], "}"}], "}"}]}], "]"}], ".", RowBox[{"Transpose", "[", "FFINV", "]"}], ".", "FFINV"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "elasticity", " ", "dyad", " ", "of", " ", "isotropic", " ", "plate"}], "*)"}], "\[IndentingNewLine]", RowBox[{"II0", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"FFINV", "[", RowBox[{"[", "i", "]"}], "]"}], ",", RowBox[{"FFINV", "[", RowBox[{"[", "i", "]"}], "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIII", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "i", ",", "j", ",", "j", ",", "i"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "FFINV"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "FFINV"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIII1", "=", RowBox[{"Outer", "[", RowBox[{"Times", ",", "II0", ",", "II0"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIII2", "=", RowBox[{ RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"IIII", "[", RowBox[{"[", RowBox[{"i", ",", "j", ",", "k", ",", "l"}], "]"}], "]"}], "+", RowBox[{"IIII", "[", RowBox[{"[", RowBox[{"j", ",", "i", ",", "k", ",", "l"}], "]"}], "]"}], "+", RowBox[{"IIII", "[", RowBox[{"[", RowBox[{"i", ",", "j", ",", "l", ",", "k"}], "]"}], "]"}], "+", RowBox[{"IIII", "[", RowBox[{"[", RowBox[{"j", ",", "i", ",", "l", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"l", ",", "1", ",", "3"}], "}"}]}], "]"}], "/", "4"}], "-", RowBox[{"Outer", "[", RowBox[{"Times", ",", "in0", ",", "in0", ",", "in0", ",", "in0"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{ RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "+", "\[Nu]\[Nu]"}], ")"}]}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Nu]\[Nu]", "/", RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}]}], "*", "IIII1"}], "+", "IIII2"}], ")"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"AE", " ", "=", RowBox[{"tt", "*", "EEEE"}]}], ";", "\[IndentingNewLine]", RowBox[{"CE", "=", RowBox[{"st", "*", "EEEE"}]}], ";", "\[IndentingNewLine]", RowBox[{"BE", " ", "=", RowBox[{"it", "*", "EEEE"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "resultants"}], "*)"}], "\[IndentingNewLine]", RowBox[{"F", "=", RowBox[{"tt", "*", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "k", ",", "l"}], "]"}], "]"}], "*", RowBox[{"GG", "[", RowBox[{"[", RowBox[{"l", ",", "m"}], "]"}], "]"}], "*", RowBox[{"GG", "[", RowBox[{"[", RowBox[{"k", ",", "n"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"m", ",", "n"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"l", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"m", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", "3"}], "}"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M", "=", RowBox[{"it", "*", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "k", ",", "l"}], "]"}], "]"}], "*", RowBox[{"GG", "[", RowBox[{"[", RowBox[{"l", ",", "m"}], "]"}], "]"}], "*", RowBox[{"GG", "[", RowBox[{"[", RowBox[{"k", ",", "n"}], "]"}], "]"}], "*", RowBox[{"\[Kappa]", "[", RowBox[{"[", RowBox[{"m", ",", "n"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"l", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"m", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", "3"}], "}"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "densities"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"M", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"GG", "[", RowBox[{"[", RowBox[{"j", ",", "l"}], "]"}], "]"}], "*", RowBox[{"GG", "[", RowBox[{"[", RowBox[{"i", ",", "k"}], "]"}], "]"}], "*", RowBox[{"\[Delta]", "[", RowBox[{"\[Kappa]", "[", RowBox[{"[", RowBox[{"k", ",", "l"}], "]"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"l", ",", "1", ",", "3"}], "}"}]}], "]"}]}], "-", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"F", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"GG", "[", RowBox[{"[", RowBox[{"j", ",", "l"}], "]"}], "]"}], "*", RowBox[{"GG", "[", RowBox[{"[", RowBox[{"i", ",", "k"}], "]"}], "]"}], "*", RowBox[{"\[Delta]", "[", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"k", ",", "l"}], "]"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"l", ",", "1", ",", "3"}], "}"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "u00", "]"}], ".", "GG", ".", "f00"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", "\[Alpha]", "}"}]}], "]"}], ",", RowBox[{"{", "\[Beta]", "}"}]}], "]"}]}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "enode_", "]"}]}], "}"}]}], "]"}], ":=", RowBox[{ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]", ",", "nne", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "NN", ",", "r0", ",", "r\[Alpha]0", ",", "r\[Beta]0", ",", "rn0", ",", "h\[Alpha]0", ",", "h\[Beta]0", ",", "hn0", ",", "i\[Alpha]0", ",", "i\[Beta]0", ",", "in0", ",", "jac", ",", "FF", ",", "FFINV", ",", "GG", ",", "PP", ",", "u0", ",", "\[Theta]0", ",", "u00", ",", "\[Theta]00", ",", "\[Omega]00", ",", "f00", ",", "F", ",", "M", ",", "\[Epsilon]", ",", "\[Kappa]", ",", "II0", ",", "III", ",", "IIII", ",", "IIII1", ",", "IIII2", ",", "EEEE", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]WW"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "rule", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", "u_", "]"}], ":=", RowBox[{"u", "/.", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"a", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]a", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"b", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]b", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"c", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]c", "[", "any", "]"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"nne", "=", RowBox[{"Dimensions", "[", "enode", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "[", RowBox[{"{", "3", "}"}], "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "[", RowBox[{"{", "10", "}"}], "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"1", "/", "2"}], "*", "\[Alpha]", "*", RowBox[{"(", RowBox[{"2", "-", RowBox[{"9", "*", "\[Alpha]"}], "+", RowBox[{"9", "*", SuperscriptBox["\[Alpha]", "2"]}]}], ")"}]}], ",", RowBox[{ RowBox[{"1", "/", "2"}], "*", " ", "\[Beta]", "*", RowBox[{"(", RowBox[{"2", "-", RowBox[{"9", "*", " ", "\[Beta]"}], "+", RowBox[{"9", " ", "*", SuperscriptBox["\[Beta]", "2"]}]}], ")"}]}], ",", RowBox[{ RowBox[{"1", "/", "2"}], "*", RowBox[{"(", RowBox[{"2", "-", RowBox[{"9", " ", SuperscriptBox["\[Alpha]", "3"]}], "-", RowBox[{"11", " ", "\[Beta]"}], "+", RowBox[{"18", " ", SuperscriptBox["\[Beta]", "2"]}], "-", RowBox[{"9", " ", SuperscriptBox["\[Beta]", "3"]}], "-", RowBox[{"9", " ", "*", SuperscriptBox["\[Alpha]", "2"], "*", RowBox[{"(", RowBox[{ RowBox[{"-", "2"}], "+", RowBox[{"3", "*", "\[Beta]"}]}], ")"}]}], "+", RowBox[{"\[Alpha]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "11"}], "+", RowBox[{"36", "*", "\[Beta]"}], "-", RowBox[{"27", "*", SuperscriptBox["\[Beta]", "2"]}]}], ")"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"9", "/", "2"}], "*", " ", "\[Alpha]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"3", "*", "\[Alpha]"}]}], ")"}], "*", "\[Beta]"}], ",", RowBox[{ RowBox[{"9", "/", "2"}], "*", " ", "\[Alpha]", "*", "\[Beta]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"3", "*", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{ RowBox[{"-", "9"}], "/", "2"}], "*", " ", "\[Beta]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}], "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"3", "*", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"9", "/", "2"}], "*", " ", "\[Beta]", "*", RowBox[{"(", RowBox[{"2", "+", RowBox[{"3", "*", SuperscriptBox["\[Alpha]", "2"]}], "-", RowBox[{"5", "*", "\[Beta]"}], "+", RowBox[{"3", "*", SuperscriptBox["\[Beta]", "2"]}], "+", RowBox[{"\[Alpha]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "5"}], "+", RowBox[{"6", "*", "\[Beta]"}]}], ")"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"9", "/", "2"}], "*", "\[Alpha]", "*", RowBox[{"(", RowBox[{"2", "+", RowBox[{"3", "*", SuperscriptBox["\[Alpha]", "2"]}], "-", RowBox[{"5", "*", "\[Beta]"}], "+", RowBox[{"3", "*", SuperscriptBox["\[Beta]", "2"]}], "+", RowBox[{"\[Alpha]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "5"}], "+", RowBox[{"6", "*", "\[Beta]"}]}], ")"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{ RowBox[{"-", "9"}], "/", "2"}], "*", " ", "\[Alpha]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"3", "*", "\[Alpha]"}]}], ")"}], "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}]}], ",", RowBox[{ RowBox[{"-", "27"}], "*", "\[Alpha]", "*", "\[Beta]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"generic", " ", "basis", " ", "vectors"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{ RowBox[{"NN", "[", "nne", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]0", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r0"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "3"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Beta]0", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r0"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "3"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"rn0", "=", RowBox[{ RowBox[{"r\[Alpha]0", "\[Cross]", "r\[Beta]0"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "3"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"hn0", "=", RowBox[{"Norm", "[", "rn0", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"in0", "=", RowBox[{"rn0", "/", "hn0"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", " ", "=", "hn0"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "metric", " ", "dyad", " ", "and", " ", "permutation", " ", "symbol", " ", "of", " ", "generic", " ", "metrics"}], "*)"}], "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"r\[Alpha]0", ",", "r\[Beta]0", ",", "in0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", "=", RowBox[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GG", " ", "=", RowBox[{"FF", ".", RowBox[{"Transpose", "[", "FF", "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"PP", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"FF", "[", RowBox[{"[", RowBox[{"a", ",", "i"}], "]"}], "]"}], "*", RowBox[{"FF", "[", RowBox[{"[", RowBox[{"b", ",", "j"}], "]"}], "]"}], "*", RowBox[{"FFINV", "[", RowBox[{"[", RowBox[{"k", ",", "c"}], "]"}], "]"}], "*", RowBox[{ RowBox[{"LeviCivitaTensor", "[", "3", "]"}], "[", RowBox[{"[", RowBox[{"i", ",", "j", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"a", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"b", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"c", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"displacement", " ", "and", " ", "rotation"}], "*)"}], "\[IndentingNewLine]", RowBox[{"u0", "=", RowBox[{ RowBox[{"NN", "[", "nne", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]0", "=", RowBox[{ RowBox[{"NN", "[", "nne", "]"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"transform", " ", "to", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"u00", "=", RowBox[{"u0", ".", "FFINV"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]00", "=", RowBox[{"\[Theta]0", ".", "FFINV"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Omega]00", "=", RowBox[{"in0", ".", RowBox[{"(", RowBox[{"\[Theta]00", ".", "PP"}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"f00", "=", RowBox[{ RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}], ".", "FFINV"}]}], ";", "\[IndentingNewLine]", RowBox[{"m00", "=", RowBox[{ RowBox[{"{", RowBox[{"mX", ",", "mY", ",", "mZ"}], "}"}], ".", "FFINV"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "strain", " ", "measures", " ", "of", " ", "plate", " ", "model"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{ RowBox[{ RowBox[{"D", "[", RowBox[{"u00", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "n"}], "}"}], "}"}]}], "]"}], ".", RowBox[{"Transpose", "[", "FFINV", "]"}], ".", "FFINV"}], "+", RowBox[{"Outer", "[", RowBox[{"Times", ",", "in0", ",", "\[Omega]00"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]", "=", RowBox[{ RowBox[{"D", "[", RowBox[{"\[Omega]00", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "n"}], "}"}], "}"}]}], "]"}], ".", RowBox[{"Transpose", "[", "FFINV", "]"}], ".", "FFINV"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "elasticity", " ", "dyad", " ", "of", " ", "isotropic", " ", "plate"}], "*)"}], "\[IndentingNewLine]", RowBox[{"II0", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"FFINV", "[", RowBox[{"[", "i", "]"}], "]"}], ",", RowBox[{"FFINV", "[", RowBox[{"[", "i", "]"}], "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIII", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "i", ",", "j", ",", "j", ",", "i"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "FFINV"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "FFINV"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIII1", "=", RowBox[{"Outer", "[", RowBox[{"Times", ",", "II0", ",", "II0"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIII2", "=", RowBox[{ RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"IIII", "[", RowBox[{"[", RowBox[{"i", ",", "j", ",", "k", ",", "l"}], "]"}], "]"}], "+", RowBox[{"IIII", "[", RowBox[{"[", RowBox[{"j", ",", "i", ",", "k", ",", "l"}], "]"}], "]"}], "+", RowBox[{"IIII", "[", RowBox[{"[", RowBox[{"i", ",", "j", ",", "l", ",", "k"}], "]"}], "]"}], "+", RowBox[{"IIII", "[", RowBox[{"[", RowBox[{"j", ",", "i", ",", "l", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"l", ",", "1", ",", "3"}], "}"}]}], "]"}], "/", "4"}], "-", RowBox[{"Outer", "[", RowBox[{"Times", ",", "in0", ",", "in0", ",", "in0", ",", "in0"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{ RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "+", "\[Nu]\[Nu]"}], ")"}]}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Nu]\[Nu]", "/", RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}]}], "*", "IIII1"}], "+", "IIII2"}], ")"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "resultants"}], "*)"}], "\[IndentingNewLine]", RowBox[{"F", "=", RowBox[{"tt", "*", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "k", ",", "l"}], "]"}], "]"}], "*", RowBox[{"GG", "[", RowBox[{"[", RowBox[{"l", ",", "m"}], "]"}], "]"}], "*", RowBox[{"GG", "[", RowBox[{"[", RowBox[{"k", ",", "n"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"m", ",", "n"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"l", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"m", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", "3"}], "}"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M", "=", RowBox[{ RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "k", ",", "l"}], "]"}], "]"}], "*", RowBox[{"GG", "[", RowBox[{"[", RowBox[{"l", ",", "m"}], "]"}], "]"}], "*", RowBox[{"GG", "[", RowBox[{"[", RowBox[{"k", ",", "n"}], "]"}], "]"}], "*", RowBox[{"\[Kappa]", "[", RowBox[{"[", RowBox[{"m", ",", "n"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"l", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"m", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", "3"}], "}"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "density"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"M", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"GG", "[", RowBox[{"[", RowBox[{"j", ",", "l"}], "]"}], "]"}], "*", RowBox[{"GG", "[", RowBox[{"[", RowBox[{"i", ",", "k"}], "]"}], "]"}], "*", RowBox[{"\[Delta]", "[", RowBox[{"\[Kappa]", "[", RowBox[{"[", RowBox[{"k", ",", "l"}], "]"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"l", ",", "1", ",", "3"}], "}"}]}], "]"}]}], "-", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"F", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"GG", "[", RowBox[{"[", RowBox[{"j", ",", "l"}], "]"}], "]"}], "*", RowBox[{"GG", "[", RowBox[{"[", RowBox[{"i", ",", "k"}], "]"}], "]"}], "*", RowBox[{"\[Delta]", "[", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"k", ",", "l"}], "]"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"l", ",", "1", ",", "3"}], "}"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "u00", "]"}], ".", "GG", ".", "f00"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"TRI28", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}]}], "]"}], "/;", " ", RowBox[{ RowBox[{"Dimensions", "[", "enode", "]"}], "\[Equal]", RowBox[{"{", "10", "}"}]}]}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{ 3.4426474258030453`*^9, {3.4444401255942*^9, 3.4444401388073997`*^9}, { 3.4444401803034*^9, 3.4444401844062*^9}, 3.4444402418922*^9, { 3.4444402805022*^9, 3.4444403134026003`*^9}, {3.4444403443062*^9, 3.4444404484049997`*^9}, {3.444483267101*^9, 3.444483267335*^9}, { 3.4444833136046*^9, 3.4444835622998*^9}, {3.4444836421094*^9, 3.4444837777981997`*^9}, {3.444483920429*^9, 3.4444839412237997`*^9}, 3.4444842905546*^9, {3.4444843207406*^9, 3.4444844162282*^9}, { 3.4444844465078*^9, 3.4444844624354*^9}, {3.4444845255998*^9, 3.4444845894505997`*^9}, {3.4444846290746*^9, 3.444484933025*^9}, { 3.4444849790917997`*^9, 3.4444851148742*^9}, {3.444534936054*^9, 3.4445349675348*^9}, {3.4445355821731997`*^9, 3.44453585174*^9}, { 3.4445372162198*^9, 3.4445372264378*^9}, 3.444537384731*^9, { 3.4445377585382*^9, 3.4445377605818*^9}, {3.4445379733658*^9, 3.4445379736934*^9}, {3.4445380176762*^9, 3.444538032777*^9}, { 3.4445381079222*^9, 3.4445381581386003`*^9}, {3.4445382726456003`*^9, 3.4445382910067997`*^9}, {3.4445383401312*^9, 3.4445383475880003`*^9}, { 3.444538438458*^9, 3.4445384464608*^9}, {3.4445385680783997`*^9, 3.4445385687648*^9}, {3.4445389411991997`*^9, 3.4445389431024*^9}, { 3.444539746605*^9, 3.4445397807846003`*^9}, {3.4445408839765997`*^9, 3.4445409234133997`*^9}, {3.4445409681698*^9, 3.4445409932702*^9}, { 3.4445415452906*^9, 3.4445415706717997`*^9}, {3.4445416647242002`*^9, 3.4445416909477997`*^9}, {3.4445417660150003`*^9, 3.444541788557*^9}, { 3.4445420906977997`*^9, 3.444542104847*^9}, {3.4445421885878*^9, 3.4445421941414003`*^9}, {3.4445422252166*^9, 3.4445422386014*^9}, { 3.444542280425*^9, 3.4445423014538*^9}, {3.444542455769*^9, 3.4445424578282003`*^9}, {3.4445431739214*^9, 3.444543175809*^9}, { 3.4445647020962*^9, 3.4445648405618*^9}, {3.4445648825414*^9, 3.4445648858486*^9}, {3.4445649382646*^9, 3.4445651882702*^9}, { 3.4446164822206*^9, 3.4446165344494*^9}, {3.4446166121842003`*^9, 3.4446166738822002`*^9}, {3.4446167223046*^9, 3.4446168047974*^9}, { 3.444616843033*^9, 3.444616906447*^9}, {3.4446444694708*^9, 3.4446444700948*^9}, {3.4446477738310003`*^9, 3.4446477939862003`*^9}, { 3.4446478467298*^9, 3.4446478681018*^9}, 3.4446480456142*^9, { 3.4446487557418003`*^9, 3.4446487636198*^9}, 3.4446488179974003`*^9, { 3.4446488971205997`*^9, 3.4446489152478*^9}, {3.4446490003458*^9, 3.4446490008294*^9}, {3.4447042728942003`*^9, 3.4447042751562*^9}, { 3.4447044703278*^9, 3.4447044865362*^9}, 3.4447046475282*^9, 3.4447047993786*^9, {3.444704908329*^9, 3.4447049292642*^9}, { 3.4447049861926003`*^9, 3.4447049877214003`*^9}, {3.4447050279296*^9, 3.4447050419695997`*^9}, {3.4447053486656*^9, 3.4447053739376*^9}, 3.4447054561963997`*^9, 3.44470561612*^9, {3.4472133996876*^9, 3.4472134108571997`*^9}, {3.4472134470179996`*^9, 3.4472134648332*^9}, { 3.4472135032872*^9, 3.4472135245344*^9}, {3.4472136963059998`*^9, 3.4472137794384003`*^9}, {3.4472138235708*^9, 3.4472138388900003`*^9}, { 3.4472139099792*^9, 3.4472141367096*^9}, {3.447214202682*^9, 3.4472142975924*^9}, {3.4472144187732*^9, 3.4472145910284*^9}, { 3.4472146560492*^9, 3.4472147023968*^9}, {3.447214803594*^9, 3.4472148728736*^9}, {3.4472149156956*^9, 3.447214940484*^9}, { 3.447216227284*^9, 3.4472162419948*^9}, {3.4472163068908*^9, 3.4472163720832*^9}, {3.4472164665880003`*^9, 3.447216530392*^9}, { 3.4472166237268*^9, 3.4472167058452*^9}, 3.4472167362808*^9, { 3.4472171394658003`*^9, 3.4472171532874002`*^9}, {3.4472172028993998`*^9, 3.4472172216661997`*^9}, {3.4472172524606*^9, 3.4472172690278*^9}, { 3.4472173209133997`*^9, 3.4472173334245996`*^9}, {3.4472173920846*^9, 3.447217404861*^9}, {3.4472179572548*^9, 3.4472180351456003`*^9}, { 3.4472509764091997`*^9, 3.4472511017396*^9}, {3.4473910422216*^9, 3.4473912901524*^9}, 3.4473918688344*^9, {3.447392021185*^9, 3.4473920346633997`*^9}, {3.4473921383304*^9, 3.4473921479088*^9}, { 3.4473923024112*^9, 3.4473923734379997`*^9}, {3.4473928098168*^9, 3.4473928648691998`*^9}, {3.4473931872432003`*^9, 3.4473932461800003`*^9}, {3.4473933026675997`*^9, 3.4473934579812*^9}, { 3.4473935755271997`*^9, 3.447393742572*^9}, {3.4473939032676*^9, 3.4473939384144*^9}, {3.447395257644*^9, 3.4473953141628*^9}, { 3.4473954231132*^9, 3.4473954756384*^9}, {3.4473955348716*^9, 3.4473955723272*^9}, {3.447395648502*^9, 3.4473957588876*^9}, { 3.4473957903996*^9, 3.4473958488372*^9}, 3.4473962894154*^9, { 3.447396350817*^9, 3.447396352611*^9}, {3.4474625379146*^9, 3.4474625637326*^9}, {3.558360651728078*^9, 3.558360652102478*^9}, { 3.5619791319820857`*^9, 3.561979135788492*^9}, 3.561979369382504*^9, { 3.5619794930439215`*^9, 3.5619795010155354`*^9}, {3.561979569218855*^9, 3.56197960614412*^9}, {3.5619797417551584`*^9, 3.5619797448751636`*^9}, { 3.618719065033702*^9, 3.618719075426296*^9}, {3.6187194011669273`*^9, 3.6187194449454317`*^9}, {3.6187196998040085`*^9, 3.6187197102436056`*^9}, {3.618719902254588*^9, 3.6187199711455283`*^9}, { 3.618722365406472*^9, 3.6187225412555304`*^9}, {3.6187226885009522`*^9, 3.6187227109872384`*^9}, {3.618722756922866*^9, 3.6187231317203026`*^9}, { 3.618723424250035*^9, 3.6187234267291765`*^9}, {3.6187235105259695`*^9, 3.6187236491028957`*^9}, {3.618723691580325*^9, 3.618723745975436*^9}, { 3.618723778837316*^9, 3.6187238310002995`*^9}, {3.6187239055875654`*^9, 3.618723940035536*^9}, {3.6187239782667227`*^9, 3.6187240219352207`*^9}, { 3.618724166762504*^9, 3.618724177411113*^9}, {3.618729321696159*^9, 3.618729328067523*^9}, 3.618729374058154*^9, {3.6187294379838104`*^9, 3.618729708464281*^9}, {3.6187297631904106`*^9, 3.618729773195983*^9}, { 3.618729822648812*^9, 3.6187299321490746`*^9}, {3.618729984399063*^9, 3.61873000654133*^9}, {3.6187300746012225`*^9, 3.6187300860458775`*^9}, { 3.618731390835507*^9, 3.6187315116174154`*^9}, {3.618731747324897*^9, 3.6187318214091344`*^9}, {3.6187318769243097`*^9, 3.618732065297084*^9}, { 3.6187321012351394`*^9, 3.618732157420353*^9}, {3.618732188384124*^9, 3.6187322435542793`*^9}, {3.6187322786112847`*^9, 3.6187325478446836`*^9}, {3.6187325819856367`*^9, 3.6187326817653437`*^9}, {3.618732810863728*^9, 3.61873282594359*^9}, { 3.6187336474335766`*^9, 3.618733754678711*^9}, {3.618733827497876*^9, 3.61873396201257*^9}, {3.6187342020362988`*^9, 3.618734236455267*^9}, 3.618734298201799*^9, {3.618734712498495*^9, 3.618734712716508*^9}, 3.6187347739640107`*^9, {3.618738817361748*^9, 3.6187388333816643`*^9}, { 3.6187391349349127`*^9, 3.6187391457955337`*^9}, {3.618739376900752*^9, 3.618739397023903*^9}, {3.618739528394417*^9, 3.618739534809784*^9}, { 3.618739972366811*^9, 3.61873997340687*^9}, {3.6187400416617737`*^9, 3.618740043022852*^9}, {3.6187400971579485`*^9, 3.618740107902563*^9}, { 3.6187401713671927`*^9, 3.6187401723312483`*^9}, {3.6187402613443394`*^9, 3.618740268819767*^9}, {3.6187403697625403`*^9, 3.6187404057615995`*^9}, { 3.618740488277319*^9, 3.618740516244919*^9}, {3.618740647782442*^9, 3.6187406551668644`*^9}, 3.6187407823021364`*^9, {3.6187418050786357`*^9, 3.618741805749674*^9}, {3.6187418557605343`*^9, 3.6187419895921893`*^9}, { 3.618742022944097*^9, 3.61874204379729*^9}, {3.6187420836395683`*^9, 3.618742103384698*^9}, {3.620462440882641*^9, 3.6204624460519366`*^9}, { 3.6204624990259666`*^9, 3.620462576450395*^9}, {3.620463682857678*^9, 3.620463713336421*^9}, 3.6204637901188126`*^9, {3.620464238835478*^9, 3.62046424411378*^9}, 3.628912429385081*^9, {3.6289135207155013`*^9, 3.6289135210805225`*^9}, 3.6289497746958513`*^9, 3.6289498371774254`*^9, { 3.62894988410911*^9, 3.6289500319795675`*^9}, {3.6289501333883677`*^9, 3.628950183744248*^9}, {3.6289503323017445`*^9, 3.628950390181055*^9}, { 3.6289505050536256`*^9, 3.6289505113579865`*^9}, {3.62895070863527*^9, 3.6289507095043197`*^9}, {3.628951013180689*^9, 3.62895101407374*^9}, { 3.629190743153632*^9, 3.629190816645361*^9}, {3.6291909709608326`*^9, 3.629190981678051*^9}, {3.629191034624544*^9, 3.6291910410049553`*^9}, { 3.6293846391370816`*^9, 3.629384641102685*^9}, {3.6294628543371735`*^9, 3.629462867097191*^9}, {3.629468063172048*^9, 3.6294681151669397`*^9}, { 3.6295205836757097`*^9, 3.6295206295085897`*^9}, {3.6295206788826766`*^9, 3.6295207067911253`*^9}, {3.6295207408927855`*^9, 3.629520753700408*^9}, { 3.629521020590745*^9, 3.6295210354395943`*^9}, {3.6295211107369013`*^9, 3.62952114882508*^9}, {3.6295212327348795`*^9, 3.6295212477237363`*^9}, { 3.6295213424816394`*^9, 3.629521343230441*^9}, {3.6295215363119802`*^9, 3.6295216753550243`*^9}, {3.629521922272258*^9, 3.6295219939855833`*^9}, { 3.6295220298188467`*^9, 3.629522446058778*^9}, {3.629522499348471*^9, 3.629522604352256*^9}, {3.629522755188921*^9, 3.62952288580795*^9}, { 3.629522918084407*^9, 3.6295233421087513`*^9}, {3.6295233808436193`*^9, 3.629523390936837*^9}, {3.629523424274096*^9, 3.6295234533369465`*^9}, { 3.6295235190130625`*^9, 3.629523521680667*^9}, 3.6295235894315863`*^9, { 3.6295237270706277`*^9, 3.629523799454755*^9}, {3.6295238514808464`*^9, 3.629523883460902*^9}, {3.6295239376085978`*^9, 3.6295239442386093`*^9}, { 3.6295241089904985`*^9, 3.629524177537019*^9}, 3.629524211888279*^9, { 3.629524277423994*^9, 3.629524396904604*^9}, {3.6295244794839497`*^9, 3.6295246248450055`*^9}, 3.629524657090262*^9, {3.6295259599109507`*^9, 3.629526013465844*^9}, {3.6295261092188125`*^9, 3.629526201414974*^9}, 3.6295263436092243`*^9, {3.6295263910333076`*^9, 3.629526583303645*^9}, { 3.629526616672104*^9, 3.629526647653758*^9}, {3.629526687558628*^9, 3.629526744888729*^9}, {3.629526804075233*^9, 3.6295268598453307`*^9}, { 3.6295269393898706`*^9, 3.6295269586559043`*^9}, {3.6295271490074387`*^9, 3.6295272149019547`*^9}, {3.6295272553684254`*^9, 3.6295272827620735`*^9}, {3.6295274137087035`*^9, 3.6295274761244135`*^9}, {3.6295275252801*^9, 3.6295279912529182`*^9}, { 3.6295281572216096`*^9, 3.629528160435215*^9}, {3.6295282905550437`*^9, 3.6295284308616905`*^9}, 3.6295285402022824`*^9, {3.629528582088356*^9, 3.629528616798417*^9}, {3.6295287666834803`*^9, 3.6295290316343455`*^9}, { 3.629529086515242*^9, 3.629529118432898*^9}, {3.6295291548121614`*^9, 3.629529292794404*^9}, {3.6295293426208916`*^9, 3.6295293491261034`*^9}, { 3.629529420699029*^9, 3.629529571535694*^9}, {3.6295296539506383`*^9, 3.629529656103442*^9}, {3.6295296894407005`*^9, 3.629529692295506*^9}, { 3.6295297445555973`*^9, 3.629529766426836*^9}, {3.6295298053333044`*^9, 3.6295298209489317`*^9}, {3.6295308380551186`*^9, 3.6295308386635194`*^9}, {3.629532377840223*^9, 3.6295323811630287`*^9}, { 3.629532480020402*^9, 3.629532482454006*^9}, {3.629532520720874*^9, 3.629532564619351*^9}, {3.62953259842461*^9, 3.6295326002654133`*^9}, { 3.6295326327758703`*^9, 3.6295326715107384`*^9}, {3.629532742428463*^9, 3.6295328288058147`*^9}, {3.6295329692184625`*^9, 3.6295330530062094`*^9}, {3.6295331824396367`*^9, 3.629533193562456*^9}, 3.6295350321720915`*^9, 3.629535158485513*^9, {3.629535245471266*^9, 3.6295352687465067`*^9}, {3.62953541293756*^9, 3.629535446384019*^9}, { 3.6295355043381205`*^9, 3.6295355262249594`*^9}, {3.629543790136781*^9, 3.629543791181983*^9}, {3.629543871350524*^9, 3.629544001673153*^9}, { 3.6295446682009234`*^9, 3.629544668466124*^9}, {3.6296010216162376`*^9, 3.6296010236442413`*^9}, {3.629601079336339*^9, 3.6296010902875586`*^9}, 3.6296011425476503`*^9, {3.6296043522397404`*^9, 3.629604399031022*^9}, { 3.629623884428093*^9, 3.629623914723346*^9}, {3.6296239662190366`*^9, 3.6296239738006496`*^9}, {3.6296240514731865`*^9, 3.6296240920176573`*^9}, {3.629624125947717*^9, 3.629624369432945*^9}, { 3.6296256512247963`*^9, 3.6296256817072496`*^9}, {3.6296260472626915`*^9, 3.629626047434292*^9}, {3.629628055568204*^9, 3.629628056098605*^9}, { 3.6296280911206665`*^9, 3.6296281088266973`*^9}, {3.6296281406819534`*^9, 3.629628273032586*^9}, {3.629628378831972*^9, 3.6296283814995766`*^9}, { 3.629628459562114*^9, 3.629628466379326*^9}, {3.629628519419419*^9, 3.6296285390754533`*^9}, {3.629633008133008*^9, 3.629633008835009*^9}, { 3.6296337764967575`*^9, 3.6296338344040594`*^9}, {3.6296342997684765`*^9, 3.629634432150309*^9}, {3.629634494035618*^9, 3.6296345320060844`*^9}, { 3.629634594499794*^9, 3.629634812182576*^9}, {3.6296348599810605`*^9, 3.6296348746918864`*^9}, {3.6296349071867433`*^9, 3.629635023172947*^9}, 3.6296350995818815`*^9, {3.6296363797201295`*^9, 3.6296363868961425`*^9}, { 3.629636462025874*^9, 3.6296364833355117`*^9}, {3.629636555922439*^9, 3.62963656780966*^9}, {3.629636770469616*^9, 3.629636774151222*^9}, { 3.6296369192782774`*^9, 3.6296369318830996`*^9}, {3.629637058539722*^9, 3.6296370719401455`*^9}, {3.629637278172508*^9, 3.629637286814923*^9}, { 3.6296376418091464`*^9, 3.629637662385583*^9}, {3.629637773551378*^9, 3.629637795360216*^9}, {3.6296390041751394`*^9, 3.629639039571602*^9}, 3.6296393829750047`*^9, {3.6296395546065063`*^9, 3.6296395649961243`*^9}, { 3.62964113386068*^9, 3.6296412507048855`*^9}, {3.629641303167777*^9, 3.629641313744596*^9}, {3.6296416285116315`*^9, 3.629641628886032*^9}, { 3.6296416658736973`*^9, 3.6296416815049243`*^9}, 3.6296417376338234`*^9, { 3.6296855551269727`*^9, 3.6296855804270077`*^9}, {3.6297079065796247`*^9, 3.6297079070476255`*^9}, {3.6297080850439377`*^9, 3.629708135728427*^9}, { 3.6297083496516027`*^9, 3.6297084025512953`*^9}, {3.629708781767563*^9, 3.629708790940379*^9}, {3.6297089402482414`*^9, 3.6297089618542795`*^9}, { 3.6297105345398417`*^9, 3.629710538580249*^9}, {3.6297107810514746`*^9, 3.6297107850138817`*^9}, {3.6297109100481014`*^9, 3.629710915710911*^9}, { 3.629711201534613*^9, 3.629711204311418*^9}, {3.629711236307074*^9, 3.6297115007275386`*^9}, {3.6297115377464037`*^9, 3.6297115441112146`*^9}, 3.6297116025645175`*^9, {3.6298716505389357`*^9, 3.629871851841689*^9}, { 3.62987837458679*^9, 3.629878383510006*^9}, {3.6298784402629056`*^9, 3.629878447345318*^9}, {3.6298785221786494`*^9, 3.6298786580236883`*^9}, { 3.629878689613744*^9, 3.629878737147027*^9}, 3.629878783853509*^9, { 3.629878832322794*^9, 3.6298789171723433`*^9}, {3.6298802128122005`*^9, 3.6298802929723125`*^9}, 3.6298813644148126`*^9, {3.629882428887303*^9, 3.629882435887313*^9}, {3.6298986251827383`*^9, 3.6298988530367384`*^9}, { 3.6298989036744275`*^9, 3.6298989486493063`*^9}, {3.629899016868226*^9, 3.6298991622448816`*^9}, {3.6298997154530535`*^9, 3.629899740147897*^9}, { 3.6298998248560457`*^9, 3.629899978048314*^9}, {3.6299000396372223`*^9, 3.6299001557638264`*^9}, {3.6299001966826982`*^9, 3.6299002595352087`*^9}, 3.6299005011236343`*^9, {3.6299005468317146`*^9, 3.629900567642151*^9}, { 3.629900887676713*^9, 3.629900990153293*^9}, {3.6299011689220085`*^9, 3.6299012295125146`*^9}, {3.6299013754039707`*^9, 3.6299014166036434`*^9}, 3.6299014589733176`*^9, {3.6299015096734066`*^9, 3.629901588765546*^9}, { 3.629901662569275*^9, 3.6299016974665365`*^9}, {3.629901952339784*^9, 3.6299019599057975`*^9}, 3.6299020306051216`*^9, {3.6299022330934772`*^9, 3.6299022682559395`*^9}, {3.6299023020455985`*^9, 3.629902332808852*^9}, { 3.6299024532566643`*^9, 3.629902462850681*^9}, {3.629949880225117*^9, 3.6299498807867184`*^9}, {3.6299503101150723`*^9, 3.6299503156998825`*^9}, {3.629950355058751*^9, 3.629950498937804*^9}, { 3.6299555415202007`*^9, 3.6299555507086167`*^9}, {3.6299556061667137`*^9, 3.6299557553497763`*^9}, {3.629955788499834*^9, 3.6299558948608212`*^9}, { 3.629956042764681*^9, 3.629956043809883*^9}, {3.6299560914211664`*^9, 3.6299561017327843`*^9}, 3.629956145849662*^9, {3.6299584813821354`*^9, 3.6299585082765827`*^9}, 3.6299585652946825`*^9, {3.629958616587573*^9, 3.6299586356508064`*^9}, {3.629958715073346*^9, 3.6299588186419287`*^9}, { 3.629958857454797*^9, 3.629958927249319*^9}, {3.629959427994599*^9, 3.629959494669116*^9}, {3.6299595293323765`*^9, 3.6299596037913074`*^9}, { 3.62995966795422*^9, 3.62995967360143*^9}, {3.6299597835972233`*^9, 3.6299597841120243`*^9}, {3.629959826622099*^9, 3.629959862533362*^9}, { 3.6299599051682367`*^9, 3.6299599235918694`*^9}, 3.629959979939168*^9, { 3.6299601345354395`*^9, 3.62996014612626*^9}, 3.6299601769831142`*^9, { 3.629960253142448*^9, 3.629960269538077*^9}, {3.6299603041701374`*^9, 3.6299603078205442`*^9}, {3.6299604300467587`*^9, 3.629960435491168*^9}, { 3.6299605300585346`*^9, 3.6299605636609936`*^9}, {3.6299606195870914`*^9, 3.6299606581971593`*^9}, {3.629960824228251*^9, 3.6299608755367413`*^9}, { 3.629960906658796*^9, 3.6299609978409557`*^9}, {3.6299610312250147`*^9, 3.629961070646284*^9}, {3.629961135698398*^9, 3.6299611643088484`*^9}, { 3.6299720458358483`*^9, 3.6299721791536827`*^9}, {3.6299722439717965`*^9, 3.629972300007095*^9}, {3.6299723670872126`*^9, 3.6299723937008595`*^9}, { 3.629972457801372*^9, 3.6299724710613956`*^9}, {3.629972740193068*^9, 3.6299728251196175`*^9}, {3.6299729203577843`*^9, 3.6299729350218105`*^9}, {3.6299729720874753`*^9, 3.6299730462188053`*^9}, {3.629973116044528*^9, 3.6299731230177402`*^9}, { 3.629973184310248*^9, 3.6299732090830917`*^9}, {3.629973349982539*^9, 3.6299734360166903`*^9}, 3.629973534562063*^9, {3.629973577446539*^9, 3.629973586104554*^9}, {3.6299740374133463`*^9, 3.629974083823428*^9}, { 3.6299742505565205`*^9, 3.629974337089873*^9}, {3.629974382907153*^9, 3.6299744466176653`*^9}, {3.629974589794717*^9, 3.629974590761918*^9}, { 3.629974776215044*^9, 3.6299747850134597`*^9}, {3.6299748226095257`*^9, 3.6299748237483273`*^9}, 3.6299748618435946`*^9, {3.629975198476586*^9, 3.6299752545898843`*^9}, {3.62997531475919*^9, 3.6299753175515947`*^9}, { 3.6299754601982455`*^9, 3.6299754625382495`*^9}, {3.629975592034077*^9, 3.629975592502078*^9}, {3.629983277446268*^9, 3.6299832946842985`*^9}, { 3.62998342081052*^9, 3.6299835439883366`*^9}, {3.629983615514462*^9, 3.629983931009416*^9}, {3.6299919807040443`*^9, 3.6299919808912444`*^9}, { 3.629992028330928*^9, 3.6299920922130404`*^9}, 3.629992198480427*^9, { 3.6299922299300823`*^9, 3.629992250506518*^9}, {3.629992292657792*^9, 3.6299923603151107`*^9}, {3.6299924387676487`*^9, 3.6299924398440504`*^9}, {3.6299925764846907`*^9, 3.6299926096347485`*^9}, {3.6299928122323046`*^9, 3.629992818768716*^9}, { 3.6299929049120674`*^9, 3.629992905411268*^9}, {3.6299929850338078`*^9, 3.6299929866250105`*^9}, {3.6299931061992207`*^9, 3.62999312270405*^9}, { 3.629993172312137*^9, 3.6299932618718944`*^9}, {3.6299933276572104`*^9, 3.6299933842073092`*^9}, {3.630287775665962*^9, 3.630287795852398*^9}, { 3.6303896387100534`*^9, 3.630389666774503*^9}, {3.6303896967889557`*^9, 3.6303897095341783`*^9}, {3.6303897587054644`*^9, 3.630389880448078*^9}, { 3.6303899127557354`*^9, 3.630390009444705*^9}, 3.630390057321189*^9, 3.630390443484267*^9, {3.63039095720877*^9, 3.6303909789240074`*^9}, { 3.6303910572205453`*^9, 3.6303911291054716`*^9}, {3.630391163035531*^9, 3.6303911740803504`*^9}, {3.630391240224467*^9, 3.6303912875081496`*^9}, { 3.6303913396902413`*^9, 3.630391404570755*^9}, {3.630391479513287*^9, 3.6303917572873745`*^9}, {3.630391868905571*^9, 3.6303920027226057`*^9}, { 3.630392064327114*^9, 3.630392219843787*^9}, {3.63039226121506*^9, 3.63039232943398*^9}, {3.6303924315985594`*^9, 3.6303924441097813`*^9}, { 3.6303926866122074`*^9, 3.6303927118530517`*^9}, {3.630392795671999*^9, 3.6303928006172075`*^9}, {3.6303986032190485`*^9, 3.6303986046230516`*^9}, {3.6303986654631586`*^9, 3.6303987936485834`*^9}, {3.63039889979117*^9, 3.6303989091199865`*^9}, { 3.630399006323757*^9, 3.630399007259759*^9}, {3.630399117224352*^9, 3.630399214771323*^9}, {3.6303992555185947`*^9, 3.6303993036758795`*^9}, { 3.630399467725767*^9, 3.630399502731636*^9}, {3.6303995748037624`*^9, 3.630399595614199*^9}, {3.6303996329294643`*^9, 3.630399658076709*^9}, { 3.630399711335202*^9, 3.6303997453120623`*^9}, {3.6303998546994543`*^9, 3.6303999880484886`*^9}, {3.6304000742074394`*^9, 3.630400123441126*^9}, { 3.6304001724564123`*^9, 3.630400251595351*^9}, {3.630400324166679*^9, 3.630400327052684*^9}, {3.630400358190338*^9, 3.6304003597503414`*^9}, { 3.6304004587481155`*^9, 3.6304004640521245`*^9}, {3.630400521975026*^9, 3.630400526124634*^9}, {3.630400567199506*^9, 3.630400593516752*^9}, { 3.6304012340070767`*^9, 3.6304013035207987`*^9}, {3.6304013614749007`*^9, 3.630401367933312*^9}, {3.630401686939398*^9, 3.6304017294598303`*^9}, { 3.630401794020523*^9, 3.6304018922061386`*^9}, {3.6304019687775183`*^9, 3.630401987153569*^9}, {3.630402072749465*^9, 3.63040208297405*^9}, { 3.6304022247881613`*^9, 3.630402255931943*^9}, 3.630402329306139*^9, { 3.6304023806970787`*^9, 3.6304024212403975`*^9}, {3.6304025002259154`*^9, 3.630402528595538*^9}, {3.6304025620694523`*^9, 3.630402575015193*^9}, { 3.6304026411829777`*^9, 3.630402649073429*^9}, {3.630402695548087*^9, 3.6304027128260756`*^9}, {3.630402783923142*^9, 3.6304027982389607`*^9}, { 3.6304028797236214`*^9, 3.6304030111811404`*^9}, {3.6304030562107162`*^9, 3.6304031598846455`*^9}, {3.630403236330018*^9, 3.6304032404072514`*^9}, { 3.630403373001835*^9, 3.6304033888147397`*^9}, {3.6304039420953856`*^9, 3.6304039512829113`*^9}, 3.6304039831437335`*^9, {3.630404015975611*^9, 3.6304040663624935`*^9}, {3.630404173614628*^9, 3.630404246945822*^9}, { 3.6304042891772375`*^9, 3.630404299595834*^9}, {3.630404391083066*^9, 3.630404392406142*^9}, {3.6304045301800222`*^9, 3.6304045579486103`*^9}, { 3.630404640215316*^9, 3.630404762796327*^9}, {3.630404877629895*^9, 3.630404883104208*^9}, {3.6304050364729805`*^9, 3.630405098270515*^9}, { 3.6304051736118245`*^9, 3.6304051965901384`*^9}, {3.6304053802536435`*^9, 3.63040539242334*^9}, {3.630406035965148*^9, 3.630406041998493*^9}, { 3.630406072049212*^9, 3.6304060962065935`*^9}, {3.630406264081196*^9, 3.6304062707025747`*^9}, {3.63040632219952*^9, 3.630406385461138*^9}, { 3.630406477200385*^9, 3.630406482095665*^9}, {3.6304066170883865`*^9, 3.6304066222256804`*^9}, {3.630406957868878*^9, 3.630406973411767*^9}, { 3.6304070081447535`*^9, 3.630407018199329*^9}, {3.630407411376817*^9, 3.630407412542884*^9}, {3.6304080609339695`*^9, 3.630408121202417*^9}, { 3.6304081585485525`*^9, 3.6304081832129636`*^9}, {3.63040821409673*^9, 3.630408421131572*^9}, 3.6304934333363276`*^9, {3.63049350751357*^9, 3.630493677593298*^9}, {3.630493716898546*^9, 3.6304937846684227`*^9}, 3.630493922944331*^9, {3.6304939556752033`*^9, 3.630494117430455*^9}, { 3.6304941486092386`*^9, 3.6304941767788496`*^9}, {3.6304942118648567`*^9, 3.6304942530272107`*^9}, {3.6304942838399734`*^9, 3.6304942845820155`*^9}, {3.6304943454054947`*^9, 3.6304944442451477`*^9}, {3.63080749995092*^9, 3.6308075480801234`*^9}, { 3.630807586536323*^9, 3.630807621440319*^9}, {3.630807680459695*^9, 3.630807682914836*^9}, {3.630807736889923*^9, 3.6308077644745007`*^9}, { 3.6308078081089964`*^9, 3.6308078670123653`*^9}, {3.630807991648494*^9, 3.630807997541831*^9}, {3.6308081080891542`*^9, 3.6308081919599514`*^9}, { 3.630808306368495*^9, 3.630808345060708*^9}, {3.6308087281906223`*^9, 3.6308087555171847`*^9}, {3.630809110815507*^9, 3.630809169033837*^9}, { 3.6308091998195972`*^9, 3.630809448512822*^9}, {3.6308095328996487`*^9, 3.6308095448223305`*^9}, {3.630809582269472*^9, 3.6308095873607635`*^9}, { 3.630809665529235*^9, 3.630809684808337*^9}, {3.6308316258485594`*^9, 3.6308318380886984`*^9}, {3.63083188164919*^9, 3.630831966930068*^9}, 3.6320400558356075`*^9, {3.6354749882908883`*^9, 3.635474989418953*^9}, { 3.635475084557395*^9, 3.6354750875145636`*^9}, {3.6354751334091887`*^9, 3.635475162315842*^9}, {3.6354754001974483`*^9, 3.6354754820331287`*^9}, 3.635475512931896*^9, {3.6354756222781506`*^9, 3.635475622861184*^9}, { 3.635475691642118*^9, 3.6354757057969275`*^9}, {3.6354757798291616`*^9, 3.635475797395167*^9}, {3.635475884848169*^9, 3.6354758981309285`*^9}, { 3.635475961488552*^9, 3.6354759738382587`*^9}, {3.6354760213729773`*^9, 3.6354760572050266`*^9}, {3.6354761282470903`*^9, 3.635476136040536*^9}, { 3.6354761719365892`*^9, 3.635476212217893*^9}, {3.6593346599546614`*^9, 3.659334660890663*^9}, {3.6593347077219453`*^9, 3.659334720701168*^9}, { 3.6593348752974396`*^9, 3.6593348758122406`*^9}, {3.6593349140947075`*^9, 3.6593350070240707`*^9}, {3.6593350466949406`*^9, 3.6593350543701544`*^9}, {3.659335103791041*^9, 3.6593351614487424`*^9}, 3.659335217686841*^9, {3.659335262084519*^9, 3.6593352995869846`*^9}, { 3.6593356899482727`*^9, 3.659335701819893*^9}, {3.659335964227954*^9, 3.659335964602355*^9}, {3.65933603594128*^9, 3.6593360629605274`*^9}, { 3.6593361352354546`*^9, 3.6593361504454813`*^9}, {3.6593363929479074`*^9, 3.6593364061611304`*^9}, 3.6593368946915884`*^9, {3.6884748265656157`*^9, 3.6884748268716326`*^9}, {3.6884748600075283`*^9, 3.688474861420609*^9}, { 3.6885242858240776`*^9, 3.6885243001140976`*^9}, {3.6888842911675606`*^9, 3.6888843311676164`*^9}, {3.688966242423658*^9, 3.688966263933688*^9}, { 3.6897393587897596`*^9, 3.6897393649897685`*^9}, 3.689739477049925*^9, { 3.6898595970621734`*^9, 3.689859597272174*^9}, {3.6898596707522764`*^9, 3.6898597190523443`*^9}, {3.689859768552414*^9, 3.6898597721424184`*^9}, { 3.689859855272535*^9, 3.689859859882541*^9}, {3.6898605078334484`*^9, 3.6898607266237545`*^9}, 3.6898608811139708`*^9, {3.6898609634740863`*^9, 3.689860974304102*^9}, 3.6898610140141573`*^9, {3.6898611496043468`*^9, 3.6898611683243732`*^9}, {3.689861462024784*^9, 3.6898615624849253`*^9}, { 3.6898616142149973`*^9, 3.6898616164350004`*^9}, 3.6898616657950697`*^9, { 3.689861716805141*^9, 3.689861749905187*^9}, {3.732677920575506*^9, 3.7326779208190203`*^9}, {3.7519672427004185`*^9, 3.7519672444968877`*^9}, {3.7519674022097683`*^9, 3.75196742976579*^9}, { 3.751967484127989*^9, 3.751967510853814*^9}, {3.7519675409404893`*^9, 3.751967541549782*^9}, {3.7519675797751045`*^9, 3.751967592209671*^9}, { 3.7519676829383273`*^9, 3.7519676841255474`*^9}, {3.7519677154775553`*^9, 3.7519677953499403`*^9}, 3.751967827811061*^9, {3.7519679545625095`*^9, 3.751967957999185*^9}, {3.751968003754015*^9, 3.7519681477513895`*^9}, { 3.751968264817631*^9, 3.751968270722477*^9}, {3.7519689618119907`*^9, 3.751968969888235*^9}, {3.7519691168917775`*^9, 3.7519691395895615`*^9}, { 3.751969242782174*^9, 3.7519692581691785`*^9}, {3.7519693625211954`*^9, 3.751969378579924*^9}, {3.751969409572627*^9, 3.751969438643936*^9}, { 3.7519695894526725`*^9, 3.751969614306203*^9}, {3.7523200108586655`*^9, 3.752320012354121*^9}, {3.7553831315619707`*^9, 3.755383134119626*^9}, { 3.7553831893197794`*^9, 3.755383241814331*^9}, {3.7553832736267967`*^9, 3.7553832810757113`*^9}, {3.7554336536222963`*^9, 3.755433684797229*^9}, { 3.7554337764737434`*^9, 3.7554338315300155`*^9}, {3.755433998047738*^9, 3.7554340265485487`*^9}, {3.755446573138784*^9, 3.755446636911299*^9}, { 3.75544667493072*^9, 3.755446753435521*^9}, {3.755446891541581*^9, 3.7554468921547422`*^9}, {3.7554469323588533`*^9, 3.755446936867403*^9}, { 3.7554470190332975`*^9, 3.7554472776872244`*^9}, {3.7555217323692026`*^9, 3.755521732847602*^9}, {3.755521767127169*^9, 3.7555217972041793`*^9}, { 3.755522561453134*^9, 3.755522564231819*^9}, {3.755522601885935*^9, 3.7555226037287407`*^9}, {3.7555226758687305`*^9, 3.755522678585092*^9}, { 3.7555234832604623`*^9, 3.7555235920444417`*^9}, {3.7555239506007543`*^9, 3.755524013893358*^9}, {3.755524076791689*^9, 3.7555240812793446`*^9}, { 3.7555241238138275`*^9, 3.7555241268985643`*^9}, {3.7555242930449886`*^9, 3.7555243378577013`*^9}, {3.7555256673767824`*^9, 3.7555256808205338`*^9}, {3.7555258588384123`*^9, 3.755525900317296*^9}, { 3.755525930708299*^9, 3.7555260436531134`*^9}, {3.755607147401991*^9, 3.7556071504143705`*^9}, {3.755607992884314*^9, 3.7556080025382996`*^9}, { 3.7556094344057455`*^9, 3.7556094348690443`*^9}, {3.7559613653116636`*^9, 3.755961445097105*^9}, 3.755961484246889*^9, {3.7559618979231987`*^9, 3.755961939470047*^9}, {3.7559620323724904`*^9, 3.7559620330864005`*^9}, { 3.755962155557907*^9, 3.7559621601593847`*^9}, {3.755962303755834*^9, 3.755962343830135*^9}, {3.7559624058018165`*^9, 3.7559624450501757`*^9}, 3.756002186674869*^9, 3.7560029626855392`*^9, {3.756003222110388*^9, 3.756003295034633*^9}, {3.7560056331492863`*^9, 3.7560056663855457`*^9}, { 3.7560057813555765`*^9, 3.7560057863836613`*^9}, {3.7560058917172394`*^9, 3.756005927847292*^9}, 3.756006092376186*^9, 3.756009112317705*^9, { 3.756091886039587*^9, 3.756091887764086*^9}, {3.756092005435152*^9, 3.7560920727337685`*^9}, {3.75609212911592*^9, 3.7560921293252516`*^9}, { 3.756092262958163*^9, 3.756092263157668*^9}, {3.756092342487877*^9, 3.756092347894502*^9}, {3.7560929036769304`*^9, 3.7560929278911004`*^9}, { 3.7560930741522417`*^9, 3.756093083420331*^9}, {3.7560932986236534`*^9, 3.7560933139459305`*^9}, {3.756093449985523*^9, 3.7560934874491863`*^9}, { 3.756093592694581*^9, 3.7560936019456573`*^9}, {3.756093634438078*^9, 3.756093673866626*^9}, {3.756093873069885*^9, 3.756093897964734*^9}, { 3.7560940650109406`*^9, 3.756094078056768*^9}, {3.756442536546026*^9, 3.756442607904289*^9}, {3.7564436397451363`*^9, 3.7564436403231254`*^9}, { 3.7636034984570236`*^9, 3.7636034989933815`*^9}, {3.763603551051456*^9, 3.7636035527617817`*^9}, {3.7636036049384193`*^9, 3.7636036392233057`*^9}, {3.7636036850937223`*^9, 3.763603692587598*^9}, { 3.7636037258272257`*^9, 3.7636037459031096`*^9}, {3.7636037792254367`*^9, 3.76360387572289*^9}, {3.763603971837229*^9, 3.7636040341423655`*^9}, { 3.763604066526084*^9, 3.7636040756798687`*^9}, {3.7636041452118535`*^9, 3.763604278007333*^9}, {3.763604317710966*^9, 3.7636043271387568`*^9}, { 3.7636043584877644`*^9, 3.763604415561053*^9}, {3.763604445680462*^9, 3.7636044504114943`*^9}, {3.763604615444647*^9, 3.7636048082554193`*^9}, 3.763604854904996*^9, {3.7636133594095488`*^9, 3.7636133618464766`*^9}, { 3.7636136063756704`*^9, 3.7636136315671196`*^9}, {3.7636990373827705`*^9, 3.7636990431157646`*^9}, {3.763699090332087*^9, 3.763699110952259*^9}, { 3.763699227420497*^9, 3.7636993642943506`*^9}, {3.763700085627533*^9, 3.763700088329999*^9}, {3.7637001721125274`*^9, 3.763700181422837*^9}, { 3.763700248063385*^9, 3.7637003918630466`*^9}, {3.763700591783223*^9, 3.7637006017496295`*^9}, {3.7637007583576717`*^9, 3.7637007603074865`*^9}, {3.7637137795793185`*^9, 3.7637137822587233`*^9}, {3.7637148704355187`*^9, 3.763714870624051*^9}, { 3.763727592158518*^9, 3.7637275933445053`*^9}, {3.7637276688363667`*^9, 3.7637276694756594`*^9}, 3.763803448896332*^9, {3.76380349501632*^9, 3.7638036835067654`*^9}, {3.763804829093463*^9, 3.7638048385675254`*^9}, 3.7638051033646154`*^9, 3.7638053924528885`*^9, {3.763805557684454*^9, 3.763805634255308*^9}, {3.763806843847647*^9, 3.763806847966059*^9}, { 3.763806942652097*^9, 3.7638071770752254`*^9}, {3.7638141184594107`*^9, 3.763814134133461*^9}, {3.7638146808628216`*^9, 3.7638146925645113`*^9}, { 3.7638147709278784`*^9, 3.7638147811883087`*^9}, {3.7638148155281043`*^9, 3.763814819843194*^9}, {3.7638150259647446`*^9, 3.763815028601293*^9}, { 3.7638151529595194`*^9, 3.763815155849978*^9}, {3.7638163770262136`*^9, 3.763816380851597*^9}, {3.7638164181856327`*^9, 3.7638164950537987`*^9}, 3.763816568304102*^9, {3.7638166173645625`*^9, 3.763816618808757*^9}, { 3.7638167204462805`*^9, 3.763816721012859*^9}, {3.763857602253485*^9, 3.7638579604183645`*^9}, {3.7638580038507566`*^9, 3.7638580060526443`*^9}, {3.763858082269992*^9, 3.7638581746835337`*^9}, { 3.7638582163351564`*^9, 3.7638582415275116`*^9}, {3.7638582983238*^9, 3.763858907503306*^9}, {3.763858941318697*^9, 3.763858956626134*^9}, { 3.7638602435602536`*^9, 3.763860245408451*^9}, {3.7638694636456347`*^9, 3.7638694647177277`*^9}, {3.7638708199536576`*^9, 3.763870829436488*^9}, { 3.763871287170555*^9, 3.7638712876184006`*^9}, {3.763943214376035*^9, 3.7639432984591475`*^9}, {3.763943418832348*^9, 3.7639434335508127`*^9}, { 3.76394347113767*^9, 3.7639435187320576`*^9}, {3.763943585908682*^9, 3.7639436125255404`*^9}, {3.763951722152746*^9, 3.76395172989299*^9}, { 3.7639517863423367`*^9, 3.7639519945900664`*^9}, {3.763952081515512*^9, 3.7639521530710773`*^9}, {3.763952353248129*^9, 3.763952357026309*^9}, { 3.7639524211903834`*^9, 3.7639524243979177`*^9}, {3.7639527174925117`*^9, 3.7639527180252266`*^9}, {3.7641265625745993`*^9, 3.7641265632314167`*^9}, {3.764126605555829*^9, 3.7641266075095396`*^9}, { 3.7641268313964133`*^9, 3.7641268543573804`*^9}, {3.764127044657903*^9, 3.7641270479422092`*^9}, {3.7641271442332697`*^9, 3.7641271469362774`*^9}, {3.764127227626192*^9, 3.7641272592640233`*^9}, { 3.764127335707515*^9, 3.7641273386484756`*^9}, {3.764127429843852*^9, 3.7641274364304185`*^9}, {3.7641275071859307`*^9, 3.764127516803895*^9}, 3.7641276043548007`*^9, {3.7641276925365753`*^9, 3.764127697080591*^9}, 3.764127798472331*^9, 3.764127853631323*^9, 3.764127908496078*^9, { 3.7641280050343323`*^9, 3.764128022046494*^9}, {3.764128128597419*^9, 3.764128154116727*^9}, {3.7641286864636617`*^9, 3.764128701643106*^9}, { 3.7641289910924444`*^9, 3.7641290126680794`*^9}, {3.7641290672285347`*^9, 3.7641290737798567`*^9}, {3.7641325425120363`*^9, 3.764132565390477*^9}, { 3.7641327425004654`*^9, 3.764132750040793*^9}, 3.7641327968340364`*^9, { 3.764133146776842*^9, 3.764133204874522*^9}, {3.7641333488187037`*^9, 3.7641333525577593`*^9}, {3.764413145593136*^9, 3.7644131471236105`*^9}, { 3.764413201645049*^9, 3.7644132349609704`*^9}, {3.764413325008136*^9, 3.7644133748980193`*^9}, {3.7644134113425665`*^9, 3.7644135151187*^9}, { 3.764413554409053*^9, 3.7644136160674934`*^9}, {3.76441371984758*^9, 3.764413730103909*^9}, 3.764419641962368*^9, {3.7644198522879405`*^9, 3.764419879249356*^9}, 3.764419909536559*^9, {3.764419991012162*^9, 3.764420000171088*^9}, {3.7644200798862047`*^9, 3.7644200950961914`*^9}, { 3.7644201529471693`*^9, 3.764420153715966*^9}, {3.764420210346301*^9, 3.764420255343707*^9}, {3.764420296178318*^9, 3.7644203000939393`*^9}, { 3.7644203803359275`*^9, 3.7644203931390867`*^9}, 3.7644204418727274`*^9, { 3.7647259720700207`*^9, 3.7647261047260523`*^9}, {3.7647263483375626`*^9, 3.76472635879602*^9}, 3.764726656736601*^9, {3.764727009127914*^9, 3.764727020100875*^9}, {3.7647270591828785`*^9, 3.7647270819631023`*^9}, { 3.7647272109090505`*^9, 3.764727227846332*^9}, {3.76473247809907*^9, 3.7647324813925114`*^9}, {3.7647349484962797`*^9, 3.7647349979358416`*^9}, {3.7647351097258167`*^9, 3.764735124772463*^9}, { 3.7647352810674453`*^9, 3.7647352901139917`*^9}, {3.7647353746429515`*^9, 3.764735379550926*^9}, {3.7647354596539807`*^9, 3.764735507677454*^9}, { 3.7647355546341*^9, 3.764735728811817*^9}, {3.764735837449795*^9, 3.76473584132898*^9}, {3.76473603649269*^9, 3.7647360592982664`*^9}, { 3.7647360998228803`*^9, 3.76473621551197*^9}, {3.7647362545599003`*^9, 3.764736286430997*^9}, {3.7647364592833533`*^9, 3.764736464019006*^9}, { 3.764736566167658*^9, 3.7647365918958225`*^9}, {3.764764761680134*^9, 3.7647648482473745`*^9}, 3.764764917763693*^9, {3.764764964821686*^9, 3.764765090741813*^9}, {3.7647651742140284`*^9, 3.7647652517335076`*^9}, { 3.764765341266399*^9, 3.7647653614173465`*^9}, 3.764765400284145*^9, { 3.764765691384389*^9, 3.764765708710143*^9}, 3.7647657454275875`*^9, { 3.76476578351686*^9, 3.764765871262255*^9}, {3.7647661045180917`*^9, 3.76476612822571*^9}, {3.7647661964223824`*^9, 3.764766239375331*^9}, { 3.764766330361228*^9, 3.764766338297905*^9}, {3.764767015060799*^9, 3.7647670193029037`*^9}, {3.764767076590926*^9, 3.7647671160277977`*^9}, { 3.7647671493139205`*^9, 3.7647672079236426`*^9}, {3.764767458938404*^9, 3.7647674608323865`*^9}, {3.764810938444873*^9, 3.7648109399353456`*^9}, { 3.7648118616019874`*^9, 3.7648118695079126`*^9}, {3.7648120589477816`*^9, 3.7648124600413237`*^9}, {3.76481250476682*^9, 3.7648125259602103`*^9}, { 3.764812601341893*^9, 3.7648126577763243`*^9}, {3.7648126944039307`*^9, 3.7648128855627623`*^9}, {3.764812924923909*^9, 3.764812926481821*^9}, { 3.764813041485982*^9, 3.764813131254232*^9}, {3.7648134679328885`*^9, 3.7648136479313235`*^9}, {3.7648136917777314`*^9, 3.764813697753367*^9}, { 3.7648137297570653`*^9, 3.764813747862262*^9}, 3.764813784221693*^9, { 3.7648138370678406`*^9, 3.7648141387969923`*^9}, {3.764814321050164*^9, 3.764814422489184*^9}, {3.764814461366684*^9, 3.7648145835728483`*^9}, { 3.764814614769511*^9, 3.7648147525825167`*^9}, {3.764815363375289*^9, 3.7648153644907384`*^9}, {3.764815451671169*^9, 3.7648154601533747`*^9}, { 3.7648175917802963`*^9, 3.7648176401910563`*^9}, {3.765885491237231*^9, 3.765885501131465*^9}, {3.766572999289345*^9, 3.7665729996020145`*^9}, { 3.7665730613126965`*^9, 3.7665730616706066`*^9}, {3.7840103262125545`*^9, 3.7840103546413517`*^9}, {3.784011309725755*^9, 3.7840113197719574`*^9}, { 3.784013374800973*^9, 3.7840133842981763`*^9}, {3.7840238533665447`*^9, 3.78402395932942*^9}, {3.784024091276659*^9, 3.784024112209529*^9}, { 3.7840242793219643`*^9, 3.784024296655184*^9}, {3.7840290670892677`*^9, 3.7840291348388853`*^9}, {3.784029222997594*^9, 3.784029542926179*^9}, { 3.784375172285057*^9, 3.784375319701829*^9}, {3.7843753678421807`*^9, 3.7843753788103914`*^9}, {3.7843754844339557`*^9, 3.784375827494117*^9}, { 3.784375862317687*^9, 3.7843759567563844`*^9}, {3.784376004941759*^9, 3.7843760080157185`*^9}, {3.784376101918992*^9, 3.7843761244332943`*^9}, { 3.784376181191763*^9, 3.7843762145091863`*^9}, {3.7843792489960337`*^9, 3.78437926273014*^9}, {3.7843793293934345`*^9, 3.784379368676588*^9}, { 3.7843796529835215`*^9, 3.7843796858862267`*^9}, {3.784450863324359*^9, 3.7844508986076546`*^9}, {3.7844510208392324`*^9, 3.784451027915551*^9}, { 3.7844511176315613`*^9, 3.7844511673791957`*^9}, {3.784451235055628*^9, 3.78445132575735*^9}, {3.784451995615477*^9, 3.7844520110330954`*^9}, { 3.7844522907551537`*^9, 3.7844523421551*^9}, {3.784700119490345*^9, 3.7847001627913013`*^9}, {3.7847004221290607`*^9, 3.7847004380767317`*^9}, 3.7847007913506136`*^9, {3.784781955129138*^9, 3.784781977787957*^9}, { 3.78488170216677*^9, 3.784881704210422*^9}, 3.784882130557441*^9, { 3.78488220347418*^9, 3.7848822064697027`*^9}, {3.784883393455822*^9, 3.784883458551924*^9}, 3.7848835306495824`*^9, {3.7848836822092113`*^9, 3.7848837303696923`*^9}, 3.7848838199009576`*^9, {3.7848842507527857`*^9, 3.7848842836585226`*^9}, 3.7848843847882996`*^9, {3.784884461405264*^9, 3.7848844645041113`*^9}, {3.784884559404122*^9, 3.7848845656634912`*^9}, { 3.7848852409944844`*^9, 3.7848852740337477`*^9}, {3.7848854548929386`*^9, 3.7848854893046365`*^9}, {3.7848856741783943`*^9, 3.784885691704702*^9}, { 3.784885809660874*^9, 3.784885811424426*^9}, {3.7848860031948376`*^9, 3.784886020570098*^9}, 3.7848861057105627`*^9, {3.7848861627726107`*^9, 3.7848862212876124`*^9}, {3.784886306497995*^9, 3.7848863509322224`*^9}, 3.784886472690192*^9, {3.7848866596243*^9, 3.784886664116289*^9}, { 3.7848866987282944`*^9, 3.7848867077911897`*^9}, {3.78488676128524*^9, 3.7848868667029366`*^9}, {3.7848869381224003`*^9, 3.7848869414281464`*^9}, {3.7848870104508753`*^9, 3.784887039889447*^9}, { 3.7848871795058794`*^9, 3.7848871976746817`*^9}, {3.7848872311446314`*^9, 3.78488724075662*^9}, 3.784887405188785*^9, {3.784887591926689*^9, 3.7848876119305134`*^9}, {3.784887676620901*^9, 3.7848876786672792`*^9}, { 3.78488771054331*^9, 3.784887714354906*^9}, {3.7848877625809546`*^9, 3.7848878103041153`*^9}, 3.7848878862881575`*^9, {3.787717235155089*^9, 3.787717269464238*^9}, {3.7877174592607603`*^9, 3.7877174674038067`*^9}, { 3.7877271032841845`*^9, 3.787727136247201*^9}, 3.787727355369296*^9, 3.7877274973278403`*^9, {3.787727855959008*^9, 3.78772792141208*^9}, 3.787728113487193*^9, {3.7877281704571557`*^9, 3.7877281735077004`*^9}, 3.7877282789827795`*^9, {3.7877286510229864`*^9, 3.787728665729192*^9}, { 3.7877287942225084`*^9, 3.787728807671986*^9}, {3.787729044867985*^9, 3.787729045536916*^9}, {3.787729589732438*^9, 3.7877296062090626`*^9}, { 3.787729794037467*^9, 3.7877297950347877`*^9}, {3.787729855548402*^9, 3.7877299039179935`*^9}, {3.7877300373241186`*^9, 3.787730068136018*^9}, { 3.7877301999859333`*^9, 3.7877302014150777`*^9}, {3.787732033225385*^9, 3.7877320471634016`*^9}, {3.787732077195259*^9, 3.7877320780358667`*^9}, 3.787732189759206*^9, {3.78773231889835*^9, 3.787732327710633*^9}, { 3.7877324857166643`*^9, 3.787732496655479*^9}, {3.7877325848303585`*^9, 3.78773258503596*^9}, {3.7877328504631166`*^9, 3.7877328625892415`*^9}, { 3.7877330254884944`*^9, 3.7877330271019044`*^9}, {3.787733136128061*^9, 3.7877331422258835`*^9}, {3.787733243513567*^9, 3.78773324558677*^9}, 3.787733310555999*^9, 3.7877334085329347`*^9, {3.7877337955932293`*^9, 3.7877337970498257`*^9}, {3.787733867727028*^9, 3.7877338687324905`*^9}, { 3.7877352224369583`*^9, 3.787735224161746*^9}, {3.787735343322833*^9, 3.787735348772827*^9}, {3.787735422704711*^9, 3.7877354268945775`*^9}, { 3.7877355100355635`*^9, 3.787735514671461*^9}, {3.7877356541994534`*^9, 3.7877356632141013`*^9}, 3.7877357913476543`*^9, 3.787736261837074*^9, { 3.7882542159043374`*^9, 3.7882542747998285`*^9}, {3.788254310967661*^9, 3.788254318430212*^9}, {3.788254585790197*^9, 3.7882545888318524`*^9}, { 3.7882547349987383`*^9, 3.788254735940298*^9}, 3.788254830063775*^9, 3.7882549155286837`*^9, {3.7882550121437798`*^9, 3.788255037735396*^9}, { 3.7882551764404287`*^9, 3.78825518352113*^9}, {3.7882552540030313`*^9, 3.788255290224329*^9}, {3.7882553843544893`*^9, 3.788255423248046*^9}, { 3.78825567982127*^9, 3.7882556852479534`*^9}, {3.7882557908576803`*^9, 3.7882558029800806`*^9}, {3.7882560240494256`*^9, 3.7882560388846164`*^9}, 3.788256102343512*^9, {3.788256161397396*^9, 3.7882561626372194`*^9}, { 3.7882562304311895`*^9, 3.78825629590362*^9}, {3.7882563614677362`*^9, 3.7882563620189795`*^9}, {3.7882564138122153`*^9, 3.7882564294158382`*^9}, {3.788256467457189*^9, 3.7882564889521217`*^9}, { 3.7882565883311844`*^9, 3.788256591497148*^9}, {3.7882568409513097`*^9, 3.7882568724526567`*^9}, {3.788256965258837*^9, 3.788256966444976*^9}, { 3.7882570073831463`*^9, 3.7882570497349973`*^9}, {3.7882570992487097`*^9, 3.788257144206352*^9}, {3.78825721252205*^9, 3.788257307277931*^9}, { 3.788257350410209*^9, 3.7882573617262745`*^9}, {3.788257424936472*^9, 3.788257434118204*^9}, {3.788276311330668*^9, 3.788276311647092*^9}, { 3.7882765465512347`*^9, 3.788276608568333*^9}, {3.7882767715851693`*^9, 3.7882768045752783`*^9}, {3.7882769342607436`*^9, 3.7882769409894867`*^9}, {3.7882770202208567`*^9, 3.7882770424485188`*^9}, {3.7882770760040703`*^9, 3.788277077341468*^9}, { 3.788277147336176*^9, 3.788277150397852*^9}, {3.7882772069909*^9, 3.7882772101572385`*^9}, {3.7882772503366175`*^9, 3.7882772773759403`*^9}, {3.7882773922958755`*^9, 3.7882773927832017`*^9}, {3.788277450684473*^9, 3.788277482126852*^9}, { 3.78827754293396*^9, 3.788277545027956*^9}, 3.7890961565048018`*^9, { 3.789096242941472*^9, 3.7890962452874937`*^9}, {3.789096286771101*^9, 3.789096287939043*^9}, {3.7890963300637918`*^9, 3.789096330454324*^9}, { 3.789096421623994*^9, 3.789096482010544*^9}, {3.789123616007924*^9, 3.789123644103528*^9}},ExpressionUUID->"8c146a0a-8398-489f-8e7b-\ cf853995ea71"] }, Closed]], Cell[CellGroupData[{ Cell["PLATE ELEMENT (evnt) defs", "Subsection", InitializationCell->True, CellChangeTimes->{{3.753018875511382*^9, 3.7530188786265306`*^9}, { 3.781589886623744*^9, 3.7815898932426767`*^9}, {3.7878947601549573`*^9, 3.787894760728943*^9}, 3.7878948945295725`*^9, {3.817439343565061*^9, 3.8174393448082724`*^9}, {3.817439544553817*^9, 3.8174395452236648`*^9}, { 3.817439659219601*^9, 3.8174396600345135`*^9}, 3.817439764967313*^9, 3.843182905672008*^9},ExpressionUUID->"746ec010-b55b-4f1c-a482-\ 156a399311ff"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"EVNT", ",", RowBox[{"{", RowBox[{"s0_", ",", "sol0_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"PLATE", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLATE", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, { 3.7530189177531705`*^9, 3.753018918350237*^9}, {3.753018991800671*^9, 3.753019041865839*^9}, {3.7530191095313196`*^9, 3.7530191100576744`*^9}, 3.753019155952956*^9, {3.7530192458219423`*^9, 3.753019353286773*^9}, { 3.773986323215969*^9, 3.7739864366876383`*^9}, {3.7739864700193005`*^9, 3.7739865885966825`*^9}, {3.7739869332783327`*^9, 3.7739870501829805`*^9}, 3.773987085528166*^9, {3.7739872536160583`*^9, 3.773987270466986*^9}, { 3.773987482712697*^9, 3.7739875221812735`*^9}, {3.773987740298462*^9, 3.7739877466065903`*^9}, {3.7739878599976892`*^9, 3.7739878861137896`*^9}, {3.773987965425336*^9, 3.7739879715632877`*^9}, 3.773988098774023*^9, 3.7739883193781385`*^9, {3.7739884099852057`*^9, 3.7739885862960095`*^9}, {3.773988628922502*^9, 3.773988632767228*^9}, { 3.7739891227568517`*^9, 3.77398915009042*^9}, {3.7739892774900556`*^9, 3.773989291800435*^9}, {3.7739896060525217`*^9, 3.773989635013425*^9}, { 3.7751890832095585`*^9, 3.7751890882413054`*^9}, {3.7751894923762302`*^9, 3.7751895008441906`*^9}, {3.7751911834227276`*^9, 3.775191222686661*^9}, 3.7751912606478214`*^9, {3.7751943412188396`*^9, 3.775194461553982*^9}, { 3.775194496052539*^9, 3.7751945353727713`*^9}, {3.7751945737174063`*^9, 3.775194621343042*^9}, {3.775194667862669*^9, 3.7751947598351893`*^9}, { 3.7751948235734253`*^9, 3.7751949415953684`*^9}, {3.775195100078847*^9, 3.77519512113822*^9}, {3.7751954506873007`*^9, 3.775195467864645*^9}, { 3.775270786870551*^9, 3.775270796325161*^9}, {3.7752708274391947`*^9, 3.775270839737406*^9}, {3.7752709283091574`*^9, 3.7752709474534383`*^9}, { 3.7752710502850266`*^9, 3.7752711744130797`*^9}, {3.7752712273079033`*^9, 3.7752713060364757`*^9}, {3.775271448825513*^9, 3.7752714699277525`*^9}, { 3.775271509321142*^9, 3.775271585609558*^9}, {3.775271620653377*^9, 3.77527180192237*^9}, {3.781589928213842*^9, 3.781590052438653*^9}, { 3.7815900898176003`*^9, 3.781590109307678*^9}, {3.781590201383393*^9, 3.7815902433873234`*^9}, {3.7815905445265956`*^9, 3.781590569573782*^9}, { 3.7815906952864275`*^9, 3.781590715680611*^9}, {3.7815908323678637`*^9, 3.781590881239719*^9}, {3.7815911048122363`*^9, 3.781591119274813*^9}, { 3.817439386305109*^9, 3.8174394287787733`*^9}, {3.8174395552770724`*^9, 3.8174395603447847`*^9}, {3.8174396709099665`*^9, 3.817439676294123*^9}, { 3.8174397747716293`*^9, 3.8174397780717535`*^9}, 3.817521343573311*^9, 3.843182901255577*^9}, CellLabel-> "In[196]:=",ExpressionUUID->"2eb5706f-5726-4702-b960-6b10b57e5450"] }, Closed]], Cell[CellGroupData[{ Cell["PLATE ELEMENT (vibr) defs ", "Subsection", CellChangeTimes->{{3.6302475626780834`*^9, 3.6302475636452847`*^9}, { 3.6303896204112215`*^9, 3.630389621175623*^9}, {3.7658855359334097`*^9, 3.7658855563942738`*^9}, {3.7882511594490995`*^9, 3.788251160663724*^9}, { 3.7883213876221266`*^9, 3.788321388914168*^9}},ExpressionUUID->"eb7cfdca-700f-4b39-b577-\ f326a187aea4"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "n\[Alpha]", ",", "n\[Beta]", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "NN", ",", "mat", ",", "MM", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "r\[Gamma]", ",", "rn", ",", "jac", ",", "h\[Alpha]", ",", "e\[Alpha]", ",", "h\[Beta]", ",", "h\[Gamma]", ",", "e\[Beta]", ",", "en", ",", "e\[Gamma]", ",", "FF", ",", "\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]", ",", "edg", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "u0", ",", "v0", ",", "w0", ",", "\[Phi]0", ",", "\[Theta]0", ",", "\[Psi]0", ",", "u2", ",", "v2", ",", "w2", ",", "\[Phi]2", ",", "\[Theta]2", ",", "\[Psi]2", ",", "\[Pi]u", ",", "\[Pi]v", ",", "\[Pi]w", ",", "\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]", ",", "\[Pi]u0", ",", "\[Pi]v0", ",", "\[Pi]w0", ",", "\[Pi]\[Phi]0", ",", "\[Pi]\[Theta]0", ",", "\[Pi]\[Psi]0", ",", "\[Pi]u2", ",", "\[Pi]v2", ",", "\[Pi]w2", ",", "\[Pi]\[Phi]2", ",", "\[Pi]\[Theta]2", ",", "\[Pi]\[Psi]2", ",", "f\[Alpha]", ",", "f\[Gamma]", ",", "fn", ",", "m\[Alpha]", ",", "m\[Gamma]", ",", "mn", ",", "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]", ",", "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]", ",", "\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]", ",", "GG", ",", "N\[Alpha]\[Alpha]", ",", "N\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Gamma]", ",", "N\[Gamma]\[Alpha]", ",", "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]", ",", "Q\[Alpha]", ",", "Q\[Gamma]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wine", ",", "\[Delta]wmap", ",", "AA"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"mat", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]", "=", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}]}], ";", " ", RowBox[{"r\[Beta]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Norm", "[", "r\[Beta]", "]"}]}], ";", " ", RowBox[{"h\[Alpha]", "=", RowBox[{"Norm", "[", "r\[Alpha]", "]"}]}], ";", RowBox[{"jac", "=", RowBox[{"Norm", "[", RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Alpha]", "=", RowBox[{"r\[Alpha]", "/", "h\[Alpha]"}]}], ";", RowBox[{"e\[Beta]", "=", RowBox[{"r\[Beta]", "/", "h\[Beta]"}]}], ";", " ", RowBox[{"en", "=", RowBox[{ RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], " ", "/", "jac"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r\[Gamma]", "=", RowBox[{"r\[Beta]", "-", RowBox[{ RowBox[{"(", RowBox[{"r\[Beta]", ".", "e\[Alpha]"}], ")"}], " ", "e\[Alpha]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Gamma]", "=", RowBox[{"Norm", "[", "r\[Gamma]", "]"}]}], ";", RowBox[{"e\[Gamma]", "=", RowBox[{"r\[Gamma]", "/", "h\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", "e\[Gamma]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]"}], "}"}], "=", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Alpha]"}], ",", RowBox[{"r\[Alpha]", ".", "r\[Beta]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Beta]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Beta]"}]}], "}"}]}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Gamma]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Gamma]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"edg", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Sort", "[", "#", "]"}], "&"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"time", " ", "derivatives"}], "*)"}], "\[IndentingNewLine]", RowBox[{"w0", "=", RowBox[{"w", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", RowBox[{"w2", "=", RowBox[{"w", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]0", "=", RowBox[{"\[Phi]", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", RowBox[{"\[Phi]2", "=", RowBox[{"\[Phi]", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]0", "=", RowBox[{"\[Theta]", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", RowBox[{"\[Theta]2", "=", RowBox[{"\[Theta]", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "projections", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Pi]\[Phi]", "=", RowBox[{ RowBox[{ RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], "/", "60"}], "+", " ", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Theta]", "=", RowBox[{ RowBox[{ RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], "/", "60"}], "+", " ", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"continuous", " ", "displacement"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Pi]w", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Phi]0", "=", RowBox[{"\[Pi]\[Phi]", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", RowBox[{"\[Pi]\[Phi]2", "=", RowBox[{"\[Pi]\[Phi]", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Theta]0", "=", RowBox[{"\[Pi]\[Theta]", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", RowBox[{"\[Pi]\[Theta]2", "=", RowBox[{"\[Pi]\[Theta]", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]w0", "=", RowBox[{"\[Pi]w", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", RowBox[{"\[Pi]w2", "=", RowBox[{"\[Pi]w", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]0", ",", "\[Theta]0"}], "}"}], "=", RowBox[{ RowBox[{"FF", "[", RowBox[{"[", RowBox[{ RowBox[{"1", ";;", "2"}], ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{"\[Phi]0", ",", "\[Theta]0"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]2", ",", "\[Theta]2"}], "}"}], "=", RowBox[{ RowBox[{"FF", "[", RowBox[{"[", RowBox[{ RowBox[{"1", ";;", "2"}], ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{"\[Phi]2", ",", "\[Theta]2"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]\[Phi]0", ",", "\[Pi]\[Theta]0"}], "}"}], "=", RowBox[{ RowBox[{"FF", "[", RowBox[{"[", RowBox[{ RowBox[{"1", ";;", "2"}], ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{"\[Pi]\[Phi]0", ",", "\[Pi]\[Theta]0"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]\[Phi]2", ",", "\[Pi]\[Theta]2"}], "}"}], "=", RowBox[{ RowBox[{"FF", "[", RowBox[{"[", RowBox[{ RowBox[{"1", ";;", "2"}], ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{"\[Pi]\[Phi]2", ",", "\[Pi]\[Theta]2"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"fn", "=", RowBox[{ RowBox[{"FF", "[", RowBox[{"[", "3", "]"}], "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"strain", " ", "measures", " ", "with", " ", "non"}], "-", RowBox[{"symmetric", " ", "\[Epsilon]"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]0"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]0"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]0"}]}]}], ")"}]}], "/", "h\[Gamma]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", " ", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]0"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Theta]0"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]0"}], "/", "h\[Alpha]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w0"}], "/", "h\[Alpha]"}], "+", "\[Pi]\[Theta]0"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w0"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w0"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", "\[Pi]\[Phi]0"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Alpha]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Gamma]\[Gamma]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Gamma]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Gamma]\[Gamma]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", " ", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}], "*", "\[Kappa]\[Alpha]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{ RowBox[{"5", "/", "6"}], " ", "*", "GG", "*", "tt", "*", "\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Gamma]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]"}], "}"}]}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Gamma]"}], "}"}]}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "w0", "]"}], "*", "fn"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wine", "=", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", "w0", "]"}]}], "*", "tt", "*", "\[Rho]\[Rho]", "*", "w2"}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Phi]0", "]"}], "*", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", "\[Rho]\[Rho]", "*", "\[Phi]2"}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Theta]0", "]"}], "*", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", "\[Rho]\[Rho]", "*", "\[Theta]2"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wmap", "=", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "/", "100000"}], "*", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]w0", "-", "w0"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]w0", "-", "w0"}], ")"}]}], ")"}], "*", "tt", "*", RowBox[{"EE", "/", "jac"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI3", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wine", "+", "\[Delta]wmap"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.4426474258030453`*^9, {3.4444401255942*^9, 3.4444401388073997`*^9}, { 3.4444401803034*^9, 3.4444401844062*^9}, 3.4444402418922*^9, { 3.4444402805022*^9, 3.4444403134026003`*^9}, {3.4444403443062*^9, 3.4444404484049997`*^9}, {3.444483267101*^9, 3.444483267335*^9}, { 3.4444833136046*^9, 3.4444835622998*^9}, {3.4444836421094*^9, 3.4444837777981997`*^9}, {3.444483920429*^9, 3.4444839412237997`*^9}, 3.4444842905546*^9, {3.4444843207406*^9, 3.4444844162282*^9}, { 3.4444844465078*^9, 3.4444844624354*^9}, {3.4444845255998*^9, 3.4444845894505997`*^9}, {3.4444846290746*^9, 3.444484933025*^9}, { 3.4444849790917997`*^9, 3.4444851148742*^9}, {3.444534936054*^9, 3.4445349675348*^9}, {3.4445355821731997`*^9, 3.44453585174*^9}, { 3.4445372162198*^9, 3.4445372264378*^9}, 3.444537384731*^9, { 3.4445377585382*^9, 3.4445377605818*^9}, {3.4445379733658*^9, 3.4445379736934*^9}, {3.4445380176762*^9, 3.444538032777*^9}, { 3.4445381079222*^9, 3.4445381581386003`*^9}, {3.4445382726456003`*^9, 3.4445382910067997`*^9}, {3.4445383401312*^9, 3.4445383475880003`*^9}, { 3.444538438458*^9, 3.4445384464608*^9}, {3.4445385680783997`*^9, 3.4445385687648*^9}, {3.4445389411991997`*^9, 3.4445389431024*^9}, { 3.444539746605*^9, 3.4445397807846003`*^9}, {3.4445408839765997`*^9, 3.4445409234133997`*^9}, {3.4445409681698*^9, 3.4445409932702*^9}, { 3.4445415452906*^9, 3.4445415706717997`*^9}, {3.4445416647242002`*^9, 3.4445416909477997`*^9}, {3.4445417660150003`*^9, 3.444541788557*^9}, { 3.4445420906977997`*^9, 3.444542104847*^9}, {3.4445421885878*^9, 3.4445421941414003`*^9}, {3.4445422252166*^9, 3.4445422386014*^9}, { 3.444542280425*^9, 3.4445423014538*^9}, {3.444542455769*^9, 3.4445424578282003`*^9}, {3.4445431739214*^9, 3.444543175809*^9}, { 3.4445647020962*^9, 3.4445648405618*^9}, {3.4445648825414*^9, 3.4445648858486*^9}, {3.4445649382646*^9, 3.4445651882702*^9}, { 3.4446164822206*^9, 3.4446165344494*^9}, {3.4446166121842003`*^9, 3.4446166738822002`*^9}, {3.4446167223046*^9, 3.4446168047974*^9}, { 3.444616843033*^9, 3.444616906447*^9}, {3.4446444694708*^9, 3.4446444700948*^9}, {3.4446477738310003`*^9, 3.4446477939862003`*^9}, { 3.4446478467298*^9, 3.4446478681018*^9}, 3.4446480456142*^9, { 3.4446487557418003`*^9, 3.4446487636198*^9}, 3.4446488179974003`*^9, { 3.4446488971205997`*^9, 3.4446489152478*^9}, {3.4446490003458*^9, 3.4446490008294*^9}, {3.4447042728942003`*^9, 3.4447042751562*^9}, { 3.4447044703278*^9, 3.4447044865362*^9}, 3.4447046475282*^9, 3.4447047993786*^9, {3.444704908329*^9, 3.4447049292642*^9}, { 3.4447049861926003`*^9, 3.4447049877214003`*^9}, {3.4447050279296*^9, 3.4447050419695997`*^9}, {3.4447053486656*^9, 3.4447053739376*^9}, 3.4447054561963997`*^9, 3.44470561612*^9, {3.4472133996876*^9, 3.4472134108571997`*^9}, {3.4472134470179996`*^9, 3.4472134648332*^9}, { 3.4472135032872*^9, 3.4472135245344*^9}, {3.4472136963059998`*^9, 3.4472137794384003`*^9}, {3.4472138235708*^9, 3.4472138388900003`*^9}, { 3.4472139099792*^9, 3.4472141367096*^9}, {3.447214202682*^9, 3.4472142975924*^9}, {3.4472144187732*^9, 3.4472145910284*^9}, { 3.4472146560492*^9, 3.4472147023968*^9}, {3.447214803594*^9, 3.4472148728736*^9}, {3.4472149156956*^9, 3.447214940484*^9}, { 3.447216227284*^9, 3.4472162419948*^9}, {3.4472163068908*^9, 3.4472163720832*^9}, {3.4472164665880003`*^9, 3.447216530392*^9}, { 3.4472166237268*^9, 3.4472167058452*^9}, 3.4472167362808*^9, { 3.4472171394658003`*^9, 3.4472171532874002`*^9}, {3.4472172028993998`*^9, 3.4472172216661997`*^9}, {3.4472172524606*^9, 3.4472172690278*^9}, { 3.4472173209133997`*^9, 3.4472173334245996`*^9}, {3.4472173920846*^9, 3.447217404861*^9}, {3.4472179572548*^9, 3.4472180351456003`*^9}, { 3.4472509764091997`*^9, 3.4472511017396*^9}, {3.4473910422216*^9, 3.4473912901524*^9}, 3.4473918688344*^9, {3.447392021185*^9, 3.4473920346633997`*^9}, {3.4473921383304*^9, 3.4473921479088*^9}, { 3.4473923024112*^9, 3.4473923734379997`*^9}, {3.4473928098168*^9, 3.4473928648691998`*^9}, {3.4473931872432003`*^9, 3.4473932461800003`*^9}, {3.4473933026675997`*^9, 3.4473934579812*^9}, { 3.4473935755271997`*^9, 3.447393742572*^9}, {3.4473939032676*^9, 3.4473939384144*^9}, {3.447395257644*^9, 3.4473953141628*^9}, { 3.4473954231132*^9, 3.4473954756384*^9}, {3.4473955348716*^9, 3.4473955723272*^9}, {3.447395648502*^9, 3.4473957588876*^9}, { 3.4473957903996*^9, 3.4473958488372*^9}, 3.4473962894154*^9, { 3.447396350817*^9, 3.447396352611*^9}, {3.4474625379146*^9, 3.4474625637326*^9}, {3.558360651728078*^9, 3.558360652102478*^9}, { 3.5619791319820857`*^9, 3.561979135788492*^9}, 3.561979369382504*^9, { 3.5619794930439215`*^9, 3.5619795010155354`*^9}, {3.561979569218855*^9, 3.56197960614412*^9}, {3.5619797417551584`*^9, 3.5619797448751636`*^9}, { 3.618719065033702*^9, 3.618719075426296*^9}, {3.6187194011669273`*^9, 3.6187194449454317`*^9}, {3.6187196998040085`*^9, 3.6187197102436056`*^9}, {3.618719902254588*^9, 3.6187199711455283`*^9}, { 3.618722365406472*^9, 3.6187225412555304`*^9}, {3.6187226885009522`*^9, 3.6187227109872384`*^9}, {3.618722756922866*^9, 3.6187231317203026`*^9}, { 3.618723424250035*^9, 3.6187234267291765`*^9}, {3.6187235105259695`*^9, 3.6187236491028957`*^9}, {3.618723691580325*^9, 3.618723745975436*^9}, { 3.618723778837316*^9, 3.6187238310002995`*^9}, {3.6187239055875654`*^9, 3.618723940035536*^9}, {3.6187239782667227`*^9, 3.6187240219352207`*^9}, { 3.618724166762504*^9, 3.618724177411113*^9}, {3.618729321696159*^9, 3.618729328067523*^9}, 3.618729374058154*^9, {3.6187294379838104`*^9, 3.618729708464281*^9}, {3.6187297631904106`*^9, 3.618729773195983*^9}, { 3.618729822648812*^9, 3.6187299321490746`*^9}, {3.618729984399063*^9, 3.61873000654133*^9}, {3.6187300746012225`*^9, 3.6187300860458775`*^9}, { 3.618731390835507*^9, 3.6187315116174154`*^9}, {3.618731747324897*^9, 3.6187318214091344`*^9}, {3.6187318769243097`*^9, 3.618732065297084*^9}, { 3.6187321012351394`*^9, 3.618732157420353*^9}, {3.618732188384124*^9, 3.6187322435542793`*^9}, {3.6187322786112847`*^9, 3.6187325478446836`*^9}, {3.6187325819856367`*^9, 3.6187326817653437`*^9}, {3.618732810863728*^9, 3.61873282594359*^9}, { 3.6187336474335766`*^9, 3.618733754678711*^9}, {3.618733827497876*^9, 3.61873396201257*^9}, {3.6187342020362988`*^9, 3.618734236455267*^9}, 3.618734298201799*^9, {3.618734712498495*^9, 3.618734712716508*^9}, 3.6187347739640107`*^9, {3.618738817361748*^9, 3.6187388333816643`*^9}, { 3.6187391349349127`*^9, 3.6187391457955337`*^9}, {3.618739376900752*^9, 3.618739397023903*^9}, {3.618739528394417*^9, 3.618739534809784*^9}, { 3.618739972366811*^9, 3.61873997340687*^9}, {3.6187400416617737`*^9, 3.618740043022852*^9}, {3.6187400971579485`*^9, 3.618740107902563*^9}, { 3.6187401713671927`*^9, 3.6187401723312483`*^9}, {3.6187402613443394`*^9, 3.618740268819767*^9}, {3.6187403697625403`*^9, 3.6187404057615995`*^9}, { 3.618740488277319*^9, 3.618740516244919*^9}, {3.618740647782442*^9, 3.6187406551668644`*^9}, 3.6187407823021364`*^9, {3.6187418050786357`*^9, 3.618741805749674*^9}, {3.6187418557605343`*^9, 3.6187419895921893`*^9}, { 3.618742022944097*^9, 3.61874204379729*^9}, {3.6187420836395683`*^9, 3.618742103384698*^9}, {3.620462440882641*^9, 3.6204624460519366`*^9}, { 3.6204624990259666`*^9, 3.620462576450395*^9}, {3.620463682857678*^9, 3.620463713336421*^9}, 3.6204637901188126`*^9, {3.620464238835478*^9, 3.62046424411378*^9}, 3.628912429385081*^9, {3.6289135207155013`*^9, 3.6289135210805225`*^9}, 3.6289497746958513`*^9, 3.6289498371774254`*^9, { 3.62894988410911*^9, 3.6289500319795675`*^9}, {3.6289501333883677`*^9, 3.628950183744248*^9}, {3.6289503323017445`*^9, 3.628950390181055*^9}, { 3.6289505050536256`*^9, 3.6289505113579865`*^9}, {3.62895070863527*^9, 3.6289507095043197`*^9}, {3.628951013180689*^9, 3.62895101407374*^9}, { 3.629190743153632*^9, 3.629190816645361*^9}, {3.6291909709608326`*^9, 3.629190981678051*^9}, {3.629191034624544*^9, 3.6291910410049553`*^9}, { 3.6293846391370816`*^9, 3.629384641102685*^9}, {3.6294628543371735`*^9, 3.629462867097191*^9}, {3.629468063172048*^9, 3.6294681151669397`*^9}, { 3.6295205836757097`*^9, 3.6295206295085897`*^9}, {3.6295206788826766`*^9, 3.6295207067911253`*^9}, {3.6295207408927855`*^9, 3.629520753700408*^9}, { 3.629521020590745*^9, 3.6295210354395943`*^9}, {3.6295211107369013`*^9, 3.62952114882508*^9}, {3.6295212327348795`*^9, 3.6295212477237363`*^9}, { 3.6295213424816394`*^9, 3.629521343230441*^9}, {3.6295215363119802`*^9, 3.6295216753550243`*^9}, {3.629521922272258*^9, 3.6295219939855833`*^9}, { 3.6295220298188467`*^9, 3.629522446058778*^9}, {3.629522499348471*^9, 3.629522604352256*^9}, {3.629522755188921*^9, 3.62952288580795*^9}, { 3.629522918084407*^9, 3.6295233421087513`*^9}, {3.6295233808436193`*^9, 3.629523390936837*^9}, {3.629523424274096*^9, 3.6295234533369465`*^9}, { 3.6295235190130625`*^9, 3.629523521680667*^9}, 3.6295235894315863`*^9, { 3.6295237270706277`*^9, 3.629523799454755*^9}, {3.6295238514808464`*^9, 3.629523883460902*^9}, {3.6295239376085978`*^9, 3.6295239442386093`*^9}, { 3.6295241089904985`*^9, 3.629524177537019*^9}, 3.629524211888279*^9, { 3.629524277423994*^9, 3.629524396904604*^9}, {3.6295244794839497`*^9, 3.6295246248450055`*^9}, 3.629524657090262*^9, {3.6295259599109507`*^9, 3.629526013465844*^9}, {3.6295261092188125`*^9, 3.629526201414974*^9}, 3.6295263436092243`*^9, {3.6295263910333076`*^9, 3.629526583303645*^9}, { 3.629526616672104*^9, 3.629526647653758*^9}, {3.629526687558628*^9, 3.629526744888729*^9}, {3.629526804075233*^9, 3.6295268598453307`*^9}, { 3.6295269393898706`*^9, 3.6295269586559043`*^9}, {3.6295271490074387`*^9, 3.6295272149019547`*^9}, {3.6295272553684254`*^9, 3.6295272827620735`*^9}, {3.6295274137087035`*^9, 3.6295274761244135`*^9}, {3.6295275252801*^9, 3.6295279912529182`*^9}, { 3.6295281572216096`*^9, 3.629528160435215*^9}, {3.6295282905550437`*^9, 3.6295284308616905`*^9}, 3.6295285402022824`*^9, {3.629528582088356*^9, 3.629528616798417*^9}, {3.6295287666834803`*^9, 3.6295290316343455`*^9}, { 3.629529086515242*^9, 3.629529118432898*^9}, {3.6295291548121614`*^9, 3.629529292794404*^9}, {3.6295293426208916`*^9, 3.6295293491261034`*^9}, { 3.629529420699029*^9, 3.629529571535694*^9}, {3.6295296539506383`*^9, 3.629529656103442*^9}, {3.6295296894407005`*^9, 3.629529692295506*^9}, { 3.6295297445555973`*^9, 3.629529766426836*^9}, {3.6295298053333044`*^9, 3.6295298209489317`*^9}, {3.6295308380551186`*^9, 3.6295308386635194`*^9}, {3.629532377840223*^9, 3.6295323811630287`*^9}, { 3.629532480020402*^9, 3.629532482454006*^9}, {3.629532520720874*^9, 3.629532564619351*^9}, {3.62953259842461*^9, 3.6295326002654133`*^9}, { 3.6295326327758703`*^9, 3.6295326715107384`*^9}, {3.629532742428463*^9, 3.6295328288058147`*^9}, {3.6295329692184625`*^9, 3.6295330530062094`*^9}, {3.6295331824396367`*^9, 3.629533193562456*^9}, 3.6295350321720915`*^9, 3.629535158485513*^9, {3.629535245471266*^9, 3.6295352687465067`*^9}, {3.62953541293756*^9, 3.629535446384019*^9}, { 3.6295355043381205`*^9, 3.6295355262249594`*^9}, {3.629543790136781*^9, 3.629543791181983*^9}, {3.629543871350524*^9, 3.629544001673153*^9}, { 3.6295446682009234`*^9, 3.629544668466124*^9}, {3.6296010216162376`*^9, 3.6296010236442413`*^9}, {3.629601079336339*^9, 3.6296010902875586`*^9}, 3.6296011425476503`*^9, {3.6296043522397404`*^9, 3.629604399031022*^9}, { 3.629623884428093*^9, 3.629623914723346*^9}, {3.6296239662190366`*^9, 3.6296239738006496`*^9}, {3.6296240514731865`*^9, 3.6296240920176573`*^9}, {3.629624125947717*^9, 3.629624369432945*^9}, { 3.6296256512247963`*^9, 3.6296256817072496`*^9}, {3.6296260472626915`*^9, 3.629626047434292*^9}, {3.629628055568204*^9, 3.629628056098605*^9}, { 3.6296280911206665`*^9, 3.6296281088266973`*^9}, {3.6296281406819534`*^9, 3.629628273032586*^9}, {3.629628378831972*^9, 3.6296283814995766`*^9}, { 3.629628459562114*^9, 3.629628466379326*^9}, {3.629628519419419*^9, 3.6296285390754533`*^9}, {3.629633008133008*^9, 3.629633008835009*^9}, { 3.6296337764967575`*^9, 3.6296338344040594`*^9}, {3.6296342997684765`*^9, 3.629634432150309*^9}, {3.629634494035618*^9, 3.6296345320060844`*^9}, { 3.629634594499794*^9, 3.629634812182576*^9}, {3.6296348599810605`*^9, 3.6296348746918864`*^9}, {3.6296349071867433`*^9, 3.629635023172947*^9}, 3.6296350995818815`*^9, {3.6296363797201295`*^9, 3.6296363868961425`*^9}, { 3.629636462025874*^9, 3.6296364833355117`*^9}, {3.629636555922439*^9, 3.62963656780966*^9}, {3.629636770469616*^9, 3.629636774151222*^9}, { 3.6296369192782774`*^9, 3.6296369318830996`*^9}, {3.629637058539722*^9, 3.6296370719401455`*^9}, {3.629637278172508*^9, 3.629637286814923*^9}, { 3.6296376418091464`*^9, 3.629637662385583*^9}, {3.629637773551378*^9, 3.629637795360216*^9}, {3.6296390041751394`*^9, 3.629639039571602*^9}, 3.6296393829750047`*^9, {3.6296395546065063`*^9, 3.6296395649961243`*^9}, { 3.62964113386068*^9, 3.6296412507048855`*^9}, {3.629641303167777*^9, 3.629641313744596*^9}, {3.6296416285116315`*^9, 3.629641628886032*^9}, { 3.6296416658736973`*^9, 3.6296416815049243`*^9}, 3.6296417376338234`*^9, { 3.6296855551269727`*^9, 3.6296855804270077`*^9}, {3.6297079065796247`*^9, 3.6297079070476255`*^9}, {3.6297080850439377`*^9, 3.629708135728427*^9}, { 3.6297083496516027`*^9, 3.6297084025512953`*^9}, {3.629708781767563*^9, 3.629708790940379*^9}, {3.6297089402482414`*^9, 3.6297089618542795`*^9}, { 3.6297105345398417`*^9, 3.629710538580249*^9}, {3.6297107810514746`*^9, 3.6297107850138817`*^9}, {3.6297109100481014`*^9, 3.629710915710911*^9}, { 3.629711201534613*^9, 3.629711204311418*^9}, {3.629711236307074*^9, 3.6297115007275386`*^9}, {3.6297115377464037`*^9, 3.6297115441112146`*^9}, 3.6297116025645175`*^9, {3.6298716505389357`*^9, 3.629871851841689*^9}, { 3.62987837458679*^9, 3.629878383510006*^9}, {3.6298784402629056`*^9, 3.629878447345318*^9}, {3.6298785221786494`*^9, 3.6298786580236883`*^9}, { 3.629878689613744*^9, 3.629878737147027*^9}, 3.629878783853509*^9, { 3.629878832322794*^9, 3.6298789171723433`*^9}, {3.6298802128122005`*^9, 3.6298802929723125`*^9}, 3.6298813644148126`*^9, {3.629882428887303*^9, 3.629882435887313*^9}, {3.6298986251827383`*^9, 3.6298988530367384`*^9}, { 3.6298989036744275`*^9, 3.6298989486493063`*^9}, {3.629899016868226*^9, 3.6298991622448816`*^9}, {3.6298997154530535`*^9, 3.629899740147897*^9}, { 3.6298998248560457`*^9, 3.629899978048314*^9}, {3.6299000396372223`*^9, 3.6299001557638264`*^9}, {3.6299001966826982`*^9, 3.6299002595352087`*^9}, 3.6299005011236343`*^9, {3.6299005468317146`*^9, 3.629900567642151*^9}, { 3.629900887676713*^9, 3.629900990153293*^9}, {3.6299011689220085`*^9, 3.6299012295125146`*^9}, {3.6299013754039707`*^9, 3.6299014166036434`*^9}, 3.6299014589733176`*^9, {3.6299015096734066`*^9, 3.629901588765546*^9}, { 3.629901662569275*^9, 3.6299016974665365`*^9}, {3.629901952339784*^9, 3.6299019599057975`*^9}, 3.6299020306051216`*^9, {3.6299022330934772`*^9, 3.6299022682559395`*^9}, {3.6299023020455985`*^9, 3.629902332808852*^9}, { 3.6299024532566643`*^9, 3.629902462850681*^9}, {3.629949880225117*^9, 3.6299498807867184`*^9}, {3.6299503101150723`*^9, 3.6299503156998825`*^9}, {3.629950355058751*^9, 3.629950498937804*^9}, { 3.6299555415202007`*^9, 3.6299555507086167`*^9}, {3.6299556061667137`*^9, 3.6299557553497763`*^9}, {3.629955788499834*^9, 3.6299558948608212`*^9}, { 3.629956042764681*^9, 3.629956043809883*^9}, {3.6299560914211664`*^9, 3.6299561017327843`*^9}, 3.629956145849662*^9, {3.6299584813821354`*^9, 3.6299585082765827`*^9}, 3.6299585652946825`*^9, {3.629958616587573*^9, 3.6299586356508064`*^9}, {3.629958715073346*^9, 3.6299588186419287`*^9}, { 3.629958857454797*^9, 3.629958927249319*^9}, {3.629959427994599*^9, 3.629959494669116*^9}, {3.6299595293323765`*^9, 3.6299596037913074`*^9}, { 3.62995966795422*^9, 3.62995967360143*^9}, {3.6299597835972233`*^9, 3.6299597841120243`*^9}, {3.629959826622099*^9, 3.629959862533362*^9}, { 3.6299599051682367`*^9, 3.6299599235918694`*^9}, 3.629959979939168*^9, { 3.6299601345354395`*^9, 3.62996014612626*^9}, 3.6299601769831142`*^9, { 3.629960253142448*^9, 3.629960269538077*^9}, {3.6299603041701374`*^9, 3.6299603078205442`*^9}, {3.6299604300467587`*^9, 3.629960435491168*^9}, { 3.6299605300585346`*^9, 3.6299605636609936`*^9}, {3.6299606195870914`*^9, 3.6299606581971593`*^9}, {3.629960824228251*^9, 3.6299608755367413`*^9}, { 3.629960906658796*^9, 3.6299609978409557`*^9}, {3.6299610312250147`*^9, 3.629961070646284*^9}, {3.629961135698398*^9, 3.6299611643088484`*^9}, { 3.6299720458358483`*^9, 3.6299721791536827`*^9}, {3.6299722439717965`*^9, 3.629972300007095*^9}, {3.6299723670872126`*^9, 3.6299723937008595`*^9}, { 3.629972457801372*^9, 3.6299724710613956`*^9}, {3.629972740193068*^9, 3.6299728251196175`*^9}, {3.6299729203577843`*^9, 3.6299729350218105`*^9}, {3.6299729720874753`*^9, 3.6299730462188053`*^9}, {3.629973116044528*^9, 3.6299731230177402`*^9}, { 3.629973184310248*^9, 3.6299732090830917`*^9}, {3.629973349982539*^9, 3.6299734360166903`*^9}, 3.629973534562063*^9, {3.629973577446539*^9, 3.629973586104554*^9}, {3.6299740374133463`*^9, 3.629974083823428*^9}, { 3.6299742505565205`*^9, 3.629974337089873*^9}, {3.629974382907153*^9, 3.6299744466176653`*^9}, {3.629974589794717*^9, 3.629974590761918*^9}, { 3.629974776215044*^9, 3.6299747850134597`*^9}, {3.6299748226095257`*^9, 3.6299748237483273`*^9}, 3.6299748618435946`*^9, {3.629975198476586*^9, 3.6299752545898843`*^9}, {3.62997531475919*^9, 3.6299753175515947`*^9}, { 3.6299754601982455`*^9, 3.6299754625382495`*^9}, {3.629975592034077*^9, 3.629975592502078*^9}, {3.629983277446268*^9, 3.6299832946842985`*^9}, { 3.62998342081052*^9, 3.6299835439883366`*^9}, {3.629983615514462*^9, 3.629983931009416*^9}, {3.6299919807040443`*^9, 3.6299919808912444`*^9}, { 3.629992028330928*^9, 3.6299920922130404`*^9}, 3.629992198480427*^9, { 3.6299922299300823`*^9, 3.629992250506518*^9}, {3.629992292657792*^9, 3.6299923603151107`*^9}, {3.6299924387676487`*^9, 3.6299924398440504`*^9}, {3.6299925764846907`*^9, 3.6299926096347485`*^9}, {3.6299928122323046`*^9, 3.629992818768716*^9}, { 3.6299929049120674`*^9, 3.629992905411268*^9}, {3.6299929850338078`*^9, 3.6299929866250105`*^9}, {3.6299931061992207`*^9, 3.62999312270405*^9}, { 3.629993172312137*^9, 3.6299932618718944`*^9}, {3.6299933276572104`*^9, 3.6299933842073092`*^9}, {3.630287775665962*^9, 3.630287795852398*^9}, { 3.6303896387100534`*^9, 3.630389666774503*^9}, {3.6303896967889557`*^9, 3.6303897095341783`*^9}, {3.6303897587054644`*^9, 3.630389880448078*^9}, { 3.6303899127557354`*^9, 3.630390009444705*^9}, 3.630390057321189*^9, 3.630390443484267*^9, {3.63039095720877*^9, 3.6303909789240074`*^9}, { 3.6303910572205453`*^9, 3.6303911291054716`*^9}, {3.630391163035531*^9, 3.6303911740803504`*^9}, {3.630391240224467*^9, 3.6303912875081496`*^9}, { 3.6303913396902413`*^9, 3.630391404570755*^9}, {3.630391479513287*^9, 3.6303917572873745`*^9}, {3.630391868905571*^9, 3.6303920027226057`*^9}, { 3.630392064327114*^9, 3.630392219843787*^9}, {3.63039226121506*^9, 3.63039232943398*^9}, {3.6303924315985594`*^9, 3.6303924441097813`*^9}, { 3.6303926866122074`*^9, 3.6303927118530517`*^9}, {3.630392795671999*^9, 3.6303928006172075`*^9}, {3.6303986032190485`*^9, 3.6303986046230516`*^9}, {3.6303986654631586`*^9, 3.6303987936485834`*^9}, {3.63039889979117*^9, 3.6303989091199865`*^9}, { 3.630399006323757*^9, 3.630399007259759*^9}, {3.630399117224352*^9, 3.630399214771323*^9}, {3.6303992555185947`*^9, 3.6303993036758795`*^9}, { 3.630399467725767*^9, 3.630399502731636*^9}, {3.6303995748037624`*^9, 3.630399595614199*^9}, {3.6303996329294643`*^9, 3.630399658076709*^9}, { 3.630399711335202*^9, 3.6303997453120623`*^9}, {3.6303998546994543`*^9, 3.6303999880484886`*^9}, {3.6304000742074394`*^9, 3.630400123441126*^9}, { 3.6304001724564123`*^9, 3.630400251595351*^9}, {3.630400324166679*^9, 3.630400327052684*^9}, {3.630400358190338*^9, 3.6304003597503414`*^9}, { 3.6304004587481155`*^9, 3.6304004640521245`*^9}, {3.630400521975026*^9, 3.630400526124634*^9}, {3.630400567199506*^9, 3.630400593516752*^9}, { 3.6304012340070767`*^9, 3.6304013035207987`*^9}, {3.6304013614749007`*^9, 3.630401367933312*^9}, {3.630401686939398*^9, 3.6304017294598303`*^9}, { 3.630401794020523*^9, 3.6304018922061386`*^9}, {3.6304019687775183`*^9, 3.630401987153569*^9}, {3.630402072749465*^9, 3.63040208297405*^9}, { 3.6304022247881613`*^9, 3.630402255931943*^9}, 3.630402329306139*^9, { 3.6304023806970787`*^9, 3.6304024212403975`*^9}, {3.6304025002259154`*^9, 3.630402528595538*^9}, {3.6304025620694523`*^9, 3.630402575015193*^9}, { 3.6304026411829777`*^9, 3.630402649073429*^9}, {3.630402695548087*^9, 3.6304027128260756`*^9}, {3.630402783923142*^9, 3.6304027982389607`*^9}, { 3.6304028797236214`*^9, 3.6304030111811404`*^9}, {3.6304030562107162`*^9, 3.6304031598846455`*^9}, {3.630403236330018*^9, 3.6304032404072514`*^9}, { 3.630403373001835*^9, 3.6304033888147397`*^9}, {3.6304039420953856`*^9, 3.6304039512829113`*^9}, 3.6304039831437335`*^9, {3.630404015975611*^9, 3.6304040663624935`*^9}, {3.630404173614628*^9, 3.630404246945822*^9}, { 3.6304042891772375`*^9, 3.630404299595834*^9}, {3.630404391083066*^9, 3.630404392406142*^9}, {3.6304045301800222`*^9, 3.6304045579486103`*^9}, { 3.630404640215316*^9, 3.630404762796327*^9}, {3.630404877629895*^9, 3.630404883104208*^9}, {3.6304050364729805`*^9, 3.630405098270515*^9}, { 3.6304051736118245`*^9, 3.6304051965901384`*^9}, {3.6304053802536435`*^9, 3.63040539242334*^9}, {3.630406035965148*^9, 3.630406041998493*^9}, { 3.630406072049212*^9, 3.6304060962065935`*^9}, {3.630406264081196*^9, 3.6304062707025747`*^9}, {3.63040632219952*^9, 3.630406385461138*^9}, { 3.630406477200385*^9, 3.630406482095665*^9}, {3.6304066170883865`*^9, 3.6304066222256804`*^9}, {3.630406957868878*^9, 3.630406973411767*^9}, { 3.6304070081447535`*^9, 3.630407018199329*^9}, {3.630407411376817*^9, 3.630407412542884*^9}, {3.6304080609339695`*^9, 3.630408121202417*^9}, { 3.6304081585485525`*^9, 3.6304081832129636`*^9}, {3.63040821409673*^9, 3.630408421131572*^9}, 3.6304934333363276`*^9, {3.63049350751357*^9, 3.630493677593298*^9}, {3.630493716898546*^9, 3.6304937846684227`*^9}, 3.630493922944331*^9, {3.6304939556752033`*^9, 3.630494117430455*^9}, { 3.6304941486092386`*^9, 3.6304941767788496`*^9}, {3.6304942118648567`*^9, 3.6304942530272107`*^9}, {3.6304942838399734`*^9, 3.6304942845820155`*^9}, {3.6304943454054947`*^9, 3.6304944442451477`*^9}, {3.63080749995092*^9, 3.6308075480801234`*^9}, { 3.630807586536323*^9, 3.630807621440319*^9}, {3.630807680459695*^9, 3.630807682914836*^9}, {3.630807736889923*^9, 3.6308077644745007`*^9}, { 3.6308078081089964`*^9, 3.6308078670123653`*^9}, {3.630807991648494*^9, 3.630807997541831*^9}, {3.6308081080891542`*^9, 3.6308081919599514`*^9}, { 3.630808306368495*^9, 3.630808345060708*^9}, {3.6308087281906223`*^9, 3.6308087555171847`*^9}, {3.630809110815507*^9, 3.630809169033837*^9}, { 3.6308091998195972`*^9, 3.630809448512822*^9}, {3.6308095328996487`*^9, 3.6308095448223305`*^9}, {3.630809582269472*^9, 3.6308095873607635`*^9}, { 3.630809665529235*^9, 3.630809684808337*^9}, {3.6308316258485594`*^9, 3.6308318380886984`*^9}, {3.63083188164919*^9, 3.630831966930068*^9}, 3.6320400558356075`*^9, {3.6354749882908883`*^9, 3.635474989418953*^9}, { 3.635475084557395*^9, 3.6354750875145636`*^9}, {3.6354751334091887`*^9, 3.635475162315842*^9}, {3.6354754001974483`*^9, 3.6354754820331287`*^9}, 3.635475512931896*^9, {3.6354756222781506`*^9, 3.635475622861184*^9}, { 3.635475691642118*^9, 3.6354757057969275`*^9}, {3.6354757798291616`*^9, 3.635475797395167*^9}, {3.635475884848169*^9, 3.6354758981309285`*^9}, { 3.635475961488552*^9, 3.6354759738382587`*^9}, {3.6354760213729773`*^9, 3.6354760572050266`*^9}, {3.6354761282470903`*^9, 3.635476136040536*^9}, { 3.6354761719365892`*^9, 3.635476212217893*^9}, {3.6593346599546614`*^9, 3.659334660890663*^9}, {3.6593347077219453`*^9, 3.659334720701168*^9}, { 3.6593348752974396`*^9, 3.6593348758122406`*^9}, {3.6593349140947075`*^9, 3.6593350070240707`*^9}, {3.6593350466949406`*^9, 3.6593350543701544`*^9}, {3.659335103791041*^9, 3.6593351614487424`*^9}, 3.659335217686841*^9, {3.659335262084519*^9, 3.6593352995869846`*^9}, { 3.6593356899482727`*^9, 3.659335701819893*^9}, {3.659335964227954*^9, 3.659335964602355*^9}, {3.65933603594128*^9, 3.6593360629605274`*^9}, { 3.6593361352354546`*^9, 3.6593361504454813`*^9}, {3.6593363929479074`*^9, 3.6593364061611304`*^9}, 3.6593368946915884`*^9, {3.6884748265656157`*^9, 3.6884748268716326`*^9}, {3.6884748600075283`*^9, 3.688474861420609*^9}, { 3.6885242858240776`*^9, 3.6885243001140976`*^9}, {3.6888842911675606`*^9, 3.6888843311676164`*^9}, {3.688966242423658*^9, 3.688966263933688*^9}, { 3.6897393587897596`*^9, 3.6897393649897685`*^9}, 3.689739477049925*^9, { 3.6898595970621734`*^9, 3.689859597272174*^9}, {3.6898596707522764`*^9, 3.6898597190523443`*^9}, {3.689859768552414*^9, 3.6898597721424184`*^9}, { 3.689859855272535*^9, 3.689859859882541*^9}, {3.6898605078334484`*^9, 3.6898607266237545`*^9}, 3.6898608811139708`*^9, {3.6898609634740863`*^9, 3.689860974304102*^9}, 3.6898610140141573`*^9, {3.6898611496043468`*^9, 3.6898611683243732`*^9}, {3.689861462024784*^9, 3.6898615624849253`*^9}, { 3.6898616142149973`*^9, 3.6898616164350004`*^9}, 3.6898616657950697`*^9, { 3.689861716805141*^9, 3.689861749905187*^9}, {3.732677920575506*^9, 3.7326779208190203`*^9}, {3.7519672427004185`*^9, 3.7519672444968877`*^9}, {3.7519674022097683`*^9, 3.75196742976579*^9}, { 3.751967484127989*^9, 3.751967510853814*^9}, {3.7519675409404893`*^9, 3.751967541549782*^9}, {3.7519675797751045`*^9, 3.751967592209671*^9}, { 3.7519676829383273`*^9, 3.7519676841255474`*^9}, {3.7519677154775553`*^9, 3.7519677953499403`*^9}, 3.751967827811061*^9, {3.7519679545625095`*^9, 3.751967957999185*^9}, {3.751968003754015*^9, 3.7519681477513895`*^9}, { 3.751968264817631*^9, 3.751968270722477*^9}, {3.7519689618119907`*^9, 3.751968969888235*^9}, {3.7519691168917775`*^9, 3.7519691395895615`*^9}, { 3.751969242782174*^9, 3.7519692581691785`*^9}, {3.7519693625211954`*^9, 3.751969378579924*^9}, {3.751969409572627*^9, 3.751969438643936*^9}, { 3.7519695894526725`*^9, 3.751969614306203*^9}, {3.7523200108586655`*^9, 3.752320012354121*^9}, {3.7553831315619707`*^9, 3.755383134119626*^9}, { 3.7553831893197794`*^9, 3.755383241814331*^9}, {3.7553832736267967`*^9, 3.7553832810757113`*^9}, {3.7554336536222963`*^9, 3.755433684797229*^9}, { 3.7554337764737434`*^9, 3.7554338315300155`*^9}, {3.755433998047738*^9, 3.7554340265485487`*^9}, {3.755446573138784*^9, 3.755446636911299*^9}, { 3.75544667493072*^9, 3.755446753435521*^9}, {3.755446891541581*^9, 3.7554468921547422`*^9}, {3.7554469323588533`*^9, 3.755446936867403*^9}, { 3.7554470190332975`*^9, 3.7554472776872244`*^9}, {3.7555217323692026`*^9, 3.755521732847602*^9}, {3.755521767127169*^9, 3.7555217972041793`*^9}, { 3.755522561453134*^9, 3.755522564231819*^9}, {3.755522601885935*^9, 3.7555226037287407`*^9}, {3.7555226758687305`*^9, 3.755522678585092*^9}, { 3.7555234832604623`*^9, 3.7555235920444417`*^9}, {3.7555239506007543`*^9, 3.755524013893358*^9}, {3.755524076791689*^9, 3.7555240812793446`*^9}, { 3.7555241238138275`*^9, 3.7555241268985643`*^9}, {3.7555242930449886`*^9, 3.7555243378577013`*^9}, {3.7555256673767824`*^9, 3.7555256808205338`*^9}, {3.7555258588384123`*^9, 3.755525900317296*^9}, { 3.755525930708299*^9, 3.7555260436531134`*^9}, {3.755607147401991*^9, 3.7556071504143705`*^9}, {3.755607992884314*^9, 3.7556080025382996`*^9}, { 3.7556094344057455`*^9, 3.7556094348690443`*^9}, {3.7559613653116636`*^9, 3.755961445097105*^9}, 3.755961484246889*^9, {3.7559618979231987`*^9, 3.755961939470047*^9}, {3.7559620323724904`*^9, 3.7559620330864005`*^9}, { 3.755962155557907*^9, 3.7559621601593847`*^9}, {3.755962303755834*^9, 3.755962343830135*^9}, {3.7559624058018165`*^9, 3.7559624450501757`*^9}, 3.756002186674869*^9, 3.7560029626855392`*^9, {3.756003222110388*^9, 3.756003295034633*^9}, {3.7560056331492863`*^9, 3.7560056663855457`*^9}, { 3.7560057813555765`*^9, 3.7560057863836613`*^9}, {3.7560058917172394`*^9, 3.756005927847292*^9}, 3.756006092376186*^9, 3.756009112317705*^9, { 3.756091886039587*^9, 3.756091887764086*^9}, {3.756092005435152*^9, 3.7560920727337685`*^9}, {3.75609212911592*^9, 3.7560921293252516`*^9}, { 3.756092262958163*^9, 3.756092263157668*^9}, {3.756092342487877*^9, 3.756092347894502*^9}, {3.7560929036769304`*^9, 3.7560929278911004`*^9}, { 3.7560930741522417`*^9, 3.756093083420331*^9}, {3.7560932986236534`*^9, 3.7560933139459305`*^9}, {3.756093449985523*^9, 3.7560934874491863`*^9}, { 3.756093592694581*^9, 3.7560936019456573`*^9}, {3.756093634438078*^9, 3.756093673866626*^9}, {3.756093873069885*^9, 3.756093897964734*^9}, { 3.7560940650109406`*^9, 3.756094078056768*^9}, {3.756442536546026*^9, 3.756442607904289*^9}, {3.7564436397451363`*^9, 3.7564436403231254`*^9}, { 3.7636034984570236`*^9, 3.7636034989933815`*^9}, {3.763603551051456*^9, 3.7636035527617817`*^9}, {3.7636036049384193`*^9, 3.7636036392233057`*^9}, {3.7636036850937223`*^9, 3.763603692587598*^9}, { 3.7636037258272257`*^9, 3.7636037459031096`*^9}, {3.7636037792254367`*^9, 3.76360387572289*^9}, {3.763603971837229*^9, 3.7636040341423655`*^9}, { 3.763604066526084*^9, 3.7636040756798687`*^9}, {3.7636041452118535`*^9, 3.763604278007333*^9}, {3.763604317710966*^9, 3.7636043271387568`*^9}, { 3.7636043584877644`*^9, 3.763604415561053*^9}, {3.763604445680462*^9, 3.7636044504114943`*^9}, {3.763604615444647*^9, 3.7636048082554193`*^9}, 3.763604854904996*^9, {3.7636133594095488`*^9, 3.7636133618464766`*^9}, { 3.7636136063756704`*^9, 3.7636136315671196`*^9}, {3.7636990373827705`*^9, 3.7636990431157646`*^9}, {3.763699090332087*^9, 3.763699110952259*^9}, { 3.763699227420497*^9, 3.7636993642943506`*^9}, {3.763700085627533*^9, 3.763700088329999*^9}, {3.7637001721125274`*^9, 3.763700181422837*^9}, { 3.763700248063385*^9, 3.7637003918630466`*^9}, {3.763700591783223*^9, 3.7637006017496295`*^9}, {3.7637007583576717`*^9, 3.7637007603074865`*^9}, {3.7637137795793185`*^9, 3.7637137822587233`*^9}, {3.7637148704355187`*^9, 3.763714870624051*^9}, { 3.763727592158518*^9, 3.7637275933445053`*^9}, {3.7637276688363667`*^9, 3.7637276694756594`*^9}, 3.763803448896332*^9, {3.76380349501632*^9, 3.7638036835067654`*^9}, {3.763804829093463*^9, 3.7638048385675254`*^9}, 3.7638051033646154`*^9, 3.7638053924528885`*^9, {3.763805557684454*^9, 3.763805634255308*^9}, {3.763806843847647*^9, 3.763806847966059*^9}, { 3.763806942652097*^9, 3.7638071770752254`*^9}, {3.7638141184594107`*^9, 3.763814134133461*^9}, {3.7638146808628216`*^9, 3.7638146925645113`*^9}, { 3.7638147709278784`*^9, 3.7638147811883087`*^9}, {3.7638148155281043`*^9, 3.763814819843194*^9}, {3.7638150259647446`*^9, 3.763815028601293*^9}, { 3.7638151529595194`*^9, 3.763815155849978*^9}, {3.7638163770262136`*^9, 3.763816380851597*^9}, {3.7638164181856327`*^9, 3.7638164950537987`*^9}, 3.763816568304102*^9, {3.7638166173645625`*^9, 3.763816618808757*^9}, { 3.7638167204462805`*^9, 3.763816721012859*^9}, {3.763857602253485*^9, 3.7638579604183645`*^9}, {3.7638580038507566`*^9, 3.7638580060526443`*^9}, {3.763858082269992*^9, 3.7638581746835337`*^9}, { 3.7638582163351564`*^9, 3.7638582415275116`*^9}, {3.7638582983238*^9, 3.763858907503306*^9}, {3.763858941318697*^9, 3.763858956626134*^9}, { 3.7638602435602536`*^9, 3.763860245408451*^9}, {3.7638694636456347`*^9, 3.7638694647177277`*^9}, {3.7638708199536576`*^9, 3.763870829436488*^9}, { 3.763871287170555*^9, 3.7638712876184006`*^9}, {3.763943214376035*^9, 3.7639432984591475`*^9}, {3.763943418832348*^9, 3.7639434335508127`*^9}, { 3.76394347113767*^9, 3.7639435187320576`*^9}, {3.763943585908682*^9, 3.7639436125255404`*^9}, {3.763951722152746*^9, 3.76395172989299*^9}, { 3.7639517863423367`*^9, 3.7639519945900664`*^9}, {3.763952081515512*^9, 3.7639521530710773`*^9}, {3.763952353248129*^9, 3.763952357026309*^9}, { 3.7639524211903834`*^9, 3.7639524243979177`*^9}, {3.7639527174925117`*^9, 3.7639527180252266`*^9}, {3.7641265625745993`*^9, 3.7641265632314167`*^9}, {3.764126605555829*^9, 3.7641266075095396`*^9}, { 3.7641268313964133`*^9, 3.7641268543573804`*^9}, {3.764127044657903*^9, 3.7641270479422092`*^9}, {3.7641271442332697`*^9, 3.7641271469362774`*^9}, {3.764127227626192*^9, 3.7641272592640233`*^9}, { 3.764127335707515*^9, 3.7641273386484756`*^9}, {3.764127429843852*^9, 3.7641274364304185`*^9}, {3.7641275071859307`*^9, 3.764127516803895*^9}, 3.7641276043548007`*^9, {3.7641276925365753`*^9, 3.764127697080591*^9}, 3.764127798472331*^9, 3.764127853631323*^9, 3.764127908496078*^9, { 3.7641280050343323`*^9, 3.764128022046494*^9}, {3.764128128597419*^9, 3.764128154116727*^9}, {3.7641286864636617`*^9, 3.764128701643106*^9}, { 3.7641289910924444`*^9, 3.7641290126680794`*^9}, {3.7641290672285347`*^9, 3.7641290737798567`*^9}, {3.7641325425120363`*^9, 3.764132565390477*^9}, { 3.7641327425004654`*^9, 3.764132750040793*^9}, 3.7641327968340364`*^9, { 3.764133146776842*^9, 3.764133204874522*^9}, {3.7641333488187037`*^9, 3.7641333525577593`*^9}, {3.764413145593136*^9, 3.7644131471236105`*^9}, { 3.764413201645049*^9, 3.7644132349609704`*^9}, {3.764413325008136*^9, 3.7644133748980193`*^9}, {3.7644134113425665`*^9, 3.7644135151187*^9}, { 3.764413554409053*^9, 3.7644136160674934`*^9}, {3.76441371984758*^9, 3.764413730103909*^9}, 3.764419641962368*^9, {3.7644198522879405`*^9, 3.764419879249356*^9}, 3.764419909536559*^9, {3.764419991012162*^9, 3.764420000171088*^9}, {3.7644200798862047`*^9, 3.7644200950961914`*^9}, { 3.7644201529471693`*^9, 3.764420153715966*^9}, {3.764420210346301*^9, 3.764420255343707*^9}, {3.764420296178318*^9, 3.7644203000939393`*^9}, { 3.7644203803359275`*^9, 3.7644203931390867`*^9}, 3.7644204418727274`*^9, { 3.7647259720700207`*^9, 3.7647261047260523`*^9}, {3.7647263483375626`*^9, 3.76472635879602*^9}, 3.764726656736601*^9, {3.764727009127914*^9, 3.764727020100875*^9}, {3.7647270591828785`*^9, 3.7647270819631023`*^9}, { 3.7647272109090505`*^9, 3.764727227846332*^9}, {3.76473247809907*^9, 3.7647324813925114`*^9}, {3.7647349484962797`*^9, 3.7647349979358416`*^9}, {3.7647351097258167`*^9, 3.764735124772463*^9}, { 3.7647352810674453`*^9, 3.7647352901139917`*^9}, {3.7647353746429515`*^9, 3.764735379550926*^9}, {3.7647354596539807`*^9, 3.764735507677454*^9}, { 3.7647355546341*^9, 3.764735728811817*^9}, {3.764735837449795*^9, 3.76473584132898*^9}, {3.76473603649269*^9, 3.7647360592982664`*^9}, { 3.7647360998228803`*^9, 3.76473621551197*^9}, {3.7647362545599003`*^9, 3.764736286430997*^9}, {3.7647364592833533`*^9, 3.764736464019006*^9}, { 3.764736566167658*^9, 3.7647365918958225`*^9}, {3.764764761680134*^9, 3.7647648482473745`*^9}, 3.764764917763693*^9, {3.764764964821686*^9, 3.764765090741813*^9}, {3.7647651742140284`*^9, 3.7647652517335076`*^9}, { 3.764765341266399*^9, 3.7647653614173465`*^9}, 3.764765400284145*^9, { 3.764765691384389*^9, 3.764765708710143*^9}, 3.7647657454275875`*^9, { 3.76476578351686*^9, 3.764765871262255*^9}, {3.7647661045180917`*^9, 3.76476612822571*^9}, {3.7647661964223824`*^9, 3.764766239375331*^9}, { 3.764766330361228*^9, 3.764766338297905*^9}, {3.764767015060799*^9, 3.7647670193029037`*^9}, {3.764767076590926*^9, 3.7647671160277977`*^9}, { 3.7647671493139205`*^9, 3.7647672079236426`*^9}, {3.764767458938404*^9, 3.7647674608323865`*^9}, {3.764810938444873*^9, 3.7648109399353456`*^9}, { 3.7648118616019874`*^9, 3.7648118695079126`*^9}, {3.7648120589477816`*^9, 3.7648124600413237`*^9}, {3.76481250476682*^9, 3.7648125259602103`*^9}, { 3.764812601341893*^9, 3.7648126577763243`*^9}, {3.7648126944039307`*^9, 3.7648128855627623`*^9}, {3.764812924923909*^9, 3.764812926481821*^9}, { 3.764813041485982*^9, 3.764813131254232*^9}, {3.7648134679328885`*^9, 3.7648136479313235`*^9}, {3.7648136917777314`*^9, 3.764813697753367*^9}, { 3.7648137297570653`*^9, 3.764813747862262*^9}, 3.764813784221693*^9, { 3.7648138370678406`*^9, 3.7648141387969923`*^9}, {3.764814321050164*^9, 3.764814422489184*^9}, {3.764814461366684*^9, 3.7648145835728483`*^9}, { 3.764814614769511*^9, 3.7648147525825167`*^9}, {3.764815363375289*^9, 3.7648153644907384`*^9}, {3.764815451671169*^9, 3.7648154601533747`*^9}, { 3.7648175917802963`*^9, 3.7648176401910563`*^9}, {3.765885491237231*^9, 3.765885501131465*^9}, {3.766572999289345*^9, 3.7665729996020145`*^9}, { 3.7665730613126965`*^9, 3.7665730616706066`*^9}, {3.7840103262125545`*^9, 3.7840103546413517`*^9}, {3.784011309725755*^9, 3.7840113197719574`*^9}, { 3.784013374800973*^9, 3.7840133842981763`*^9}, {3.7840238533665447`*^9, 3.78402395932942*^9}, {3.784024091276659*^9, 3.784024112209529*^9}, { 3.7840242793219643`*^9, 3.784024296655184*^9}, {3.7840290670892677`*^9, 3.7840291348388853`*^9}, {3.784029222997594*^9, 3.784029542926179*^9}, { 3.784375172285057*^9, 3.784375319701829*^9}, {3.7843753678421807`*^9, 3.7843753788103914`*^9}, {3.7843754844339557`*^9, 3.784375827494117*^9}, { 3.784375862317687*^9, 3.7843759567563844`*^9}, {3.784376004941759*^9, 3.7843760080157185`*^9}, {3.784376101918992*^9, 3.7843761244332943`*^9}, { 3.784376181191763*^9, 3.7843762145091863`*^9}, {3.7843792489960337`*^9, 3.78437926273014*^9}, {3.7843793293934345`*^9, 3.784379368676588*^9}, { 3.7843796529835215`*^9, 3.7843796858862267`*^9}, {3.784450863324359*^9, 3.7844508986076546`*^9}, {3.7844510208392324`*^9, 3.784451027915551*^9}, { 3.7844511176315613`*^9, 3.7844511673791957`*^9}, {3.784451235055628*^9, 3.78445132575735*^9}, {3.784451995615477*^9, 3.7844520110330954`*^9}, { 3.7844522907551537`*^9, 3.7844523421551*^9}, {3.784700119490345*^9, 3.7847001627913013`*^9}, {3.7847004221290607`*^9, 3.7847004380767317`*^9}, 3.7847007913506136`*^9, {3.784781955129138*^9, 3.784781977787957*^9}, { 3.78488170216677*^9, 3.784881704210422*^9}, 3.784882130557441*^9, { 3.78488220347418*^9, 3.7848822064697027`*^9}, {3.784883393455822*^9, 3.784883458551924*^9}, 3.7848835306495824`*^9, {3.7848836822092113`*^9, 3.7848837303696923`*^9}, 3.7848838199009576`*^9, {3.7848842507527857`*^9, 3.7848842836585226`*^9}, 3.7848843847882996`*^9, {3.784884461405264*^9, 3.7848844645041113`*^9}, {3.784884559404122*^9, 3.7848845656634912`*^9}, { 3.7848852409944844`*^9, 3.7848852740337477`*^9}, {3.7848854548929386`*^9, 3.7848854893046365`*^9}, {3.7848856741783943`*^9, 3.784885691704702*^9}, { 3.784885809660874*^9, 3.784885811424426*^9}, {3.7848860031948376`*^9, 3.784886020570098*^9}, 3.7848861057105627`*^9, {3.7848861627726107`*^9, 3.7848862212876124`*^9}, {3.784886306497995*^9, 3.7848863509322224`*^9}, 3.784886472690192*^9, {3.7848866596243*^9, 3.784886664116289*^9}, { 3.7848866987282944`*^9, 3.7848867077911897`*^9}, {3.78488676128524*^9, 3.7848868667029366`*^9}, {3.7848869381224003`*^9, 3.7848869414281464`*^9}, {3.7848870104508753`*^9, 3.784887039889447*^9}, { 3.7848871795058794`*^9, 3.7848871976746817`*^9}, {3.7848872311446314`*^9, 3.78488724075662*^9}, 3.784887405188785*^9, {3.784887591926689*^9, 3.7848876119305134`*^9}, {3.784887676620901*^9, 3.7848876786672792`*^9}, { 3.78488771054331*^9, 3.784887714354906*^9}, {3.7848877625809546`*^9, 3.7848878103041153`*^9}, 3.7848878862881575`*^9, {3.787717235155089*^9, 3.787717269464238*^9}, {3.7877174592607603`*^9, 3.7877174674038067`*^9}, { 3.7877271032841845`*^9, 3.787727136247201*^9}, 3.787727355369296*^9, 3.7877274973278403`*^9, {3.787727855959008*^9, 3.78772792141208*^9}, 3.787728113487193*^9, {3.7877281704571557`*^9, 3.7877281735077004`*^9}, 3.7877282789827795`*^9, {3.7877286510229864`*^9, 3.787728665729192*^9}, { 3.7877287942225084`*^9, 3.787728807671986*^9}, {3.787729044867985*^9, 3.787729045536916*^9}, {3.787729589732438*^9, 3.7877296062090626`*^9}, { 3.787729794037467*^9, 3.7877297950347877`*^9}, {3.787729855548402*^9, 3.7877299039179935`*^9}, {3.7877300373241186`*^9, 3.787730068136018*^9}, { 3.7877301999859333`*^9, 3.7877302014150777`*^9}, {3.787732033225385*^9, 3.7877320471634016`*^9}, {3.787732077195259*^9, 3.7877320780358667`*^9}, 3.787732189759206*^9, {3.78773231889835*^9, 3.787732327710633*^9}, { 3.7877324857166643`*^9, 3.787732496655479*^9}, {3.7877325848303585`*^9, 3.78773258503596*^9}, {3.7877328504631166`*^9, 3.7877328625892415`*^9}, { 3.7877330254884944`*^9, 3.7877330271019044`*^9}, {3.787733136128061*^9, 3.7877331422258835`*^9}, {3.787733243513567*^9, 3.78773324558677*^9}, 3.787733310555999*^9, 3.7877334085329347`*^9, {3.7877337955932293`*^9, 3.7877337970498257`*^9}, {3.787733867727028*^9, 3.7877338687324905`*^9}, { 3.7877352224369583`*^9, 3.787735224161746*^9}, {3.787735343322833*^9, 3.787735348772827*^9}, {3.787735422704711*^9, 3.7877354268945775`*^9}, { 3.7877355100355635`*^9, 3.787735514671461*^9}, {3.7877356541994534`*^9, 3.7877356632141013`*^9}, 3.7877357913476543`*^9, 3.787736261837074*^9, { 3.7882542159043374`*^9, 3.7882542747998285`*^9}, {3.788254310967661*^9, 3.788254318430212*^9}, {3.788254585790197*^9, 3.7882545888318524`*^9}, { 3.7882547349987383`*^9, 3.788254735940298*^9}, 3.788254830063775*^9, 3.7882549155286837`*^9, {3.7882550121437798`*^9, 3.788255037735396*^9}, { 3.7882551764404287`*^9, 3.78825518352113*^9}, {3.7882552540030313`*^9, 3.788255290224329*^9}, {3.7882553843544893`*^9, 3.788255423248046*^9}, { 3.78825567982127*^9, 3.7882556852479534`*^9}, {3.7882557908576803`*^9, 3.7882558029800806`*^9}, {3.7882560240494256`*^9, 3.7882560388846164`*^9}, 3.788256102343512*^9, {3.788256161397396*^9, 3.7882561626372194`*^9}, { 3.7882562304311895`*^9, 3.78825629590362*^9}, {3.7882563614677362`*^9, 3.7882563620189795`*^9}, {3.7882564138122153`*^9, 3.7882564294158382`*^9}, {3.788256467457189*^9, 3.7882564889521217`*^9}, { 3.7882565883311844`*^9, 3.788256591497148*^9}, {3.7882568409513097`*^9, 3.7882568724526567`*^9}, {3.788256965258837*^9, 3.788256966444976*^9}, { 3.7882570073831463`*^9, 3.7882570497349973`*^9}, {3.7882570992487097`*^9, 3.788257144206352*^9}, {3.78825721252205*^9, 3.788257307277931*^9}, { 3.788257350410209*^9, 3.7882573617262745`*^9}, {3.788257424936472*^9, 3.788257434118204*^9}, {3.788276311330668*^9, 3.788276311647092*^9}, { 3.7882765465512347`*^9, 3.788276608568333*^9}, {3.7882767715851693`*^9, 3.7882768045752783`*^9}, {3.7882769342607436`*^9, 3.7882769409894867`*^9}, {3.7882770202208567`*^9, 3.7882770424485188`*^9}, {3.7882770760040703`*^9, 3.788277077341468*^9}, { 3.788277147336176*^9, 3.788277150397852*^9}, {3.7882772069909*^9, 3.7882772101572385`*^9}, {3.7882772503366175`*^9, 3.7882772773759403`*^9}, {3.7882773922958755`*^9, 3.7882773927832017`*^9}, {3.788277450684473*^9, 3.788277482126852*^9}, { 3.78827754293396*^9, 3.788277545027956*^9}, {3.7883214550230436`*^9, 3.7883214742097826`*^9}, {3.788321520104019*^9, 3.788321685390153*^9}, { 3.788321717307153*^9, 3.788321801831746*^9}, {3.788321836768508*^9, 3.788322037754008*^9}, {3.7883220686363816`*^9, 3.788322220085001*^9}, { 3.7883255906192427`*^9, 3.788325646609389*^9}, {3.7883257976991563`*^9, 3.788325804097658*^9}, {3.788325969279187*^9, 3.7883259830028267`*^9}, { 3.788326975877249*^9, 3.788326979070017*^9}, {3.788328539286415*^9, 3.788328618410488*^9}, {3.788328648595448*^9, 3.788328762662589*^9}, { 3.7883288060890923`*^9, 3.7883288805716724`*^9}, {3.7883319188300047`*^9, 3.78833193230753*^9}, {3.7883321144947567`*^9, 3.788332115050151*^9}, { 3.7883333680456443`*^9, 3.7883333686272163`*^9}, 3.7883336421611414`*^9, { 3.788333691323177*^9, 3.7883336916362*^9}, {3.788333797629262*^9, 3.7883338348662343`*^9}, {3.7883339555470386`*^9, 3.7883339660305166`*^9}, {3.7883340291758356`*^9, 3.788334031484354*^9}, { 3.788334368484807*^9, 3.7883343918754945`*^9}, {3.7883345963739557`*^9, 3.788334645315611*^9}, {3.788411405608647*^9, 3.788411409092114*^9}, { 3.7884115644712825`*^9, 3.7884115911998663`*^9}, {3.7884116673998833`*^9, 3.788411758799066*^9}, {3.788411985303985*^9, 3.788412002701314*^9}, { 3.78841218266156*^9, 3.788412217652734*^9}, {3.788412679618697*^9, 3.78841268296084*^9}, {3.788412968920223*^9, 3.7884129782039633`*^9}, { 3.7884155241723013`*^9, 3.7884155243798914`*^9}, 3.7884156619519596`*^9, { 3.7884162343262696`*^9, 3.788416236013459*^9}, {3.85139673094703*^9, 3.8513967635772033`*^9}, {3.851396794996914*^9, 3.8513968005297565`*^9}, { 3.851396903521887*^9, 3.851397033396193*^9}, {3.8513970811416616`*^9, 3.8513970815960226`*^9}, {3.851397112451356*^9, 3.851397167400435*^9}, { 3.851397221869113*^9, 3.8513972289141245`*^9}, {3.851397278401065*^9, 3.851397290260914*^9}, {3.851397328228505*^9, 3.851397546519593*^9}, { 3.8513976077985477`*^9, 3.8513976208246136`*^9}, {3.851397684162203*^9, 3.85139779749853*^9}, 3.851407281084627*^9, {3.8514075225388107`*^9, 3.8514075229755898`*^9}, {3.8518313520199227`*^9, 3.85183135349047*^9}, { 3.8518317250655546`*^9, 3.851831750957345*^9}}, CellLabel-> "In[197]:=",ExpressionUUID->"89c0204a-fb4f-4908-9034-80bcab446e30"] }, Closed]], Cell[CellGroupData[{ Cell["PLATE ELEMENT (stab) defs ", "Subsection", CellChangeTimes->{{3.6302475626780834`*^9, 3.6302475636452847`*^9}, { 3.6303896204112215`*^9, 3.630389621175623*^9}, {3.7658855359334097`*^9, 3.7658855563942738`*^9}, {3.7882511594490995`*^9, 3.788251160663724*^9}, { 3.7883213876221266`*^9, 3.788321388914168*^9}, {3.7890220324441195`*^9, 3.789022033389088*^9}},ExpressionUUID->"3c79e90f-496d-48fd-9ed6-\ 750c6fa2d168"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "r\[Gamma]", ",", "FF", ",", "FFINV", ",", "jac", ",", "NN", ",", "u", ",", "ux", ",", "uy", ",", "uz", ",", "v", ",", "vx", ",", "vy", ",", "vz", ",", "w", ",", "wx", ",", "wy", ",", "wz", ",", "\[Phi]", ",", "\[Phi]x", ",", "\[Phi]y", ",", "\[Phi]z", ",", "\[Theta]", ",", "\[Theta]x", ",", "\[Theta]y", ",", "\[Theta]z", ",", "AA", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Phi]", ",", "wc", ",", "E\[Sigma]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wsta", ",", "\[Delta]wmap", ",", "\[Epsilon]\[Epsilon]", ",", "\[Kappa]\[Kappa]", ",", "\[Gamma]\[Gamma]", ",", "MM", ",", "QQ", ",", "tri", ",", RowBox[{"mat", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}]}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"ARNOLD", "-", "FALCK"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "mapping", " ", "for", " ", "the", " ", "plate", " ", "geometry"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"r\[Alpha]", ",", "r\[Beta]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Gamma]", "=", RowBox[{"r\[Alpha]", StyleBox["\[Cross]", "OperatorCharacter"], "r\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Sqrt", "[", RowBox[{"r\[Gamma]", ".", "r\[Gamma]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"r\[Alpha]", ",", "r\[Beta]", ",", RowBox[{"r\[Gamma]", "/", "jac"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", " ", RowBox[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "approximations", "*)"}], "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"wc", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "projection", "*)"}], "\[IndentingNewLine]", RowBox[{"AA", "=", RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", "jac", ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]"}], "}"}], "=", RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]"}], "}"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "/", "AA"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "derivatives", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"ux", ",", "uy", ",", "uz"}], "}"}], "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}], ",", "0"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"vx", ",", "vy", ",", "vz"}], "}"}], "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}], ",", "0"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"wx", ",", "wy", ",", "wz"}], "}"}], "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}], ",", "0"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]x", ",", "\[Phi]y", ",", "\[Phi]z"}], "}"}], "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}], ",", "0"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Theta]x", ",", "\[Theta]y", ",", "\[Theta]z"}], "}"}], "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Theta]"}], ",", "0"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"strain", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]\[Epsilon]", "=", RowBox[{"{", RowBox[{"ux", ",", "vy", ",", RowBox[{"uy", "+", "vx"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]\[Kappa]", "=", RowBox[{"{", RowBox[{"\[Theta]x", ",", RowBox[{"-", "\[Phi]y"}], ",", RowBox[{ RowBox[{"-", "\[Phi]x"}], "+", "\[Theta]y"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Gamma]\[Gamma]", "=", RowBox[{ RowBox[{"{", RowBox[{"wx", ",", "wy"}], "}"}], "+", RowBox[{"{", RowBox[{"\[Pi]\[Theta]", ",", RowBox[{"-", "\[Pi]\[Phi]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"E\[Sigma]", "=", RowBox[{ RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "\[Nu]\[Nu]", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Nu]\[Nu]", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}]}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"MM", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", "E\[Sigma]"}], ")"}], ".", "\[Kappa]\[Kappa]"}]}], ";", "\[IndentingNewLine]", RowBox[{"QQ", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "tt", "*", "GG", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"tt", "*", RowBox[{"E\[Sigma]", ".", "\[Epsilon]\[Epsilon]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Epsilon]\[Epsilon]", "]"}], ".", "NN"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Kappa]\[Kappa]", "]"}], ".", "MM"}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Gamma]\[Gamma]", "]"}], ".", "QQ"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"fX", " ", ",", "fY", ",", "fZ"}], "}"}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wsta", "=", RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"wx", ",", "wy"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], ",", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}]}], "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{"wx", ",", "wy"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wmap", "=", RowBox[{ RowBox[{"-", "0.1"}], "*", RowBox[{"\[Delta]", "[", RowBox[{"wc", "-", "w"}], "]"}], "*", RowBox[{"(", RowBox[{"wc", "-", "w"}], ")"}], "*", RowBox[{"tt", "/", "AA"}], "*", "EE"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wsta"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI1", ",", RowBox[{"\[Delta]wmap", "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "n\[Alpha]", ",", "n\[Beta]", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "NN", ",", "mat", ",", "MM", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "r\[Gamma]", ",", "rn", ",", "jac", ",", "h\[Alpha]", ",", "e\[Alpha]", ",", "h\[Beta]", ",", "h\[Gamma]", ",", "e\[Beta]", ",", "en", ",", "e\[Gamma]", ",", "FF", ",", "\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]", ",", "edg", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "\[Pi]u", ",", "\[Pi]v", ",", "\[Pi]w", ",", "\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]", ",", "f\[Alpha]", ",", "f\[Gamma]", ",", "fn", ",", "m\[Alpha]", ",", "m\[Gamma]", ",", "mn", ",", "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]", ",", "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]", ",", "\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]", ",", "GG", ",", "N\[Alpha]\[Alpha]", ",", "N\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Gamma]", ",", "N\[Gamma]\[Alpha]", ",", "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]", ",", "Q\[Alpha]", ",", "Q\[Gamma]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wsta", ",", "\[Delta]wmap", ",", "AA"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"mat", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]", "=", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}]}], ";", " ", RowBox[{"r\[Beta]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Norm", "[", "r\[Beta]", "]"}]}], ";", " ", RowBox[{"h\[Alpha]", "=", RowBox[{"Norm", "[", "r\[Alpha]", "]"}]}], ";", RowBox[{"jac", "=", RowBox[{"Norm", "[", RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Alpha]", "=", RowBox[{"r\[Alpha]", "/", "h\[Alpha]"}]}], ";", RowBox[{"e\[Beta]", "=", RowBox[{"r\[Beta]", "/", "h\[Beta]"}]}], ";", " ", RowBox[{"en", "=", RowBox[{ RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], " ", "/", "jac"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r\[Gamma]", "=", RowBox[{"r\[Beta]", "-", RowBox[{ RowBox[{"(", RowBox[{"r\[Beta]", ".", "e\[Alpha]"}], ")"}], " ", "e\[Alpha]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Gamma]", "=", RowBox[{"Norm", "[", "r\[Gamma]", "]"}]}], ";", RowBox[{"e\[Gamma]", "=", RowBox[{"r\[Gamma]", "/", "h\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", "e\[Gamma]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]"}], "}"}], "=", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Alpha]"}], ",", RowBox[{"r\[Alpha]", ".", "r\[Beta]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Beta]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Beta]"}]}], "}"}]}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Gamma]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Gamma]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"edg", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Sort", "[", "#", "]"}], "&"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"uX", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"uY", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "3"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Z", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"projection", " ", "mapping"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Pi]\[Phi]", "=", RowBox[{ RowBox[{ RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], "/", "60"}], "+", " ", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Theta]", "=", RowBox[{ RowBox[{ RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], "/", "60"}], "+", " ", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Psi]", "=", RowBox[{ RowBox[{ RowBox[{"\[Theta]Z", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], "/", "60"}], "+", " ", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "3"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Pi]u", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]v", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]w", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]u", ",", "\[Pi]v", ",", "\[Pi]w"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"\[Pi]u", ",", "\[Pi]v", ",", "\[Pi]w"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Gamma]", ",", "fn"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"strain", " ", "measures", " ", "with", " ", "non"}], "-", RowBox[{"symmetric", " ", "\[Epsilon]"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}]}]}], ")"}], "/", "h\[Gamma]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], "/", "h\[Alpha]"}], "-", "\[Psi]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}]}]}], ")"}], "/", "h\[Gamma]"}], "+", "\[Psi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}]}]}], ")"}]}], "/", "h\[Gamma]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", " ", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Theta]"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], "/", "h\[Alpha]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], "+", "\[Pi]\[Theta]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", "\[Pi]\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "stress", " ", "resultants", " ", "with", " ", "a", " ", "nonsymmetric", " ", "N"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Alpha]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Gamma]\[Gamma]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Gamma]\[Gamma]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Gamma]\[Gamma]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Gamma]", "=", RowBox[{ "tt", "*", "2", " ", "GG", "*", "\[Epsilon]\[Alpha]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Gamma]\[Alpha]", "=", RowBox[{ "tt", "*", "2", " ", "GG", "*", "\[Epsilon]\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Alpha]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Gamma]\[Gamma]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Gamma]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Gamma]\[Gamma]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", " ", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "\[Nu]\[Nu]"}]}], ")"}]}], "*", "\[Kappa]\[Alpha]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{ RowBox[{"5", "/", "6"}], " ", "*", "GG", "*", "tt", "*", "\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Gamma]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "N\[Alpha]\[Alpha]", ",", "N\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Gamma]", ",", "N\[Gamma]\[Alpha]"}], "}"}]}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]"}], "}"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Gamma]"}], "}"}]}]}]}], ";", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Gamma]", ",", "fn"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wsta", "=", RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}]}]}], ")"}], "/", "h\[Gamma]"}]}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"N\[Alpha]\[Alpha]", ",", "N\[Alpha]\[Gamma]"}], "}"}], ",", RowBox[{"{", RowBox[{"N\[Gamma]\[Alpha]", ",", "N\[Gamma]\[Gamma]"}], "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}]}]}], ")"}], "/", "h\[Gamma]"}]}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wmap", "=", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "/", "100000"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]u", "-", "u"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]u", "-", "u"}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]v", "-", "v"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]v", "-", "v"}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]w", "-", "w"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]w", "-", "w"}], ")"}]}]}], ")"}], "*", "tt", "*", RowBox[{"EE", "/", "jac"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI3", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wsta", "+", "\[Delta]wmap"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.4426474258030453`*^9, {3.4444401255942*^9, 3.4444401388073997`*^9}, { 3.4444401803034*^9, 3.4444401844062*^9}, 3.4444402418922*^9, { 3.4444402805022*^9, 3.4444403134026003`*^9}, {3.4444403443062*^9, 3.4444404484049997`*^9}, {3.444483267101*^9, 3.444483267335*^9}, { 3.4444833136046*^9, 3.4444835622998*^9}, {3.4444836421094*^9, 3.4444837777981997`*^9}, {3.444483920429*^9, 3.4444839412237997`*^9}, 3.4444842905546*^9, {3.4444843207406*^9, 3.4444844162282*^9}, { 3.4444844465078*^9, 3.4444844624354*^9}, {3.4444845255998*^9, 3.4444845894505997`*^9}, {3.4444846290746*^9, 3.444484933025*^9}, { 3.4444849790917997`*^9, 3.4444851148742*^9}, {3.444534936054*^9, 3.4445349675348*^9}, {3.4445355821731997`*^9, 3.44453585174*^9}, { 3.4445372162198*^9, 3.4445372264378*^9}, 3.444537384731*^9, { 3.4445377585382*^9, 3.4445377605818*^9}, {3.4445379733658*^9, 3.4445379736934*^9}, {3.4445380176762*^9, 3.444538032777*^9}, { 3.4445381079222*^9, 3.4445381581386003`*^9}, {3.4445382726456003`*^9, 3.4445382910067997`*^9}, {3.4445383401312*^9, 3.4445383475880003`*^9}, { 3.444538438458*^9, 3.4445384464608*^9}, {3.4445385680783997`*^9, 3.4445385687648*^9}, {3.4445389411991997`*^9, 3.4445389431024*^9}, { 3.444539746605*^9, 3.4445397807846003`*^9}, {3.4445408839765997`*^9, 3.4445409234133997`*^9}, {3.4445409681698*^9, 3.4445409932702*^9}, { 3.4445415452906*^9, 3.4445415706717997`*^9}, {3.4445416647242002`*^9, 3.4445416909477997`*^9}, {3.4445417660150003`*^9, 3.444541788557*^9}, { 3.4445420906977997`*^9, 3.444542104847*^9}, {3.4445421885878*^9, 3.4445421941414003`*^9}, {3.4445422252166*^9, 3.4445422386014*^9}, { 3.444542280425*^9, 3.4445423014538*^9}, {3.444542455769*^9, 3.4445424578282003`*^9}, {3.4445431739214*^9, 3.444543175809*^9}, { 3.4445647020962*^9, 3.4445648405618*^9}, {3.4445648825414*^9, 3.4445648858486*^9}, {3.4445649382646*^9, 3.4445651882702*^9}, { 3.4446164822206*^9, 3.4446165344494*^9}, {3.4446166121842003`*^9, 3.4446166738822002`*^9}, {3.4446167223046*^9, 3.4446168047974*^9}, { 3.444616843033*^9, 3.444616906447*^9}, {3.4446444694708*^9, 3.4446444700948*^9}, {3.4446477738310003`*^9, 3.4446477939862003`*^9}, { 3.4446478467298*^9, 3.4446478681018*^9}, 3.4446480456142*^9, { 3.4446487557418003`*^9, 3.4446487636198*^9}, 3.4446488179974003`*^9, { 3.4446488971205997`*^9, 3.4446489152478*^9}, {3.4446490003458*^9, 3.4446490008294*^9}, {3.4447042728942003`*^9, 3.4447042751562*^9}, { 3.4447044703278*^9, 3.4447044865362*^9}, 3.4447046475282*^9, 3.4447047993786*^9, {3.444704908329*^9, 3.4447049292642*^9}, { 3.4447049861926003`*^9, 3.4447049877214003`*^9}, {3.4447050279296*^9, 3.4447050419695997`*^9}, {3.4447053486656*^9, 3.4447053739376*^9}, 3.4447054561963997`*^9, 3.44470561612*^9, {3.4472133996876*^9, 3.4472134108571997`*^9}, {3.4472134470179996`*^9, 3.4472134648332*^9}, { 3.4472135032872*^9, 3.4472135245344*^9}, {3.4472136963059998`*^9, 3.4472137794384003`*^9}, {3.4472138235708*^9, 3.4472138388900003`*^9}, { 3.4472139099792*^9, 3.4472141367096*^9}, {3.447214202682*^9, 3.4472142975924*^9}, {3.4472144187732*^9, 3.4472145910284*^9}, { 3.4472146560492*^9, 3.4472147023968*^9}, {3.447214803594*^9, 3.4472148728736*^9}, {3.4472149156956*^9, 3.447214940484*^9}, { 3.447216227284*^9, 3.4472162419948*^9}, {3.4472163068908*^9, 3.4472163720832*^9}, {3.4472164665880003`*^9, 3.447216530392*^9}, { 3.4472166237268*^9, 3.4472167058452*^9}, 3.4472167362808*^9, { 3.4472171394658003`*^9, 3.4472171532874002`*^9}, {3.4472172028993998`*^9, 3.4472172216661997`*^9}, {3.4472172524606*^9, 3.4472172690278*^9}, { 3.4472173209133997`*^9, 3.4472173334245996`*^9}, {3.4472173920846*^9, 3.447217404861*^9}, {3.4472179572548*^9, 3.4472180351456003`*^9}, { 3.4472509764091997`*^9, 3.4472511017396*^9}, {3.4473910422216*^9, 3.4473912901524*^9}, 3.4473918688344*^9, {3.447392021185*^9, 3.4473920346633997`*^9}, {3.4473921383304*^9, 3.4473921479088*^9}, { 3.4473923024112*^9, 3.4473923734379997`*^9}, {3.4473928098168*^9, 3.4473928648691998`*^9}, {3.4473931872432003`*^9, 3.4473932461800003`*^9}, {3.4473933026675997`*^9, 3.4473934579812*^9}, { 3.4473935755271997`*^9, 3.447393742572*^9}, {3.4473939032676*^9, 3.4473939384144*^9}, {3.447395257644*^9, 3.4473953141628*^9}, { 3.4473954231132*^9, 3.4473954756384*^9}, {3.4473955348716*^9, 3.4473955723272*^9}, {3.447395648502*^9, 3.4473957588876*^9}, { 3.4473957903996*^9, 3.4473958488372*^9}, 3.4473962894154*^9, { 3.447396350817*^9, 3.447396352611*^9}, {3.4474625379146*^9, 3.4474625637326*^9}, {3.558360651728078*^9, 3.558360652102478*^9}, { 3.5619791319820857`*^9, 3.561979135788492*^9}, 3.561979369382504*^9, { 3.5619794930439215`*^9, 3.5619795010155354`*^9}, {3.561979569218855*^9, 3.56197960614412*^9}, {3.5619797417551584`*^9, 3.5619797448751636`*^9}, { 3.618719065033702*^9, 3.618719075426296*^9}, {3.6187194011669273`*^9, 3.6187194449454317`*^9}, {3.6187196998040085`*^9, 3.6187197102436056`*^9}, {3.618719902254588*^9, 3.6187199711455283`*^9}, { 3.618722365406472*^9, 3.6187225412555304`*^9}, {3.6187226885009522`*^9, 3.6187227109872384`*^9}, {3.618722756922866*^9, 3.6187231317203026`*^9}, { 3.618723424250035*^9, 3.6187234267291765`*^9}, {3.6187235105259695`*^9, 3.6187236491028957`*^9}, {3.618723691580325*^9, 3.618723745975436*^9}, { 3.618723778837316*^9, 3.6187238310002995`*^9}, {3.6187239055875654`*^9, 3.618723940035536*^9}, {3.6187239782667227`*^9, 3.6187240219352207`*^9}, { 3.618724166762504*^9, 3.618724177411113*^9}, {3.618729321696159*^9, 3.618729328067523*^9}, 3.618729374058154*^9, {3.6187294379838104`*^9, 3.618729708464281*^9}, {3.6187297631904106`*^9, 3.618729773195983*^9}, { 3.618729822648812*^9, 3.6187299321490746`*^9}, {3.618729984399063*^9, 3.61873000654133*^9}, {3.6187300746012225`*^9, 3.6187300860458775`*^9}, { 3.618731390835507*^9, 3.6187315116174154`*^9}, {3.618731747324897*^9, 3.6187318214091344`*^9}, {3.6187318769243097`*^9, 3.618732065297084*^9}, { 3.6187321012351394`*^9, 3.618732157420353*^9}, {3.618732188384124*^9, 3.6187322435542793`*^9}, {3.6187322786112847`*^9, 3.6187325478446836`*^9}, {3.6187325819856367`*^9, 3.6187326817653437`*^9}, {3.618732810863728*^9, 3.61873282594359*^9}, { 3.6187336474335766`*^9, 3.618733754678711*^9}, {3.618733827497876*^9, 3.61873396201257*^9}, {3.6187342020362988`*^9, 3.618734236455267*^9}, 3.618734298201799*^9, {3.618734712498495*^9, 3.618734712716508*^9}, 3.6187347739640107`*^9, {3.618738817361748*^9, 3.6187388333816643`*^9}, { 3.6187391349349127`*^9, 3.6187391457955337`*^9}, {3.618739376900752*^9, 3.618739397023903*^9}, {3.618739528394417*^9, 3.618739534809784*^9}, { 3.618739972366811*^9, 3.61873997340687*^9}, {3.6187400416617737`*^9, 3.618740043022852*^9}, {3.6187400971579485`*^9, 3.618740107902563*^9}, { 3.6187401713671927`*^9, 3.6187401723312483`*^9}, {3.6187402613443394`*^9, 3.618740268819767*^9}, {3.6187403697625403`*^9, 3.6187404057615995`*^9}, { 3.618740488277319*^9, 3.618740516244919*^9}, {3.618740647782442*^9, 3.6187406551668644`*^9}, 3.6187407823021364`*^9, {3.6187418050786357`*^9, 3.618741805749674*^9}, {3.6187418557605343`*^9, 3.6187419895921893`*^9}, { 3.618742022944097*^9, 3.61874204379729*^9}, {3.6187420836395683`*^9, 3.618742103384698*^9}, {3.620462440882641*^9, 3.6204624460519366`*^9}, { 3.6204624990259666`*^9, 3.620462576450395*^9}, {3.620463682857678*^9, 3.620463713336421*^9}, 3.6204637901188126`*^9, {3.620464238835478*^9, 3.62046424411378*^9}, 3.628912429385081*^9, {3.6289135207155013`*^9, 3.6289135210805225`*^9}, 3.6289497746958513`*^9, 3.6289498371774254`*^9, { 3.62894988410911*^9, 3.6289500319795675`*^9}, {3.6289501333883677`*^9, 3.628950183744248*^9}, {3.6289503323017445`*^9, 3.628950390181055*^9}, { 3.6289505050536256`*^9, 3.6289505113579865`*^9}, {3.62895070863527*^9, 3.6289507095043197`*^9}, {3.628951013180689*^9, 3.62895101407374*^9}, { 3.629190743153632*^9, 3.629190816645361*^9}, {3.6291909709608326`*^9, 3.629190981678051*^9}, {3.629191034624544*^9, 3.6291910410049553`*^9}, { 3.6293846391370816`*^9, 3.629384641102685*^9}, {3.6294628543371735`*^9, 3.629462867097191*^9}, {3.629468063172048*^9, 3.6294681151669397`*^9}, { 3.6295205836757097`*^9, 3.6295206295085897`*^9}, {3.6295206788826766`*^9, 3.6295207067911253`*^9}, {3.6295207408927855`*^9, 3.629520753700408*^9}, { 3.629521020590745*^9, 3.6295210354395943`*^9}, {3.6295211107369013`*^9, 3.62952114882508*^9}, {3.6295212327348795`*^9, 3.6295212477237363`*^9}, { 3.6295213424816394`*^9, 3.629521343230441*^9}, {3.6295215363119802`*^9, 3.6295216753550243`*^9}, {3.629521922272258*^9, 3.6295219939855833`*^9}, { 3.6295220298188467`*^9, 3.629522446058778*^9}, {3.629522499348471*^9, 3.629522604352256*^9}, {3.629522755188921*^9, 3.62952288580795*^9}, { 3.629522918084407*^9, 3.6295233421087513`*^9}, {3.6295233808436193`*^9, 3.629523390936837*^9}, {3.629523424274096*^9, 3.6295234533369465`*^9}, { 3.6295235190130625`*^9, 3.629523521680667*^9}, 3.6295235894315863`*^9, { 3.6295237270706277`*^9, 3.629523799454755*^9}, {3.6295238514808464`*^9, 3.629523883460902*^9}, {3.6295239376085978`*^9, 3.6295239442386093`*^9}, { 3.6295241089904985`*^9, 3.629524177537019*^9}, 3.629524211888279*^9, { 3.629524277423994*^9, 3.629524396904604*^9}, {3.6295244794839497`*^9, 3.6295246248450055`*^9}, 3.629524657090262*^9, {3.6295259599109507`*^9, 3.629526013465844*^9}, {3.6295261092188125`*^9, 3.629526201414974*^9}, 3.6295263436092243`*^9, {3.6295263910333076`*^9, 3.629526583303645*^9}, { 3.629526616672104*^9, 3.629526647653758*^9}, {3.629526687558628*^9, 3.629526744888729*^9}, {3.629526804075233*^9, 3.6295268598453307`*^9}, { 3.6295269393898706`*^9, 3.6295269586559043`*^9}, {3.6295271490074387`*^9, 3.6295272149019547`*^9}, {3.6295272553684254`*^9, 3.6295272827620735`*^9}, {3.6295274137087035`*^9, 3.6295274761244135`*^9}, {3.6295275252801*^9, 3.6295279912529182`*^9}, { 3.6295281572216096`*^9, 3.629528160435215*^9}, {3.6295282905550437`*^9, 3.6295284308616905`*^9}, 3.6295285402022824`*^9, {3.629528582088356*^9, 3.629528616798417*^9}, {3.6295287666834803`*^9, 3.6295290316343455`*^9}, { 3.629529086515242*^9, 3.629529118432898*^9}, {3.6295291548121614`*^9, 3.629529292794404*^9}, {3.6295293426208916`*^9, 3.6295293491261034`*^9}, { 3.629529420699029*^9, 3.629529571535694*^9}, {3.6295296539506383`*^9, 3.629529656103442*^9}, {3.6295296894407005`*^9, 3.629529692295506*^9}, { 3.6295297445555973`*^9, 3.629529766426836*^9}, {3.6295298053333044`*^9, 3.6295298209489317`*^9}, {3.6295308380551186`*^9, 3.6295308386635194`*^9}, {3.629532377840223*^9, 3.6295323811630287`*^9}, { 3.629532480020402*^9, 3.629532482454006*^9}, {3.629532520720874*^9, 3.629532564619351*^9}, {3.62953259842461*^9, 3.6295326002654133`*^9}, { 3.6295326327758703`*^9, 3.6295326715107384`*^9}, {3.629532742428463*^9, 3.6295328288058147`*^9}, {3.6295329692184625`*^9, 3.6295330530062094`*^9}, {3.6295331824396367`*^9, 3.629533193562456*^9}, 3.6295350321720915`*^9, 3.629535158485513*^9, {3.629535245471266*^9, 3.6295352687465067`*^9}, {3.62953541293756*^9, 3.629535446384019*^9}, { 3.6295355043381205`*^9, 3.6295355262249594`*^9}, {3.629543790136781*^9, 3.629543791181983*^9}, {3.629543871350524*^9, 3.629544001673153*^9}, { 3.6295446682009234`*^9, 3.629544668466124*^9}, {3.6296010216162376`*^9, 3.6296010236442413`*^9}, {3.629601079336339*^9, 3.6296010902875586`*^9}, 3.6296011425476503`*^9, {3.6296043522397404`*^9, 3.629604399031022*^9}, { 3.629623884428093*^9, 3.629623914723346*^9}, {3.6296239662190366`*^9, 3.6296239738006496`*^9}, {3.6296240514731865`*^9, 3.6296240920176573`*^9}, {3.629624125947717*^9, 3.629624369432945*^9}, { 3.6296256512247963`*^9, 3.6296256817072496`*^9}, {3.6296260472626915`*^9, 3.629626047434292*^9}, {3.629628055568204*^9, 3.629628056098605*^9}, { 3.6296280911206665`*^9, 3.6296281088266973`*^9}, {3.6296281406819534`*^9, 3.629628273032586*^9}, {3.629628378831972*^9, 3.6296283814995766`*^9}, { 3.629628459562114*^9, 3.629628466379326*^9}, {3.629628519419419*^9, 3.6296285390754533`*^9}, {3.629633008133008*^9, 3.629633008835009*^9}, { 3.6296337764967575`*^9, 3.6296338344040594`*^9}, {3.6296342997684765`*^9, 3.629634432150309*^9}, {3.629634494035618*^9, 3.6296345320060844`*^9}, { 3.629634594499794*^9, 3.629634812182576*^9}, {3.6296348599810605`*^9, 3.6296348746918864`*^9}, {3.6296349071867433`*^9, 3.629635023172947*^9}, 3.6296350995818815`*^9, {3.6296363797201295`*^9, 3.6296363868961425`*^9}, { 3.629636462025874*^9, 3.6296364833355117`*^9}, {3.629636555922439*^9, 3.62963656780966*^9}, {3.629636770469616*^9, 3.629636774151222*^9}, { 3.6296369192782774`*^9, 3.6296369318830996`*^9}, {3.629637058539722*^9, 3.6296370719401455`*^9}, {3.629637278172508*^9, 3.629637286814923*^9}, { 3.6296376418091464`*^9, 3.629637662385583*^9}, {3.629637773551378*^9, 3.629637795360216*^9}, {3.6296390041751394`*^9, 3.629639039571602*^9}, 3.6296393829750047`*^9, {3.6296395546065063`*^9, 3.6296395649961243`*^9}, { 3.62964113386068*^9, 3.6296412507048855`*^9}, {3.629641303167777*^9, 3.629641313744596*^9}, {3.6296416285116315`*^9, 3.629641628886032*^9}, { 3.6296416658736973`*^9, 3.6296416815049243`*^9}, 3.6296417376338234`*^9, { 3.6296855551269727`*^9, 3.6296855804270077`*^9}, {3.6297079065796247`*^9, 3.6297079070476255`*^9}, {3.6297080850439377`*^9, 3.629708135728427*^9}, { 3.6297083496516027`*^9, 3.6297084025512953`*^9}, {3.629708781767563*^9, 3.629708790940379*^9}, {3.6297089402482414`*^9, 3.6297089618542795`*^9}, { 3.6297105345398417`*^9, 3.629710538580249*^9}, {3.6297107810514746`*^9, 3.6297107850138817`*^9}, {3.6297109100481014`*^9, 3.629710915710911*^9}, { 3.629711201534613*^9, 3.629711204311418*^9}, {3.629711236307074*^9, 3.6297115007275386`*^9}, {3.6297115377464037`*^9, 3.6297115441112146`*^9}, 3.6297116025645175`*^9, {3.6298716505389357`*^9, 3.629871851841689*^9}, { 3.62987837458679*^9, 3.629878383510006*^9}, {3.6298784402629056`*^9, 3.629878447345318*^9}, {3.6298785221786494`*^9, 3.6298786580236883`*^9}, { 3.629878689613744*^9, 3.629878737147027*^9}, 3.629878783853509*^9, { 3.629878832322794*^9, 3.6298789171723433`*^9}, {3.6298802128122005`*^9, 3.6298802929723125`*^9}, 3.6298813644148126`*^9, {3.629882428887303*^9, 3.629882435887313*^9}, {3.6298986251827383`*^9, 3.6298988530367384`*^9}, { 3.6298989036744275`*^9, 3.6298989486493063`*^9}, {3.629899016868226*^9, 3.6298991622448816`*^9}, {3.6298997154530535`*^9, 3.629899740147897*^9}, { 3.6298998248560457`*^9, 3.629899978048314*^9}, {3.6299000396372223`*^9, 3.6299001557638264`*^9}, {3.6299001966826982`*^9, 3.6299002595352087`*^9}, 3.6299005011236343`*^9, {3.6299005468317146`*^9, 3.629900567642151*^9}, { 3.629900887676713*^9, 3.629900990153293*^9}, {3.6299011689220085`*^9, 3.6299012295125146`*^9}, {3.6299013754039707`*^9, 3.6299014166036434`*^9}, 3.6299014589733176`*^9, {3.6299015096734066`*^9, 3.629901588765546*^9}, { 3.629901662569275*^9, 3.6299016974665365`*^9}, {3.629901952339784*^9, 3.6299019599057975`*^9}, 3.6299020306051216`*^9, {3.6299022330934772`*^9, 3.6299022682559395`*^9}, {3.6299023020455985`*^9, 3.629902332808852*^9}, { 3.6299024532566643`*^9, 3.629902462850681*^9}, {3.629949880225117*^9, 3.6299498807867184`*^9}, {3.6299503101150723`*^9, 3.6299503156998825`*^9}, {3.629950355058751*^9, 3.629950498937804*^9}, { 3.6299555415202007`*^9, 3.6299555507086167`*^9}, {3.6299556061667137`*^9, 3.6299557553497763`*^9}, {3.629955788499834*^9, 3.6299558948608212`*^9}, { 3.629956042764681*^9, 3.629956043809883*^9}, {3.6299560914211664`*^9, 3.6299561017327843`*^9}, 3.629956145849662*^9, {3.6299584813821354`*^9, 3.6299585082765827`*^9}, 3.6299585652946825`*^9, {3.629958616587573*^9, 3.6299586356508064`*^9}, {3.629958715073346*^9, 3.6299588186419287`*^9}, { 3.629958857454797*^9, 3.629958927249319*^9}, {3.629959427994599*^9, 3.629959494669116*^9}, {3.6299595293323765`*^9, 3.6299596037913074`*^9}, { 3.62995966795422*^9, 3.62995967360143*^9}, {3.6299597835972233`*^9, 3.6299597841120243`*^9}, {3.629959826622099*^9, 3.629959862533362*^9}, { 3.6299599051682367`*^9, 3.6299599235918694`*^9}, 3.629959979939168*^9, { 3.6299601345354395`*^9, 3.62996014612626*^9}, 3.6299601769831142`*^9, { 3.629960253142448*^9, 3.629960269538077*^9}, {3.6299603041701374`*^9, 3.6299603078205442`*^9}, {3.6299604300467587`*^9, 3.629960435491168*^9}, { 3.6299605300585346`*^9, 3.6299605636609936`*^9}, {3.6299606195870914`*^9, 3.6299606581971593`*^9}, {3.629960824228251*^9, 3.6299608755367413`*^9}, { 3.629960906658796*^9, 3.6299609978409557`*^9}, {3.6299610312250147`*^9, 3.629961070646284*^9}, {3.629961135698398*^9, 3.6299611643088484`*^9}, { 3.6299720458358483`*^9, 3.6299721791536827`*^9}, {3.6299722439717965`*^9, 3.629972300007095*^9}, {3.6299723670872126`*^9, 3.6299723937008595`*^9}, { 3.629972457801372*^9, 3.6299724710613956`*^9}, {3.629972740193068*^9, 3.6299728251196175`*^9}, {3.6299729203577843`*^9, 3.6299729350218105`*^9}, {3.6299729720874753`*^9, 3.6299730462188053`*^9}, {3.629973116044528*^9, 3.6299731230177402`*^9}, { 3.629973184310248*^9, 3.6299732090830917`*^9}, {3.629973349982539*^9, 3.6299734360166903`*^9}, 3.629973534562063*^9, {3.629973577446539*^9, 3.629973586104554*^9}, {3.6299740374133463`*^9, 3.629974083823428*^9}, { 3.6299742505565205`*^9, 3.629974337089873*^9}, {3.629974382907153*^9, 3.6299744466176653`*^9}, {3.629974589794717*^9, 3.629974590761918*^9}, { 3.629974776215044*^9, 3.6299747850134597`*^9}, {3.6299748226095257`*^9, 3.6299748237483273`*^9}, 3.6299748618435946`*^9, {3.629975198476586*^9, 3.6299752545898843`*^9}, {3.62997531475919*^9, 3.6299753175515947`*^9}, { 3.6299754601982455`*^9, 3.6299754625382495`*^9}, {3.629975592034077*^9, 3.629975592502078*^9}, {3.629983277446268*^9, 3.6299832946842985`*^9}, { 3.62998342081052*^9, 3.6299835439883366`*^9}, {3.629983615514462*^9, 3.629983931009416*^9}, {3.6299919807040443`*^9, 3.6299919808912444`*^9}, { 3.629992028330928*^9, 3.6299920922130404`*^9}, 3.629992198480427*^9, { 3.6299922299300823`*^9, 3.629992250506518*^9}, {3.629992292657792*^9, 3.6299923603151107`*^9}, {3.6299924387676487`*^9, 3.6299924398440504`*^9}, {3.6299925764846907`*^9, 3.6299926096347485`*^9}, {3.6299928122323046`*^9, 3.629992818768716*^9}, { 3.6299929049120674`*^9, 3.629992905411268*^9}, {3.6299929850338078`*^9, 3.6299929866250105`*^9}, {3.6299931061992207`*^9, 3.62999312270405*^9}, { 3.629993172312137*^9, 3.6299932618718944`*^9}, {3.6299933276572104`*^9, 3.6299933842073092`*^9}, {3.630287775665962*^9, 3.630287795852398*^9}, { 3.6303896387100534`*^9, 3.630389666774503*^9}, {3.6303896967889557`*^9, 3.6303897095341783`*^9}, {3.6303897587054644`*^9, 3.630389880448078*^9}, { 3.6303899127557354`*^9, 3.630390009444705*^9}, 3.630390057321189*^9, 3.630390443484267*^9, {3.63039095720877*^9, 3.6303909789240074`*^9}, { 3.6303910572205453`*^9, 3.6303911291054716`*^9}, {3.630391163035531*^9, 3.6303911740803504`*^9}, {3.630391240224467*^9, 3.6303912875081496`*^9}, { 3.6303913396902413`*^9, 3.630391404570755*^9}, {3.630391479513287*^9, 3.6303917572873745`*^9}, {3.630391868905571*^9, 3.6303920027226057`*^9}, { 3.630392064327114*^9, 3.630392219843787*^9}, {3.63039226121506*^9, 3.63039232943398*^9}, {3.6303924315985594`*^9, 3.6303924441097813`*^9}, { 3.6303926866122074`*^9, 3.6303927118530517`*^9}, {3.630392795671999*^9, 3.6303928006172075`*^9}, {3.6303986032190485`*^9, 3.6303986046230516`*^9}, {3.6303986654631586`*^9, 3.6303987936485834`*^9}, {3.63039889979117*^9, 3.6303989091199865`*^9}, { 3.630399006323757*^9, 3.630399007259759*^9}, {3.630399117224352*^9, 3.630399214771323*^9}, {3.6303992555185947`*^9, 3.6303993036758795`*^9}, { 3.630399467725767*^9, 3.630399502731636*^9}, {3.6303995748037624`*^9, 3.630399595614199*^9}, {3.6303996329294643`*^9, 3.630399658076709*^9}, { 3.630399711335202*^9, 3.6303997453120623`*^9}, {3.6303998546994543`*^9, 3.6303999880484886`*^9}, {3.6304000742074394`*^9, 3.630400123441126*^9}, { 3.6304001724564123`*^9, 3.630400251595351*^9}, {3.630400324166679*^9, 3.630400327052684*^9}, {3.630400358190338*^9, 3.6304003597503414`*^9}, { 3.6304004587481155`*^9, 3.6304004640521245`*^9}, {3.630400521975026*^9, 3.630400526124634*^9}, {3.630400567199506*^9, 3.630400593516752*^9}, { 3.6304012340070767`*^9, 3.6304013035207987`*^9}, {3.6304013614749007`*^9, 3.630401367933312*^9}, {3.630401686939398*^9, 3.6304017294598303`*^9}, { 3.630401794020523*^9, 3.6304018922061386`*^9}, {3.6304019687775183`*^9, 3.630401987153569*^9}, {3.630402072749465*^9, 3.63040208297405*^9}, { 3.6304022247881613`*^9, 3.630402255931943*^9}, 3.630402329306139*^9, { 3.6304023806970787`*^9, 3.6304024212403975`*^9}, {3.6304025002259154`*^9, 3.630402528595538*^9}, {3.6304025620694523`*^9, 3.630402575015193*^9}, { 3.6304026411829777`*^9, 3.630402649073429*^9}, {3.630402695548087*^9, 3.6304027128260756`*^9}, {3.630402783923142*^9, 3.6304027982389607`*^9}, { 3.6304028797236214`*^9, 3.6304030111811404`*^9}, {3.6304030562107162`*^9, 3.6304031598846455`*^9}, {3.630403236330018*^9, 3.6304032404072514`*^9}, { 3.630403373001835*^9, 3.6304033888147397`*^9}, {3.6304039420953856`*^9, 3.6304039512829113`*^9}, 3.6304039831437335`*^9, {3.630404015975611*^9, 3.6304040663624935`*^9}, {3.630404173614628*^9, 3.630404246945822*^9}, { 3.6304042891772375`*^9, 3.630404299595834*^9}, {3.630404391083066*^9, 3.630404392406142*^9}, {3.6304045301800222`*^9, 3.6304045579486103`*^9}, { 3.630404640215316*^9, 3.630404762796327*^9}, {3.630404877629895*^9, 3.630404883104208*^9}, {3.6304050364729805`*^9, 3.630405098270515*^9}, { 3.6304051736118245`*^9, 3.6304051965901384`*^9}, {3.6304053802536435`*^9, 3.63040539242334*^9}, {3.630406035965148*^9, 3.630406041998493*^9}, { 3.630406072049212*^9, 3.6304060962065935`*^9}, {3.630406264081196*^9, 3.6304062707025747`*^9}, {3.63040632219952*^9, 3.630406385461138*^9}, { 3.630406477200385*^9, 3.630406482095665*^9}, {3.6304066170883865`*^9, 3.6304066222256804`*^9}, {3.630406957868878*^9, 3.630406973411767*^9}, { 3.6304070081447535`*^9, 3.630407018199329*^9}, {3.630407411376817*^9, 3.630407412542884*^9}, {3.6304080609339695`*^9, 3.630408121202417*^9}, { 3.6304081585485525`*^9, 3.6304081832129636`*^9}, {3.63040821409673*^9, 3.630408421131572*^9}, 3.6304934333363276`*^9, {3.63049350751357*^9, 3.630493677593298*^9}, {3.630493716898546*^9, 3.6304937846684227`*^9}, 3.630493922944331*^9, {3.6304939556752033`*^9, 3.630494117430455*^9}, { 3.6304941486092386`*^9, 3.6304941767788496`*^9}, {3.6304942118648567`*^9, 3.6304942530272107`*^9}, {3.6304942838399734`*^9, 3.6304942845820155`*^9}, {3.6304943454054947`*^9, 3.6304944442451477`*^9}, {3.63080749995092*^9, 3.6308075480801234`*^9}, { 3.630807586536323*^9, 3.630807621440319*^9}, {3.630807680459695*^9, 3.630807682914836*^9}, {3.630807736889923*^9, 3.6308077644745007`*^9}, { 3.6308078081089964`*^9, 3.6308078670123653`*^9}, {3.630807991648494*^9, 3.630807997541831*^9}, {3.6308081080891542`*^9, 3.6308081919599514`*^9}, { 3.630808306368495*^9, 3.630808345060708*^9}, {3.6308087281906223`*^9, 3.6308087555171847`*^9}, {3.630809110815507*^9, 3.630809169033837*^9}, { 3.6308091998195972`*^9, 3.630809448512822*^9}, {3.6308095328996487`*^9, 3.6308095448223305`*^9}, {3.630809582269472*^9, 3.6308095873607635`*^9}, { 3.630809665529235*^9, 3.630809684808337*^9}, {3.6308316258485594`*^9, 3.6308318380886984`*^9}, {3.63083188164919*^9, 3.630831966930068*^9}, 3.6320400558356075`*^9, {3.6354749882908883`*^9, 3.635474989418953*^9}, { 3.635475084557395*^9, 3.6354750875145636`*^9}, {3.6354751334091887`*^9, 3.635475162315842*^9}, {3.6354754001974483`*^9, 3.6354754820331287`*^9}, 3.635475512931896*^9, {3.6354756222781506`*^9, 3.635475622861184*^9}, { 3.635475691642118*^9, 3.6354757057969275`*^9}, {3.6354757798291616`*^9, 3.635475797395167*^9}, {3.635475884848169*^9, 3.6354758981309285`*^9}, { 3.635475961488552*^9, 3.6354759738382587`*^9}, {3.6354760213729773`*^9, 3.6354760572050266`*^9}, {3.6354761282470903`*^9, 3.635476136040536*^9}, { 3.6354761719365892`*^9, 3.635476212217893*^9}, {3.6593346599546614`*^9, 3.659334660890663*^9}, {3.6593347077219453`*^9, 3.659334720701168*^9}, { 3.6593348752974396`*^9, 3.6593348758122406`*^9}, {3.6593349140947075`*^9, 3.6593350070240707`*^9}, {3.6593350466949406`*^9, 3.6593350543701544`*^9}, {3.659335103791041*^9, 3.6593351614487424`*^9}, 3.659335217686841*^9, {3.659335262084519*^9, 3.6593352995869846`*^9}, { 3.6593356899482727`*^9, 3.659335701819893*^9}, {3.659335964227954*^9, 3.659335964602355*^9}, {3.65933603594128*^9, 3.6593360629605274`*^9}, { 3.6593361352354546`*^9, 3.6593361504454813`*^9}, {3.6593363929479074`*^9, 3.6593364061611304`*^9}, 3.6593368946915884`*^9, {3.6884748265656157`*^9, 3.6884748268716326`*^9}, {3.6884748600075283`*^9, 3.688474861420609*^9}, { 3.6885242858240776`*^9, 3.6885243001140976`*^9}, {3.6888842911675606`*^9, 3.6888843311676164`*^9}, {3.688966242423658*^9, 3.688966263933688*^9}, { 3.6897393587897596`*^9, 3.6897393649897685`*^9}, 3.689739477049925*^9, { 3.6898595970621734`*^9, 3.689859597272174*^9}, {3.6898596707522764`*^9, 3.6898597190523443`*^9}, {3.689859768552414*^9, 3.6898597721424184`*^9}, { 3.689859855272535*^9, 3.689859859882541*^9}, {3.6898605078334484`*^9, 3.6898607266237545`*^9}, 3.6898608811139708`*^9, {3.6898609634740863`*^9, 3.689860974304102*^9}, 3.6898610140141573`*^9, {3.6898611496043468`*^9, 3.6898611683243732`*^9}, {3.689861462024784*^9, 3.6898615624849253`*^9}, { 3.6898616142149973`*^9, 3.6898616164350004`*^9}, 3.6898616657950697`*^9, { 3.689861716805141*^9, 3.689861749905187*^9}, {3.732677920575506*^9, 3.7326779208190203`*^9}, {3.7519672427004185`*^9, 3.7519672444968877`*^9}, {3.7519674022097683`*^9, 3.75196742976579*^9}, { 3.751967484127989*^9, 3.751967510853814*^9}, {3.7519675409404893`*^9, 3.751967541549782*^9}, {3.7519675797751045`*^9, 3.751967592209671*^9}, { 3.7519676829383273`*^9, 3.7519676841255474`*^9}, {3.7519677154775553`*^9, 3.7519677953499403`*^9}, 3.751967827811061*^9, {3.7519679545625095`*^9, 3.751967957999185*^9}, {3.751968003754015*^9, 3.7519681477513895`*^9}, { 3.751968264817631*^9, 3.751968270722477*^9}, {3.7519689618119907`*^9, 3.751968969888235*^9}, {3.7519691168917775`*^9, 3.7519691395895615`*^9}, { 3.751969242782174*^9, 3.7519692581691785`*^9}, {3.7519693625211954`*^9, 3.751969378579924*^9}, {3.751969409572627*^9, 3.751969438643936*^9}, { 3.7519695894526725`*^9, 3.751969614306203*^9}, {3.7523200108586655`*^9, 3.752320012354121*^9}, {3.7553831315619707`*^9, 3.755383134119626*^9}, { 3.7553831893197794`*^9, 3.755383241814331*^9}, {3.7553832736267967`*^9, 3.7553832810757113`*^9}, {3.7554336536222963`*^9, 3.755433684797229*^9}, { 3.7554337764737434`*^9, 3.7554338315300155`*^9}, {3.755433998047738*^9, 3.7554340265485487`*^9}, {3.755446573138784*^9, 3.755446636911299*^9}, { 3.75544667493072*^9, 3.755446753435521*^9}, {3.755446891541581*^9, 3.7554468921547422`*^9}, {3.7554469323588533`*^9, 3.755446936867403*^9}, { 3.7554470190332975`*^9, 3.7554472776872244`*^9}, {3.7555217323692026`*^9, 3.755521732847602*^9}, {3.755521767127169*^9, 3.7555217972041793`*^9}, { 3.755522561453134*^9, 3.755522564231819*^9}, {3.755522601885935*^9, 3.7555226037287407`*^9}, {3.7555226758687305`*^9, 3.755522678585092*^9}, { 3.7555234832604623`*^9, 3.7555235920444417`*^9}, {3.7555239506007543`*^9, 3.755524013893358*^9}, {3.755524076791689*^9, 3.7555240812793446`*^9}, { 3.7555241238138275`*^9, 3.7555241268985643`*^9}, {3.7555242930449886`*^9, 3.7555243378577013`*^9}, {3.7555256673767824`*^9, 3.7555256808205338`*^9}, {3.7555258588384123`*^9, 3.755525900317296*^9}, { 3.755525930708299*^9, 3.7555260436531134`*^9}, {3.755607147401991*^9, 3.7556071504143705`*^9}, {3.755607992884314*^9, 3.7556080025382996`*^9}, { 3.7556094344057455`*^9, 3.7556094348690443`*^9}, {3.7559613653116636`*^9, 3.755961445097105*^9}, 3.755961484246889*^9, {3.7559618979231987`*^9, 3.755961939470047*^9}, {3.7559620323724904`*^9, 3.7559620330864005`*^9}, { 3.755962155557907*^9, 3.7559621601593847`*^9}, {3.755962303755834*^9, 3.755962343830135*^9}, {3.7559624058018165`*^9, 3.7559624450501757`*^9}, 3.756002186674869*^9, 3.7560029626855392`*^9, {3.756003222110388*^9, 3.756003295034633*^9}, {3.7560056331492863`*^9, 3.7560056663855457`*^9}, { 3.7560057813555765`*^9, 3.7560057863836613`*^9}, {3.7560058917172394`*^9, 3.756005927847292*^9}, 3.756006092376186*^9, 3.756009112317705*^9, { 3.756091886039587*^9, 3.756091887764086*^9}, {3.756092005435152*^9, 3.7560920727337685`*^9}, {3.75609212911592*^9, 3.7560921293252516`*^9}, { 3.756092262958163*^9, 3.756092263157668*^9}, {3.756092342487877*^9, 3.756092347894502*^9}, {3.7560929036769304`*^9, 3.7560929278911004`*^9}, { 3.7560930741522417`*^9, 3.756093083420331*^9}, {3.7560932986236534`*^9, 3.7560933139459305`*^9}, {3.756093449985523*^9, 3.7560934874491863`*^9}, { 3.756093592694581*^9, 3.7560936019456573`*^9}, {3.756093634438078*^9, 3.756093673866626*^9}, {3.756093873069885*^9, 3.756093897964734*^9}, { 3.7560940650109406`*^9, 3.756094078056768*^9}, {3.756442536546026*^9, 3.756442607904289*^9}, {3.7564436397451363`*^9, 3.7564436403231254`*^9}, { 3.7636034984570236`*^9, 3.7636034989933815`*^9}, {3.763603551051456*^9, 3.7636035527617817`*^9}, {3.7636036049384193`*^9, 3.7636036392233057`*^9}, {3.7636036850937223`*^9, 3.763603692587598*^9}, { 3.7636037258272257`*^9, 3.7636037459031096`*^9}, {3.7636037792254367`*^9, 3.76360387572289*^9}, {3.763603971837229*^9, 3.7636040341423655`*^9}, { 3.763604066526084*^9, 3.7636040756798687`*^9}, {3.7636041452118535`*^9, 3.763604278007333*^9}, {3.763604317710966*^9, 3.7636043271387568`*^9}, { 3.7636043584877644`*^9, 3.763604415561053*^9}, {3.763604445680462*^9, 3.7636044504114943`*^9}, {3.763604615444647*^9, 3.7636048082554193`*^9}, 3.763604854904996*^9, {3.7636133594095488`*^9, 3.7636133618464766`*^9}, { 3.7636136063756704`*^9, 3.7636136315671196`*^9}, {3.7636990373827705`*^9, 3.7636990431157646`*^9}, {3.763699090332087*^9, 3.763699110952259*^9}, { 3.763699227420497*^9, 3.7636993642943506`*^9}, {3.763700085627533*^9, 3.763700088329999*^9}, {3.7637001721125274`*^9, 3.763700181422837*^9}, { 3.763700248063385*^9, 3.7637003918630466`*^9}, {3.763700591783223*^9, 3.7637006017496295`*^9}, {3.7637007583576717`*^9, 3.7637007603074865`*^9}, {3.7637137795793185`*^9, 3.7637137822587233`*^9}, {3.7637148704355187`*^9, 3.763714870624051*^9}, { 3.763727592158518*^9, 3.7637275933445053`*^9}, {3.7637276688363667`*^9, 3.7637276694756594`*^9}, 3.763803448896332*^9, {3.76380349501632*^9, 3.7638036835067654`*^9}, {3.763804829093463*^9, 3.7638048385675254`*^9}, 3.7638051033646154`*^9, 3.7638053924528885`*^9, {3.763805557684454*^9, 3.763805634255308*^9}, {3.763806843847647*^9, 3.763806847966059*^9}, { 3.763806942652097*^9, 3.7638071770752254`*^9}, {3.7638141184594107`*^9, 3.763814134133461*^9}, {3.7638146808628216`*^9, 3.7638146925645113`*^9}, { 3.7638147709278784`*^9, 3.7638147811883087`*^9}, {3.7638148155281043`*^9, 3.763814819843194*^9}, {3.7638150259647446`*^9, 3.763815028601293*^9}, { 3.7638151529595194`*^9, 3.763815155849978*^9}, {3.7638163770262136`*^9, 3.763816380851597*^9}, {3.7638164181856327`*^9, 3.7638164950537987`*^9}, 3.763816568304102*^9, {3.7638166173645625`*^9, 3.763816618808757*^9}, { 3.7638167204462805`*^9, 3.763816721012859*^9}, {3.763857602253485*^9, 3.7638579604183645`*^9}, {3.7638580038507566`*^9, 3.7638580060526443`*^9}, {3.763858082269992*^9, 3.7638581746835337`*^9}, { 3.7638582163351564`*^9, 3.7638582415275116`*^9}, {3.7638582983238*^9, 3.763858907503306*^9}, {3.763858941318697*^9, 3.763858956626134*^9}, { 3.7638602435602536`*^9, 3.763860245408451*^9}, {3.7638694636456347`*^9, 3.7638694647177277`*^9}, {3.7638708199536576`*^9, 3.763870829436488*^9}, { 3.763871287170555*^9, 3.7638712876184006`*^9}, {3.763943214376035*^9, 3.7639432984591475`*^9}, {3.763943418832348*^9, 3.7639434335508127`*^9}, { 3.76394347113767*^9, 3.7639435187320576`*^9}, {3.763943585908682*^9, 3.7639436125255404`*^9}, {3.763951722152746*^9, 3.76395172989299*^9}, { 3.7639517863423367`*^9, 3.7639519945900664`*^9}, {3.763952081515512*^9, 3.7639521530710773`*^9}, {3.763952353248129*^9, 3.763952357026309*^9}, { 3.7639524211903834`*^9, 3.7639524243979177`*^9}, {3.7639527174925117`*^9, 3.7639527180252266`*^9}, {3.7641265625745993`*^9, 3.7641265632314167`*^9}, {3.764126605555829*^9, 3.7641266075095396`*^9}, { 3.7641268313964133`*^9, 3.7641268543573804`*^9}, {3.764127044657903*^9, 3.7641270479422092`*^9}, {3.7641271442332697`*^9, 3.7641271469362774`*^9}, {3.764127227626192*^9, 3.7641272592640233`*^9}, { 3.764127335707515*^9, 3.7641273386484756`*^9}, {3.764127429843852*^9, 3.7641274364304185`*^9}, {3.7641275071859307`*^9, 3.764127516803895*^9}, 3.7641276043548007`*^9, {3.7641276925365753`*^9, 3.764127697080591*^9}, 3.764127798472331*^9, 3.764127853631323*^9, 3.764127908496078*^9, { 3.7641280050343323`*^9, 3.764128022046494*^9}, {3.764128128597419*^9, 3.764128154116727*^9}, {3.7641286864636617`*^9, 3.764128701643106*^9}, { 3.7641289910924444`*^9, 3.7641290126680794`*^9}, {3.7641290672285347`*^9, 3.7641290737798567`*^9}, {3.7641325425120363`*^9, 3.764132565390477*^9}, { 3.7641327425004654`*^9, 3.764132750040793*^9}, 3.7641327968340364`*^9, { 3.764133146776842*^9, 3.764133204874522*^9}, {3.7641333488187037`*^9, 3.7641333525577593`*^9}, {3.764413145593136*^9, 3.7644131471236105`*^9}, { 3.764413201645049*^9, 3.7644132349609704`*^9}, {3.764413325008136*^9, 3.7644133748980193`*^9}, {3.7644134113425665`*^9, 3.7644135151187*^9}, { 3.764413554409053*^9, 3.7644136160674934`*^9}, {3.76441371984758*^9, 3.764413730103909*^9}, 3.764419641962368*^9, {3.7644198522879405`*^9, 3.764419879249356*^9}, 3.764419909536559*^9, {3.764419991012162*^9, 3.764420000171088*^9}, {3.7644200798862047`*^9, 3.7644200950961914`*^9}, { 3.7644201529471693`*^9, 3.764420153715966*^9}, {3.764420210346301*^9, 3.764420255343707*^9}, {3.764420296178318*^9, 3.7644203000939393`*^9}, { 3.7644203803359275`*^9, 3.7644203931390867`*^9}, 3.7644204418727274`*^9, { 3.7647259720700207`*^9, 3.7647261047260523`*^9}, {3.7647263483375626`*^9, 3.76472635879602*^9}, 3.764726656736601*^9, {3.764727009127914*^9, 3.764727020100875*^9}, {3.7647270591828785`*^9, 3.7647270819631023`*^9}, { 3.7647272109090505`*^9, 3.764727227846332*^9}, {3.76473247809907*^9, 3.7647324813925114`*^9}, {3.7647349484962797`*^9, 3.7647349979358416`*^9}, {3.7647351097258167`*^9, 3.764735124772463*^9}, { 3.7647352810674453`*^9, 3.7647352901139917`*^9}, {3.7647353746429515`*^9, 3.764735379550926*^9}, {3.7647354596539807`*^9, 3.764735507677454*^9}, { 3.7647355546341*^9, 3.764735728811817*^9}, {3.764735837449795*^9, 3.76473584132898*^9}, {3.76473603649269*^9, 3.7647360592982664`*^9}, { 3.7647360998228803`*^9, 3.76473621551197*^9}, {3.7647362545599003`*^9, 3.764736286430997*^9}, {3.7647364592833533`*^9, 3.764736464019006*^9}, { 3.764736566167658*^9, 3.7647365918958225`*^9}, {3.764764761680134*^9, 3.7647648482473745`*^9}, 3.764764917763693*^9, {3.764764964821686*^9, 3.764765090741813*^9}, {3.7647651742140284`*^9, 3.7647652517335076`*^9}, { 3.764765341266399*^9, 3.7647653614173465`*^9}, 3.764765400284145*^9, { 3.764765691384389*^9, 3.764765708710143*^9}, 3.7647657454275875`*^9, { 3.76476578351686*^9, 3.764765871262255*^9}, {3.7647661045180917`*^9, 3.76476612822571*^9}, {3.7647661964223824`*^9, 3.764766239375331*^9}, { 3.764766330361228*^9, 3.764766338297905*^9}, {3.764767015060799*^9, 3.7647670193029037`*^9}, {3.764767076590926*^9, 3.7647671160277977`*^9}, { 3.7647671493139205`*^9, 3.7647672079236426`*^9}, {3.764767458938404*^9, 3.7647674608323865`*^9}, {3.764810938444873*^9, 3.7648109399353456`*^9}, { 3.7648118616019874`*^9, 3.7648118695079126`*^9}, {3.7648120589477816`*^9, 3.7648124600413237`*^9}, {3.76481250476682*^9, 3.7648125259602103`*^9}, { 3.764812601341893*^9, 3.7648126577763243`*^9}, {3.7648126944039307`*^9, 3.7648128855627623`*^9}, {3.764812924923909*^9, 3.764812926481821*^9}, { 3.764813041485982*^9, 3.764813131254232*^9}, {3.7648134679328885`*^9, 3.7648136479313235`*^9}, {3.7648136917777314`*^9, 3.764813697753367*^9}, { 3.7648137297570653`*^9, 3.764813747862262*^9}, 3.764813784221693*^9, { 3.7648138370678406`*^9, 3.7648141387969923`*^9}, {3.764814321050164*^9, 3.764814422489184*^9}, {3.764814461366684*^9, 3.7648145835728483`*^9}, { 3.764814614769511*^9, 3.7648147525825167`*^9}, {3.764815363375289*^9, 3.7648153644907384`*^9}, {3.764815451671169*^9, 3.7648154601533747`*^9}, { 3.7648175917802963`*^9, 3.7648176401910563`*^9}, {3.765885491237231*^9, 3.765885501131465*^9}, {3.766572999289345*^9, 3.7665729996020145`*^9}, { 3.7665730613126965`*^9, 3.7665730616706066`*^9}, {3.7840103262125545`*^9, 3.7840103546413517`*^9}, {3.784011309725755*^9, 3.7840113197719574`*^9}, { 3.784013374800973*^9, 3.7840133842981763`*^9}, {3.7840238533665447`*^9, 3.78402395932942*^9}, {3.784024091276659*^9, 3.784024112209529*^9}, { 3.7840242793219643`*^9, 3.784024296655184*^9}, {3.7840290670892677`*^9, 3.7840291348388853`*^9}, {3.784029222997594*^9, 3.784029542926179*^9}, { 3.784375172285057*^9, 3.784375319701829*^9}, {3.7843753678421807`*^9, 3.7843753788103914`*^9}, {3.7843754844339557`*^9, 3.784375827494117*^9}, { 3.784375862317687*^9, 3.7843759567563844`*^9}, {3.784376004941759*^9, 3.7843760080157185`*^9}, {3.784376101918992*^9, 3.7843761244332943`*^9}, { 3.784376181191763*^9, 3.7843762145091863`*^9}, {3.7843792489960337`*^9, 3.78437926273014*^9}, {3.7843793293934345`*^9, 3.784379368676588*^9}, { 3.7843796529835215`*^9, 3.7843796858862267`*^9}, {3.784450863324359*^9, 3.7844508986076546`*^9}, {3.7844510208392324`*^9, 3.784451027915551*^9}, { 3.7844511176315613`*^9, 3.7844511673791957`*^9}, {3.784451235055628*^9, 3.78445132575735*^9}, {3.784451995615477*^9, 3.7844520110330954`*^9}, { 3.7844522907551537`*^9, 3.7844523421551*^9}, {3.784700119490345*^9, 3.7847001627913013`*^9}, {3.7847004221290607`*^9, 3.7847004380767317`*^9}, 3.7847007913506136`*^9, {3.784781955129138*^9, 3.784781977787957*^9}, { 3.78488170216677*^9, 3.784881704210422*^9}, 3.784882130557441*^9, { 3.78488220347418*^9, 3.7848822064697027`*^9}, {3.784883393455822*^9, 3.784883458551924*^9}, 3.7848835306495824`*^9, {3.7848836822092113`*^9, 3.7848837303696923`*^9}, 3.7848838199009576`*^9, {3.7848842507527857`*^9, 3.7848842836585226`*^9}, 3.7848843847882996`*^9, {3.784884461405264*^9, 3.7848844645041113`*^9}, {3.784884559404122*^9, 3.7848845656634912`*^9}, { 3.7848852409944844`*^9, 3.7848852740337477`*^9}, {3.7848854548929386`*^9, 3.7848854893046365`*^9}, {3.7848856741783943`*^9, 3.784885691704702*^9}, { 3.784885809660874*^9, 3.784885811424426*^9}, {3.7848860031948376`*^9, 3.784886020570098*^9}, 3.7848861057105627`*^9, {3.7848861627726107`*^9, 3.7848862212876124`*^9}, {3.784886306497995*^9, 3.7848863509322224`*^9}, 3.784886472690192*^9, {3.7848866596243*^9, 3.784886664116289*^9}, { 3.7848866987282944`*^9, 3.7848867077911897`*^9}, {3.78488676128524*^9, 3.7848868667029366`*^9}, {3.7848869381224003`*^9, 3.7848869414281464`*^9}, {3.7848870104508753`*^9, 3.784887039889447*^9}, { 3.7848871795058794`*^9, 3.7848871976746817`*^9}, {3.7848872311446314`*^9, 3.78488724075662*^9}, 3.784887405188785*^9, {3.784887591926689*^9, 3.7848876119305134`*^9}, {3.784887676620901*^9, 3.7848876786672792`*^9}, { 3.78488771054331*^9, 3.784887714354906*^9}, {3.7848877625809546`*^9, 3.7848878103041153`*^9}, 3.7848878862881575`*^9, {3.787717235155089*^9, 3.787717269464238*^9}, {3.7877174592607603`*^9, 3.7877174674038067`*^9}, { 3.7877271032841845`*^9, 3.787727136247201*^9}, 3.787727355369296*^9, 3.7877274973278403`*^9, {3.787727855959008*^9, 3.78772792141208*^9}, 3.787728113487193*^9, {3.7877281704571557`*^9, 3.7877281735077004`*^9}, 3.7877282789827795`*^9, {3.7877286510229864`*^9, 3.787728665729192*^9}, { 3.7877287942225084`*^9, 3.787728807671986*^9}, {3.787729044867985*^9, 3.787729045536916*^9}, {3.787729589732438*^9, 3.7877296062090626`*^9}, { 3.787729794037467*^9, 3.7877297950347877`*^9}, {3.787729855548402*^9, 3.7877299039179935`*^9}, {3.7877300373241186`*^9, 3.787730068136018*^9}, { 3.7877301999859333`*^9, 3.7877302014150777`*^9}, {3.787732033225385*^9, 3.7877320471634016`*^9}, {3.787732077195259*^9, 3.7877320780358667`*^9}, 3.787732189759206*^9, {3.78773231889835*^9, 3.787732327710633*^9}, { 3.7877324857166643`*^9, 3.787732496655479*^9}, {3.7877325848303585`*^9, 3.78773258503596*^9}, {3.7877328504631166`*^9, 3.7877328625892415`*^9}, { 3.7877330254884944`*^9, 3.7877330271019044`*^9}, {3.787733136128061*^9, 3.7877331422258835`*^9}, {3.787733243513567*^9, 3.78773324558677*^9}, 3.787733310555999*^9, 3.7877334085329347`*^9, {3.7877337955932293`*^9, 3.7877337970498257`*^9}, {3.787733867727028*^9, 3.7877338687324905`*^9}, { 3.7877352224369583`*^9, 3.787735224161746*^9}, {3.787735343322833*^9, 3.787735348772827*^9}, {3.787735422704711*^9, 3.7877354268945775`*^9}, { 3.7877355100355635`*^9, 3.787735514671461*^9}, {3.7877356541994534`*^9, 3.7877356632141013`*^9}, 3.7877357913476543`*^9, 3.787736261837074*^9, { 3.7882542159043374`*^9, 3.7882542747998285`*^9}, {3.788254310967661*^9, 3.788254318430212*^9}, {3.788254585790197*^9, 3.7882545888318524`*^9}, { 3.7882547349987383`*^9, 3.788254735940298*^9}, 3.788254830063775*^9, 3.7882549155286837`*^9, {3.7882550121437798`*^9, 3.788255037735396*^9}, { 3.7882551764404287`*^9, 3.78825518352113*^9}, {3.7882552540030313`*^9, 3.788255290224329*^9}, {3.7882553843544893`*^9, 3.788255423248046*^9}, { 3.78825567982127*^9, 3.7882556852479534`*^9}, {3.7882557908576803`*^9, 3.7882558029800806`*^9}, {3.7882560240494256`*^9, 3.7882560388846164`*^9}, 3.788256102343512*^9, {3.788256161397396*^9, 3.7882561626372194`*^9}, { 3.7882562304311895`*^9, 3.78825629590362*^9}, {3.7882563614677362`*^9, 3.7882563620189795`*^9}, {3.7882564138122153`*^9, 3.7882564294158382`*^9}, {3.788256467457189*^9, 3.7882564889521217`*^9}, { 3.7882565883311844`*^9, 3.788256591497148*^9}, {3.7882568409513097`*^9, 3.7882568724526567`*^9}, {3.788256965258837*^9, 3.788256966444976*^9}, { 3.7882570073831463`*^9, 3.7882570497349973`*^9}, {3.7882570992487097`*^9, 3.788257144206352*^9}, {3.78825721252205*^9, 3.788257307277931*^9}, { 3.788257350410209*^9, 3.7882573617262745`*^9}, {3.788257424936472*^9, 3.788257434118204*^9}, {3.788276311330668*^9, 3.788276311647092*^9}, { 3.7882765465512347`*^9, 3.788276608568333*^9}, {3.7882767715851693`*^9, 3.7882768045752783`*^9}, {3.7882769342607436`*^9, 3.7882769409894867`*^9}, {3.7882770202208567`*^9, 3.7882770424485188`*^9}, {3.7882770760040703`*^9, 3.788277077341468*^9}, { 3.788277147336176*^9, 3.788277150397852*^9}, {3.7882772069909*^9, 3.7882772101572385`*^9}, {3.7882772503366175`*^9, 3.7882772773759403`*^9}, {3.7882773922958755`*^9, 3.7882773927832017`*^9}, {3.788277450684473*^9, 3.788277482126852*^9}, { 3.78827754293396*^9, 3.788277545027956*^9}, {3.7883214550230436`*^9, 3.7883214742097826`*^9}, {3.788321520104019*^9, 3.788321685390153*^9}, { 3.788321717307153*^9, 3.788321801831746*^9}, {3.788321836768508*^9, 3.788322037754008*^9}, {3.7883220686363816`*^9, 3.788322220085001*^9}, { 3.7883255906192427`*^9, 3.788325646609389*^9}, {3.7883257976991563`*^9, 3.788325804097658*^9}, {3.788325969279187*^9, 3.7883259830028267`*^9}, { 3.788326975877249*^9, 3.788326979070017*^9}, {3.788328539286415*^9, 3.788328618410488*^9}, {3.788328648595448*^9, 3.788328762662589*^9}, { 3.7883288060890923`*^9, 3.7883288805716724`*^9}, {3.7883319188300047`*^9, 3.78833193230753*^9}, {3.7883321144947567`*^9, 3.788332115050151*^9}, { 3.7883333680456443`*^9, 3.7883333686272163`*^9}, 3.7883336421611414`*^9, { 3.788333691323177*^9, 3.7883336916362*^9}, {3.788333797629262*^9, 3.7883338348662343`*^9}, {3.7883339555470386`*^9, 3.7883339660305166`*^9}, {3.7883340291758356`*^9, 3.788334031484354*^9}, { 3.788334368484807*^9, 3.7883343918754945`*^9}, {3.7883345963739557`*^9, 3.788334645315611*^9}, {3.788411405608647*^9, 3.788411409092114*^9}, { 3.7884115644712825`*^9, 3.7884115911998663`*^9}, {3.7884116673998833`*^9, 3.788411758799066*^9}, {3.788411985303985*^9, 3.788412002701314*^9}, { 3.78841218266156*^9, 3.788412217652734*^9}, {3.788412679618697*^9, 3.78841268296084*^9}, {3.788412968920223*^9, 3.7884129782039633`*^9}, { 3.7884155241723013`*^9, 3.7884155243798914`*^9}, 3.7884156619519596`*^9, { 3.7884162343262696`*^9, 3.788416236013459*^9}, {3.789022054245319*^9, 3.7890221116154556`*^9}, {3.7890222001685014`*^9, 3.789022205961149*^9}, { 3.789094077050009*^9, 3.7890940781167436`*^9}, {3.7890941254883175`*^9, 3.7890942919861226`*^9}, {3.789094340508856*^9, 3.789094543716852*^9}, { 3.789094583794143*^9, 3.7890947278803444`*^9}, {3.7890947714417076`*^9, 3.7890948342626343`*^9}, {3.789095197615344*^9, 3.789095215073329*^9}, { 3.789095256390032*^9, 3.78909525710861*^9}, {3.7890954241290827`*^9, 3.78909583987399*^9}, {3.789096056032333*^9, 3.7890960602768464`*^9}, { 3.7890960928429904`*^9, 3.789096098149865*^9}, {3.789096721918685*^9, 3.789096734998893*^9}, {3.7890967741973257`*^9, 3.78909683859006*^9}, { 3.789096947653244*^9, 3.789097122315098*^9}, {3.7890971528708224`*^9, 3.789097530683948*^9}, {3.7890975852885656`*^9, 3.7890975882562447`*^9}, { 3.7890976430709224`*^9, 3.789097656213524*^9}, {3.789107592314107*^9, 3.7891076537760305`*^9}, {3.789107685160589*^9, 3.789107760590632*^9}, { 3.7891078105008087`*^9, 3.789107846610609*^9}, {3.789107989236459*^9, 3.7891080001561875`*^9}, {3.7891082032172785`*^9, 3.7891082064574785`*^9}, {3.7891083013630204`*^9, 3.789108444864075*^9}, { 3.7891084751958127`*^9, 3.7891085010044174`*^9}, {3.7891085322441816`*^9, 3.7891085353767447`*^9}, {3.789108620037199*^9, 3.789108662297584*^9}, 3.7891087252471294`*^9, {3.789108773507248*^9, 3.7891088501491203`*^9}, { 3.7891088829987*^9, 3.789108918319019*^9}, {3.7891089606286983`*^9, 3.7891090044788837`*^9}, {3.789109048556943*^9, 3.7891091177554493`*^9}, { 3.7891091628149347`*^9, 3.7891092922346783`*^9}, {3.789109382870388*^9, 3.789109402625166*^9}, {3.7891111380334797`*^9, 3.7891113582877145`*^9}, { 3.789111396694514*^9, 3.7891114221541777`*^9}, {3.7891114539845037`*^9, 3.7891114952359962`*^9}, {3.789112929457416*^9, 3.7891129318274393`*^9}, { 3.789112963290578*^9, 3.7891131302196255`*^9}, {3.789113202949188*^9, 3.789113203379569*^9}, {3.7891144371217365`*^9, 3.789114518411393*^9}, { 3.789114638487608*^9, 3.78911468069436*^9}, {3.789114763918976*^9, 3.789114777923211*^9}, {3.789114809301983*^9, 3.7891148392057247`*^9}, { 3.7891148923150015`*^9, 3.789114904054755*^9}, {3.7891149560740595`*^9, 3.7891150071774015`*^9}, {3.789115109642312*^9, 3.7891151147637*^9}, { 3.7891185439211864`*^9, 3.789118561569729*^9}, {3.7891187834106455`*^9, 3.7891187854068985`*^9}, {3.7891188764873776`*^9, 3.7891188767373095`*^9}, {3.789121799028477*^9, 3.789121806719482*^9}, { 3.7891222627163153`*^9, 3.7891222774782734`*^9}, {3.7891223914541044`*^9, 3.7891224006004095`*^9}, {3.789122431773783*^9, 3.7891224422816577`*^9}, { 3.7891224731160736`*^9, 3.789122501042121*^9}, {3.7891226653529224`*^9, 3.7891226664045706`*^9}, 3.789122819901965*^9, {3.789122893844426*^9, 3.7891229543768473`*^9}, {3.7891229964274464`*^9, 3.7891231044294157`*^9}, {3.789123228485856*^9, 3.789123374714591*^9}, { 3.789124218156231*^9, 3.789124220106046*^9}, {3.789124254593116*^9, 3.7891242583777695`*^9}, {3.7891243156014767`*^9, 3.789124326373148*^9}, { 3.789125154499303*^9, 3.7891252228031907`*^9}, {3.8200454708911095`*^9, 3.8200454840718527`*^9}, {3.8509666497276897`*^9, 3.8509666516620097`*^9}, {3.850966717721876*^9, 3.8509667189933705`*^9}, 3.8509667763101106`*^9, {3.8509668228841643`*^9, 3.850966844061469*^9}, { 3.8509668794855585`*^9, 3.8509669485542307`*^9}, {3.850966982527851*^9, 3.8509670397380314`*^9}}, CellLabel-> "In[199]:=",ExpressionUUID->"00aec84a-89ef-40e4-a783-0877f479d20c"] }, Closed]], Cell[CellGroupData[{ Cell["PLATE ELEMENT (nonl) defs ", "Subsection", CellChangeTimes->{{3.6302475626780834`*^9, 3.6302475636452847`*^9}, { 3.6303896204112215`*^9, 3.630389621175623*^9}, {3.7658855359334097`*^9, 3.7658855563942738`*^9}, {3.7882511594490995`*^9, 3.788251160663724*^9}, { 3.8508856098994403`*^9, 3.8508856108810315`*^9}},ExpressionUUID->"fc5dac56-bcbb-46bb-a381-\ 801edad5d733"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"MEC", "-", "E1050"}], "|", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "n\[Alpha]", ",", "n\[Beta]", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "NN", ",", "mat", ",", "MM", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "r\[Gamma]", ",", "rn", ",", "jac", ",", "h\[Alpha]", ",", "e\[Alpha]", ",", "h\[Beta]", ",", "h\[Gamma]", ",", "e\[Beta]", ",", "en", ",", "e\[Gamma]", ",", "FF", ",", "\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]", ",", "edg", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "\[Pi]u", ",", "\[Pi]v", ",", "\[Pi]w", ",", "\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]", ",", "f\[Alpha]", ",", "f\[Gamma]", ",", "fn", ",", "m\[Alpha]", ",", "m\[Gamma]", ",", "mn", ",", "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]", ",", "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]", ",", "\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]", ",", "GG", ",", "N\[Alpha]\[Alpha]", ",", "N\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Gamma]", ",", "N\[Gamma]\[Alpha]", ",", "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]", ",", "Q\[Alpha]", ",", "Q\[Gamma]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wmap", ",", "AA"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"mat", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]", "=", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}]}], ";", " ", RowBox[{"r\[Beta]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Norm", "[", "r\[Beta]", "]"}]}], ";", " ", RowBox[{"h\[Alpha]", "=", RowBox[{"Norm", "[", "r\[Alpha]", "]"}]}], ";", RowBox[{"jac", "=", RowBox[{"Norm", "[", RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Alpha]", "=", RowBox[{"r\[Alpha]", "/", "h\[Alpha]"}]}], ";", RowBox[{"e\[Beta]", "=", RowBox[{"r\[Beta]", "/", "h\[Beta]"}]}], ";", " ", RowBox[{"en", "=", RowBox[{ RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], " ", "/", "jac"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r\[Gamma]", "=", RowBox[{"r\[Beta]", "-", RowBox[{ RowBox[{"(", RowBox[{"r\[Beta]", ".", "e\[Alpha]"}], ")"}], " ", "e\[Alpha]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Gamma]", "=", RowBox[{"Norm", "[", "r\[Gamma]", "]"}]}], ";", RowBox[{"e\[Gamma]", "=", RowBox[{"r\[Gamma]", "/", "h\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", "e\[Gamma]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]"}], "}"}], "=", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Alpha]"}], ",", RowBox[{"r\[Alpha]", ".", "r\[Beta]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Beta]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Beta]"}]}], "}"}]}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Gamma]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Gamma]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"edg", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Sort", "[", "#", "]"}], "&"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "projection", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Pi]\[Phi]", "=", RowBox[{ RowBox[{ RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], "/", "60"}], "+", " ", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Theta]", "=", RowBox[{ RowBox[{ RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], "/", "60"}], "+", " ", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"continuous", " ", "displacement"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Pi]w", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]"}], "}"}], "=", RowBox[{ RowBox[{"FF", "[", RowBox[{"[", RowBox[{ RowBox[{"1", ";;", "2"}], ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]"}], "}"}], "=", RowBox[{ RowBox[{"FF", "[", RowBox[{"[", RowBox[{ RowBox[{"1", ";;", "2"}], ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}], ".", RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"fn", "=", RowBox[{ RowBox[{"FF", "[", RowBox[{"[", "3", "]"}], "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"strain", " ", "measures", " ", "with", " ", "non"}], "-", RowBox[{"symmetric", " ", "\[Epsilon]"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}]}]}], ")"}]}], "/", "h\[Gamma]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", " ", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Theta]"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], "/", "h\[Alpha]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], "+", "\[Pi]\[Theta]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", "\[Pi]\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Alpha]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Gamma]\[Gamma]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Gamma]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Gamma]\[Gamma]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", " ", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}], "*", "\[Kappa]\[Alpha]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{ RowBox[{"5", "/", "6"}], " ", "*", "GG", "*", "tt", "*", "\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Gamma]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]"}], "}"}]}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Gamma]"}], "}"}]}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "w", "]"}], "*", "fn"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wmap", "=", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "/", "100000"}], "*", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]w", "-", "w"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]w", "-", "w"}], ")"}]}], ")"}], "*", "tt", "*", RowBox[{"EE", "/", "jac"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI3", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wmap"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{ 3.4426474258030453`*^9, {3.4444401255942*^9, 3.4444401388073997`*^9}, { 3.4444401803034*^9, 3.4444401844062*^9}, 3.4444402418922*^9, { 3.4444402805022*^9, 3.4444403134026003`*^9}, {3.4444403443062*^9, 3.4444404484049997`*^9}, {3.444483267101*^9, 3.444483267335*^9}, { 3.4444833136046*^9, 3.4444835622998*^9}, {3.4444836421094*^9, 3.4444837777981997`*^9}, {3.444483920429*^9, 3.4444839412237997`*^9}, 3.4444842905546*^9, {3.4444843207406*^9, 3.4444844162282*^9}, { 3.4444844465078*^9, 3.4444844624354*^9}, {3.4444845255998*^9, 3.4444845894505997`*^9}, {3.4444846290746*^9, 3.444484933025*^9}, { 3.4444849790917997`*^9, 3.4444851148742*^9}, {3.444534936054*^9, 3.4445349675348*^9}, {3.4445355821731997`*^9, 3.44453585174*^9}, { 3.4445372162198*^9, 3.4445372264378*^9}, 3.444537384731*^9, { 3.4445377585382*^9, 3.4445377605818*^9}, {3.4445379733658*^9, 3.4445379736934*^9}, {3.4445380176762*^9, 3.444538032777*^9}, { 3.4445381079222*^9, 3.4445381581386003`*^9}, {3.4445382726456003`*^9, 3.4445382910067997`*^9}, {3.4445383401312*^9, 3.4445383475880003`*^9}, { 3.444538438458*^9, 3.4445384464608*^9}, {3.4445385680783997`*^9, 3.4445385687648*^9}, {3.4445389411991997`*^9, 3.4445389431024*^9}, { 3.444539746605*^9, 3.4445397807846003`*^9}, {3.4445408839765997`*^9, 3.4445409234133997`*^9}, {3.4445409681698*^9, 3.4445409932702*^9}, { 3.4445415452906*^9, 3.4445415706717997`*^9}, {3.4445416647242002`*^9, 3.4445416909477997`*^9}, {3.4445417660150003`*^9, 3.444541788557*^9}, { 3.4445420906977997`*^9, 3.444542104847*^9}, {3.4445421885878*^9, 3.4445421941414003`*^9}, {3.4445422252166*^9, 3.4445422386014*^9}, { 3.444542280425*^9, 3.4445423014538*^9}, {3.444542455769*^9, 3.4445424578282003`*^9}, {3.4445431739214*^9, 3.444543175809*^9}, { 3.4445647020962*^9, 3.4445648405618*^9}, {3.4445648825414*^9, 3.4445648858486*^9}, {3.4445649382646*^9, 3.4445651882702*^9}, { 3.4446164822206*^9, 3.4446165344494*^9}, {3.4446166121842003`*^9, 3.4446166738822002`*^9}, {3.4446167223046*^9, 3.4446168047974*^9}, { 3.444616843033*^9, 3.444616906447*^9}, {3.4446444694708*^9, 3.4446444700948*^9}, {3.4446477738310003`*^9, 3.4446477939862003`*^9}, { 3.4446478467298*^9, 3.4446478681018*^9}, 3.4446480456142*^9, { 3.4446487557418003`*^9, 3.4446487636198*^9}, 3.4446488179974003`*^9, { 3.4446488971205997`*^9, 3.4446489152478*^9}, {3.4446490003458*^9, 3.4446490008294*^9}, {3.4447042728942003`*^9, 3.4447042751562*^9}, { 3.4447044703278*^9, 3.4447044865362*^9}, 3.4447046475282*^9, 3.4447047993786*^9, {3.444704908329*^9, 3.4447049292642*^9}, { 3.4447049861926003`*^9, 3.4447049877214003`*^9}, {3.4447050279296*^9, 3.4447050419695997`*^9}, {3.4447053486656*^9, 3.4447053739376*^9}, 3.4447054561963997`*^9, 3.44470561612*^9, {3.4472133996876*^9, 3.4472134108571997`*^9}, {3.4472134470179996`*^9, 3.4472134648332*^9}, { 3.4472135032872*^9, 3.4472135245344*^9}, {3.4472136963059998`*^9, 3.4472137794384003`*^9}, {3.4472138235708*^9, 3.4472138388900003`*^9}, { 3.4472139099792*^9, 3.4472141367096*^9}, {3.447214202682*^9, 3.4472142975924*^9}, {3.4472144187732*^9, 3.4472145910284*^9}, { 3.4472146560492*^9, 3.4472147023968*^9}, {3.447214803594*^9, 3.4472148728736*^9}, {3.4472149156956*^9, 3.447214940484*^9}, { 3.447216227284*^9, 3.4472162419948*^9}, {3.4472163068908*^9, 3.4472163720832*^9}, {3.4472164665880003`*^9, 3.447216530392*^9}, { 3.4472166237268*^9, 3.4472167058452*^9}, 3.4472167362808*^9, { 3.4472171394658003`*^9, 3.4472171532874002`*^9}, {3.4472172028993998`*^9, 3.4472172216661997`*^9}, {3.4472172524606*^9, 3.4472172690278*^9}, { 3.4472173209133997`*^9, 3.4472173334245996`*^9}, {3.4472173920846*^9, 3.447217404861*^9}, {3.4472179572548*^9, 3.4472180351456003`*^9}, { 3.4472509764091997`*^9, 3.4472511017396*^9}, {3.4473910422216*^9, 3.4473912901524*^9}, 3.4473918688344*^9, {3.447392021185*^9, 3.4473920346633997`*^9}, {3.4473921383304*^9, 3.4473921479088*^9}, { 3.4473923024112*^9, 3.4473923734379997`*^9}, {3.4473928098168*^9, 3.4473928648691998`*^9}, {3.4473931872432003`*^9, 3.4473932461800003`*^9}, {3.4473933026675997`*^9, 3.4473934579812*^9}, { 3.4473935755271997`*^9, 3.447393742572*^9}, {3.4473939032676*^9, 3.4473939384144*^9}, {3.447395257644*^9, 3.4473953141628*^9}, { 3.4473954231132*^9, 3.4473954756384*^9}, {3.4473955348716*^9, 3.4473955723272*^9}, {3.447395648502*^9, 3.4473957588876*^9}, { 3.4473957903996*^9, 3.4473958488372*^9}, 3.4473962894154*^9, { 3.447396350817*^9, 3.447396352611*^9}, {3.4474625379146*^9, 3.4474625637326*^9}, {3.558360651728078*^9, 3.558360652102478*^9}, { 3.5619791319820857`*^9, 3.561979135788492*^9}, 3.561979369382504*^9, { 3.5619794930439215`*^9, 3.5619795010155354`*^9}, {3.561979569218855*^9, 3.56197960614412*^9}, {3.5619797417551584`*^9, 3.5619797448751636`*^9}, { 3.618719065033702*^9, 3.618719075426296*^9}, {3.6187194011669273`*^9, 3.6187194449454317`*^9}, {3.6187196998040085`*^9, 3.6187197102436056`*^9}, {3.618719902254588*^9, 3.6187199711455283`*^9}, { 3.618722365406472*^9, 3.6187225412555304`*^9}, {3.6187226885009522`*^9, 3.6187227109872384`*^9}, {3.618722756922866*^9, 3.6187231317203026`*^9}, { 3.618723424250035*^9, 3.6187234267291765`*^9}, {3.6187235105259695`*^9, 3.6187236491028957`*^9}, {3.618723691580325*^9, 3.618723745975436*^9}, { 3.618723778837316*^9, 3.6187238310002995`*^9}, {3.6187239055875654`*^9, 3.618723940035536*^9}, {3.6187239782667227`*^9, 3.6187240219352207`*^9}, { 3.618724166762504*^9, 3.618724177411113*^9}, {3.618729321696159*^9, 3.618729328067523*^9}, 3.618729374058154*^9, {3.6187294379838104`*^9, 3.618729708464281*^9}, {3.6187297631904106`*^9, 3.618729773195983*^9}, { 3.618729822648812*^9, 3.6187299321490746`*^9}, {3.618729984399063*^9, 3.61873000654133*^9}, {3.6187300746012225`*^9, 3.6187300860458775`*^9}, { 3.618731390835507*^9, 3.6187315116174154`*^9}, {3.618731747324897*^9, 3.6187318214091344`*^9}, {3.6187318769243097`*^9, 3.618732065297084*^9}, { 3.6187321012351394`*^9, 3.618732157420353*^9}, {3.618732188384124*^9, 3.6187322435542793`*^9}, {3.6187322786112847`*^9, 3.6187325478446836`*^9}, {3.6187325819856367`*^9, 3.6187326817653437`*^9}, {3.618732810863728*^9, 3.61873282594359*^9}, { 3.6187336474335766`*^9, 3.618733754678711*^9}, {3.618733827497876*^9, 3.61873396201257*^9}, {3.6187342020362988`*^9, 3.618734236455267*^9}, 3.618734298201799*^9, {3.618734712498495*^9, 3.618734712716508*^9}, 3.6187347739640107`*^9, {3.618738817361748*^9, 3.6187388333816643`*^9}, { 3.6187391349349127`*^9, 3.6187391457955337`*^9}, {3.618739376900752*^9, 3.618739397023903*^9}, {3.618739528394417*^9, 3.618739534809784*^9}, { 3.618739972366811*^9, 3.61873997340687*^9}, {3.6187400416617737`*^9, 3.618740043022852*^9}, {3.6187400971579485`*^9, 3.618740107902563*^9}, { 3.6187401713671927`*^9, 3.6187401723312483`*^9}, {3.6187402613443394`*^9, 3.618740268819767*^9}, {3.6187403697625403`*^9, 3.6187404057615995`*^9}, { 3.618740488277319*^9, 3.618740516244919*^9}, {3.618740647782442*^9, 3.6187406551668644`*^9}, 3.6187407823021364`*^9, {3.6187418050786357`*^9, 3.618741805749674*^9}, {3.6187418557605343`*^9, 3.6187419895921893`*^9}, { 3.618742022944097*^9, 3.61874204379729*^9}, {3.6187420836395683`*^9, 3.618742103384698*^9}, {3.620462440882641*^9, 3.6204624460519366`*^9}, { 3.6204624990259666`*^9, 3.620462576450395*^9}, {3.620463682857678*^9, 3.620463713336421*^9}, 3.6204637901188126`*^9, {3.620464238835478*^9, 3.62046424411378*^9}, 3.628912429385081*^9, {3.6289135207155013`*^9, 3.6289135210805225`*^9}, 3.6289497746958513`*^9, 3.6289498371774254`*^9, { 3.62894988410911*^9, 3.6289500319795675`*^9}, {3.6289501333883677`*^9, 3.628950183744248*^9}, {3.6289503323017445`*^9, 3.628950390181055*^9}, { 3.6289505050536256`*^9, 3.6289505113579865`*^9}, {3.62895070863527*^9, 3.6289507095043197`*^9}, {3.628951013180689*^9, 3.62895101407374*^9}, { 3.629190743153632*^9, 3.629190816645361*^9}, {3.6291909709608326`*^9, 3.629190981678051*^9}, {3.629191034624544*^9, 3.6291910410049553`*^9}, { 3.6293846391370816`*^9, 3.629384641102685*^9}, {3.6294628543371735`*^9, 3.629462867097191*^9}, {3.629468063172048*^9, 3.6294681151669397`*^9}, { 3.6295205836757097`*^9, 3.6295206295085897`*^9}, {3.6295206788826766`*^9, 3.6295207067911253`*^9}, {3.6295207408927855`*^9, 3.629520753700408*^9}, { 3.629521020590745*^9, 3.6295210354395943`*^9}, {3.6295211107369013`*^9, 3.62952114882508*^9}, {3.6295212327348795`*^9, 3.6295212477237363`*^9}, { 3.6295213424816394`*^9, 3.629521343230441*^9}, {3.6295215363119802`*^9, 3.6295216753550243`*^9}, {3.629521922272258*^9, 3.6295219939855833`*^9}, { 3.6295220298188467`*^9, 3.629522446058778*^9}, {3.629522499348471*^9, 3.629522604352256*^9}, {3.629522755188921*^9, 3.62952288580795*^9}, { 3.629522918084407*^9, 3.6295233421087513`*^9}, {3.6295233808436193`*^9, 3.629523390936837*^9}, {3.629523424274096*^9, 3.6295234533369465`*^9}, { 3.6295235190130625`*^9, 3.629523521680667*^9}, 3.6295235894315863`*^9, { 3.6295237270706277`*^9, 3.629523799454755*^9}, {3.6295238514808464`*^9, 3.629523883460902*^9}, {3.6295239376085978`*^9, 3.6295239442386093`*^9}, { 3.6295241089904985`*^9, 3.629524177537019*^9}, 3.629524211888279*^9, { 3.629524277423994*^9, 3.629524396904604*^9}, {3.6295244794839497`*^9, 3.6295246248450055`*^9}, 3.629524657090262*^9, {3.6295259599109507`*^9, 3.629526013465844*^9}, {3.6295261092188125`*^9, 3.629526201414974*^9}, 3.6295263436092243`*^9, {3.6295263910333076`*^9, 3.629526583303645*^9}, { 3.629526616672104*^9, 3.629526647653758*^9}, {3.629526687558628*^9, 3.629526744888729*^9}, {3.629526804075233*^9, 3.6295268598453307`*^9}, { 3.6295269393898706`*^9, 3.6295269586559043`*^9}, {3.6295271490074387`*^9, 3.6295272149019547`*^9}, {3.6295272553684254`*^9, 3.6295272827620735`*^9}, {3.6295274137087035`*^9, 3.6295274761244135`*^9}, {3.6295275252801*^9, 3.6295279912529182`*^9}, { 3.6295281572216096`*^9, 3.629528160435215*^9}, {3.6295282905550437`*^9, 3.6295284308616905`*^9}, 3.6295285402022824`*^9, {3.629528582088356*^9, 3.629528616798417*^9}, {3.6295287666834803`*^9, 3.6295290316343455`*^9}, { 3.629529086515242*^9, 3.629529118432898*^9}, {3.6295291548121614`*^9, 3.629529292794404*^9}, {3.6295293426208916`*^9, 3.6295293491261034`*^9}, { 3.629529420699029*^9, 3.629529571535694*^9}, {3.6295296539506383`*^9, 3.629529656103442*^9}, {3.6295296894407005`*^9, 3.629529692295506*^9}, { 3.6295297445555973`*^9, 3.629529766426836*^9}, {3.6295298053333044`*^9, 3.6295298209489317`*^9}, {3.6295308380551186`*^9, 3.6295308386635194`*^9}, {3.629532377840223*^9, 3.6295323811630287`*^9}, { 3.629532480020402*^9, 3.629532482454006*^9}, {3.629532520720874*^9, 3.629532564619351*^9}, {3.62953259842461*^9, 3.6295326002654133`*^9}, { 3.6295326327758703`*^9, 3.6295326715107384`*^9}, {3.629532742428463*^9, 3.6295328288058147`*^9}, {3.6295329692184625`*^9, 3.6295330530062094`*^9}, {3.6295331824396367`*^9, 3.629533193562456*^9}, 3.6295350321720915`*^9, 3.629535158485513*^9, {3.629535245471266*^9, 3.6295352687465067`*^9}, {3.62953541293756*^9, 3.629535446384019*^9}, { 3.6295355043381205`*^9, 3.6295355262249594`*^9}, {3.629543790136781*^9, 3.629543791181983*^9}, {3.629543871350524*^9, 3.629544001673153*^9}, { 3.6295446682009234`*^9, 3.629544668466124*^9}, {3.6296010216162376`*^9, 3.6296010236442413`*^9}, {3.629601079336339*^9, 3.6296010902875586`*^9}, 3.6296011425476503`*^9, {3.6296043522397404`*^9, 3.629604399031022*^9}, { 3.629623884428093*^9, 3.629623914723346*^9}, {3.6296239662190366`*^9, 3.6296239738006496`*^9}, {3.6296240514731865`*^9, 3.6296240920176573`*^9}, {3.629624125947717*^9, 3.629624369432945*^9}, { 3.6296256512247963`*^9, 3.6296256817072496`*^9}, {3.6296260472626915`*^9, 3.629626047434292*^9}, {3.629628055568204*^9, 3.629628056098605*^9}, { 3.6296280911206665`*^9, 3.6296281088266973`*^9}, {3.6296281406819534`*^9, 3.629628273032586*^9}, {3.629628378831972*^9, 3.6296283814995766`*^9}, { 3.629628459562114*^9, 3.629628466379326*^9}, {3.629628519419419*^9, 3.6296285390754533`*^9}, {3.629633008133008*^9, 3.629633008835009*^9}, { 3.6296337764967575`*^9, 3.6296338344040594`*^9}, {3.6296342997684765`*^9, 3.629634432150309*^9}, {3.629634494035618*^9, 3.6296345320060844`*^9}, { 3.629634594499794*^9, 3.629634812182576*^9}, {3.6296348599810605`*^9, 3.6296348746918864`*^9}, {3.6296349071867433`*^9, 3.629635023172947*^9}, 3.6296350995818815`*^9, {3.6296363797201295`*^9, 3.6296363868961425`*^9}, { 3.629636462025874*^9, 3.6296364833355117`*^9}, {3.629636555922439*^9, 3.62963656780966*^9}, {3.629636770469616*^9, 3.629636774151222*^9}, { 3.6296369192782774`*^9, 3.6296369318830996`*^9}, {3.629637058539722*^9, 3.6296370719401455`*^9}, {3.629637278172508*^9, 3.629637286814923*^9}, { 3.6296376418091464`*^9, 3.629637662385583*^9}, {3.629637773551378*^9, 3.629637795360216*^9}, {3.6296390041751394`*^9, 3.629639039571602*^9}, 3.6296393829750047`*^9, {3.6296395546065063`*^9, 3.6296395649961243`*^9}, { 3.62964113386068*^9, 3.6296412507048855`*^9}, {3.629641303167777*^9, 3.629641313744596*^9}, {3.6296416285116315`*^9, 3.629641628886032*^9}, { 3.6296416658736973`*^9, 3.6296416815049243`*^9}, 3.6296417376338234`*^9, { 3.6296855551269727`*^9, 3.6296855804270077`*^9}, {3.6297079065796247`*^9, 3.6297079070476255`*^9}, {3.6297080850439377`*^9, 3.629708135728427*^9}, { 3.6297083496516027`*^9, 3.6297084025512953`*^9}, {3.629708781767563*^9, 3.629708790940379*^9}, {3.6297089402482414`*^9, 3.6297089618542795`*^9}, { 3.6297105345398417`*^9, 3.629710538580249*^9}, {3.6297107810514746`*^9, 3.6297107850138817`*^9}, {3.6297109100481014`*^9, 3.629710915710911*^9}, { 3.629711201534613*^9, 3.629711204311418*^9}, {3.629711236307074*^9, 3.6297115007275386`*^9}, {3.6297115377464037`*^9, 3.6297115441112146`*^9}, 3.6297116025645175`*^9, {3.6298716505389357`*^9, 3.629871851841689*^9}, { 3.62987837458679*^9, 3.629878383510006*^9}, {3.6298784402629056`*^9, 3.629878447345318*^9}, {3.6298785221786494`*^9, 3.6298786580236883`*^9}, { 3.629878689613744*^9, 3.629878737147027*^9}, 3.629878783853509*^9, { 3.629878832322794*^9, 3.6298789171723433`*^9}, {3.6298802128122005`*^9, 3.6298802929723125`*^9}, 3.6298813644148126`*^9, {3.629882428887303*^9, 3.629882435887313*^9}, {3.6298986251827383`*^9, 3.6298988530367384`*^9}, { 3.6298989036744275`*^9, 3.6298989486493063`*^9}, {3.629899016868226*^9, 3.6298991622448816`*^9}, {3.6298997154530535`*^9, 3.629899740147897*^9}, { 3.6298998248560457`*^9, 3.629899978048314*^9}, {3.6299000396372223`*^9, 3.6299001557638264`*^9}, {3.6299001966826982`*^9, 3.6299002595352087`*^9}, 3.6299005011236343`*^9, {3.6299005468317146`*^9, 3.629900567642151*^9}, { 3.629900887676713*^9, 3.629900990153293*^9}, {3.6299011689220085`*^9, 3.6299012295125146`*^9}, {3.6299013754039707`*^9, 3.6299014166036434`*^9}, 3.6299014589733176`*^9, {3.6299015096734066`*^9, 3.629901588765546*^9}, { 3.629901662569275*^9, 3.6299016974665365`*^9}, {3.629901952339784*^9, 3.6299019599057975`*^9}, 3.6299020306051216`*^9, {3.6299022330934772`*^9, 3.6299022682559395`*^9}, {3.6299023020455985`*^9, 3.629902332808852*^9}, { 3.6299024532566643`*^9, 3.629902462850681*^9}, {3.629949880225117*^9, 3.6299498807867184`*^9}, {3.6299503101150723`*^9, 3.6299503156998825`*^9}, {3.629950355058751*^9, 3.629950498937804*^9}, { 3.6299555415202007`*^9, 3.6299555507086167`*^9}, {3.6299556061667137`*^9, 3.6299557553497763`*^9}, {3.629955788499834*^9, 3.6299558948608212`*^9}, { 3.629956042764681*^9, 3.629956043809883*^9}, {3.6299560914211664`*^9, 3.6299561017327843`*^9}, 3.629956145849662*^9, {3.6299584813821354`*^9, 3.6299585082765827`*^9}, 3.6299585652946825`*^9, {3.629958616587573*^9, 3.6299586356508064`*^9}, {3.629958715073346*^9, 3.6299588186419287`*^9}, { 3.629958857454797*^9, 3.629958927249319*^9}, {3.629959427994599*^9, 3.629959494669116*^9}, {3.6299595293323765`*^9, 3.6299596037913074`*^9}, { 3.62995966795422*^9, 3.62995967360143*^9}, {3.6299597835972233`*^9, 3.6299597841120243`*^9}, {3.629959826622099*^9, 3.629959862533362*^9}, { 3.6299599051682367`*^9, 3.6299599235918694`*^9}, 3.629959979939168*^9, { 3.6299601345354395`*^9, 3.62996014612626*^9}, 3.6299601769831142`*^9, { 3.629960253142448*^9, 3.629960269538077*^9}, {3.6299603041701374`*^9, 3.6299603078205442`*^9}, {3.6299604300467587`*^9, 3.629960435491168*^9}, { 3.6299605300585346`*^9, 3.6299605636609936`*^9}, {3.6299606195870914`*^9, 3.6299606581971593`*^9}, {3.629960824228251*^9, 3.6299608755367413`*^9}, { 3.629960906658796*^9, 3.6299609978409557`*^9}, {3.6299610312250147`*^9, 3.629961070646284*^9}, {3.629961135698398*^9, 3.6299611643088484`*^9}, { 3.6299720458358483`*^9, 3.6299721791536827`*^9}, {3.6299722439717965`*^9, 3.629972300007095*^9}, {3.6299723670872126`*^9, 3.6299723937008595`*^9}, { 3.629972457801372*^9, 3.6299724710613956`*^9}, {3.629972740193068*^9, 3.6299728251196175`*^9}, {3.6299729203577843`*^9, 3.6299729350218105`*^9}, {3.6299729720874753`*^9, 3.6299730462188053`*^9}, {3.629973116044528*^9, 3.6299731230177402`*^9}, { 3.629973184310248*^9, 3.6299732090830917`*^9}, {3.629973349982539*^9, 3.6299734360166903`*^9}, 3.629973534562063*^9, {3.629973577446539*^9, 3.629973586104554*^9}, {3.6299740374133463`*^9, 3.629974083823428*^9}, { 3.6299742505565205`*^9, 3.629974337089873*^9}, {3.629974382907153*^9, 3.6299744466176653`*^9}, {3.629974589794717*^9, 3.629974590761918*^9}, { 3.629974776215044*^9, 3.6299747850134597`*^9}, {3.6299748226095257`*^9, 3.6299748237483273`*^9}, 3.6299748618435946`*^9, {3.629975198476586*^9, 3.6299752545898843`*^9}, {3.62997531475919*^9, 3.6299753175515947`*^9}, { 3.6299754601982455`*^9, 3.6299754625382495`*^9}, {3.629975592034077*^9, 3.629975592502078*^9}, {3.629983277446268*^9, 3.6299832946842985`*^9}, { 3.62998342081052*^9, 3.6299835439883366`*^9}, {3.629983615514462*^9, 3.629983931009416*^9}, {3.6299919807040443`*^9, 3.6299919808912444`*^9}, { 3.629992028330928*^9, 3.6299920922130404`*^9}, 3.629992198480427*^9, { 3.6299922299300823`*^9, 3.629992250506518*^9}, {3.629992292657792*^9, 3.6299923603151107`*^9}, {3.6299924387676487`*^9, 3.6299924398440504`*^9}, {3.6299925764846907`*^9, 3.6299926096347485`*^9}, {3.6299928122323046`*^9, 3.629992818768716*^9}, { 3.6299929049120674`*^9, 3.629992905411268*^9}, {3.6299929850338078`*^9, 3.6299929866250105`*^9}, {3.6299931061992207`*^9, 3.62999312270405*^9}, { 3.629993172312137*^9, 3.6299932618718944`*^9}, {3.6299933276572104`*^9, 3.6299933842073092`*^9}, {3.630287775665962*^9, 3.630287795852398*^9}, { 3.6303896387100534`*^9, 3.630389666774503*^9}, {3.6303896967889557`*^9, 3.6303897095341783`*^9}, {3.6303897587054644`*^9, 3.630389880448078*^9}, { 3.6303899127557354`*^9, 3.630390009444705*^9}, 3.630390057321189*^9, 3.630390443484267*^9, {3.63039095720877*^9, 3.6303909789240074`*^9}, { 3.6303910572205453`*^9, 3.6303911291054716`*^9}, {3.630391163035531*^9, 3.6303911740803504`*^9}, {3.630391240224467*^9, 3.6303912875081496`*^9}, { 3.6303913396902413`*^9, 3.630391404570755*^9}, {3.630391479513287*^9, 3.6303917572873745`*^9}, {3.630391868905571*^9, 3.6303920027226057`*^9}, { 3.630392064327114*^9, 3.630392219843787*^9}, {3.63039226121506*^9, 3.63039232943398*^9}, {3.6303924315985594`*^9, 3.6303924441097813`*^9}, { 3.6303926866122074`*^9, 3.6303927118530517`*^9}, {3.630392795671999*^9, 3.6303928006172075`*^9}, {3.6303986032190485`*^9, 3.6303986046230516`*^9}, {3.6303986654631586`*^9, 3.6303987936485834`*^9}, {3.63039889979117*^9, 3.6303989091199865`*^9}, { 3.630399006323757*^9, 3.630399007259759*^9}, {3.630399117224352*^9, 3.630399214771323*^9}, {3.6303992555185947`*^9, 3.6303993036758795`*^9}, { 3.630399467725767*^9, 3.630399502731636*^9}, {3.6303995748037624`*^9, 3.630399595614199*^9}, {3.6303996329294643`*^9, 3.630399658076709*^9}, { 3.630399711335202*^9, 3.6303997453120623`*^9}, {3.6303998546994543`*^9, 3.6303999880484886`*^9}, {3.6304000742074394`*^9, 3.630400123441126*^9}, { 3.6304001724564123`*^9, 3.630400251595351*^9}, {3.630400324166679*^9, 3.630400327052684*^9}, {3.630400358190338*^9, 3.6304003597503414`*^9}, { 3.6304004587481155`*^9, 3.6304004640521245`*^9}, {3.630400521975026*^9, 3.630400526124634*^9}, {3.630400567199506*^9, 3.630400593516752*^9}, { 3.6304012340070767`*^9, 3.6304013035207987`*^9}, {3.6304013614749007`*^9, 3.630401367933312*^9}, {3.630401686939398*^9, 3.6304017294598303`*^9}, { 3.630401794020523*^9, 3.6304018922061386`*^9}, {3.6304019687775183`*^9, 3.630401987153569*^9}, {3.630402072749465*^9, 3.63040208297405*^9}, { 3.6304022247881613`*^9, 3.630402255931943*^9}, 3.630402329306139*^9, { 3.6304023806970787`*^9, 3.6304024212403975`*^9}, {3.6304025002259154`*^9, 3.630402528595538*^9}, {3.6304025620694523`*^9, 3.630402575015193*^9}, { 3.6304026411829777`*^9, 3.630402649073429*^9}, {3.630402695548087*^9, 3.6304027128260756`*^9}, {3.630402783923142*^9, 3.6304027982389607`*^9}, { 3.6304028797236214`*^9, 3.6304030111811404`*^9}, {3.6304030562107162`*^9, 3.6304031598846455`*^9}, {3.630403236330018*^9, 3.6304032404072514`*^9}, { 3.630403373001835*^9, 3.6304033888147397`*^9}, {3.6304039420953856`*^9, 3.6304039512829113`*^9}, 3.6304039831437335`*^9, {3.630404015975611*^9, 3.6304040663624935`*^9}, {3.630404173614628*^9, 3.630404246945822*^9}, { 3.6304042891772375`*^9, 3.630404299595834*^9}, {3.630404391083066*^9, 3.630404392406142*^9}, {3.6304045301800222`*^9, 3.6304045579486103`*^9}, { 3.630404640215316*^9, 3.630404762796327*^9}, {3.630404877629895*^9, 3.630404883104208*^9}, {3.6304050364729805`*^9, 3.630405098270515*^9}, { 3.6304051736118245`*^9, 3.6304051965901384`*^9}, {3.6304053802536435`*^9, 3.63040539242334*^9}, {3.630406035965148*^9, 3.630406041998493*^9}, { 3.630406072049212*^9, 3.6304060962065935`*^9}, {3.630406264081196*^9, 3.6304062707025747`*^9}, {3.63040632219952*^9, 3.630406385461138*^9}, { 3.630406477200385*^9, 3.630406482095665*^9}, {3.6304066170883865`*^9, 3.6304066222256804`*^9}, {3.630406957868878*^9, 3.630406973411767*^9}, { 3.6304070081447535`*^9, 3.630407018199329*^9}, {3.630407411376817*^9, 3.630407412542884*^9}, {3.6304080609339695`*^9, 3.630408121202417*^9}, { 3.6304081585485525`*^9, 3.6304081832129636`*^9}, {3.63040821409673*^9, 3.630408421131572*^9}, 3.6304934333363276`*^9, {3.63049350751357*^9, 3.630493677593298*^9}, {3.630493716898546*^9, 3.6304937846684227`*^9}, 3.630493922944331*^9, {3.6304939556752033`*^9, 3.630494117430455*^9}, { 3.6304941486092386`*^9, 3.6304941767788496`*^9}, {3.6304942118648567`*^9, 3.6304942530272107`*^9}, {3.6304942838399734`*^9, 3.6304942845820155`*^9}, {3.6304943454054947`*^9, 3.6304944442451477`*^9}, {3.63080749995092*^9, 3.6308075480801234`*^9}, { 3.630807586536323*^9, 3.630807621440319*^9}, {3.630807680459695*^9, 3.630807682914836*^9}, {3.630807736889923*^9, 3.6308077644745007`*^9}, { 3.6308078081089964`*^9, 3.6308078670123653`*^9}, {3.630807991648494*^9, 3.630807997541831*^9}, {3.6308081080891542`*^9, 3.6308081919599514`*^9}, { 3.630808306368495*^9, 3.630808345060708*^9}, {3.6308087281906223`*^9, 3.6308087555171847`*^9}, {3.630809110815507*^9, 3.630809169033837*^9}, { 3.6308091998195972`*^9, 3.630809448512822*^9}, {3.6308095328996487`*^9, 3.6308095448223305`*^9}, {3.630809582269472*^9, 3.6308095873607635`*^9}, { 3.630809665529235*^9, 3.630809684808337*^9}, {3.6308316258485594`*^9, 3.6308318380886984`*^9}, {3.63083188164919*^9, 3.630831966930068*^9}, 3.6320400558356075`*^9, {3.6354749882908883`*^9, 3.635474989418953*^9}, { 3.635475084557395*^9, 3.6354750875145636`*^9}, {3.6354751334091887`*^9, 3.635475162315842*^9}, {3.6354754001974483`*^9, 3.6354754820331287`*^9}, 3.635475512931896*^9, {3.6354756222781506`*^9, 3.635475622861184*^9}, { 3.635475691642118*^9, 3.6354757057969275`*^9}, {3.6354757798291616`*^9, 3.635475797395167*^9}, {3.635475884848169*^9, 3.6354758981309285`*^9}, { 3.635475961488552*^9, 3.6354759738382587`*^9}, {3.6354760213729773`*^9, 3.6354760572050266`*^9}, {3.6354761282470903`*^9, 3.635476136040536*^9}, { 3.6354761719365892`*^9, 3.635476212217893*^9}, {3.6593346599546614`*^9, 3.659334660890663*^9}, {3.6593347077219453`*^9, 3.659334720701168*^9}, { 3.6593348752974396`*^9, 3.6593348758122406`*^9}, {3.6593349140947075`*^9, 3.6593350070240707`*^9}, {3.6593350466949406`*^9, 3.6593350543701544`*^9}, {3.659335103791041*^9, 3.6593351614487424`*^9}, 3.659335217686841*^9, {3.659335262084519*^9, 3.6593352995869846`*^9}, { 3.6593356899482727`*^9, 3.659335701819893*^9}, {3.659335964227954*^9, 3.659335964602355*^9}, {3.65933603594128*^9, 3.6593360629605274`*^9}, { 3.6593361352354546`*^9, 3.6593361504454813`*^9}, {3.6593363929479074`*^9, 3.6593364061611304`*^9}, 3.6593368946915884`*^9, {3.6884748265656157`*^9, 3.6884748268716326`*^9}, {3.6884748600075283`*^9, 3.688474861420609*^9}, { 3.6885242858240776`*^9, 3.6885243001140976`*^9}, {3.6888842911675606`*^9, 3.6888843311676164`*^9}, {3.688966242423658*^9, 3.688966263933688*^9}, { 3.6897393587897596`*^9, 3.6897393649897685`*^9}, 3.689739477049925*^9, { 3.6898595970621734`*^9, 3.689859597272174*^9}, {3.6898596707522764`*^9, 3.6898597190523443`*^9}, {3.689859768552414*^9, 3.6898597721424184`*^9}, { 3.689859855272535*^9, 3.689859859882541*^9}, {3.6898605078334484`*^9, 3.6898607266237545`*^9}, 3.6898608811139708`*^9, {3.6898609634740863`*^9, 3.689860974304102*^9}, 3.6898610140141573`*^9, {3.6898611496043468`*^9, 3.6898611683243732`*^9}, {3.689861462024784*^9, 3.6898615624849253`*^9}, { 3.6898616142149973`*^9, 3.6898616164350004`*^9}, 3.6898616657950697`*^9, { 3.689861716805141*^9, 3.689861749905187*^9}, {3.732677920575506*^9, 3.7326779208190203`*^9}, {3.7519672427004185`*^9, 3.7519672444968877`*^9}, {3.7519674022097683`*^9, 3.75196742976579*^9}, { 3.751967484127989*^9, 3.751967510853814*^9}, {3.7519675409404893`*^9, 3.751967541549782*^9}, {3.7519675797751045`*^9, 3.751967592209671*^9}, { 3.7519676829383273`*^9, 3.7519676841255474`*^9}, {3.7519677154775553`*^9, 3.7519677953499403`*^9}, 3.751967827811061*^9, {3.7519679545625095`*^9, 3.751967957999185*^9}, {3.751968003754015*^9, 3.7519681477513895`*^9}, { 3.751968264817631*^9, 3.751968270722477*^9}, {3.7519689618119907`*^9, 3.751968969888235*^9}, {3.7519691168917775`*^9, 3.7519691395895615`*^9}, { 3.751969242782174*^9, 3.7519692581691785`*^9}, {3.7519693625211954`*^9, 3.751969378579924*^9}, {3.751969409572627*^9, 3.751969438643936*^9}, { 3.7519695894526725`*^9, 3.751969614306203*^9}, {3.7523200108586655`*^9, 3.752320012354121*^9}, {3.7553831315619707`*^9, 3.755383134119626*^9}, { 3.7553831893197794`*^9, 3.755383241814331*^9}, {3.7553832736267967`*^9, 3.7553832810757113`*^9}, {3.7554336536222963`*^9, 3.755433684797229*^9}, { 3.7554337764737434`*^9, 3.7554338315300155`*^9}, {3.755433998047738*^9, 3.7554340265485487`*^9}, {3.755446573138784*^9, 3.755446636911299*^9}, { 3.75544667493072*^9, 3.755446753435521*^9}, {3.755446891541581*^9, 3.7554468921547422`*^9}, {3.7554469323588533`*^9, 3.755446936867403*^9}, { 3.7554470190332975`*^9, 3.7554472776872244`*^9}, {3.7555217323692026`*^9, 3.755521732847602*^9}, {3.755521767127169*^9, 3.7555217972041793`*^9}, { 3.755522561453134*^9, 3.755522564231819*^9}, {3.755522601885935*^9, 3.7555226037287407`*^9}, {3.7555226758687305`*^9, 3.755522678585092*^9}, { 3.7555234832604623`*^9, 3.7555235920444417`*^9}, {3.7555239506007543`*^9, 3.755524013893358*^9}, {3.755524076791689*^9, 3.7555240812793446`*^9}, { 3.7555241238138275`*^9, 3.7555241268985643`*^9}, {3.7555242930449886`*^9, 3.7555243378577013`*^9}, {3.7555256673767824`*^9, 3.7555256808205338`*^9}, {3.7555258588384123`*^9, 3.755525900317296*^9}, { 3.755525930708299*^9, 3.7555260436531134`*^9}, {3.755607147401991*^9, 3.7556071504143705`*^9}, {3.755607992884314*^9, 3.7556080025382996`*^9}, { 3.7556094344057455`*^9, 3.7556094348690443`*^9}, {3.7559613653116636`*^9, 3.755961445097105*^9}, 3.755961484246889*^9, {3.7559618979231987`*^9, 3.755961939470047*^9}, {3.7559620323724904`*^9, 3.7559620330864005`*^9}, { 3.755962155557907*^9, 3.7559621601593847`*^9}, {3.755962303755834*^9, 3.755962343830135*^9}, {3.7559624058018165`*^9, 3.7559624450501757`*^9}, 3.756002186674869*^9, 3.7560029626855392`*^9, {3.756003222110388*^9, 3.756003295034633*^9}, {3.7560056331492863`*^9, 3.7560056663855457`*^9}, { 3.7560057813555765`*^9, 3.7560057863836613`*^9}, {3.7560058917172394`*^9, 3.756005927847292*^9}, 3.756006092376186*^9, 3.756009112317705*^9, { 3.756091886039587*^9, 3.756091887764086*^9}, {3.756092005435152*^9, 3.7560920727337685`*^9}, {3.75609212911592*^9, 3.7560921293252516`*^9}, { 3.756092262958163*^9, 3.756092263157668*^9}, {3.756092342487877*^9, 3.756092347894502*^9}, {3.7560929036769304`*^9, 3.7560929278911004`*^9}, { 3.7560930741522417`*^9, 3.756093083420331*^9}, {3.7560932986236534`*^9, 3.7560933139459305`*^9}, {3.756093449985523*^9, 3.7560934874491863`*^9}, { 3.756093592694581*^9, 3.7560936019456573`*^9}, {3.756093634438078*^9, 3.756093673866626*^9}, {3.756093873069885*^9, 3.756093897964734*^9}, { 3.7560940650109406`*^9, 3.756094078056768*^9}, {3.756442536546026*^9, 3.756442607904289*^9}, {3.7564436397451363`*^9, 3.7564436403231254`*^9}, { 3.7636034984570236`*^9, 3.7636034989933815`*^9}, {3.763603551051456*^9, 3.7636035527617817`*^9}, {3.7636036049384193`*^9, 3.7636036392233057`*^9}, {3.7636036850937223`*^9, 3.763603692587598*^9}, { 3.7636037258272257`*^9, 3.7636037459031096`*^9}, {3.7636037792254367`*^9, 3.76360387572289*^9}, {3.763603971837229*^9, 3.7636040341423655`*^9}, { 3.763604066526084*^9, 3.7636040756798687`*^9}, {3.7636041452118535`*^9, 3.763604278007333*^9}, {3.763604317710966*^9, 3.7636043271387568`*^9}, { 3.7636043584877644`*^9, 3.763604415561053*^9}, {3.763604445680462*^9, 3.7636044504114943`*^9}, {3.763604615444647*^9, 3.7636048082554193`*^9}, 3.763604854904996*^9, {3.7636133594095488`*^9, 3.7636133618464766`*^9}, { 3.7636136063756704`*^9, 3.7636136315671196`*^9}, {3.7636990373827705`*^9, 3.7636990431157646`*^9}, {3.763699090332087*^9, 3.763699110952259*^9}, { 3.763699227420497*^9, 3.7636993642943506`*^9}, {3.763700085627533*^9, 3.763700088329999*^9}, {3.7637001721125274`*^9, 3.763700181422837*^9}, { 3.763700248063385*^9, 3.7637003918630466`*^9}, {3.763700591783223*^9, 3.7637006017496295`*^9}, {3.7637007583576717`*^9, 3.7637007603074865`*^9}, {3.7637137795793185`*^9, 3.7637137822587233`*^9}, {3.7637148704355187`*^9, 3.763714870624051*^9}, { 3.763727592158518*^9, 3.7637275933445053`*^9}, {3.7637276688363667`*^9, 3.7637276694756594`*^9}, 3.763803448896332*^9, {3.76380349501632*^9, 3.7638036835067654`*^9}, {3.763804829093463*^9, 3.7638048385675254`*^9}, 3.7638051033646154`*^9, 3.7638053924528885`*^9, {3.763805557684454*^9, 3.763805634255308*^9}, {3.763806843847647*^9, 3.763806847966059*^9}, { 3.763806942652097*^9, 3.7638071770752254`*^9}, {3.7638141184594107`*^9, 3.763814134133461*^9}, {3.7638146808628216`*^9, 3.7638146925645113`*^9}, { 3.7638147709278784`*^9, 3.7638147811883087`*^9}, {3.7638148155281043`*^9, 3.763814819843194*^9}, {3.7638150259647446`*^9, 3.763815028601293*^9}, { 3.7638151529595194`*^9, 3.763815155849978*^9}, {3.7638163770262136`*^9, 3.763816380851597*^9}, {3.7638164181856327`*^9, 3.7638164950537987`*^9}, 3.763816568304102*^9, {3.7638166173645625`*^9, 3.763816618808757*^9}, { 3.7638167204462805`*^9, 3.763816721012859*^9}, {3.763857602253485*^9, 3.7638579604183645`*^9}, {3.7638580038507566`*^9, 3.7638580060526443`*^9}, {3.763858082269992*^9, 3.7638581746835337`*^9}, { 3.7638582163351564`*^9, 3.7638582415275116`*^9}, {3.7638582983238*^9, 3.763858907503306*^9}, {3.763858941318697*^9, 3.763858956626134*^9}, { 3.7638602435602536`*^9, 3.763860245408451*^9}, {3.7638694636456347`*^9, 3.7638694647177277`*^9}, {3.7638708199536576`*^9, 3.763870829436488*^9}, { 3.763871287170555*^9, 3.7638712876184006`*^9}, {3.763943214376035*^9, 3.7639432984591475`*^9}, {3.763943418832348*^9, 3.7639434335508127`*^9}, { 3.76394347113767*^9, 3.7639435187320576`*^9}, {3.763943585908682*^9, 3.7639436125255404`*^9}, {3.763951722152746*^9, 3.76395172989299*^9}, { 3.7639517863423367`*^9, 3.7639519945900664`*^9}, {3.763952081515512*^9, 3.7639521530710773`*^9}, {3.763952353248129*^9, 3.763952357026309*^9}, { 3.7639524211903834`*^9, 3.7639524243979177`*^9}, {3.7639527174925117`*^9, 3.7639527180252266`*^9}, {3.7641265625745993`*^9, 3.7641265632314167`*^9}, {3.764126605555829*^9, 3.7641266075095396`*^9}, { 3.7641268313964133`*^9, 3.7641268543573804`*^9}, {3.764127044657903*^9, 3.7641270479422092`*^9}, {3.7641271442332697`*^9, 3.7641271469362774`*^9}, {3.764127227626192*^9, 3.7641272592640233`*^9}, { 3.764127335707515*^9, 3.7641273386484756`*^9}, {3.764127429843852*^9, 3.7641274364304185`*^9}, {3.7641275071859307`*^9, 3.764127516803895*^9}, 3.7641276043548007`*^9, {3.7641276925365753`*^9, 3.764127697080591*^9}, 3.764127798472331*^9, 3.764127853631323*^9, 3.764127908496078*^9, { 3.7641280050343323`*^9, 3.764128022046494*^9}, {3.764128128597419*^9, 3.764128154116727*^9}, {3.7641286864636617`*^9, 3.764128701643106*^9}, { 3.7641289910924444`*^9, 3.7641290126680794`*^9}, {3.7641290672285347`*^9, 3.7641290737798567`*^9}, {3.7641325425120363`*^9, 3.764132565390477*^9}, { 3.7641327425004654`*^9, 3.764132750040793*^9}, 3.7641327968340364`*^9, { 3.764133146776842*^9, 3.764133204874522*^9}, {3.7641333488187037`*^9, 3.7641333525577593`*^9}, {3.764413145593136*^9, 3.7644131471236105`*^9}, { 3.764413201645049*^9, 3.7644132349609704`*^9}, {3.764413325008136*^9, 3.7644133748980193`*^9}, {3.7644134113425665`*^9, 3.7644135151187*^9}, { 3.764413554409053*^9, 3.7644136160674934`*^9}, {3.76441371984758*^9, 3.764413730103909*^9}, 3.764419641962368*^9, {3.7644198522879405`*^9, 3.764419879249356*^9}, 3.764419909536559*^9, {3.764419991012162*^9, 3.764420000171088*^9}, {3.7644200798862047`*^9, 3.7644200950961914`*^9}, { 3.7644201529471693`*^9, 3.764420153715966*^9}, {3.764420210346301*^9, 3.764420255343707*^9}, {3.764420296178318*^9, 3.7644203000939393`*^9}, { 3.7644203803359275`*^9, 3.7644203931390867`*^9}, 3.7644204418727274`*^9, { 3.7647259720700207`*^9, 3.7647261047260523`*^9}, {3.7647263483375626`*^9, 3.76472635879602*^9}, 3.764726656736601*^9, {3.764727009127914*^9, 3.764727020100875*^9}, {3.7647270591828785`*^9, 3.7647270819631023`*^9}, { 3.7647272109090505`*^9, 3.764727227846332*^9}, {3.76473247809907*^9, 3.7647324813925114`*^9}, {3.7647349484962797`*^9, 3.7647349979358416`*^9}, {3.7647351097258167`*^9, 3.764735124772463*^9}, { 3.7647352810674453`*^9, 3.7647352901139917`*^9}, {3.7647353746429515`*^9, 3.764735379550926*^9}, {3.7647354596539807`*^9, 3.764735507677454*^9}, { 3.7647355546341*^9, 3.764735728811817*^9}, {3.764735837449795*^9, 3.76473584132898*^9}, {3.76473603649269*^9, 3.7647360592982664`*^9}, { 3.7647360998228803`*^9, 3.76473621551197*^9}, {3.7647362545599003`*^9, 3.764736286430997*^9}, {3.7647364592833533`*^9, 3.764736464019006*^9}, { 3.764736566167658*^9, 3.7647365918958225`*^9}, {3.764764761680134*^9, 3.7647648482473745`*^9}, 3.764764917763693*^9, {3.764764964821686*^9, 3.764765090741813*^9}, {3.7647651742140284`*^9, 3.7647652517335076`*^9}, { 3.764765341266399*^9, 3.7647653614173465`*^9}, 3.764765400284145*^9, { 3.764765691384389*^9, 3.764765708710143*^9}, 3.7647657454275875`*^9, { 3.76476578351686*^9, 3.764765871262255*^9}, {3.7647661045180917`*^9, 3.76476612822571*^9}, {3.7647661964223824`*^9, 3.764766239375331*^9}, { 3.764766330361228*^9, 3.764766338297905*^9}, {3.764767015060799*^9, 3.7647670193029037`*^9}, {3.764767076590926*^9, 3.7647671160277977`*^9}, { 3.7647671493139205`*^9, 3.7647672079236426`*^9}, {3.764767458938404*^9, 3.7647674608323865`*^9}, {3.764810938444873*^9, 3.7648109399353456`*^9}, { 3.7648118616019874`*^9, 3.7648118695079126`*^9}, {3.7648120589477816`*^9, 3.7648124600413237`*^9}, {3.76481250476682*^9, 3.7648125259602103`*^9}, { 3.764812601341893*^9, 3.7648126577763243`*^9}, {3.7648126944039307`*^9, 3.7648128855627623`*^9}, {3.764812924923909*^9, 3.764812926481821*^9}, { 3.764813041485982*^9, 3.764813131254232*^9}, {3.7648134679328885`*^9, 3.7648136479313235`*^9}, {3.7648136917777314`*^9, 3.764813697753367*^9}, { 3.7648137297570653`*^9, 3.764813747862262*^9}, 3.764813784221693*^9, { 3.7648138370678406`*^9, 3.7648141387969923`*^9}, {3.764814321050164*^9, 3.764814422489184*^9}, {3.764814461366684*^9, 3.7648145835728483`*^9}, { 3.764814614769511*^9, 3.7648147525825167`*^9}, {3.764815363375289*^9, 3.7648153644907384`*^9}, {3.764815451671169*^9, 3.7648154601533747`*^9}, { 3.7648175917802963`*^9, 3.7648176401910563`*^9}, {3.765885491237231*^9, 3.765885501131465*^9}, {3.766572999289345*^9, 3.7665729996020145`*^9}, { 3.7665730613126965`*^9, 3.7665730616706066`*^9}, {3.7840103262125545`*^9, 3.7840103546413517`*^9}, {3.784011309725755*^9, 3.7840113197719574`*^9}, { 3.784013374800973*^9, 3.7840133842981763`*^9}, {3.7840238533665447`*^9, 3.78402395932942*^9}, {3.784024091276659*^9, 3.784024112209529*^9}, { 3.7840242793219643`*^9, 3.784024296655184*^9}, {3.7840290670892677`*^9, 3.7840291348388853`*^9}, {3.784029222997594*^9, 3.784029542926179*^9}, { 3.784375172285057*^9, 3.784375319701829*^9}, {3.7843753678421807`*^9, 3.7843753788103914`*^9}, {3.7843754844339557`*^9, 3.784375827494117*^9}, { 3.784375862317687*^9, 3.7843759567563844`*^9}, {3.784376004941759*^9, 3.7843760080157185`*^9}, {3.784376101918992*^9, 3.7843761244332943`*^9}, { 3.784376181191763*^9, 3.7843762145091863`*^9}, {3.7843792489960337`*^9, 3.78437926273014*^9}, {3.7843793293934345`*^9, 3.784379368676588*^9}, { 3.7843796529835215`*^9, 3.7843796858862267`*^9}, {3.784450863324359*^9, 3.7844508986076546`*^9}, {3.7844510208392324`*^9, 3.784451027915551*^9}, { 3.7844511176315613`*^9, 3.7844511673791957`*^9}, {3.784451235055628*^9, 3.78445132575735*^9}, {3.784451995615477*^9, 3.7844520110330954`*^9}, { 3.7844522907551537`*^9, 3.7844523421551*^9}, {3.784700119490345*^9, 3.7847001627913013`*^9}, {3.7847004221290607`*^9, 3.7847004380767317`*^9}, 3.7847007913506136`*^9, {3.784781955129138*^9, 3.784781977787957*^9}, { 3.78488170216677*^9, 3.784881704210422*^9}, 3.784882130557441*^9, { 3.78488220347418*^9, 3.7848822064697027`*^9}, {3.784883393455822*^9, 3.784883458551924*^9}, 3.7848835306495824`*^9, {3.7848836822092113`*^9, 3.7848837303696923`*^9}, 3.7848838199009576`*^9, {3.7848842507527857`*^9, 3.7848842836585226`*^9}, 3.7848843847882996`*^9, {3.784884461405264*^9, 3.7848844645041113`*^9}, {3.784884559404122*^9, 3.7848845656634912`*^9}, { 3.7848852409944844`*^9, 3.7848852740337477`*^9}, {3.7848854548929386`*^9, 3.7848854893046365`*^9}, {3.7848856741783943`*^9, 3.784885691704702*^9}, { 3.784885809660874*^9, 3.784885811424426*^9}, {3.7848860031948376`*^9, 3.784886020570098*^9}, 3.7848861057105627`*^9, {3.7848861627726107`*^9, 3.7848862212876124`*^9}, {3.784886306497995*^9, 3.7848863509322224`*^9}, 3.784886472690192*^9, {3.7848866596243*^9, 3.784886664116289*^9}, { 3.7848866987282944`*^9, 3.7848867077911897`*^9}, {3.78488676128524*^9, 3.7848868667029366`*^9}, {3.7848869381224003`*^9, 3.7848869414281464`*^9}, {3.7848870104508753`*^9, 3.784887039889447*^9}, { 3.7848871795058794`*^9, 3.7848871976746817`*^9}, {3.7848872311446314`*^9, 3.78488724075662*^9}, 3.784887405188785*^9, {3.784887591926689*^9, 3.7848876119305134`*^9}, {3.784887676620901*^9, 3.7848876786672792`*^9}, { 3.78488771054331*^9, 3.784887714354906*^9}, {3.7848877625809546`*^9, 3.7848878103041153`*^9}, 3.7848878862881575`*^9, {3.787717235155089*^9, 3.787717269464238*^9}, {3.7877174592607603`*^9, 3.7877174674038067`*^9}, { 3.7877271032841845`*^9, 3.787727136247201*^9}, 3.787727355369296*^9, 3.7877274973278403`*^9, {3.787727855959008*^9, 3.78772792141208*^9}, 3.787728113487193*^9, {3.7877281704571557`*^9, 3.7877281735077004`*^9}, 3.7877282789827795`*^9, {3.7877286510229864`*^9, 3.787728665729192*^9}, { 3.7877287942225084`*^9, 3.787728807671986*^9}, {3.787729044867985*^9, 3.787729045536916*^9}, {3.787729589732438*^9, 3.7877296062090626`*^9}, { 3.787729794037467*^9, 3.7877297950347877`*^9}, {3.787729855548402*^9, 3.7877299039179935`*^9}, {3.7877300373241186`*^9, 3.787730068136018*^9}, { 3.7877301999859333`*^9, 3.7877302014150777`*^9}, {3.787732033225385*^9, 3.7877320471634016`*^9}, {3.787732077195259*^9, 3.7877320780358667`*^9}, 3.787732189759206*^9, {3.78773231889835*^9, 3.787732327710633*^9}, { 3.7877324857166643`*^9, 3.787732496655479*^9}, {3.7877325848303585`*^9, 3.78773258503596*^9}, {3.7877328504631166`*^9, 3.7877328625892415`*^9}, { 3.7877330254884944`*^9, 3.7877330271019044`*^9}, {3.787733136128061*^9, 3.7877331422258835`*^9}, {3.787733243513567*^9, 3.78773324558677*^9}, 3.787733310555999*^9, 3.7877334085329347`*^9, {3.7877337955932293`*^9, 3.7877337970498257`*^9}, {3.787733867727028*^9, 3.7877338687324905`*^9}, { 3.7877352224369583`*^9, 3.787735224161746*^9}, {3.787735343322833*^9, 3.787735348772827*^9}, {3.787735422704711*^9, 3.7877354268945775`*^9}, { 3.7877355100355635`*^9, 3.787735514671461*^9}, {3.7877356541994534`*^9, 3.7877356632141013`*^9}, 3.7877357913476543`*^9, 3.787736261837074*^9, { 3.7882542159043374`*^9, 3.7882542747998285`*^9}, {3.788254310967661*^9, 3.788254318430212*^9}, {3.788254585790197*^9, 3.7882545888318524`*^9}, { 3.7882547349987383`*^9, 3.788254735940298*^9}, 3.788254830063775*^9, 3.7882549155286837`*^9, {3.7882550121437798`*^9, 3.788255037735396*^9}, { 3.7882551764404287`*^9, 3.78825518352113*^9}, {3.7882552540030313`*^9, 3.788255290224329*^9}, {3.7882553843544893`*^9, 3.788255423248046*^9}, { 3.78825567982127*^9, 3.7882556852479534`*^9}, {3.7882557908576803`*^9, 3.7882558029800806`*^9}, {3.7882560240494256`*^9, 3.7882560388846164`*^9}, 3.788256102343512*^9, {3.788256161397396*^9, 3.7882561626372194`*^9}, { 3.7882562304311895`*^9, 3.78825629590362*^9}, {3.7882563614677362`*^9, 3.7882563620189795`*^9}, {3.7882564138122153`*^9, 3.7882564294158382`*^9}, {3.788256467457189*^9, 3.7882564889521217`*^9}, { 3.7882565883311844`*^9, 3.788256591497148*^9}, {3.7882568409513097`*^9, 3.7882568724526567`*^9}, {3.788256965258837*^9, 3.788256966444976*^9}, { 3.7882570073831463`*^9, 3.7882570497349973`*^9}, {3.7882570992487097`*^9, 3.788257144206352*^9}, {3.78825721252205*^9, 3.788257307277931*^9}, { 3.788257350410209*^9, 3.7882573617262745`*^9}, {3.788257424936472*^9, 3.788257434118204*^9}, {3.788276311330668*^9, 3.788276311647092*^9}, { 3.7882765465512347`*^9, 3.788276608568333*^9}, {3.7882767715851693`*^9, 3.7882768045752783`*^9}, {3.7882769342607436`*^9, 3.7882769409894867`*^9}, {3.7882770202208567`*^9, 3.7882770424485188`*^9}, {3.7882770760040703`*^9, 3.788277077341468*^9}, { 3.788277147336176*^9, 3.788277150397852*^9}, {3.7882772069909*^9, 3.7882772101572385`*^9}, {3.7882772503366175`*^9, 3.7882772773759403`*^9}, {3.7882773922958755`*^9, 3.7882773927832017`*^9}, {3.788277450684473*^9, 3.788277482126852*^9}, { 3.78827754293396*^9, 3.788277545027956*^9}, 3.7890961565048018`*^9, { 3.789096242941472*^9, 3.7890962452874937`*^9}, {3.789096286771101*^9, 3.789096287939043*^9}, {3.7890963300637918`*^9, 3.789096330454324*^9}, { 3.789096421623994*^9, 3.789096482010544*^9}, {3.789123616007924*^9, 3.7891236603119373`*^9}, {3.82004560462539*^9, 3.820045628865552*^9}, { 3.820045711583801*^9, 3.82004571444415*^9}, {3.82004574552601*^9, 3.8200458146656227`*^9}, {3.8200459471200194`*^9, 3.820045947496038*^9}, { 3.820113346283964*^9, 3.820113420687029*^9}, {3.843547853319944*^9, 3.8435478596811757`*^9}, {3.8435479019503555`*^9, 3.8435479743034277`*^9}, {3.843560932189252*^9, 3.8435609338416433`*^9}, { 3.8435611914261384`*^9, 3.8435611920632486`*^9}, {3.8435624320536933`*^9, 3.8435624411683536`*^9}, {3.8437295238924494`*^9, 3.843729569229367*^9}, { 3.8443920425579967`*^9, 3.844392043749901*^9}, {3.844392085066965*^9, 3.84439210220125*^9}, 3.8443921338951335`*^9, {3.8443921701680193`*^9, 3.8443921937971706`*^9}, {3.844513395563983*^9, 3.8445134085996456`*^9}, { 3.8447683674104347`*^9, 3.844768368670556*^9}, {3.8447684443309875`*^9, 3.8447684484900866`*^9}, 3.8447686520157948`*^9, {3.844768745687599*^9, 3.844768745855211*^9}, 3.845183304458513*^9, {3.8451835940010877`*^9, 3.845183594542489*^9}, {3.845184390302038*^9, 3.845184391945329*^9}, { 3.8451845184651327`*^9, 3.845184537503073*^9}, {3.845184725810747*^9, 3.845184727862517*^9}, 3.8451848085572977`*^9, {3.845255005543473*^9, 3.8452550701614428`*^9}, {3.845255116528925*^9, 3.845255130817441*^9}, { 3.8452553159491444`*^9, 3.845255398239421*^9}, {3.8452554316887584`*^9, 3.845255516323632*^9}, {3.845255572312236*^9, 3.84525558031181*^9}, { 3.8452556104383307`*^9, 3.845255693908064*^9}, {3.845527992682146*^9, 3.8455280119549503`*^9}, {3.8455280677849493`*^9, 3.8455282068632755`*^9}, 3.845528296510269*^9, {3.84552838544649*^9, 3.8455283972662654`*^9}, { 3.8455285111156416`*^9, 3.845528620724532*^9}, {3.8455286507394857`*^9, 3.8455286778537693`*^9}, {3.84552875397721*^9, 3.8455287832150126`*^9}, { 3.8455288134263644`*^9, 3.8455288242659492`*^9}, {3.845528882756366*^9, 3.845528933497317*^9}, {3.845529287839986*^9, 3.8455293012812443`*^9}, { 3.8455293978278055`*^9, 3.8455293981111383`*^9}, {3.845529499537836*^9, 3.8455295004065795`*^9}, {3.845609477072257*^9, 3.8456096065189395`*^9}, { 3.845609662788809*^9, 3.845609668689152*^9}, {3.845609712860342*^9, 3.8456097209108343`*^9}, {3.845609845478004*^9, 3.845609907655341*^9}, { 3.8456103094907556`*^9, 3.845610323020236*^9}, {3.845610368769788*^9, 3.845610376316151*^9}, {3.845610434176654*^9, 3.84561049090069*^9}, 3.845610522214707*^9, 3.8456107866420207`*^9, {3.8456108553684444`*^9, 3.845610855574578*^9}, {3.845611041459861*^9, 3.845611043810052*^9}, { 3.8456116165491714`*^9, 3.8456117283491564`*^9}, {3.8456117769969835`*^9, 3.8456118220363483`*^9}, {3.8456118703237553`*^9, 3.8456119831151495`*^9}, {3.8456124022981386`*^9, 3.8456124224583464`*^9}, {3.8456127164733524`*^9, 3.845612740344495*^9}, { 3.845780852075635*^9, 3.8457808657114325`*^9}, {3.8457821230286026`*^9, 3.845782123716519*^9}, {3.8457825521920204`*^9, 3.845782609179036*^9}, { 3.845782729323619*^9, 3.8457827515157847`*^9}, {3.845782785128273*^9, 3.845782803453997*^9}, {3.8457828344736314`*^9, 3.8457828358311925`*^9}, { 3.845783094796917*^9, 3.8457830991701584`*^9}, {3.8457833361542873`*^9, 3.845783501335464*^9}, {3.845783531957113*^9, 3.8457835680525503`*^9}, 3.845783764414663*^9, 3.84578597144022*^9, 3.8457864896793737`*^9, { 3.845787119546991*^9, 3.84578713411397*^9}, {3.845787696751997*^9, 3.8457877204318814`*^9}, 3.8457882983714895`*^9, {3.8457885986921697`*^9, 3.8457886169047403`*^9}, {3.8457887088707514`*^9, 3.8457887217894297`*^9}, {3.8457887909210815`*^9, 3.8457888144201937`*^9}, {3.8457888906519327`*^9, 3.8457889466368628`*^9}, {3.8457890416459827`*^9, 3.845789052312254*^9}, { 3.845789116545609*^9, 3.8457891180744157`*^9}, {3.845789226429738*^9, 3.8457892292024574`*^9}, {3.845790510151396*^9, 3.845790519684927*^9}, 3.8457906357570543`*^9, {3.8458635760826883`*^9, 3.845863582446103*^9}, { 3.8458636696732097`*^9, 3.845863680633752*^9}, {3.8458637198783617`*^9, 3.845863725217595*^9}, 3.8458643039964285`*^9, {3.845864896377093*^9, 3.8458649228570347`*^9}, 3.8458654592977276`*^9, {3.8458655305222178`*^9, 3.845865533812125*^9}, 3.8458656269752007`*^9, 3.8458662253983583`*^9, { 3.845866315341114*^9, 3.845866316735467*^9}, {3.8458664630238924`*^9, 3.845866520383334*^9}, {3.845866555205945*^9, 3.845866566614134*^9}, { 3.845866724894957*^9, 3.8458667295073595`*^9}, {3.8458670210920024`*^9, 3.8458670231028185`*^9}, 3.8458671129063563`*^9, 3.8458672295699835`*^9, 3.845867522574538*^9, {3.845867616322856*^9, 3.845867616819559*^9}, { 3.8458677144565196`*^9, 3.8458677161961637`*^9}, {3.845867821061138*^9, 3.845867825279958*^9}, 3.8458680066485095`*^9, {3.845868278532402*^9, 3.845868302364672*^9}, {3.8458688185729504`*^9, 3.845868834819693*^9}, { 3.845869294519817*^9, 3.845869295105886*^9}, {3.8508856215909443`*^9, 3.8508856323318715`*^9}, 3.8508857589241543`*^9},ExpressionUUID->"6ff08674-2241-4cd8-8297-\ 12ad7cb39b48"] }, Closed]], Cell[CellGroupData[{ Cell["SHELL ELEMENT (disp) defs ", "Subsection", CellChangeTimes->{{3.6303896070263977`*^9, 3.6303896080872*^9}, 3.8435394517660627`*^9},ExpressionUUID->"37cdd6b0-516c-4445-ba8a-\ c7931007bf1e"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"MEC", "-", "E1050"}], " ", "|", " ", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "n\[Alpha]", ",", "n\[Beta]", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "NN", ",", "mat", ",", "MM", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "r\[Gamma]", ",", "rn", ",", "jac", ",", "h\[Alpha]", ",", "e\[Alpha]", ",", "h\[Beta]", ",", "h\[Gamma]", ",", "e\[Beta]", ",", "en", ",", "e\[Gamma]", ",", "FF", ",", "\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]", ",", "edg", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "\[Pi]u", ",", "\[Pi]v", ",", "\[Pi]w", ",", "\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]", ",", "f\[Alpha]", ",", "f\[Gamma]", ",", "fn", ",", "m\[Alpha]", ",", "m\[Gamma]", ",", "mn", ",", "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]", ",", "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]", ",", "\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]", ",", "GG", ",", "N\[Alpha]\[Alpha]", ",", "N\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Gamma]", ",", "N\[Gamma]\[Alpha]", ",", "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]", ",", "Q\[Alpha]", ",", "Q\[Gamma]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wmap", ",", "AA"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"mat", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]", "=", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}]}], ";", " ", RowBox[{"r\[Beta]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Norm", "[", "r\[Beta]", "]"}]}], ";", " ", RowBox[{"h\[Alpha]", "=", RowBox[{"Norm", "[", "r\[Alpha]", "]"}]}], ";", RowBox[{"jac", "=", RowBox[{"Norm", "[", RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Alpha]", "=", RowBox[{"r\[Alpha]", "/", "h\[Alpha]"}]}], ";", RowBox[{"e\[Beta]", "=", RowBox[{"r\[Beta]", "/", "h\[Beta]"}]}], ";", " ", RowBox[{"en", "=", RowBox[{ RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], " ", "/", "jac"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r\[Gamma]", "=", RowBox[{"r\[Beta]", "-", RowBox[{ RowBox[{"(", RowBox[{"r\[Beta]", ".", "e\[Alpha]"}], ")"}], " ", "e\[Alpha]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Gamma]", "=", RowBox[{"Norm", "[", "r\[Gamma]", "]"}]}], ";", RowBox[{"e\[Gamma]", "=", RowBox[{"r\[Gamma]", "/", "h\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", "e\[Gamma]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]"}], "}"}], "=", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Alpha]"}], ",", RowBox[{"r\[Alpha]", ".", "r\[Beta]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Beta]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Beta]"}]}], "}"}]}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Gamma]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Gamma]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"edg", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Sort", "[", "#", "]"}], "&"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"uX", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"uY", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "3"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Z", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"projection", " ", "mapping"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Pi]\[Phi]", "=", RowBox[{ RowBox[{ RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], "/", "60"}], "+", " ", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Theta]", "=", RowBox[{ RowBox[{ RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], "/", "60"}], "+", " ", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Psi]", "=", RowBox[{ RowBox[{ RowBox[{"\[Theta]Z", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], "/", "60"}], "+", " ", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "3"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Pi]u", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]v", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]w", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]u", ",", "\[Pi]v", ",", "\[Pi]w"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"\[Pi]u", ",", "\[Pi]v", ",", "\[Pi]w"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Gamma]", ",", "fn"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"strain", " ", "measures", " ", "with", " ", "non"}], "-", RowBox[{"symmetric", " ", "\[Epsilon]"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}]}]}], ")"}], "/", "h\[Gamma]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], "/", "h\[Alpha]"}], "-", "\[Psi]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}]}]}], ")"}], "/", "h\[Gamma]"}], "+", "\[Psi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}]}]}], ")"}]}], "/", "h\[Gamma]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", " ", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Theta]"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], "/", "h\[Alpha]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], "+", "\[Pi]\[Theta]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", "\[Pi]\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "stress", " ", "resultants", " ", "with", " ", "a", " ", "nonsymmetric", " ", "N"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Alpha]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Gamma]\[Gamma]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Gamma]\[Gamma]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Gamma]\[Gamma]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Gamma]", "=", RowBox[{ "tt", "*", "2", " ", "GG", "*", "\[Epsilon]\[Alpha]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Gamma]\[Alpha]", "=", RowBox[{ "tt", "*", "2", " ", "GG", "*", "\[Epsilon]\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Alpha]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Gamma]\[Gamma]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Gamma]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Gamma]\[Gamma]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", " ", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "\[Nu]\[Nu]"}]}], ")"}]}], "*", "\[Kappa]\[Alpha]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{ RowBox[{"5", "/", "6"}], " ", "*", "GG", "*", "tt", "*", "\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Gamma]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "N\[Alpha]\[Alpha]", ",", "N\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Gamma]", ",", "N\[Gamma]\[Alpha]"}], "}"}]}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]"}], "}"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Gamma]"}], "}"}]}]}]}], ";", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Gamma]", ",", "fn"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wmap", "=", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "/", "100000"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]u", "-", "u"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]u", "-", "u"}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]v", "-", "v"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]v", "-", "v"}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]w", "-", "w"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]w", "-", "w"}], ")"}]}]}], ")"}], "*", "tt", "*", RowBox[{"EE", "/", "jac"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI3", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wmap"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\n", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "n\[Alpha]", ",", "n\[Beta]", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "NN", ",", "mat", ",", "MM", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "r\[Gamma]", ",", "rn", ",", "jac", ",", "h\[Alpha]", ",", "e\[Alpha]", ",", "h\[Beta]", ",", "h\[Gamma]", ",", "e\[Beta]", ",", "en", ",", "e\[Gamma]", ",", "FF", ",", "\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]", ",", "edg", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]", ",", "f\[Alpha]", ",", "f\[Gamma]", ",", "fn", ",", "m\[Alpha]", ",", "m\[Gamma]", ",", "mn", ",", "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]", ",", "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]", ",", "\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Alpha]", ",", "N\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Gamma]", ",", "N\[Gamma]\[Alpha]", ",", "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]", ",", "Q\[Alpha]", ",", "Q\[Gamma]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wmap"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "n1", ",", "n2", ",", "n3", ",", "n12", ",", "n23", ",", "n31"}], "*)"}], "\[IndentingNewLine]", RowBox[{"MM", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "+", RowBox[{"2", " ", SuperscriptBox["\[Alpha]", "2"]}], "-", RowBox[{"3", " ", "\[Beta]"}], "+", RowBox[{"2", " ", SuperscriptBox["\[Beta]", "2"]}], "+", RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"4", " ", "\[Beta]"}]}], ")"}]}]}], ",", RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}]}], ",", RowBox[{"\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"-", "4"}], " ", "\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}]}], ",", RowBox[{"4", " ", "\[Alpha]", " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"-", "4"}], " ", "\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]", "=", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}]}], ";", " ", RowBox[{"r\[Beta]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Norm", "[", "r\[Beta]", "]"}]}], ";", " ", RowBox[{"h\[Alpha]", "=", RowBox[{"Norm", "[", "r\[Alpha]", "]"}]}], ";", RowBox[{"jac", "=", RowBox[{"Norm", "[", RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Alpha]", "=", RowBox[{"r\[Alpha]", "/", "h\[Alpha]"}]}], ";", RowBox[{"e\[Beta]", "=", RowBox[{"r\[Beta]", "/", "h\[Beta]"}]}], ";", " ", RowBox[{"en", "=", RowBox[{ RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], " ", "/", "jac"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r\[Gamma]", "=", RowBox[{"r\[Beta]", "-", RowBox[{ RowBox[{"(", RowBox[{"r\[Beta]", ".", "e\[Alpha]"}], ")"}], " ", "e\[Alpha]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Gamma]", "=", RowBox[{"Norm", "[", "r\[Gamma]", "]"}]}], ";", RowBox[{"e\[Gamma]", "=", RowBox[{"r\[Gamma]", "/", "h\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", "e\[Gamma]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]"}], "}"}], "=", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Alpha]"}], ",", RowBox[{"r\[Alpha]", ".", "r\[Beta]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Beta]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Beta]"}]}], "}"}]}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Gamma]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Gamma]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"edg", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Sort", "[", "#", "]"}], "&"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"MM", ".", RowBox[{"Join", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"uX", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}], ",", RowBox[{"uX", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "2"}], "}"}], "]"}], ",", RowBox[{"uX", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"uX", "[", "#", "]"}], "&"}], ",", "edg"}], "]"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"MM", ".", RowBox[{"Join", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"uY", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}], ",", RowBox[{"uY", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "2"}], "}"}], "]"}], ",", RowBox[{"uY", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"uY", "[", "#", "]"}], "&"}], ",", "edg"}], "]"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"MM", ".", RowBox[{"Join", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"uZ", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "2"}], "}"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"uZ", "[", "#", "]"}], "&"}], ",", "edg"}], "]"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "2"}], "}"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}]}]}], ")"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "2"}], "}"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}]}]}], ")"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "3"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"\[Theta]Z", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"\[Theta]Z", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "2"}], "}"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Z", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}]}]}], ")"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Theta]", "=", RowBox[{"NN", ".", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"5", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "5", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "5"}], "}"}]}], "}"}], "/", "420"}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "2"}], "}"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}]}], "}"}]}]}], ")"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "projection", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Pi]\[Phi]", "=", RowBox[{"NN", ".", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"5", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "5", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "5"}], "}"}]}], "}"}], "/", "420"}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}], ",", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "2"}], "}"}], "]"}], ",", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}]}], "}"}]}]}], ")"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Theta]", "=", RowBox[{"NN", ".", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"5", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "5", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "5"}], "}"}]}], "}"}], "/", "420"}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "2"}], "}"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}]}], "}"}]}]}], ")"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Psi]", "=", RowBox[{"NN", ".", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "3"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"5", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "5", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "5"}], "}"}]}], "}"}], "/", "420"}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]Z", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "1"}], "}"}], "]"}], ",", RowBox[{"\[Theta]Z", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "2"}], "}"}], "]"}], ",", RowBox[{"\[Theta]Z", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "3"}], "}"}], "]"}]}], "}"}]}]}], ")"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Pi]u", "=", RowBox[{"MM", ".", RowBox[{"Join", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "1"}], "]"}], "]"}], ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"uX", "[", "#", "]"}], "&"}], ",", "edg"}], "]"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Pi]v", "=", RowBox[{"MM", ".", RowBox[{"Join", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "2"}], "]"}], "]"}], ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"uY", "[", "#", "]"}], "&"}], ",", "edg"}], "]"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Pi]w", "=", RowBox[{"MM", ".", RowBox[{"Join", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "3"}], "]"}], "]"}], ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"uZ", "[", "#", "]"}], "&"}], ",", "edg"}], "]"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Gamma]", ",", "fn"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"strain", " ", "measures", " ", "with", " ", "non"}], "-", RowBox[{"symmetric", " ", "\[Epsilon]"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}]}]}], ")"}], "/", "h\[Gamma]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], "/", "h\[Alpha]"}], "-", "\[Psi]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}]}]}], ")"}], "/", "h\[Gamma]"}], "+", "\[Psi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}]}]}], ")"}]}], "/", "h\[Gamma]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", " ", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Theta]"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], "/", "h\[Alpha]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], "+", "\[Pi]\[Theta]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", "\[Pi]\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "stress", " ", "resultants", " ", "with", " ", "a", " ", "nonsymmetric", " ", "N"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Alpha]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Gamma]\[Gamma]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Gamma]\[Gamma]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Gamma]\[Gamma]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Gamma]", "=", RowBox[{ "tt", "*", "2", " ", "GG", "*", "\[Epsilon]\[Alpha]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Gamma]\[Alpha]", "=", RowBox[{ "tt", "*", "2", " ", "GG", "*", "\[Epsilon]\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Alpha]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Gamma]\[Gamma]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Gamma]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Gamma]\[Gamma]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", " ", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "\[Nu]\[Nu]"}]}], ")"}]}], "*", "\[Kappa]\[Alpha]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{ RowBox[{"5", "/", "6"}], " ", "*", "GG", "*", "tt", "*", "\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Gamma]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "N\[Alpha]\[Alpha]", ",", "N\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Gamma]", ",", "N\[Gamma]\[Alpha]"}], "}"}]}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]"}], "}"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Gamma]"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Gamma]", ",", "fn"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wmap", "=", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "/", "100"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]u", "-", "u"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]u", "-", "u"}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]v", "-", "v"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]v", "-", "v"}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]w", "-", "w"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]w", "-", "w"}], ")"}]}]}], ")"}], "*", "tt", "*", RowBox[{"EE", "/", "jac"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI28", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.4426474258030453`*^9, {3.4444401255942*^9, 3.4444401388073997`*^9}, { 3.4444401803034*^9, 3.4444401844062*^9}, 3.4444402418922*^9, { 3.4444402805022*^9, 3.4444403134026003`*^9}, {3.4444403443062*^9, 3.4444404484049997`*^9}, {3.444483267101*^9, 3.444483267335*^9}, { 3.4444833136046*^9, 3.4444835622998*^9}, {3.4444836421094*^9, 3.4444837777981997`*^9}, {3.444483920429*^9, 3.4444839412237997`*^9}, 3.4444842905546*^9, {3.4444843207406*^9, 3.4444844162282*^9}, { 3.4444844465078*^9, 3.4444844624354*^9}, {3.4444845255998*^9, 3.4444845894505997`*^9}, {3.4444846290746*^9, 3.444484933025*^9}, { 3.4444849790917997`*^9, 3.4444851148742*^9}, {3.444534936054*^9, 3.4445349675348*^9}, {3.4445355821731997`*^9, 3.44453585174*^9}, { 3.4445372162198*^9, 3.4445372264378*^9}, 3.444537384731*^9, { 3.4445377585382*^9, 3.4445377605818*^9}, {3.4445379733658*^9, 3.4445379736934*^9}, {3.4445380176762*^9, 3.444538032777*^9}, { 3.4445381079222*^9, 3.4445381581386003`*^9}, {3.4445382726456003`*^9, 3.4445382910067997`*^9}, {3.4445383401312*^9, 3.4445383475880003`*^9}, { 3.444538438458*^9, 3.4445384464608*^9}, {3.4445385680783997`*^9, 3.4445385687648*^9}, {3.4445389411991997`*^9, 3.4445389431024*^9}, { 3.444539746605*^9, 3.4445397807846003`*^9}, {3.4445408839765997`*^9, 3.4445409234133997`*^9}, {3.4445409681698*^9, 3.4445409932702*^9}, { 3.4445415452906*^9, 3.4445415706717997`*^9}, {3.4445416647242002`*^9, 3.4445416909477997`*^9}, {3.4445417660150003`*^9, 3.444541788557*^9}, { 3.4445420906977997`*^9, 3.444542104847*^9}, {3.4445421885878*^9, 3.4445421941414003`*^9}, {3.4445422252166*^9, 3.4445422386014*^9}, { 3.444542280425*^9, 3.4445423014538*^9}, {3.444542455769*^9, 3.4445424578282003`*^9}, {3.4445431739214*^9, 3.444543175809*^9}, { 3.4445647020962*^9, 3.4445648405618*^9}, {3.4445648825414*^9, 3.4445648858486*^9}, {3.4445649382646*^9, 3.4445651882702*^9}, { 3.4446164822206*^9, 3.4446165344494*^9}, {3.4446166121842003`*^9, 3.4446166738822002`*^9}, {3.4446167223046*^9, 3.4446168047974*^9}, { 3.444616843033*^9, 3.444616906447*^9}, {3.4446444694708*^9, 3.4446444700948*^9}, {3.4446477738310003`*^9, 3.4446477939862003`*^9}, { 3.4446478467298*^9, 3.4446478681018*^9}, 3.4446480456142*^9, { 3.4446487557418003`*^9, 3.4446487636198*^9}, 3.4446488179974003`*^9, { 3.4446488971205997`*^9, 3.4446489152478*^9}, {3.4446490003458*^9, 3.4446490008294*^9}, {3.4447042728942003`*^9, 3.4447042751562*^9}, { 3.4447044703278*^9, 3.4447044865362*^9}, 3.4447046475282*^9, 3.4447047993786*^9, {3.444704908329*^9, 3.4447049292642*^9}, { 3.4447049861926003`*^9, 3.4447049877214003`*^9}, {3.4447050279296*^9, 3.4447050419695997`*^9}, {3.4447053486656*^9, 3.4447053739376*^9}, 3.4447054561963997`*^9, 3.44470561612*^9, {3.4472133996876*^9, 3.4472134108571997`*^9}, {3.4472134470179996`*^9, 3.4472134648332*^9}, { 3.4472135032872*^9, 3.4472135245344*^9}, {3.4472136963059998`*^9, 3.4472137794384003`*^9}, {3.4472138235708*^9, 3.4472138388900003`*^9}, { 3.4472139099792*^9, 3.4472141367096*^9}, {3.447214202682*^9, 3.4472142975924*^9}, {3.4472144187732*^9, 3.4472145910284*^9}, { 3.4472146560492*^9, 3.4472147023968*^9}, {3.447214803594*^9, 3.4472148728736*^9}, {3.4472149156956*^9, 3.447214940484*^9}, { 3.447216227284*^9, 3.4472162419948*^9}, {3.4472163068908*^9, 3.4472163720832*^9}, {3.4472164665880003`*^9, 3.447216530392*^9}, { 3.4472166237268*^9, 3.4472167058452*^9}, 3.4472167362808*^9, { 3.4472171394658003`*^9, 3.4472171532874002`*^9}, {3.4472172028993998`*^9, 3.4472172216661997`*^9}, {3.4472172524606*^9, 3.4472172690278*^9}, { 3.4472173209133997`*^9, 3.4472173334245996`*^9}, {3.4472173920846*^9, 3.447217404861*^9}, {3.4472179572548*^9, 3.4472180351456003`*^9}, { 3.4472509764091997`*^9, 3.4472511017396*^9}, {3.4473910422216*^9, 3.4473912901524*^9}, 3.4473918688344*^9, {3.447392021185*^9, 3.4473920346633997`*^9}, {3.4473921383304*^9, 3.4473921479088*^9}, { 3.4473923024112*^9, 3.4473923734379997`*^9}, {3.4473928098168*^9, 3.4473928648691998`*^9}, {3.4473931872432003`*^9, 3.4473932461800003`*^9}, {3.4473933026675997`*^9, 3.4473934579812*^9}, { 3.4473935755271997`*^9, 3.447393742572*^9}, {3.4473939032676*^9, 3.4473939384144*^9}, {3.447395257644*^9, 3.4473953141628*^9}, { 3.4473954231132*^9, 3.4473954756384*^9}, {3.4473955348716*^9, 3.4473955723272*^9}, {3.447395648502*^9, 3.4473957588876*^9}, { 3.4473957903996*^9, 3.4473958488372*^9}, 3.4473962894154*^9, { 3.447396350817*^9, 3.447396352611*^9}, {3.4474625379146*^9, 3.4474625637326*^9}, {3.558360651728078*^9, 3.558360652102478*^9}, { 3.5619791319820857`*^9, 3.561979135788492*^9}, 3.561979369382504*^9, { 3.5619794930439215`*^9, 3.5619795010155354`*^9}, {3.561979569218855*^9, 3.56197960614412*^9}, {3.5619797417551584`*^9, 3.5619797448751636`*^9}, { 3.618719065033702*^9, 3.618719075426296*^9}, {3.6187194011669273`*^9, 3.6187194449454317`*^9}, {3.6187196998040085`*^9, 3.6187197102436056`*^9}, {3.618719902254588*^9, 3.6187199711455283`*^9}, { 3.618722365406472*^9, 3.6187225412555304`*^9}, {3.6187226885009522`*^9, 3.6187227109872384`*^9}, {3.618722756922866*^9, 3.6187231317203026`*^9}, { 3.618723424250035*^9, 3.6187234267291765`*^9}, {3.6187235105259695`*^9, 3.6187236491028957`*^9}, {3.618723691580325*^9, 3.618723745975436*^9}, { 3.618723778837316*^9, 3.6187238310002995`*^9}, {3.6187239055875654`*^9, 3.618723940035536*^9}, {3.6187239782667227`*^9, 3.6187240219352207`*^9}, { 3.618724166762504*^9, 3.618724177411113*^9}, {3.618729321696159*^9, 3.618729328067523*^9}, 3.618729374058154*^9, {3.6187294379838104`*^9, 3.618729708464281*^9}, {3.6187297631904106`*^9, 3.618729773195983*^9}, { 3.618729822648812*^9, 3.6187299321490746`*^9}, {3.618729984399063*^9, 3.61873000654133*^9}, {3.6187300746012225`*^9, 3.6187300860458775`*^9}, { 3.618731390835507*^9, 3.6187315116174154`*^9}, {3.618731747324897*^9, 3.6187318214091344`*^9}, {3.6187318769243097`*^9, 3.618732065297084*^9}, { 3.6187321012351394`*^9, 3.618732157420353*^9}, {3.618732188384124*^9, 3.6187322435542793`*^9}, {3.6187322786112847`*^9, 3.6187325478446836`*^9}, {3.6187325819856367`*^9, 3.6187326817653437`*^9}, {3.618732810863728*^9, 3.61873282594359*^9}, { 3.6187336474335766`*^9, 3.618733754678711*^9}, {3.618733827497876*^9, 3.61873396201257*^9}, {3.6187342020362988`*^9, 3.618734236455267*^9}, 3.618734298201799*^9, {3.618734712498495*^9, 3.618734712716508*^9}, 3.6187347739640107`*^9, {3.618738817361748*^9, 3.6187388333816643`*^9}, { 3.6187391349349127`*^9, 3.6187391457955337`*^9}, {3.618739376900752*^9, 3.618739397023903*^9}, {3.618739528394417*^9, 3.618739534809784*^9}, { 3.618739972366811*^9, 3.61873997340687*^9}, {3.6187400416617737`*^9, 3.618740043022852*^9}, {3.6187400971579485`*^9, 3.618740107902563*^9}, { 3.6187401713671927`*^9, 3.6187401723312483`*^9}, {3.6187402613443394`*^9, 3.618740268819767*^9}, {3.6187403697625403`*^9, 3.6187404057615995`*^9}, { 3.618740488277319*^9, 3.618740516244919*^9}, {3.618740647782442*^9, 3.6187406551668644`*^9}, 3.6187407823021364`*^9, {3.6187418050786357`*^9, 3.618741805749674*^9}, {3.6187418557605343`*^9, 3.6187419895921893`*^9}, { 3.618742022944097*^9, 3.61874204379729*^9}, {3.6187420836395683`*^9, 3.618742103384698*^9}, {3.620462440882641*^9, 3.6204624460519366`*^9}, { 3.6204624990259666`*^9, 3.620462576450395*^9}, {3.620463682857678*^9, 3.620463713336421*^9}, 3.6204637901188126`*^9, {3.620464238835478*^9, 3.62046424411378*^9}, 3.628912429385081*^9, {3.6289135207155013`*^9, 3.6289135210805225`*^9}, 3.6289497746958513`*^9, 3.6289498371774254`*^9, { 3.62894988410911*^9, 3.6289500319795675`*^9}, {3.6289501333883677`*^9, 3.628950183744248*^9}, {3.6289503323017445`*^9, 3.628950390181055*^9}, { 3.6289505050536256`*^9, 3.6289505113579865`*^9}, {3.62895070863527*^9, 3.6289507095043197`*^9}, {3.628951013180689*^9, 3.62895101407374*^9}, { 3.629190743153632*^9, 3.629190816645361*^9}, {3.6291909709608326`*^9, 3.629190981678051*^9}, {3.629191034624544*^9, 3.6291910410049553`*^9}, { 3.6293846391370816`*^9, 3.629384641102685*^9}, {3.6294628543371735`*^9, 3.629462867097191*^9}, {3.629468063172048*^9, 3.6294681151669397`*^9}, { 3.6295205836757097`*^9, 3.6295206295085897`*^9}, {3.6295206788826766`*^9, 3.6295207067911253`*^9}, {3.6295207408927855`*^9, 3.629520753700408*^9}, { 3.629521020590745*^9, 3.6295210354395943`*^9}, {3.6295211107369013`*^9, 3.62952114882508*^9}, {3.6295212327348795`*^9, 3.6295212477237363`*^9}, { 3.6295213424816394`*^9, 3.629521343230441*^9}, {3.6295215363119802`*^9, 3.6295216753550243`*^9}, {3.629521922272258*^9, 3.6295219939855833`*^9}, { 3.6295220298188467`*^9, 3.629522446058778*^9}, {3.629522499348471*^9, 3.629522604352256*^9}, {3.629522755188921*^9, 3.62952288580795*^9}, { 3.629522918084407*^9, 3.6295233421087513`*^9}, {3.6295233808436193`*^9, 3.629523390936837*^9}, {3.629523424274096*^9, 3.6295234533369465`*^9}, { 3.6295235190130625`*^9, 3.629523521680667*^9}, 3.6295235894315863`*^9, { 3.6295237270706277`*^9, 3.629523799454755*^9}, {3.6295238514808464`*^9, 3.629523883460902*^9}, {3.6295239376085978`*^9, 3.6295239442386093`*^9}, { 3.6295241089904985`*^9, 3.629524177537019*^9}, 3.629524211888279*^9, { 3.629524277423994*^9, 3.629524396904604*^9}, {3.6295244794839497`*^9, 3.6295246248450055`*^9}, 3.629524657090262*^9, {3.6295259599109507`*^9, 3.629526013465844*^9}, {3.6295261092188125`*^9, 3.629526201414974*^9}, 3.6295263436092243`*^9, {3.6295263910333076`*^9, 3.629526583303645*^9}, { 3.629526616672104*^9, 3.629526647653758*^9}, {3.629526687558628*^9, 3.629526744888729*^9}, {3.629526804075233*^9, 3.6295268598453307`*^9}, { 3.6295269393898706`*^9, 3.6295269586559043`*^9}, {3.6295271490074387`*^9, 3.6295272149019547`*^9}, {3.6295272553684254`*^9, 3.6295272827620735`*^9}, {3.6295274137087035`*^9, 3.6295274761244135`*^9}, {3.6295275252801*^9, 3.6295279912529182`*^9}, { 3.6295281572216096`*^9, 3.629528160435215*^9}, {3.6295282905550437`*^9, 3.6295284308616905`*^9}, 3.6295285402022824`*^9, {3.629528582088356*^9, 3.629528616798417*^9}, {3.6295287666834803`*^9, 3.6295290316343455`*^9}, { 3.629529086515242*^9, 3.629529118432898*^9}, {3.6295291548121614`*^9, 3.629529292794404*^9}, {3.6295293426208916`*^9, 3.6295293491261034`*^9}, { 3.629529420699029*^9, 3.629529571535694*^9}, {3.6295296539506383`*^9, 3.629529656103442*^9}, {3.6295296894407005`*^9, 3.629529692295506*^9}, { 3.6295297445555973`*^9, 3.629529766426836*^9}, {3.6295298053333044`*^9, 3.6295298209489317`*^9}, {3.6295308380551186`*^9, 3.6295308386635194`*^9}, {3.629532377840223*^9, 3.6295323811630287`*^9}, { 3.629532480020402*^9, 3.629532482454006*^9}, {3.629532520720874*^9, 3.629532564619351*^9}, {3.62953259842461*^9, 3.6295326002654133`*^9}, { 3.6295326327758703`*^9, 3.6295326715107384`*^9}, {3.629532742428463*^9, 3.6295328288058147`*^9}, {3.6295329692184625`*^9, 3.6295330530062094`*^9}, {3.6295331824396367`*^9, 3.629533193562456*^9}, 3.6295350321720915`*^9, 3.629535158485513*^9, {3.629535245471266*^9, 3.6295352687465067`*^9}, {3.62953541293756*^9, 3.629535446384019*^9}, { 3.6295355043381205`*^9, 3.6295355262249594`*^9}, {3.629543790136781*^9, 3.629543791181983*^9}, {3.629543871350524*^9, 3.629544001673153*^9}, { 3.6295446682009234`*^9, 3.629544668466124*^9}, {3.6296010216162376`*^9, 3.6296010236442413`*^9}, {3.629601079336339*^9, 3.6296010902875586`*^9}, 3.6296011425476503`*^9, {3.6296043522397404`*^9, 3.629604399031022*^9}, { 3.629623884428093*^9, 3.629623914723346*^9}, {3.6296239662190366`*^9, 3.6296239738006496`*^9}, {3.6296240514731865`*^9, 3.6296240920176573`*^9}, {3.629624125947717*^9, 3.629624369432945*^9}, { 3.6296256512247963`*^9, 3.6296256817072496`*^9}, {3.6296260472626915`*^9, 3.629626047434292*^9}, {3.629628055568204*^9, 3.629628056098605*^9}, { 3.6296280911206665`*^9, 3.6296281088266973`*^9}, {3.6296281406819534`*^9, 3.629628273032586*^9}, {3.629628378831972*^9, 3.6296283814995766`*^9}, { 3.629628459562114*^9, 3.629628466379326*^9}, {3.629628519419419*^9, 3.6296285390754533`*^9}, {3.629633008133008*^9, 3.629633008835009*^9}, { 3.6296337764967575`*^9, 3.6296338344040594`*^9}, {3.6296342997684765`*^9, 3.629634432150309*^9}, {3.629634494035618*^9, 3.6296345320060844`*^9}, { 3.629634594499794*^9, 3.629634812182576*^9}, {3.6296348599810605`*^9, 3.6296348746918864`*^9}, {3.6296349071867433`*^9, 3.629635023172947*^9}, 3.6296350995818815`*^9, {3.6296363797201295`*^9, 3.6296363868961425`*^9}, { 3.629636462025874*^9, 3.6296364833355117`*^9}, {3.629636555922439*^9, 3.62963656780966*^9}, {3.629636770469616*^9, 3.629636774151222*^9}, { 3.6296369192782774`*^9, 3.6296369318830996`*^9}, {3.629637058539722*^9, 3.6296370719401455`*^9}, {3.629637278172508*^9, 3.629637286814923*^9}, { 3.6296376418091464`*^9, 3.629637662385583*^9}, {3.629637773551378*^9, 3.629637795360216*^9}, {3.6296390041751394`*^9, 3.629639039571602*^9}, 3.6296393829750047`*^9, {3.6296395546065063`*^9, 3.6296395649961243`*^9}, { 3.62964113386068*^9, 3.6296412507048855`*^9}, {3.629641303167777*^9, 3.629641313744596*^9}, {3.6296416285116315`*^9, 3.629641628886032*^9}, { 3.6296416658736973`*^9, 3.6296416815049243`*^9}, 3.6296417376338234`*^9, { 3.6296855551269727`*^9, 3.6296855804270077`*^9}, {3.6297079065796247`*^9, 3.6297079070476255`*^9}, {3.6297080850439377`*^9, 3.629708135728427*^9}, { 3.6297083496516027`*^9, 3.6297084025512953`*^9}, {3.629708781767563*^9, 3.629708790940379*^9}, {3.6297089402482414`*^9, 3.6297089618542795`*^9}, { 3.6297105345398417`*^9, 3.629710538580249*^9}, {3.6297107810514746`*^9, 3.6297107850138817`*^9}, {3.6297109100481014`*^9, 3.629710915710911*^9}, { 3.629711201534613*^9, 3.629711204311418*^9}, {3.629711236307074*^9, 3.6297115007275386`*^9}, {3.6297115377464037`*^9, 3.6297115441112146`*^9}, 3.6297116025645175`*^9, {3.6298716505389357`*^9, 3.629871851841689*^9}, { 3.62987837458679*^9, 3.629878383510006*^9}, {3.6298784402629056`*^9, 3.629878447345318*^9}, {3.6298785221786494`*^9, 3.6298786580236883`*^9}, { 3.629878689613744*^9, 3.629878737147027*^9}, 3.629878783853509*^9, { 3.629878832322794*^9, 3.6298789171723433`*^9}, {3.6298802128122005`*^9, 3.6298802929723125`*^9}, 3.6298813644148126`*^9, {3.629882428887303*^9, 3.629882435887313*^9}, {3.6298986251827383`*^9, 3.6298988530367384`*^9}, { 3.6298989036744275`*^9, 3.6298989486493063`*^9}, {3.629899016868226*^9, 3.6298991622448816`*^9}, {3.6298997154530535`*^9, 3.629899740147897*^9}, { 3.6298998248560457`*^9, 3.629899978048314*^9}, {3.6299000396372223`*^9, 3.6299001557638264`*^9}, {3.6299001966826982`*^9, 3.6299002595352087`*^9}, 3.6299005011236343`*^9, {3.6299005468317146`*^9, 3.629900567642151*^9}, { 3.629900887676713*^9, 3.629900990153293*^9}, {3.6299011689220085`*^9, 3.6299012295125146`*^9}, {3.6299013754039707`*^9, 3.6299014166036434`*^9}, 3.6299014589733176`*^9, {3.6299015096734066`*^9, 3.629901588765546*^9}, { 3.629901662569275*^9, 3.6299016974665365`*^9}, {3.629901952339784*^9, 3.6299019599057975`*^9}, 3.6299020306051216`*^9, {3.6299022330934772`*^9, 3.6299022682559395`*^9}, {3.6299023020455985`*^9, 3.629902332808852*^9}, { 3.6299024532566643`*^9, 3.629902462850681*^9}, {3.629949880225117*^9, 3.6299498807867184`*^9}, {3.6299503101150723`*^9, 3.6299503156998825`*^9}, {3.629950355058751*^9, 3.629950498937804*^9}, { 3.6299555415202007`*^9, 3.6299555507086167`*^9}, {3.6299556061667137`*^9, 3.6299557553497763`*^9}, {3.629955788499834*^9, 3.6299558948608212`*^9}, { 3.629956042764681*^9, 3.629956043809883*^9}, {3.6299560914211664`*^9, 3.6299561017327843`*^9}, 3.629956145849662*^9, {3.6299584813821354`*^9, 3.6299585082765827`*^9}, 3.6299585652946825`*^9, {3.629958616587573*^9, 3.6299586356508064`*^9}, {3.629958715073346*^9, 3.6299588186419287`*^9}, { 3.629958857454797*^9, 3.629958927249319*^9}, {3.629959427994599*^9, 3.629959494669116*^9}, {3.6299595293323765`*^9, 3.6299596037913074`*^9}, { 3.62995966795422*^9, 3.62995967360143*^9}, {3.6299597835972233`*^9, 3.6299597841120243`*^9}, {3.629959826622099*^9, 3.629959862533362*^9}, { 3.6299599051682367`*^9, 3.6299599235918694`*^9}, 3.629959979939168*^9, { 3.6299601345354395`*^9, 3.62996014612626*^9}, 3.6299601769831142`*^9, { 3.629960253142448*^9, 3.629960269538077*^9}, {3.6299603041701374`*^9, 3.6299603078205442`*^9}, {3.6299604300467587`*^9, 3.629960435491168*^9}, { 3.6299605300585346`*^9, 3.6299605636609936`*^9}, {3.6299606195870914`*^9, 3.6299606581971593`*^9}, {3.629960824228251*^9, 3.6299608755367413`*^9}, { 3.629960906658796*^9, 3.6299609978409557`*^9}, {3.6299610312250147`*^9, 3.629961070646284*^9}, {3.629961135698398*^9, 3.6299611643088484`*^9}, { 3.6299720458358483`*^9, 3.6299721791536827`*^9}, {3.6299722439717965`*^9, 3.629972300007095*^9}, {3.6299723670872126`*^9, 3.6299723937008595`*^9}, { 3.629972457801372*^9, 3.6299724710613956`*^9}, {3.629972740193068*^9, 3.6299728251196175`*^9}, {3.6299729203577843`*^9, 3.6299729350218105`*^9}, {3.6299729720874753`*^9, 3.6299730462188053`*^9}, {3.629973116044528*^9, 3.6299731230177402`*^9}, { 3.629973184310248*^9, 3.6299732090830917`*^9}, {3.629973349982539*^9, 3.6299734360166903`*^9}, 3.629973534562063*^9, {3.629973577446539*^9, 3.629973586104554*^9}, {3.6299740374133463`*^9, 3.629974083823428*^9}, { 3.6299742505565205`*^9, 3.629974337089873*^9}, {3.629974382907153*^9, 3.6299744466176653`*^9}, {3.629974589794717*^9, 3.629974590761918*^9}, { 3.629974776215044*^9, 3.6299747850134597`*^9}, {3.6299748226095257`*^9, 3.6299748237483273`*^9}, 3.6299748618435946`*^9, {3.629975198476586*^9, 3.6299752545898843`*^9}, {3.62997531475919*^9, 3.6299753175515947`*^9}, { 3.6299754601982455`*^9, 3.6299754625382495`*^9}, {3.629975592034077*^9, 3.629975592502078*^9}, {3.629983277446268*^9, 3.6299832946842985`*^9}, { 3.62998342081052*^9, 3.6299835439883366`*^9}, {3.629983615514462*^9, 3.629983931009416*^9}, {3.6299919807040443`*^9, 3.6299919808912444`*^9}, { 3.629992028330928*^9, 3.6299920922130404`*^9}, 3.629992198480427*^9, { 3.6299922299300823`*^9, 3.629992250506518*^9}, {3.629992292657792*^9, 3.6299923603151107`*^9}, {3.6299924387676487`*^9, 3.6299924398440504`*^9}, {3.6299925764846907`*^9, 3.6299926096347485`*^9}, {3.6299928122323046`*^9, 3.629992818768716*^9}, { 3.6299929049120674`*^9, 3.629992905411268*^9}, {3.6299929850338078`*^9, 3.6299929866250105`*^9}, {3.6299931061992207`*^9, 3.62999312270405*^9}, { 3.629993172312137*^9, 3.6299932618718944`*^9}, {3.6299933276572104`*^9, 3.6299933842073092`*^9}, {3.630287775665962*^9, 3.630287795852398*^9}, { 3.6303896387100534`*^9, 3.630389666774503*^9}, {3.6303896967889557`*^9, 3.6303897095341783`*^9}, {3.6303897587054644`*^9, 3.630389880448078*^9}, { 3.6303899127557354`*^9, 3.630390009444705*^9}, 3.630390057321189*^9, 3.630390443484267*^9, {3.63039095720877*^9, 3.6303909789240074`*^9}, { 3.6303910572205453`*^9, 3.6303911291054716`*^9}, {3.630391163035531*^9, 3.6303911740803504`*^9}, {3.630391240224467*^9, 3.6303912875081496`*^9}, { 3.6303913396902413`*^9, 3.630391404570755*^9}, {3.630391479513287*^9, 3.6303917572873745`*^9}, {3.630391868905571*^9, 3.6303920027226057`*^9}, { 3.630392064327114*^9, 3.630392219843787*^9}, {3.63039226121506*^9, 3.63039232943398*^9}, {3.6303924315985594`*^9, 3.6303924441097813`*^9}, { 3.6303926866122074`*^9, 3.6303927118530517`*^9}, {3.630392795671999*^9, 3.6303928006172075`*^9}, {3.6303986032190485`*^9, 3.6303986046230516`*^9}, {3.6303986654631586`*^9, 3.6303987936485834`*^9}, {3.63039889979117*^9, 3.6303989091199865`*^9}, { 3.630399006323757*^9, 3.630399007259759*^9}, {3.630399117224352*^9, 3.630399214771323*^9}, {3.6303992555185947`*^9, 3.6303993036758795`*^9}, { 3.630399467725767*^9, 3.630399502731636*^9}, {3.6303995748037624`*^9, 3.630399595614199*^9}, {3.6303996329294643`*^9, 3.630399658076709*^9}, { 3.630399711335202*^9, 3.6303997453120623`*^9}, {3.6303998546994543`*^9, 3.6303999880484886`*^9}, {3.6304000742074394`*^9, 3.630400123441126*^9}, { 3.6304001724564123`*^9, 3.630400251595351*^9}, {3.630400324166679*^9, 3.630400327052684*^9}, {3.630400358190338*^9, 3.6304003597503414`*^9}, { 3.6304004587481155`*^9, 3.6304004640521245`*^9}, {3.630400521975026*^9, 3.630400526124634*^9}, {3.630400567199506*^9, 3.630400593516752*^9}, { 3.6304012340070767`*^9, 3.6304013035207987`*^9}, {3.6304013614749007`*^9, 3.630401367933312*^9}, {3.630401686939398*^9, 3.6304017294598303`*^9}, { 3.630401794020523*^9, 3.6304018922061386`*^9}, {3.6304019687775183`*^9, 3.630401987153569*^9}, {3.630402072749465*^9, 3.63040208297405*^9}, { 3.6304022247881613`*^9, 3.630402255931943*^9}, 3.630402329306139*^9, { 3.6304023806970787`*^9, 3.6304024212403975`*^9}, {3.6304025002259154`*^9, 3.630402528595538*^9}, {3.6304025620694523`*^9, 3.630402575015193*^9}, { 3.6304026411829777`*^9, 3.630402649073429*^9}, {3.630402695548087*^9, 3.6304027128260756`*^9}, {3.630402783923142*^9, 3.6304027982389607`*^9}, { 3.6304028797236214`*^9, 3.6304030111811404`*^9}, {3.6304030562107162`*^9, 3.6304031598846455`*^9}, {3.630403236330018*^9, 3.6304032404072514`*^9}, { 3.630403373001835*^9, 3.6304033888147397`*^9}, {3.6304039420953856`*^9, 3.6304039512829113`*^9}, 3.6304039831437335`*^9, {3.630404015975611*^9, 3.6304040663624935`*^9}, {3.630404173614628*^9, 3.630404246945822*^9}, { 3.6304042891772375`*^9, 3.630404299595834*^9}, {3.630404391083066*^9, 3.630404392406142*^9}, {3.6304045301800222`*^9, 3.6304045579486103`*^9}, { 3.630404640215316*^9, 3.630404762796327*^9}, {3.630404877629895*^9, 3.630404883104208*^9}, {3.6304050364729805`*^9, 3.630405098270515*^9}, { 3.6304051736118245`*^9, 3.6304051965901384`*^9}, {3.6304053802536435`*^9, 3.63040539242334*^9}, {3.630406035965148*^9, 3.630406041998493*^9}, { 3.630406072049212*^9, 3.6304060962065935`*^9}, {3.630406264081196*^9, 3.6304062707025747`*^9}, {3.63040632219952*^9, 3.630406385461138*^9}, { 3.630406477200385*^9, 3.630406482095665*^9}, {3.6304066170883865`*^9, 3.6304066222256804`*^9}, {3.630406957868878*^9, 3.630406973411767*^9}, { 3.6304070081447535`*^9, 3.630407018199329*^9}, {3.630407411376817*^9, 3.630407412542884*^9}, {3.6304080609339695`*^9, 3.630408121202417*^9}, { 3.6304081585485525`*^9, 3.6304081832129636`*^9}, {3.63040821409673*^9, 3.630408421131572*^9}, 3.6304934333363276`*^9, {3.63049350751357*^9, 3.630493677593298*^9}, {3.630493716898546*^9, 3.6304937846684227`*^9}, 3.630493922944331*^9, {3.6304939556752033`*^9, 3.630494117430455*^9}, { 3.6304941486092386`*^9, 3.6304941767788496`*^9}, {3.6304942118648567`*^9, 3.6304942530272107`*^9}, {3.6304942838399734`*^9, 3.6304942845820155`*^9}, {3.6304943454054947`*^9, 3.6304944442451477`*^9}, {3.63080749995092*^9, 3.6308075480801234`*^9}, { 3.630807586536323*^9, 3.630807621440319*^9}, {3.630807680459695*^9, 3.630807682914836*^9}, {3.630807736889923*^9, 3.6308077644745007`*^9}, { 3.6308078081089964`*^9, 3.6308078670123653`*^9}, {3.630807991648494*^9, 3.630807997541831*^9}, {3.6308081080891542`*^9, 3.6308081919599514`*^9}, { 3.630808306368495*^9, 3.630808345060708*^9}, {3.6308087281906223`*^9, 3.6308087555171847`*^9}, {3.630809110815507*^9, 3.630809169033837*^9}, { 3.6308091998195972`*^9, 3.630809448512822*^9}, {3.6308095328996487`*^9, 3.6308095448223305`*^9}, {3.630809582269472*^9, 3.6308095873607635`*^9}, { 3.630809665529235*^9, 3.630809684808337*^9}, {3.6308316258485594`*^9, 3.6308318380886984`*^9}, {3.63083188164919*^9, 3.630831966930068*^9}, 3.6320400558356075`*^9, {3.6354749882908883`*^9, 3.635474989418953*^9}, { 3.635475084557395*^9, 3.6354750875145636`*^9}, {3.6354751334091887`*^9, 3.635475162315842*^9}, {3.6354754001974483`*^9, 3.6354754820331287`*^9}, 3.635475512931896*^9, {3.6354756222781506`*^9, 3.635475622861184*^9}, { 3.635475691642118*^9, 3.6354757057969275`*^9}, {3.6354757798291616`*^9, 3.635475797395167*^9}, {3.635475884848169*^9, 3.6354758981309285`*^9}, { 3.635475961488552*^9, 3.6354759738382587`*^9}, {3.6354760213729773`*^9, 3.6354760572050266`*^9}, {3.6354761282470903`*^9, 3.635476136040536*^9}, { 3.6354761719365892`*^9, 3.635476212217893*^9}, {3.6593346599546614`*^9, 3.659334660890663*^9}, {3.6593347077219453`*^9, 3.659334720701168*^9}, { 3.6593348752974396`*^9, 3.6593348758122406`*^9}, {3.6593349140947075`*^9, 3.6593350070240707`*^9}, {3.6593350466949406`*^9, 3.6593350543701544`*^9}, {3.659335103791041*^9, 3.6593351614487424`*^9}, 3.659335217686841*^9, {3.659335262084519*^9, 3.6593352995869846`*^9}, { 3.6593356899482727`*^9, 3.659335701819893*^9}, {3.659335964227954*^9, 3.659335964602355*^9}, {3.65933603594128*^9, 3.6593360629605274`*^9}, { 3.6593361352354546`*^9, 3.6593361504454813`*^9}, {3.6593363929479074`*^9, 3.6593364061611304`*^9}, 3.6593368946915884`*^9, {3.6884748265656157`*^9, 3.6884748268716326`*^9}, {3.6884748600075283`*^9, 3.688474861420609*^9}, { 3.6885242858240776`*^9, 3.6885243001140976`*^9}, {3.6888842911675606`*^9, 3.6888843311676164`*^9}, {3.688966242423658*^9, 3.688966263933688*^9}, { 3.6897393587897596`*^9, 3.6897393649897685`*^9}, 3.689739477049925*^9, { 3.6898595970621734`*^9, 3.689859597272174*^9}, {3.6898596707522764`*^9, 3.6898597190523443`*^9}, {3.689859768552414*^9, 3.6898597721424184`*^9}, { 3.689859855272535*^9, 3.689859859882541*^9}, {3.6898605078334484`*^9, 3.6898607266237545`*^9}, 3.6898608811139708`*^9, {3.6898609634740863`*^9, 3.689860974304102*^9}, 3.6898610140141573`*^9, {3.6898611496043468`*^9, 3.6898611683243732`*^9}, {3.689861462024784*^9, 3.6898615624849253`*^9}, { 3.6898616142149973`*^9, 3.6898616164350004`*^9}, 3.6898616657950697`*^9, { 3.689861716805141*^9, 3.689861749905187*^9}, {3.732677920575506*^9, 3.7326779208190203`*^9}, {3.7519672427004185`*^9, 3.7519672444968877`*^9}, {3.7519674022097683`*^9, 3.75196742976579*^9}, { 3.751967484127989*^9, 3.751967510853814*^9}, {3.7519675409404893`*^9, 3.751967541549782*^9}, {3.7519675797751045`*^9, 3.751967592209671*^9}, { 3.7519676829383273`*^9, 3.7519676841255474`*^9}, {3.7519677154775553`*^9, 3.7519677953499403`*^9}, 3.751967827811061*^9, {3.7519679545625095`*^9, 3.751967957999185*^9}, {3.751968003754015*^9, 3.7519681477513895`*^9}, { 3.751968264817631*^9, 3.751968270722477*^9}, {3.7519689618119907`*^9, 3.751968969888235*^9}, {3.7519691168917775`*^9, 3.7519691395895615`*^9}, { 3.751969242782174*^9, 3.7519692581691785`*^9}, {3.7519693625211954`*^9, 3.751969378579924*^9}, {3.751969409572627*^9, 3.751969438643936*^9}, { 3.7519695894526725`*^9, 3.751969614306203*^9}, {3.7523200108586655`*^9, 3.752320012354121*^9}, {3.7553831315619707`*^9, 3.755383134119626*^9}, { 3.7553831893197794`*^9, 3.755383241814331*^9}, {3.7553832736267967`*^9, 3.7553832810757113`*^9}, {3.7554336536222963`*^9, 3.755433684797229*^9}, { 3.7554337764737434`*^9, 3.7554338315300155`*^9}, {3.755433998047738*^9, 3.7554340265485487`*^9}, {3.755446573138784*^9, 3.755446636911299*^9}, { 3.75544667493072*^9, 3.755446753435521*^9}, {3.755446891541581*^9, 3.7554468921547422`*^9}, {3.7554469323588533`*^9, 3.755446936867403*^9}, { 3.7554470190332975`*^9, 3.7554472776872244`*^9}, {3.7555217323692026`*^9, 3.755521732847602*^9}, {3.755521767127169*^9, 3.7555217972041793`*^9}, { 3.755522561453134*^9, 3.755522564231819*^9}, {3.755522601885935*^9, 3.7555226037287407`*^9}, {3.7555226758687305`*^9, 3.755522678585092*^9}, { 3.7555234832604623`*^9, 3.7555235920444417`*^9}, {3.7555239506007543`*^9, 3.755524013893358*^9}, {3.755524076791689*^9, 3.7555240812793446`*^9}, { 3.7555241238138275`*^9, 3.7555241268985643`*^9}, {3.7555242930449886`*^9, 3.7555243378577013`*^9}, {3.7555256673767824`*^9, 3.7555256808205338`*^9}, {3.7555258588384123`*^9, 3.755525900317296*^9}, { 3.755525930708299*^9, 3.7555260436531134`*^9}, {3.755607147401991*^9, 3.7556071504143705`*^9}, {3.755607992884314*^9, 3.7556080025382996`*^9}, { 3.7556094344057455`*^9, 3.7556094348690443`*^9}, {3.7559613653116636`*^9, 3.755961445097105*^9}, 3.755961484246889*^9, {3.7559618979231987`*^9, 3.755961939470047*^9}, {3.7559620323724904`*^9, 3.7559620330864005`*^9}, { 3.755962155557907*^9, 3.7559621601593847`*^9}, {3.755962303755834*^9, 3.755962343830135*^9}, {3.7559624058018165`*^9, 3.7559624450501757`*^9}, 3.756002186674869*^9, 3.7560029626855392`*^9, {3.756003222110388*^9, 3.756003295034633*^9}, {3.7560056331492863`*^9, 3.7560056663855457`*^9}, { 3.7560057813555765`*^9, 3.7560057863836613`*^9}, {3.7560058917172394`*^9, 3.756005927847292*^9}, 3.756006092376186*^9, 3.756009112317705*^9, { 3.756091886039587*^9, 3.756091887764086*^9}, {3.756092005435152*^9, 3.7560920727337685`*^9}, {3.75609212911592*^9, 3.7560921293252516`*^9}, { 3.756092262958163*^9, 3.756092263157668*^9}, {3.756092342487877*^9, 3.756092347894502*^9}, {3.7560929036769304`*^9, 3.7560929278911004`*^9}, { 3.7560930741522417`*^9, 3.756093083420331*^9}, {3.7560932986236534`*^9, 3.7560933139459305`*^9}, {3.756093449985523*^9, 3.7560934874491863`*^9}, { 3.756093592694581*^9, 3.7560936019456573`*^9}, {3.756093634438078*^9, 3.756093673866626*^9}, {3.756093873069885*^9, 3.756093897964734*^9}, { 3.7560940650109406`*^9, 3.756094078056768*^9}, {3.756442536546026*^9, 3.756442607904289*^9}, {3.7564436397451363`*^9, 3.7564436403231254`*^9}, { 3.7636034984570236`*^9, 3.7636034989933815`*^9}, {3.763603551051456*^9, 3.7636035527617817`*^9}, {3.7636036049384193`*^9, 3.7636036392233057`*^9}, {3.7636036850937223`*^9, 3.763603692587598*^9}, { 3.7636037258272257`*^9, 3.7636037459031096`*^9}, {3.7636037792254367`*^9, 3.76360387572289*^9}, {3.763603971837229*^9, 3.7636040341423655`*^9}, { 3.763604066526084*^9, 3.7636040756798687`*^9}, {3.7636041452118535`*^9, 3.763604278007333*^9}, {3.763604317710966*^9, 3.7636043271387568`*^9}, { 3.7636043584877644`*^9, 3.763604415561053*^9}, {3.763604445680462*^9, 3.7636044504114943`*^9}, {3.763604615444647*^9, 3.7636048082554193`*^9}, 3.763604854904996*^9, {3.7636133594095488`*^9, 3.7636133618464766`*^9}, { 3.7636136063756704`*^9, 3.7636136315671196`*^9}, {3.7636990373827705`*^9, 3.7636990431157646`*^9}, {3.763699090332087*^9, 3.763699110952259*^9}, { 3.763699227420497*^9, 3.7636993642943506`*^9}, {3.763700085627533*^9, 3.763700088329999*^9}, {3.7637001721125274`*^9, 3.763700181422837*^9}, { 3.763700248063385*^9, 3.7637003918630466`*^9}, {3.763700591783223*^9, 3.7637006017496295`*^9}, {3.7637007583576717`*^9, 3.7637007603074865`*^9}, {3.7637137795793185`*^9, 3.7637137822587233`*^9}, {3.7637148704355187`*^9, 3.763714870624051*^9}, { 3.763727592158518*^9, 3.7637275933445053`*^9}, {3.7637276688363667`*^9, 3.7637276694756594`*^9}, 3.763803448896332*^9, {3.76380349501632*^9, 3.7638036835067654`*^9}, {3.763804829093463*^9, 3.7638048385675254`*^9}, 3.7638051033646154`*^9, 3.7638053924528885`*^9, {3.763805557684454*^9, 3.763805634255308*^9}, {3.763806843847647*^9, 3.763806847966059*^9}, { 3.763806942652097*^9, 3.7638071770752254`*^9}, {3.7638141184594107`*^9, 3.763814134133461*^9}, {3.7638146808628216`*^9, 3.7638146925645113`*^9}, { 3.7638147709278784`*^9, 3.7638147811883087`*^9}, {3.7638148155281043`*^9, 3.763814819843194*^9}, {3.7638150259647446`*^9, 3.763815028601293*^9}, { 3.7638151529595194`*^9, 3.763815155849978*^9}, {3.7638163770262136`*^9, 3.763816380851597*^9}, {3.7638164181856327`*^9, 3.7638164950537987`*^9}, 3.763816568304102*^9, {3.7638166173645625`*^9, 3.763816618808757*^9}, { 3.7638167204462805`*^9, 3.763816721012859*^9}, {3.763857602253485*^9, 3.7638579604183645`*^9}, {3.7638580038507566`*^9, 3.7638580060526443`*^9}, {3.763858082269992*^9, 3.7638581746835337`*^9}, { 3.7638582163351564`*^9, 3.7638582415275116`*^9}, {3.7638582983238*^9, 3.763858907503306*^9}, {3.763858941318697*^9, 3.763858956626134*^9}, { 3.7638602435602536`*^9, 3.763860245408451*^9}, {3.7638694636456347`*^9, 3.7638694647177277`*^9}, {3.7638708199536576`*^9, 3.763870829436488*^9}, { 3.763871287170555*^9, 3.7638712876184006`*^9}, {3.763943214376035*^9, 3.7639432984591475`*^9}, {3.763943418832348*^9, 3.7639434335508127`*^9}, { 3.76394347113767*^9, 3.7639435187320576`*^9}, {3.763943585908682*^9, 3.7639436125255404`*^9}, {3.763951722152746*^9, 3.76395172989299*^9}, { 3.7639517863423367`*^9, 3.7639519945900664`*^9}, {3.763952081515512*^9, 3.7639521530710773`*^9}, {3.763952353248129*^9, 3.763952357026309*^9}, { 3.7639524211903834`*^9, 3.7639524243979177`*^9}, {3.7639527174925117`*^9, 3.7639527180252266`*^9}, {3.7641265625745993`*^9, 3.7641265632314167`*^9}, {3.764126605555829*^9, 3.7641266075095396`*^9}, { 3.7641268313964133`*^9, 3.7641268543573804`*^9}, {3.764127044657903*^9, 3.7641270479422092`*^9}, {3.7641271442332697`*^9, 3.7641271469362774`*^9}, {3.764127227626192*^9, 3.7641272592640233`*^9}, { 3.764127335707515*^9, 3.7641273386484756`*^9}, {3.764127429843852*^9, 3.7641274364304185`*^9}, {3.7641275071859307`*^9, 3.764127516803895*^9}, 3.7641276043548007`*^9, {3.7641276925365753`*^9, 3.764127697080591*^9}, 3.764127798472331*^9, 3.764127853631323*^9, 3.764127908496078*^9, { 3.7641280050343323`*^9, 3.764128022046494*^9}, {3.764128128597419*^9, 3.764128154116727*^9}, {3.7641286864636617`*^9, 3.764128701643106*^9}, { 3.7641289910924444`*^9, 3.7641290126680794`*^9}, {3.7641290672285347`*^9, 3.7641290737798567`*^9}, {3.7641325425120363`*^9, 3.764132565390477*^9}, { 3.7641327425004654`*^9, 3.764132750040793*^9}, 3.7641327968340364`*^9, { 3.764133146776842*^9, 3.764133204874522*^9}, {3.7641333488187037`*^9, 3.7641333525577593`*^9}, {3.764413145593136*^9, 3.7644131471236105`*^9}, { 3.764413201645049*^9, 3.7644132349609704`*^9}, {3.764413325008136*^9, 3.7644133748980193`*^9}, {3.7644134113425665`*^9, 3.7644135151187*^9}, { 3.764413554409053*^9, 3.7644136160674934`*^9}, {3.76441371984758*^9, 3.764413730103909*^9}, 3.764419641962368*^9, {3.7644198522879405`*^9, 3.764419879249356*^9}, 3.764419909536559*^9, {3.764419991012162*^9, 3.764420000171088*^9}, {3.7644200798862047`*^9, 3.7644200950961914`*^9}, { 3.7644201529471693`*^9, 3.764420153715966*^9}, {3.764420210346301*^9, 3.764420255343707*^9}, {3.764420296178318*^9, 3.7644203000939393`*^9}, { 3.7644203803359275`*^9, 3.7644203931390867`*^9}, 3.7644204418727274`*^9, { 3.7647259720700207`*^9, 3.7647261047260523`*^9}, {3.7647263483375626`*^9, 3.76472635879602*^9}, 3.764726656736601*^9, {3.764727009127914*^9, 3.764727020100875*^9}, {3.7647270591828785`*^9, 3.7647270819631023`*^9}, { 3.7647272109090505`*^9, 3.764727227846332*^9}, {3.76473247809907*^9, 3.7647324813925114`*^9}, {3.7647349484962797`*^9, 3.7647349979358416`*^9}, {3.7647351097258167`*^9, 3.764735124772463*^9}, { 3.7647352810674453`*^9, 3.7647352901139917`*^9}, {3.7647353746429515`*^9, 3.764735379550926*^9}, {3.7647354596539807`*^9, 3.764735507677454*^9}, { 3.7647355546341*^9, 3.764735728811817*^9}, {3.764735837449795*^9, 3.76473584132898*^9}, {3.76473603649269*^9, 3.7647360592982664`*^9}, { 3.7647360998228803`*^9, 3.76473621551197*^9}, {3.7647362545599003`*^9, 3.764736286430997*^9}, {3.7647364592833533`*^9, 3.764736464019006*^9}, { 3.764736566167658*^9, 3.7647365918958225`*^9}, {3.764764761680134*^9, 3.7647648482473745`*^9}, 3.764764917763693*^9, {3.764764964821686*^9, 3.764765090741813*^9}, {3.7647651742140284`*^9, 3.7647652517335076`*^9}, { 3.764765341266399*^9, 3.7647653614173465`*^9}, 3.764765400284145*^9, { 3.764765691384389*^9, 3.764765708710143*^9}, 3.7647657454275875`*^9, { 3.76476578351686*^9, 3.764765871262255*^9}, {3.7647661045180917`*^9, 3.76476612822571*^9}, {3.7647661964223824`*^9, 3.764766239375331*^9}, { 3.764766330361228*^9, 3.764766338297905*^9}, {3.764767015060799*^9, 3.7647670193029037`*^9}, {3.764767076590926*^9, 3.7647671160277977`*^9}, { 3.7647671493139205`*^9, 3.7647672079236426`*^9}, {3.764767458938404*^9, 3.7647674608323865`*^9}, {3.764810938444873*^9, 3.7648109399353456`*^9}, { 3.7648118616019874`*^9, 3.7648118695079126`*^9}, {3.7648120589477816`*^9, 3.7648124600413237`*^9}, {3.76481250476682*^9, 3.7648125259602103`*^9}, { 3.764812601341893*^9, 3.7648126577763243`*^9}, {3.7648126944039307`*^9, 3.7648128855627623`*^9}, {3.764812924923909*^9, 3.764812926481821*^9}, { 3.764813041485982*^9, 3.764813131254232*^9}, {3.7648134679328885`*^9, 3.7648136479313235`*^9}, {3.7648136917777314`*^9, 3.764813697753367*^9}, { 3.7648137297570653`*^9, 3.764813747862262*^9}, 3.764813784221693*^9, { 3.7648138370678406`*^9, 3.7648141387969923`*^9}, {3.764814321050164*^9, 3.764814422489184*^9}, {3.764814461366684*^9, 3.7648145835728483`*^9}, { 3.764814614769511*^9, 3.7648147525825167`*^9}, {3.764815363375289*^9, 3.7648153644907384`*^9}, {3.764815451671169*^9, 3.7648154601533747`*^9}, { 3.7648175917802963`*^9, 3.7648176401910563`*^9}, {3.765885491237231*^9, 3.765885501131465*^9}, {3.766572999289345*^9, 3.7665729996020145`*^9}, { 3.7665730613126965`*^9, 3.7665730616706066`*^9}, {3.7840103262125545`*^9, 3.7840103546413517`*^9}, {3.784011309725755*^9, 3.7840113197719574`*^9}, { 3.784013374800973*^9, 3.7840133842981763`*^9}, {3.7840238533665447`*^9, 3.78402395932942*^9}, {3.784024091276659*^9, 3.784024112209529*^9}, { 3.7840242793219643`*^9, 3.784024296655184*^9}, {3.7840290670892677`*^9, 3.7840291348388853`*^9}, {3.784029222997594*^9, 3.784029542926179*^9}, { 3.784375172285057*^9, 3.784375319701829*^9}, {3.7843753678421807`*^9, 3.7843753788103914`*^9}, {3.7843754844339557`*^9, 3.784375827494117*^9}, { 3.784375862317687*^9, 3.7843759567563844`*^9}, {3.784376004941759*^9, 3.7843760080157185`*^9}, {3.784376101918992*^9, 3.7843761244332943`*^9}, { 3.784376181191763*^9, 3.7843762145091863`*^9}, {3.7843792489960337`*^9, 3.78437926273014*^9}, {3.7843793293934345`*^9, 3.784379368676588*^9}, { 3.7843796529835215`*^9, 3.7843796858862267`*^9}, {3.784450863324359*^9, 3.7844508986076546`*^9}, {3.7844510208392324`*^9, 3.784451027915551*^9}, { 3.7844511176315613`*^9, 3.7844511673791957`*^9}, {3.784451235055628*^9, 3.78445132575735*^9}, {3.784451995615477*^9, 3.7844520110330954`*^9}, { 3.7844522907551537`*^9, 3.7844523421551*^9}, {3.784700119490345*^9, 3.7847001627913013`*^9}, {3.7847004221290607`*^9, 3.7847004380767317`*^9}, 3.7847007913506136`*^9, {3.784781955129138*^9, 3.784781977787957*^9}, { 3.78488170216677*^9, 3.784881704210422*^9}, 3.784882130557441*^9, { 3.78488220347418*^9, 3.7848822064697027`*^9}, {3.784883393455822*^9, 3.784883458551924*^9}, 3.7848835306495824`*^9, {3.7848836822092113`*^9, 3.7848837303696923`*^9}, 3.7848838199009576`*^9, {3.7848842507527857`*^9, 3.7848842836585226`*^9}, 3.7848843847882996`*^9, {3.784884461405264*^9, 3.7848844645041113`*^9}, {3.784884559404122*^9, 3.7848845656634912`*^9}, { 3.7848852409944844`*^9, 3.7848852740337477`*^9}, {3.7848854548929386`*^9, 3.7848854893046365`*^9}, {3.7848856741783943`*^9, 3.784885691704702*^9}, { 3.784885809660874*^9, 3.784885811424426*^9}, {3.7848860031948376`*^9, 3.784886020570098*^9}, 3.7848861057105627`*^9, {3.7848861627726107`*^9, 3.7848862212876124`*^9}, {3.784886306497995*^9, 3.7848863509322224`*^9}, 3.784886472690192*^9, {3.7848866596243*^9, 3.784886664116289*^9}, { 3.7848866987282944`*^9, 3.7848867077911897`*^9}, {3.78488676128524*^9, 3.7848868667029366`*^9}, {3.7848869381224003`*^9, 3.7848869414281464`*^9}, {3.7848870104508753`*^9, 3.784887039889447*^9}, { 3.7848871795058794`*^9, 3.7848871976746817`*^9}, {3.7848872311446314`*^9, 3.78488724075662*^9}, 3.784887405188785*^9, {3.784887591926689*^9, 3.7848876119305134`*^9}, {3.784887676620901*^9, 3.7848876786672792`*^9}, { 3.78488771054331*^9, 3.784887714354906*^9}, {3.7848877625809546`*^9, 3.7848878103041153`*^9}, 3.7848878862881575`*^9, {3.787717235155089*^9, 3.787717269464238*^9}, {3.7877174592607603`*^9, 3.7877174674038067`*^9}, { 3.7877271032841845`*^9, 3.787727136247201*^9}, 3.787727355369296*^9, 3.7877274973278403`*^9, {3.787727855959008*^9, 3.78772792141208*^9}, 3.787728113487193*^9, {3.7877281704571557`*^9, 3.7877281735077004`*^9}, 3.7877282789827795`*^9, {3.7877286510229864`*^9, 3.787728665729192*^9}, { 3.7877287942225084`*^9, 3.787728807671986*^9}, {3.787729044867985*^9, 3.787729045536916*^9}, {3.787729589732438*^9, 3.7877296062090626`*^9}, { 3.787729794037467*^9, 3.7877297950347877`*^9}, {3.787729855548402*^9, 3.7877299039179935`*^9}, {3.7877300373241186`*^9, 3.787730068136018*^9}, { 3.7877301999859333`*^9, 3.7877302014150777`*^9}, {3.787732033225385*^9, 3.7877320471634016`*^9}, {3.787732077195259*^9, 3.7877320780358667`*^9}, 3.787732189759206*^9, {3.78773231889835*^9, 3.787732327710633*^9}, { 3.7877324857166643`*^9, 3.787732496655479*^9}, {3.7877325848303585`*^9, 3.78773258503596*^9}, {3.7877328504631166`*^9, 3.7877328625892415`*^9}, { 3.7877330254884944`*^9, 3.7877330271019044`*^9}, {3.787733136128061*^9, 3.7877331422258835`*^9}, {3.787733243513567*^9, 3.78773324558677*^9}, 3.787733310555999*^9, 3.7877334085329347`*^9, {3.7877337955932293`*^9, 3.7877337970498257`*^9}, {3.787733867727028*^9, 3.7877338687324905`*^9}, { 3.7877352224369583`*^9, 3.787735224161746*^9}, {3.787735343322833*^9, 3.787735348772827*^9}, {3.787735422704711*^9, 3.7877354268945775`*^9}, { 3.7877355100355635`*^9, 3.787735514671461*^9}, {3.7877356541994534`*^9, 3.7877356632141013`*^9}, 3.7877357913476543`*^9, 3.787736261837074*^9, { 3.7882542159043374`*^9, 3.7882542747998285`*^9}, {3.788254310967661*^9, 3.788254318430212*^9}, {3.788254585790197*^9, 3.7882545888318524`*^9}, { 3.7882547349987383`*^9, 3.788254735940298*^9}, 3.788254830063775*^9, 3.7882549155286837`*^9, {3.7882550121437798`*^9, 3.788255037735396*^9}, { 3.7882551764404287`*^9, 3.78825518352113*^9}, {3.7882552540030313`*^9, 3.788255290224329*^9}, {3.7882553843544893`*^9, 3.788255423248046*^9}, { 3.78825567982127*^9, 3.7882556852479534`*^9}, {3.7882557908576803`*^9, 3.7882558029800806`*^9}, {3.7882560240494256`*^9, 3.7882560388846164`*^9}, 3.788256102343512*^9, {3.788256161397396*^9, 3.7882561626372194`*^9}, { 3.7882562304311895`*^9, 3.78825629590362*^9}, {3.7882563614677362`*^9, 3.7882563620189795`*^9}, {3.7882564138122153`*^9, 3.7882564294158382`*^9}, {3.788256467457189*^9, 3.7882564889521217`*^9}, { 3.7882565883311844`*^9, 3.788256591497148*^9}, {3.7882568409513097`*^9, 3.7882568724526567`*^9}, {3.788256965258837*^9, 3.788256966444976*^9}, { 3.7882570073831463`*^9, 3.7882570497349973`*^9}, {3.7882570992487097`*^9, 3.788257144206352*^9}, {3.78825721252205*^9, 3.788257307277931*^9}, { 3.788257350410209*^9, 3.7882573617262745`*^9}, {3.788257424936472*^9, 3.788257434118204*^9}, {3.788276311330668*^9, 3.788276311647092*^9}, { 3.7882765465512347`*^9, 3.788276608568333*^9}, {3.7882767715851693`*^9, 3.7882768045752783`*^9}, {3.7882769342607436`*^9, 3.7882769409894867`*^9}, {3.7882770202208567`*^9, 3.7882770424485188`*^9}, {3.7882770760040703`*^9, 3.788277077341468*^9}, { 3.788277147336176*^9, 3.788277150397852*^9}, {3.7882772069909*^9, 3.7882772101572385`*^9}, {3.7882772503366175`*^9, 3.7882772773759403`*^9}, {3.7882773922958755`*^9, 3.7882773927832017`*^9}, {3.788277450684473*^9, 3.788277482126852*^9}, { 3.78827754293396*^9, 3.788277545027956*^9}, {3.7883214550230436`*^9, 3.7883214742097826`*^9}, {3.788321520104019*^9, 3.788321685390153*^9}, { 3.788321717307153*^9, 3.788321801831746*^9}, {3.788321836768508*^9, 3.788322037754008*^9}, {3.7883220686363816`*^9, 3.788322220085001*^9}, { 3.7883255906192427`*^9, 3.788325646609389*^9}, {3.7883257976991563`*^9, 3.788325804097658*^9}, {3.788325969279187*^9, 3.7883259830028267`*^9}, { 3.788326975877249*^9, 3.788326979070017*^9}, {3.788328539286415*^9, 3.788328618410488*^9}, {3.788328648595448*^9, 3.788328762662589*^9}, { 3.7883288060890923`*^9, 3.7883288805716724`*^9}, {3.7883319188300047`*^9, 3.78833193230753*^9}, {3.7883321144947567`*^9, 3.788332115050151*^9}, { 3.7883333680456443`*^9, 3.7883333686272163`*^9}, 3.7883336421611414`*^9, { 3.788333691323177*^9, 3.7883336916362*^9}, {3.788333797629262*^9, 3.7883338348662343`*^9}, {3.7883339555470386`*^9, 3.7883339660305166`*^9}, {3.7883340291758356`*^9, 3.788334031484354*^9}, { 3.788334368484807*^9, 3.7883343918754945`*^9}, {3.7883345963739557`*^9, 3.788334645315611*^9}, {3.788411405608647*^9, 3.788411409092114*^9}, { 3.7884115644712825`*^9, 3.7884115911998663`*^9}, {3.7884116673998833`*^9, 3.788411758799066*^9}, {3.788411985303985*^9, 3.788412002701314*^9}, { 3.78841218266156*^9, 3.788412217652734*^9}, {3.788412679618697*^9, 3.78841268296084*^9}, {3.788412968920223*^9, 3.7884129782039633`*^9}, { 3.7884155241723013`*^9, 3.7884155243798914`*^9}, 3.7884156619519596`*^9, { 3.7884162343262696`*^9, 3.788416236013459*^9}, {3.789022054245319*^9, 3.7890221116154556`*^9}, {3.7890222001685014`*^9, 3.789022205961149*^9}, { 3.789094077050009*^9, 3.7890940781167436`*^9}, {3.7890941254883175`*^9, 3.7890942919861226`*^9}, {3.789094340508856*^9, 3.789094543716852*^9}, { 3.789094583794143*^9, 3.7890947278803444`*^9}, {3.7890947714417076`*^9, 3.7890948342626343`*^9}, {3.789095197615344*^9, 3.789095215073329*^9}, { 3.789095256390032*^9, 3.78909525710861*^9}, {3.7890954241290827`*^9, 3.78909583987399*^9}, {3.789096056032333*^9, 3.7890960602768464`*^9}, { 3.7890960928429904`*^9, 3.789096098149865*^9}, {3.789096721918685*^9, 3.789096734998893*^9}, {3.7890967741973257`*^9, 3.78909683859006*^9}, { 3.789096947653244*^9, 3.789097122315098*^9}, {3.7890971528708224`*^9, 3.789097530683948*^9}, {3.7890975852885656`*^9, 3.7890975882562447`*^9}, { 3.7890976430709224`*^9, 3.789097656213524*^9}, {3.789107592314107*^9, 3.7891076537760305`*^9}, {3.789107685160589*^9, 3.789107760590632*^9}, { 3.7891078105008087`*^9, 3.789107846610609*^9}, {3.789107989236459*^9, 3.7891080001561875`*^9}, {3.7891082032172785`*^9, 3.7891082064574785`*^9}, {3.7891083013630204`*^9, 3.789108444864075*^9}, { 3.7891084751958127`*^9, 3.7891085010044174`*^9}, {3.7891085322441816`*^9, 3.7891085353767447`*^9}, {3.789108620037199*^9, 3.789108662297584*^9}, 3.7891087252471294`*^9, {3.789108773507248*^9, 3.7891088501491203`*^9}, { 3.7891088829987*^9, 3.789108918319019*^9}, {3.7891089606286983`*^9, 3.7891090044788837`*^9}, {3.789109048556943*^9, 3.7891091177554493`*^9}, { 3.7891091628149347`*^9, 3.7891092922346783`*^9}, {3.789109382870388*^9, 3.789109402625166*^9}, {3.7891111380334797`*^9, 3.7891113582877145`*^9}, { 3.789111396694514*^9, 3.7891114221541777`*^9}, {3.7891114539845037`*^9, 3.7891114952359962`*^9}, {3.789112929457416*^9, 3.7891129318274393`*^9}, { 3.789112963290578*^9, 3.7891131302196255`*^9}, {3.789113202949188*^9, 3.789113203379569*^9}, {3.7891144371217365`*^9, 3.789114518411393*^9}, { 3.789114638487608*^9, 3.78911468069436*^9}, {3.789114763918976*^9, 3.789114777923211*^9}, {3.789114809301983*^9, 3.7891148392057247`*^9}, { 3.7891148923150015`*^9, 3.789114904054755*^9}, {3.7891149560740595`*^9, 3.7891150071774015`*^9}, {3.789115109642312*^9, 3.7891151147637*^9}, { 3.7891185439211864`*^9, 3.789118561569729*^9}, {3.7891187834106455`*^9, 3.7891187854068985`*^9}, {3.7891188764873776`*^9, 3.7891188767373095`*^9}, {3.789121799028477*^9, 3.789121806719482*^9}, { 3.7891222627163153`*^9, 3.7891222774782734`*^9}, {3.7891223914541044`*^9, 3.7891224006004095`*^9}, {3.789122431773783*^9, 3.7891224422816577`*^9}, { 3.7891224731160736`*^9, 3.789122501042121*^9}, {3.7891226653529224`*^9, 3.7891226664045706`*^9}, 3.789122819901965*^9, {3.789122893844426*^9, 3.7891229543768473`*^9}, {3.7891229964274464`*^9, 3.7891231044294157`*^9}, {3.789123228485856*^9, 3.789123374714591*^9}, { 3.7891235661360893`*^9, 3.7891235688754067`*^9}, {3.8435393751961174`*^9, 3.84353937620569*^9}, {3.843539421737421*^9, 3.843539430280121*^9}, { 3.8435484777900076`*^9, 3.8435484882620373`*^9}, {3.8435489691083994`*^9, 3.843548981201047*^9}, {3.8435491420371304`*^9, 3.8435491556997023`*^9}, { 3.8435491977347035`*^9, 3.8435491982438793`*^9}, 3.8435492510860806`*^9, { 3.8435495081660933`*^9, 3.8435495131948795`*^9}, {3.8435495856936626`*^9, 3.843549589991126*^9}, {3.8435496998060937`*^9, 3.843549707814079*^9}, { 3.84355004136615*^9, 3.843550041760812*^9}, {3.843550160256809*^9, 3.8435501604677615`*^9}, {3.8435532120250945`*^9, 3.843553317388692*^9}, { 3.8435535239731655`*^9, 3.8435535314678483`*^9}, {3.8435535808757987`*^9, 3.843553663159541*^9}, {3.843553779645311*^9, 3.843553786004609*^9}, 3.843553906141655*^9, 3.84355405714793*^9, {3.843554149489615*^9, 3.8435541503712645`*^9}, {3.843554206843628*^9, 3.8435542071044455`*^9}, { 3.8435543508802266`*^9, 3.843554351606327*^9}, {3.843554424038799*^9, 3.8435544242271614`*^9}, {3.8435607207357883`*^9, 3.843560727908863*^9}, { 3.843560832774662*^9, 3.8435608400783997`*^9}, {3.843561442743278*^9, 3.8435614495857325`*^9}, {3.8435616862804203`*^9, 3.8435617473408427`*^9}, {3.8435618416220255`*^9, 3.84356184949818*^9}, { 3.843561965458202*^9, 3.843561967390591*^9}, {3.8435620399418516`*^9, 3.8435620427564726`*^9}, 3.8435620999099693`*^9, {3.843562319425266*^9, 3.843562335822353*^9}, {3.843562479271407*^9, 3.8435624872362185`*^9}, { 3.8435625915602407`*^9, 3.843562614304778*^9}, {3.843562735879742*^9, 3.843562741836786*^9}, {3.8436143557463255`*^9, 3.843614430899438*^9}, { 3.843614466526642*^9, 3.843614494745638*^9}, {3.84361472265639*^9, 3.8436147354884176`*^9}, {3.843614883845476*^9, 3.8436148880544443`*^9}, { 3.843615637703328*^9, 3.8436156940260696`*^9}, {3.843615818169777*^9, 3.8436159022117233`*^9}, {3.843621164525605*^9, 3.8436211674899387`*^9}, { 3.8436212248219557`*^9, 3.8436212383818884`*^9}, {3.843623395248974*^9, 3.8436234811296377`*^9}, 3.8436235228419657`*^9, {3.843710421018984*^9, 3.843710422106656*^9}, {3.843710498981309*^9, 3.843710537614964*^9}, { 3.843710579319264*^9, 3.843710645627423*^9}, {3.8437106875546417`*^9, 3.843710688153476*^9}, {3.843710725428294*^9, 3.843710785146202*^9}, { 3.843710821351383*^9, 3.8437110234294205`*^9}, {3.8437111173417163`*^9, 3.843711129714572*^9}, {3.843711236237468*^9, 3.8437112372387085`*^9}, { 3.8437113572143283`*^9, 3.8437113718734703`*^9}, {3.8437115790188246`*^9, 3.843711601014681*^9}, {3.843711741747123*^9, 3.843711755218405*^9}, { 3.8437118059023905`*^9, 3.8437118104255657`*^9}, {3.843711922772312*^9, 3.8437119230384417`*^9}, {3.8437119637523017`*^9, 3.8437119924289055`*^9}, {3.843712070094509*^9, 3.843712071922304*^9}, { 3.8437303811976614`*^9, 3.84373041381275*^9}, {3.843730744283455*^9, 3.8437307459908094`*^9}, {3.8437396200557556`*^9, 3.8437396419414387`*^9}, 3.843886670451059*^9, 3.8438867203204308`*^9, 3.84388678658553*^9, { 3.843886846967881*^9, 3.843886872522117*^9}, {3.8438869150992565`*^9, 3.8438869153482804`*^9}, {3.8443227935999327`*^9, 3.8443228741400695`*^9}, 3.84432529516883*^9, 3.84432540227769*^9, {3.844325496215137*^9, 3.8443254968116083`*^9}, {3.8443255607450824`*^9, 3.84432556531176*^9}, { 3.8443257292349973`*^9, 3.844325729451268*^9}, {3.8443271837653055`*^9, 3.8443271897353077`*^9}, 3.844327630363053*^9, 3.844327741570508*^9, { 3.8443278373713217`*^9, 3.84432790019408*^9}, {3.844328356730674*^9, 3.8443283589066696`*^9}, {3.8443286085720377`*^9, 3.844328633889926*^9}, { 3.844328780662943*^9, 3.844328797514555*^9}, 3.844328890335701*^9, 3.844329541823058*^9, 3.8443297290733314`*^9, 3.8443298258170156`*^9, 3.8443299792211103`*^9, {3.844330023182226*^9, 3.8443300241626625`*^9}, { 3.844330096584533*^9, 3.8443300969210296`*^9}, {3.8443301540407066`*^9, 3.844330184720361*^9}, 3.844330343560071*^9, 3.8443304466315546`*^9, 3.84438870778086*^9, {3.844388798979218*^9, 3.8443888166069407`*^9}, { 3.844388850689955*^9, 3.84438889324323*^9}, 3.8443891579040785`*^9, { 3.8443893096760817`*^9, 3.844389351546801*^9}, {3.8443894390725183`*^9, 3.8443894521629066`*^9}, 3.844389648527203*^9, {3.8443897876199207`*^9, 3.844389824625575*^9}, 3.8443900109195027`*^9, {3.844390820677456*^9, 3.8443908278248734`*^9}, {3.8443909207770224`*^9, 3.8443910088808312`*^9}, 3.844391050490807*^9, 3.844391867983138*^9, {3.844394157403282*^9, 3.844394211279689*^9}, {3.844394341187828*^9, 3.8443943435847197`*^9}, { 3.8443944350783367`*^9, 3.8443944719623637`*^9}, 3.844394554883594*^9, 3.844394790974487*^9, 3.844394878078925*^9, 3.844395085745798*^9, { 3.8443953351049013`*^9, 3.844395416952881*^9}, {3.844395746514305*^9, 3.844395749726533*^9}, 3.8443958397241535`*^9, {3.8443959211672125`*^9, 3.8443959248882713`*^9}, {3.8443960479537315`*^9, 3.844396058908654*^9}, 3.844396301967287*^9, 3.844396496810913*^9, {3.8443967365950084`*^9, 3.8443967370378094`*^9}, 3.8443972200199785`*^9, {3.8444115993210382`*^9, 3.8444115995187025`*^9}, {3.8444116721502385`*^9, 3.8444116838525047`*^9}, 3.8444117955604706`*^9, 3.8444120838091917`*^9, 3.8444123486564503`*^9, { 3.8444124716223226`*^9, 3.8444124796999335`*^9}, {3.8444125495255537`*^9, 3.844412567726659*^9}, 3.844412769483656*^9, {3.844499964651905*^9, 3.84449997397132*^9}, {3.844500043831334*^9, 3.8445000552814937`*^9}, 3.844500094473071*^9, {3.844500426135293*^9, 3.8445004336024866`*^9}, 3.844500503309535*^9, {3.84450071418834*^9, 3.8445007145632133`*^9}, 3.84450075086576*^9, {3.844500802343947*^9, 3.844500805685542*^9}, { 3.844500857916894*^9, 3.844500860801999*^9}, {3.8445009435074234`*^9, 3.8445010378770485`*^9}, {3.844501486443882*^9, 3.844501488956464*^9}, { 3.844501593768973*^9, 3.8445016087484674`*^9}, {3.8445019589459047`*^9, 3.8445019618400517`*^9}, {3.8445142536442575`*^9, 3.844514303852824*^9}, { 3.844514457425339*^9, 3.8445145337724867`*^9}, {3.8445146121090136`*^9, 3.844514612805125*^9}, {3.8445152618516026`*^9, 3.8445152626808715`*^9}, { 3.84451667854188*^9, 3.8445166978368387`*^9}, {3.8445168384209423`*^9, 3.8445168531952915`*^9}, 3.844516936102404*^9, {3.844517144912083*^9, 3.8445171602908783`*^9}, {3.844517313347111*^9, 3.844517374315425*^9}, { 3.844563740797083*^9, 3.844563842955555*^9}, {3.8445647632618103`*^9, 3.844564764558693*^9}, {3.844564893032794*^9, 3.8445648966363597`*^9}, 3.844566001126281*^9, {3.8445661160863905`*^9, 3.844566152674224*^9}, { 3.844566264323254*^9, 3.8445663747877293`*^9}, {3.8445664543449287`*^9, 3.844566491779601*^9}, {3.8445666670048437`*^9, 3.8445667378245735`*^9}, { 3.84456677184741*^9, 3.8445669208491745`*^9}, {3.8445681586856985`*^9, 3.8445681603926296`*^9}, {3.844568433360468*^9, 3.8445684731196322`*^9}, { 3.844568732407946*^9, 3.844568737446255*^9}, 3.844568945877626*^9, { 3.844569099528115*^9, 3.844569106514072*^9}, {3.8445691536508603`*^9, 3.8445691542699223`*^9}, {3.8445698639037194`*^9, 3.8445698642398653`*^9}, {3.844570012985527*^9, 3.84457001409229*^9}, { 3.844570136399222*^9, 3.84457022295549*^9}, {3.8445702927401485`*^9, 3.8445702943727927`*^9}, {3.8445703589410896`*^9, 3.844570359479988*^9}, { 3.844570433361819*^9, 3.844570434479186*^9}, {3.8445708385437922`*^9, 3.844570865548447*^9}, 3.8445719038536615`*^9, {3.84457369886672*^9, 3.844573716165063*^9}, {3.844573766574627*^9, 3.844573766741207*^9}, { 3.8445738390520935`*^9, 3.8445738397153697`*^9}, {3.844574626193658*^9, 3.844574626336315*^9}, 3.8445754934014444`*^9, {3.844575765512229*^9, 3.8445757670064106`*^9}, {3.8445797808579626`*^9, 3.8445797824906826`*^9}, {3.8445801889436493`*^9, 3.8445802499386616`*^9}, {3.8445802832055655`*^9, 3.8445804322445507`*^9}, {3.8445806095243425`*^9, 3.844580784490394*^9}, { 3.8445808660823193`*^9, 3.8445808672575426`*^9}, {3.8445810704154396`*^9, 3.844581084375619*^9}, {3.8445812578925953`*^9, 3.8445812836521835`*^9}, { 3.8445814486128545`*^9, 3.844581454694955*^9}, 3.8445815919025917`*^9, 3.8445816963679733`*^9, 3.8445818761230197`*^9, {3.844581973276004*^9, 3.84458197871758*^9}, {3.8445820591801286`*^9, 3.8445820669279137`*^9}, { 3.844766120152509*^9, 3.844766220989109*^9}, {3.8447666299757333`*^9, 3.844766632861744*^9}, {3.8447669924782996`*^9, 3.844766998824834*^9}, { 3.844767166360729*^9, 3.8447671685821986`*^9}, {3.8447672972644825`*^9, 3.844767489140806*^9}, {3.8447675202758884`*^9, 3.8447677076499157`*^9}, { 3.8447677386160955`*^9, 3.844767751930085*^9}, {3.8447678367494764`*^9, 3.8447678460718756`*^9}, {3.8447679275644846`*^9, 3.844767951604962*^9}, { 3.844823802025931*^9, 3.8448238152889323`*^9}, {3.844823957041947*^9, 3.8448239585139303`*^9}, {3.8448243004194326`*^9, 3.8448243149899445`*^9}, 3.8448243583360662`*^9, 3.844934867394837*^9, 3.845011466205801*^9, { 3.8450117207709064`*^9, 3.8450117245772066`*^9}, 3.845012400796516*^9, { 3.8450126148924513`*^9, 3.8450126150945854`*^9}, 3.845012697578274*^9, 3.845014370057255*^9, {3.8451838607018776`*^9, 3.845183871901742*^9}, { 3.845183946334877*^9, 3.84518395366415*^9}, {3.8451840514184165`*^9, 3.8451840516680007`*^9}, {3.8451841516428566`*^9, 3.845184154374053*^9}, { 3.845184357905266*^9, 3.8451843580652475`*^9}, {3.845184866633246*^9, 3.845184879284834*^9}, {3.8451856542674866`*^9, 3.845185661519927*^9}, 3.845185843485832*^9, 3.845188805837329*^9, {3.845208711326853*^9, 3.8452087400435753`*^9}, {3.8452088755132847`*^9, 3.845208885710583*^9}, { 3.8452090240719767`*^9, 3.8452090275669355`*^9}, {3.845209172626273*^9, 3.8452091859860196`*^9}, {3.845209314813764*^9, 3.8452093153470325`*^9}, { 3.8452093525944805`*^9, 3.845209356766179*^9}, {3.8452094333426437`*^9, 3.845209437202387*^9}, {3.845209581540662*^9, 3.8452096027603593`*^9}, { 3.845209834131934*^9, 3.845209849152528*^9}, {3.8452099760880327`*^9, 3.8452099795576005`*^9}, {3.84521001531735*^9, 3.845210023119549*^9}, { 3.8452101492309895`*^9, 3.8452101507171693`*^9}, {3.845210218508196*^9, 3.8452102205052843`*^9}, {3.845210284636221*^9, 3.8452102908524485`*^9}, { 3.8452104469844484`*^9, 3.845210448865471*^9}, {3.845210722276207*^9, 3.8452107618886013`*^9}, {3.8452108540735493`*^9, 3.8452108566476297`*^9}, 3.8452108885672226`*^9, 3.8452113817145267`*^9, {3.8452544138546667`*^9, 3.845254415221461*^9}, {3.8452544682669744`*^9, 3.845254497242826*^9}, { 3.845254813158949*^9, 3.845254813962109*^9}, {3.845255159389332*^9, 3.8452551602997503`*^9}, 3.8453713836088*^9, 3.8453728273858185`*^9, { 3.8453730671369777`*^9, 3.845373072521226*^9}, {3.8453735876364107`*^9, 3.8453736185890512`*^9}, 3.8453741162299414`*^9, {3.8453744985094943`*^9, 3.8453745049495716`*^9}, {3.845374723838398*^9, 3.8453747280613575`*^9}, 3.845375413181964*^9, {3.845375667874572*^9, 3.845375678759179*^9}, { 3.8453757305367117`*^9, 3.8453757318964834`*^9}, {3.845375795765346*^9, 3.8453759475892797`*^9}, 3.8453762911344376`*^9, {3.845376343496214*^9, 3.845376394269949*^9}, 3.8454413952988825`*^9, {3.8454605213498316`*^9, 3.845460526259059*^9}, {3.8454605688149014`*^9, 3.845460571220699*^9}, { 3.8454607495560193`*^9, 3.8454607590768337`*^9}, {3.845462509735139*^9, 3.845462509985168*^9}, {3.8454655927984095`*^9, 3.8454655941092844`*^9}, { 3.8454656351939297`*^9, 3.8454657716449366`*^9}, {3.8454659031914606`*^9, 3.8454659091378775`*^9}, {3.8454660264366956`*^9, 3.845466050881938*^9}, { 3.8454670388067656`*^9, 3.8454670407645473`*^9}, {3.8454695818972855`*^9, 3.8454695927423058`*^9}, 3.8458628196288977`*^9, {3.8458629698321857`*^9, 3.8458629918325853`*^9}, {3.84586302904202*^9, 3.845863076602502*^9}, { 3.8458631448574963`*^9, 3.8458632007479205`*^9}, {3.845863269580724*^9, 3.8458632726734605`*^9}, {3.845863307748892*^9, 3.8458633353940535`*^9}, { 3.845863395099148*^9, 3.8458634980995226`*^9}, 3.845863530554716*^9, { 3.8458725905500464`*^9, 3.8458726644563165`*^9}, {3.845872707441972*^9, 3.8458727236944923`*^9}, {3.8458728091280556`*^9, 3.845872842539483*^9}, 3.8458728978104*^9, {3.8458730281409388`*^9, 3.8458730351358786`*^9}}, CellLabel-> "In[201]:=",ExpressionUUID->"38a1d62e-f4fc-40f7-87e9-9b1e5d40372c"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SHELLS", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nod", ",", "edg", ",", "row", ",", "dof", ",", "n\[Alpha]", ",", "n\[Beta]", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "NN", ",", "mat", ",", "MM", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "r\[Gamma]", ",", "rn", ",", "jac", ",", "h\[Alpha]", ",", "e\[Alpha]", ",", "h\[Beta]", ",", "h\[Gamma]", ",", "e\[Beta]", ",", "en", ",", "e\[Gamma]", ",", "FF", ",", "\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]", ",", "f\[Alpha]", ",", "f\[Gamma]", ",", "fn", ",", "m\[Alpha]", ",", "m\[Gamma]", ",", "mn", ",", "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]", ",", "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]", ",", "\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]", ",", "GG", ",", "N\[Alpha]\[Alpha]", ",", "N\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Gamma]", ",", "N\[Gamma]\[Alpha]", ",", "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]", ",", "Q\[Alpha]", ",", "Q\[Gamma]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wmap"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nod", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"edg", "=", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{"nod", ",", RowBox[{"RotateLeft", "[", "nod", "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"uX", ",", "uY", ",", "uZ"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Theta]X", ",", "\[Theta]Y", ",", "\[Theta]Z"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"dof", "[", RowBox[{"i_", ",", "j_"}], "]"}], ":=", RowBox[{"Flatten", "[", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nod", ",", "i", ",", "j"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}]}], "}"}], ",", "i", ",", "j"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], ",", "2", ",", "1"}], "]"}], "]"}]}], "+", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], ",", "i", ",", "j"}], "]"}], "]"}]}], ")"}], "/", "3"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], ",", "2", ",", "1"}], "]"}], "]"}], "+", RowBox[{"2", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], ",", "i", ",", "j"}], "]"}], "]"}]}]}], ")"}], "/", "3"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"row", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], ",", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}], "]"}], "]"}], ",", RowBox[{ RowBox[{"row", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], ",", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}]}], "}"}], "]"}], "]"}]}], "}"}]}], "]"}], "&"}], ",", "edg"}], "]"}], ",", RowBox[{ RowBox[{"row", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "[", "nod", "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", " ", "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"MM", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"1", "/", "2"}], "*", "\[Alpha]", "*", RowBox[{"(", RowBox[{"2", "-", RowBox[{"9", "*", "\[Alpha]"}], "+", RowBox[{"9", "*", SuperscriptBox["\[Alpha]", "2"]}]}], ")"}]}], ",", RowBox[{ RowBox[{"1", "/", "2"}], "*", " ", "\[Beta]", "*", RowBox[{"(", RowBox[{"2", "-", RowBox[{"9", "*", " ", "\[Beta]"}], "+", RowBox[{"9", " ", "*", SuperscriptBox["\[Beta]", "2"]}]}], ")"}]}], ",", RowBox[{ RowBox[{"1", "/", "2"}], "*", RowBox[{"(", RowBox[{"2", "-", RowBox[{"9", " ", SuperscriptBox["\[Alpha]", "3"]}], "-", RowBox[{"11", " ", "\[Beta]"}], "+", RowBox[{"18", " ", SuperscriptBox["\[Beta]", "2"]}], "-", RowBox[{"9", " ", SuperscriptBox["\[Beta]", "3"]}], "-", RowBox[{"9", " ", "*", SuperscriptBox["\[Alpha]", "2"], "*", RowBox[{"(", RowBox[{ RowBox[{"-", "2"}], "+", RowBox[{"3", "*", "\[Beta]"}]}], ")"}]}], "+", RowBox[{"\[Alpha]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "11"}], "+", RowBox[{"36", "*", "\[Beta]"}], "-", RowBox[{"27", "*", SuperscriptBox["\[Beta]", "2"]}]}], ")"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"9", "/", "2"}], "*", " ", "\[Alpha]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"3", "*", "\[Alpha]"}]}], ")"}], "*", "\[Beta]"}], ",", RowBox[{ RowBox[{"9", "/", "2"}], "*", " ", "\[Alpha]", "*", "\[Beta]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"3", "*", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{ RowBox[{"-", "9"}], "/", "2"}], "*", " ", "\[Beta]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}], "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"3", "*", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"9", "/", "2"}], "*", " ", "\[Beta]", "*", RowBox[{"(", RowBox[{"2", "+", RowBox[{"3", "*", SuperscriptBox["\[Alpha]", "2"]}], "-", RowBox[{"5", "*", "\[Beta]"}], "+", RowBox[{"3", "*", SuperscriptBox["\[Beta]", "2"]}], "+", RowBox[{"\[Alpha]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "5"}], "+", RowBox[{"6", "*", "\[Beta]"}]}], ")"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"9", "/", "2"}], "*", "\[Alpha]", "*", RowBox[{"(", RowBox[{"2", "+", RowBox[{"3", "*", SuperscriptBox["\[Alpha]", "2"]}], "-", RowBox[{"5", "*", "\[Beta]"}], "+", RowBox[{"3", "*", SuperscriptBox["\[Beta]", "2"]}], "+", RowBox[{"\[Alpha]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "5"}], "+", RowBox[{"6", "*", "\[Beta]"}]}], ")"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{ RowBox[{"-", "9"}], "/", "2"}], "*", " ", "\[Alpha]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"3", "*", "\[Alpha]"}]}], ")"}], "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}]}], ",", RowBox[{ RowBox[{"-", "27"}], "*", "\[Alpha]", "*", "\[Beta]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nod", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]", "=", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}]}], ";", " ", RowBox[{"r\[Beta]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Norm", "[", "r\[Beta]", "]"}]}], ";", " ", RowBox[{"h\[Alpha]", "=", RowBox[{"Norm", "[", "r\[Alpha]", "]"}]}], ";", RowBox[{"jac", "=", RowBox[{"Norm", "[", RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Alpha]", "=", RowBox[{"r\[Alpha]", "/", "h\[Alpha]"}]}], ";", RowBox[{"e\[Beta]", "=", RowBox[{"r\[Beta]", "/", "h\[Beta]"}]}], ";", " ", RowBox[{"en", "=", RowBox[{ RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], " ", "/", "jac"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r\[Gamma]", "=", RowBox[{"r\[Beta]", "-", RowBox[{ RowBox[{"(", RowBox[{"r\[Beta]", ".", "e\[Alpha]"}], ")"}], " ", "e\[Alpha]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Gamma]", "=", RowBox[{"Norm", "[", "r\[Gamma]", "]"}]}], ";", RowBox[{"e\[Gamma]", "=", RowBox[{"r\[Gamma]", "/", "h\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", "e\[Gamma]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]"}], "}"}], "=", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Alpha]"}], ",", RowBox[{"r\[Alpha]", ".", "r\[Beta]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Beta]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Beta]"}]}], "}"}]}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Gamma]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Gamma]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"MM", ".", RowBox[{"dof", "[", RowBox[{"2", ",", "1"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"MM", ".", RowBox[{"dof", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"MM", ".", RowBox[{"dof", "[", RowBox[{"2", ",", "3"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{"MM", ".", RowBox[{"dof", "[", RowBox[{"3", ",", "1"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{"MM", ".", RowBox[{"dof", "[", RowBox[{"3", ",", "2"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{"MM", ".", RowBox[{"dof", "[", RowBox[{"3", ",", "3"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Gamma]", ",", "fn"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"strain", " ", "measures", " ", "with", " ", "non"}], "-", RowBox[{"symmetric", " ", "\[Epsilon]"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}]}]}], ")"}], "/", "h\[Gamma]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], "/", "h\[Alpha]"}], "-", "\[Psi]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}]}]}], ")"}], "/", "h\[Gamma]"}], "+", "\[Psi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}]}]}], ")"}]}], "/", "h\[Gamma]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", " ", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Theta]"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], "/", "h\[Alpha]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], "+", "\[Theta]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", "\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "stress", " ", "resultants", " ", "with", " ", "a", " ", "nonsymmetric", " ", "N"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Alpha]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Gamma]\[Gamma]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Gamma]\[Gamma]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Gamma]\[Gamma]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Gamma]", "=", RowBox[{ "tt", "*", "2", " ", "GG", "*", "\[Epsilon]\[Alpha]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Gamma]\[Alpha]", "=", RowBox[{ "tt", "*", "2", " ", "GG", "*", "\[Epsilon]\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Alpha]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Gamma]\[Gamma]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Gamma]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Gamma]\[Gamma]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", " ", "GG", "*", "\[Kappa]\[Alpha]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{ RowBox[{"5", "/", "6"}], " ", "*", "GG", "*", "tt", "*", "\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Gamma]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "N\[Alpha]\[Alpha]", ",", "N\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Gamma]", ",", "N\[Gamma]\[Alpha]"}], "}"}]}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]"}], "}"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Gamma]"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Gamma]", ",", "fn"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI28", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.8448250537576227`*^9, 3.8448251771278715`*^9}, { 3.8448252137845707`*^9, 3.8448252155580893`*^9}, {3.8448254288715434`*^9, 3.8448254325068684`*^9}, {3.844825473502449*^9, 3.844825487394247*^9}, { 3.8448255700281677`*^9, 3.8448256123923707`*^9}, {3.8448258113699675`*^9, 3.8448259039303937`*^9}, {3.8448259506719284`*^9, 3.844826284306115*^9}, { 3.8448268689947243`*^9, 3.8448268699886227`*^9}, 3.8448270259285955`*^9, { 3.8448271042647657`*^9, 3.8448271098964405`*^9}, {3.844827241092888*^9, 3.844827245842145*^9}, {3.8449345617461205`*^9, 3.844934602408169*^9}, { 3.844934658197948*^9, 3.8449348350524793`*^9}, {3.844935059720586*^9, 3.8449350605941477`*^9}, {3.844936139535534*^9, 3.8449361403797927`*^9}, { 3.8449953938751106`*^9, 3.8449953942218556`*^9}, {3.844995606823018*^9, 3.8449956071318903`*^9}, {3.8449970717317686`*^9, 3.8449970738159122`*^9}, 3.844997131164296*^9, {3.8449973802320213`*^9, 3.844997380443988*^9}, 3.8450114546701565`*^9, {3.8450127082731895`*^9, 3.84501270987388*^9}, { 3.8450127530150876`*^9, 3.845012810587885*^9}, 3.8450128586967945`*^9, { 3.8450132292910776`*^9, 3.8450132368337135`*^9}, {3.8450133572020845`*^9, 3.845013369791489*^9}, {3.845013427008649*^9, 3.845013479380189*^9}, { 3.8450138434327407`*^9, 3.845013858812168*^9}, {3.8450141220982046`*^9, 3.84501413941072*^9}, 3.8450144174596987`*^9},ExpressionUUID->"11762837-f9ea-4ad2-bb92-\ 27671ab9b1fb"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "n\[Alpha]", ",", "n\[Beta]", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "NN", ",", "mat", ",", "MM", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "r\[Gamma]", ",", "rn", ",", "jac", ",", "h\[Alpha]", ",", "e\[Alpha]", ",", "h\[Beta]", ",", "h\[Gamma]", ",", "e\[Beta]", ",", "en", ",", "e\[Gamma]", ",", "FF", ",", "\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]", ",", "edg", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "\[Pi]u", ",", "\[Pi]v", ",", "\[Pi]w", ",", "\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]", ",", "f\[Alpha]", ",", "f\[Gamma]", ",", "fn", ",", "m\[Alpha]", ",", "m\[Gamma]", ",", "mn", ",", "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]", ",", "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]", ",", "\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]", ",", "GG", ",", "N\[Alpha]\[Alpha]", ",", "N\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Gamma]", ",", "N\[Gamma]\[Alpha]", ",", "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]", ",", "Q\[Alpha]", ",", "Q\[Gamma]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wmap"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"mat", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]", "=", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}]}], ";", " ", RowBox[{"r\[Beta]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Norm", "[", "r\[Beta]", "]"}]}], ";", " ", RowBox[{"h\[Alpha]", "=", RowBox[{"Norm", "[", "r\[Alpha]", "]"}]}], ";", RowBox[{"jac", "=", RowBox[{"Norm", "[", RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Alpha]", "=", RowBox[{"r\[Alpha]", "/", "h\[Alpha]"}]}], ";", RowBox[{"e\[Beta]", "=", RowBox[{"r\[Beta]", "/", "h\[Beta]"}]}], ";", " ", RowBox[{"en", "=", RowBox[{ RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], " ", "/", "jac"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r\[Gamma]", "=", RowBox[{"r\[Beta]", "-", RowBox[{ RowBox[{"(", RowBox[{"r\[Beta]", ".", "e\[Alpha]"}], ")"}], " ", "e\[Alpha]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Gamma]", "=", RowBox[{"Norm", "[", "r\[Gamma]", "]"}]}], ";", RowBox[{"e\[Gamma]", "=", RowBox[{"r\[Gamma]", "/", "h\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", "e\[Gamma]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]"}], "}"}], "=", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Alpha]"}], ",", RowBox[{"r\[Alpha]", ".", "r\[Beta]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Beta]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Beta]"}]}], "}"}]}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Gamma]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Gamma]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"edg", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Sort", "[", "#", "]"}], "&"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"uX", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"uY", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "3"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Z", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "projection", "*)"}], "\[IndentingNewLine]", RowBox[{"AA", "=", RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", "jac", ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]"}], "}"}], "=", RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "/", "AA"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]u", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]v", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]w", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Gamma]", ",", "fn"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"strain", " ", "measures", " ", "with", " ", "non"}], "-", RowBox[{"symmetric", " ", "\[Epsilon]"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}]}]}], ")"}], "/", "h\[Gamma]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], "/", "h\[Alpha]"}], "-", "\[Psi]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}]}]}], ")"}], "/", "h\[Gamma]"}], "+", "\[Psi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}]}]}], ")"}]}], "/", "h\[Gamma]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", " ", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Theta]"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], "/", "h\[Alpha]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], "+", "\[Pi]\[Theta]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", "\[Pi]\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "stress", " ", "resultants", " ", "with", " ", "a", " ", "nonsymmetric", " ", "N"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Alpha]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Gamma]\[Gamma]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Gamma]\[Gamma]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Gamma]\[Gamma]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Gamma]", "=", RowBox[{ "tt", "*", "2", " ", "GG", "*", "\[Epsilon]\[Alpha]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Gamma]\[Alpha]", "=", RowBox[{ "tt", "*", "2", " ", "GG", "*", "\[Epsilon]\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Alpha]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Gamma]\[Gamma]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Gamma]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Gamma]\[Gamma]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", " ", "GG", "*", "\[Kappa]\[Alpha]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{ RowBox[{"5", "/", "6"}], " ", "*", "GG", "*", "tt", "*", "\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Gamma]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "N\[Alpha]\[Alpha]", ",", "N\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Gamma]", ",", "N\[Gamma]\[Alpha]"}], "}"}]}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]"}], "}"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Gamma]"}], "}"}]}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Gamma]", ",", "fn"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wmap", "=", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "/", "10"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]u", "-", "u"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]u", "-", "u"}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]v", "-", "v"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]v", "-", "v"}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]w", "-", "w"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]w", "-", "w"}], ")"}]}]}], ")"}], "*", "tt", "*", RowBox[{"EE", "/", "jac"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI3", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI1", ",", RowBox[{ RowBox[{"(", "\[Delta]wmap", ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{ 3.4426474258030453`*^9, {3.4444401255942*^9, 3.4444401388073997`*^9}, { 3.4444401803034*^9, 3.4444401844062*^9}, 3.4444402418922*^9, { 3.4444402805022*^9, 3.4444403134026003`*^9}, {3.4444403443062*^9, 3.4444404484049997`*^9}, {3.444483267101*^9, 3.444483267335*^9}, { 3.4444833136046*^9, 3.4444835622998*^9}, {3.4444836421094*^9, 3.4444837777981997`*^9}, {3.444483920429*^9, 3.4444839412237997`*^9}, 3.4444842905546*^9, {3.4444843207406*^9, 3.4444844162282*^9}, { 3.4444844465078*^9, 3.4444844624354*^9}, {3.4444845255998*^9, 3.4444845894505997`*^9}, {3.4444846290746*^9, 3.444484933025*^9}, { 3.4444849790917997`*^9, 3.4444851148742*^9}, {3.444534936054*^9, 3.4445349675348*^9}, {3.4445355821731997`*^9, 3.44453585174*^9}, { 3.4445372162198*^9, 3.4445372264378*^9}, 3.444537384731*^9, { 3.4445377585382*^9, 3.4445377605818*^9}, {3.4445379733658*^9, 3.4445379736934*^9}, {3.4445380176762*^9, 3.444538032777*^9}, { 3.4445381079222*^9, 3.4445381581386003`*^9}, {3.4445382726456003`*^9, 3.4445382910067997`*^9}, {3.4445383401312*^9, 3.4445383475880003`*^9}, { 3.444538438458*^9, 3.4445384464608*^9}, {3.4445385680783997`*^9, 3.4445385687648*^9}, {3.4445389411991997`*^9, 3.4445389431024*^9}, { 3.444539746605*^9, 3.4445397807846003`*^9}, {3.4445408839765997`*^9, 3.4445409234133997`*^9}, {3.4445409681698*^9, 3.4445409932702*^9}, { 3.4445415452906*^9, 3.4445415706717997`*^9}, {3.4445416647242002`*^9, 3.4445416909477997`*^9}, {3.4445417660150003`*^9, 3.444541788557*^9}, { 3.4445420906977997`*^9, 3.444542104847*^9}, {3.4445421885878*^9, 3.4445421941414003`*^9}, {3.4445422252166*^9, 3.4445422386014*^9}, { 3.444542280425*^9, 3.4445423014538*^9}, {3.444542455769*^9, 3.4445424578282003`*^9}, {3.4445431739214*^9, 3.444543175809*^9}, { 3.4445647020962*^9, 3.4445648405618*^9}, {3.4445648825414*^9, 3.4445648858486*^9}, {3.4445649382646*^9, 3.4445651882702*^9}, { 3.4446164822206*^9, 3.4446165344494*^9}, {3.4446166121842003`*^9, 3.4446166738822002`*^9}, {3.4446167223046*^9, 3.4446168047974*^9}, { 3.444616843033*^9, 3.444616906447*^9}, {3.4446444694708*^9, 3.4446444700948*^9}, {3.4446477738310003`*^9, 3.4446477939862003`*^9}, { 3.4446478467298*^9, 3.4446478681018*^9}, 3.4446480456142*^9, { 3.4446487557418003`*^9, 3.4446487636198*^9}, 3.4446488179974003`*^9, { 3.4446488971205997`*^9, 3.4446489152478*^9}, {3.4446490003458*^9, 3.4446490008294*^9}, {3.4447042728942003`*^9, 3.4447042751562*^9}, { 3.4447044703278*^9, 3.4447044865362*^9}, 3.4447046475282*^9, 3.4447047993786*^9, {3.444704908329*^9, 3.4447049292642*^9}, { 3.4447049861926003`*^9, 3.4447049877214003`*^9}, {3.4447050279296*^9, 3.4447050419695997`*^9}, {3.4447053486656*^9, 3.4447053739376*^9}, 3.4447054561963997`*^9, 3.44470561612*^9, {3.4472133996876*^9, 3.4472134108571997`*^9}, {3.4472134470179996`*^9, 3.4472134648332*^9}, { 3.4472135032872*^9, 3.4472135245344*^9}, {3.4472136963059998`*^9, 3.4472137794384003`*^9}, {3.4472138235708*^9, 3.4472138388900003`*^9}, { 3.4472139099792*^9, 3.4472141367096*^9}, {3.447214202682*^9, 3.4472142975924*^9}, {3.4472144187732*^9, 3.4472145910284*^9}, { 3.4472146560492*^9, 3.4472147023968*^9}, {3.447214803594*^9, 3.4472148728736*^9}, {3.4472149156956*^9, 3.447214940484*^9}, { 3.447216227284*^9, 3.4472162419948*^9}, {3.4472163068908*^9, 3.4472163720832*^9}, {3.4472164665880003`*^9, 3.447216530392*^9}, { 3.4472166237268*^9, 3.4472167058452*^9}, 3.4472167362808*^9, { 3.4472171394658003`*^9, 3.4472171532874002`*^9}, {3.4472172028993998`*^9, 3.4472172216661997`*^9}, {3.4472172524606*^9, 3.4472172690278*^9}, { 3.4472173209133997`*^9, 3.4472173334245996`*^9}, {3.4472173920846*^9, 3.447217404861*^9}, {3.4472179572548*^9, 3.4472180351456003`*^9}, { 3.4472509764091997`*^9, 3.4472511017396*^9}, {3.4473910422216*^9, 3.4473912901524*^9}, 3.4473918688344*^9, {3.447392021185*^9, 3.4473920346633997`*^9}, {3.4473921383304*^9, 3.4473921479088*^9}, { 3.4473923024112*^9, 3.4473923734379997`*^9}, {3.4473928098168*^9, 3.4473928648691998`*^9}, {3.4473931872432003`*^9, 3.4473932461800003`*^9}, {3.4473933026675997`*^9, 3.4473934579812*^9}, { 3.4473935755271997`*^9, 3.447393742572*^9}, {3.4473939032676*^9, 3.4473939384144*^9}, {3.447395257644*^9, 3.4473953141628*^9}, { 3.4473954231132*^9, 3.4473954756384*^9}, {3.4473955348716*^9, 3.4473955723272*^9}, {3.447395648502*^9, 3.4473957588876*^9}, { 3.4473957903996*^9, 3.4473958488372*^9}, 3.4473962894154*^9, { 3.447396350817*^9, 3.447396352611*^9}, {3.4474625379146*^9, 3.4474625637326*^9}, {3.558360651728078*^9, 3.558360652102478*^9}, { 3.5619791319820857`*^9, 3.561979135788492*^9}, 3.561979369382504*^9, { 3.5619794930439215`*^9, 3.5619795010155354`*^9}, {3.561979569218855*^9, 3.56197960614412*^9}, {3.5619797417551584`*^9, 3.5619797448751636`*^9}, { 3.618719065033702*^9, 3.618719075426296*^9}, {3.6187194011669273`*^9, 3.6187194449454317`*^9}, {3.6187196998040085`*^9, 3.6187197102436056`*^9}, {3.618719902254588*^9, 3.6187199711455283`*^9}, { 3.618722365406472*^9, 3.6187225412555304`*^9}, {3.6187226885009522`*^9, 3.6187227109872384`*^9}, {3.618722756922866*^9, 3.6187231317203026`*^9}, { 3.618723424250035*^9, 3.6187234267291765`*^9}, {3.6187235105259695`*^9, 3.6187236491028957`*^9}, {3.618723691580325*^9, 3.618723745975436*^9}, { 3.618723778837316*^9, 3.6187238310002995`*^9}, {3.6187239055875654`*^9, 3.618723940035536*^9}, {3.6187239782667227`*^9, 3.6187240219352207`*^9}, { 3.618724166762504*^9, 3.618724177411113*^9}, {3.618729321696159*^9, 3.618729328067523*^9}, 3.618729374058154*^9, {3.6187294379838104`*^9, 3.618729708464281*^9}, {3.6187297631904106`*^9, 3.618729773195983*^9}, { 3.618729822648812*^9, 3.6187299321490746`*^9}, {3.618729984399063*^9, 3.61873000654133*^9}, {3.6187300746012225`*^9, 3.6187300860458775`*^9}, { 3.618731390835507*^9, 3.6187315116174154`*^9}, {3.618731747324897*^9, 3.6187318214091344`*^9}, {3.6187318769243097`*^9, 3.618732065297084*^9}, { 3.6187321012351394`*^9, 3.618732157420353*^9}, {3.618732188384124*^9, 3.6187322435542793`*^9}, {3.6187322786112847`*^9, 3.6187325478446836`*^9}, {3.6187325819856367`*^9, 3.6187326817653437`*^9}, {3.618732810863728*^9, 3.61873282594359*^9}, { 3.6187336474335766`*^9, 3.618733754678711*^9}, {3.618733827497876*^9, 3.61873396201257*^9}, {3.6187342020362988`*^9, 3.618734236455267*^9}, 3.618734298201799*^9, {3.618734712498495*^9, 3.618734712716508*^9}, 3.6187347739640107`*^9, {3.618738817361748*^9, 3.6187388333816643`*^9}, { 3.6187391349349127`*^9, 3.6187391457955337`*^9}, {3.618739376900752*^9, 3.618739397023903*^9}, {3.618739528394417*^9, 3.618739534809784*^9}, { 3.618739972366811*^9, 3.61873997340687*^9}, {3.6187400416617737`*^9, 3.618740043022852*^9}, {3.6187400971579485`*^9, 3.618740107902563*^9}, { 3.6187401713671927`*^9, 3.6187401723312483`*^9}, {3.6187402613443394`*^9, 3.618740268819767*^9}, {3.6187403697625403`*^9, 3.6187404057615995`*^9}, { 3.618740488277319*^9, 3.618740516244919*^9}, {3.618740647782442*^9, 3.6187406551668644`*^9}, 3.6187407823021364`*^9, {3.6187418050786357`*^9, 3.618741805749674*^9}, {3.6187418557605343`*^9, 3.6187419895921893`*^9}, { 3.618742022944097*^9, 3.61874204379729*^9}, {3.6187420836395683`*^9, 3.618742103384698*^9}, {3.620462440882641*^9, 3.6204624460519366`*^9}, { 3.6204624990259666`*^9, 3.620462576450395*^9}, {3.620463682857678*^9, 3.620463713336421*^9}, 3.6204637901188126`*^9, {3.620464238835478*^9, 3.62046424411378*^9}, 3.628912429385081*^9, {3.6289135207155013`*^9, 3.6289135210805225`*^9}, 3.6289497746958513`*^9, 3.6289498371774254`*^9, { 3.62894988410911*^9, 3.6289500319795675`*^9}, {3.6289501333883677`*^9, 3.628950183744248*^9}, {3.6289503323017445`*^9, 3.628950390181055*^9}, { 3.6289505050536256`*^9, 3.6289505113579865`*^9}, {3.62895070863527*^9, 3.6289507095043197`*^9}, {3.628951013180689*^9, 3.62895101407374*^9}, { 3.629190743153632*^9, 3.629190816645361*^9}, {3.6291909709608326`*^9, 3.629190981678051*^9}, {3.629191034624544*^9, 3.6291910410049553`*^9}, { 3.6293846391370816`*^9, 3.629384641102685*^9}, {3.6294628543371735`*^9, 3.629462867097191*^9}, {3.629468063172048*^9, 3.6294681151669397`*^9}, { 3.6295205836757097`*^9, 3.6295206295085897`*^9}, {3.6295206788826766`*^9, 3.6295207067911253`*^9}, {3.6295207408927855`*^9, 3.629520753700408*^9}, { 3.629521020590745*^9, 3.6295210354395943`*^9}, {3.6295211107369013`*^9, 3.62952114882508*^9}, {3.6295212327348795`*^9, 3.6295212477237363`*^9}, { 3.6295213424816394`*^9, 3.629521343230441*^9}, {3.6295215363119802`*^9, 3.6295216753550243`*^9}, {3.629521922272258*^9, 3.6295219939855833`*^9}, { 3.6295220298188467`*^9, 3.629522446058778*^9}, {3.629522499348471*^9, 3.629522604352256*^9}, {3.629522755188921*^9, 3.62952288580795*^9}, { 3.629522918084407*^9, 3.6295233421087513`*^9}, {3.6295233808436193`*^9, 3.629523390936837*^9}, {3.629523424274096*^9, 3.6295234533369465`*^9}, { 3.6295235190130625`*^9, 3.629523521680667*^9}, 3.6295235894315863`*^9, { 3.6295237270706277`*^9, 3.629523799454755*^9}, {3.6295238514808464`*^9, 3.629523883460902*^9}, {3.6295239376085978`*^9, 3.6295239442386093`*^9}, { 3.6295241089904985`*^9, 3.629524177537019*^9}, 3.629524211888279*^9, { 3.629524277423994*^9, 3.629524396904604*^9}, {3.6295244794839497`*^9, 3.6295246248450055`*^9}, 3.629524657090262*^9, {3.6295259599109507`*^9, 3.629526013465844*^9}, {3.6295261092188125`*^9, 3.629526201414974*^9}, 3.6295263436092243`*^9, {3.6295263910333076`*^9, 3.629526583303645*^9}, { 3.629526616672104*^9, 3.629526647653758*^9}, {3.629526687558628*^9, 3.629526744888729*^9}, {3.629526804075233*^9, 3.6295268598453307`*^9}, { 3.6295269393898706`*^9, 3.6295269586559043`*^9}, {3.6295271490074387`*^9, 3.6295272149019547`*^9}, {3.6295272553684254`*^9, 3.6295272827620735`*^9}, {3.6295274137087035`*^9, 3.6295274761244135`*^9}, {3.6295275252801*^9, 3.6295279912529182`*^9}, { 3.6295281572216096`*^9, 3.629528160435215*^9}, {3.6295282905550437`*^9, 3.6295284308616905`*^9}, 3.6295285402022824`*^9, {3.629528582088356*^9, 3.629528616798417*^9}, {3.6295287666834803`*^9, 3.6295290316343455`*^9}, { 3.629529086515242*^9, 3.629529118432898*^9}, {3.6295291548121614`*^9, 3.629529292794404*^9}, {3.6295293426208916`*^9, 3.6295293491261034`*^9}, { 3.629529420699029*^9, 3.629529571535694*^9}, {3.6295296539506383`*^9, 3.629529656103442*^9}, {3.6295296894407005`*^9, 3.629529692295506*^9}, { 3.6295297445555973`*^9, 3.629529766426836*^9}, {3.6295298053333044`*^9, 3.6295298209489317`*^9}, {3.6295308380551186`*^9, 3.6295308386635194`*^9}, {3.629532377840223*^9, 3.6295323811630287`*^9}, { 3.629532480020402*^9, 3.629532482454006*^9}, {3.629532520720874*^9, 3.629532564619351*^9}, {3.62953259842461*^9, 3.6295326002654133`*^9}, { 3.6295326327758703`*^9, 3.6295326715107384`*^9}, {3.629532742428463*^9, 3.6295328288058147`*^9}, {3.6295329692184625`*^9, 3.6295330530062094`*^9}, {3.6295331824396367`*^9, 3.629533193562456*^9}, 3.6295350321720915`*^9, 3.629535158485513*^9, {3.629535245471266*^9, 3.6295352687465067`*^9}, {3.62953541293756*^9, 3.629535446384019*^9}, { 3.6295355043381205`*^9, 3.6295355262249594`*^9}, {3.629543790136781*^9, 3.629543791181983*^9}, {3.629543871350524*^9, 3.629544001673153*^9}, { 3.6295446682009234`*^9, 3.629544668466124*^9}, {3.6296010216162376`*^9, 3.6296010236442413`*^9}, {3.629601079336339*^9, 3.6296010902875586`*^9}, 3.6296011425476503`*^9, {3.6296043522397404`*^9, 3.629604399031022*^9}, { 3.629623884428093*^9, 3.629623914723346*^9}, {3.6296239662190366`*^9, 3.6296239738006496`*^9}, {3.6296240514731865`*^9, 3.6296240920176573`*^9}, {3.629624125947717*^9, 3.629624369432945*^9}, { 3.6296256512247963`*^9, 3.6296256817072496`*^9}, {3.6296260472626915`*^9, 3.629626047434292*^9}, {3.629628055568204*^9, 3.629628056098605*^9}, { 3.6296280911206665`*^9, 3.6296281088266973`*^9}, {3.6296281406819534`*^9, 3.629628273032586*^9}, {3.629628378831972*^9, 3.6296283814995766`*^9}, { 3.629628459562114*^9, 3.629628466379326*^9}, {3.629628519419419*^9, 3.6296285390754533`*^9}, {3.629633008133008*^9, 3.629633008835009*^9}, { 3.6296337764967575`*^9, 3.6296338344040594`*^9}, {3.6296342997684765`*^9, 3.629634432150309*^9}, {3.629634494035618*^9, 3.6296345320060844`*^9}, { 3.629634594499794*^9, 3.629634812182576*^9}, {3.6296348599810605`*^9, 3.6296348746918864`*^9}, {3.6296349071867433`*^9, 3.629635023172947*^9}, 3.6296350995818815`*^9, {3.6296363797201295`*^9, 3.6296363868961425`*^9}, { 3.629636462025874*^9, 3.6296364833355117`*^9}, {3.629636555922439*^9, 3.62963656780966*^9}, {3.629636770469616*^9, 3.629636774151222*^9}, { 3.6296369192782774`*^9, 3.6296369318830996`*^9}, {3.629637058539722*^9, 3.6296370719401455`*^9}, {3.629637278172508*^9, 3.629637286814923*^9}, { 3.6296376418091464`*^9, 3.629637662385583*^9}, {3.629637773551378*^9, 3.629637795360216*^9}, {3.6296390041751394`*^9, 3.629639039571602*^9}, 3.6296393829750047`*^9, {3.6296395546065063`*^9, 3.6296395649961243`*^9}, { 3.62964113386068*^9, 3.6296412507048855`*^9}, {3.629641303167777*^9, 3.629641313744596*^9}, {3.6296416285116315`*^9, 3.629641628886032*^9}, { 3.6296416658736973`*^9, 3.6296416815049243`*^9}, 3.6296417376338234`*^9, { 3.6296855551269727`*^9, 3.6296855804270077`*^9}, {3.6297079065796247`*^9, 3.6297079070476255`*^9}, {3.6297080850439377`*^9, 3.629708135728427*^9}, { 3.6297083496516027`*^9, 3.6297084025512953`*^9}, {3.629708781767563*^9, 3.629708790940379*^9}, {3.6297089402482414`*^9, 3.6297089618542795`*^9}, { 3.6297105345398417`*^9, 3.629710538580249*^9}, {3.6297107810514746`*^9, 3.6297107850138817`*^9}, {3.6297109100481014`*^9, 3.629710915710911*^9}, { 3.629711201534613*^9, 3.629711204311418*^9}, {3.629711236307074*^9, 3.6297115007275386`*^9}, {3.6297115377464037`*^9, 3.6297115441112146`*^9}, 3.6297116025645175`*^9, {3.6298716505389357`*^9, 3.629871851841689*^9}, { 3.62987837458679*^9, 3.629878383510006*^9}, {3.6298784402629056`*^9, 3.629878447345318*^9}, {3.6298785221786494`*^9, 3.6298786580236883`*^9}, { 3.629878689613744*^9, 3.629878737147027*^9}, 3.629878783853509*^9, { 3.629878832322794*^9, 3.6298789171723433`*^9}, {3.6298802128122005`*^9, 3.6298802929723125`*^9}, 3.6298813644148126`*^9, {3.629882428887303*^9, 3.629882435887313*^9}, {3.6298986251827383`*^9, 3.6298988530367384`*^9}, { 3.6298989036744275`*^9, 3.6298989486493063`*^9}, {3.629899016868226*^9, 3.6298991622448816`*^9}, {3.6298997154530535`*^9, 3.629899740147897*^9}, { 3.6298998248560457`*^9, 3.629899978048314*^9}, {3.6299000396372223`*^9, 3.6299001557638264`*^9}, {3.6299001966826982`*^9, 3.6299002595352087`*^9}, 3.6299005011236343`*^9, {3.6299005468317146`*^9, 3.629900567642151*^9}, { 3.629900887676713*^9, 3.629900990153293*^9}, {3.6299011689220085`*^9, 3.6299012295125146`*^9}, {3.6299013754039707`*^9, 3.6299014166036434`*^9}, 3.6299014589733176`*^9, {3.6299015096734066`*^9, 3.629901588765546*^9}, { 3.629901662569275*^9, 3.6299016974665365`*^9}, {3.629901952339784*^9, 3.6299019599057975`*^9}, 3.6299020306051216`*^9, {3.6299022330934772`*^9, 3.6299022682559395`*^9}, {3.6299023020455985`*^9, 3.629902332808852*^9}, { 3.6299024532566643`*^9, 3.629902462850681*^9}, {3.629949880225117*^9, 3.6299498807867184`*^9}, {3.6299503101150723`*^9, 3.6299503156998825`*^9}, {3.629950355058751*^9, 3.629950498937804*^9}, { 3.6299555415202007`*^9, 3.6299555507086167`*^9}, {3.6299556061667137`*^9, 3.6299557553497763`*^9}, {3.629955788499834*^9, 3.6299558948608212`*^9}, { 3.629956042764681*^9, 3.629956043809883*^9}, {3.6299560914211664`*^9, 3.6299561017327843`*^9}, 3.629956145849662*^9, {3.6299584813821354`*^9, 3.6299585082765827`*^9}, 3.6299585652946825`*^9, {3.629958616587573*^9, 3.6299586356508064`*^9}, {3.629958715073346*^9, 3.6299588186419287`*^9}, { 3.629958857454797*^9, 3.629958927249319*^9}, {3.629959427994599*^9, 3.629959494669116*^9}, {3.6299595293323765`*^9, 3.6299596037913074`*^9}, { 3.62995966795422*^9, 3.62995967360143*^9}, {3.6299597835972233`*^9, 3.6299597841120243`*^9}, {3.629959826622099*^9, 3.629959862533362*^9}, { 3.6299599051682367`*^9, 3.6299599235918694`*^9}, 3.629959979939168*^9, { 3.6299601345354395`*^9, 3.62996014612626*^9}, 3.6299601769831142`*^9, { 3.629960253142448*^9, 3.629960269538077*^9}, {3.6299603041701374`*^9, 3.6299603078205442`*^9}, {3.6299604300467587`*^9, 3.629960435491168*^9}, { 3.6299605300585346`*^9, 3.6299605636609936`*^9}, {3.6299606195870914`*^9, 3.6299606581971593`*^9}, {3.629960824228251*^9, 3.6299608755367413`*^9}, { 3.629960906658796*^9, 3.6299609978409557`*^9}, {3.6299610312250147`*^9, 3.629961070646284*^9}, {3.629961135698398*^9, 3.6299611643088484`*^9}, { 3.6299720458358483`*^9, 3.6299721791536827`*^9}, {3.6299722439717965`*^9, 3.629972300007095*^9}, {3.6299723670872126`*^9, 3.6299723937008595`*^9}, { 3.629972457801372*^9, 3.6299724710613956`*^9}, {3.629972740193068*^9, 3.6299728251196175`*^9}, {3.6299729203577843`*^9, 3.6299729350218105`*^9}, {3.6299729720874753`*^9, 3.6299730462188053`*^9}, {3.629973116044528*^9, 3.6299731230177402`*^9}, { 3.629973184310248*^9, 3.6299732090830917`*^9}, {3.629973349982539*^9, 3.6299734360166903`*^9}, 3.629973534562063*^9, {3.629973577446539*^9, 3.629973586104554*^9}, {3.6299740374133463`*^9, 3.629974083823428*^9}, { 3.6299742505565205`*^9, 3.629974337089873*^9}, {3.629974382907153*^9, 3.6299744466176653`*^9}, {3.629974589794717*^9, 3.629974590761918*^9}, { 3.629974776215044*^9, 3.6299747850134597`*^9}, {3.6299748226095257`*^9, 3.6299748237483273`*^9}, 3.6299748618435946`*^9, {3.629975198476586*^9, 3.6299752545898843`*^9}, {3.62997531475919*^9, 3.6299753175515947`*^9}, { 3.6299754601982455`*^9, 3.6299754625382495`*^9}, {3.629975592034077*^9, 3.629975592502078*^9}, {3.629983277446268*^9, 3.6299832946842985`*^9}, { 3.62998342081052*^9, 3.6299835439883366`*^9}, {3.629983615514462*^9, 3.629983931009416*^9}, {3.6299919807040443`*^9, 3.6299919808912444`*^9}, { 3.629992028330928*^9, 3.6299920922130404`*^9}, 3.629992198480427*^9, { 3.6299922299300823`*^9, 3.629992250506518*^9}, {3.629992292657792*^9, 3.6299923603151107`*^9}, {3.6299924387676487`*^9, 3.6299924398440504`*^9}, {3.6299925764846907`*^9, 3.6299926096347485`*^9}, {3.6299928122323046`*^9, 3.629992818768716*^9}, { 3.6299929049120674`*^9, 3.629992905411268*^9}, {3.6299929850338078`*^9, 3.6299929866250105`*^9}, {3.6299931061992207`*^9, 3.62999312270405*^9}, { 3.629993172312137*^9, 3.6299932618718944`*^9}, {3.6299933276572104`*^9, 3.6299933842073092`*^9}, {3.630287775665962*^9, 3.630287795852398*^9}, { 3.6303896387100534`*^9, 3.630389666774503*^9}, {3.6303896967889557`*^9, 3.6303897095341783`*^9}, {3.6303897587054644`*^9, 3.630389880448078*^9}, { 3.6303899127557354`*^9, 3.630390009444705*^9}, 3.630390057321189*^9, 3.630390443484267*^9, {3.63039095720877*^9, 3.6303909789240074`*^9}, { 3.6303910572205453`*^9, 3.6303911291054716`*^9}, {3.630391163035531*^9, 3.6303911740803504`*^9}, {3.630391240224467*^9, 3.6303912875081496`*^9}, { 3.6303913396902413`*^9, 3.630391404570755*^9}, {3.630391479513287*^9, 3.6303917572873745`*^9}, {3.630391868905571*^9, 3.6303920027226057`*^9}, { 3.630392064327114*^9, 3.630392219843787*^9}, {3.63039226121506*^9, 3.63039232943398*^9}, {3.6303924315985594`*^9, 3.6303924441097813`*^9}, { 3.6303926866122074`*^9, 3.6303927118530517`*^9}, {3.630392795671999*^9, 3.6303928006172075`*^9}, {3.6303986032190485`*^9, 3.6303986046230516`*^9}, {3.6303986654631586`*^9, 3.6303987936485834`*^9}, {3.63039889979117*^9, 3.6303989091199865`*^9}, { 3.630399006323757*^9, 3.630399007259759*^9}, {3.630399117224352*^9, 3.630399214771323*^9}, {3.6303992555185947`*^9, 3.6303993036758795`*^9}, { 3.630399467725767*^9, 3.630399502731636*^9}, {3.6303995748037624`*^9, 3.630399595614199*^9}, {3.6303996329294643`*^9, 3.630399658076709*^9}, { 3.630399711335202*^9, 3.6303997453120623`*^9}, {3.6303998546994543`*^9, 3.6303999880484886`*^9}, {3.6304000742074394`*^9, 3.630400123441126*^9}, { 3.6304001724564123`*^9, 3.630400251595351*^9}, {3.630400324166679*^9, 3.630400327052684*^9}, {3.630400358190338*^9, 3.6304003597503414`*^9}, { 3.6304004587481155`*^9, 3.6304004640521245`*^9}, {3.630400521975026*^9, 3.630400526124634*^9}, {3.630400567199506*^9, 3.630400593516752*^9}, { 3.6304012340070767`*^9, 3.6304013035207987`*^9}, {3.6304013614749007`*^9, 3.630401367933312*^9}, {3.630401686939398*^9, 3.6304017294598303`*^9}, { 3.630401794020523*^9, 3.6304018922061386`*^9}, {3.6304019687775183`*^9, 3.630401987153569*^9}, {3.630402072749465*^9, 3.63040208297405*^9}, { 3.6304022247881613`*^9, 3.630402255931943*^9}, 3.630402329306139*^9, { 3.6304023806970787`*^9, 3.6304024212403975`*^9}, {3.6304025002259154`*^9, 3.630402528595538*^9}, {3.6304025620694523`*^9, 3.630402575015193*^9}, { 3.6304026411829777`*^9, 3.630402649073429*^9}, {3.630402695548087*^9, 3.6304027128260756`*^9}, {3.630402783923142*^9, 3.6304027982389607`*^9}, { 3.6304028797236214`*^9, 3.6304030111811404`*^9}, {3.6304030562107162`*^9, 3.6304031598846455`*^9}, {3.630403236330018*^9, 3.6304032404072514`*^9}, { 3.630403373001835*^9, 3.6304033888147397`*^9}, {3.6304039420953856`*^9, 3.6304039512829113`*^9}, 3.6304039831437335`*^9, {3.630404015975611*^9, 3.6304040663624935`*^9}, {3.630404173614628*^9, 3.630404246945822*^9}, { 3.6304042891772375`*^9, 3.630404299595834*^9}, {3.630404391083066*^9, 3.630404392406142*^9}, {3.6304045301800222`*^9, 3.6304045579486103`*^9}, { 3.630404640215316*^9, 3.630404762796327*^9}, {3.630404877629895*^9, 3.630404883104208*^9}, {3.6304050364729805`*^9, 3.630405098270515*^9}, { 3.6304051736118245`*^9, 3.6304051965901384`*^9}, {3.6304053802536435`*^9, 3.63040539242334*^9}, {3.630406035965148*^9, 3.630406041998493*^9}, { 3.630406072049212*^9, 3.6304060962065935`*^9}, {3.630406264081196*^9, 3.6304062707025747`*^9}, {3.63040632219952*^9, 3.630406385461138*^9}, { 3.630406477200385*^9, 3.630406482095665*^9}, {3.6304066170883865`*^9, 3.6304066222256804`*^9}, {3.630406957868878*^9, 3.630406973411767*^9}, { 3.6304070081447535`*^9, 3.630407018199329*^9}, {3.630407411376817*^9, 3.630407412542884*^9}, {3.6304080609339695`*^9, 3.630408121202417*^9}, { 3.6304081585485525`*^9, 3.6304081832129636`*^9}, {3.63040821409673*^9, 3.630408421131572*^9}, 3.6304934333363276`*^9, {3.63049350751357*^9, 3.630493677593298*^9}, {3.630493716898546*^9, 3.6304937846684227`*^9}, 3.630493922944331*^9, {3.6304939556752033`*^9, 3.630494117430455*^9}, { 3.6304941486092386`*^9, 3.6304941767788496`*^9}, {3.6304942118648567`*^9, 3.6304942530272107`*^9}, {3.6304942838399734`*^9, 3.6304942845820155`*^9}, {3.6304943454054947`*^9, 3.6304944442451477`*^9}, {3.63080749995092*^9, 3.6308075480801234`*^9}, { 3.630807586536323*^9, 3.630807621440319*^9}, {3.630807680459695*^9, 3.630807682914836*^9}, {3.630807736889923*^9, 3.6308077644745007`*^9}, { 3.6308078081089964`*^9, 3.6308078670123653`*^9}, {3.630807991648494*^9, 3.630807997541831*^9}, {3.6308081080891542`*^9, 3.6308081919599514`*^9}, { 3.630808306368495*^9, 3.630808345060708*^9}, {3.6308087281906223`*^9, 3.6308087555171847`*^9}, {3.630809110815507*^9, 3.630809169033837*^9}, { 3.6308091998195972`*^9, 3.630809448512822*^9}, {3.6308095328996487`*^9, 3.6308095448223305`*^9}, {3.630809582269472*^9, 3.6308095873607635`*^9}, { 3.630809665529235*^9, 3.630809684808337*^9}, {3.6308316258485594`*^9, 3.6308318380886984`*^9}, {3.63083188164919*^9, 3.630831966930068*^9}, 3.6320400558356075`*^9, {3.6354749882908883`*^9, 3.635474989418953*^9}, { 3.635475084557395*^9, 3.6354750875145636`*^9}, {3.6354751334091887`*^9, 3.635475162315842*^9}, {3.6354754001974483`*^9, 3.6354754820331287`*^9}, 3.635475512931896*^9, {3.6354756222781506`*^9, 3.635475622861184*^9}, { 3.635475691642118*^9, 3.6354757057969275`*^9}, {3.6354757798291616`*^9, 3.635475797395167*^9}, {3.635475884848169*^9, 3.6354758981309285`*^9}, { 3.635475961488552*^9, 3.6354759738382587`*^9}, {3.6354760213729773`*^9, 3.6354760572050266`*^9}, {3.6354761282470903`*^9, 3.635476136040536*^9}, { 3.6354761719365892`*^9, 3.635476212217893*^9}, {3.6593346599546614`*^9, 3.659334660890663*^9}, {3.6593347077219453`*^9, 3.659334720701168*^9}, { 3.6593348752974396`*^9, 3.6593348758122406`*^9}, {3.6593349140947075`*^9, 3.6593350070240707`*^9}, {3.6593350466949406`*^9, 3.6593350543701544`*^9}, {3.659335103791041*^9, 3.6593351614487424`*^9}, 3.659335217686841*^9, {3.659335262084519*^9, 3.6593352995869846`*^9}, { 3.6593356899482727`*^9, 3.659335701819893*^9}, {3.659335964227954*^9, 3.659335964602355*^9}, {3.65933603594128*^9, 3.6593360629605274`*^9}, { 3.6593361352354546`*^9, 3.6593361504454813`*^9}, {3.6593363929479074`*^9, 3.6593364061611304`*^9}, 3.6593368946915884`*^9, {3.6884748265656157`*^9, 3.6884748268716326`*^9}, {3.6884748600075283`*^9, 3.688474861420609*^9}, { 3.6885242858240776`*^9, 3.6885243001140976`*^9}, {3.6888842911675606`*^9, 3.6888843311676164`*^9}, {3.688966242423658*^9, 3.688966263933688*^9}, { 3.6897393587897596`*^9, 3.6897393649897685`*^9}, 3.689739477049925*^9, { 3.6898595970621734`*^9, 3.689859597272174*^9}, {3.6898596707522764`*^9, 3.6898597190523443`*^9}, {3.689859768552414*^9, 3.6898597721424184`*^9}, { 3.689859855272535*^9, 3.689859859882541*^9}, {3.6898605078334484`*^9, 3.6898607266237545`*^9}, 3.6898608811139708`*^9, {3.6898609634740863`*^9, 3.689860974304102*^9}, 3.6898610140141573`*^9, {3.6898611496043468`*^9, 3.6898611683243732`*^9}, {3.689861462024784*^9, 3.6898615624849253`*^9}, { 3.6898616142149973`*^9, 3.6898616164350004`*^9}, 3.6898616657950697`*^9, { 3.689861716805141*^9, 3.689861749905187*^9}, {3.732677920575506*^9, 3.7326779208190203`*^9}, {3.7519672427004185`*^9, 3.7519672444968877`*^9}, {3.7519674022097683`*^9, 3.75196742976579*^9}, { 3.751967484127989*^9, 3.751967510853814*^9}, {3.7519675409404893`*^9, 3.751967541549782*^9}, {3.7519675797751045`*^9, 3.751967592209671*^9}, { 3.7519676829383273`*^9, 3.7519676841255474`*^9}, {3.7519677154775553`*^9, 3.7519677953499403`*^9}, 3.751967827811061*^9, {3.7519679545625095`*^9, 3.751967957999185*^9}, {3.751968003754015*^9, 3.7519681477513895`*^9}, { 3.751968264817631*^9, 3.751968270722477*^9}, {3.7519689618119907`*^9, 3.751968969888235*^9}, {3.7519691168917775`*^9, 3.7519691395895615`*^9}, { 3.751969242782174*^9, 3.7519692581691785`*^9}, {3.7519693625211954`*^9, 3.751969378579924*^9}, {3.751969409572627*^9, 3.751969438643936*^9}, { 3.7519695894526725`*^9, 3.751969614306203*^9}, {3.7523200108586655`*^9, 3.752320012354121*^9}, {3.7553831315619707`*^9, 3.755383134119626*^9}, { 3.7553831893197794`*^9, 3.755383241814331*^9}, {3.7553832736267967`*^9, 3.7553832810757113`*^9}, {3.7554336536222963`*^9, 3.755433684797229*^9}, { 3.7554337764737434`*^9, 3.7554338315300155`*^9}, {3.755433998047738*^9, 3.7554340265485487`*^9}, {3.755446573138784*^9, 3.755446636911299*^9}, { 3.75544667493072*^9, 3.755446753435521*^9}, {3.755446891541581*^9, 3.7554468921547422`*^9}, {3.7554469323588533`*^9, 3.755446936867403*^9}, { 3.7554470190332975`*^9, 3.7554472776872244`*^9}, {3.7555217323692026`*^9, 3.755521732847602*^9}, {3.755521767127169*^9, 3.7555217972041793`*^9}, { 3.755522561453134*^9, 3.755522564231819*^9}, {3.755522601885935*^9, 3.7555226037287407`*^9}, {3.7555226758687305`*^9, 3.755522678585092*^9}, { 3.7555234832604623`*^9, 3.7555235920444417`*^9}, {3.7555239506007543`*^9, 3.755524013893358*^9}, {3.755524076791689*^9, 3.7555240812793446`*^9}, { 3.7555241238138275`*^9, 3.7555241268985643`*^9}, {3.7555242930449886`*^9, 3.7555243378577013`*^9}, {3.7555256673767824`*^9, 3.7555256808205338`*^9}, {3.7555258588384123`*^9, 3.755525900317296*^9}, { 3.755525930708299*^9, 3.7555260436531134`*^9}, {3.755607147401991*^9, 3.7556071504143705`*^9}, {3.755607992884314*^9, 3.7556080025382996`*^9}, { 3.7556094344057455`*^9, 3.7556094348690443`*^9}, {3.7559613653116636`*^9, 3.755961445097105*^9}, 3.755961484246889*^9, {3.7559618979231987`*^9, 3.755961939470047*^9}, {3.7559620323724904`*^9, 3.7559620330864005`*^9}, { 3.755962155557907*^9, 3.7559621601593847`*^9}, {3.755962303755834*^9, 3.755962343830135*^9}, {3.7559624058018165`*^9, 3.7559624450501757`*^9}, 3.756002186674869*^9, 3.7560029626855392`*^9, {3.756003222110388*^9, 3.756003295034633*^9}, {3.7560056331492863`*^9, 3.7560056663855457`*^9}, { 3.7560057813555765`*^9, 3.7560057863836613`*^9}, {3.7560058917172394`*^9, 3.756005927847292*^9}, 3.756006092376186*^9, 3.756009112317705*^9, { 3.756091886039587*^9, 3.756091887764086*^9}, {3.756092005435152*^9, 3.7560920727337685`*^9}, {3.75609212911592*^9, 3.7560921293252516`*^9}, { 3.756092262958163*^9, 3.756092263157668*^9}, {3.756092342487877*^9, 3.756092347894502*^9}, {3.7560929036769304`*^9, 3.7560929278911004`*^9}, { 3.7560930741522417`*^9, 3.756093083420331*^9}, {3.7560932986236534`*^9, 3.7560933139459305`*^9}, {3.756093449985523*^9, 3.7560934874491863`*^9}, { 3.756093592694581*^9, 3.7560936019456573`*^9}, {3.756093634438078*^9, 3.756093673866626*^9}, {3.756093873069885*^9, 3.756093897964734*^9}, { 3.7560940650109406`*^9, 3.756094078056768*^9}, {3.756442536546026*^9, 3.756442607904289*^9}, {3.7564436397451363`*^9, 3.7564436403231254`*^9}, { 3.7636034984570236`*^9, 3.7636034989933815`*^9}, {3.763603551051456*^9, 3.7636035527617817`*^9}, {3.7636036049384193`*^9, 3.7636036392233057`*^9}, {3.7636036850937223`*^9, 3.763603692587598*^9}, { 3.7636037258272257`*^9, 3.7636037459031096`*^9}, {3.7636037792254367`*^9, 3.76360387572289*^9}, {3.763603971837229*^9, 3.7636040341423655`*^9}, { 3.763604066526084*^9, 3.7636040756798687`*^9}, {3.7636041452118535`*^9, 3.763604278007333*^9}, {3.763604317710966*^9, 3.7636043271387568`*^9}, { 3.7636043584877644`*^9, 3.763604415561053*^9}, {3.763604445680462*^9, 3.7636044504114943`*^9}, {3.763604615444647*^9, 3.7636048082554193`*^9}, 3.763604854904996*^9, {3.7636133594095488`*^9, 3.7636133618464766`*^9}, { 3.7636136063756704`*^9, 3.7636136315671196`*^9}, {3.7636990373827705`*^9, 3.7636990431157646`*^9}, {3.763699090332087*^9, 3.763699110952259*^9}, { 3.763699227420497*^9, 3.7636993642943506`*^9}, {3.763700085627533*^9, 3.763700088329999*^9}, {3.7637001721125274`*^9, 3.763700181422837*^9}, { 3.763700248063385*^9, 3.7637003918630466`*^9}, {3.763700591783223*^9, 3.7637006017496295`*^9}, {3.7637007583576717`*^9, 3.7637007603074865`*^9}, {3.7637137795793185`*^9, 3.7637137822587233`*^9}, {3.7637148704355187`*^9, 3.763714870624051*^9}, { 3.763727592158518*^9, 3.7637275933445053`*^9}, {3.7637276688363667`*^9, 3.7637276694756594`*^9}, 3.763803448896332*^9, {3.76380349501632*^9, 3.7638036835067654`*^9}, {3.763804829093463*^9, 3.7638048385675254`*^9}, 3.7638051033646154`*^9, 3.7638053924528885`*^9, {3.763805557684454*^9, 3.763805634255308*^9}, {3.763806843847647*^9, 3.763806847966059*^9}, { 3.763806942652097*^9, 3.7638071770752254`*^9}, {3.7638141184594107`*^9, 3.763814134133461*^9}, {3.7638146808628216`*^9, 3.7638146925645113`*^9}, { 3.7638147709278784`*^9, 3.7638147811883087`*^9}, {3.7638148155281043`*^9, 3.763814819843194*^9}, {3.7638150259647446`*^9, 3.763815028601293*^9}, { 3.7638151529595194`*^9, 3.763815155849978*^9}, {3.7638163770262136`*^9, 3.763816380851597*^9}, {3.7638164181856327`*^9, 3.7638164950537987`*^9}, 3.763816568304102*^9, {3.7638166173645625`*^9, 3.763816618808757*^9}, { 3.7638167204462805`*^9, 3.763816721012859*^9}, {3.763857602253485*^9, 3.7638579604183645`*^9}, {3.7638580038507566`*^9, 3.7638580060526443`*^9}, {3.763858082269992*^9, 3.7638581746835337`*^9}, { 3.7638582163351564`*^9, 3.7638582415275116`*^9}, {3.7638582983238*^9, 3.763858907503306*^9}, {3.763858941318697*^9, 3.763858956626134*^9}, { 3.7638602435602536`*^9, 3.763860245408451*^9}, {3.7638694636456347`*^9, 3.7638694647177277`*^9}, {3.7638708199536576`*^9, 3.763870829436488*^9}, { 3.763871287170555*^9, 3.7638712876184006`*^9}, {3.763943214376035*^9, 3.7639432984591475`*^9}, {3.763943418832348*^9, 3.7639434335508127`*^9}, { 3.76394347113767*^9, 3.7639435187320576`*^9}, {3.763943585908682*^9, 3.7639436125255404`*^9}, {3.763951722152746*^9, 3.76395172989299*^9}, { 3.7639517863423367`*^9, 3.7639519945900664`*^9}, {3.763952081515512*^9, 3.7639521530710773`*^9}, {3.763952353248129*^9, 3.763952357026309*^9}, { 3.7639524211903834`*^9, 3.7639524243979177`*^9}, {3.7639527174925117`*^9, 3.7639527180252266`*^9}, {3.7641265625745993`*^9, 3.7641265632314167`*^9}, {3.764126605555829*^9, 3.7641266075095396`*^9}, { 3.7641268313964133`*^9, 3.7641268543573804`*^9}, {3.764127044657903*^9, 3.7641270479422092`*^9}, {3.7641271442332697`*^9, 3.7641271469362774`*^9}, {3.764127227626192*^9, 3.7641272592640233`*^9}, { 3.764127335707515*^9, 3.7641273386484756`*^9}, {3.764127429843852*^9, 3.7641274364304185`*^9}, {3.7641275071859307`*^9, 3.764127516803895*^9}, 3.7641276043548007`*^9, {3.7641276925365753`*^9, 3.764127697080591*^9}, 3.764127798472331*^9, 3.764127853631323*^9, 3.764127908496078*^9, { 3.7641280050343323`*^9, 3.764128022046494*^9}, {3.764128128597419*^9, 3.764128154116727*^9}, {3.7641286864636617`*^9, 3.764128701643106*^9}, { 3.7641289910924444`*^9, 3.7641290126680794`*^9}, {3.7641290672285347`*^9, 3.7641290737798567`*^9}, {3.7641325425120363`*^9, 3.764132565390477*^9}, { 3.7641327425004654`*^9, 3.764132750040793*^9}, 3.7641327968340364`*^9, { 3.764133146776842*^9, 3.764133204874522*^9}, {3.7641333488187037`*^9, 3.7641333525577593`*^9}, {3.764413145593136*^9, 3.7644131471236105`*^9}, { 3.764413201645049*^9, 3.7644132349609704`*^9}, {3.764413325008136*^9, 3.7644133748980193`*^9}, {3.7644134113425665`*^9, 3.7644135151187*^9}, { 3.764413554409053*^9, 3.7644136160674934`*^9}, {3.76441371984758*^9, 3.764413730103909*^9}, 3.764419641962368*^9, {3.7644198522879405`*^9, 3.764419879249356*^9}, 3.764419909536559*^9, {3.764419991012162*^9, 3.764420000171088*^9}, {3.7644200798862047`*^9, 3.7644200950961914`*^9}, { 3.7644201529471693`*^9, 3.764420153715966*^9}, {3.764420210346301*^9, 3.764420255343707*^9}, {3.764420296178318*^9, 3.7644203000939393`*^9}, { 3.7644203803359275`*^9, 3.7644203931390867`*^9}, 3.7644204418727274`*^9, { 3.7647259720700207`*^9, 3.7647261047260523`*^9}, {3.7647263483375626`*^9, 3.76472635879602*^9}, 3.764726656736601*^9, {3.764727009127914*^9, 3.764727020100875*^9}, {3.7647270591828785`*^9, 3.7647270819631023`*^9}, { 3.7647272109090505`*^9, 3.764727227846332*^9}, {3.76473247809907*^9, 3.7647324813925114`*^9}, {3.7647349484962797`*^9, 3.7647349979358416`*^9}, {3.7647351097258167`*^9, 3.764735124772463*^9}, { 3.7647352810674453`*^9, 3.7647352901139917`*^9}, {3.7647353746429515`*^9, 3.764735379550926*^9}, {3.7647354596539807`*^9, 3.764735507677454*^9}, { 3.7647355546341*^9, 3.764735728811817*^9}, {3.764735837449795*^9, 3.76473584132898*^9}, {3.76473603649269*^9, 3.7647360592982664`*^9}, { 3.7647360998228803`*^9, 3.76473621551197*^9}, {3.7647362545599003`*^9, 3.764736286430997*^9}, {3.7647364592833533`*^9, 3.764736464019006*^9}, { 3.764736566167658*^9, 3.7647365918958225`*^9}, {3.764764761680134*^9, 3.7647648482473745`*^9}, 3.764764917763693*^9, {3.764764964821686*^9, 3.764765090741813*^9}, {3.7647651742140284`*^9, 3.7647652517335076`*^9}, { 3.764765341266399*^9, 3.7647653614173465`*^9}, 3.764765400284145*^9, { 3.764765691384389*^9, 3.764765708710143*^9}, 3.7647657454275875`*^9, { 3.76476578351686*^9, 3.764765871262255*^9}, {3.7647661045180917`*^9, 3.76476612822571*^9}, {3.7647661964223824`*^9, 3.764766239375331*^9}, { 3.764766330361228*^9, 3.764766338297905*^9}, {3.764767015060799*^9, 3.7647670193029037`*^9}, {3.764767076590926*^9, 3.7647671160277977`*^9}, { 3.7647671493139205`*^9, 3.7647672079236426`*^9}, {3.764767458938404*^9, 3.7647674608323865`*^9}, {3.764810938444873*^9, 3.7648109399353456`*^9}, { 3.7648118616019874`*^9, 3.7648118695079126`*^9}, {3.7648120589477816`*^9, 3.7648124600413237`*^9}, {3.76481250476682*^9, 3.7648125259602103`*^9}, { 3.764812601341893*^9, 3.7648126577763243`*^9}, {3.7648126944039307`*^9, 3.7648128855627623`*^9}, {3.764812924923909*^9, 3.764812926481821*^9}, { 3.764813041485982*^9, 3.764813131254232*^9}, {3.7648134679328885`*^9, 3.7648136479313235`*^9}, {3.7648136917777314`*^9, 3.764813697753367*^9}, { 3.7648137297570653`*^9, 3.764813747862262*^9}, 3.764813784221693*^9, { 3.7648138370678406`*^9, 3.7648141387969923`*^9}, {3.764814321050164*^9, 3.764814422489184*^9}, {3.764814461366684*^9, 3.7648145835728483`*^9}, { 3.764814614769511*^9, 3.7648147525825167`*^9}, {3.764815363375289*^9, 3.7648153644907384`*^9}, {3.764815451671169*^9, 3.7648154601533747`*^9}, { 3.7648175917802963`*^9, 3.7648176401910563`*^9}, {3.765885491237231*^9, 3.765885501131465*^9}, {3.766572999289345*^9, 3.7665729996020145`*^9}, { 3.7665730613126965`*^9, 3.7665730616706066`*^9}, {3.7840103262125545`*^9, 3.7840103546413517`*^9}, {3.784011309725755*^9, 3.7840113197719574`*^9}, { 3.784013374800973*^9, 3.7840133842981763`*^9}, {3.7840238533665447`*^9, 3.78402395932942*^9}, {3.784024091276659*^9, 3.784024112209529*^9}, { 3.7840242793219643`*^9, 3.784024296655184*^9}, {3.7840290670892677`*^9, 3.7840291348388853`*^9}, {3.784029222997594*^9, 3.784029542926179*^9}, { 3.784375172285057*^9, 3.784375319701829*^9}, {3.7843753678421807`*^9, 3.7843753788103914`*^9}, {3.7843754844339557`*^9, 3.784375827494117*^9}, { 3.784375862317687*^9, 3.7843759567563844`*^9}, {3.784376004941759*^9, 3.7843760080157185`*^9}, {3.784376101918992*^9, 3.7843761244332943`*^9}, { 3.784376181191763*^9, 3.7843762145091863`*^9}, {3.7843792489960337`*^9, 3.78437926273014*^9}, {3.7843793293934345`*^9, 3.784379368676588*^9}, { 3.7843796529835215`*^9, 3.7843796858862267`*^9}, {3.784450863324359*^9, 3.7844508986076546`*^9}, {3.7844510208392324`*^9, 3.784451027915551*^9}, { 3.7844511176315613`*^9, 3.7844511673791957`*^9}, {3.784451235055628*^9, 3.78445132575735*^9}, {3.784451995615477*^9, 3.7844520110330954`*^9}, { 3.7844522907551537`*^9, 3.7844523421551*^9}, {3.784700119490345*^9, 3.7847001627913013`*^9}, {3.7847004221290607`*^9, 3.7847004380767317`*^9}, 3.7847007913506136`*^9, {3.784781955129138*^9, 3.784781977787957*^9}, { 3.78488170216677*^9, 3.784881704210422*^9}, 3.784882130557441*^9, { 3.78488220347418*^9, 3.7848822064697027`*^9}, {3.784883393455822*^9, 3.784883458551924*^9}, 3.7848835306495824`*^9, {3.7848836822092113`*^9, 3.7848837303696923`*^9}, 3.7848838199009576`*^9, {3.7848842507527857`*^9, 3.7848842836585226`*^9}, 3.7848843847882996`*^9, {3.784884461405264*^9, 3.7848844645041113`*^9}, {3.784884559404122*^9, 3.7848845656634912`*^9}, { 3.7848852409944844`*^9, 3.7848852740337477`*^9}, {3.7848854548929386`*^9, 3.7848854893046365`*^9}, {3.7848856741783943`*^9, 3.784885691704702*^9}, { 3.784885809660874*^9, 3.784885811424426*^9}, {3.7848860031948376`*^9, 3.784886020570098*^9}, 3.7848861057105627`*^9, {3.7848861627726107`*^9, 3.7848862212876124`*^9}, {3.784886306497995*^9, 3.7848863509322224`*^9}, 3.784886472690192*^9, {3.7848866596243*^9, 3.784886664116289*^9}, { 3.7848866987282944`*^9, 3.7848867077911897`*^9}, {3.78488676128524*^9, 3.7848868667029366`*^9}, {3.7848869381224003`*^9, 3.7848869414281464`*^9}, {3.7848870104508753`*^9, 3.784887039889447*^9}, { 3.7848871795058794`*^9, 3.7848871976746817`*^9}, {3.7848872311446314`*^9, 3.78488724075662*^9}, 3.784887405188785*^9, {3.784887591926689*^9, 3.7848876119305134`*^9}, {3.784887676620901*^9, 3.7848876786672792`*^9}, { 3.78488771054331*^9, 3.784887714354906*^9}, {3.7848877625809546`*^9, 3.7848878103041153`*^9}, 3.7848878862881575`*^9, {3.787717235155089*^9, 3.787717269464238*^9}, {3.7877174592607603`*^9, 3.7877174674038067`*^9}, { 3.7877271032841845`*^9, 3.787727136247201*^9}, 3.787727355369296*^9, 3.7877274973278403`*^9, {3.787727855959008*^9, 3.78772792141208*^9}, 3.787728113487193*^9, {3.7877281704571557`*^9, 3.7877281735077004`*^9}, 3.7877282789827795`*^9, {3.7877286510229864`*^9, 3.787728665729192*^9}, { 3.7877287942225084`*^9, 3.787728807671986*^9}, {3.787729044867985*^9, 3.787729045536916*^9}, {3.787729589732438*^9, 3.7877296062090626`*^9}, { 3.787729794037467*^9, 3.7877297950347877`*^9}, {3.787729855548402*^9, 3.7877299039179935`*^9}, {3.7877300373241186`*^9, 3.787730068136018*^9}, { 3.7877301999859333`*^9, 3.7877302014150777`*^9}, {3.787732033225385*^9, 3.7877320471634016`*^9}, {3.787732077195259*^9, 3.7877320780358667`*^9}, 3.787732189759206*^9, {3.78773231889835*^9, 3.787732327710633*^9}, { 3.7877324857166643`*^9, 3.787732496655479*^9}, {3.7877325848303585`*^9, 3.78773258503596*^9}, {3.7877328504631166`*^9, 3.7877328625892415`*^9}, { 3.7877330254884944`*^9, 3.7877330271019044`*^9}, {3.787733136128061*^9, 3.7877331422258835`*^9}, {3.787733243513567*^9, 3.78773324558677*^9}, 3.787733310555999*^9, 3.7877334085329347`*^9, {3.7877337955932293`*^9, 3.7877337970498257`*^9}, {3.787733867727028*^9, 3.7877338687324905`*^9}, { 3.7877352224369583`*^9, 3.787735224161746*^9}, {3.787735343322833*^9, 3.787735348772827*^9}, {3.787735422704711*^9, 3.7877354268945775`*^9}, { 3.7877355100355635`*^9, 3.787735514671461*^9}, {3.7877356541994534`*^9, 3.7877356632141013`*^9}, 3.7877357913476543`*^9, 3.787736261837074*^9, { 3.7882542159043374`*^9, 3.7882542747998285`*^9}, {3.788254310967661*^9, 3.788254318430212*^9}, {3.788254585790197*^9, 3.7882545888318524`*^9}, { 3.7882547349987383`*^9, 3.788254735940298*^9}, 3.788254830063775*^9, 3.7882549155286837`*^9, {3.7882550121437798`*^9, 3.788255037735396*^9}, { 3.7882551764404287`*^9, 3.78825518352113*^9}, {3.7882552540030313`*^9, 3.788255290224329*^9}, {3.7882553843544893`*^9, 3.788255423248046*^9}, { 3.78825567982127*^9, 3.7882556852479534`*^9}, {3.7882557908576803`*^9, 3.7882558029800806`*^9}, {3.7882560240494256`*^9, 3.7882560388846164`*^9}, 3.788256102343512*^9, {3.788256161397396*^9, 3.7882561626372194`*^9}, { 3.7882562304311895`*^9, 3.78825629590362*^9}, {3.7882563614677362`*^9, 3.7882563620189795`*^9}, {3.7882564138122153`*^9, 3.7882564294158382`*^9}, {3.788256467457189*^9, 3.7882564889521217`*^9}, { 3.7882565883311844`*^9, 3.788256591497148*^9}, {3.7882568409513097`*^9, 3.7882568724526567`*^9}, {3.788256965258837*^9, 3.788256966444976*^9}, { 3.7882570073831463`*^9, 3.7882570497349973`*^9}, {3.7882570992487097`*^9, 3.788257144206352*^9}, {3.78825721252205*^9, 3.788257307277931*^9}, { 3.788257350410209*^9, 3.7882573617262745`*^9}, {3.788257424936472*^9, 3.788257434118204*^9}, {3.788276311330668*^9, 3.788276311647092*^9}, { 3.7882765465512347`*^9, 3.788276608568333*^9}, {3.7882767715851693`*^9, 3.7882768045752783`*^9}, {3.7882769342607436`*^9, 3.7882769409894867`*^9}, {3.7882770202208567`*^9, 3.7882770424485188`*^9}, {3.7882770760040703`*^9, 3.788277077341468*^9}, { 3.788277147336176*^9, 3.788277150397852*^9}, {3.7882772069909*^9, 3.7882772101572385`*^9}, {3.7882772503366175`*^9, 3.7882772773759403`*^9}, {3.7882773922958755`*^9, 3.7882773927832017`*^9}, {3.788277450684473*^9, 3.788277482126852*^9}, { 3.78827754293396*^9, 3.788277545027956*^9}, {3.7883214550230436`*^9, 3.7883214742097826`*^9}, {3.788321520104019*^9, 3.788321685390153*^9}, { 3.788321717307153*^9, 3.788321801831746*^9}, {3.788321836768508*^9, 3.788322037754008*^9}, {3.7883220686363816`*^9, 3.788322220085001*^9}, { 3.7883255906192427`*^9, 3.788325646609389*^9}, {3.7883257976991563`*^9, 3.788325804097658*^9}, {3.788325969279187*^9, 3.7883259830028267`*^9}, { 3.788326975877249*^9, 3.788326979070017*^9}, {3.788328539286415*^9, 3.788328618410488*^9}, {3.788328648595448*^9, 3.788328762662589*^9}, { 3.7883288060890923`*^9, 3.7883288805716724`*^9}, {3.7883319188300047`*^9, 3.78833193230753*^9}, {3.7883321144947567`*^9, 3.788332115050151*^9}, { 3.7883333680456443`*^9, 3.7883333686272163`*^9}, 3.7883336421611414`*^9, { 3.788333691323177*^9, 3.7883336916362*^9}, {3.788333797629262*^9, 3.7883338348662343`*^9}, {3.7883339555470386`*^9, 3.7883339660305166`*^9}, {3.7883340291758356`*^9, 3.788334031484354*^9}, { 3.788334368484807*^9, 3.7883343918754945`*^9}, {3.7883345963739557`*^9, 3.788334645315611*^9}, {3.788411405608647*^9, 3.788411409092114*^9}, { 3.7884115644712825`*^9, 3.7884115911998663`*^9}, {3.7884116673998833`*^9, 3.788411758799066*^9}, {3.788411985303985*^9, 3.788412002701314*^9}, { 3.78841218266156*^9, 3.788412217652734*^9}, {3.788412679618697*^9, 3.78841268296084*^9}, {3.788412968920223*^9, 3.7884129782039633`*^9}, { 3.7884155241723013`*^9, 3.7884155243798914`*^9}, 3.7884156619519596`*^9, { 3.7884162343262696`*^9, 3.788416236013459*^9}, {3.789022054245319*^9, 3.7890221116154556`*^9}, {3.7890222001685014`*^9, 3.789022205961149*^9}, { 3.789094077050009*^9, 3.7890940781167436`*^9}, {3.7890941254883175`*^9, 3.7890942919861226`*^9}, {3.789094340508856*^9, 3.789094543716852*^9}, { 3.789094583794143*^9, 3.7890947278803444`*^9}, {3.7890947714417076`*^9, 3.7890948342626343`*^9}, {3.789095197615344*^9, 3.789095215073329*^9}, { 3.789095256390032*^9, 3.78909525710861*^9}, {3.7890954241290827`*^9, 3.78909583987399*^9}, {3.789096056032333*^9, 3.7890960602768464`*^9}, { 3.7890960928429904`*^9, 3.789096098149865*^9}, {3.789096721918685*^9, 3.789096734998893*^9}, {3.7890967741973257`*^9, 3.78909683859006*^9}, { 3.789096947653244*^9, 3.789097122315098*^9}, {3.7890971528708224`*^9, 3.789097530683948*^9}, {3.7890975852885656`*^9, 3.7890975882562447`*^9}, { 3.7890976430709224`*^9, 3.789097656213524*^9}, {3.789107592314107*^9, 3.7891076537760305`*^9}, {3.789107685160589*^9, 3.789107760590632*^9}, { 3.7891078105008087`*^9, 3.789107846610609*^9}, {3.789107989236459*^9, 3.7891080001561875`*^9}, {3.7891082032172785`*^9, 3.7891082064574785`*^9}, {3.7891083013630204`*^9, 3.789108444864075*^9}, { 3.7891084751958127`*^9, 3.7891085010044174`*^9}, {3.7891085322441816`*^9, 3.7891085353767447`*^9}, {3.789108620037199*^9, 3.789108662297584*^9}, 3.7891087252471294`*^9, {3.789108773507248*^9, 3.7891088501491203`*^9}, { 3.7891088829987*^9, 3.789108918319019*^9}, {3.7891089606286983`*^9, 3.7891090044788837`*^9}, {3.789109048556943*^9, 3.7891091177554493`*^9}, { 3.7891091628149347`*^9, 3.7891092922346783`*^9}, {3.789109382870388*^9, 3.789109402625166*^9}, {3.7891111380334797`*^9, 3.7891113582877145`*^9}, { 3.789111396694514*^9, 3.7891114221541777`*^9}, {3.7891114539845037`*^9, 3.7891114952359962`*^9}, {3.789112929457416*^9, 3.7891129318274393`*^9}, { 3.789112963290578*^9, 3.7891131302196255`*^9}, {3.789113202949188*^9, 3.789113203379569*^9}, {3.7891144371217365`*^9, 3.789114518411393*^9}, { 3.789114638487608*^9, 3.78911468069436*^9}, {3.789114763918976*^9, 3.789114777923211*^9}, {3.789114809301983*^9, 3.7891148392057247`*^9}, { 3.7891148923150015`*^9, 3.789114904054755*^9}, {3.7891149560740595`*^9, 3.7891150071774015`*^9}, {3.789115109642312*^9, 3.7891151147637*^9}, { 3.7891185439211864`*^9, 3.789118561569729*^9}, {3.7891187834106455`*^9, 3.7891187854068985`*^9}, {3.7891188764873776`*^9, 3.7891188767373095`*^9}, {3.789121799028477*^9, 3.789121806719482*^9}, { 3.7891222627163153`*^9, 3.7891222774782734`*^9}, {3.7891223914541044`*^9, 3.7891224006004095`*^9}, {3.789122431773783*^9, 3.7891224422816577`*^9}, { 3.7891224731160736`*^9, 3.789122501042121*^9}, {3.7891226653529224`*^9, 3.7891226664045706`*^9}, 3.789122819901965*^9, {3.789122893844426*^9, 3.7891229543768473`*^9}, {3.7891229964274464`*^9, 3.7891231044294157`*^9}, {3.789123228485856*^9, 3.789123374714591*^9}, { 3.7891235661360893`*^9, 3.7891235688754067`*^9}, {3.8435393751961174`*^9, 3.84353937620569*^9}, {3.843539421737421*^9, 3.843539430280121*^9}, { 3.8435484777900076`*^9, 3.8435484882620373`*^9}, {3.8435489691083994`*^9, 3.843548981201047*^9}, {3.8435491420371304`*^9, 3.8435491556997023`*^9}, { 3.8435491977347035`*^9, 3.8435491982438793`*^9}, 3.8435492510860806`*^9, { 3.8435495081660933`*^9, 3.8435495131948795`*^9}, {3.8435495856936626`*^9, 3.843549589991126*^9}, {3.8435496998060937`*^9, 3.843549707814079*^9}, { 3.84355004136615*^9, 3.843550041760812*^9}, {3.843550160256809*^9, 3.8435501604677615`*^9}, {3.8435532120250945`*^9, 3.843553317388692*^9}, { 3.8435535239731655`*^9, 3.8435535314678483`*^9}, {3.8435535808757987`*^9, 3.843553663159541*^9}, {3.843553779645311*^9, 3.843553786004609*^9}, 3.843553906141655*^9, 3.84355405714793*^9, {3.843554149489615*^9, 3.8435541503712645`*^9}, {3.843554206843628*^9, 3.8435542071044455`*^9}, { 3.8435543508802266`*^9, 3.843554351606327*^9}, {3.843554424038799*^9, 3.8435544242271614`*^9}, {3.8435607207357883`*^9, 3.843560727908863*^9}, { 3.843560832774662*^9, 3.8435608400783997`*^9}, {3.843561442743278*^9, 3.8435614495857325`*^9}, {3.8435616862804203`*^9, 3.8435617473408427`*^9}, {3.8435618416220255`*^9, 3.84356184949818*^9}, { 3.843561965458202*^9, 3.843561967390591*^9}, {3.8435620399418516`*^9, 3.8435620427564726`*^9}, 3.8435620999099693`*^9, {3.843562319425266*^9, 3.843562335822353*^9}, {3.843562479271407*^9, 3.8435624872362185`*^9}, { 3.8435625915602407`*^9, 3.843562614304778*^9}, {3.843562735879742*^9, 3.843562741836786*^9}, {3.8436143557463255`*^9, 3.843614430899438*^9}, { 3.843614466526642*^9, 3.843614494745638*^9}, {3.84361472265639*^9, 3.8436147354884176`*^9}, {3.843614883845476*^9, 3.8436148880544443`*^9}, { 3.843615637703328*^9, 3.8436156940260696`*^9}, {3.843615818169777*^9, 3.8436159022117233`*^9}, {3.843621164525605*^9, 3.8436211674899387`*^9}, { 3.8436212248219557`*^9, 3.8436212383818884`*^9}, {3.843623395248974*^9, 3.8436234811296377`*^9}, 3.8436235228419657`*^9, {3.843710421018984*^9, 3.843710422106656*^9}, {3.843710498981309*^9, 3.843710537614964*^9}, { 3.843710579319264*^9, 3.843710645627423*^9}, {3.8437106875546417`*^9, 3.843710688153476*^9}, {3.843710725428294*^9, 3.843710785146202*^9}, { 3.843710821351383*^9, 3.8437110234294205`*^9}, {3.8437111173417163`*^9, 3.843711129714572*^9}, {3.843711236237468*^9, 3.8437112372387085`*^9}, { 3.8437113572143283`*^9, 3.8437113718734703`*^9}, {3.8437115790188246`*^9, 3.843711601014681*^9}, {3.843711741747123*^9, 3.843711755218405*^9}, { 3.8437118059023905`*^9, 3.8437118104255657`*^9}, {3.843711922772312*^9, 3.8437119230384417`*^9}, {3.8437119637523017`*^9, 3.8437119924289055`*^9}, {3.843712070094509*^9, 3.843712071922304*^9}, { 3.8437303811976614`*^9, 3.84373041381275*^9}, {3.843730744283455*^9, 3.8437307459908094`*^9}, {3.8437396200557556`*^9, 3.8437396419414387`*^9}, 3.843886670451059*^9, 3.8438867203204308`*^9, 3.84388678658553*^9, { 3.843886846967881*^9, 3.843886872522117*^9}, {3.8438869150992565`*^9, 3.8438869153482804`*^9}, {3.8443227935999327`*^9, 3.8443228741400695`*^9}, 3.84432529516883*^9, 3.84432540227769*^9, {3.844325496215137*^9, 3.8443254968116083`*^9}, {3.8443255607450824`*^9, 3.84432556531176*^9}, { 3.8443257292349973`*^9, 3.844325729451268*^9}, {3.8443271837653055`*^9, 3.8443271897353077`*^9}, 3.844327630363053*^9, 3.844327741570508*^9, { 3.8443278373713217`*^9, 3.84432790019408*^9}, {3.844328356730674*^9, 3.8443283589066696`*^9}, {3.8443286085720377`*^9, 3.844328633889926*^9}, { 3.844328780662943*^9, 3.844328797514555*^9}, 3.844328890335701*^9, 3.844329541823058*^9, 3.8443297290733314`*^9, 3.8443298258170156`*^9, 3.8443299792211103`*^9, {3.844330023182226*^9, 3.8443300241626625`*^9}, { 3.844330096584533*^9, 3.8443300969210296`*^9}, {3.8443301540407066`*^9, 3.844330184720361*^9}, 3.844330343560071*^9, 3.8443304466315546`*^9, 3.84438870778086*^9, {3.844388798979218*^9, 3.8443888166069407`*^9}, { 3.844388850689955*^9, 3.84438889324323*^9}, 3.8443891579040785`*^9, { 3.8443893096760817`*^9, 3.844389351546801*^9}, {3.8443894390725183`*^9, 3.8443894521629066`*^9}, 3.844389648527203*^9, {3.8443897876199207`*^9, 3.844389824625575*^9}, 3.8443900109195027`*^9, {3.844390820677456*^9, 3.8443908278248734`*^9}, {3.8443909207770224`*^9, 3.8443910088808312`*^9}, 3.844391050490807*^9, 3.844391867983138*^9, {3.844394157403282*^9, 3.844394211279689*^9}, {3.844394341187828*^9, 3.8443943435847197`*^9}, { 3.8443944350783367`*^9, 3.8443944719623637`*^9}, 3.844394554883594*^9, 3.844394790974487*^9, 3.844394878078925*^9, 3.844395085745798*^9, { 3.8443953351049013`*^9, 3.844395416952881*^9}, {3.844395746514305*^9, 3.844395749726533*^9}, 3.8443958397241535`*^9, {3.8443959211672125`*^9, 3.8443959248882713`*^9}, {3.8443960479537315`*^9, 3.844396058908654*^9}, 3.844396301967287*^9, 3.844396496810913*^9, {3.8443967365950084`*^9, 3.8443967370378094`*^9}, 3.8443972200199785`*^9, {3.8444115993210382`*^9, 3.8444115995187025`*^9}, {3.8444116721502385`*^9, 3.8444116838525047`*^9}, 3.8444117955604706`*^9, 3.8444120838091917`*^9, 3.8444123486564503`*^9, { 3.8444124716223226`*^9, 3.8444124796999335`*^9}, {3.8444125495255537`*^9, 3.844412567726659*^9}, 3.844412769483656*^9, {3.844499964651905*^9, 3.84449997397132*^9}, {3.844500043831334*^9, 3.8445000552814937`*^9}, 3.844500094473071*^9, {3.844500426135293*^9, 3.8445004336024866`*^9}, 3.844500503309535*^9, {3.84450071418834*^9, 3.8445007145632133`*^9}, 3.84450075086576*^9, {3.844500802343947*^9, 3.844500805685542*^9}, { 3.844500857916894*^9, 3.844500860801999*^9}, {3.8445009435074234`*^9, 3.8445010378770485`*^9}, {3.844501486443882*^9, 3.844501488956464*^9}, { 3.844501593768973*^9, 3.8445016087484674`*^9}, {3.8445019589459047`*^9, 3.8445019618400517`*^9}, {3.8445142536442575`*^9, 3.844514303852824*^9}, { 3.844514457425339*^9, 3.8445145337724867`*^9}, {3.8445146121090136`*^9, 3.844514612805125*^9}, {3.8445152618516026`*^9, 3.8445152626808715`*^9}, { 3.84451667854188*^9, 3.8445166978368387`*^9}, {3.8445168384209423`*^9, 3.8445168531952915`*^9}, 3.844516936102404*^9, {3.844517144912083*^9, 3.8445171602908783`*^9}, {3.844517313347111*^9, 3.844517374315425*^9}, { 3.844563740797083*^9, 3.844563842955555*^9}, {3.8445647632618103`*^9, 3.844564764558693*^9}, {3.844564893032794*^9, 3.8445648966363597`*^9}, 3.844566001126281*^9, {3.8445661160863905`*^9, 3.844566152674224*^9}, { 3.844566264323254*^9, 3.8445663747877293`*^9}, {3.8445664543449287`*^9, 3.844566491779601*^9}, {3.8445666670048437`*^9, 3.8445667378245735`*^9}, { 3.84456677184741*^9, 3.8445669208491745`*^9}, {3.8445681586856985`*^9, 3.8445681603926296`*^9}, {3.844568433360468*^9, 3.8445684731196322`*^9}, { 3.844568732407946*^9, 3.844568737446255*^9}, 3.844568945877626*^9, { 3.844569099528115*^9, 3.844569106514072*^9}, {3.8445691536508603`*^9, 3.8445691542699223`*^9}, {3.8445698639037194`*^9, 3.8445698642398653`*^9}, {3.844570012985527*^9, 3.84457001409229*^9}, { 3.844570136399222*^9, 3.84457022295549*^9}, {3.8445702927401485`*^9, 3.8445702943727927`*^9}, {3.8445703589410896`*^9, 3.844570359479988*^9}, { 3.844570433361819*^9, 3.844570434479186*^9}, {3.8445708385437922`*^9, 3.844570865548447*^9}, 3.8445719038536615`*^9, {3.84457369886672*^9, 3.844573716165063*^9}, {3.844573766574627*^9, 3.844573766741207*^9}, { 3.8445738390520935`*^9, 3.8445738397153697`*^9}, {3.844574626193658*^9, 3.844574626336315*^9}, 3.8445754934014444`*^9, {3.844575765512229*^9, 3.8445757670064106`*^9}, {3.8445797808579626`*^9, 3.8445797824906826`*^9}, {3.8445801889436493`*^9, 3.8445802499386616`*^9}, {3.8445802832055655`*^9, 3.8445804322445507`*^9}, {3.8445806095243425`*^9, 3.844580784490394*^9}, { 3.8445808660823193`*^9, 3.8445808672575426`*^9}, {3.8445810704154396`*^9, 3.844581084375619*^9}, {3.8445812578925953`*^9, 3.8445812836521835`*^9}, { 3.8445814486128545`*^9, 3.844581454694955*^9}, 3.8445815919025917`*^9, 3.8445816963679733`*^9, 3.8445818761230197`*^9, {3.844581973276004*^9, 3.84458197871758*^9}, {3.8445820591801286`*^9, 3.8445820669279137`*^9}, { 3.844766120152509*^9, 3.844766220989109*^9}, {3.8447666299757333`*^9, 3.844766632861744*^9}, {3.8447669924782996`*^9, 3.844766998824834*^9}, { 3.844767166360729*^9, 3.8447671685821986`*^9}, {3.8447672972644825`*^9, 3.844767489140806*^9}, {3.8447675202758884`*^9, 3.8447677076499157`*^9}, { 3.8447677386160955`*^9, 3.844767751930085*^9}, {3.8447678367494764`*^9, 3.8447678460718756`*^9}, {3.8447679275644846`*^9, 3.844767951604962*^9}, { 3.844823802025931*^9, 3.8448238152889323`*^9}, {3.844823957041947*^9, 3.8448239585139303`*^9}, {3.8448243004194326`*^9, 3.8448243266930485`*^9}, 3.8451858142422566`*^9},ExpressionUUID->"e3e2b6a6-a76c-4ab4-b328-\ fc173879191d"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "r\[Gamma]", ",", "FF", ",", "FFINV", ",", "jac", ",", "NN", ",", "u", ",", "ux", ",", "uy", ",", "uz", ",", "v", ",", "vx", ",", "vy", ",", "vz", ",", "w", ",", "wx", ",", "wy", ",", "wz", ",", "\[Phi]", ",", "\[Phi]x", ",", "\[Phi]y", ",", "\[Phi]z", ",", "\[Theta]", ",", "\[Theta]x", ",", "\[Theta]y", ",", "\[Theta]z", ",", "AA", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Phi]", ",", "wc", ",", "E\[Sigma]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wsta", ",", "\[Delta]wmap", ",", "\[Epsilon]\[Epsilon]", ",", "\[Kappa]\[Kappa]", ",", "\[Gamma]\[Gamma]", ",", "MM", ",", "QQ", ",", "tri", ",", RowBox[{"mat", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}]}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "mapping", " ", "for", " ", "the", " ", "plate", " ", "geometry"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"r\[Alpha]", ",", "r\[Beta]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Gamma]", "=", RowBox[{"r\[Alpha]", StyleBox["\[Cross]", "OperatorCharacter"], "r\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Sqrt", "[", RowBox[{"r\[Gamma]", ".", "r\[Gamma]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"r\[Alpha]", ",", "r\[Beta]", ",", RowBox[{"r\[Gamma]", "/", "jac"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", " ", RowBox[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "approximations", "*)"}], "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"wc", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "projection", "*)"}], "\[IndentingNewLine]", RowBox[{"AA", "=", RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", "jac", ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]"}], "}"}], "=", RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]"}], "}"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "/", "AA"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "derivatives", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"ux", ",", "uy", ",", "uz"}], "}"}], "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}], ",", "0"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"vx", ",", "vy", ",", "vz"}], "}"}], "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}], ",", "0"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"wx", ",", "wy", ",", "wz"}], "}"}], "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}], ",", "0"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]x", ",", "\[Phi]y", ",", "\[Phi]z"}], "}"}], "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}], ",", "0"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Theta]x", ",", "\[Theta]y", ",", "\[Theta]z"}], "}"}], "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Theta]"}], ",", "0"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"strain", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]\[Epsilon]", "=", RowBox[{"{", RowBox[{"ux", ",", "vy", ",", RowBox[{"uy", "+", "vx"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]\[Kappa]", "=", RowBox[{"{", RowBox[{"\[Theta]x", ",", RowBox[{"-", "\[Phi]y"}], ",", RowBox[{ RowBox[{"-", "\[Phi]x"}], "+", "\[Theta]y"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Gamma]\[Gamma]", "=", RowBox[{ RowBox[{"{", RowBox[{"wx", ",", "wy"}], "}"}], "+", RowBox[{"{", RowBox[{"\[Pi]\[Theta]", ",", RowBox[{"-", "\[Pi]\[Phi]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"E\[Sigma]", "=", RowBox[{ RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "\[Nu]\[Nu]", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Nu]\[Nu]", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}]}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"MM", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", "E\[Sigma]"}], ")"}], ".", "\[Kappa]\[Kappa]"}]}], ";", "\[IndentingNewLine]", RowBox[{"QQ", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "tt", "*", "GG", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"tt", "*", RowBox[{"E\[Sigma]", ".", "\[Epsilon]\[Epsilon]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Epsilon]\[Epsilon]", "]"}], ".", "NN"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Kappa]\[Kappa]", "]"}], ".", "MM"}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Gamma]\[Gamma]", "]"}], ".", "QQ"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"fX", " ", ",", "fY", ",", "fZ"}], "}"}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"\[Delta]wsta", "=", RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"wx", ",", "wy"}], "}"}], "]"}], ".", "NN", ".", RowBox[{"{", RowBox[{"wx", ",", "wy"}], "}"}]}]}]}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wmap", "=", RowBox[{ RowBox[{"-", "0.1"}], "*", RowBox[{"\[Delta]", "[", RowBox[{"wc", "-", "w"}], "]"}], "*", RowBox[{"(", RowBox[{"wc", "-", "w"}], ")"}], "*", RowBox[{"tt", "/", "AA"}], "*", "EE"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI1", ",", RowBox[{"\[Delta]wmap", "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}]}]], "Input", CellChangeTimes->{ 3.4426474258030453`*^9, {3.4444401255942*^9, 3.4444401388073997`*^9}, { 3.4444401803034*^9, 3.4444401844062*^9}, 3.4444402418922*^9, { 3.4444402805022*^9, 3.4444403134026003`*^9}, {3.4444403443062*^9, 3.4444404484049997`*^9}, {3.444483267101*^9, 3.444483267335*^9}, { 3.4444833136046*^9, 3.4444835622998*^9}, {3.4444836421094*^9, 3.4444837777981997`*^9}, {3.444483920429*^9, 3.4444839412237997`*^9}, 3.4444842905546*^9, {3.4444843207406*^9, 3.4444844162282*^9}, { 3.4444844465078*^9, 3.4444844624354*^9}, {3.4444845255998*^9, 3.4444845894505997`*^9}, {3.4444846290746*^9, 3.444484933025*^9}, { 3.4444849790917997`*^9, 3.4444851148742*^9}, {3.444534936054*^9, 3.4445349675348*^9}, {3.4445355821731997`*^9, 3.44453585174*^9}, { 3.4445372162198*^9, 3.4445372264378*^9}, 3.444537384731*^9, { 3.4445377585382*^9, 3.4445377605818*^9}, {3.4445379733658*^9, 3.4445379736934*^9}, {3.4445380176762*^9, 3.444538032777*^9}, { 3.4445381079222*^9, 3.4445381581386003`*^9}, {3.4445382726456003`*^9, 3.4445382910067997`*^9}, {3.4445383401312*^9, 3.4445383475880003`*^9}, { 3.444538438458*^9, 3.4445384464608*^9}, {3.4445385680783997`*^9, 3.4445385687648*^9}, {3.4445389411991997`*^9, 3.4445389431024*^9}, { 3.444539746605*^9, 3.4445397807846003`*^9}, {3.4445408839765997`*^9, 3.4445409234133997`*^9}, {3.4445409681698*^9, 3.4445409932702*^9}, { 3.4445415452906*^9, 3.4445415706717997`*^9}, {3.4445416647242002`*^9, 3.4445416909477997`*^9}, {3.4445417660150003`*^9, 3.444541788557*^9}, { 3.4445420906977997`*^9, 3.444542104847*^9}, {3.4445421885878*^9, 3.4445421941414003`*^9}, {3.4445422252166*^9, 3.4445422386014*^9}, { 3.444542280425*^9, 3.4445423014538*^9}, {3.444542455769*^9, 3.4445424578282003`*^9}, {3.4445431739214*^9, 3.444543175809*^9}, { 3.4445647020962*^9, 3.4445648405618*^9}, {3.4445648825414*^9, 3.4445648858486*^9}, {3.4445649382646*^9, 3.4445651882702*^9}, { 3.4446164822206*^9, 3.4446165344494*^9}, {3.4446166121842003`*^9, 3.4446166738822002`*^9}, {3.4446167223046*^9, 3.4446168047974*^9}, { 3.444616843033*^9, 3.444616906447*^9}, {3.4446444694708*^9, 3.4446444700948*^9}, {3.4446477738310003`*^9, 3.4446477939862003`*^9}, { 3.4446478467298*^9, 3.4446478681018*^9}, 3.4446480456142*^9, { 3.4446487557418003`*^9, 3.4446487636198*^9}, 3.4446488179974003`*^9, { 3.4446488971205997`*^9, 3.4446489152478*^9}, {3.4446490003458*^9, 3.4446490008294*^9}, {3.4447042728942003`*^9, 3.4447042751562*^9}, { 3.4447044703278*^9, 3.4447044865362*^9}, 3.4447046475282*^9, 3.4447047993786*^9, {3.444704908329*^9, 3.4447049292642*^9}, { 3.4447049861926003`*^9, 3.4447049877214003`*^9}, {3.4447050279296*^9, 3.4447050419695997`*^9}, {3.4447053486656*^9, 3.4447053739376*^9}, 3.4447054561963997`*^9, 3.44470561612*^9, {3.4472133996876*^9, 3.4472134108571997`*^9}, {3.4472134470179996`*^9, 3.4472134648332*^9}, { 3.4472135032872*^9, 3.4472135245344*^9}, {3.4472136963059998`*^9, 3.4472137794384003`*^9}, {3.4472138235708*^9, 3.4472138388900003`*^9}, { 3.4472139099792*^9, 3.4472141367096*^9}, {3.447214202682*^9, 3.4472142975924*^9}, {3.4472144187732*^9, 3.4472145910284*^9}, { 3.4472146560492*^9, 3.4472147023968*^9}, {3.447214803594*^9, 3.4472148728736*^9}, {3.4472149156956*^9, 3.447214940484*^9}, { 3.447216227284*^9, 3.4472162419948*^9}, {3.4472163068908*^9, 3.4472163720832*^9}, {3.4472164665880003`*^9, 3.447216530392*^9}, { 3.4472166237268*^9, 3.4472167058452*^9}, 3.4472167362808*^9, { 3.4472171394658003`*^9, 3.4472171532874002`*^9}, {3.4472172028993998`*^9, 3.4472172216661997`*^9}, {3.4472172524606*^9, 3.4472172690278*^9}, { 3.4472173209133997`*^9, 3.4472173334245996`*^9}, {3.4472173920846*^9, 3.447217404861*^9}, {3.4472179572548*^9, 3.4472180351456003`*^9}, { 3.4472509764091997`*^9, 3.4472511017396*^9}, {3.4473910422216*^9, 3.4473912901524*^9}, 3.4473918688344*^9, {3.447392021185*^9, 3.4473920346633997`*^9}, {3.4473921383304*^9, 3.4473921479088*^9}, { 3.4473923024112*^9, 3.4473923734379997`*^9}, {3.4473928098168*^9, 3.4473928648691998`*^9}, {3.4473931872432003`*^9, 3.4473932461800003`*^9}, {3.4473933026675997`*^9, 3.4473934579812*^9}, { 3.4473935755271997`*^9, 3.447393742572*^9}, {3.4473939032676*^9, 3.4473939384144*^9}, {3.447395257644*^9, 3.4473953141628*^9}, { 3.4473954231132*^9, 3.4473954756384*^9}, {3.4473955348716*^9, 3.4473955723272*^9}, {3.447395648502*^9, 3.4473957588876*^9}, { 3.4473957903996*^9, 3.4473958488372*^9}, 3.4473962894154*^9, { 3.447396350817*^9, 3.447396352611*^9}, {3.4474625379146*^9, 3.4474625637326*^9}, {3.558360651728078*^9, 3.558360652102478*^9}, { 3.5619791319820857`*^9, 3.561979135788492*^9}, 3.561979369382504*^9, { 3.5619794930439215`*^9, 3.5619795010155354`*^9}, {3.561979569218855*^9, 3.56197960614412*^9}, {3.5619797417551584`*^9, 3.5619797448751636`*^9}, { 3.618719065033702*^9, 3.618719075426296*^9}, {3.6187194011669273`*^9, 3.6187194449454317`*^9}, {3.6187196998040085`*^9, 3.6187197102436056`*^9}, {3.618719902254588*^9, 3.6187199711455283`*^9}, { 3.618722365406472*^9, 3.6187225412555304`*^9}, {3.6187226885009522`*^9, 3.6187227109872384`*^9}, {3.618722756922866*^9, 3.6187231317203026`*^9}, { 3.618723424250035*^9, 3.6187234267291765`*^9}, {3.6187235105259695`*^9, 3.6187236491028957`*^9}, {3.618723691580325*^9, 3.618723745975436*^9}, { 3.618723778837316*^9, 3.6187238310002995`*^9}, {3.6187239055875654`*^9, 3.618723940035536*^9}, {3.6187239782667227`*^9, 3.6187240219352207`*^9}, { 3.618724166762504*^9, 3.618724177411113*^9}, {3.618729321696159*^9, 3.618729328067523*^9}, 3.618729374058154*^9, {3.6187294379838104`*^9, 3.618729708464281*^9}, {3.6187297631904106`*^9, 3.618729773195983*^9}, { 3.618729822648812*^9, 3.6187299321490746`*^9}, {3.618729984399063*^9, 3.61873000654133*^9}, {3.6187300746012225`*^9, 3.6187300860458775`*^9}, { 3.618731390835507*^9, 3.6187315116174154`*^9}, {3.618731747324897*^9, 3.6187318214091344`*^9}, {3.6187318769243097`*^9, 3.618732065297084*^9}, { 3.6187321012351394`*^9, 3.618732157420353*^9}, {3.618732188384124*^9, 3.6187322435542793`*^9}, {3.6187322786112847`*^9, 3.6187325478446836`*^9}, {3.6187325819856367`*^9, 3.6187326817653437`*^9}, {3.618732810863728*^9, 3.61873282594359*^9}, { 3.6187336474335766`*^9, 3.618733754678711*^9}, {3.618733827497876*^9, 3.61873396201257*^9}, {3.6187342020362988`*^9, 3.618734236455267*^9}, 3.618734298201799*^9, {3.618734712498495*^9, 3.618734712716508*^9}, 3.6187347739640107`*^9, {3.618738817361748*^9, 3.6187388333816643`*^9}, { 3.6187391349349127`*^9, 3.6187391457955337`*^9}, {3.618739376900752*^9, 3.618739397023903*^9}, {3.618739528394417*^9, 3.618739534809784*^9}, { 3.618739972366811*^9, 3.61873997340687*^9}, {3.6187400416617737`*^9, 3.618740043022852*^9}, {3.6187400971579485`*^9, 3.618740107902563*^9}, { 3.6187401713671927`*^9, 3.6187401723312483`*^9}, {3.6187402613443394`*^9, 3.618740268819767*^9}, {3.6187403697625403`*^9, 3.6187404057615995`*^9}, { 3.618740488277319*^9, 3.618740516244919*^9}, {3.618740647782442*^9, 3.6187406551668644`*^9}, 3.6187407823021364`*^9, {3.6187418050786357`*^9, 3.618741805749674*^9}, {3.6187418557605343`*^9, 3.6187419895921893`*^9}, { 3.618742022944097*^9, 3.61874204379729*^9}, {3.6187420836395683`*^9, 3.618742103384698*^9}, {3.620462440882641*^9, 3.6204624460519366`*^9}, { 3.6204624990259666`*^9, 3.620462576450395*^9}, {3.620463682857678*^9, 3.620463713336421*^9}, 3.6204637901188126`*^9, {3.620464238835478*^9, 3.62046424411378*^9}, 3.628912429385081*^9, {3.6289135207155013`*^9, 3.6289135210805225`*^9}, 3.6289497746958513`*^9, 3.6289498371774254`*^9, { 3.62894988410911*^9, 3.6289500319795675`*^9}, {3.6289501333883677`*^9, 3.628950183744248*^9}, {3.6289503323017445`*^9, 3.628950390181055*^9}, { 3.6289505050536256`*^9, 3.6289505113579865`*^9}, {3.62895070863527*^9, 3.6289507095043197`*^9}, {3.628951013180689*^9, 3.62895101407374*^9}, { 3.629190743153632*^9, 3.629190816645361*^9}, {3.6291909709608326`*^9, 3.629190981678051*^9}, {3.629191034624544*^9, 3.6291910410049553`*^9}, { 3.6293846391370816`*^9, 3.629384641102685*^9}, {3.6294628543371735`*^9, 3.629462867097191*^9}, {3.629468063172048*^9, 3.6294681151669397`*^9}, { 3.6295205836757097`*^9, 3.6295206295085897`*^9}, {3.6295206788826766`*^9, 3.6295207067911253`*^9}, {3.6295207408927855`*^9, 3.629520753700408*^9}, { 3.629521020590745*^9, 3.6295210354395943`*^9}, {3.6295211107369013`*^9, 3.62952114882508*^9}, {3.6295212327348795`*^9, 3.6295212477237363`*^9}, { 3.6295213424816394`*^9, 3.629521343230441*^9}, {3.6295215363119802`*^9, 3.6295216753550243`*^9}, {3.629521922272258*^9, 3.6295219939855833`*^9}, { 3.6295220298188467`*^9, 3.629522446058778*^9}, {3.629522499348471*^9, 3.629522604352256*^9}, {3.629522755188921*^9, 3.62952288580795*^9}, { 3.629522918084407*^9, 3.6295233421087513`*^9}, {3.6295233808436193`*^9, 3.629523390936837*^9}, {3.629523424274096*^9, 3.6295234533369465`*^9}, { 3.6295235190130625`*^9, 3.629523521680667*^9}, 3.6295235894315863`*^9, { 3.6295237270706277`*^9, 3.629523799454755*^9}, {3.6295238514808464`*^9, 3.629523883460902*^9}, {3.6295239376085978`*^9, 3.6295239442386093`*^9}, { 3.6295241089904985`*^9, 3.629524177537019*^9}, 3.629524211888279*^9, { 3.629524277423994*^9, 3.629524396904604*^9}, {3.6295244794839497`*^9, 3.6295246248450055`*^9}, 3.629524657090262*^9, {3.6295259599109507`*^9, 3.629526013465844*^9}, {3.6295261092188125`*^9, 3.629526201414974*^9}, 3.6295263436092243`*^9, {3.6295263910333076`*^9, 3.629526583303645*^9}, { 3.629526616672104*^9, 3.629526647653758*^9}, {3.629526687558628*^9, 3.629526744888729*^9}, {3.629526804075233*^9, 3.6295268598453307`*^9}, { 3.6295269393898706`*^9, 3.6295269586559043`*^9}, {3.6295271490074387`*^9, 3.6295272149019547`*^9}, {3.6295272553684254`*^9, 3.6295272827620735`*^9}, {3.6295274137087035`*^9, 3.6295274761244135`*^9}, {3.6295275252801*^9, 3.6295279912529182`*^9}, { 3.6295281572216096`*^9, 3.629528160435215*^9}, {3.6295282905550437`*^9, 3.6295284308616905`*^9}, 3.6295285402022824`*^9, {3.629528582088356*^9, 3.629528616798417*^9}, {3.6295287666834803`*^9, 3.6295290316343455`*^9}, { 3.629529086515242*^9, 3.629529118432898*^9}, {3.6295291548121614`*^9, 3.629529292794404*^9}, {3.6295293426208916`*^9, 3.6295293491261034`*^9}, { 3.629529420699029*^9, 3.629529571535694*^9}, {3.6295296539506383`*^9, 3.629529656103442*^9}, {3.6295296894407005`*^9, 3.629529692295506*^9}, { 3.6295297445555973`*^9, 3.629529766426836*^9}, {3.6295298053333044`*^9, 3.6295298209489317`*^9}, {3.6295308380551186`*^9, 3.6295308386635194`*^9}, {3.629532377840223*^9, 3.6295323811630287`*^9}, { 3.629532480020402*^9, 3.629532482454006*^9}, {3.629532520720874*^9, 3.629532564619351*^9}, {3.62953259842461*^9, 3.6295326002654133`*^9}, { 3.6295326327758703`*^9, 3.6295326715107384`*^9}, {3.629532742428463*^9, 3.6295328288058147`*^9}, {3.6295329692184625`*^9, 3.6295330530062094`*^9}, {3.6295331824396367`*^9, 3.629533193562456*^9}, 3.6295350321720915`*^9, 3.629535158485513*^9, {3.629535245471266*^9, 3.6295352687465067`*^9}, {3.62953541293756*^9, 3.629535446384019*^9}, { 3.6295355043381205`*^9, 3.6295355262249594`*^9}, {3.629543790136781*^9, 3.629543791181983*^9}, {3.629543871350524*^9, 3.629544001673153*^9}, { 3.6295446682009234`*^9, 3.629544668466124*^9}, {3.6296010216162376`*^9, 3.6296010236442413`*^9}, {3.629601079336339*^9, 3.6296010902875586`*^9}, 3.6296011425476503`*^9, {3.6296043522397404`*^9, 3.629604399031022*^9}, { 3.629623884428093*^9, 3.629623914723346*^9}, {3.6296239662190366`*^9, 3.6296239738006496`*^9}, {3.6296240514731865`*^9, 3.6296240920176573`*^9}, {3.629624125947717*^9, 3.629624369432945*^9}, { 3.6296256512247963`*^9, 3.6296256817072496`*^9}, {3.6296260472626915`*^9, 3.629626047434292*^9}, {3.629628055568204*^9, 3.629628056098605*^9}, { 3.6296280911206665`*^9, 3.6296281088266973`*^9}, {3.6296281406819534`*^9, 3.629628273032586*^9}, {3.629628378831972*^9, 3.6296283814995766`*^9}, { 3.629628459562114*^9, 3.629628466379326*^9}, {3.629628519419419*^9, 3.6296285390754533`*^9}, {3.629633008133008*^9, 3.629633008835009*^9}, { 3.6296337764967575`*^9, 3.6296338344040594`*^9}, {3.6296342997684765`*^9, 3.629634432150309*^9}, {3.629634494035618*^9, 3.6296345320060844`*^9}, { 3.629634594499794*^9, 3.629634812182576*^9}, {3.6296348599810605`*^9, 3.6296348746918864`*^9}, {3.6296349071867433`*^9, 3.629635023172947*^9}, 3.6296350995818815`*^9, {3.6296363797201295`*^9, 3.6296363868961425`*^9}, { 3.629636462025874*^9, 3.6296364833355117`*^9}, {3.629636555922439*^9, 3.62963656780966*^9}, {3.629636770469616*^9, 3.629636774151222*^9}, { 3.6296369192782774`*^9, 3.6296369318830996`*^9}, {3.629637058539722*^9, 3.6296370719401455`*^9}, {3.629637278172508*^9, 3.629637286814923*^9}, { 3.6296376418091464`*^9, 3.629637662385583*^9}, {3.629637773551378*^9, 3.629637795360216*^9}, {3.6296390041751394`*^9, 3.629639039571602*^9}, 3.6296393829750047`*^9, {3.6296395546065063`*^9, 3.6296395649961243`*^9}, { 3.62964113386068*^9, 3.6296412507048855`*^9}, {3.629641303167777*^9, 3.629641313744596*^9}, {3.6296416285116315`*^9, 3.629641628886032*^9}, { 3.6296416658736973`*^9, 3.6296416815049243`*^9}, 3.6296417376338234`*^9, { 3.6296855551269727`*^9, 3.6296855804270077`*^9}, {3.6297079065796247`*^9, 3.6297079070476255`*^9}, {3.6297080850439377`*^9, 3.629708135728427*^9}, { 3.6297083496516027`*^9, 3.6297084025512953`*^9}, {3.629708781767563*^9, 3.629708790940379*^9}, {3.6297089402482414`*^9, 3.6297089618542795`*^9}, { 3.6297105345398417`*^9, 3.629710538580249*^9}, {3.6297107810514746`*^9, 3.6297107850138817`*^9}, {3.6297109100481014`*^9, 3.629710915710911*^9}, { 3.629711201534613*^9, 3.629711204311418*^9}, {3.629711236307074*^9, 3.6297115007275386`*^9}, {3.6297115377464037`*^9, 3.6297115441112146`*^9}, 3.6297116025645175`*^9, {3.6298716505389357`*^9, 3.629871851841689*^9}, { 3.62987837458679*^9, 3.629878383510006*^9}, {3.6298784402629056`*^9, 3.629878447345318*^9}, {3.6298785221786494`*^9, 3.6298786580236883`*^9}, { 3.629878689613744*^9, 3.629878737147027*^9}, 3.629878783853509*^9, { 3.629878832322794*^9, 3.6298789171723433`*^9}, {3.6298802128122005`*^9, 3.6298802929723125`*^9}, 3.6298813644148126`*^9, {3.629882428887303*^9, 3.629882435887313*^9}, {3.6298986251827383`*^9, 3.6298988530367384`*^9}, { 3.6298989036744275`*^9, 3.6298989486493063`*^9}, {3.629899016868226*^9, 3.6298991622448816`*^9}, {3.6298997154530535`*^9, 3.629899740147897*^9}, { 3.6298998248560457`*^9, 3.629899978048314*^9}, {3.6299000396372223`*^9, 3.6299001557638264`*^9}, {3.6299001966826982`*^9, 3.6299002595352087`*^9}, 3.6299005011236343`*^9, {3.6299005468317146`*^9, 3.629900567642151*^9}, { 3.629900887676713*^9, 3.629900990153293*^9}, {3.6299011689220085`*^9, 3.6299012295125146`*^9}, {3.6299013754039707`*^9, 3.6299014166036434`*^9}, 3.6299014589733176`*^9, {3.6299015096734066`*^9, 3.629901588765546*^9}, { 3.629901662569275*^9, 3.6299016974665365`*^9}, {3.629901952339784*^9, 3.6299019599057975`*^9}, 3.6299020306051216`*^9, {3.6299022330934772`*^9, 3.6299022682559395`*^9}, {3.6299023020455985`*^9, 3.629902332808852*^9}, { 3.6299024532566643`*^9, 3.629902462850681*^9}, {3.629949880225117*^9, 3.6299498807867184`*^9}, {3.6299503101150723`*^9, 3.6299503156998825`*^9}, {3.629950355058751*^9, 3.629950498937804*^9}, { 3.6299555415202007`*^9, 3.6299555507086167`*^9}, {3.6299556061667137`*^9, 3.6299557553497763`*^9}, {3.629955788499834*^9, 3.6299558948608212`*^9}, { 3.629956042764681*^9, 3.629956043809883*^9}, {3.6299560914211664`*^9, 3.6299561017327843`*^9}, 3.629956145849662*^9, {3.6299584813821354`*^9, 3.6299585082765827`*^9}, 3.6299585652946825`*^9, {3.629958616587573*^9, 3.6299586356508064`*^9}, {3.629958715073346*^9, 3.6299588186419287`*^9}, { 3.629958857454797*^9, 3.629958927249319*^9}, {3.629959427994599*^9, 3.629959494669116*^9}, {3.6299595293323765`*^9, 3.6299596037913074`*^9}, { 3.62995966795422*^9, 3.62995967360143*^9}, {3.6299597835972233`*^9, 3.6299597841120243`*^9}, {3.629959826622099*^9, 3.629959862533362*^9}, { 3.6299599051682367`*^9, 3.6299599235918694`*^9}, 3.629959979939168*^9, { 3.6299601345354395`*^9, 3.62996014612626*^9}, 3.6299601769831142`*^9, { 3.629960253142448*^9, 3.629960269538077*^9}, {3.6299603041701374`*^9, 3.6299603078205442`*^9}, {3.6299604300467587`*^9, 3.629960435491168*^9}, { 3.6299605300585346`*^9, 3.6299605636609936`*^9}, {3.6299606195870914`*^9, 3.6299606581971593`*^9}, {3.629960824228251*^9, 3.6299608755367413`*^9}, { 3.629960906658796*^9, 3.6299609978409557`*^9}, {3.6299610312250147`*^9, 3.629961070646284*^9}, {3.629961135698398*^9, 3.6299611643088484`*^9}, { 3.6299720458358483`*^9, 3.6299721791536827`*^9}, {3.6299722439717965`*^9, 3.629972300007095*^9}, {3.6299723670872126`*^9, 3.6299723937008595`*^9}, { 3.629972457801372*^9, 3.6299724710613956`*^9}, {3.629972740193068*^9, 3.6299728251196175`*^9}, {3.6299729203577843`*^9, 3.6299729350218105`*^9}, {3.6299729720874753`*^9, 3.6299730462188053`*^9}, {3.629973116044528*^9, 3.6299731230177402`*^9}, { 3.629973184310248*^9, 3.6299732090830917`*^9}, {3.629973349982539*^9, 3.6299734360166903`*^9}, 3.629973534562063*^9, {3.629973577446539*^9, 3.629973586104554*^9}, {3.6299740374133463`*^9, 3.629974083823428*^9}, { 3.6299742505565205`*^9, 3.629974337089873*^9}, {3.629974382907153*^9, 3.6299744466176653`*^9}, {3.629974589794717*^9, 3.629974590761918*^9}, { 3.629974776215044*^9, 3.6299747850134597`*^9}, {3.6299748226095257`*^9, 3.6299748237483273`*^9}, 3.6299748618435946`*^9, {3.629975198476586*^9, 3.6299752545898843`*^9}, {3.62997531475919*^9, 3.6299753175515947`*^9}, { 3.6299754601982455`*^9, 3.6299754625382495`*^9}, {3.629975592034077*^9, 3.629975592502078*^9}, {3.629983277446268*^9, 3.6299832946842985`*^9}, { 3.62998342081052*^9, 3.6299835439883366`*^9}, {3.629983615514462*^9, 3.629983931009416*^9}, {3.6299919807040443`*^9, 3.6299919808912444`*^9}, { 3.629992028330928*^9, 3.6299920922130404`*^9}, 3.629992198480427*^9, { 3.6299922299300823`*^9, 3.629992250506518*^9}, {3.629992292657792*^9, 3.6299923603151107`*^9}, {3.6299924387676487`*^9, 3.6299924398440504`*^9}, {3.6299925764846907`*^9, 3.6299926096347485`*^9}, {3.6299928122323046`*^9, 3.629992818768716*^9}, { 3.6299929049120674`*^9, 3.629992905411268*^9}, {3.6299929850338078`*^9, 3.6299929866250105`*^9}, {3.6299931061992207`*^9, 3.62999312270405*^9}, { 3.629993172312137*^9, 3.6299932618718944`*^9}, {3.6299933276572104`*^9, 3.6299933842073092`*^9}, {3.630287775665962*^9, 3.630287795852398*^9}, { 3.6303896387100534`*^9, 3.630389666774503*^9}, {3.6303896967889557`*^9, 3.6303897095341783`*^9}, {3.6303897587054644`*^9, 3.630389880448078*^9}, { 3.6303899127557354`*^9, 3.630390009444705*^9}, 3.630390057321189*^9, 3.630390443484267*^9, {3.63039095720877*^9, 3.6303909789240074`*^9}, { 3.6303910572205453`*^9, 3.6303911291054716`*^9}, {3.630391163035531*^9, 3.6303911740803504`*^9}, {3.630391240224467*^9, 3.6303912875081496`*^9}, { 3.6303913396902413`*^9, 3.630391404570755*^9}, {3.630391479513287*^9, 3.6303917572873745`*^9}, {3.630391868905571*^9, 3.6303920027226057`*^9}, { 3.630392064327114*^9, 3.630392219843787*^9}, {3.63039226121506*^9, 3.63039232943398*^9}, {3.6303924315985594`*^9, 3.6303924441097813`*^9}, { 3.6303926866122074`*^9, 3.6303927118530517`*^9}, {3.630392795671999*^9, 3.6303928006172075`*^9}, {3.6303986032190485`*^9, 3.6303986046230516`*^9}, {3.6303986654631586`*^9, 3.6303987936485834`*^9}, {3.63039889979117*^9, 3.6303989091199865`*^9}, { 3.630399006323757*^9, 3.630399007259759*^9}, {3.630399117224352*^9, 3.630399214771323*^9}, {3.6303992555185947`*^9, 3.6303993036758795`*^9}, { 3.630399467725767*^9, 3.630399502731636*^9}, {3.6303995748037624`*^9, 3.630399595614199*^9}, {3.6303996329294643`*^9, 3.630399658076709*^9}, { 3.630399711335202*^9, 3.6303997453120623`*^9}, {3.6303998546994543`*^9, 3.6303999880484886`*^9}, {3.6304000742074394`*^9, 3.630400123441126*^9}, { 3.6304001724564123`*^9, 3.630400251595351*^9}, {3.630400324166679*^9, 3.630400327052684*^9}, {3.630400358190338*^9, 3.6304003597503414`*^9}, { 3.6304004587481155`*^9, 3.6304004640521245`*^9}, {3.630400521975026*^9, 3.630400526124634*^9}, {3.630400567199506*^9, 3.630400593516752*^9}, { 3.6304012340070767`*^9, 3.6304013035207987`*^9}, {3.6304013614749007`*^9, 3.630401367933312*^9}, {3.630401686939398*^9, 3.6304017294598303`*^9}, { 3.630401794020523*^9, 3.6304018922061386`*^9}, {3.6304019687775183`*^9, 3.630401987153569*^9}, {3.630402072749465*^9, 3.63040208297405*^9}, { 3.6304022247881613`*^9, 3.630402255931943*^9}, 3.630402329306139*^9, { 3.6304023806970787`*^9, 3.6304024212403975`*^9}, {3.6304025002259154`*^9, 3.630402528595538*^9}, {3.6304025620694523`*^9, 3.630402575015193*^9}, { 3.6304026411829777`*^9, 3.630402649073429*^9}, {3.630402695548087*^9, 3.6304027128260756`*^9}, {3.630402783923142*^9, 3.6304027982389607`*^9}, { 3.6304028797236214`*^9, 3.6304030111811404`*^9}, {3.6304030562107162`*^9, 3.6304031598846455`*^9}, {3.630403236330018*^9, 3.6304032404072514`*^9}, { 3.630403373001835*^9, 3.6304033888147397`*^9}, {3.6304039420953856`*^9, 3.6304039512829113`*^9}, 3.6304039831437335`*^9, {3.630404015975611*^9, 3.6304040663624935`*^9}, {3.630404173614628*^9, 3.630404246945822*^9}, { 3.6304042891772375`*^9, 3.630404299595834*^9}, {3.630404391083066*^9, 3.630404392406142*^9}, {3.6304045301800222`*^9, 3.6304045579486103`*^9}, { 3.630404640215316*^9, 3.630404762796327*^9}, {3.630404877629895*^9, 3.630404883104208*^9}, {3.6304050364729805`*^9, 3.630405098270515*^9}, { 3.6304051736118245`*^9, 3.6304051965901384`*^9}, {3.6304053802536435`*^9, 3.63040539242334*^9}, {3.630406035965148*^9, 3.630406041998493*^9}, { 3.630406072049212*^9, 3.6304060962065935`*^9}, {3.630406264081196*^9, 3.6304062707025747`*^9}, {3.63040632219952*^9, 3.630406385461138*^9}, { 3.630406477200385*^9, 3.630406482095665*^9}, {3.6304066170883865`*^9, 3.6304066222256804`*^9}, {3.630406957868878*^9, 3.630406973411767*^9}, { 3.6304070081447535`*^9, 3.630407018199329*^9}, {3.630407411376817*^9, 3.630407412542884*^9}, {3.6304080609339695`*^9, 3.630408121202417*^9}, { 3.6304081585485525`*^9, 3.6304081832129636`*^9}, {3.63040821409673*^9, 3.630408421131572*^9}, 3.6304934333363276`*^9, {3.63049350751357*^9, 3.630493677593298*^9}, {3.630493716898546*^9, 3.6304937846684227`*^9}, 3.630493922944331*^9, {3.6304939556752033`*^9, 3.630494117430455*^9}, { 3.6304941486092386`*^9, 3.6304941767788496`*^9}, {3.6304942118648567`*^9, 3.6304942530272107`*^9}, {3.6304942838399734`*^9, 3.6304942845820155`*^9}, {3.6304943454054947`*^9, 3.6304944442451477`*^9}, {3.63080749995092*^9, 3.6308075480801234`*^9}, { 3.630807586536323*^9, 3.630807621440319*^9}, {3.630807680459695*^9, 3.630807682914836*^9}, {3.630807736889923*^9, 3.6308077644745007`*^9}, { 3.6308078081089964`*^9, 3.6308078670123653`*^9}, {3.630807991648494*^9, 3.630807997541831*^9}, {3.6308081080891542`*^9, 3.6308081919599514`*^9}, { 3.630808306368495*^9, 3.630808345060708*^9}, {3.6308087281906223`*^9, 3.6308087555171847`*^9}, {3.630809110815507*^9, 3.630809169033837*^9}, { 3.6308091998195972`*^9, 3.630809448512822*^9}, {3.6308095328996487`*^9, 3.6308095448223305`*^9}, {3.630809582269472*^9, 3.6308095873607635`*^9}, { 3.630809665529235*^9, 3.630809684808337*^9}, {3.6308316258485594`*^9, 3.6308318380886984`*^9}, {3.63083188164919*^9, 3.630831966930068*^9}, 3.6320400558356075`*^9, {3.6354749882908883`*^9, 3.635474989418953*^9}, { 3.635475084557395*^9, 3.6354750875145636`*^9}, {3.6354751334091887`*^9, 3.635475162315842*^9}, {3.6354754001974483`*^9, 3.6354754820331287`*^9}, 3.635475512931896*^9, {3.6354756222781506`*^9, 3.635475622861184*^9}, { 3.635475691642118*^9, 3.6354757057969275`*^9}, {3.6354757798291616`*^9, 3.635475797395167*^9}, {3.635475884848169*^9, 3.6354758981309285`*^9}, { 3.635475961488552*^9, 3.6354759738382587`*^9}, {3.6354760213729773`*^9, 3.6354760572050266`*^9}, {3.6354761282470903`*^9, 3.635476136040536*^9}, { 3.6354761719365892`*^9, 3.635476212217893*^9}, {3.6593346599546614`*^9, 3.659334660890663*^9}, {3.6593347077219453`*^9, 3.659334720701168*^9}, { 3.6593348752974396`*^9, 3.6593348758122406`*^9}, {3.6593349140947075`*^9, 3.6593350070240707`*^9}, {3.6593350466949406`*^9, 3.6593350543701544`*^9}, {3.659335103791041*^9, 3.6593351614487424`*^9}, 3.659335217686841*^9, {3.659335262084519*^9, 3.6593352995869846`*^9}, { 3.6593356899482727`*^9, 3.659335701819893*^9}, {3.659335964227954*^9, 3.659335964602355*^9}, {3.65933603594128*^9, 3.6593360629605274`*^9}, { 3.6593361352354546`*^9, 3.6593361504454813`*^9}, {3.6593363929479074`*^9, 3.6593364061611304`*^9}, 3.6593368946915884`*^9, {3.6884748265656157`*^9, 3.6884748268716326`*^9}, {3.6884748600075283`*^9, 3.688474861420609*^9}, { 3.6885242858240776`*^9, 3.6885243001140976`*^9}, {3.6888842911675606`*^9, 3.6888843311676164`*^9}, {3.688966242423658*^9, 3.688966263933688*^9}, { 3.6897393587897596`*^9, 3.6897393649897685`*^9}, 3.689739477049925*^9, { 3.6898595970621734`*^9, 3.689859597272174*^9}, {3.6898596707522764`*^9, 3.6898597190523443`*^9}, {3.689859768552414*^9, 3.6898597721424184`*^9}, { 3.689859855272535*^9, 3.689859859882541*^9}, {3.6898605078334484`*^9, 3.6898607266237545`*^9}, 3.6898608811139708`*^9, {3.6898609634740863`*^9, 3.689860974304102*^9}, 3.6898610140141573`*^9, {3.6898611496043468`*^9, 3.6898611683243732`*^9}, {3.689861462024784*^9, 3.6898615624849253`*^9}, { 3.6898616142149973`*^9, 3.6898616164350004`*^9}, 3.6898616657950697`*^9, { 3.689861716805141*^9, 3.689861749905187*^9}, {3.732677920575506*^9, 3.7326779208190203`*^9}, {3.7519672427004185`*^9, 3.7519672444968877`*^9}, {3.7519674022097683`*^9, 3.75196742976579*^9}, { 3.751967484127989*^9, 3.751967510853814*^9}, {3.7519675409404893`*^9, 3.751967541549782*^9}, {3.7519675797751045`*^9, 3.751967592209671*^9}, { 3.7519676829383273`*^9, 3.7519676841255474`*^9}, {3.7519677154775553`*^9, 3.7519677953499403`*^9}, 3.751967827811061*^9, {3.7519679545625095`*^9, 3.751967957999185*^9}, {3.751968003754015*^9, 3.7519681477513895`*^9}, { 3.751968264817631*^9, 3.751968270722477*^9}, {3.7519689618119907`*^9, 3.751968969888235*^9}, {3.7519691168917775`*^9, 3.7519691395895615`*^9}, { 3.751969242782174*^9, 3.7519692581691785`*^9}, {3.7519693625211954`*^9, 3.751969378579924*^9}, {3.751969409572627*^9, 3.751969438643936*^9}, { 3.7519695894526725`*^9, 3.751969614306203*^9}, {3.7523200108586655`*^9, 3.752320012354121*^9}, {3.7553831315619707`*^9, 3.755383134119626*^9}, { 3.7553831893197794`*^9, 3.755383241814331*^9}, {3.7553832736267967`*^9, 3.7553832810757113`*^9}, {3.7554336536222963`*^9, 3.755433684797229*^9}, { 3.7554337764737434`*^9, 3.7554338315300155`*^9}, {3.755433998047738*^9, 3.7554340265485487`*^9}, {3.755446573138784*^9, 3.755446636911299*^9}, { 3.75544667493072*^9, 3.755446753435521*^9}, {3.755446891541581*^9, 3.7554468921547422`*^9}, {3.7554469323588533`*^9, 3.755446936867403*^9}, { 3.7554470190332975`*^9, 3.7554472776872244`*^9}, {3.7555217323692026`*^9, 3.755521732847602*^9}, {3.755521767127169*^9, 3.7555217972041793`*^9}, { 3.755522561453134*^9, 3.755522564231819*^9}, {3.755522601885935*^9, 3.7555226037287407`*^9}, {3.7555226758687305`*^9, 3.755522678585092*^9}, { 3.7555234832604623`*^9, 3.7555235920444417`*^9}, {3.7555239506007543`*^9, 3.755524013893358*^9}, {3.755524076791689*^9, 3.7555240812793446`*^9}, { 3.7555241238138275`*^9, 3.7555241268985643`*^9}, {3.7555242930449886`*^9, 3.7555243378577013`*^9}, {3.7555256673767824`*^9, 3.7555256808205338`*^9}, {3.7555258588384123`*^9, 3.755525900317296*^9}, { 3.755525930708299*^9, 3.7555260436531134`*^9}, {3.755607147401991*^9, 3.7556071504143705`*^9}, {3.755607992884314*^9, 3.7556080025382996`*^9}, { 3.7556094344057455`*^9, 3.7556094348690443`*^9}, {3.7559613653116636`*^9, 3.755961445097105*^9}, 3.755961484246889*^9, {3.7559618979231987`*^9, 3.755961939470047*^9}, {3.7559620323724904`*^9, 3.7559620330864005`*^9}, { 3.755962155557907*^9, 3.7559621601593847`*^9}, {3.755962303755834*^9, 3.755962343830135*^9}, {3.7559624058018165`*^9, 3.7559624450501757`*^9}, 3.756002186674869*^9, 3.7560029626855392`*^9, {3.756003222110388*^9, 3.756003295034633*^9}, {3.7560056331492863`*^9, 3.7560056663855457`*^9}, { 3.7560057813555765`*^9, 3.7560057863836613`*^9}, {3.7560058917172394`*^9, 3.756005927847292*^9}, 3.756006092376186*^9, 3.756009112317705*^9, { 3.756091886039587*^9, 3.756091887764086*^9}, {3.756092005435152*^9, 3.7560920727337685`*^9}, {3.75609212911592*^9, 3.7560921293252516`*^9}, { 3.756092262958163*^9, 3.756092263157668*^9}, {3.756092342487877*^9, 3.756092347894502*^9}, {3.7560929036769304`*^9, 3.7560929278911004`*^9}, { 3.7560930741522417`*^9, 3.756093083420331*^9}, {3.7560932986236534`*^9, 3.7560933139459305`*^9}, {3.756093449985523*^9, 3.7560934874491863`*^9}, { 3.756093592694581*^9, 3.7560936019456573`*^9}, {3.756093634438078*^9, 3.756093673866626*^9}, {3.756093873069885*^9, 3.756093897964734*^9}, { 3.7560940650109406`*^9, 3.756094078056768*^9}, {3.756442536546026*^9, 3.756442607904289*^9}, {3.7564436397451363`*^9, 3.7564436403231254`*^9}, { 3.7636034984570236`*^9, 3.7636034989933815`*^9}, {3.763603551051456*^9, 3.7636035527617817`*^9}, {3.7636036049384193`*^9, 3.7636036392233057`*^9}, {3.7636036850937223`*^9, 3.763603692587598*^9}, { 3.7636037258272257`*^9, 3.7636037459031096`*^9}, {3.7636037792254367`*^9, 3.76360387572289*^9}, {3.763603971837229*^9, 3.7636040341423655`*^9}, { 3.763604066526084*^9, 3.7636040756798687`*^9}, {3.7636041452118535`*^9, 3.763604278007333*^9}, {3.763604317710966*^9, 3.7636043271387568`*^9}, { 3.7636043584877644`*^9, 3.763604415561053*^9}, {3.763604445680462*^9, 3.7636044504114943`*^9}, {3.763604615444647*^9, 3.7636048082554193`*^9}, 3.763604854904996*^9, {3.7636133594095488`*^9, 3.7636133618464766`*^9}, { 3.7636136063756704`*^9, 3.7636136315671196`*^9}, {3.7636990373827705`*^9, 3.7636990431157646`*^9}, {3.763699090332087*^9, 3.763699110952259*^9}, { 3.763699227420497*^9, 3.7636993642943506`*^9}, {3.763700085627533*^9, 3.763700088329999*^9}, {3.7637001721125274`*^9, 3.763700181422837*^9}, { 3.763700248063385*^9, 3.7637003918630466`*^9}, {3.763700591783223*^9, 3.7637006017496295`*^9}, {3.7637007583576717`*^9, 3.7637007603074865`*^9}, {3.7637137795793185`*^9, 3.7637137822587233`*^9}, {3.7637148704355187`*^9, 3.763714870624051*^9}, { 3.763727592158518*^9, 3.7637275933445053`*^9}, {3.7637276688363667`*^9, 3.7637276694756594`*^9}, 3.763803448896332*^9, {3.76380349501632*^9, 3.7638036835067654`*^9}, {3.763804829093463*^9, 3.7638048385675254`*^9}, 3.7638051033646154`*^9, 3.7638053924528885`*^9, {3.763805557684454*^9, 3.763805634255308*^9}, {3.763806843847647*^9, 3.763806847966059*^9}, { 3.763806942652097*^9, 3.7638071770752254`*^9}, {3.7638141184594107`*^9, 3.763814134133461*^9}, {3.7638146808628216`*^9, 3.7638146925645113`*^9}, { 3.7638147709278784`*^9, 3.7638147811883087`*^9}, {3.7638148155281043`*^9, 3.763814819843194*^9}, {3.7638150259647446`*^9, 3.763815028601293*^9}, { 3.7638151529595194`*^9, 3.763815155849978*^9}, {3.7638163770262136`*^9, 3.763816380851597*^9}, {3.7638164181856327`*^9, 3.7638164950537987`*^9}, 3.763816568304102*^9, {3.7638166173645625`*^9, 3.763816618808757*^9}, { 3.7638167204462805`*^9, 3.763816721012859*^9}, {3.763857602253485*^9, 3.7638579604183645`*^9}, {3.7638580038507566`*^9, 3.7638580060526443`*^9}, {3.763858082269992*^9, 3.7638581746835337`*^9}, { 3.7638582163351564`*^9, 3.7638582415275116`*^9}, {3.7638582983238*^9, 3.763858907503306*^9}, {3.763858941318697*^9, 3.763858956626134*^9}, { 3.7638602435602536`*^9, 3.763860245408451*^9}, {3.7638694636456347`*^9, 3.7638694647177277`*^9}, {3.7638708199536576`*^9, 3.763870829436488*^9}, { 3.763871287170555*^9, 3.7638712876184006`*^9}, {3.763943214376035*^9, 3.7639432984591475`*^9}, {3.763943418832348*^9, 3.7639434335508127`*^9}, { 3.76394347113767*^9, 3.7639435187320576`*^9}, {3.763943585908682*^9, 3.7639436125255404`*^9}, {3.763951722152746*^9, 3.76395172989299*^9}, { 3.7639517863423367`*^9, 3.7639519945900664`*^9}, {3.763952081515512*^9, 3.7639521530710773`*^9}, {3.763952353248129*^9, 3.763952357026309*^9}, { 3.7639524211903834`*^9, 3.7639524243979177`*^9}, {3.7639527174925117`*^9, 3.7639527180252266`*^9}, {3.7641265625745993`*^9, 3.7641265632314167`*^9}, {3.764126605555829*^9, 3.7641266075095396`*^9}, { 3.7641268313964133`*^9, 3.7641268543573804`*^9}, {3.764127044657903*^9, 3.7641270479422092`*^9}, {3.7641271442332697`*^9, 3.7641271469362774`*^9}, {3.764127227626192*^9, 3.7641272592640233`*^9}, { 3.764127335707515*^9, 3.7641273386484756`*^9}, {3.764127429843852*^9, 3.7641274364304185`*^9}, {3.7641275071859307`*^9, 3.764127516803895*^9}, 3.7641276043548007`*^9, {3.7641276925365753`*^9, 3.764127697080591*^9}, 3.764127798472331*^9, 3.764127853631323*^9, 3.764127908496078*^9, { 3.7641280050343323`*^9, 3.764128022046494*^9}, {3.764128128597419*^9, 3.764128154116727*^9}, {3.7641286864636617`*^9, 3.764128701643106*^9}, { 3.7641289910924444`*^9, 3.7641290126680794`*^9}, {3.7641290672285347`*^9, 3.7641290737798567`*^9}, {3.7641325425120363`*^9, 3.764132565390477*^9}, { 3.7641327425004654`*^9, 3.764132750040793*^9}, 3.7641327968340364`*^9, { 3.764133146776842*^9, 3.764133204874522*^9}, {3.7641333488187037`*^9, 3.7641333525577593`*^9}, {3.764413145593136*^9, 3.7644131471236105`*^9}, { 3.764413201645049*^9, 3.7644132349609704`*^9}, {3.764413325008136*^9, 3.7644133748980193`*^9}, {3.7644134113425665`*^9, 3.7644135151187*^9}, { 3.764413554409053*^9, 3.7644136160674934`*^9}, {3.76441371984758*^9, 3.764413730103909*^9}, 3.764419641962368*^9, {3.7644198522879405`*^9, 3.764419879249356*^9}, 3.764419909536559*^9, {3.764419991012162*^9, 3.764420000171088*^9}, {3.7644200798862047`*^9, 3.7644200950961914`*^9}, { 3.7644201529471693`*^9, 3.764420153715966*^9}, {3.764420210346301*^9, 3.764420255343707*^9}, {3.764420296178318*^9, 3.7644203000939393`*^9}, { 3.7644203803359275`*^9, 3.7644203931390867`*^9}, 3.7644204418727274`*^9, { 3.7647259720700207`*^9, 3.7647261047260523`*^9}, {3.7647263483375626`*^9, 3.76472635879602*^9}, 3.764726656736601*^9, {3.764727009127914*^9, 3.764727020100875*^9}, {3.7647270591828785`*^9, 3.7647270819631023`*^9}, { 3.7647272109090505`*^9, 3.764727227846332*^9}, {3.76473247809907*^9, 3.7647324813925114`*^9}, {3.7647349484962797`*^9, 3.7647349979358416`*^9}, {3.7647351097258167`*^9, 3.764735124772463*^9}, { 3.7647352810674453`*^9, 3.7647352901139917`*^9}, {3.7647353746429515`*^9, 3.764735379550926*^9}, {3.7647354596539807`*^9, 3.764735507677454*^9}, { 3.7647355546341*^9, 3.764735728811817*^9}, {3.764735837449795*^9, 3.76473584132898*^9}, {3.76473603649269*^9, 3.7647360592982664`*^9}, { 3.7647360998228803`*^9, 3.76473621551197*^9}, {3.7647362545599003`*^9, 3.764736286430997*^9}, {3.7647364592833533`*^9, 3.764736464019006*^9}, { 3.764736566167658*^9, 3.7647365918958225`*^9}, {3.764764761680134*^9, 3.7647648482473745`*^9}, 3.764764917763693*^9, {3.764764964821686*^9, 3.764765090741813*^9}, {3.7647651742140284`*^9, 3.7647652517335076`*^9}, { 3.764765341266399*^9, 3.7647653614173465`*^9}, 3.764765400284145*^9, { 3.764765691384389*^9, 3.764765708710143*^9}, 3.7647657454275875`*^9, { 3.76476578351686*^9, 3.764765871262255*^9}, {3.7647661045180917`*^9, 3.76476612822571*^9}, {3.7647661964223824`*^9, 3.764766239375331*^9}, { 3.764766330361228*^9, 3.764766338297905*^9}, {3.764767015060799*^9, 3.7647670193029037`*^9}, {3.764767076590926*^9, 3.7647671160277977`*^9}, { 3.7647671493139205`*^9, 3.7647672079236426`*^9}, {3.764767458938404*^9, 3.7647674608323865`*^9}, {3.764810938444873*^9, 3.7648109399353456`*^9}, { 3.7648118616019874`*^9, 3.7648118695079126`*^9}, {3.7648120589477816`*^9, 3.7648124600413237`*^9}, {3.76481250476682*^9, 3.7648125259602103`*^9}, { 3.764812601341893*^9, 3.7648126577763243`*^9}, {3.7648126944039307`*^9, 3.7648128855627623`*^9}, {3.764812924923909*^9, 3.764812926481821*^9}, { 3.764813041485982*^9, 3.764813131254232*^9}, {3.7648134679328885`*^9, 3.7648136479313235`*^9}, {3.7648136917777314`*^9, 3.764813697753367*^9}, { 3.7648137297570653`*^9, 3.764813747862262*^9}, 3.764813784221693*^9, { 3.7648138370678406`*^9, 3.7648141387969923`*^9}, {3.764814321050164*^9, 3.764814422489184*^9}, {3.764814461366684*^9, 3.7648145835728483`*^9}, { 3.764814614769511*^9, 3.7648147525825167`*^9}, {3.764815363375289*^9, 3.7648153644907384`*^9}, {3.764815451671169*^9, 3.7648154601533747`*^9}, { 3.7648175917802963`*^9, 3.7648176401910563`*^9}, {3.765885491237231*^9, 3.765885501131465*^9}, {3.766572999289345*^9, 3.7665729996020145`*^9}, { 3.7665730613126965`*^9, 3.7665730616706066`*^9}, {3.7840103262125545`*^9, 3.7840103546413517`*^9}, {3.784011309725755*^9, 3.7840113197719574`*^9}, { 3.784013374800973*^9, 3.7840133842981763`*^9}, {3.7840238533665447`*^9, 3.78402395932942*^9}, {3.784024091276659*^9, 3.784024112209529*^9}, { 3.7840242793219643`*^9, 3.784024296655184*^9}, {3.7840290670892677`*^9, 3.7840291348388853`*^9}, {3.784029222997594*^9, 3.784029542926179*^9}, { 3.784375172285057*^9, 3.784375319701829*^9}, {3.7843753678421807`*^9, 3.7843753788103914`*^9}, {3.7843754844339557`*^9, 3.784375827494117*^9}, { 3.784375862317687*^9, 3.7843759567563844`*^9}, {3.784376004941759*^9, 3.7843760080157185`*^9}, {3.784376101918992*^9, 3.7843761244332943`*^9}, { 3.784376181191763*^9, 3.7843762145091863`*^9}, {3.7843792489960337`*^9, 3.78437926273014*^9}, {3.7843793293934345`*^9, 3.784379368676588*^9}, { 3.7843796529835215`*^9, 3.7843796858862267`*^9}, {3.784450863324359*^9, 3.7844508986076546`*^9}, {3.7844510208392324`*^9, 3.784451027915551*^9}, { 3.7844511176315613`*^9, 3.7844511673791957`*^9}, {3.784451235055628*^9, 3.78445132575735*^9}, {3.784451995615477*^9, 3.7844520110330954`*^9}, { 3.7844522907551537`*^9, 3.7844523421551*^9}, {3.784700119490345*^9, 3.7847001627913013`*^9}, {3.7847004221290607`*^9, 3.7847004380767317`*^9}, 3.7847007913506136`*^9, {3.784781955129138*^9, 3.784781977787957*^9}, { 3.78488170216677*^9, 3.784881704210422*^9}, 3.784882130557441*^9, { 3.78488220347418*^9, 3.7848822064697027`*^9}, {3.784883393455822*^9, 3.784883458551924*^9}, 3.7848835306495824`*^9, {3.7848836822092113`*^9, 3.7848837303696923`*^9}, 3.7848838199009576`*^9, {3.7848842507527857`*^9, 3.7848842836585226`*^9}, 3.7848843847882996`*^9, {3.784884461405264*^9, 3.7848844645041113`*^9}, {3.784884559404122*^9, 3.7848845656634912`*^9}, { 3.7848852409944844`*^9, 3.7848852740337477`*^9}, {3.7848854548929386`*^9, 3.7848854893046365`*^9}, {3.7848856741783943`*^9, 3.784885691704702*^9}, { 3.784885809660874*^9, 3.784885811424426*^9}, {3.7848860031948376`*^9, 3.784886020570098*^9}, 3.7848861057105627`*^9, {3.7848861627726107`*^9, 3.7848862212876124`*^9}, {3.784886306497995*^9, 3.7848863509322224`*^9}, 3.784886472690192*^9, {3.7848866596243*^9, 3.784886664116289*^9}, { 3.7848866987282944`*^9, 3.7848867077911897`*^9}, {3.78488676128524*^9, 3.7848868667029366`*^9}, {3.7848869381224003`*^9, 3.7848869414281464`*^9}, {3.7848870104508753`*^9, 3.784887039889447*^9}, { 3.7848871795058794`*^9, 3.7848871976746817`*^9}, {3.7848872311446314`*^9, 3.78488724075662*^9}, 3.784887405188785*^9, {3.784887591926689*^9, 3.7848876119305134`*^9}, {3.784887676620901*^9, 3.7848876786672792`*^9}, { 3.78488771054331*^9, 3.784887714354906*^9}, {3.7848877625809546`*^9, 3.7848878103041153`*^9}, 3.7848878862881575`*^9, {3.787717235155089*^9, 3.787717269464238*^9}, {3.7877174592607603`*^9, 3.7877174674038067`*^9}, { 3.7877271032841845`*^9, 3.787727136247201*^9}, 3.787727355369296*^9, 3.7877274973278403`*^9, {3.787727855959008*^9, 3.78772792141208*^9}, 3.787728113487193*^9, {3.7877281704571557`*^9, 3.7877281735077004`*^9}, 3.7877282789827795`*^9, {3.7877286510229864`*^9, 3.787728665729192*^9}, { 3.7877287942225084`*^9, 3.787728807671986*^9}, {3.787729044867985*^9, 3.787729045536916*^9}, {3.787729589732438*^9, 3.7877296062090626`*^9}, { 3.787729794037467*^9, 3.7877297950347877`*^9}, {3.787729855548402*^9, 3.7877299039179935`*^9}, {3.7877300373241186`*^9, 3.787730068136018*^9}, { 3.7877301999859333`*^9, 3.7877302014150777`*^9}, {3.787732033225385*^9, 3.7877320471634016`*^9}, {3.787732077195259*^9, 3.7877320780358667`*^9}, 3.787732189759206*^9, {3.78773231889835*^9, 3.787732327710633*^9}, { 3.7877324857166643`*^9, 3.787732496655479*^9}, {3.7877325848303585`*^9, 3.78773258503596*^9}, {3.7877328504631166`*^9, 3.7877328625892415`*^9}, { 3.7877330254884944`*^9, 3.7877330271019044`*^9}, {3.787733136128061*^9, 3.7877331422258835`*^9}, {3.787733243513567*^9, 3.78773324558677*^9}, 3.787733310555999*^9, 3.7877334085329347`*^9, {3.7877337955932293`*^9, 3.7877337970498257`*^9}, {3.787733867727028*^9, 3.7877338687324905`*^9}, { 3.7877352224369583`*^9, 3.787735224161746*^9}, {3.787735343322833*^9, 3.787735348772827*^9}, {3.787735422704711*^9, 3.7877354268945775`*^9}, { 3.7877355100355635`*^9, 3.787735514671461*^9}, {3.7877356541994534`*^9, 3.7877356632141013`*^9}, 3.7877357913476543`*^9, 3.787736261837074*^9, { 3.7882542159043374`*^9, 3.7882542747998285`*^9}, {3.788254310967661*^9, 3.788254318430212*^9}, {3.788254585790197*^9, 3.7882545888318524`*^9}, { 3.7882547349987383`*^9, 3.788254735940298*^9}, 3.788254830063775*^9, 3.7882549155286837`*^9, {3.7882550121437798`*^9, 3.788255037735396*^9}, { 3.7882551764404287`*^9, 3.78825518352113*^9}, {3.7882552540030313`*^9, 3.788255290224329*^9}, {3.7882553843544893`*^9, 3.788255423248046*^9}, { 3.78825567982127*^9, 3.7882556852479534`*^9}, {3.7882557908576803`*^9, 3.7882558029800806`*^9}, {3.7882560240494256`*^9, 3.7882560388846164`*^9}, 3.788256102343512*^9, {3.788256161397396*^9, 3.7882561626372194`*^9}, { 3.7882562304311895`*^9, 3.78825629590362*^9}, {3.7882563614677362`*^9, 3.7882563620189795`*^9}, {3.7882564138122153`*^9, 3.7882564294158382`*^9}, {3.788256467457189*^9, 3.7882564889521217`*^9}, { 3.7882565883311844`*^9, 3.788256591497148*^9}, {3.7882568409513097`*^9, 3.7882568724526567`*^9}, {3.788256965258837*^9, 3.788256966444976*^9}, { 3.7882570073831463`*^9, 3.7882570497349973`*^9}, {3.7882570992487097`*^9, 3.788257144206352*^9}, {3.78825721252205*^9, 3.788257307277931*^9}, { 3.788257350410209*^9, 3.7882573617262745`*^9}, {3.788257424936472*^9, 3.788257434118204*^9}, {3.788276311330668*^9, 3.788276311647092*^9}, { 3.7882765465512347`*^9, 3.788276608568333*^9}, {3.7882767715851693`*^9, 3.7882768045752783`*^9}, {3.7882769342607436`*^9, 3.7882769409894867`*^9}, {3.7882770202208567`*^9, 3.7882770424485188`*^9}, {3.7882770760040703`*^9, 3.788277077341468*^9}, { 3.788277147336176*^9, 3.788277150397852*^9}, {3.7882772069909*^9, 3.7882772101572385`*^9}, {3.7882772503366175`*^9, 3.7882772773759403`*^9}, {3.7882773922958755`*^9, 3.7882773927832017`*^9}, {3.788277450684473*^9, 3.788277482126852*^9}, { 3.78827754293396*^9, 3.788277545027956*^9}, {3.7883214550230436`*^9, 3.7883214742097826`*^9}, {3.788321520104019*^9, 3.788321685390153*^9}, { 3.788321717307153*^9, 3.788321801831746*^9}, {3.788321836768508*^9, 3.788322037754008*^9}, {3.7883220686363816`*^9, 3.788322220085001*^9}, { 3.7883255906192427`*^9, 3.788325646609389*^9}, {3.7883257976991563`*^9, 3.788325804097658*^9}, {3.788325969279187*^9, 3.7883259830028267`*^9}, { 3.788326975877249*^9, 3.788326979070017*^9}, {3.788328539286415*^9, 3.788328618410488*^9}, {3.788328648595448*^9, 3.788328762662589*^9}, { 3.7883288060890923`*^9, 3.7883288805716724`*^9}, {3.7883319188300047`*^9, 3.78833193230753*^9}, {3.7883321144947567`*^9, 3.788332115050151*^9}, { 3.7883333680456443`*^9, 3.7883333686272163`*^9}, 3.7883336421611414`*^9, { 3.788333691323177*^9, 3.7883336916362*^9}, {3.788333797629262*^9, 3.7883338348662343`*^9}, {3.7883339555470386`*^9, 3.7883339660305166`*^9}, {3.7883340291758356`*^9, 3.788334031484354*^9}, { 3.788334368484807*^9, 3.7883343918754945`*^9}, {3.7883345963739557`*^9, 3.788334645315611*^9}, {3.788411405608647*^9, 3.788411409092114*^9}, { 3.7884115644712825`*^9, 3.7884115911998663`*^9}, {3.7884116673998833`*^9, 3.788411758799066*^9}, {3.788411985303985*^9, 3.788412002701314*^9}, { 3.78841218266156*^9, 3.788412217652734*^9}, {3.788412679618697*^9, 3.78841268296084*^9}, {3.788412968920223*^9, 3.7884129782039633`*^9}, { 3.7884155241723013`*^9, 3.7884155243798914`*^9}, 3.7884156619519596`*^9, { 3.7884162343262696`*^9, 3.788416236013459*^9}, {3.789022054245319*^9, 3.7890221116154556`*^9}, {3.7890222001685014`*^9, 3.789022205961149*^9}, { 3.789094077050009*^9, 3.7890940781167436`*^9}, {3.7890941254883175`*^9, 3.7890942919861226`*^9}, {3.789094340508856*^9, 3.789094543716852*^9}, { 3.789094583794143*^9, 3.7890947278803444`*^9}, {3.7890947714417076`*^9, 3.7890948342626343`*^9}, {3.789095197615344*^9, 3.789095215073329*^9}, { 3.789095256390032*^9, 3.78909525710861*^9}, {3.7890954241290827`*^9, 3.78909583987399*^9}, {3.789096056032333*^9, 3.7890960602768464`*^9}, { 3.7890960928429904`*^9, 3.789096098149865*^9}, {3.789096721918685*^9, 3.789096734998893*^9}, {3.7890967741973257`*^9, 3.78909683859006*^9}, { 3.789096947653244*^9, 3.789097122315098*^9}, {3.7890971528708224`*^9, 3.789097530683948*^9}, {3.7890975852885656`*^9, 3.7890975882562447`*^9}, { 3.7890976430709224`*^9, 3.789097656213524*^9}, {3.789107592314107*^9, 3.7891076537760305`*^9}, {3.789107685160589*^9, 3.789107760590632*^9}, { 3.7891078105008087`*^9, 3.789107846610609*^9}, {3.789107989236459*^9, 3.7891080001561875`*^9}, {3.7891082032172785`*^9, 3.7891082064574785`*^9}, {3.7891083013630204`*^9, 3.789108444864075*^9}, { 3.7891084751958127`*^9, 3.7891085010044174`*^9}, {3.7891085322441816`*^9, 3.7891085353767447`*^9}, {3.789108620037199*^9, 3.789108662297584*^9}, 3.7891087252471294`*^9, {3.789108773507248*^9, 3.7891088501491203`*^9}, { 3.7891088829987*^9, 3.789108918319019*^9}, {3.7891089606286983`*^9, 3.7891090044788837`*^9}, {3.789109048556943*^9, 3.7891091177554493`*^9}, { 3.7891091628149347`*^9, 3.7891092922346783`*^9}, {3.789109382870388*^9, 3.789109402625166*^9}, {3.7891111380334797`*^9, 3.7891113582877145`*^9}, { 3.789111396694514*^9, 3.7891114221541777`*^9}, {3.7891114539845037`*^9, 3.7891114952359962`*^9}, {3.789112929457416*^9, 3.7891129318274393`*^9}, { 3.789112963290578*^9, 3.7891131302196255`*^9}, {3.789113202949188*^9, 3.789113203379569*^9}, {3.7891144371217365`*^9, 3.789114518411393*^9}, { 3.789114638487608*^9, 3.78911468069436*^9}, {3.789114763918976*^9, 3.789114777923211*^9}, {3.789114809301983*^9, 3.7891148392057247`*^9}, { 3.7891148923150015`*^9, 3.789114904054755*^9}, {3.7891149560740595`*^9, 3.7891150071774015`*^9}, {3.789115109642312*^9, 3.7891151147637*^9}, { 3.7891185439211864`*^9, 3.789118561569729*^9}, {3.7891187834106455`*^9, 3.7891187854068985`*^9}, {3.7891188764873776`*^9, 3.7891188767373095`*^9}, {3.789121799028477*^9, 3.789121806719482*^9}, { 3.7891222627163153`*^9, 3.7891222774782734`*^9}, {3.7891223914541044`*^9, 3.7891224006004095`*^9}, {3.789122431773783*^9, 3.7891224422816577`*^9}, { 3.7891224731160736`*^9, 3.789122501042121*^9}, {3.7891226653529224`*^9, 3.7891226664045706`*^9}, 3.789122819901965*^9, {3.789122893844426*^9, 3.7891229543768473`*^9}, {3.7891229964274464`*^9, 3.7891231044294157`*^9}, {3.789123228485856*^9, 3.789123374714591*^9}, { 3.7891235661360893`*^9, 3.7891235688754067`*^9}}, CellLabel-> "In[399]:=",ExpressionUUID->"5daf46ec-6720-4b2e-babe-01c85a382836"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E1005", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ "n1_", ",", "n2_", ",", "n3_", ",", "n4_", ",", "n5_", ",", "n6_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "node", ",", "n\[Alpha]", ",", "n\[Beta]", ",", "\[Alpha]", ",", "\[Beta]", ",", "NN", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "rn", ",", "jac", ",", "h\[Alpha]", ",", "e\[Alpha]", ",", "h\[Beta]", ",", "e\[Beta]", ",", "en", ",", "FF", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]", ",", "f\[Alpha]", ",", "f\[Beta]", ",", "fn", ",", "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]", ",", "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]", ",", "\[Gamma]\[Alpha]", ",", "\[Gamma]\[Beta]", ",", "GG", ",", "N\[Alpha]\[Alpha]", ",", "N\[Beta]\[Beta]", ",", "N\[Alpha]\[Beta]", ",", "N\[Beta]\[Alpha]", ",", "M\[Alpha]\[Alpha]", ",", "M\[Beta]\[Beta]", ",", "M\[Alpha]\[Beta]", ",", "Q\[Alpha]", ",", "Q\[Beta]", ",", "\[Delta]wint", ",", "\[Delta]wext"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ")"}], "-", RowBox[{"2", RowBox[{"(", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ")"}], "\[Alpha]"}], "-", RowBox[{"2", " ", RowBox[{"(", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ")"}], "\[Beta]"}]}], ",", RowBox[{"4", RowBox[{"(", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ")"}], "\[Alpha]"}], ",", "\[IndentingNewLine]", RowBox[{"\[Alpha]", "-", RowBox[{"2", RowBox[{"(", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ")"}], "\[Alpha]"}], "-", RowBox[{"2", " ", "\[Alpha]", " ", "\[Beta]"}]}], ",", RowBox[{"4", " ", "\[Alpha]", " ", "\[Beta]"}], ",", RowBox[{"\[Beta]", "-", RowBox[{"2", " ", "\[Alpha]", " ", "\[Beta]"}], "-", RowBox[{"2", " ", RowBox[{"(", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ")"}], "\[Beta]"}]}], " ", ",", RowBox[{"4", RowBox[{"(", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ")"}], "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"node", "=", RowBox[{"{", RowBox[{ "n1", ",", "n2", ",", "n3", ",", "n4", ",", "n5", ",", "n6"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "mapping", " ", "to", " ", "orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "3"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Alpha]", "=", RowBox[{"Norm", "[", "r\[Alpha]", "]"}]}], ";", RowBox[{"e\[Alpha]", "=", RowBox[{"r\[Alpha]", "/", "h\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Beta]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "3"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Beta]", "=", RowBox[{"r\[Beta]", "-", RowBox[{ RowBox[{"(", RowBox[{"r\[Beta]", ".", "e\[Alpha]"}], ")"}], "*", "e\[Alpha]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Norm", "[", "r\[Beta]", "]"}]}], ";", RowBox[{"e\[Beta]", "=", RowBox[{"r\[Beta]", "/", "h\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{"e\[Alpha]", "\[Cross]", "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", " ", "=", RowBox[{"h\[Alpha]", "*", "h\[Beta]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"in", " ", "flat", " ", "geometry"}], "*)"}], "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", "e\[Beta]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "transform", " ", "into", " ", "the", " ", "material", " ", "\[Alpha]\[Beta]n"}], "-", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"(", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "2"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"(", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "3"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fz"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"strain", " ", "measures", " ", "with", " ", "non"}], "-", RowBox[{"symmetric", " ", "\[Epsilon]"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}], "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], "/", "h\[Alpha]"}], "-", "\[Psi]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}], "/", "h\[Beta]"}], "+", "\[Psi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[CapitalTheta]"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}]}], "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[CapitalTheta]"}], "/", "h\[Beta]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], "/", "h\[Alpha]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Beta]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], "+", "\[CapitalTheta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}], "/", "h\[Beta]"}], "-", "\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "stress", " ", "resultants", " ", "with", " ", "a", " ", "nonsymmetric", " ", "N"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Alpha]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Beta]\[Beta]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Beta]\[Beta]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Beta]\[Beta]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Beta]", "=", RowBox[{"tt", "*", "GG", "*", "\[Epsilon]\[Alpha]\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Beta]\[Alpha]", "=", RowBox[{"tt", "*", "GG", "*", "\[Epsilon]\[Beta]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Alpha]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Beta]\[Beta]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Beta]\[Beta]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Beta]\[Beta]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Beta]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", "GG", "*", "\[Kappa]\[Alpha]\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Beta]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Beta]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint1", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "N\[Alpha]\[Alpha]", ",", "N\[Beta]\[Beta]", ",", "N\[Alpha]\[Beta]", ",", "N\[Beta]\[Alpha]"}], "}"}]}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Beta]\[Beta]", ",", "M\[Alpha]\[Beta]"}], "}"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Beta]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Beta]"}], "}"}]}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint2", "=", RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Beta]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Beta]"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint1", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "+", RowBox[{"QUAD", "[", RowBox[{"TRI4", ",", RowBox[{ RowBox[{"(", "\[Delta]wint2", ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"ELEMENT", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "n\[Alpha]", ",", "n\[Beta]", ",", "\[Alpha]", ",", "\[Beta]", ",", "NN", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "rn", ",", "jac", ",", "h\[Alpha]", ",", "e\[Alpha]", ",", "h\[Beta]", ",", "e\[Beta]", ",", "en", ",", "FF", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]", ",", "f\[Alpha]", ",", "f\[Beta]", ",", "fn", ",", "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]", ",", "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]", ",", "\[Gamma]\[Alpha]", ",", "\[Gamma]\[Beta]", ",", "GG", ",", "N\[Alpha]\[Alpha]", ",", "N\[Beta]\[Beta]", ",", "N\[Alpha]\[Beta]", ",", "N\[Beta]\[Alpha]", ",", "M\[Alpha]\[Alpha]", ",", "M\[Beta]\[Beta]", ",", "M\[Alpha]\[Beta]", ",", "Q\[Alpha]", ",", "Q\[Beta]", ",", "\[Delta]wint", ",", "\[Delta]wext"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"1", "/", "2"}], "*", "\[Alpha]", "*", RowBox[{"(", RowBox[{"2", "-", RowBox[{"9", "*", "\[Alpha]"}], "+", RowBox[{"9", "*", SuperscriptBox["\[Alpha]", "2"]}]}], ")"}]}], ",", RowBox[{ RowBox[{"1", "/", "2"}], "*", " ", "\[Beta]", "*", RowBox[{"(", RowBox[{"2", "-", RowBox[{"9", "*", " ", "\[Beta]"}], "+", RowBox[{"9", " ", "*", SuperscriptBox["\[Beta]", "2"]}]}], ")"}]}], ",", RowBox[{ RowBox[{"1", "/", "2"}], "*", RowBox[{"(", RowBox[{"2", "-", RowBox[{"9", " ", SuperscriptBox["\[Alpha]", "3"]}], "-", RowBox[{"11", " ", "\[Beta]"}], "+", RowBox[{"18", " ", SuperscriptBox["\[Beta]", "2"]}], "-", RowBox[{"9", " ", SuperscriptBox["\[Beta]", "3"]}], "-", RowBox[{"9", " ", "*", SuperscriptBox["\[Alpha]", "2"], "*", RowBox[{"(", RowBox[{ RowBox[{"-", "2"}], "+", RowBox[{"3", "*", "\[Beta]"}]}], ")"}]}], "+", RowBox[{"\[Alpha]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "11"}], "+", RowBox[{"36", "*", "\[Beta]"}], "-", RowBox[{"27", "*", SuperscriptBox["\[Beta]", "2"]}]}], ")"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"9", "/", "2"}], "*", " ", "\[Alpha]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"3", "*", "\[Alpha]"}]}], ")"}], "*", "\[Beta]"}], ",", RowBox[{ RowBox[{"9", "/", "2"}], "*", " ", "\[Alpha]", "*", "\[Beta]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"3", "*", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{ RowBox[{"-", "9"}], "/", "2"}], "*", " ", "\[Beta]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}], "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"3", "*", "\[Beta]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"9", "/", "2"}], "*", " ", "\[Beta]", "*", RowBox[{"(", RowBox[{"2", "+", RowBox[{"3", "*", SuperscriptBox["\[Alpha]", "2"]}], "-", RowBox[{"5", "*", "\[Beta]"}], "+", RowBox[{"3", "*", SuperscriptBox["\[Beta]", "2"]}], "+", RowBox[{"\[Alpha]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "5"}], "+", RowBox[{"6", "*", "\[Beta]"}]}], ")"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{"9", "/", "2"}], "*", "\[Alpha]", "*", RowBox[{"(", RowBox[{"2", "+", RowBox[{"3", "*", SuperscriptBox["\[Alpha]", "2"]}], "-", RowBox[{"5", "*", "\[Beta]"}], "+", RowBox[{"3", "*", SuperscriptBox["\[Beta]", "2"]}], "+", RowBox[{"\[Alpha]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "5"}], "+", RowBox[{"6", "*", "\[Beta]"}]}], ")"}]}]}], ")"}]}], ",", RowBox[{ RowBox[{ RowBox[{"-", "9"}], "/", "2"}], "*", " ", "\[Alpha]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"3", "*", "\[Alpha]"}]}], ")"}], "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}]}], ",", RowBox[{ RowBox[{"-", "27"}], "*", "\[Alpha]", "*", "\[Beta]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "mapping", " ", "to", " ", "orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "3"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Alpha]", "=", RowBox[{"Norm", "[", "r\[Alpha]", "]"}]}], ";", RowBox[{"e\[Alpha]", "=", RowBox[{"r\[Alpha]", "/", "h\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Beta]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "3"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Beta]", "=", RowBox[{"r\[Beta]", "-", RowBox[{ RowBox[{"(", RowBox[{"r\[Beta]", ".", "e\[Alpha]"}], ")"}], "*", "e\[Alpha]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Norm", "[", "r\[Beta]", "]"}]}], ";", RowBox[{"e\[Beta]", "=", RowBox[{"r\[Beta]", "/", "h\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{"e\[Alpha]", "\[Cross]", "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", " ", "=", RowBox[{"h\[Alpha]", "*", "h\[Beta]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"in", " ", "flat", " ", "geometry"}], "*)"}], "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", "e\[Beta]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "transform", " ", "into", " ", "the", " ", "material", " ", "\[Alpha]\[Beta]n"}], "-", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"(", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "2"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"(", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "3"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fz"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"strain", " ", "measures", " ", "with", " ", "non"}], "-", RowBox[{"symmetric", " ", "\[Epsilon]"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}], "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], "/", "h\[Alpha]"}], "-", "\[Psi]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}], "/", "h\[Beta]"}], "+", "\[Psi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[CapitalTheta]"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}]}], "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[CapitalTheta]"}], "/", "h\[Beta]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], "/", "h\[Alpha]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Beta]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], "+", "\[CapitalTheta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}], "/", "h\[Beta]"}], "-", "\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "stress", " ", "resultants", " ", "with", " ", "a", " ", "nonsymmetric", " ", "N"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Alpha]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Beta]\[Beta]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Beta]\[Beta]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Beta]\[Beta]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Beta]", "=", RowBox[{"tt", "*", "GG", "*", "\[Epsilon]\[Alpha]\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Beta]\[Alpha]", "=", RowBox[{"tt", "*", "GG", "*", "\[Epsilon]\[Beta]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Alpha]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Beta]\[Beta]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Beta]\[Beta]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Beta]\[Beta]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Beta]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", "GG", "*", "\[Kappa]\[Alpha]\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Beta]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Beta]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "N\[Alpha]\[Alpha]", ",", "N\[Beta]\[Beta]", ",", "N\[Alpha]\[Beta]", ",", "N\[Beta]\[Alpha]"}], "}"}]}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Beta]\[Beta]", ",", "M\[Alpha]\[Beta]"}], "}"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Beta]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Beta]"}], "}"}]}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI28", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}], "]"}], "/;", " ", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", "10", "}"}]}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"ELEMENT", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "n\[Alpha]", ",", "n\[Beta]", ",", "nne", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "enode", ",", "NN", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "rn", ",", "jac", ",", "h\[Alpha]", ",", "e\[Alpha]", ",", "h\[Beta]", ",", "e\[Beta]", ",", "en", ",", "FF", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]", ",", "f\[Alpha]", ",", "f\[Beta]", ",", "fn", ",", "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]", ",", "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]", ",", "\[Gamma]\[Alpha]", ",", "\[Gamma]\[Beta]", ",", "GG", ",", "N\[Alpha]\[Alpha]", ",", "N\[Beta]\[Beta]", ",", "N\[Alpha]\[Beta]", ",", "N\[Beta]\[Alpha]", ",", "M\[Alpha]\[Alpha]", ",", "M\[Beta]\[Beta]", ",", "M\[Alpha]\[Beta]", ",", "Q\[Alpha]", ",", "Q\[Beta]", ",", "\[Delta]wint", ",", "\[Delta]wext"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "nodes", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"n\[Alpha]", ",", "n\[Beta]"}], "}"}], "=", RowBox[{"Dimensions", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"nne", " ", "=", RowBox[{"n\[Alpha]", "*", "n\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"enode", "=", RowBox[{"Flatten", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n\[Alpha]", ",", "\[Alpha]"}], "}"}], ",", RowBox[{"{", RowBox[{"n\[Beta]", ",", "\[Beta]"}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "mapping", " ", "to", " ", "orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Alpha]", "=", RowBox[{"Norm", "[", "r\[Alpha]", "]"}]}], ";", RowBox[{"e\[Alpha]", "=", RowBox[{"r\[Alpha]", "/", "h\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Beta]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Beta]", "=", RowBox[{"r\[Beta]", "-", RowBox[{ RowBox[{"(", RowBox[{"r\[Beta]", ".", "e\[Alpha]"}], ")"}], "*", "e\[Alpha]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Norm", "[", "r\[Beta]", "]"}]}], ";", RowBox[{"e\[Beta]", "=", RowBox[{"r\[Beta]", "/", "h\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{"e\[Alpha]", "\[Cross]", "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", " ", "=", RowBox[{"h\[Alpha]", "*", "h\[Beta]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"in", " ", "flat", " ", "geometry"}], "*)"}], "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", "e\[Beta]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "transform", " ", "into", " ", "the", " ", "material", " ", "\[Alpha]\[Beta]n"}], "-", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"(", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "2"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"(", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "3"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fz"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"strain", " ", "measures", " ", "with", " ", "non"}], "-", RowBox[{"symmetric", " ", "\[Epsilon]"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}], "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], "/", "h\[Alpha]"}], "-", "\[Psi]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}], "/", "h\[Beta]"}], "+", "\[Psi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[CapitalTheta]"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}]}], "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[CapitalTheta]"}], "/", "h\[Beta]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], "/", "h\[Alpha]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Beta]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], "+", "\[CapitalTheta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}], "/", "h\[Beta]"}], "-", "\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "stress", " ", "resultants", " ", "with", " ", "a", " ", "nonsymmetric", " ", "N"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Alpha]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Beta]\[Beta]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Beta]\[Beta]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Beta]\[Beta]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Beta]", "=", RowBox[{"tt", "*", "GG", "*", "\[Epsilon]\[Alpha]\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Beta]\[Alpha]", "=", RowBox[{"tt", "*", "GG", "*", "\[Epsilon]\[Beta]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Alpha]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Beta]\[Beta]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Beta]\[Beta]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Beta]\[Beta]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Beta]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", "GG", "*", "\[Kappa]\[Alpha]\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Beta]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Beta]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "N\[Alpha]\[Alpha]", ",", "N\[Beta]\[Beta]", ",", "N\[Alpha]\[Beta]", ",", "N\[Beta]\[Alpha]"}], "}"}]}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Beta]\[Beta]", ",", "M\[Alpha]\[Beta]"}], "}"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Beta]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Beta]"}], "}"}]}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", "\[Alpha]"}], "]"}], ",", "\[Beta]"}], "]"}]}]}], "]"}], "/;", " ", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", RowBox[{"4", ",", "4"}], "}"}]}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{ "fx_", ",", "fy_", ",", "fz_", ",", "mx_", ",", "my_", ",", "mz_"}], "}"}]}], "}"}], ",", RowBox[{"ELEMENT", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "n\[Alpha]", ",", "n\[Beta]", ",", "nne", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "enode", ",", "NN", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "rn", ",", "jac", ",", "h\[Alpha]", ",", "e\[Alpha]", ",", "h\[Beta]", ",", "e\[Beta]", ",", "en", ",", "FF", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]", ",", "f\[Alpha]", ",", "f\[Beta]", ",", "fn", ",", "m\[Alpha]", ",", "m\[Beta]", ",", "mn", ",", "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]", ",", "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]", ",", "\[Gamma]\[Alpha]", ",", "\[Gamma]\[Beta]", ",", "GG", ",", "N\[Alpha]\[Alpha]", ",", "N\[Beta]\[Beta]", ",", "N\[Alpha]\[Beta]", ",", "N\[Beta]\[Alpha]", ",", "M\[Alpha]\[Alpha]", ",", "M\[Beta]\[Beta]", ",", "M\[Alpha]\[Beta]", ",", "Q\[Alpha]", ",", "Q\[Beta]", ",", "\[Delta]wint", ",", "\[Delta]wext"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "nodes", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"n\[Alpha]", ",", "n\[Beta]"}], "}"}], "=", RowBox[{"Dimensions", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"nne", " ", "=", RowBox[{"n\[Alpha]", "*", "n\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"enode", "=", RowBox[{"Flatten", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n\[Alpha]", ",", "\[Alpha]"}], "}"}], ",", RowBox[{"{", RowBox[{"n\[Beta]", ",", "\[Beta]"}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "mapping", " ", "to", " ", "orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Alpha]", "=", RowBox[{"Norm", "[", "r\[Alpha]", "]"}]}], ";", RowBox[{"e\[Alpha]", "=", RowBox[{"r\[Alpha]", "/", "h\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Beta]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Beta]", "=", RowBox[{"r\[Beta]", "-", RowBox[{ RowBox[{"(", RowBox[{"r\[Beta]", ".", "e\[Alpha]"}], ")"}], "*", "e\[Alpha]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Norm", "[", "r\[Beta]", "]"}]}], ";", RowBox[{"e\[Beta]", "=", RowBox[{"r\[Beta]", "/", "h\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{"e\[Alpha]", "\[Cross]", "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", " ", "=", RowBox[{"h\[Alpha]", "*", "h\[Beta]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"in", " ", "flat", " ", "geometry"}], "*)"}], "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", "e\[Beta]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "transform", " ", "into", " ", "the", " ", "material", " ", "\[Alpha]\[Beta]n"}], "-", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"(", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "2"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"(", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "3"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fz"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"m\[Alpha]", ",", "m\[Beta]", ",", "mn"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"mx", ",", "my", ",", "mz"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"strain", " ", "measures", " ", "with", " ", "non"}], "-", RowBox[{"symmetric", " ", "\[Epsilon]"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}], "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], "/", "h\[Alpha]"}], "-", "\[Psi]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}], "/", "h\[Beta]"}], "+", "\[Psi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[CapitalTheta]"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}]}], "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[CapitalTheta]"}], "/", "h\[Beta]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], "/", "h\[Alpha]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Beta]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], "+", "\[CapitalTheta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}], "/", "h\[Beta]"}], "-", "\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "stress", " ", "resultants", " ", "with", " ", "a", " ", "nonsymmetric", " ", "N"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Alpha]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Beta]\[Beta]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Beta]\[Beta]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Beta]\[Beta]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Beta]", "=", RowBox[{"tt", "*", "GG", "*", "\[Epsilon]\[Alpha]\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Beta]\[Alpha]", "=", RowBox[{"tt", "*", "GG", "*", "\[Epsilon]\[Beta]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Alpha]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Beta]\[Beta]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Beta]\[Beta]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Beta]\[Beta]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Beta]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", "GG", "*", "\[Kappa]\[Alpha]\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Beta]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Beta]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "N\[Alpha]\[Alpha]", ",", "N\[Beta]\[Beta]", ",", "N\[Alpha]\[Beta]", ",", "N\[Beta]\[Alpha]"}], "}"}]}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Beta]\[Beta]", ",", "M\[Alpha]\[Beta]"}], "}"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Beta]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Beta]"}], "}"}]}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"m\[Alpha]", ",", "m\[Beta]", ",", "mn"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", "\[Alpha]"}], "]"}], ",", "\[Beta]"}], "]"}]}]}], "]"}], "/;", " ", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", RowBox[{"4", ",", "4"}], "}"}]}]}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{ 3.4426474258030453`*^9, {3.4444401255942*^9, 3.4444401388073997`*^9}, { 3.4444401803034*^9, 3.4444401844062*^9}, 3.4444402418922*^9, { 3.4444402805022*^9, 3.4444403134026003`*^9}, {3.4444403443062*^9, 3.4444404484049997`*^9}, {3.444483267101*^9, 3.444483267335*^9}, { 3.4444833136046*^9, 3.4444835622998*^9}, {3.4444836421094*^9, 3.4444837777981997`*^9}, {3.444483920429*^9, 3.4444839412237997`*^9}, 3.4444842905546*^9, {3.4444843207406*^9, 3.4444844162282*^9}, { 3.4444844465078*^9, 3.4444844624354*^9}, {3.4444845255998*^9, 3.4444845894505997`*^9}, {3.4444846290746*^9, 3.444484933025*^9}, { 3.4444849790917997`*^9, 3.4444851148742*^9}, {3.444534936054*^9, 3.4445349675348*^9}, {3.4445355821731997`*^9, 3.44453585174*^9}, { 3.4445372162198*^9, 3.4445372264378*^9}, 3.444537384731*^9, { 3.4445377585382*^9, 3.4445377605818*^9}, {3.4445379733658*^9, 3.4445379736934*^9}, {3.4445380176762*^9, 3.444538032777*^9}, { 3.4445381079222*^9, 3.4445381581386003`*^9}, {3.4445382726456003`*^9, 3.4445382910067997`*^9}, {3.4445383401312*^9, 3.4445383475880003`*^9}, { 3.444538438458*^9, 3.4445384464608*^9}, {3.4445385680783997`*^9, 3.4445385687648*^9}, {3.4445389411991997`*^9, 3.4445389431024*^9}, { 3.444539746605*^9, 3.4445397807846003`*^9}, {3.4445408839765997`*^9, 3.4445409234133997`*^9}, {3.4445409681698*^9, 3.4445409932702*^9}, { 3.4445415452906*^9, 3.4445415706717997`*^9}, {3.4445416647242002`*^9, 3.4445416909477997`*^9}, {3.4445417660150003`*^9, 3.444541788557*^9}, { 3.4445420906977997`*^9, 3.444542104847*^9}, {3.4445421885878*^9, 3.4445421941414003`*^9}, {3.4445422252166*^9, 3.4445422386014*^9}, { 3.444542280425*^9, 3.4445423014538*^9}, {3.444542455769*^9, 3.4445424578282003`*^9}, {3.4445431739214*^9, 3.444543175809*^9}, { 3.4445647020962*^9, 3.4445648405618*^9}, {3.4445648825414*^9, 3.4445648858486*^9}, {3.4445649382646*^9, 3.4445651882702*^9}, { 3.4446164822206*^9, 3.4446165344494*^9}, {3.4446166121842003`*^9, 3.4446166738822002`*^9}, {3.4446167223046*^9, 3.4446168047974*^9}, { 3.444616843033*^9, 3.444616906447*^9}, {3.4446444694708*^9, 3.4446444700948*^9}, {3.4446477738310003`*^9, 3.4446477939862003`*^9}, { 3.4446478467298*^9, 3.4446478681018*^9}, 3.4446480456142*^9, { 3.4446487557418003`*^9, 3.4446487636198*^9}, 3.4446488179974003`*^9, { 3.4446488971205997`*^9, 3.4446489152478*^9}, {3.4446490003458*^9, 3.4446490008294*^9}, {3.4447042728942003`*^9, 3.4447042751562*^9}, { 3.4447044703278*^9, 3.4447044865362*^9}, 3.4447046475282*^9, 3.4447047993786*^9, {3.444704908329*^9, 3.4447049292642*^9}, { 3.4447049861926003`*^9, 3.4447049877214003`*^9}, {3.4447050279296*^9, 3.4447050419695997`*^9}, {3.4447053486656*^9, 3.4447053739376*^9}, 3.4447054561963997`*^9, 3.44470561612*^9, {3.4472133996876*^9, 3.4472134108571997`*^9}, {3.4472134470179996`*^9, 3.4472134648332*^9}, { 3.4472135032872*^9, 3.4472135245344*^9}, {3.4472136963059998`*^9, 3.4472137794384003`*^9}, {3.4472138235708*^9, 3.4472138388900003`*^9}, { 3.4472139099792*^9, 3.4472141367096*^9}, {3.447214202682*^9, 3.4472142975924*^9}, {3.4472144187732*^9, 3.4472145910284*^9}, { 3.4472146560492*^9, 3.4472147023968*^9}, {3.447214803594*^9, 3.4472148728736*^9}, {3.4472149156956*^9, 3.447214940484*^9}, { 3.447216227284*^9, 3.4472162419948*^9}, {3.4472163068908*^9, 3.4472163720832*^9}, {3.4472164665880003`*^9, 3.447216530392*^9}, { 3.4472166237268*^9, 3.4472167058452*^9}, 3.4472167362808*^9, { 3.4472171394658003`*^9, 3.4472171532874002`*^9}, {3.4472172028993998`*^9, 3.4472172216661997`*^9}, {3.4472172524606*^9, 3.4472172690278*^9}, { 3.4472173209133997`*^9, 3.4472173334245996`*^9}, {3.4472173920846*^9, 3.447217404861*^9}, {3.4472179572548*^9, 3.4472180351456003`*^9}, { 3.4472509764091997`*^9, 3.4472511017396*^9}, {3.4473910422216*^9, 3.4473912901524*^9}, 3.4473918688344*^9, {3.447392021185*^9, 3.4473920346633997`*^9}, {3.4473921383304*^9, 3.4473921479088*^9}, { 3.4473923024112*^9, 3.4473923734379997`*^9}, {3.4473928098168*^9, 3.4473928648691998`*^9}, {3.4473931872432003`*^9, 3.4473932461800003`*^9}, {3.4473933026675997`*^9, 3.4473934579812*^9}, { 3.4473935755271997`*^9, 3.447393742572*^9}, {3.4473939032676*^9, 3.4473939384144*^9}, {3.447395257644*^9, 3.4473953141628*^9}, { 3.4473954231132*^9, 3.4473954756384*^9}, {3.4473955348716*^9, 3.4473955723272*^9}, {3.447395648502*^9, 3.4473957588876*^9}, { 3.4473957903996*^9, 3.4473958488372*^9}, 3.4473962894154*^9, { 3.447396350817*^9, 3.447396352611*^9}, {3.4474625379146*^9, 3.4474625637326*^9}, {3.558360651728078*^9, 3.558360652102478*^9}, { 3.5619791319820857`*^9, 3.561979135788492*^9}, 3.561979369382504*^9, { 3.5619794930439215`*^9, 3.5619795010155354`*^9}, {3.561979569218855*^9, 3.56197960614412*^9}, {3.5619797417551584`*^9, 3.5619797448751636`*^9}, { 3.618719065033702*^9, 3.618719075426296*^9}, {3.6187194011669273`*^9, 3.6187194449454317`*^9}, {3.6187196998040085`*^9, 3.6187197102436056`*^9}, {3.618719902254588*^9, 3.6187199711455283`*^9}, { 3.618722365406472*^9, 3.6187225412555304`*^9}, {3.6187226885009522`*^9, 3.6187227109872384`*^9}, {3.618722756922866*^9, 3.6187231317203026`*^9}, { 3.618723424250035*^9, 3.6187234267291765`*^9}, {3.6187235105259695`*^9, 3.6187236491028957`*^9}, {3.618723691580325*^9, 3.618723745975436*^9}, { 3.618723778837316*^9, 3.6187238310002995`*^9}, {3.6187239055875654`*^9, 3.618723940035536*^9}, {3.6187239782667227`*^9, 3.6187240219352207`*^9}, { 3.618724166762504*^9, 3.618724177411113*^9}, {3.618729321696159*^9, 3.618729328067523*^9}, 3.618729374058154*^9, {3.6187294379838104`*^9, 3.618729708464281*^9}, {3.6187297631904106`*^9, 3.618729773195983*^9}, { 3.618729822648812*^9, 3.6187299321490746`*^9}, {3.618729984399063*^9, 3.61873000654133*^9}, {3.6187300746012225`*^9, 3.6187300860458775`*^9}, { 3.618731390835507*^9, 3.6187315116174154`*^9}, {3.618731747324897*^9, 3.6187318214091344`*^9}, {3.6187318769243097`*^9, 3.618732065297084*^9}, { 3.6187321012351394`*^9, 3.618732157420353*^9}, {3.618732188384124*^9, 3.6187322435542793`*^9}, {3.6187322786112847`*^9, 3.6187325478446836`*^9}, {3.6187325819856367`*^9, 3.6187326817653437`*^9}, {3.618732810863728*^9, 3.61873282594359*^9}, { 3.6187336474335766`*^9, 3.618733754678711*^9}, {3.618733827497876*^9, 3.61873396201257*^9}, {3.6187342020362988`*^9, 3.618734236455267*^9}, 3.618734298201799*^9, {3.618734712498495*^9, 3.618734712716508*^9}, 3.6187347739640107`*^9, {3.618738817361748*^9, 3.6187388333816643`*^9}, { 3.6187391349349127`*^9, 3.6187391457955337`*^9}, {3.618739376900752*^9, 3.618739397023903*^9}, {3.618739528394417*^9, 3.618739534809784*^9}, { 3.618739972366811*^9, 3.61873997340687*^9}, {3.6187400416617737`*^9, 3.618740043022852*^9}, {3.6187400971579485`*^9, 3.618740107902563*^9}, { 3.6187401713671927`*^9, 3.6187401723312483`*^9}, {3.6187402613443394`*^9, 3.618740268819767*^9}, {3.6187403697625403`*^9, 3.6187404057615995`*^9}, { 3.618740488277319*^9, 3.618740516244919*^9}, {3.618740647782442*^9, 3.6187406551668644`*^9}, 3.6187407823021364`*^9, {3.6187418050786357`*^9, 3.618741805749674*^9}, {3.6187418557605343`*^9, 3.6187419895921893`*^9}, { 3.618742022944097*^9, 3.61874204379729*^9}, {3.6187420836395683`*^9, 3.618742103384698*^9}, {3.620462440882641*^9, 3.6204624460519366`*^9}, { 3.6204624990259666`*^9, 3.620462576450395*^9}, {3.620463682857678*^9, 3.620463713336421*^9}, 3.6204637901188126`*^9, {3.620464238835478*^9, 3.62046424411378*^9}, 3.628912429385081*^9, {3.6289135207155013`*^9, 3.6289135210805225`*^9}, 3.6289497746958513`*^9, 3.6289498371774254`*^9, { 3.62894988410911*^9, 3.6289500319795675`*^9}, {3.6289501333883677`*^9, 3.628950183744248*^9}, {3.6289503323017445`*^9, 3.628950390181055*^9}, { 3.6289505050536256`*^9, 3.6289505113579865`*^9}, {3.62895070863527*^9, 3.6289507095043197`*^9}, {3.628951013180689*^9, 3.62895101407374*^9}, { 3.629190743153632*^9, 3.629190816645361*^9}, {3.6291909709608326`*^9, 3.629190981678051*^9}, {3.629191034624544*^9, 3.6291910410049553`*^9}, { 3.6293846391370816`*^9, 3.629384641102685*^9}, {3.6294628543371735`*^9, 3.629462867097191*^9}, {3.629468063172048*^9, 3.6294681151669397`*^9}, { 3.6295205836757097`*^9, 3.6295206295085897`*^9}, {3.6295206788826766`*^9, 3.6295207067911253`*^9}, {3.6295207408927855`*^9, 3.629520753700408*^9}, { 3.629521020590745*^9, 3.6295210354395943`*^9}, {3.6295211107369013`*^9, 3.62952114882508*^9}, {3.6295212327348795`*^9, 3.6295212477237363`*^9}, { 3.6295213424816394`*^9, 3.629521343230441*^9}, {3.6295215363119802`*^9, 3.6295216753550243`*^9}, {3.629521922272258*^9, 3.6295219939855833`*^9}, { 3.6295220298188467`*^9, 3.629522446058778*^9}, {3.629522499348471*^9, 3.629522604352256*^9}, {3.629522755188921*^9, 3.62952288580795*^9}, { 3.629522918084407*^9, 3.6295233421087513`*^9}, {3.6295233808436193`*^9, 3.629523390936837*^9}, {3.629523424274096*^9, 3.6295234533369465`*^9}, { 3.6295235190130625`*^9, 3.629523521680667*^9}, 3.6295235894315863`*^9, { 3.6295237270706277`*^9, 3.629523799454755*^9}, {3.6295238514808464`*^9, 3.629523883460902*^9}, {3.6295239376085978`*^9, 3.6295239442386093`*^9}, { 3.6295241089904985`*^9, 3.629524177537019*^9}, 3.629524211888279*^9, { 3.629524277423994*^9, 3.629524396904604*^9}, {3.6295244794839497`*^9, 3.6295246248450055`*^9}, 3.629524657090262*^9, {3.6295259599109507`*^9, 3.629526013465844*^9}, {3.6295261092188125`*^9, 3.629526201414974*^9}, 3.6295263436092243`*^9, {3.6295263910333076`*^9, 3.629526583303645*^9}, { 3.629526616672104*^9, 3.629526647653758*^9}, {3.629526687558628*^9, 3.629526744888729*^9}, {3.629526804075233*^9, 3.6295268598453307`*^9}, { 3.6295269393898706`*^9, 3.6295269586559043`*^9}, {3.6295271490074387`*^9, 3.6295272149019547`*^9}, {3.6295272553684254`*^9, 3.6295272827620735`*^9}, {3.6295274137087035`*^9, 3.6295274761244135`*^9}, {3.6295275252801*^9, 3.6295279912529182`*^9}, { 3.6295281572216096`*^9, 3.629528160435215*^9}, {3.6295282905550437`*^9, 3.6295284308616905`*^9}, 3.6295285402022824`*^9, {3.629528582088356*^9, 3.629528616798417*^9}, {3.6295287666834803`*^9, 3.6295290316343455`*^9}, { 3.629529086515242*^9, 3.629529118432898*^9}, {3.6295291548121614`*^9, 3.629529292794404*^9}, {3.6295293426208916`*^9, 3.6295293491261034`*^9}, { 3.629529420699029*^9, 3.629529571535694*^9}, {3.6295296539506383`*^9, 3.629529656103442*^9}, {3.6295296894407005`*^9, 3.629529692295506*^9}, { 3.6295297445555973`*^9, 3.629529766426836*^9}, {3.6295298053333044`*^9, 3.6295298209489317`*^9}, {3.6295308380551186`*^9, 3.6295308386635194`*^9}, {3.629532377840223*^9, 3.6295323811630287`*^9}, { 3.629532480020402*^9, 3.629532482454006*^9}, {3.629532520720874*^9, 3.629532564619351*^9}, {3.62953259842461*^9, 3.6295326002654133`*^9}, { 3.6295326327758703`*^9, 3.6295326715107384`*^9}, {3.629532742428463*^9, 3.6295328288058147`*^9}, {3.6295329692184625`*^9, 3.6295330530062094`*^9}, {3.6295331824396367`*^9, 3.629533193562456*^9}, 3.6295350321720915`*^9, 3.629535158485513*^9, {3.629535245471266*^9, 3.6295352687465067`*^9}, {3.62953541293756*^9, 3.629535446384019*^9}, { 3.6295355043381205`*^9, 3.6295355262249594`*^9}, {3.629543790136781*^9, 3.629543791181983*^9}, {3.629543871350524*^9, 3.629544001673153*^9}, { 3.6295446682009234`*^9, 3.629544668466124*^9}, {3.6296010216162376`*^9, 3.6296010236442413`*^9}, {3.629601079336339*^9, 3.6296010902875586`*^9}, 3.6296011425476503`*^9, {3.6296043522397404`*^9, 3.629604399031022*^9}, { 3.629623884428093*^9, 3.629623914723346*^9}, {3.6296239662190366`*^9, 3.6296239738006496`*^9}, {3.6296240514731865`*^9, 3.6296240920176573`*^9}, {3.629624125947717*^9, 3.629624369432945*^9}, { 3.6296256512247963`*^9, 3.6296256817072496`*^9}, {3.6296260472626915`*^9, 3.629626047434292*^9}, {3.629628055568204*^9, 3.629628056098605*^9}, { 3.6296280911206665`*^9, 3.6296281088266973`*^9}, {3.6296281406819534`*^9, 3.629628273032586*^9}, {3.629628378831972*^9, 3.6296283814995766`*^9}, { 3.629628459562114*^9, 3.629628466379326*^9}, {3.629628519419419*^9, 3.6296285390754533`*^9}, {3.629633008133008*^9, 3.629633008835009*^9}, { 3.6296337764967575`*^9, 3.6296338344040594`*^9}, {3.6296342997684765`*^9, 3.629634432150309*^9}, {3.629634494035618*^9, 3.6296345320060844`*^9}, { 3.629634594499794*^9, 3.629634812182576*^9}, {3.6296348599810605`*^9, 3.6296348746918864`*^9}, {3.6296349071867433`*^9, 3.629635023172947*^9}, 3.6296350995818815`*^9, {3.6296363797201295`*^9, 3.6296363868961425`*^9}, { 3.629636462025874*^9, 3.6296364833355117`*^9}, {3.629636555922439*^9, 3.62963656780966*^9}, {3.629636770469616*^9, 3.629636774151222*^9}, { 3.6296369192782774`*^9, 3.6296369318830996`*^9}, {3.629637058539722*^9, 3.6296370719401455`*^9}, {3.629637278172508*^9, 3.629637286814923*^9}, { 3.6296376418091464`*^9, 3.629637662385583*^9}, {3.629637773551378*^9, 3.629637795360216*^9}, {3.6296390041751394`*^9, 3.629639039571602*^9}, 3.6296393829750047`*^9, {3.6296395546065063`*^9, 3.6296395649961243`*^9}, { 3.62964113386068*^9, 3.6296412507048855`*^9}, {3.629641303167777*^9, 3.629641313744596*^9}, {3.6296416285116315`*^9, 3.629641628886032*^9}, { 3.6296416658736973`*^9, 3.6296416815049243`*^9}, 3.6296417376338234`*^9, { 3.6296855551269727`*^9, 3.6296855804270077`*^9}, {3.6297079065796247`*^9, 3.6297079070476255`*^9}, {3.6297080850439377`*^9, 3.629708135728427*^9}, { 3.6297083496516027`*^9, 3.6297084025512953`*^9}, {3.629708781767563*^9, 3.629708790940379*^9}, {3.6297089402482414`*^9, 3.6297089618542795`*^9}, { 3.6297105345398417`*^9, 3.629710538580249*^9}, {3.6297107810514746`*^9, 3.6297107850138817`*^9}, {3.6297109100481014`*^9, 3.629710915710911*^9}, { 3.629711201534613*^9, 3.629711204311418*^9}, {3.629711236307074*^9, 3.6297115007275386`*^9}, {3.6297115377464037`*^9, 3.6297115441112146`*^9}, 3.6297116025645175`*^9, {3.6298716505389357`*^9, 3.629871851841689*^9}, { 3.62987837458679*^9, 3.629878383510006*^9}, {3.6298784402629056`*^9, 3.629878447345318*^9}, {3.6298785221786494`*^9, 3.6298786580236883`*^9}, { 3.629878689613744*^9, 3.629878737147027*^9}, 3.629878783853509*^9, { 3.629878832322794*^9, 3.6298789171723433`*^9}, {3.6298802128122005`*^9, 3.6298802929723125`*^9}, 3.6298813644148126`*^9, {3.629882428887303*^9, 3.629882435887313*^9}, {3.6298986251827383`*^9, 3.6298988530367384`*^9}, { 3.6298989036744275`*^9, 3.6298989486493063`*^9}, {3.629899016868226*^9, 3.6298991622448816`*^9}, {3.6298997154530535`*^9, 3.629899740147897*^9}, { 3.6298998248560457`*^9, 3.629899978048314*^9}, {3.6299000396372223`*^9, 3.6299001557638264`*^9}, {3.6299001966826982`*^9, 3.6299002595352087`*^9}, 3.6299005011236343`*^9, {3.6299005468317146`*^9, 3.629900567642151*^9}, { 3.629900887676713*^9, 3.629900990153293*^9}, {3.6299011689220085`*^9, 3.6299012295125146`*^9}, {3.6299013754039707`*^9, 3.6299014166036434`*^9}, 3.6299014589733176`*^9, {3.6299015096734066`*^9, 3.629901588765546*^9}, { 3.629901662569275*^9, 3.6299016974665365`*^9}, {3.629901952339784*^9, 3.6299019599057975`*^9}, 3.6299020306051216`*^9, {3.6299022330934772`*^9, 3.6299022682559395`*^9}, {3.6299023020455985`*^9, 3.629902332808852*^9}, { 3.6299024532566643`*^9, 3.629902462850681*^9}, {3.629949880225117*^9, 3.6299498807867184`*^9}, {3.6299503101150723`*^9, 3.6299503156998825`*^9}, {3.629950355058751*^9, 3.629950498937804*^9}, { 3.6299555415202007`*^9, 3.6299555507086167`*^9}, {3.6299556061667137`*^9, 3.6299557553497763`*^9}, {3.629955788499834*^9, 3.6299558948608212`*^9}, { 3.629956042764681*^9, 3.629956043809883*^9}, {3.6299560914211664`*^9, 3.6299561017327843`*^9}, 3.629956145849662*^9, {3.6299584813821354`*^9, 3.6299585082765827`*^9}, 3.6299585652946825`*^9, {3.629958616587573*^9, 3.6299586356508064`*^9}, {3.629958715073346*^9, 3.6299588186419287`*^9}, { 3.629958857454797*^9, 3.629958927249319*^9}, {3.629959427994599*^9, 3.629959494669116*^9}, {3.6299595293323765`*^9, 3.6299596037913074`*^9}, { 3.62995966795422*^9, 3.62995967360143*^9}, {3.6299597835972233`*^9, 3.6299597841120243`*^9}, {3.629959826622099*^9, 3.629959862533362*^9}, { 3.6299599051682367`*^9, 3.6299599235918694`*^9}, 3.629959979939168*^9, { 3.6299601345354395`*^9, 3.62996014612626*^9}, 3.6299601769831142`*^9, { 3.629960253142448*^9, 3.629960269538077*^9}, {3.6299603041701374`*^9, 3.6299603078205442`*^9}, {3.6299604300467587`*^9, 3.629960435491168*^9}, { 3.6299605300585346`*^9, 3.6299605636609936`*^9}, {3.6299606195870914`*^9, 3.6299606581971593`*^9}, {3.629960824228251*^9, 3.6299608755367413`*^9}, { 3.629960906658796*^9, 3.6299609978409557`*^9}, {3.6299610312250147`*^9, 3.629961070646284*^9}, {3.629961135698398*^9, 3.6299611643088484`*^9}, { 3.6299720458358483`*^9, 3.6299721791536827`*^9}, {3.6299722439717965`*^9, 3.629972300007095*^9}, {3.6299723670872126`*^9, 3.6299723937008595`*^9}, { 3.629972457801372*^9, 3.6299724710613956`*^9}, {3.629972740193068*^9, 3.6299728251196175`*^9}, {3.6299729203577843`*^9, 3.6299729350218105`*^9}, {3.6299729720874753`*^9, 3.6299730462188053`*^9}, {3.629973116044528*^9, 3.6299731230177402`*^9}, { 3.629973184310248*^9, 3.6299732090830917`*^9}, {3.629973349982539*^9, 3.6299734360166903`*^9}, 3.629973534562063*^9, {3.629973577446539*^9, 3.629973586104554*^9}, {3.6299740374133463`*^9, 3.629974083823428*^9}, { 3.6299742505565205`*^9, 3.629974337089873*^9}, {3.629974382907153*^9, 3.6299744466176653`*^9}, {3.629974589794717*^9, 3.629974590761918*^9}, { 3.629974776215044*^9, 3.6299747850134597`*^9}, {3.6299748226095257`*^9, 3.6299748237483273`*^9}, 3.6299748618435946`*^9, {3.629975198476586*^9, 3.6299752545898843`*^9}, {3.62997531475919*^9, 3.6299753175515947`*^9}, { 3.6299754601982455`*^9, 3.6299754625382495`*^9}, {3.629975592034077*^9, 3.629975592502078*^9}, {3.629983277446268*^9, 3.6299832946842985`*^9}, { 3.62998342081052*^9, 3.6299835439883366`*^9}, {3.629983615514462*^9, 3.629983931009416*^9}, {3.6299919807040443`*^9, 3.6299919808912444`*^9}, { 3.629992028330928*^9, 3.6299920922130404`*^9}, 3.629992198480427*^9, { 3.6299922299300823`*^9, 3.629992250506518*^9}, {3.629992292657792*^9, 3.6299923603151107`*^9}, {3.6299924387676487`*^9, 3.6299924398440504`*^9}, {3.6299925764846907`*^9, 3.6299926096347485`*^9}, {3.6299928122323046`*^9, 3.629992818768716*^9}, { 3.6299929049120674`*^9, 3.629992905411268*^9}, {3.6299929850338078`*^9, 3.6299929866250105`*^9}, {3.6299931061992207`*^9, 3.62999312270405*^9}, { 3.629993172312137*^9, 3.6299932618718944`*^9}, {3.6299933276572104`*^9, 3.6299933842073092`*^9}, {3.6302476464502306`*^9, 3.6302477023607283`*^9}, {3.630247749738012*^9, 3.6302479456119556`*^9}, { 3.630247987076829*^9, 3.6302480916126122`*^9}, {3.6302481317670827`*^9, 3.630248155245124*^9}, {3.6302481927163897`*^9, 3.63024823257446*^9}, { 3.6302869660869403`*^9, 3.6302871959065437`*^9}, {3.6302872330814095`*^9, 3.630287236560216*^9}, {3.630287274421482*^9, 3.6302874119357233`*^9}, { 3.6302874551009994`*^9, 3.6302874699990253`*^9}, {3.6302875003722787`*^9, 3.6302877505343184`*^9}, {3.63038960251799*^9, 3.630389603672392*^9}, { 3.630808954640574*^9, 3.6308089697374372`*^9}, {3.6308090558753643`*^9, 3.63080905807349*^9}, {3.633681137596347*^9, 3.6336812675647807`*^9}, { 3.633692346227066*^9, 3.6336923608039*^9}, {3.6336924823428516`*^9, 3.633692482984888*^9}, {3.6336927709053564`*^9, 3.633692779378841*^9}, { 3.635474649291499*^9, 3.6354747135141726`*^9}, {3.635474757347679*^9, 3.635474767084236*^9}, {3.7326781791979923`*^9, 3.7326782541070137`*^9}, { 3.732678384546839*^9, 3.732678387154627*^9}, {3.7326784528278866`*^9, 3.7326784536419926`*^9}, {3.7326785658888392`*^9, 3.732678606948255*^9}, { 3.7326786429394207`*^9, 3.732678671328236*^9}, 3.7326787139495087`*^9, 3.7326824710029726`*^9, {3.732682535085518*^9, 3.7326825394060144`*^9}, { 3.732788367344186*^9, 3.7327883679512634`*^9}, {3.733659479173915*^9, 3.733659479686716*^9}, {3.733659736778194*^9, 3.733659738223981*^9}, { 3.733660235678305*^9, 3.7336603371354585`*^9}, {3.733660451788246*^9, 3.733660466320716*^9}, {3.733660509132059*^9, 3.7336605685538363`*^9}, 3.7336606346231527`*^9, {3.7336606902677946`*^9, 3.7336607839480886`*^9}, { 3.7336608179615364`*^9, 3.7336608319530153`*^9}, {3.733660881327427*^9, 3.733660897330119*^9}, {3.7336609300986814`*^9, 3.7336609594994287`*^9}, { 3.73366136360488*^9, 3.733661402781823*^9}, {3.733661450979083*^9, 3.7336615506703176`*^9}, {3.733661609102705*^9, 3.7336616507411423`*^9}, { 3.7336616844880095`*^9, 3.7336616852837515`*^9}, 3.7336618066988688`*^9, { 3.7336620707975283`*^9, 3.7336621071155624`*^9}, {3.7337028629370823`*^9, 3.733703205450749*^9}, {3.733703243487465*^9, 3.7337032610824347`*^9}, { 3.733703298061898*^9, 3.7337033664147425`*^9}, {3.7337033982918806`*^9, 3.73370344248729*^9}, {3.7337034777924*^9, 3.7337035051606703`*^9}, { 3.733703582604458*^9, 3.733703668421293*^9}, 3.73370371853176*^9, { 3.7337039455508604`*^9, 3.7337039986094637`*^9}, 3.7337040398626404`*^9, { 3.733709014619094*^9, 3.733709032928876*^9}, {3.733710962294444*^9, 3.7337109655993176`*^9}, {3.7337116551468105`*^9, 3.7337116628867064`*^9}, {3.734177223332971*^9, 3.7341772262673383`*^9}, { 3.734177304096835*^9, 3.7341773117663164`*^9}, {3.7341773527732897`*^9, 3.7341774236892753`*^9}, {3.734177567269784*^9, 3.7341775896576233`*^9}, { 3.7341776260785637`*^9, 3.7341776336188316`*^9}, {3.7341776647735634`*^9, 3.734177725567827*^9}, {3.7341777815164194`*^9, 3.734177803193592*^9}, { 3.76372700789438*^9, 3.763727008977229*^9}, {3.826362782570422*^9, 3.8263628105149765`*^9}, {3.826362869553932*^9, 3.826362899896824*^9}, 3.826363328101153*^9, {3.840426739187541*^9, 3.840426900661952*^9}, { 3.8411217229845905`*^9, 3.8411217360480766`*^9}, {3.8411217736618304`*^9, 3.84112182564371*^9}, {3.8411218641628623`*^9, 3.8411221348500795`*^9}, { 3.8411222111856875`*^9, 3.8411224614927535`*^9}, {3.8411226025233316`*^9, 3.84112265659787*^9}, {3.841122702844118*^9, 3.8411227358089767`*^9}, { 3.841122767000372*^9, 3.841122789115695*^9}, {3.8411228263291655`*^9, 3.841122840147561*^9}, {3.8411229052717075`*^9, 3.8411229596287527`*^9}, { 3.8411230527118196`*^9, 3.841123112582203*^9}, 3.8411231449179096`*^9, 3.8411234197043743`*^9, {3.8411252927002463`*^9, 3.8411252949718075`*^9}, { 3.841128200732338*^9, 3.841128200920005*^9}, {3.841128712216941*^9, 3.8411287125067186`*^9}, {3.841133254755392*^9, 3.8411332882095027`*^9}, { 3.8411333562672715`*^9, 3.8411333591533422`*^9}, {3.841134926084315*^9, 3.8411349277121115`*^9}, {3.841134957993024*^9, 3.841135019642999*^9}, 3.8448244774776583`*^9},ExpressionUUID->"d063c5b7-f601-414e-adaa-\ f8def9fd5096"] }, Closed]], Cell[CellGroupData[{ Cell["SHELL ELEMENT (vibr) defs ", "Subsection", CellChangeTimes->{{3.6303896070263977`*^9, 3.6303896080872*^9}, 3.8435394517660627`*^9, {3.8518302209271307`*^9, 3.851830225833006*^9}},ExpressionUUID->"2efb13fd-b3b7-44c9-95ba-\ e06234fe92ea"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "n\[Alpha]", ",", "n\[Beta]", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "NN", ",", "mat", ",", "MM", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "r\[Gamma]", ",", "rn", ",", "jac", ",", "h\[Alpha]", ",", "e\[Alpha]", ",", "h\[Beta]", ",", "h\[Gamma]", ",", "e\[Beta]", ",", "en", ",", "e\[Gamma]", ",", "FF", ",", "\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]", ",", "edg", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "\[Pi]u", ",", "\[Pi]v", ",", "\[Pi]w", ",", "\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]", ",", "u0", ",", "v0", ",", "w0", ",", "\[Phi]0", ",", "\[Theta]0", ",", "\[Psi]0", ",", "\[Pi]u0", ",", "\[Pi]v0", ",", "\[Pi]w0", ",", "\[Pi]\[Phi]0", ",", "\[Pi]\[Theta]0", ",", "\[Pi]\[Psi]0", ",", "u2", ",", "v2", ",", "w2", ",", "\[Phi]2", ",", "\[Theta]2", ",", "\[Psi]2", ",", "\[Pi]u2", ",", "\[Pi]v2", ",", "\[Pi]w2", ",", "\[Pi]\[Phi]2", ",", "\[Pi]\[Theta]2", ",", "\[Pi]\[Psi]2", ",", "f\[Alpha]", ",", "f\[Gamma]", ",", "fn", ",", "m\[Alpha]", ",", "m\[Gamma]", ",", "mn", ",", "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]", ",", "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]", ",", "\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]", ",", "GG", ",", "N\[Alpha]\[Alpha]", ",", "N\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Gamma]", ",", "N\[Gamma]\[Alpha]", ",", "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]", ",", "Q\[Alpha]", ",", "Q\[Gamma]", ",", "\[Delta]wint", ",", "\[Delta]wine", ",", "\[Delta]wext", ",", "\[Delta]wmap", ",", "AA"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"mat", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]", "=", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}]}], ";", " ", RowBox[{"r\[Beta]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Norm", "[", "r\[Beta]", "]"}]}], ";", " ", RowBox[{"h\[Alpha]", "=", RowBox[{"Norm", "[", "r\[Alpha]", "]"}]}], ";", RowBox[{"jac", "=", RowBox[{"Norm", "[", RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Alpha]", "=", RowBox[{"r\[Alpha]", "/", "h\[Alpha]"}]}], ";", RowBox[{"e\[Beta]", "=", RowBox[{"r\[Beta]", "/", "h\[Beta]"}]}], ";", " ", RowBox[{"en", "=", RowBox[{ RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], " ", "/", "jac"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r\[Gamma]", "=", RowBox[{"r\[Beta]", "-", RowBox[{ RowBox[{"(", RowBox[{"r\[Beta]", ".", "e\[Alpha]"}], ")"}], " ", "e\[Alpha]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Gamma]", "=", RowBox[{"Norm", "[", "r\[Gamma]", "]"}]}], ";", RowBox[{"e\[Gamma]", "=", RowBox[{"r\[Gamma]", "/", "h\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", "e\[Gamma]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]"}], "}"}], "=", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Alpha]"}], ",", RowBox[{"r\[Alpha]", ".", "r\[Beta]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Beta]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Beta]"}]}], "}"}]}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Gamma]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Gamma]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"edg", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Sort", "[", "#", "]"}], "&"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"uX", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"uY", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "3"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Z", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "projections", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Pi]u", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]v", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]w", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Phi]", "=", RowBox[{ RowBox[{ RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], "/", "60"}], "+", " ", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Theta]", "=", RowBox[{ RowBox[{ RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], "/", "60"}], "+", " ", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Psi]", "=", RowBox[{ RowBox[{ RowBox[{"\[Theta]Z", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], "/", "60"}], "+", " ", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "3"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]u", ",", "\[Pi]v", ",", "\[Pi]w"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"\[Pi]u", ",", "\[Pi]v", ",", "\[Pi]w"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Gamma]", ",", "fn"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"time", " ", "derivatives"}], "*)"}], "\[IndentingNewLine]", RowBox[{"u0", "=", RowBox[{"u", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", RowBox[{"u2", "=", RowBox[{"u", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v0", "=", RowBox[{"v", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", RowBox[{"v2", "=", RowBox[{"v", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w0", "=", RowBox[{"w", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", RowBox[{"w2", "=", RowBox[{"w", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]0", "=", RowBox[{"\[Phi]", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", RowBox[{"\[Phi]2", "=", RowBox[{"\[Phi]", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]0", "=", RowBox[{"\[Theta]", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", RowBox[{"\[Theta]2", "=", RowBox[{"\[Theta]", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]0", "=", RowBox[{"\[Psi]", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", RowBox[{"\[Psi]2", "=", RowBox[{"\[Psi]", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]u0", "=", RowBox[{"\[Pi]u", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", RowBox[{"\[Pi]u2", "=", RowBox[{"\[Pi]u", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]v0", "=", RowBox[{"\[Pi]v", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", RowBox[{"\[Pi]v2", "=", RowBox[{"\[Pi]v", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]w0", "=", RowBox[{"\[Pi]w", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", RowBox[{"\[Pi]w2", "=", RowBox[{"\[Pi]w", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Phi]0", "=", RowBox[{"\[Pi]\[Phi]", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", RowBox[{"\[Pi]\[Phi]2", "=", RowBox[{"\[Pi]\[Phi]", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Theta]0", "=", RowBox[{"\[Pi]\[Theta]", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", RowBox[{"\[Pi]\[Theta]2", "=", RowBox[{"\[Pi]\[Theta]", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Psi]0", "=", RowBox[{"\[Pi]\[Psi]", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", RowBox[{"\[Pi]\[Psi]2", "=", RowBox[{"\[Pi]\[Psi]", " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"strain", " ", "measures", " ", "with", " ", "non"}], "-", RowBox[{"symmetric", " ", "\[Epsilon]"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u0"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v0"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v0"}]}]}], ")"}], "/", "h\[Gamma]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v0"}], "/", "h\[Alpha]"}], "-", "\[Pi]\[Psi]0"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u0"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u0"}]}]}], ")"}], "/", "h\[Gamma]"}], "+", "\[Pi]\[Psi]0"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]0"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]0"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]0"}]}]}], ")"}]}], "/", "h\[Gamma]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", " ", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]0"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Theta]0"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]0"}], "/", "h\[Alpha]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w0"}], "/", "h\[Alpha]"}], "+", "\[Pi]\[Theta]0"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w0"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w0"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", "\[Pi]\[Phi]0"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "stress", " ", "resultants", " ", "with", " ", "a", " ", "nonsymmetric", " ", "N"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Alpha]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Gamma]\[Gamma]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Gamma]\[Gamma]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Gamma]\[Gamma]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Gamma]", "=", RowBox[{ "tt", "*", "2", " ", "GG", "*", "\[Epsilon]\[Alpha]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Gamma]\[Alpha]", "=", RowBox[{ "tt", "*", "2", " ", "GG", "*", "\[Epsilon]\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Alpha]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Gamma]\[Gamma]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Gamma]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Gamma]\[Gamma]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", " ", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "\[Nu]\[Nu]"}]}], ")"}]}], "*", "\[Kappa]\[Alpha]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{ RowBox[{"5", "/", "6"}], " ", "*", "GG", "*", "tt", "*", "\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Gamma]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "N\[Alpha]\[Alpha]", ",", "N\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Gamma]", ",", "N\[Gamma]\[Alpha]"}], "}"}]}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]"}], "}"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Gamma]"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wine", "=", RowBox[{ RowBox[{ RowBox[{"-", "tt"}], "*", "\[Rho]\[Rho]", "*", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u0", ",", "v0", ",", "w0"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"u2", ",", "v2", ",", "w2"}], "}"}]}]}], "-", RowBox[{ RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", "\[Rho]\[Rho]", "*", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Phi]0", ",", "\[Theta]0", ",", "\[Psi]0"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"\[Phi]2", ",", "\[Theta]2", ",", "\[Psi]2"}], "}"}]}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u0", ",", "v0", ",", "w0"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Gamma]", ",", "fn"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wmap", "=", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "/", "100000"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]u0", "-", "u0"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]u0", "-", "u0"}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]v0", "-", "v0"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]v0", "-", "v0"}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]w0", "-", "w0"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]w0", "-", "w0"}], ")"}]}]}], ")"}], "*", "tt", "*", RowBox[{"EE", "/", "jac"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI3", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wine", "+", "\[Delta]wext", "+", "\[Delta]wmap"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.4426474258030453`*^9, {3.4444401255942*^9, 3.4444401388073997`*^9}, { 3.4444401803034*^9, 3.4444401844062*^9}, 3.4444402418922*^9, { 3.4444402805022*^9, 3.4444403134026003`*^9}, {3.4444403443062*^9, 3.4444404484049997`*^9}, {3.444483267101*^9, 3.444483267335*^9}, { 3.4444833136046*^9, 3.4444835622998*^9}, {3.4444836421094*^9, 3.4444837777981997`*^9}, {3.444483920429*^9, 3.4444839412237997`*^9}, 3.4444842905546*^9, {3.4444843207406*^9, 3.4444844162282*^9}, { 3.4444844465078*^9, 3.4444844624354*^9}, {3.4444845255998*^9, 3.4444845894505997`*^9}, {3.4444846290746*^9, 3.444484933025*^9}, { 3.4444849790917997`*^9, 3.4444851148742*^9}, {3.444534936054*^9, 3.4445349675348*^9}, {3.4445355821731997`*^9, 3.44453585174*^9}, { 3.4445372162198*^9, 3.4445372264378*^9}, 3.444537384731*^9, { 3.4445377585382*^9, 3.4445377605818*^9}, {3.4445379733658*^9, 3.4445379736934*^9}, {3.4445380176762*^9, 3.444538032777*^9}, { 3.4445381079222*^9, 3.4445381581386003`*^9}, {3.4445382726456003`*^9, 3.4445382910067997`*^9}, {3.4445383401312*^9, 3.4445383475880003`*^9}, { 3.444538438458*^9, 3.4445384464608*^9}, {3.4445385680783997`*^9, 3.4445385687648*^9}, {3.4445389411991997`*^9, 3.4445389431024*^9}, { 3.444539746605*^9, 3.4445397807846003`*^9}, {3.4445408839765997`*^9, 3.4445409234133997`*^9}, {3.4445409681698*^9, 3.4445409932702*^9}, { 3.4445415452906*^9, 3.4445415706717997`*^9}, {3.4445416647242002`*^9, 3.4445416909477997`*^9}, {3.4445417660150003`*^9, 3.444541788557*^9}, { 3.4445420906977997`*^9, 3.444542104847*^9}, {3.4445421885878*^9, 3.4445421941414003`*^9}, {3.4445422252166*^9, 3.4445422386014*^9}, { 3.444542280425*^9, 3.4445423014538*^9}, {3.444542455769*^9, 3.4445424578282003`*^9}, {3.4445431739214*^9, 3.444543175809*^9}, { 3.4445647020962*^9, 3.4445648405618*^9}, {3.4445648825414*^9, 3.4445648858486*^9}, {3.4445649382646*^9, 3.4445651882702*^9}, { 3.4446164822206*^9, 3.4446165344494*^9}, {3.4446166121842003`*^9, 3.4446166738822002`*^9}, {3.4446167223046*^9, 3.4446168047974*^9}, { 3.444616843033*^9, 3.444616906447*^9}, {3.4446444694708*^9, 3.4446444700948*^9}, {3.4446477738310003`*^9, 3.4446477939862003`*^9}, { 3.4446478467298*^9, 3.4446478681018*^9}, 3.4446480456142*^9, { 3.4446487557418003`*^9, 3.4446487636198*^9}, 3.4446488179974003`*^9, { 3.4446488971205997`*^9, 3.4446489152478*^9}, {3.4446490003458*^9, 3.4446490008294*^9}, {3.4447042728942003`*^9, 3.4447042751562*^9}, { 3.4447044703278*^9, 3.4447044865362*^9}, 3.4447046475282*^9, 3.4447047993786*^9, {3.444704908329*^9, 3.4447049292642*^9}, { 3.4447049861926003`*^9, 3.4447049877214003`*^9}, {3.4447050279296*^9, 3.4447050419695997`*^9}, {3.4447053486656*^9, 3.4447053739376*^9}, 3.4447054561963997`*^9, 3.44470561612*^9, {3.4472133996876*^9, 3.4472134108571997`*^9}, {3.4472134470179996`*^9, 3.4472134648332*^9}, { 3.4472135032872*^9, 3.4472135245344*^9}, {3.4472136963059998`*^9, 3.4472137794384003`*^9}, {3.4472138235708*^9, 3.4472138388900003`*^9}, { 3.4472139099792*^9, 3.4472141367096*^9}, {3.447214202682*^9, 3.4472142975924*^9}, {3.4472144187732*^9, 3.4472145910284*^9}, { 3.4472146560492*^9, 3.4472147023968*^9}, {3.447214803594*^9, 3.4472148728736*^9}, {3.4472149156956*^9, 3.447214940484*^9}, { 3.447216227284*^9, 3.4472162419948*^9}, {3.4472163068908*^9, 3.4472163720832*^9}, {3.4472164665880003`*^9, 3.447216530392*^9}, { 3.4472166237268*^9, 3.4472167058452*^9}, 3.4472167362808*^9, { 3.4472171394658003`*^9, 3.4472171532874002`*^9}, {3.4472172028993998`*^9, 3.4472172216661997`*^9}, {3.4472172524606*^9, 3.4472172690278*^9}, { 3.4472173209133997`*^9, 3.4472173334245996`*^9}, {3.4472173920846*^9, 3.447217404861*^9}, {3.4472179572548*^9, 3.4472180351456003`*^9}, { 3.4472509764091997`*^9, 3.4472511017396*^9}, {3.4473910422216*^9, 3.4473912901524*^9}, 3.4473918688344*^9, {3.447392021185*^9, 3.4473920346633997`*^9}, {3.4473921383304*^9, 3.4473921479088*^9}, { 3.4473923024112*^9, 3.4473923734379997`*^9}, {3.4473928098168*^9, 3.4473928648691998`*^9}, {3.4473931872432003`*^9, 3.4473932461800003`*^9}, {3.4473933026675997`*^9, 3.4473934579812*^9}, { 3.4473935755271997`*^9, 3.447393742572*^9}, {3.4473939032676*^9, 3.4473939384144*^9}, {3.447395257644*^9, 3.4473953141628*^9}, { 3.4473954231132*^9, 3.4473954756384*^9}, {3.4473955348716*^9, 3.4473955723272*^9}, {3.447395648502*^9, 3.4473957588876*^9}, { 3.4473957903996*^9, 3.4473958488372*^9}, 3.4473962894154*^9, { 3.447396350817*^9, 3.447396352611*^9}, {3.4474625379146*^9, 3.4474625637326*^9}, {3.558360651728078*^9, 3.558360652102478*^9}, { 3.5619791319820857`*^9, 3.561979135788492*^9}, 3.561979369382504*^9, { 3.5619794930439215`*^9, 3.5619795010155354`*^9}, {3.561979569218855*^9, 3.56197960614412*^9}, {3.5619797417551584`*^9, 3.5619797448751636`*^9}, { 3.618719065033702*^9, 3.618719075426296*^9}, {3.6187194011669273`*^9, 3.6187194449454317`*^9}, {3.6187196998040085`*^9, 3.6187197102436056`*^9}, {3.618719902254588*^9, 3.6187199711455283`*^9}, { 3.618722365406472*^9, 3.6187225412555304`*^9}, {3.6187226885009522`*^9, 3.6187227109872384`*^9}, {3.618722756922866*^9, 3.6187231317203026`*^9}, { 3.618723424250035*^9, 3.6187234267291765`*^9}, {3.6187235105259695`*^9, 3.6187236491028957`*^9}, {3.618723691580325*^9, 3.618723745975436*^9}, { 3.618723778837316*^9, 3.6187238310002995`*^9}, {3.6187239055875654`*^9, 3.618723940035536*^9}, {3.6187239782667227`*^9, 3.6187240219352207`*^9}, { 3.618724166762504*^9, 3.618724177411113*^9}, {3.618729321696159*^9, 3.618729328067523*^9}, 3.618729374058154*^9, {3.6187294379838104`*^9, 3.618729708464281*^9}, {3.6187297631904106`*^9, 3.618729773195983*^9}, { 3.618729822648812*^9, 3.6187299321490746`*^9}, {3.618729984399063*^9, 3.61873000654133*^9}, {3.6187300746012225`*^9, 3.6187300860458775`*^9}, { 3.618731390835507*^9, 3.6187315116174154`*^9}, {3.618731747324897*^9, 3.6187318214091344`*^9}, {3.6187318769243097`*^9, 3.618732065297084*^9}, { 3.6187321012351394`*^9, 3.618732157420353*^9}, {3.618732188384124*^9, 3.6187322435542793`*^9}, {3.6187322786112847`*^9, 3.6187325478446836`*^9}, {3.6187325819856367`*^9, 3.6187326817653437`*^9}, {3.618732810863728*^9, 3.61873282594359*^9}, { 3.6187336474335766`*^9, 3.618733754678711*^9}, {3.618733827497876*^9, 3.61873396201257*^9}, {3.6187342020362988`*^9, 3.618734236455267*^9}, 3.618734298201799*^9, {3.618734712498495*^9, 3.618734712716508*^9}, 3.6187347739640107`*^9, {3.618738817361748*^9, 3.6187388333816643`*^9}, { 3.6187391349349127`*^9, 3.6187391457955337`*^9}, {3.618739376900752*^9, 3.618739397023903*^9}, {3.618739528394417*^9, 3.618739534809784*^9}, { 3.618739972366811*^9, 3.61873997340687*^9}, {3.6187400416617737`*^9, 3.618740043022852*^9}, {3.6187400971579485`*^9, 3.618740107902563*^9}, { 3.6187401713671927`*^9, 3.6187401723312483`*^9}, {3.6187402613443394`*^9, 3.618740268819767*^9}, {3.6187403697625403`*^9, 3.6187404057615995`*^9}, { 3.618740488277319*^9, 3.618740516244919*^9}, {3.618740647782442*^9, 3.6187406551668644`*^9}, 3.6187407823021364`*^9, {3.6187418050786357`*^9, 3.618741805749674*^9}, {3.6187418557605343`*^9, 3.6187419895921893`*^9}, { 3.618742022944097*^9, 3.61874204379729*^9}, {3.6187420836395683`*^9, 3.618742103384698*^9}, {3.620462440882641*^9, 3.6204624460519366`*^9}, { 3.6204624990259666`*^9, 3.620462576450395*^9}, {3.620463682857678*^9, 3.620463713336421*^9}, 3.6204637901188126`*^9, {3.620464238835478*^9, 3.62046424411378*^9}, 3.628912429385081*^9, {3.6289135207155013`*^9, 3.6289135210805225`*^9}, 3.6289497746958513`*^9, 3.6289498371774254`*^9, { 3.62894988410911*^9, 3.6289500319795675`*^9}, {3.6289501333883677`*^9, 3.628950183744248*^9}, {3.6289503323017445`*^9, 3.628950390181055*^9}, { 3.6289505050536256`*^9, 3.6289505113579865`*^9}, {3.62895070863527*^9, 3.6289507095043197`*^9}, {3.628951013180689*^9, 3.62895101407374*^9}, { 3.629190743153632*^9, 3.629190816645361*^9}, {3.6291909709608326`*^9, 3.629190981678051*^9}, {3.629191034624544*^9, 3.6291910410049553`*^9}, { 3.6293846391370816`*^9, 3.629384641102685*^9}, {3.6294628543371735`*^9, 3.629462867097191*^9}, {3.629468063172048*^9, 3.6294681151669397`*^9}, { 3.6295205836757097`*^9, 3.6295206295085897`*^9}, {3.6295206788826766`*^9, 3.6295207067911253`*^9}, {3.6295207408927855`*^9, 3.629520753700408*^9}, { 3.629521020590745*^9, 3.6295210354395943`*^9}, {3.6295211107369013`*^9, 3.62952114882508*^9}, {3.6295212327348795`*^9, 3.6295212477237363`*^9}, { 3.6295213424816394`*^9, 3.629521343230441*^9}, {3.6295215363119802`*^9, 3.6295216753550243`*^9}, {3.629521922272258*^9, 3.6295219939855833`*^9}, { 3.6295220298188467`*^9, 3.629522446058778*^9}, {3.629522499348471*^9, 3.629522604352256*^9}, {3.629522755188921*^9, 3.62952288580795*^9}, { 3.629522918084407*^9, 3.6295233421087513`*^9}, {3.6295233808436193`*^9, 3.629523390936837*^9}, {3.629523424274096*^9, 3.6295234533369465`*^9}, { 3.6295235190130625`*^9, 3.629523521680667*^9}, 3.6295235894315863`*^9, { 3.6295237270706277`*^9, 3.629523799454755*^9}, {3.6295238514808464`*^9, 3.629523883460902*^9}, {3.6295239376085978`*^9, 3.6295239442386093`*^9}, { 3.6295241089904985`*^9, 3.629524177537019*^9}, 3.629524211888279*^9, { 3.629524277423994*^9, 3.629524396904604*^9}, {3.6295244794839497`*^9, 3.6295246248450055`*^9}, 3.629524657090262*^9, {3.6295259599109507`*^9, 3.629526013465844*^9}, {3.6295261092188125`*^9, 3.629526201414974*^9}, 3.6295263436092243`*^9, {3.6295263910333076`*^9, 3.629526583303645*^9}, { 3.629526616672104*^9, 3.629526647653758*^9}, {3.629526687558628*^9, 3.629526744888729*^9}, {3.629526804075233*^9, 3.6295268598453307`*^9}, { 3.6295269393898706`*^9, 3.6295269586559043`*^9}, {3.6295271490074387`*^9, 3.6295272149019547`*^9}, {3.6295272553684254`*^9, 3.6295272827620735`*^9}, {3.6295274137087035`*^9, 3.6295274761244135`*^9}, {3.6295275252801*^9, 3.6295279912529182`*^9}, { 3.6295281572216096`*^9, 3.629528160435215*^9}, {3.6295282905550437`*^9, 3.6295284308616905`*^9}, 3.6295285402022824`*^9, {3.629528582088356*^9, 3.629528616798417*^9}, {3.6295287666834803`*^9, 3.6295290316343455`*^9}, { 3.629529086515242*^9, 3.629529118432898*^9}, {3.6295291548121614`*^9, 3.629529292794404*^9}, {3.6295293426208916`*^9, 3.6295293491261034`*^9}, { 3.629529420699029*^9, 3.629529571535694*^9}, {3.6295296539506383`*^9, 3.629529656103442*^9}, {3.6295296894407005`*^9, 3.629529692295506*^9}, { 3.6295297445555973`*^9, 3.629529766426836*^9}, {3.6295298053333044`*^9, 3.6295298209489317`*^9}, {3.6295308380551186`*^9, 3.6295308386635194`*^9}, {3.629532377840223*^9, 3.6295323811630287`*^9}, { 3.629532480020402*^9, 3.629532482454006*^9}, {3.629532520720874*^9, 3.629532564619351*^9}, {3.62953259842461*^9, 3.6295326002654133`*^9}, { 3.6295326327758703`*^9, 3.6295326715107384`*^9}, {3.629532742428463*^9, 3.6295328288058147`*^9}, {3.6295329692184625`*^9, 3.6295330530062094`*^9}, {3.6295331824396367`*^9, 3.629533193562456*^9}, 3.6295350321720915`*^9, 3.629535158485513*^9, {3.629535245471266*^9, 3.6295352687465067`*^9}, {3.62953541293756*^9, 3.629535446384019*^9}, { 3.6295355043381205`*^9, 3.6295355262249594`*^9}, {3.629543790136781*^9, 3.629543791181983*^9}, {3.629543871350524*^9, 3.629544001673153*^9}, { 3.6295446682009234`*^9, 3.629544668466124*^9}, {3.6296010216162376`*^9, 3.6296010236442413`*^9}, {3.629601079336339*^9, 3.6296010902875586`*^9}, 3.6296011425476503`*^9, {3.6296043522397404`*^9, 3.629604399031022*^9}, { 3.629623884428093*^9, 3.629623914723346*^9}, {3.6296239662190366`*^9, 3.6296239738006496`*^9}, {3.6296240514731865`*^9, 3.6296240920176573`*^9}, {3.629624125947717*^9, 3.629624369432945*^9}, { 3.6296256512247963`*^9, 3.6296256817072496`*^9}, {3.6296260472626915`*^9, 3.629626047434292*^9}, {3.629628055568204*^9, 3.629628056098605*^9}, { 3.6296280911206665`*^9, 3.6296281088266973`*^9}, {3.6296281406819534`*^9, 3.629628273032586*^9}, {3.629628378831972*^9, 3.6296283814995766`*^9}, { 3.629628459562114*^9, 3.629628466379326*^9}, {3.629628519419419*^9, 3.6296285390754533`*^9}, {3.629633008133008*^9, 3.629633008835009*^9}, { 3.6296337764967575`*^9, 3.6296338344040594`*^9}, {3.6296342997684765`*^9, 3.629634432150309*^9}, {3.629634494035618*^9, 3.6296345320060844`*^9}, { 3.629634594499794*^9, 3.629634812182576*^9}, {3.6296348599810605`*^9, 3.6296348746918864`*^9}, {3.6296349071867433`*^9, 3.629635023172947*^9}, 3.6296350995818815`*^9, {3.6296363797201295`*^9, 3.6296363868961425`*^9}, { 3.629636462025874*^9, 3.6296364833355117`*^9}, {3.629636555922439*^9, 3.62963656780966*^9}, {3.629636770469616*^9, 3.629636774151222*^9}, { 3.6296369192782774`*^9, 3.6296369318830996`*^9}, {3.629637058539722*^9, 3.6296370719401455`*^9}, {3.629637278172508*^9, 3.629637286814923*^9}, { 3.6296376418091464`*^9, 3.629637662385583*^9}, {3.629637773551378*^9, 3.629637795360216*^9}, {3.6296390041751394`*^9, 3.629639039571602*^9}, 3.6296393829750047`*^9, {3.6296395546065063`*^9, 3.6296395649961243`*^9}, { 3.62964113386068*^9, 3.6296412507048855`*^9}, {3.629641303167777*^9, 3.629641313744596*^9}, {3.6296416285116315`*^9, 3.629641628886032*^9}, { 3.6296416658736973`*^9, 3.6296416815049243`*^9}, 3.6296417376338234`*^9, { 3.6296855551269727`*^9, 3.6296855804270077`*^9}, {3.6297079065796247`*^9, 3.6297079070476255`*^9}, {3.6297080850439377`*^9, 3.629708135728427*^9}, { 3.6297083496516027`*^9, 3.6297084025512953`*^9}, {3.629708781767563*^9, 3.629708790940379*^9}, {3.6297089402482414`*^9, 3.6297089618542795`*^9}, { 3.6297105345398417`*^9, 3.629710538580249*^9}, {3.6297107810514746`*^9, 3.6297107850138817`*^9}, {3.6297109100481014`*^9, 3.629710915710911*^9}, { 3.629711201534613*^9, 3.629711204311418*^9}, {3.629711236307074*^9, 3.6297115007275386`*^9}, {3.6297115377464037`*^9, 3.6297115441112146`*^9}, 3.6297116025645175`*^9, {3.6298716505389357`*^9, 3.629871851841689*^9}, { 3.62987837458679*^9, 3.629878383510006*^9}, {3.6298784402629056`*^9, 3.629878447345318*^9}, {3.6298785221786494`*^9, 3.6298786580236883`*^9}, { 3.629878689613744*^9, 3.629878737147027*^9}, 3.629878783853509*^9, { 3.629878832322794*^9, 3.6298789171723433`*^9}, {3.6298802128122005`*^9, 3.6298802929723125`*^9}, 3.6298813644148126`*^9, {3.629882428887303*^9, 3.629882435887313*^9}, {3.6298986251827383`*^9, 3.6298988530367384`*^9}, { 3.6298989036744275`*^9, 3.6298989486493063`*^9}, {3.629899016868226*^9, 3.6298991622448816`*^9}, {3.6298997154530535`*^9, 3.629899740147897*^9}, { 3.6298998248560457`*^9, 3.629899978048314*^9}, {3.6299000396372223`*^9, 3.6299001557638264`*^9}, {3.6299001966826982`*^9, 3.6299002595352087`*^9}, 3.6299005011236343`*^9, {3.6299005468317146`*^9, 3.629900567642151*^9}, { 3.629900887676713*^9, 3.629900990153293*^9}, {3.6299011689220085`*^9, 3.6299012295125146`*^9}, {3.6299013754039707`*^9, 3.6299014166036434`*^9}, 3.6299014589733176`*^9, {3.6299015096734066`*^9, 3.629901588765546*^9}, { 3.629901662569275*^9, 3.6299016974665365`*^9}, {3.629901952339784*^9, 3.6299019599057975`*^9}, 3.6299020306051216`*^9, {3.6299022330934772`*^9, 3.6299022682559395`*^9}, {3.6299023020455985`*^9, 3.629902332808852*^9}, { 3.6299024532566643`*^9, 3.629902462850681*^9}, {3.629949880225117*^9, 3.6299498807867184`*^9}, {3.6299503101150723`*^9, 3.6299503156998825`*^9}, {3.629950355058751*^9, 3.629950498937804*^9}, { 3.6299555415202007`*^9, 3.6299555507086167`*^9}, {3.6299556061667137`*^9, 3.6299557553497763`*^9}, {3.629955788499834*^9, 3.6299558948608212`*^9}, { 3.629956042764681*^9, 3.629956043809883*^9}, {3.6299560914211664`*^9, 3.6299561017327843`*^9}, 3.629956145849662*^9, {3.6299584813821354`*^9, 3.6299585082765827`*^9}, 3.6299585652946825`*^9, {3.629958616587573*^9, 3.6299586356508064`*^9}, {3.629958715073346*^9, 3.6299588186419287`*^9}, { 3.629958857454797*^9, 3.629958927249319*^9}, {3.629959427994599*^9, 3.629959494669116*^9}, {3.6299595293323765`*^9, 3.6299596037913074`*^9}, { 3.62995966795422*^9, 3.62995967360143*^9}, {3.6299597835972233`*^9, 3.6299597841120243`*^9}, {3.629959826622099*^9, 3.629959862533362*^9}, { 3.6299599051682367`*^9, 3.6299599235918694`*^9}, 3.629959979939168*^9, { 3.6299601345354395`*^9, 3.62996014612626*^9}, 3.6299601769831142`*^9, { 3.629960253142448*^9, 3.629960269538077*^9}, {3.6299603041701374`*^9, 3.6299603078205442`*^9}, {3.6299604300467587`*^9, 3.629960435491168*^9}, { 3.6299605300585346`*^9, 3.6299605636609936`*^9}, {3.6299606195870914`*^9, 3.6299606581971593`*^9}, {3.629960824228251*^9, 3.6299608755367413`*^9}, { 3.629960906658796*^9, 3.6299609978409557`*^9}, {3.6299610312250147`*^9, 3.629961070646284*^9}, {3.629961135698398*^9, 3.6299611643088484`*^9}, { 3.6299720458358483`*^9, 3.6299721791536827`*^9}, {3.6299722439717965`*^9, 3.629972300007095*^9}, {3.6299723670872126`*^9, 3.6299723937008595`*^9}, { 3.629972457801372*^9, 3.6299724710613956`*^9}, {3.629972740193068*^9, 3.6299728251196175`*^9}, {3.6299729203577843`*^9, 3.6299729350218105`*^9}, {3.6299729720874753`*^9, 3.6299730462188053`*^9}, {3.629973116044528*^9, 3.6299731230177402`*^9}, { 3.629973184310248*^9, 3.6299732090830917`*^9}, {3.629973349982539*^9, 3.6299734360166903`*^9}, 3.629973534562063*^9, {3.629973577446539*^9, 3.629973586104554*^9}, {3.6299740374133463`*^9, 3.629974083823428*^9}, { 3.6299742505565205`*^9, 3.629974337089873*^9}, {3.629974382907153*^9, 3.6299744466176653`*^9}, {3.629974589794717*^9, 3.629974590761918*^9}, { 3.629974776215044*^9, 3.6299747850134597`*^9}, {3.6299748226095257`*^9, 3.6299748237483273`*^9}, 3.6299748618435946`*^9, {3.629975198476586*^9, 3.6299752545898843`*^9}, {3.62997531475919*^9, 3.6299753175515947`*^9}, { 3.6299754601982455`*^9, 3.6299754625382495`*^9}, {3.629975592034077*^9, 3.629975592502078*^9}, {3.629983277446268*^9, 3.6299832946842985`*^9}, { 3.62998342081052*^9, 3.6299835439883366`*^9}, {3.629983615514462*^9, 3.629983931009416*^9}, {3.6299919807040443`*^9, 3.6299919808912444`*^9}, { 3.629992028330928*^9, 3.6299920922130404`*^9}, 3.629992198480427*^9, { 3.6299922299300823`*^9, 3.629992250506518*^9}, {3.629992292657792*^9, 3.6299923603151107`*^9}, {3.6299924387676487`*^9, 3.6299924398440504`*^9}, {3.6299925764846907`*^9, 3.6299926096347485`*^9}, {3.6299928122323046`*^9, 3.629992818768716*^9}, { 3.6299929049120674`*^9, 3.629992905411268*^9}, {3.6299929850338078`*^9, 3.6299929866250105`*^9}, {3.6299931061992207`*^9, 3.62999312270405*^9}, { 3.629993172312137*^9, 3.6299932618718944`*^9}, {3.6299933276572104`*^9, 3.6299933842073092`*^9}, {3.630287775665962*^9, 3.630287795852398*^9}, { 3.6303896387100534`*^9, 3.630389666774503*^9}, {3.6303896967889557`*^9, 3.6303897095341783`*^9}, {3.6303897587054644`*^9, 3.630389880448078*^9}, { 3.6303899127557354`*^9, 3.630390009444705*^9}, 3.630390057321189*^9, 3.630390443484267*^9, {3.63039095720877*^9, 3.6303909789240074`*^9}, { 3.6303910572205453`*^9, 3.6303911291054716`*^9}, {3.630391163035531*^9, 3.6303911740803504`*^9}, {3.630391240224467*^9, 3.6303912875081496`*^9}, { 3.6303913396902413`*^9, 3.630391404570755*^9}, {3.630391479513287*^9, 3.6303917572873745`*^9}, {3.630391868905571*^9, 3.6303920027226057`*^9}, { 3.630392064327114*^9, 3.630392219843787*^9}, {3.63039226121506*^9, 3.63039232943398*^9}, {3.6303924315985594`*^9, 3.6303924441097813`*^9}, { 3.6303926866122074`*^9, 3.6303927118530517`*^9}, {3.630392795671999*^9, 3.6303928006172075`*^9}, {3.6303986032190485`*^9, 3.6303986046230516`*^9}, {3.6303986654631586`*^9, 3.6303987936485834`*^9}, {3.63039889979117*^9, 3.6303989091199865`*^9}, { 3.630399006323757*^9, 3.630399007259759*^9}, {3.630399117224352*^9, 3.630399214771323*^9}, {3.6303992555185947`*^9, 3.6303993036758795`*^9}, { 3.630399467725767*^9, 3.630399502731636*^9}, {3.6303995748037624`*^9, 3.630399595614199*^9}, {3.6303996329294643`*^9, 3.630399658076709*^9}, { 3.630399711335202*^9, 3.6303997453120623`*^9}, {3.6303998546994543`*^9, 3.6303999880484886`*^9}, {3.6304000742074394`*^9, 3.630400123441126*^9}, { 3.6304001724564123`*^9, 3.630400251595351*^9}, {3.630400324166679*^9, 3.630400327052684*^9}, {3.630400358190338*^9, 3.6304003597503414`*^9}, { 3.6304004587481155`*^9, 3.6304004640521245`*^9}, {3.630400521975026*^9, 3.630400526124634*^9}, {3.630400567199506*^9, 3.630400593516752*^9}, { 3.6304012340070767`*^9, 3.6304013035207987`*^9}, {3.6304013614749007`*^9, 3.630401367933312*^9}, {3.630401686939398*^9, 3.6304017294598303`*^9}, { 3.630401794020523*^9, 3.6304018922061386`*^9}, {3.6304019687775183`*^9, 3.630401987153569*^9}, {3.630402072749465*^9, 3.63040208297405*^9}, { 3.6304022247881613`*^9, 3.630402255931943*^9}, 3.630402329306139*^9, { 3.6304023806970787`*^9, 3.6304024212403975`*^9}, {3.6304025002259154`*^9, 3.630402528595538*^9}, {3.6304025620694523`*^9, 3.630402575015193*^9}, { 3.6304026411829777`*^9, 3.630402649073429*^9}, {3.630402695548087*^9, 3.6304027128260756`*^9}, {3.630402783923142*^9, 3.6304027982389607`*^9}, { 3.6304028797236214`*^9, 3.6304030111811404`*^9}, {3.6304030562107162`*^9, 3.6304031598846455`*^9}, {3.630403236330018*^9, 3.6304032404072514`*^9}, { 3.630403373001835*^9, 3.6304033888147397`*^9}, {3.6304039420953856`*^9, 3.6304039512829113`*^9}, 3.6304039831437335`*^9, {3.630404015975611*^9, 3.6304040663624935`*^9}, {3.630404173614628*^9, 3.630404246945822*^9}, { 3.6304042891772375`*^9, 3.630404299595834*^9}, {3.630404391083066*^9, 3.630404392406142*^9}, {3.6304045301800222`*^9, 3.6304045579486103`*^9}, { 3.630404640215316*^9, 3.630404762796327*^9}, {3.630404877629895*^9, 3.630404883104208*^9}, {3.6304050364729805`*^9, 3.630405098270515*^9}, { 3.6304051736118245`*^9, 3.6304051965901384`*^9}, {3.6304053802536435`*^9, 3.63040539242334*^9}, {3.630406035965148*^9, 3.630406041998493*^9}, { 3.630406072049212*^9, 3.6304060962065935`*^9}, {3.630406264081196*^9, 3.6304062707025747`*^9}, {3.63040632219952*^9, 3.630406385461138*^9}, { 3.630406477200385*^9, 3.630406482095665*^9}, {3.6304066170883865`*^9, 3.6304066222256804`*^9}, {3.630406957868878*^9, 3.630406973411767*^9}, { 3.6304070081447535`*^9, 3.630407018199329*^9}, {3.630407411376817*^9, 3.630407412542884*^9}, {3.6304080609339695`*^9, 3.630408121202417*^9}, { 3.6304081585485525`*^9, 3.6304081832129636`*^9}, {3.63040821409673*^9, 3.630408421131572*^9}, 3.6304934333363276`*^9, {3.63049350751357*^9, 3.630493677593298*^9}, {3.630493716898546*^9, 3.6304937846684227`*^9}, 3.630493922944331*^9, {3.6304939556752033`*^9, 3.630494117430455*^9}, { 3.6304941486092386`*^9, 3.6304941767788496`*^9}, {3.6304942118648567`*^9, 3.6304942530272107`*^9}, {3.6304942838399734`*^9, 3.6304942845820155`*^9}, {3.6304943454054947`*^9, 3.6304944442451477`*^9}, {3.63080749995092*^9, 3.6308075480801234`*^9}, { 3.630807586536323*^9, 3.630807621440319*^9}, {3.630807680459695*^9, 3.630807682914836*^9}, {3.630807736889923*^9, 3.6308077644745007`*^9}, { 3.6308078081089964`*^9, 3.6308078670123653`*^9}, {3.630807991648494*^9, 3.630807997541831*^9}, {3.6308081080891542`*^9, 3.6308081919599514`*^9}, { 3.630808306368495*^9, 3.630808345060708*^9}, {3.6308087281906223`*^9, 3.6308087555171847`*^9}, {3.630809110815507*^9, 3.630809169033837*^9}, { 3.6308091998195972`*^9, 3.630809448512822*^9}, {3.6308095328996487`*^9, 3.6308095448223305`*^9}, {3.630809582269472*^9, 3.6308095873607635`*^9}, { 3.630809665529235*^9, 3.630809684808337*^9}, {3.6308316258485594`*^9, 3.6308318380886984`*^9}, {3.63083188164919*^9, 3.630831966930068*^9}, 3.6320400558356075`*^9, {3.6354749882908883`*^9, 3.635474989418953*^9}, { 3.635475084557395*^9, 3.6354750875145636`*^9}, {3.6354751334091887`*^9, 3.635475162315842*^9}, {3.6354754001974483`*^9, 3.6354754820331287`*^9}, 3.635475512931896*^9, {3.6354756222781506`*^9, 3.635475622861184*^9}, { 3.635475691642118*^9, 3.6354757057969275`*^9}, {3.6354757798291616`*^9, 3.635475797395167*^9}, {3.635475884848169*^9, 3.6354758981309285`*^9}, { 3.635475961488552*^9, 3.6354759738382587`*^9}, {3.6354760213729773`*^9, 3.6354760572050266`*^9}, {3.6354761282470903`*^9, 3.635476136040536*^9}, { 3.6354761719365892`*^9, 3.635476212217893*^9}, {3.6593346599546614`*^9, 3.659334660890663*^9}, {3.6593347077219453`*^9, 3.659334720701168*^9}, { 3.6593348752974396`*^9, 3.6593348758122406`*^9}, {3.6593349140947075`*^9, 3.6593350070240707`*^9}, {3.6593350466949406`*^9, 3.6593350543701544`*^9}, {3.659335103791041*^9, 3.6593351614487424`*^9}, 3.659335217686841*^9, {3.659335262084519*^9, 3.6593352995869846`*^9}, { 3.6593356899482727`*^9, 3.659335701819893*^9}, {3.659335964227954*^9, 3.659335964602355*^9}, {3.65933603594128*^9, 3.6593360629605274`*^9}, { 3.6593361352354546`*^9, 3.6593361504454813`*^9}, {3.6593363929479074`*^9, 3.6593364061611304`*^9}, 3.6593368946915884`*^9, {3.6884748265656157`*^9, 3.6884748268716326`*^9}, {3.6884748600075283`*^9, 3.688474861420609*^9}, { 3.6885242858240776`*^9, 3.6885243001140976`*^9}, {3.6888842911675606`*^9, 3.6888843311676164`*^9}, {3.688966242423658*^9, 3.688966263933688*^9}, { 3.6897393587897596`*^9, 3.6897393649897685`*^9}, 3.689739477049925*^9, { 3.6898595970621734`*^9, 3.689859597272174*^9}, {3.6898596707522764`*^9, 3.6898597190523443`*^9}, {3.689859768552414*^9, 3.6898597721424184`*^9}, { 3.689859855272535*^9, 3.689859859882541*^9}, {3.6898605078334484`*^9, 3.6898607266237545`*^9}, 3.6898608811139708`*^9, {3.6898609634740863`*^9, 3.689860974304102*^9}, 3.6898610140141573`*^9, {3.6898611496043468`*^9, 3.6898611683243732`*^9}, {3.689861462024784*^9, 3.6898615624849253`*^9}, { 3.6898616142149973`*^9, 3.6898616164350004`*^9}, 3.6898616657950697`*^9, { 3.689861716805141*^9, 3.689861749905187*^9}, {3.732677920575506*^9, 3.7326779208190203`*^9}, {3.7519672427004185`*^9, 3.7519672444968877`*^9}, {3.7519674022097683`*^9, 3.75196742976579*^9}, { 3.751967484127989*^9, 3.751967510853814*^9}, {3.7519675409404893`*^9, 3.751967541549782*^9}, {3.7519675797751045`*^9, 3.751967592209671*^9}, { 3.7519676829383273`*^9, 3.7519676841255474`*^9}, {3.7519677154775553`*^9, 3.7519677953499403`*^9}, 3.751967827811061*^9, {3.7519679545625095`*^9, 3.751967957999185*^9}, {3.751968003754015*^9, 3.7519681477513895`*^9}, { 3.751968264817631*^9, 3.751968270722477*^9}, {3.7519689618119907`*^9, 3.751968969888235*^9}, {3.7519691168917775`*^9, 3.7519691395895615`*^9}, { 3.751969242782174*^9, 3.7519692581691785`*^9}, {3.7519693625211954`*^9, 3.751969378579924*^9}, {3.751969409572627*^9, 3.751969438643936*^9}, { 3.7519695894526725`*^9, 3.751969614306203*^9}, {3.7523200108586655`*^9, 3.752320012354121*^9}, {3.7553831315619707`*^9, 3.755383134119626*^9}, { 3.7553831893197794`*^9, 3.755383241814331*^9}, {3.7553832736267967`*^9, 3.7553832810757113`*^9}, {3.7554336536222963`*^9, 3.755433684797229*^9}, { 3.7554337764737434`*^9, 3.7554338315300155`*^9}, {3.755433998047738*^9, 3.7554340265485487`*^9}, {3.755446573138784*^9, 3.755446636911299*^9}, { 3.75544667493072*^9, 3.755446753435521*^9}, {3.755446891541581*^9, 3.7554468921547422`*^9}, {3.7554469323588533`*^9, 3.755446936867403*^9}, { 3.7554470190332975`*^9, 3.7554472776872244`*^9}, {3.7555217323692026`*^9, 3.755521732847602*^9}, {3.755521767127169*^9, 3.7555217972041793`*^9}, { 3.755522561453134*^9, 3.755522564231819*^9}, {3.755522601885935*^9, 3.7555226037287407`*^9}, {3.7555226758687305`*^9, 3.755522678585092*^9}, { 3.7555234832604623`*^9, 3.7555235920444417`*^9}, {3.7555239506007543`*^9, 3.755524013893358*^9}, {3.755524076791689*^9, 3.7555240812793446`*^9}, { 3.7555241238138275`*^9, 3.7555241268985643`*^9}, {3.7555242930449886`*^9, 3.7555243378577013`*^9}, {3.7555256673767824`*^9, 3.7555256808205338`*^9}, {3.7555258588384123`*^9, 3.755525900317296*^9}, { 3.755525930708299*^9, 3.7555260436531134`*^9}, {3.755607147401991*^9, 3.7556071504143705`*^9}, {3.755607992884314*^9, 3.7556080025382996`*^9}, { 3.7556094344057455`*^9, 3.7556094348690443`*^9}, {3.7559613653116636`*^9, 3.755961445097105*^9}, 3.755961484246889*^9, {3.7559618979231987`*^9, 3.755961939470047*^9}, {3.7559620323724904`*^9, 3.7559620330864005`*^9}, { 3.755962155557907*^9, 3.7559621601593847`*^9}, {3.755962303755834*^9, 3.755962343830135*^9}, {3.7559624058018165`*^9, 3.7559624450501757`*^9}, 3.756002186674869*^9, 3.7560029626855392`*^9, {3.756003222110388*^9, 3.756003295034633*^9}, {3.7560056331492863`*^9, 3.7560056663855457`*^9}, { 3.7560057813555765`*^9, 3.7560057863836613`*^9}, {3.7560058917172394`*^9, 3.756005927847292*^9}, 3.756006092376186*^9, 3.756009112317705*^9, { 3.756091886039587*^9, 3.756091887764086*^9}, {3.756092005435152*^9, 3.7560920727337685`*^9}, {3.75609212911592*^9, 3.7560921293252516`*^9}, { 3.756092262958163*^9, 3.756092263157668*^9}, {3.756092342487877*^9, 3.756092347894502*^9}, {3.7560929036769304`*^9, 3.7560929278911004`*^9}, { 3.7560930741522417`*^9, 3.756093083420331*^9}, {3.7560932986236534`*^9, 3.7560933139459305`*^9}, {3.756093449985523*^9, 3.7560934874491863`*^9}, { 3.756093592694581*^9, 3.7560936019456573`*^9}, {3.756093634438078*^9, 3.756093673866626*^9}, {3.756093873069885*^9, 3.756093897964734*^9}, { 3.7560940650109406`*^9, 3.756094078056768*^9}, {3.756442536546026*^9, 3.756442607904289*^9}, {3.7564436397451363`*^9, 3.7564436403231254`*^9}, { 3.7636034984570236`*^9, 3.7636034989933815`*^9}, {3.763603551051456*^9, 3.7636035527617817`*^9}, {3.7636036049384193`*^9, 3.7636036392233057`*^9}, {3.7636036850937223`*^9, 3.763603692587598*^9}, { 3.7636037258272257`*^9, 3.7636037459031096`*^9}, {3.7636037792254367`*^9, 3.76360387572289*^9}, {3.763603971837229*^9, 3.7636040341423655`*^9}, { 3.763604066526084*^9, 3.7636040756798687`*^9}, {3.7636041452118535`*^9, 3.763604278007333*^9}, {3.763604317710966*^9, 3.7636043271387568`*^9}, { 3.7636043584877644`*^9, 3.763604415561053*^9}, {3.763604445680462*^9, 3.7636044504114943`*^9}, {3.763604615444647*^9, 3.7636048082554193`*^9}, 3.763604854904996*^9, {3.7636133594095488`*^9, 3.7636133618464766`*^9}, { 3.7636136063756704`*^9, 3.7636136315671196`*^9}, {3.7636990373827705`*^9, 3.7636990431157646`*^9}, {3.763699090332087*^9, 3.763699110952259*^9}, { 3.763699227420497*^9, 3.7636993642943506`*^9}, {3.763700085627533*^9, 3.763700088329999*^9}, {3.7637001721125274`*^9, 3.763700181422837*^9}, { 3.763700248063385*^9, 3.7637003918630466`*^9}, {3.763700591783223*^9, 3.7637006017496295`*^9}, {3.7637007583576717`*^9, 3.7637007603074865`*^9}, {3.7637137795793185`*^9, 3.7637137822587233`*^9}, {3.7637148704355187`*^9, 3.763714870624051*^9}, { 3.763727592158518*^9, 3.7637275933445053`*^9}, {3.7637276688363667`*^9, 3.7637276694756594`*^9}, 3.763803448896332*^9, {3.76380349501632*^9, 3.7638036835067654`*^9}, {3.763804829093463*^9, 3.7638048385675254`*^9}, 3.7638051033646154`*^9, 3.7638053924528885`*^9, {3.763805557684454*^9, 3.763805634255308*^9}, {3.763806843847647*^9, 3.763806847966059*^9}, { 3.763806942652097*^9, 3.7638071770752254`*^9}, {3.7638141184594107`*^9, 3.763814134133461*^9}, {3.7638146808628216`*^9, 3.7638146925645113`*^9}, { 3.7638147709278784`*^9, 3.7638147811883087`*^9}, {3.7638148155281043`*^9, 3.763814819843194*^9}, {3.7638150259647446`*^9, 3.763815028601293*^9}, { 3.7638151529595194`*^9, 3.763815155849978*^9}, {3.7638163770262136`*^9, 3.763816380851597*^9}, {3.7638164181856327`*^9, 3.7638164950537987`*^9}, 3.763816568304102*^9, {3.7638166173645625`*^9, 3.763816618808757*^9}, { 3.7638167204462805`*^9, 3.763816721012859*^9}, {3.763857602253485*^9, 3.7638579604183645`*^9}, {3.7638580038507566`*^9, 3.7638580060526443`*^9}, {3.763858082269992*^9, 3.7638581746835337`*^9}, { 3.7638582163351564`*^9, 3.7638582415275116`*^9}, {3.7638582983238*^9, 3.763858907503306*^9}, {3.763858941318697*^9, 3.763858956626134*^9}, { 3.7638602435602536`*^9, 3.763860245408451*^9}, {3.7638694636456347`*^9, 3.7638694647177277`*^9}, {3.7638708199536576`*^9, 3.763870829436488*^9}, { 3.763871287170555*^9, 3.7638712876184006`*^9}, {3.763943214376035*^9, 3.7639432984591475`*^9}, {3.763943418832348*^9, 3.7639434335508127`*^9}, { 3.76394347113767*^9, 3.7639435187320576`*^9}, {3.763943585908682*^9, 3.7639436125255404`*^9}, {3.763951722152746*^9, 3.76395172989299*^9}, { 3.7639517863423367`*^9, 3.7639519945900664`*^9}, {3.763952081515512*^9, 3.7639521530710773`*^9}, {3.763952353248129*^9, 3.763952357026309*^9}, { 3.7639524211903834`*^9, 3.7639524243979177`*^9}, {3.7639527174925117`*^9, 3.7639527180252266`*^9}, {3.7641265625745993`*^9, 3.7641265632314167`*^9}, {3.764126605555829*^9, 3.7641266075095396`*^9}, { 3.7641268313964133`*^9, 3.7641268543573804`*^9}, {3.764127044657903*^9, 3.7641270479422092`*^9}, {3.7641271442332697`*^9, 3.7641271469362774`*^9}, {3.764127227626192*^9, 3.7641272592640233`*^9}, { 3.764127335707515*^9, 3.7641273386484756`*^9}, {3.764127429843852*^9, 3.7641274364304185`*^9}, {3.7641275071859307`*^9, 3.764127516803895*^9}, 3.7641276043548007`*^9, {3.7641276925365753`*^9, 3.764127697080591*^9}, 3.764127798472331*^9, 3.764127853631323*^9, 3.764127908496078*^9, { 3.7641280050343323`*^9, 3.764128022046494*^9}, {3.764128128597419*^9, 3.764128154116727*^9}, {3.7641286864636617`*^9, 3.764128701643106*^9}, { 3.7641289910924444`*^9, 3.7641290126680794`*^9}, {3.7641290672285347`*^9, 3.7641290737798567`*^9}, {3.7641325425120363`*^9, 3.764132565390477*^9}, { 3.7641327425004654`*^9, 3.764132750040793*^9}, 3.7641327968340364`*^9, { 3.764133146776842*^9, 3.764133204874522*^9}, {3.7641333488187037`*^9, 3.7641333525577593`*^9}, {3.764413145593136*^9, 3.7644131471236105`*^9}, { 3.764413201645049*^9, 3.7644132349609704`*^9}, {3.764413325008136*^9, 3.7644133748980193`*^9}, {3.7644134113425665`*^9, 3.7644135151187*^9}, { 3.764413554409053*^9, 3.7644136160674934`*^9}, {3.76441371984758*^9, 3.764413730103909*^9}, 3.764419641962368*^9, {3.7644198522879405`*^9, 3.764419879249356*^9}, 3.764419909536559*^9, {3.764419991012162*^9, 3.764420000171088*^9}, {3.7644200798862047`*^9, 3.7644200950961914`*^9}, { 3.7644201529471693`*^9, 3.764420153715966*^9}, {3.764420210346301*^9, 3.764420255343707*^9}, {3.764420296178318*^9, 3.7644203000939393`*^9}, { 3.7644203803359275`*^9, 3.7644203931390867`*^9}, 3.7644204418727274`*^9, { 3.7647259720700207`*^9, 3.7647261047260523`*^9}, {3.7647263483375626`*^9, 3.76472635879602*^9}, 3.764726656736601*^9, {3.764727009127914*^9, 3.764727020100875*^9}, {3.7647270591828785`*^9, 3.7647270819631023`*^9}, { 3.7647272109090505`*^9, 3.764727227846332*^9}, {3.76473247809907*^9, 3.7647324813925114`*^9}, {3.7647349484962797`*^9, 3.7647349979358416`*^9}, {3.7647351097258167`*^9, 3.764735124772463*^9}, { 3.7647352810674453`*^9, 3.7647352901139917`*^9}, {3.7647353746429515`*^9, 3.764735379550926*^9}, {3.7647354596539807`*^9, 3.764735507677454*^9}, { 3.7647355546341*^9, 3.764735728811817*^9}, {3.764735837449795*^9, 3.76473584132898*^9}, {3.76473603649269*^9, 3.7647360592982664`*^9}, { 3.7647360998228803`*^9, 3.76473621551197*^9}, {3.7647362545599003`*^9, 3.764736286430997*^9}, {3.7647364592833533`*^9, 3.764736464019006*^9}, { 3.764736566167658*^9, 3.7647365918958225`*^9}, {3.764764761680134*^9, 3.7647648482473745`*^9}, 3.764764917763693*^9, {3.764764964821686*^9, 3.764765090741813*^9}, {3.7647651742140284`*^9, 3.7647652517335076`*^9}, { 3.764765341266399*^9, 3.7647653614173465`*^9}, 3.764765400284145*^9, { 3.764765691384389*^9, 3.764765708710143*^9}, 3.7647657454275875`*^9, { 3.76476578351686*^9, 3.764765871262255*^9}, {3.7647661045180917`*^9, 3.76476612822571*^9}, {3.7647661964223824`*^9, 3.764766239375331*^9}, { 3.764766330361228*^9, 3.764766338297905*^9}, {3.764767015060799*^9, 3.7647670193029037`*^9}, {3.764767076590926*^9, 3.7647671160277977`*^9}, { 3.7647671493139205`*^9, 3.7647672079236426`*^9}, {3.764767458938404*^9, 3.7647674608323865`*^9}, {3.764810938444873*^9, 3.7648109399353456`*^9}, { 3.7648118616019874`*^9, 3.7648118695079126`*^9}, {3.7648120589477816`*^9, 3.7648124600413237`*^9}, {3.76481250476682*^9, 3.7648125259602103`*^9}, { 3.764812601341893*^9, 3.7648126577763243`*^9}, {3.7648126944039307`*^9, 3.7648128855627623`*^9}, {3.764812924923909*^9, 3.764812926481821*^9}, { 3.764813041485982*^9, 3.764813131254232*^9}, {3.7648134679328885`*^9, 3.7648136479313235`*^9}, {3.7648136917777314`*^9, 3.764813697753367*^9}, { 3.7648137297570653`*^9, 3.764813747862262*^9}, 3.764813784221693*^9, { 3.7648138370678406`*^9, 3.7648141387969923`*^9}, {3.764814321050164*^9, 3.764814422489184*^9}, {3.764814461366684*^9, 3.7648145835728483`*^9}, { 3.764814614769511*^9, 3.7648147525825167`*^9}, {3.764815363375289*^9, 3.7648153644907384`*^9}, {3.764815451671169*^9, 3.7648154601533747`*^9}, { 3.7648175917802963`*^9, 3.7648176401910563`*^9}, {3.765885491237231*^9, 3.765885501131465*^9}, {3.766572999289345*^9, 3.7665729996020145`*^9}, { 3.7665730613126965`*^9, 3.7665730616706066`*^9}, {3.7840103262125545`*^9, 3.7840103546413517`*^9}, {3.784011309725755*^9, 3.7840113197719574`*^9}, { 3.784013374800973*^9, 3.7840133842981763`*^9}, {3.7840238533665447`*^9, 3.78402395932942*^9}, {3.784024091276659*^9, 3.784024112209529*^9}, { 3.7840242793219643`*^9, 3.784024296655184*^9}, {3.7840290670892677`*^9, 3.7840291348388853`*^9}, {3.784029222997594*^9, 3.784029542926179*^9}, { 3.784375172285057*^9, 3.784375319701829*^9}, {3.7843753678421807`*^9, 3.7843753788103914`*^9}, {3.7843754844339557`*^9, 3.784375827494117*^9}, { 3.784375862317687*^9, 3.7843759567563844`*^9}, {3.784376004941759*^9, 3.7843760080157185`*^9}, {3.784376101918992*^9, 3.7843761244332943`*^9}, { 3.784376181191763*^9, 3.7843762145091863`*^9}, {3.7843792489960337`*^9, 3.78437926273014*^9}, {3.7843793293934345`*^9, 3.784379368676588*^9}, { 3.7843796529835215`*^9, 3.7843796858862267`*^9}, {3.784450863324359*^9, 3.7844508986076546`*^9}, {3.7844510208392324`*^9, 3.784451027915551*^9}, { 3.7844511176315613`*^9, 3.7844511673791957`*^9}, {3.784451235055628*^9, 3.78445132575735*^9}, {3.784451995615477*^9, 3.7844520110330954`*^9}, { 3.7844522907551537`*^9, 3.7844523421551*^9}, {3.784700119490345*^9, 3.7847001627913013`*^9}, {3.7847004221290607`*^9, 3.7847004380767317`*^9}, 3.7847007913506136`*^9, {3.784781955129138*^9, 3.784781977787957*^9}, { 3.78488170216677*^9, 3.784881704210422*^9}, 3.784882130557441*^9, { 3.78488220347418*^9, 3.7848822064697027`*^9}, {3.784883393455822*^9, 3.784883458551924*^9}, 3.7848835306495824`*^9, {3.7848836822092113`*^9, 3.7848837303696923`*^9}, 3.7848838199009576`*^9, {3.7848842507527857`*^9, 3.7848842836585226`*^9}, 3.7848843847882996`*^9, {3.784884461405264*^9, 3.7848844645041113`*^9}, {3.784884559404122*^9, 3.7848845656634912`*^9}, { 3.7848852409944844`*^9, 3.7848852740337477`*^9}, {3.7848854548929386`*^9, 3.7848854893046365`*^9}, {3.7848856741783943`*^9, 3.784885691704702*^9}, { 3.784885809660874*^9, 3.784885811424426*^9}, {3.7848860031948376`*^9, 3.784886020570098*^9}, 3.7848861057105627`*^9, {3.7848861627726107`*^9, 3.7848862212876124`*^9}, {3.784886306497995*^9, 3.7848863509322224`*^9}, 3.784886472690192*^9, {3.7848866596243*^9, 3.784886664116289*^9}, { 3.7848866987282944`*^9, 3.7848867077911897`*^9}, {3.78488676128524*^9, 3.7848868667029366`*^9}, {3.7848869381224003`*^9, 3.7848869414281464`*^9}, {3.7848870104508753`*^9, 3.784887039889447*^9}, { 3.7848871795058794`*^9, 3.7848871976746817`*^9}, {3.7848872311446314`*^9, 3.78488724075662*^9}, 3.784887405188785*^9, {3.784887591926689*^9, 3.7848876119305134`*^9}, {3.784887676620901*^9, 3.7848876786672792`*^9}, { 3.78488771054331*^9, 3.784887714354906*^9}, {3.7848877625809546`*^9, 3.7848878103041153`*^9}, 3.7848878862881575`*^9, {3.787717235155089*^9, 3.787717269464238*^9}, {3.7877174592607603`*^9, 3.7877174674038067`*^9}, { 3.7877271032841845`*^9, 3.787727136247201*^9}, 3.787727355369296*^9, 3.7877274973278403`*^9, {3.787727855959008*^9, 3.78772792141208*^9}, 3.787728113487193*^9, {3.7877281704571557`*^9, 3.7877281735077004`*^9}, 3.7877282789827795`*^9, {3.7877286510229864`*^9, 3.787728665729192*^9}, { 3.7877287942225084`*^9, 3.787728807671986*^9}, {3.787729044867985*^9, 3.787729045536916*^9}, {3.787729589732438*^9, 3.7877296062090626`*^9}, { 3.787729794037467*^9, 3.7877297950347877`*^9}, {3.787729855548402*^9, 3.7877299039179935`*^9}, {3.7877300373241186`*^9, 3.787730068136018*^9}, { 3.7877301999859333`*^9, 3.7877302014150777`*^9}, {3.787732033225385*^9, 3.7877320471634016`*^9}, {3.787732077195259*^9, 3.7877320780358667`*^9}, 3.787732189759206*^9, {3.78773231889835*^9, 3.787732327710633*^9}, { 3.7877324857166643`*^9, 3.787732496655479*^9}, {3.7877325848303585`*^9, 3.78773258503596*^9}, {3.7877328504631166`*^9, 3.7877328625892415`*^9}, { 3.7877330254884944`*^9, 3.7877330271019044`*^9}, {3.787733136128061*^9, 3.7877331422258835`*^9}, {3.787733243513567*^9, 3.78773324558677*^9}, 3.787733310555999*^9, 3.7877334085329347`*^9, {3.7877337955932293`*^9, 3.7877337970498257`*^9}, {3.787733867727028*^9, 3.7877338687324905`*^9}, { 3.7877352224369583`*^9, 3.787735224161746*^9}, {3.787735343322833*^9, 3.787735348772827*^9}, {3.787735422704711*^9, 3.7877354268945775`*^9}, { 3.7877355100355635`*^9, 3.787735514671461*^9}, {3.7877356541994534`*^9, 3.7877356632141013`*^9}, 3.7877357913476543`*^9, 3.787736261837074*^9, { 3.7882542159043374`*^9, 3.7882542747998285`*^9}, {3.788254310967661*^9, 3.788254318430212*^9}, {3.788254585790197*^9, 3.7882545888318524`*^9}, { 3.7882547349987383`*^9, 3.788254735940298*^9}, 3.788254830063775*^9, 3.7882549155286837`*^9, {3.7882550121437798`*^9, 3.788255037735396*^9}, { 3.7882551764404287`*^9, 3.78825518352113*^9}, {3.7882552540030313`*^9, 3.788255290224329*^9}, {3.7882553843544893`*^9, 3.788255423248046*^9}, { 3.78825567982127*^9, 3.7882556852479534`*^9}, {3.7882557908576803`*^9, 3.7882558029800806`*^9}, {3.7882560240494256`*^9, 3.7882560388846164`*^9}, 3.788256102343512*^9, {3.788256161397396*^9, 3.7882561626372194`*^9}, { 3.7882562304311895`*^9, 3.78825629590362*^9}, {3.7882563614677362`*^9, 3.7882563620189795`*^9}, {3.7882564138122153`*^9, 3.7882564294158382`*^9}, {3.788256467457189*^9, 3.7882564889521217`*^9}, { 3.7882565883311844`*^9, 3.788256591497148*^9}, {3.7882568409513097`*^9, 3.7882568724526567`*^9}, {3.788256965258837*^9, 3.788256966444976*^9}, { 3.7882570073831463`*^9, 3.7882570497349973`*^9}, {3.7882570992487097`*^9, 3.788257144206352*^9}, {3.78825721252205*^9, 3.788257307277931*^9}, { 3.788257350410209*^9, 3.7882573617262745`*^9}, {3.788257424936472*^9, 3.788257434118204*^9}, {3.788276311330668*^9, 3.788276311647092*^9}, { 3.7882765465512347`*^9, 3.788276608568333*^9}, {3.7882767715851693`*^9, 3.7882768045752783`*^9}, {3.7882769342607436`*^9, 3.7882769409894867`*^9}, {3.7882770202208567`*^9, 3.7882770424485188`*^9}, {3.7882770760040703`*^9, 3.788277077341468*^9}, { 3.788277147336176*^9, 3.788277150397852*^9}, {3.7882772069909*^9, 3.7882772101572385`*^9}, {3.7882772503366175`*^9, 3.7882772773759403`*^9}, {3.7882773922958755`*^9, 3.7882773927832017`*^9}, {3.788277450684473*^9, 3.788277482126852*^9}, { 3.78827754293396*^9, 3.788277545027956*^9}, {3.7883214550230436`*^9, 3.7883214742097826`*^9}, {3.788321520104019*^9, 3.788321685390153*^9}, { 3.788321717307153*^9, 3.788321801831746*^9}, {3.788321836768508*^9, 3.788322037754008*^9}, {3.7883220686363816`*^9, 3.788322220085001*^9}, { 3.7883255906192427`*^9, 3.788325646609389*^9}, {3.7883257976991563`*^9, 3.788325804097658*^9}, {3.788325969279187*^9, 3.7883259830028267`*^9}, { 3.788326975877249*^9, 3.788326979070017*^9}, {3.788328539286415*^9, 3.788328618410488*^9}, {3.788328648595448*^9, 3.788328762662589*^9}, { 3.7883288060890923`*^9, 3.7883288805716724`*^9}, {3.7883319188300047`*^9, 3.78833193230753*^9}, {3.7883321144947567`*^9, 3.788332115050151*^9}, { 3.7883333680456443`*^9, 3.7883333686272163`*^9}, 3.7883336421611414`*^9, { 3.788333691323177*^9, 3.7883336916362*^9}, {3.788333797629262*^9, 3.7883338348662343`*^9}, {3.7883339555470386`*^9, 3.7883339660305166`*^9}, {3.7883340291758356`*^9, 3.788334031484354*^9}, { 3.788334368484807*^9, 3.7883343918754945`*^9}, {3.7883345963739557`*^9, 3.788334645315611*^9}, {3.788411405608647*^9, 3.788411409092114*^9}, { 3.7884115644712825`*^9, 3.7884115911998663`*^9}, {3.7884116673998833`*^9, 3.788411758799066*^9}, {3.788411985303985*^9, 3.788412002701314*^9}, { 3.78841218266156*^9, 3.788412217652734*^9}, {3.788412679618697*^9, 3.78841268296084*^9}, {3.788412968920223*^9, 3.7884129782039633`*^9}, { 3.7884155241723013`*^9, 3.7884155243798914`*^9}, 3.7884156619519596`*^9, { 3.7884162343262696`*^9, 3.788416236013459*^9}, {3.789022054245319*^9, 3.7890221116154556`*^9}, {3.7890222001685014`*^9, 3.789022205961149*^9}, { 3.789094077050009*^9, 3.7890940781167436`*^9}, {3.7890941254883175`*^9, 3.7890942919861226`*^9}, {3.789094340508856*^9, 3.789094543716852*^9}, { 3.789094583794143*^9, 3.7890947278803444`*^9}, {3.7890947714417076`*^9, 3.7890948342626343`*^9}, {3.789095197615344*^9, 3.789095215073329*^9}, { 3.789095256390032*^9, 3.78909525710861*^9}, {3.7890954241290827`*^9, 3.78909583987399*^9}, {3.789096056032333*^9, 3.7890960602768464`*^9}, { 3.7890960928429904`*^9, 3.789096098149865*^9}, {3.789096721918685*^9, 3.789096734998893*^9}, {3.7890967741973257`*^9, 3.78909683859006*^9}, { 3.789096947653244*^9, 3.789097122315098*^9}, {3.7890971528708224`*^9, 3.789097530683948*^9}, {3.7890975852885656`*^9, 3.7890975882562447`*^9}, { 3.7890976430709224`*^9, 3.789097656213524*^9}, {3.789107592314107*^9, 3.7891076537760305`*^9}, {3.789107685160589*^9, 3.789107760590632*^9}, { 3.7891078105008087`*^9, 3.789107846610609*^9}, {3.789107989236459*^9, 3.7891080001561875`*^9}, {3.7891082032172785`*^9, 3.7891082064574785`*^9}, {3.7891083013630204`*^9, 3.789108444864075*^9}, { 3.7891084751958127`*^9, 3.7891085010044174`*^9}, {3.7891085322441816`*^9, 3.7891085353767447`*^9}, {3.789108620037199*^9, 3.789108662297584*^9}, 3.7891087252471294`*^9, {3.789108773507248*^9, 3.7891088501491203`*^9}, { 3.7891088829987*^9, 3.789108918319019*^9}, {3.7891089606286983`*^9, 3.7891090044788837`*^9}, {3.789109048556943*^9, 3.7891091177554493`*^9}, { 3.7891091628149347`*^9, 3.7891092922346783`*^9}, {3.789109382870388*^9, 3.789109402625166*^9}, {3.7891111380334797`*^9, 3.7891113582877145`*^9}, { 3.789111396694514*^9, 3.7891114221541777`*^9}, {3.7891114539845037`*^9, 3.7891114952359962`*^9}, {3.789112929457416*^9, 3.7891129318274393`*^9}, { 3.789112963290578*^9, 3.7891131302196255`*^9}, {3.789113202949188*^9, 3.789113203379569*^9}, {3.7891144371217365`*^9, 3.789114518411393*^9}, { 3.789114638487608*^9, 3.78911468069436*^9}, {3.789114763918976*^9, 3.789114777923211*^9}, {3.789114809301983*^9, 3.7891148392057247`*^9}, { 3.7891148923150015`*^9, 3.789114904054755*^9}, {3.7891149560740595`*^9, 3.7891150071774015`*^9}, {3.789115109642312*^9, 3.7891151147637*^9}, { 3.7891185439211864`*^9, 3.789118561569729*^9}, {3.7891187834106455`*^9, 3.7891187854068985`*^9}, {3.7891188764873776`*^9, 3.7891188767373095`*^9}, {3.789121799028477*^9, 3.789121806719482*^9}, { 3.7891222627163153`*^9, 3.7891222774782734`*^9}, {3.7891223914541044`*^9, 3.7891224006004095`*^9}, {3.789122431773783*^9, 3.7891224422816577`*^9}, { 3.7891224731160736`*^9, 3.789122501042121*^9}, {3.7891226653529224`*^9, 3.7891226664045706`*^9}, 3.789122819901965*^9, {3.789122893844426*^9, 3.7891229543768473`*^9}, {3.7891229964274464`*^9, 3.7891231044294157`*^9}, {3.789123228485856*^9, 3.789123374714591*^9}, { 3.7891235661360893`*^9, 3.7891235688754067`*^9}, {3.8435393751961174`*^9, 3.84353937620569*^9}, {3.843539421737421*^9, 3.843539430280121*^9}, { 3.8435484777900076`*^9, 3.8435484882620373`*^9}, {3.8435489691083994`*^9, 3.843548981201047*^9}, {3.8435491420371304`*^9, 3.8435491556997023`*^9}, { 3.8435491977347035`*^9, 3.8435491982438793`*^9}, 3.8435492510860806`*^9, { 3.8435495081660933`*^9, 3.8435495131948795`*^9}, {3.8435495856936626`*^9, 3.843549589991126*^9}, {3.8435496998060937`*^9, 3.843549707814079*^9}, { 3.84355004136615*^9, 3.843550041760812*^9}, {3.843550160256809*^9, 3.8435501604677615`*^9}, {3.8435532120250945`*^9, 3.843553317388692*^9}, { 3.8435535239731655`*^9, 3.8435535314678483`*^9}, {3.8435535808757987`*^9, 3.843553663159541*^9}, {3.843553779645311*^9, 3.843553786004609*^9}, 3.843553906141655*^9, 3.84355405714793*^9, {3.843554149489615*^9, 3.8435541503712645`*^9}, {3.843554206843628*^9, 3.8435542071044455`*^9}, { 3.8435543508802266`*^9, 3.843554351606327*^9}, {3.843554424038799*^9, 3.8435544242271614`*^9}, {3.8435607207357883`*^9, 3.843560727908863*^9}, { 3.843560832774662*^9, 3.8435608400783997`*^9}, {3.843561442743278*^9, 3.8435614495857325`*^9}, {3.8435616862804203`*^9, 3.8435617473408427`*^9}, {3.8435618416220255`*^9, 3.84356184949818*^9}, { 3.843561965458202*^9, 3.843561967390591*^9}, {3.8435620399418516`*^9, 3.8435620427564726`*^9}, 3.8435620999099693`*^9, {3.843562319425266*^9, 3.843562335822353*^9}, {3.843562479271407*^9, 3.8435624872362185`*^9}, { 3.8435625915602407`*^9, 3.843562614304778*^9}, {3.843562735879742*^9, 3.843562741836786*^9}, {3.8436143557463255`*^9, 3.843614430899438*^9}, { 3.843614466526642*^9, 3.843614494745638*^9}, {3.84361472265639*^9, 3.8436147354884176`*^9}, {3.843614883845476*^9, 3.8436148880544443`*^9}, { 3.843615637703328*^9, 3.8436156940260696`*^9}, {3.843615818169777*^9, 3.8436159022117233`*^9}, {3.843621164525605*^9, 3.8436211674899387`*^9}, { 3.8436212248219557`*^9, 3.8436212383818884`*^9}, {3.843623395248974*^9, 3.8436234811296377`*^9}, 3.8436235228419657`*^9, {3.843710421018984*^9, 3.843710422106656*^9}, {3.843710498981309*^9, 3.843710537614964*^9}, { 3.843710579319264*^9, 3.843710645627423*^9}, {3.8437106875546417`*^9, 3.843710688153476*^9}, {3.843710725428294*^9, 3.843710785146202*^9}, { 3.843710821351383*^9, 3.8437110234294205`*^9}, {3.8437111173417163`*^9, 3.843711129714572*^9}, {3.843711236237468*^9, 3.8437112372387085`*^9}, { 3.8437113572143283`*^9, 3.8437113718734703`*^9}, {3.8437115790188246`*^9, 3.843711601014681*^9}, {3.843711741747123*^9, 3.843711755218405*^9}, { 3.8437118059023905`*^9, 3.8437118104255657`*^9}, {3.843711922772312*^9, 3.8437119230384417`*^9}, {3.8437119637523017`*^9, 3.8437119924289055`*^9}, {3.843712070094509*^9, 3.843712071922304*^9}, { 3.8437303811976614`*^9, 3.84373041381275*^9}, {3.843730744283455*^9, 3.8437307459908094`*^9}, {3.8437396200557556`*^9, 3.8437396419414387`*^9}, 3.843886670451059*^9, 3.8438867203204308`*^9, 3.84388678658553*^9, { 3.843886846967881*^9, 3.843886872522117*^9}, {3.8438869150992565`*^9, 3.8438869153482804`*^9}, {3.8443227935999327`*^9, 3.8443228741400695`*^9}, 3.84432529516883*^9, 3.84432540227769*^9, {3.844325496215137*^9, 3.8443254968116083`*^9}, {3.8443255607450824`*^9, 3.84432556531176*^9}, { 3.8443257292349973`*^9, 3.844325729451268*^9}, {3.8443271837653055`*^9, 3.8443271897353077`*^9}, 3.844327630363053*^9, 3.844327741570508*^9, { 3.8443278373713217`*^9, 3.84432790019408*^9}, {3.844328356730674*^9, 3.8443283589066696`*^9}, {3.8443286085720377`*^9, 3.844328633889926*^9}, { 3.844328780662943*^9, 3.844328797514555*^9}, 3.844328890335701*^9, 3.844329541823058*^9, 3.8443297290733314`*^9, 3.8443298258170156`*^9, 3.8443299792211103`*^9, {3.844330023182226*^9, 3.8443300241626625`*^9}, { 3.844330096584533*^9, 3.8443300969210296`*^9}, {3.8443301540407066`*^9, 3.844330184720361*^9}, 3.844330343560071*^9, 3.8443304466315546`*^9, 3.84438870778086*^9, {3.844388798979218*^9, 3.8443888166069407`*^9}, { 3.844388850689955*^9, 3.84438889324323*^9}, 3.8443891579040785`*^9, { 3.8443893096760817`*^9, 3.844389351546801*^9}, {3.8443894390725183`*^9, 3.8443894521629066`*^9}, 3.844389648527203*^9, {3.8443897876199207`*^9, 3.844389824625575*^9}, 3.8443900109195027`*^9, {3.844390820677456*^9, 3.8443908278248734`*^9}, {3.8443909207770224`*^9, 3.8443910088808312`*^9}, 3.844391050490807*^9, 3.844391867983138*^9, {3.844394157403282*^9, 3.844394211279689*^9}, {3.844394341187828*^9, 3.8443943435847197`*^9}, { 3.8443944350783367`*^9, 3.8443944719623637`*^9}, 3.844394554883594*^9, 3.844394790974487*^9, 3.844394878078925*^9, 3.844395085745798*^9, { 3.8443953351049013`*^9, 3.844395416952881*^9}, {3.844395746514305*^9, 3.844395749726533*^9}, 3.8443958397241535`*^9, {3.8443959211672125`*^9, 3.8443959248882713`*^9}, {3.8443960479537315`*^9, 3.844396058908654*^9}, 3.844396301967287*^9, 3.844396496810913*^9, {3.8443967365950084`*^9, 3.8443967370378094`*^9}, 3.8443972200199785`*^9, {3.8444115993210382`*^9, 3.8444115995187025`*^9}, {3.8444116721502385`*^9, 3.8444116838525047`*^9}, 3.8444117955604706`*^9, 3.8444120838091917`*^9, 3.8444123486564503`*^9, { 3.8444124716223226`*^9, 3.8444124796999335`*^9}, {3.8444125495255537`*^9, 3.844412567726659*^9}, 3.844412769483656*^9, {3.844499964651905*^9, 3.84449997397132*^9}, {3.844500043831334*^9, 3.8445000552814937`*^9}, 3.844500094473071*^9, {3.844500426135293*^9, 3.8445004336024866`*^9}, 3.844500503309535*^9, {3.84450071418834*^9, 3.8445007145632133`*^9}, 3.84450075086576*^9, {3.844500802343947*^9, 3.844500805685542*^9}, { 3.844500857916894*^9, 3.844500860801999*^9}, {3.8445009435074234`*^9, 3.8445010378770485`*^9}, {3.844501486443882*^9, 3.844501488956464*^9}, { 3.844501593768973*^9, 3.8445016087484674`*^9}, {3.8445019589459047`*^9, 3.8445019618400517`*^9}, {3.8445142536442575`*^9, 3.844514303852824*^9}, { 3.844514457425339*^9, 3.8445145337724867`*^9}, {3.8445146121090136`*^9, 3.844514612805125*^9}, {3.8445152618516026`*^9, 3.8445152626808715`*^9}, { 3.84451667854188*^9, 3.8445166978368387`*^9}, {3.8445168384209423`*^9, 3.8445168531952915`*^9}, 3.844516936102404*^9, {3.844517144912083*^9, 3.8445171602908783`*^9}, {3.844517313347111*^9, 3.844517374315425*^9}, { 3.844563740797083*^9, 3.844563842955555*^9}, {3.8445647632618103`*^9, 3.844564764558693*^9}, {3.844564893032794*^9, 3.8445648966363597`*^9}, 3.844566001126281*^9, {3.8445661160863905`*^9, 3.844566152674224*^9}, { 3.844566264323254*^9, 3.8445663747877293`*^9}, {3.8445664543449287`*^9, 3.844566491779601*^9}, {3.8445666670048437`*^9, 3.8445667378245735`*^9}, { 3.84456677184741*^9, 3.8445669208491745`*^9}, {3.8445681586856985`*^9, 3.8445681603926296`*^9}, {3.844568433360468*^9, 3.8445684731196322`*^9}, { 3.844568732407946*^9, 3.844568737446255*^9}, 3.844568945877626*^9, { 3.844569099528115*^9, 3.844569106514072*^9}, {3.8445691536508603`*^9, 3.8445691542699223`*^9}, {3.8445698639037194`*^9, 3.8445698642398653`*^9}, {3.844570012985527*^9, 3.84457001409229*^9}, { 3.844570136399222*^9, 3.84457022295549*^9}, {3.8445702927401485`*^9, 3.8445702943727927`*^9}, {3.8445703589410896`*^9, 3.844570359479988*^9}, { 3.844570433361819*^9, 3.844570434479186*^9}, {3.8445708385437922`*^9, 3.844570865548447*^9}, 3.8445719038536615`*^9, {3.84457369886672*^9, 3.844573716165063*^9}, {3.844573766574627*^9, 3.844573766741207*^9}, { 3.8445738390520935`*^9, 3.8445738397153697`*^9}, {3.844574626193658*^9, 3.844574626336315*^9}, 3.8445754934014444`*^9, {3.844575765512229*^9, 3.8445757670064106`*^9}, {3.8445797808579626`*^9, 3.8445797824906826`*^9}, {3.8445801889436493`*^9, 3.8445802499386616`*^9}, {3.8445802832055655`*^9, 3.8445804322445507`*^9}, {3.8445806095243425`*^9, 3.844580784490394*^9}, { 3.8445808660823193`*^9, 3.8445808672575426`*^9}, {3.8445810704154396`*^9, 3.844581084375619*^9}, {3.8445812578925953`*^9, 3.8445812836521835`*^9}, { 3.8445814486128545`*^9, 3.844581454694955*^9}, 3.8445815919025917`*^9, 3.8445816963679733`*^9, 3.8445818761230197`*^9, {3.844581973276004*^9, 3.84458197871758*^9}, {3.8445820591801286`*^9, 3.8445820669279137`*^9}, { 3.844766120152509*^9, 3.844766220989109*^9}, {3.8447666299757333`*^9, 3.844766632861744*^9}, {3.8447669924782996`*^9, 3.844766998824834*^9}, { 3.844767166360729*^9, 3.8447671685821986`*^9}, {3.8447672972644825`*^9, 3.844767489140806*^9}, {3.8447675202758884`*^9, 3.8447677076499157`*^9}, { 3.8447677386160955`*^9, 3.844767751930085*^9}, {3.8447678367494764`*^9, 3.8447678460718756`*^9}, {3.8447679275644846`*^9, 3.844767951604962*^9}, { 3.844823802025931*^9, 3.8448238152889323`*^9}, {3.844823957041947*^9, 3.8448239585139303`*^9}, {3.8448243004194326`*^9, 3.8448243149899445`*^9}, 3.8448243583360662`*^9, 3.844934867394837*^9, 3.845011466205801*^9, { 3.8450117207709064`*^9, 3.8450117245772066`*^9}, 3.845012400796516*^9, { 3.8450126148924513`*^9, 3.8450126150945854`*^9}, 3.845012697578274*^9, 3.845014370057255*^9, {3.8451838607018776`*^9, 3.845183871901742*^9}, { 3.845183946334877*^9, 3.84518395366415*^9}, {3.8451840514184165`*^9, 3.8451840516680007`*^9}, {3.8451841516428566`*^9, 3.845184154374053*^9}, { 3.845184357905266*^9, 3.8451843580652475`*^9}, {3.845184866633246*^9, 3.845184879284834*^9}, {3.8451856542674866`*^9, 3.845185661519927*^9}, 3.845185843485832*^9, 3.845188805837329*^9, {3.845208711326853*^9, 3.8452087400435753`*^9}, {3.8452088755132847`*^9, 3.845208885710583*^9}, { 3.8452090240719767`*^9, 3.8452090275669355`*^9}, {3.845209172626273*^9, 3.8452091859860196`*^9}, {3.845209314813764*^9, 3.8452093153470325`*^9}, { 3.8452093525944805`*^9, 3.845209356766179*^9}, {3.8452094333426437`*^9, 3.845209437202387*^9}, {3.845209581540662*^9, 3.8452096027603593`*^9}, { 3.845209834131934*^9, 3.845209849152528*^9}, {3.8452099760880327`*^9, 3.8452099795576005`*^9}, {3.84521001531735*^9, 3.845210023119549*^9}, { 3.8452101492309895`*^9, 3.8452101507171693`*^9}, {3.845210218508196*^9, 3.8452102205052843`*^9}, {3.845210284636221*^9, 3.8452102908524485`*^9}, { 3.8452104469844484`*^9, 3.845210448865471*^9}, {3.845210722276207*^9, 3.8452107618886013`*^9}, {3.8452108540735493`*^9, 3.8452108566476297`*^9}, 3.8452108885672226`*^9, 3.8452113817145267`*^9, {3.8452544138546667`*^9, 3.845254415221461*^9}, {3.8452544682669744`*^9, 3.845254497242826*^9}, { 3.845254813158949*^9, 3.845254813962109*^9}, {3.845255159389332*^9, 3.8452551602997503`*^9}, 3.8453713836088*^9, 3.8453728273858185`*^9, { 3.8453730671369777`*^9, 3.845373072521226*^9}, {3.8453735876364107`*^9, 3.8453736185890512`*^9}, 3.8453741162299414`*^9, {3.8453744985094943`*^9, 3.8453745049495716`*^9}, {3.845374723838398*^9, 3.8453747280613575`*^9}, 3.845375413181964*^9, {3.845375667874572*^9, 3.845375678759179*^9}, { 3.8453757305367117`*^9, 3.8453757318964834`*^9}, {3.845375795765346*^9, 3.8453759475892797`*^9}, 3.8453762911344376`*^9, {3.845376343496214*^9, 3.845376394269949*^9}, 3.8454413952988825`*^9, {3.8454605213498316`*^9, 3.845460526259059*^9}, {3.8454605688149014`*^9, 3.845460571220699*^9}, { 3.8454607495560193`*^9, 3.8454607590768337`*^9}, {3.845462509735139*^9, 3.845462509985168*^9}, {3.8454655927984095`*^9, 3.8454655941092844`*^9}, { 3.8454656351939297`*^9, 3.8454657716449366`*^9}, {3.8454659031914606`*^9, 3.8454659091378775`*^9}, {3.8454660264366956`*^9, 3.845466050881938*^9}, { 3.8454670388067656`*^9, 3.8454670407645473`*^9}, {3.8454695818972855`*^9, 3.8454695927423058`*^9}, 3.8458628196288977`*^9, {3.8458629698321857`*^9, 3.8458629918325853`*^9}, {3.84586302904202*^9, 3.845863076602502*^9}, { 3.8458631448574963`*^9, 3.8458632007479205`*^9}, {3.845863269580724*^9, 3.8458632726734605`*^9}, {3.845863307748892*^9, 3.8458633353940535`*^9}, { 3.845863395099148*^9, 3.8458634980995226`*^9}, 3.845863530554716*^9, { 3.8458725905500464`*^9, 3.8458726644563165`*^9}, {3.845872707441972*^9, 3.8458727236944923`*^9}, {3.8458728091280556`*^9, 3.845872842539483*^9}, 3.8458728978104*^9, {3.8458730281409388`*^9, 3.8458730351358786`*^9}, { 3.851830237371579*^9, 3.85183025145358*^9}, {3.8518305063752985`*^9, 3.8518305308315496`*^9}, {3.85183140764212*^9, 3.85183143774364*^9}, { 3.8518315502903214`*^9, 3.851831695377967*^9}, {3.8518317645218363`*^9, 3.8518318373277397`*^9}, {3.851831868636403*^9, 3.8518319116186705`*^9}, 3.8518326393678236`*^9, {3.8518327098385625`*^9, 3.8518327278877563`*^9}, { 3.8518328055583944`*^9, 3.8518328759243045`*^9}, {3.8518329524762464`*^9, 3.851833079376422*^9}, {3.8518331291035*^9, 3.8518331302995796`*^9}, { 3.851833160508073*^9, 3.8518331634172173`*^9}, {3.851833237532813*^9, 3.851833414086164*^9}, {3.851833456249548*^9, 3.8518334931437445`*^9}, { 3.851833544068002*^9, 3.8518335453597345`*^9}, {3.851833575552421*^9, 3.8518336800045*^9}, {3.8518337143881235`*^9, 3.8518337258246155`*^9}, { 3.8518346908371735`*^9, 3.8518347174611683`*^9}, {3.8518347530809784`*^9, 3.8518347692487164`*^9}, {3.8518349597532296`*^9, 3.851835071000081*^9}}, CellLabel-> "In[205]:=",ExpressionUUID->"a180b637-52a4-4fc9-9aad-d0cc1e6f83a4"] }, Closed]], Cell[CellGroupData[{ Cell["SHELL ELEMENT (stab) defs ", "Subsection", CellChangeTimes->{{3.6302475626780834`*^9, 3.6302475636452847`*^9}, { 3.6303896204112215`*^9, 3.630389621175623*^9}, {3.7658855359334097`*^9, 3.7658855563942738`*^9}, {3.7882511594490995`*^9, 3.788251160663724*^9}, { 3.7883213876221266`*^9, 3.788321388914168*^9}, {3.7890220324441195`*^9, 3.789022033389088*^9}, {3.852336979003788*^9, 3.8523369803815904`*^9}},ExpressionUUID->"66dd7a59-1024-4a03-aab8-\ a2ce73879f4a"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "r\[Gamma]", ",", "FF", ",", "FFINV", ",", "jac", ",", "NN", ",", "u", ",", "ux", ",", "uy", ",", "uz", ",", "v", ",", "vx", ",", "vy", ",", "vz", ",", "w", ",", "wx", ",", "wy", ",", "wz", ",", "\[Phi]", ",", "\[Phi]x", ",", "\[Phi]y", ",", "\[Phi]z", ",", "\[Theta]", ",", "\[Theta]x", ",", "\[Theta]y", ",", "\[Theta]z", ",", "AA", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Phi]", ",", "wc", ",", "E\[Sigma]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wsta", ",", "\[Delta]wmap", ",", "\[Epsilon]\[Epsilon]", ",", "\[Kappa]\[Kappa]", ",", "\[Gamma]\[Gamma]", ",", "MM", ",", "QQ", ",", "tri", ",", RowBox[{"mat", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}]}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"ARNOLD", "-", "FALCK"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "mapping", " ", "for", " ", "the", " ", "plate", " ", "geometry"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"r\[Alpha]", ",", "r\[Beta]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Gamma]", "=", RowBox[{"r\[Alpha]", StyleBox["\[Cross]", "OperatorCharacter"], "r\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Sqrt", "[", RowBox[{"r\[Gamma]", ".", "r\[Gamma]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"r\[Alpha]", ",", "r\[Beta]", ",", RowBox[{"r\[Gamma]", "/", "jac"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", " ", RowBox[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "approximations", "*)"}], "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"wc", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "projection", "*)"}], "\[IndentingNewLine]", RowBox[{"AA", "=", RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", "jac", ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]"}], "}"}], "=", RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]"}], "}"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "/", "AA"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "derivatives", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"ux", ",", "uy", ",", "uz"}], "}"}], "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}], ",", "0"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"vx", ",", "vy", ",", "vz"}], "}"}], "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}], ",", "0"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"wx", ",", "wy", ",", "wz"}], "}"}], "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}], ",", "0"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]x", ",", "\[Phi]y", ",", "\[Phi]z"}], "}"}], "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}], ",", "0"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Theta]x", ",", "\[Theta]y", ",", "\[Theta]z"}], "}"}], "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Theta]"}], ",", "0"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"strain", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]\[Epsilon]", "=", RowBox[{"{", RowBox[{"ux", ",", "vy", ",", RowBox[{"uy", "+", "vx"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]\[Kappa]", "=", RowBox[{"{", RowBox[{"\[Theta]x", ",", RowBox[{"-", "\[Phi]y"}], ",", RowBox[{ RowBox[{"-", "\[Phi]x"}], "+", "\[Theta]y"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Gamma]\[Gamma]", "=", RowBox[{ RowBox[{"{", RowBox[{"wx", ",", "wy"}], "}"}], "+", RowBox[{"{", RowBox[{"\[Pi]\[Theta]", ",", RowBox[{"-", "\[Pi]\[Phi]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"E\[Sigma]", "=", RowBox[{ RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "\[Nu]\[Nu]", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Nu]\[Nu]", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "/", "2"}]}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"MM", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", "E\[Sigma]"}], ")"}], ".", "\[Kappa]\[Kappa]"}]}], ";", "\[IndentingNewLine]", RowBox[{"QQ", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "tt", "*", "GG", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"tt", "*", RowBox[{"E\[Sigma]", ".", "\[Epsilon]\[Epsilon]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Epsilon]\[Epsilon]", "]"}], ".", "NN"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Kappa]\[Kappa]", "]"}], ".", "MM"}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "\[Gamma]\[Gamma]", "]"}], ".", "QQ"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"fX", " ", ",", "fY", ",", "fZ"}], "}"}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wsta", "=", RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"wx", ",", "wy"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], ",", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}]}], "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{"wx", ",", "wy"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wmap", "=", RowBox[{ RowBox[{"-", "0.1"}], "*", RowBox[{"\[Delta]", "[", RowBox[{"wc", "-", "w"}], "]"}], "*", RowBox[{"(", RowBox[{"wc", "-", "w"}], ")"}], "*", RowBox[{"tt", "/", "AA"}], "*", "EE"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wsta"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI1", ",", RowBox[{"\[Delta]wmap", "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "n\[Alpha]", ",", "n\[Beta]", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "NN", ",", "mat", ",", "MM", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "r\[Gamma]", ",", "rn", ",", "jac", ",", "h\[Alpha]", ",", "e\[Alpha]", ",", "h\[Beta]", ",", "h\[Gamma]", ",", "e\[Beta]", ",", "en", ",", "e\[Gamma]", ",", "FF", ",", "\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]", ",", "edg", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "\[Pi]u", ",", "\[Pi]v", ",", "\[Pi]w", ",", "\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]", ",", "f\[Alpha]", ",", "f\[Gamma]", ",", "fn", ",", "m\[Alpha]", ",", "m\[Gamma]", ",", "mn", ",", "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]", ",", "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]", ",", "\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]", ",", "GG", ",", "N\[Alpha]\[Alpha]", ",", "N\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Gamma]", ",", "N\[Gamma]\[Alpha]", ",", "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]", ",", "Q\[Alpha]", ",", "Q\[Gamma]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wsta", ",", "\[Delta]wmap", ",", "AA"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"mat", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]", "=", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}]}], ";", " ", RowBox[{"r\[Beta]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Norm", "[", "r\[Beta]", "]"}]}], ";", " ", RowBox[{"h\[Alpha]", "=", RowBox[{"Norm", "[", "r\[Alpha]", "]"}]}], ";", RowBox[{"jac", "=", RowBox[{"Norm", "[", RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"e\[Alpha]", "=", RowBox[{"r\[Alpha]", "/", "h\[Alpha]"}]}], ";", RowBox[{"e\[Beta]", "=", RowBox[{"r\[Beta]", "/", "h\[Beta]"}]}], ";", " ", RowBox[{"en", "=", RowBox[{ RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}], " ", "/", "jac"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r\[Gamma]", "=", RowBox[{"r\[Beta]", "-", RowBox[{ RowBox[{"(", RowBox[{"r\[Beta]", ".", "e\[Alpha]"}], ")"}], " ", "e\[Alpha]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Gamma]", "=", RowBox[{"Norm", "[", "r\[Gamma]", "]"}]}], ";", RowBox[{"e\[Gamma]", "=", RowBox[{"r\[Gamma]", "/", "h\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", "e\[Gamma]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]\[Gamma]", ",", "\[Beta]\[Gamma]"}], "}"}], "=", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Alpha]"}], ",", RowBox[{"r\[Alpha]", ".", "r\[Beta]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Beta]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Beta]"}]}], "}"}]}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"r\[Alpha]", ".", "r\[Gamma]"}], ",", RowBox[{"r\[Beta]", ".", "r\[Gamma]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"edg", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Sort", "[", "#", "]"}], "&"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], ",", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"uX", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"uY", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"(", RowBox[{"mat", ".", "NN"}], ")"}], ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"#", ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", "#", "]"}]}], "]"}], "&"}], ",", "edg"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "3"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"\[Theta]Z", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"projection", " ", "mapping"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Pi]\[Phi]", "=", RowBox[{ RowBox[{ RowBox[{"\[Theta]X", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], "/", "60"}], "+", " ", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Theta]", "=", RowBox[{ RowBox[{ RowBox[{"\[Theta]Y", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], "/", "60"}], "+", " ", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Psi]", "=", RowBox[{ RowBox[{ RowBox[{"\[Theta]Z", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], "/", "60"}], "+", " ", RowBox[{"Mean", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "3"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Pi]u", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]v", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]w", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]u", ",", "\[Pi]v", ",", "\[Pi]w"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"\[Pi]u", ",", "\[Pi]v", ",", "\[Pi]w"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"\[Pi]\[Phi]", ",", "\[Pi]\[Theta]", ",", "\[Pi]\[Psi]"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Gamma]", ",", "fn"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"strain", " ", "measures", " ", "with", " ", "non"}], "-", RowBox[{"symmetric", " ", "\[Epsilon]"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}]}]}], ")"}], "/", "h\[Gamma]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], "/", "h\[Alpha]"}], "-", "\[Psi]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}]}]}], ")"}], "/", "h\[Gamma]"}], "+", "\[Psi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}]}]}], ")"}]}], "/", "h\[Gamma]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", " ", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Theta]"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], "/", "h\[Alpha]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], "+", "\[Pi]\[Theta]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}]}]}], ")"}], "/", "h\[Gamma]"}], "-", "\[Pi]\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "stress", " ", "resultants", " ", "with", " ", "a", " ", "nonsymmetric", " ", "N"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Alpha]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Gamma]\[Gamma]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Gamma]\[Gamma]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Gamma]\[Gamma]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Gamma]", "=", RowBox[{ "tt", "*", "2", " ", "GG", "*", "\[Epsilon]\[Alpha]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Gamma]\[Alpha]", "=", RowBox[{ "tt", "*", "2", " ", "GG", "*", "\[Epsilon]\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Alpha]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Gamma]\[Gamma]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Gamma]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Gamma]\[Gamma]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Gamma]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", " ", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "\[Nu]\[Nu]"}]}], ")"}]}], "*", "\[Kappa]\[Alpha]\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{ RowBox[{"5", "/", "6"}], " ", "*", "GG", "*", "tt", "*", "\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Gamma]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Gamma]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Gamma]\[Gamma]", ",", "\[Epsilon]\[Alpha]\[Gamma]", ",", "\[Epsilon]\[Gamma]\[Alpha]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "N\[Alpha]\[Alpha]", ",", "N\[Gamma]\[Gamma]", ",", "N\[Alpha]\[Gamma]", ",", "N\[Gamma]\[Alpha]"}], "}"}]}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Gamma]\[Gamma]", ",", "\[Kappa]\[Alpha]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Gamma]\[Gamma]", ",", "M\[Alpha]\[Gamma]"}], "}"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Gamma]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Gamma]"}], "}"}]}]}]}], ";", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Gamma]", ",", "fn"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wsta", "=", RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}]}]}], ")"}], "/", "h\[Gamma]"}]}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"N\[Alpha]\[Alpha]", ",", "N\[Alpha]\[Gamma]"}], "}"}], ",", RowBox[{"{", RowBox[{"N\[Gamma]\[Alpha]", ",", "N\[Gamma]\[Gamma]"}], "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}]}], "+", RowBox[{"\[Beta]\[Gamma]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}]}]}], ")"}], "/", "h\[Gamma]"}]}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wmap", "=", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "/", "100000"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]u", "-", "u"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]u", "-", "u"}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]v", "-", "v"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]v", "-", "v"}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"\[Pi]w", "-", "w"}], "]"}], "*", RowBox[{"(", RowBox[{"\[Pi]w", "-", "w"}], ")"}]}]}], ")"}], "*", "tt", "*", RowBox[{"EE", "/", "jac"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TRI3", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wsta", "+", "\[Delta]wmap"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.4426474258030453`*^9, {3.4444401255942*^9, 3.4444401388073997`*^9}, { 3.4444401803034*^9, 3.4444401844062*^9}, 3.4444402418922*^9, { 3.4444402805022*^9, 3.4444403134026003`*^9}, {3.4444403443062*^9, 3.4444404484049997`*^9}, {3.444483267101*^9, 3.444483267335*^9}, { 3.4444833136046*^9, 3.4444835622998*^9}, {3.4444836421094*^9, 3.4444837777981997`*^9}, {3.444483920429*^9, 3.4444839412237997`*^9}, 3.4444842905546*^9, {3.4444843207406*^9, 3.4444844162282*^9}, { 3.4444844465078*^9, 3.4444844624354*^9}, {3.4444845255998*^9, 3.4444845894505997`*^9}, {3.4444846290746*^9, 3.444484933025*^9}, { 3.4444849790917997`*^9, 3.4444851148742*^9}, {3.444534936054*^9, 3.4445349675348*^9}, {3.4445355821731997`*^9, 3.44453585174*^9}, { 3.4445372162198*^9, 3.4445372264378*^9}, 3.444537384731*^9, { 3.4445377585382*^9, 3.4445377605818*^9}, {3.4445379733658*^9, 3.4445379736934*^9}, {3.4445380176762*^9, 3.444538032777*^9}, { 3.4445381079222*^9, 3.4445381581386003`*^9}, {3.4445382726456003`*^9, 3.4445382910067997`*^9}, {3.4445383401312*^9, 3.4445383475880003`*^9}, { 3.444538438458*^9, 3.4445384464608*^9}, {3.4445385680783997`*^9, 3.4445385687648*^9}, {3.4445389411991997`*^9, 3.4445389431024*^9}, { 3.444539746605*^9, 3.4445397807846003`*^9}, {3.4445408839765997`*^9, 3.4445409234133997`*^9}, {3.4445409681698*^9, 3.4445409932702*^9}, { 3.4445415452906*^9, 3.4445415706717997`*^9}, {3.4445416647242002`*^9, 3.4445416909477997`*^9}, {3.4445417660150003`*^9, 3.444541788557*^9}, { 3.4445420906977997`*^9, 3.444542104847*^9}, {3.4445421885878*^9, 3.4445421941414003`*^9}, {3.4445422252166*^9, 3.4445422386014*^9}, { 3.444542280425*^9, 3.4445423014538*^9}, {3.444542455769*^9, 3.4445424578282003`*^9}, {3.4445431739214*^9, 3.444543175809*^9}, { 3.4445647020962*^9, 3.4445648405618*^9}, {3.4445648825414*^9, 3.4445648858486*^9}, {3.4445649382646*^9, 3.4445651882702*^9}, { 3.4446164822206*^9, 3.4446165344494*^9}, {3.4446166121842003`*^9, 3.4446166738822002`*^9}, {3.4446167223046*^9, 3.4446168047974*^9}, { 3.444616843033*^9, 3.444616906447*^9}, {3.4446444694708*^9, 3.4446444700948*^9}, {3.4446477738310003`*^9, 3.4446477939862003`*^9}, { 3.4446478467298*^9, 3.4446478681018*^9}, 3.4446480456142*^9, { 3.4446487557418003`*^9, 3.4446487636198*^9}, 3.4446488179974003`*^9, { 3.4446488971205997`*^9, 3.4446489152478*^9}, {3.4446490003458*^9, 3.4446490008294*^9}, {3.4447042728942003`*^9, 3.4447042751562*^9}, { 3.4447044703278*^9, 3.4447044865362*^9}, 3.4447046475282*^9, 3.4447047993786*^9, {3.444704908329*^9, 3.4447049292642*^9}, { 3.4447049861926003`*^9, 3.4447049877214003`*^9}, {3.4447050279296*^9, 3.4447050419695997`*^9}, {3.4447053486656*^9, 3.4447053739376*^9}, 3.4447054561963997`*^9, 3.44470561612*^9, {3.4472133996876*^9, 3.4472134108571997`*^9}, {3.4472134470179996`*^9, 3.4472134648332*^9}, { 3.4472135032872*^9, 3.4472135245344*^9}, {3.4472136963059998`*^9, 3.4472137794384003`*^9}, {3.4472138235708*^9, 3.4472138388900003`*^9}, { 3.4472139099792*^9, 3.4472141367096*^9}, {3.447214202682*^9, 3.4472142975924*^9}, {3.4472144187732*^9, 3.4472145910284*^9}, { 3.4472146560492*^9, 3.4472147023968*^9}, {3.447214803594*^9, 3.4472148728736*^9}, {3.4472149156956*^9, 3.447214940484*^9}, { 3.447216227284*^9, 3.4472162419948*^9}, {3.4472163068908*^9, 3.4472163720832*^9}, {3.4472164665880003`*^9, 3.447216530392*^9}, { 3.4472166237268*^9, 3.4472167058452*^9}, 3.4472167362808*^9, { 3.4472171394658003`*^9, 3.4472171532874002`*^9}, {3.4472172028993998`*^9, 3.4472172216661997`*^9}, {3.4472172524606*^9, 3.4472172690278*^9}, { 3.4472173209133997`*^9, 3.4472173334245996`*^9}, {3.4472173920846*^9, 3.447217404861*^9}, {3.4472179572548*^9, 3.4472180351456003`*^9}, { 3.4472509764091997`*^9, 3.4472511017396*^9}, {3.4473910422216*^9, 3.4473912901524*^9}, 3.4473918688344*^9, {3.447392021185*^9, 3.4473920346633997`*^9}, {3.4473921383304*^9, 3.4473921479088*^9}, { 3.4473923024112*^9, 3.4473923734379997`*^9}, {3.4473928098168*^9, 3.4473928648691998`*^9}, {3.4473931872432003`*^9, 3.4473932461800003`*^9}, {3.4473933026675997`*^9, 3.4473934579812*^9}, { 3.4473935755271997`*^9, 3.447393742572*^9}, {3.4473939032676*^9, 3.4473939384144*^9}, {3.447395257644*^9, 3.4473953141628*^9}, { 3.4473954231132*^9, 3.4473954756384*^9}, {3.4473955348716*^9, 3.4473955723272*^9}, {3.447395648502*^9, 3.4473957588876*^9}, { 3.4473957903996*^9, 3.4473958488372*^9}, 3.4473962894154*^9, { 3.447396350817*^9, 3.447396352611*^9}, {3.4474625379146*^9, 3.4474625637326*^9}, {3.558360651728078*^9, 3.558360652102478*^9}, { 3.5619791319820857`*^9, 3.561979135788492*^9}, 3.561979369382504*^9, { 3.5619794930439215`*^9, 3.5619795010155354`*^9}, {3.561979569218855*^9, 3.56197960614412*^9}, {3.5619797417551584`*^9, 3.5619797448751636`*^9}, { 3.618719065033702*^9, 3.618719075426296*^9}, {3.6187194011669273`*^9, 3.6187194449454317`*^9}, {3.6187196998040085`*^9, 3.6187197102436056`*^9}, {3.618719902254588*^9, 3.6187199711455283`*^9}, { 3.618722365406472*^9, 3.6187225412555304`*^9}, {3.6187226885009522`*^9, 3.6187227109872384`*^9}, {3.618722756922866*^9, 3.6187231317203026`*^9}, { 3.618723424250035*^9, 3.6187234267291765`*^9}, {3.6187235105259695`*^9, 3.6187236491028957`*^9}, {3.618723691580325*^9, 3.618723745975436*^9}, { 3.618723778837316*^9, 3.6187238310002995`*^9}, {3.6187239055875654`*^9, 3.618723940035536*^9}, {3.6187239782667227`*^9, 3.6187240219352207`*^9}, { 3.618724166762504*^9, 3.618724177411113*^9}, {3.618729321696159*^9, 3.618729328067523*^9}, 3.618729374058154*^9, {3.6187294379838104`*^9, 3.618729708464281*^9}, {3.6187297631904106`*^9, 3.618729773195983*^9}, { 3.618729822648812*^9, 3.6187299321490746`*^9}, {3.618729984399063*^9, 3.61873000654133*^9}, {3.6187300746012225`*^9, 3.6187300860458775`*^9}, { 3.618731390835507*^9, 3.6187315116174154`*^9}, {3.618731747324897*^9, 3.6187318214091344`*^9}, {3.6187318769243097`*^9, 3.618732065297084*^9}, { 3.6187321012351394`*^9, 3.618732157420353*^9}, {3.618732188384124*^9, 3.6187322435542793`*^9}, {3.6187322786112847`*^9, 3.6187325478446836`*^9}, {3.6187325819856367`*^9, 3.6187326817653437`*^9}, {3.618732810863728*^9, 3.61873282594359*^9}, { 3.6187336474335766`*^9, 3.618733754678711*^9}, {3.618733827497876*^9, 3.61873396201257*^9}, {3.6187342020362988`*^9, 3.618734236455267*^9}, 3.618734298201799*^9, {3.618734712498495*^9, 3.618734712716508*^9}, 3.6187347739640107`*^9, {3.618738817361748*^9, 3.6187388333816643`*^9}, { 3.6187391349349127`*^9, 3.6187391457955337`*^9}, {3.618739376900752*^9, 3.618739397023903*^9}, {3.618739528394417*^9, 3.618739534809784*^9}, { 3.618739972366811*^9, 3.61873997340687*^9}, {3.6187400416617737`*^9, 3.618740043022852*^9}, {3.6187400971579485`*^9, 3.618740107902563*^9}, { 3.6187401713671927`*^9, 3.6187401723312483`*^9}, {3.6187402613443394`*^9, 3.618740268819767*^9}, {3.6187403697625403`*^9, 3.6187404057615995`*^9}, { 3.618740488277319*^9, 3.618740516244919*^9}, {3.618740647782442*^9, 3.6187406551668644`*^9}, 3.6187407823021364`*^9, {3.6187418050786357`*^9, 3.618741805749674*^9}, {3.6187418557605343`*^9, 3.6187419895921893`*^9}, { 3.618742022944097*^9, 3.61874204379729*^9}, {3.6187420836395683`*^9, 3.618742103384698*^9}, {3.620462440882641*^9, 3.6204624460519366`*^9}, { 3.6204624990259666`*^9, 3.620462576450395*^9}, {3.620463682857678*^9, 3.620463713336421*^9}, 3.6204637901188126`*^9, {3.620464238835478*^9, 3.62046424411378*^9}, 3.628912429385081*^9, {3.6289135207155013`*^9, 3.6289135210805225`*^9}, 3.6289497746958513`*^9, 3.6289498371774254`*^9, { 3.62894988410911*^9, 3.6289500319795675`*^9}, {3.6289501333883677`*^9, 3.628950183744248*^9}, {3.6289503323017445`*^9, 3.628950390181055*^9}, { 3.6289505050536256`*^9, 3.6289505113579865`*^9}, {3.62895070863527*^9, 3.6289507095043197`*^9}, {3.628951013180689*^9, 3.62895101407374*^9}, { 3.629190743153632*^9, 3.629190816645361*^9}, {3.6291909709608326`*^9, 3.629190981678051*^9}, {3.629191034624544*^9, 3.6291910410049553`*^9}, { 3.6293846391370816`*^9, 3.629384641102685*^9}, {3.6294628543371735`*^9, 3.629462867097191*^9}, {3.629468063172048*^9, 3.6294681151669397`*^9}, { 3.6295205836757097`*^9, 3.6295206295085897`*^9}, {3.6295206788826766`*^9, 3.6295207067911253`*^9}, {3.6295207408927855`*^9, 3.629520753700408*^9}, { 3.629521020590745*^9, 3.6295210354395943`*^9}, {3.6295211107369013`*^9, 3.62952114882508*^9}, {3.6295212327348795`*^9, 3.6295212477237363`*^9}, { 3.6295213424816394`*^9, 3.629521343230441*^9}, {3.6295215363119802`*^9, 3.6295216753550243`*^9}, {3.629521922272258*^9, 3.6295219939855833`*^9}, { 3.6295220298188467`*^9, 3.629522446058778*^9}, {3.629522499348471*^9, 3.629522604352256*^9}, {3.629522755188921*^9, 3.62952288580795*^9}, { 3.629522918084407*^9, 3.6295233421087513`*^9}, {3.6295233808436193`*^9, 3.629523390936837*^9}, {3.629523424274096*^9, 3.6295234533369465`*^9}, { 3.6295235190130625`*^9, 3.629523521680667*^9}, 3.6295235894315863`*^9, { 3.6295237270706277`*^9, 3.629523799454755*^9}, {3.6295238514808464`*^9, 3.629523883460902*^9}, {3.6295239376085978`*^9, 3.6295239442386093`*^9}, { 3.6295241089904985`*^9, 3.629524177537019*^9}, 3.629524211888279*^9, { 3.629524277423994*^9, 3.629524396904604*^9}, {3.6295244794839497`*^9, 3.6295246248450055`*^9}, 3.629524657090262*^9, {3.6295259599109507`*^9, 3.629526013465844*^9}, {3.6295261092188125`*^9, 3.629526201414974*^9}, 3.6295263436092243`*^9, {3.6295263910333076`*^9, 3.629526583303645*^9}, { 3.629526616672104*^9, 3.629526647653758*^9}, {3.629526687558628*^9, 3.629526744888729*^9}, {3.629526804075233*^9, 3.6295268598453307`*^9}, { 3.6295269393898706`*^9, 3.6295269586559043`*^9}, {3.6295271490074387`*^9, 3.6295272149019547`*^9}, {3.6295272553684254`*^9, 3.6295272827620735`*^9}, {3.6295274137087035`*^9, 3.6295274761244135`*^9}, {3.6295275252801*^9, 3.6295279912529182`*^9}, { 3.6295281572216096`*^9, 3.629528160435215*^9}, {3.6295282905550437`*^9, 3.6295284308616905`*^9}, 3.6295285402022824`*^9, {3.629528582088356*^9, 3.629528616798417*^9}, {3.6295287666834803`*^9, 3.6295290316343455`*^9}, { 3.629529086515242*^9, 3.629529118432898*^9}, {3.6295291548121614`*^9, 3.629529292794404*^9}, {3.6295293426208916`*^9, 3.6295293491261034`*^9}, { 3.629529420699029*^9, 3.629529571535694*^9}, {3.6295296539506383`*^9, 3.629529656103442*^9}, {3.6295296894407005`*^9, 3.629529692295506*^9}, { 3.6295297445555973`*^9, 3.629529766426836*^9}, {3.6295298053333044`*^9, 3.6295298209489317`*^9}, {3.6295308380551186`*^9, 3.6295308386635194`*^9}, {3.629532377840223*^9, 3.6295323811630287`*^9}, { 3.629532480020402*^9, 3.629532482454006*^9}, {3.629532520720874*^9, 3.629532564619351*^9}, {3.62953259842461*^9, 3.6295326002654133`*^9}, { 3.6295326327758703`*^9, 3.6295326715107384`*^9}, {3.629532742428463*^9, 3.6295328288058147`*^9}, {3.6295329692184625`*^9, 3.6295330530062094`*^9}, {3.6295331824396367`*^9, 3.629533193562456*^9}, 3.6295350321720915`*^9, 3.629535158485513*^9, {3.629535245471266*^9, 3.6295352687465067`*^9}, {3.62953541293756*^9, 3.629535446384019*^9}, { 3.6295355043381205`*^9, 3.6295355262249594`*^9}, {3.629543790136781*^9, 3.629543791181983*^9}, {3.629543871350524*^9, 3.629544001673153*^9}, { 3.6295446682009234`*^9, 3.629544668466124*^9}, {3.6296010216162376`*^9, 3.6296010236442413`*^9}, {3.629601079336339*^9, 3.6296010902875586`*^9}, 3.6296011425476503`*^9, {3.6296043522397404`*^9, 3.629604399031022*^9}, { 3.629623884428093*^9, 3.629623914723346*^9}, {3.6296239662190366`*^9, 3.6296239738006496`*^9}, {3.6296240514731865`*^9, 3.6296240920176573`*^9}, {3.629624125947717*^9, 3.629624369432945*^9}, { 3.6296256512247963`*^9, 3.6296256817072496`*^9}, {3.6296260472626915`*^9, 3.629626047434292*^9}, {3.629628055568204*^9, 3.629628056098605*^9}, { 3.6296280911206665`*^9, 3.6296281088266973`*^9}, {3.6296281406819534`*^9, 3.629628273032586*^9}, {3.629628378831972*^9, 3.6296283814995766`*^9}, { 3.629628459562114*^9, 3.629628466379326*^9}, {3.629628519419419*^9, 3.6296285390754533`*^9}, {3.629633008133008*^9, 3.629633008835009*^9}, { 3.6296337764967575`*^9, 3.6296338344040594`*^9}, {3.6296342997684765`*^9, 3.629634432150309*^9}, {3.629634494035618*^9, 3.6296345320060844`*^9}, { 3.629634594499794*^9, 3.629634812182576*^9}, {3.6296348599810605`*^9, 3.6296348746918864`*^9}, {3.6296349071867433`*^9, 3.629635023172947*^9}, 3.6296350995818815`*^9, {3.6296363797201295`*^9, 3.6296363868961425`*^9}, { 3.629636462025874*^9, 3.6296364833355117`*^9}, {3.629636555922439*^9, 3.62963656780966*^9}, {3.629636770469616*^9, 3.629636774151222*^9}, { 3.6296369192782774`*^9, 3.6296369318830996`*^9}, {3.629637058539722*^9, 3.6296370719401455`*^9}, {3.629637278172508*^9, 3.629637286814923*^9}, { 3.6296376418091464`*^9, 3.629637662385583*^9}, {3.629637773551378*^9, 3.629637795360216*^9}, {3.6296390041751394`*^9, 3.629639039571602*^9}, 3.6296393829750047`*^9, {3.6296395546065063`*^9, 3.6296395649961243`*^9}, { 3.62964113386068*^9, 3.6296412507048855`*^9}, {3.629641303167777*^9, 3.629641313744596*^9}, {3.6296416285116315`*^9, 3.629641628886032*^9}, { 3.6296416658736973`*^9, 3.6296416815049243`*^9}, 3.6296417376338234`*^9, { 3.6296855551269727`*^9, 3.6296855804270077`*^9}, {3.6297079065796247`*^9, 3.6297079070476255`*^9}, {3.6297080850439377`*^9, 3.629708135728427*^9}, { 3.6297083496516027`*^9, 3.6297084025512953`*^9}, {3.629708781767563*^9, 3.629708790940379*^9}, {3.6297089402482414`*^9, 3.6297089618542795`*^9}, { 3.6297105345398417`*^9, 3.629710538580249*^9}, {3.6297107810514746`*^9, 3.6297107850138817`*^9}, {3.6297109100481014`*^9, 3.629710915710911*^9}, { 3.629711201534613*^9, 3.629711204311418*^9}, {3.629711236307074*^9, 3.6297115007275386`*^9}, {3.6297115377464037`*^9, 3.6297115441112146`*^9}, 3.6297116025645175`*^9, {3.6298716505389357`*^9, 3.629871851841689*^9}, { 3.62987837458679*^9, 3.629878383510006*^9}, {3.6298784402629056`*^9, 3.629878447345318*^9}, {3.6298785221786494`*^9, 3.6298786580236883`*^9}, { 3.629878689613744*^9, 3.629878737147027*^9}, 3.629878783853509*^9, { 3.629878832322794*^9, 3.6298789171723433`*^9}, {3.6298802128122005`*^9, 3.6298802929723125`*^9}, 3.6298813644148126`*^9, {3.629882428887303*^9, 3.629882435887313*^9}, {3.6298986251827383`*^9, 3.6298988530367384`*^9}, { 3.6298989036744275`*^9, 3.6298989486493063`*^9}, {3.629899016868226*^9, 3.6298991622448816`*^9}, {3.6298997154530535`*^9, 3.629899740147897*^9}, { 3.6298998248560457`*^9, 3.629899978048314*^9}, {3.6299000396372223`*^9, 3.6299001557638264`*^9}, {3.6299001966826982`*^9, 3.6299002595352087`*^9}, 3.6299005011236343`*^9, {3.6299005468317146`*^9, 3.629900567642151*^9}, { 3.629900887676713*^9, 3.629900990153293*^9}, {3.6299011689220085`*^9, 3.6299012295125146`*^9}, {3.6299013754039707`*^9, 3.6299014166036434`*^9}, 3.6299014589733176`*^9, {3.6299015096734066`*^9, 3.629901588765546*^9}, { 3.629901662569275*^9, 3.6299016974665365`*^9}, {3.629901952339784*^9, 3.6299019599057975`*^9}, 3.6299020306051216`*^9, {3.6299022330934772`*^9, 3.6299022682559395`*^9}, {3.6299023020455985`*^9, 3.629902332808852*^9}, { 3.6299024532566643`*^9, 3.629902462850681*^9}, {3.629949880225117*^9, 3.6299498807867184`*^9}, {3.6299503101150723`*^9, 3.6299503156998825`*^9}, {3.629950355058751*^9, 3.629950498937804*^9}, { 3.6299555415202007`*^9, 3.6299555507086167`*^9}, {3.6299556061667137`*^9, 3.6299557553497763`*^9}, {3.629955788499834*^9, 3.6299558948608212`*^9}, { 3.629956042764681*^9, 3.629956043809883*^9}, {3.6299560914211664`*^9, 3.6299561017327843`*^9}, 3.629956145849662*^9, {3.6299584813821354`*^9, 3.6299585082765827`*^9}, 3.6299585652946825`*^9, {3.629958616587573*^9, 3.6299586356508064`*^9}, {3.629958715073346*^9, 3.6299588186419287`*^9}, { 3.629958857454797*^9, 3.629958927249319*^9}, {3.629959427994599*^9, 3.629959494669116*^9}, {3.6299595293323765`*^9, 3.6299596037913074`*^9}, { 3.62995966795422*^9, 3.62995967360143*^9}, {3.6299597835972233`*^9, 3.6299597841120243`*^9}, {3.629959826622099*^9, 3.629959862533362*^9}, { 3.6299599051682367`*^9, 3.6299599235918694`*^9}, 3.629959979939168*^9, { 3.6299601345354395`*^9, 3.62996014612626*^9}, 3.6299601769831142`*^9, { 3.629960253142448*^9, 3.629960269538077*^9}, {3.6299603041701374`*^9, 3.6299603078205442`*^9}, {3.6299604300467587`*^9, 3.629960435491168*^9}, { 3.6299605300585346`*^9, 3.6299605636609936`*^9}, {3.6299606195870914`*^9, 3.6299606581971593`*^9}, {3.629960824228251*^9, 3.6299608755367413`*^9}, { 3.629960906658796*^9, 3.6299609978409557`*^9}, {3.6299610312250147`*^9, 3.629961070646284*^9}, {3.629961135698398*^9, 3.6299611643088484`*^9}, { 3.6299720458358483`*^9, 3.6299721791536827`*^9}, {3.6299722439717965`*^9, 3.629972300007095*^9}, {3.6299723670872126`*^9, 3.6299723937008595`*^9}, { 3.629972457801372*^9, 3.6299724710613956`*^9}, {3.629972740193068*^9, 3.6299728251196175`*^9}, {3.6299729203577843`*^9, 3.6299729350218105`*^9}, {3.6299729720874753`*^9, 3.6299730462188053`*^9}, {3.629973116044528*^9, 3.6299731230177402`*^9}, { 3.629973184310248*^9, 3.6299732090830917`*^9}, {3.629973349982539*^9, 3.6299734360166903`*^9}, 3.629973534562063*^9, {3.629973577446539*^9, 3.629973586104554*^9}, {3.6299740374133463`*^9, 3.629974083823428*^9}, { 3.6299742505565205`*^9, 3.629974337089873*^9}, {3.629974382907153*^9, 3.6299744466176653`*^9}, {3.629974589794717*^9, 3.629974590761918*^9}, { 3.629974776215044*^9, 3.6299747850134597`*^9}, {3.6299748226095257`*^9, 3.6299748237483273`*^9}, 3.6299748618435946`*^9, {3.629975198476586*^9, 3.6299752545898843`*^9}, {3.62997531475919*^9, 3.6299753175515947`*^9}, { 3.6299754601982455`*^9, 3.6299754625382495`*^9}, {3.629975592034077*^9, 3.629975592502078*^9}, {3.629983277446268*^9, 3.6299832946842985`*^9}, { 3.62998342081052*^9, 3.6299835439883366`*^9}, {3.629983615514462*^9, 3.629983931009416*^9}, {3.6299919807040443`*^9, 3.6299919808912444`*^9}, { 3.629992028330928*^9, 3.6299920922130404`*^9}, 3.629992198480427*^9, { 3.6299922299300823`*^9, 3.629992250506518*^9}, {3.629992292657792*^9, 3.6299923603151107`*^9}, {3.6299924387676487`*^9, 3.6299924398440504`*^9}, {3.6299925764846907`*^9, 3.6299926096347485`*^9}, {3.6299928122323046`*^9, 3.629992818768716*^9}, { 3.6299929049120674`*^9, 3.629992905411268*^9}, {3.6299929850338078`*^9, 3.6299929866250105`*^9}, {3.6299931061992207`*^9, 3.62999312270405*^9}, { 3.629993172312137*^9, 3.6299932618718944`*^9}, {3.6299933276572104`*^9, 3.6299933842073092`*^9}, {3.630287775665962*^9, 3.630287795852398*^9}, { 3.6303896387100534`*^9, 3.630389666774503*^9}, {3.6303896967889557`*^9, 3.6303897095341783`*^9}, {3.6303897587054644`*^9, 3.630389880448078*^9}, { 3.6303899127557354`*^9, 3.630390009444705*^9}, 3.630390057321189*^9, 3.630390443484267*^9, {3.63039095720877*^9, 3.6303909789240074`*^9}, { 3.6303910572205453`*^9, 3.6303911291054716`*^9}, {3.630391163035531*^9, 3.6303911740803504`*^9}, {3.630391240224467*^9, 3.6303912875081496`*^9}, { 3.6303913396902413`*^9, 3.630391404570755*^9}, {3.630391479513287*^9, 3.6303917572873745`*^9}, {3.630391868905571*^9, 3.6303920027226057`*^9}, { 3.630392064327114*^9, 3.630392219843787*^9}, {3.63039226121506*^9, 3.63039232943398*^9}, {3.6303924315985594`*^9, 3.6303924441097813`*^9}, { 3.6303926866122074`*^9, 3.6303927118530517`*^9}, {3.630392795671999*^9, 3.6303928006172075`*^9}, {3.6303986032190485`*^9, 3.6303986046230516`*^9}, {3.6303986654631586`*^9, 3.6303987936485834`*^9}, {3.63039889979117*^9, 3.6303989091199865`*^9}, { 3.630399006323757*^9, 3.630399007259759*^9}, {3.630399117224352*^9, 3.630399214771323*^9}, {3.6303992555185947`*^9, 3.6303993036758795`*^9}, { 3.630399467725767*^9, 3.630399502731636*^9}, {3.6303995748037624`*^9, 3.630399595614199*^9}, {3.6303996329294643`*^9, 3.630399658076709*^9}, { 3.630399711335202*^9, 3.6303997453120623`*^9}, {3.6303998546994543`*^9, 3.6303999880484886`*^9}, {3.6304000742074394`*^9, 3.630400123441126*^9}, { 3.6304001724564123`*^9, 3.630400251595351*^9}, {3.630400324166679*^9, 3.630400327052684*^9}, {3.630400358190338*^9, 3.6304003597503414`*^9}, { 3.6304004587481155`*^9, 3.6304004640521245`*^9}, {3.630400521975026*^9, 3.630400526124634*^9}, {3.630400567199506*^9, 3.630400593516752*^9}, { 3.6304012340070767`*^9, 3.6304013035207987`*^9}, {3.6304013614749007`*^9, 3.630401367933312*^9}, {3.630401686939398*^9, 3.6304017294598303`*^9}, { 3.630401794020523*^9, 3.6304018922061386`*^9}, {3.6304019687775183`*^9, 3.630401987153569*^9}, {3.630402072749465*^9, 3.63040208297405*^9}, { 3.6304022247881613`*^9, 3.630402255931943*^9}, 3.630402329306139*^9, { 3.6304023806970787`*^9, 3.6304024212403975`*^9}, {3.6304025002259154`*^9, 3.630402528595538*^9}, {3.6304025620694523`*^9, 3.630402575015193*^9}, { 3.6304026411829777`*^9, 3.630402649073429*^9}, {3.630402695548087*^9, 3.6304027128260756`*^9}, {3.630402783923142*^9, 3.6304027982389607`*^9}, { 3.6304028797236214`*^9, 3.6304030111811404`*^9}, {3.6304030562107162`*^9, 3.6304031598846455`*^9}, {3.630403236330018*^9, 3.6304032404072514`*^9}, { 3.630403373001835*^9, 3.6304033888147397`*^9}, {3.6304039420953856`*^9, 3.6304039512829113`*^9}, 3.6304039831437335`*^9, {3.630404015975611*^9, 3.6304040663624935`*^9}, {3.630404173614628*^9, 3.630404246945822*^9}, { 3.6304042891772375`*^9, 3.630404299595834*^9}, {3.630404391083066*^9, 3.630404392406142*^9}, {3.6304045301800222`*^9, 3.6304045579486103`*^9}, { 3.630404640215316*^9, 3.630404762796327*^9}, {3.630404877629895*^9, 3.630404883104208*^9}, {3.6304050364729805`*^9, 3.630405098270515*^9}, { 3.6304051736118245`*^9, 3.6304051965901384`*^9}, {3.6304053802536435`*^9, 3.63040539242334*^9}, {3.630406035965148*^9, 3.630406041998493*^9}, { 3.630406072049212*^9, 3.6304060962065935`*^9}, {3.630406264081196*^9, 3.6304062707025747`*^9}, {3.63040632219952*^9, 3.630406385461138*^9}, { 3.630406477200385*^9, 3.630406482095665*^9}, {3.6304066170883865`*^9, 3.6304066222256804`*^9}, {3.630406957868878*^9, 3.630406973411767*^9}, { 3.6304070081447535`*^9, 3.630407018199329*^9}, {3.630407411376817*^9, 3.630407412542884*^9}, {3.6304080609339695`*^9, 3.630408121202417*^9}, { 3.6304081585485525`*^9, 3.6304081832129636`*^9}, {3.63040821409673*^9, 3.630408421131572*^9}, 3.6304934333363276`*^9, {3.63049350751357*^9, 3.630493677593298*^9}, {3.630493716898546*^9, 3.6304937846684227`*^9}, 3.630493922944331*^9, {3.6304939556752033`*^9, 3.630494117430455*^9}, { 3.6304941486092386`*^9, 3.6304941767788496`*^9}, {3.6304942118648567`*^9, 3.6304942530272107`*^9}, {3.6304942838399734`*^9, 3.6304942845820155`*^9}, {3.6304943454054947`*^9, 3.6304944442451477`*^9}, {3.63080749995092*^9, 3.6308075480801234`*^9}, { 3.630807586536323*^9, 3.630807621440319*^9}, {3.630807680459695*^9, 3.630807682914836*^9}, {3.630807736889923*^9, 3.6308077644745007`*^9}, { 3.6308078081089964`*^9, 3.6308078670123653`*^9}, {3.630807991648494*^9, 3.630807997541831*^9}, {3.6308081080891542`*^9, 3.6308081919599514`*^9}, { 3.630808306368495*^9, 3.630808345060708*^9}, {3.6308087281906223`*^9, 3.6308087555171847`*^9}, {3.630809110815507*^9, 3.630809169033837*^9}, { 3.6308091998195972`*^9, 3.630809448512822*^9}, {3.6308095328996487`*^9, 3.6308095448223305`*^9}, {3.630809582269472*^9, 3.6308095873607635`*^9}, { 3.630809665529235*^9, 3.630809684808337*^9}, {3.6308316258485594`*^9, 3.6308318380886984`*^9}, {3.63083188164919*^9, 3.630831966930068*^9}, 3.6320400558356075`*^9, {3.6354749882908883`*^9, 3.635474989418953*^9}, { 3.635475084557395*^9, 3.6354750875145636`*^9}, {3.6354751334091887`*^9, 3.635475162315842*^9}, {3.6354754001974483`*^9, 3.6354754820331287`*^9}, 3.635475512931896*^9, {3.6354756222781506`*^9, 3.635475622861184*^9}, { 3.635475691642118*^9, 3.6354757057969275`*^9}, {3.6354757798291616`*^9, 3.635475797395167*^9}, {3.635475884848169*^9, 3.6354758981309285`*^9}, { 3.635475961488552*^9, 3.6354759738382587`*^9}, {3.6354760213729773`*^9, 3.6354760572050266`*^9}, {3.6354761282470903`*^9, 3.635476136040536*^9}, { 3.6354761719365892`*^9, 3.635476212217893*^9}, {3.6593346599546614`*^9, 3.659334660890663*^9}, {3.6593347077219453`*^9, 3.659334720701168*^9}, { 3.6593348752974396`*^9, 3.6593348758122406`*^9}, {3.6593349140947075`*^9, 3.6593350070240707`*^9}, {3.6593350466949406`*^9, 3.6593350543701544`*^9}, {3.659335103791041*^9, 3.6593351614487424`*^9}, 3.659335217686841*^9, {3.659335262084519*^9, 3.6593352995869846`*^9}, { 3.6593356899482727`*^9, 3.659335701819893*^9}, {3.659335964227954*^9, 3.659335964602355*^9}, {3.65933603594128*^9, 3.6593360629605274`*^9}, { 3.6593361352354546`*^9, 3.6593361504454813`*^9}, {3.6593363929479074`*^9, 3.6593364061611304`*^9}, 3.6593368946915884`*^9, {3.6884748265656157`*^9, 3.6884748268716326`*^9}, {3.6884748600075283`*^9, 3.688474861420609*^9}, { 3.6885242858240776`*^9, 3.6885243001140976`*^9}, {3.6888842911675606`*^9, 3.6888843311676164`*^9}, {3.688966242423658*^9, 3.688966263933688*^9}, { 3.6897393587897596`*^9, 3.6897393649897685`*^9}, 3.689739477049925*^9, { 3.6898595970621734`*^9, 3.689859597272174*^9}, {3.6898596707522764`*^9, 3.6898597190523443`*^9}, {3.689859768552414*^9, 3.6898597721424184`*^9}, { 3.689859855272535*^9, 3.689859859882541*^9}, {3.6898605078334484`*^9, 3.6898607266237545`*^9}, 3.6898608811139708`*^9, {3.6898609634740863`*^9, 3.689860974304102*^9}, 3.6898610140141573`*^9, {3.6898611496043468`*^9, 3.6898611683243732`*^9}, {3.689861462024784*^9, 3.6898615624849253`*^9}, { 3.6898616142149973`*^9, 3.6898616164350004`*^9}, 3.6898616657950697`*^9, { 3.689861716805141*^9, 3.689861749905187*^9}, {3.732677920575506*^9, 3.7326779208190203`*^9}, {3.7519672427004185`*^9, 3.7519672444968877`*^9}, {3.7519674022097683`*^9, 3.75196742976579*^9}, { 3.751967484127989*^9, 3.751967510853814*^9}, {3.7519675409404893`*^9, 3.751967541549782*^9}, {3.7519675797751045`*^9, 3.751967592209671*^9}, { 3.7519676829383273`*^9, 3.7519676841255474`*^9}, {3.7519677154775553`*^9, 3.7519677953499403`*^9}, 3.751967827811061*^9, {3.7519679545625095`*^9, 3.751967957999185*^9}, {3.751968003754015*^9, 3.7519681477513895`*^9}, { 3.751968264817631*^9, 3.751968270722477*^9}, {3.7519689618119907`*^9, 3.751968969888235*^9}, {3.7519691168917775`*^9, 3.7519691395895615`*^9}, { 3.751969242782174*^9, 3.7519692581691785`*^9}, {3.7519693625211954`*^9, 3.751969378579924*^9}, {3.751969409572627*^9, 3.751969438643936*^9}, { 3.7519695894526725`*^9, 3.751969614306203*^9}, {3.7523200108586655`*^9, 3.752320012354121*^9}, {3.7553831315619707`*^9, 3.755383134119626*^9}, { 3.7553831893197794`*^9, 3.755383241814331*^9}, {3.7553832736267967`*^9, 3.7553832810757113`*^9}, {3.7554336536222963`*^9, 3.755433684797229*^9}, { 3.7554337764737434`*^9, 3.7554338315300155`*^9}, {3.755433998047738*^9, 3.7554340265485487`*^9}, {3.755446573138784*^9, 3.755446636911299*^9}, { 3.75544667493072*^9, 3.755446753435521*^9}, {3.755446891541581*^9, 3.7554468921547422`*^9}, {3.7554469323588533`*^9, 3.755446936867403*^9}, { 3.7554470190332975`*^9, 3.7554472776872244`*^9}, {3.7555217323692026`*^9, 3.755521732847602*^9}, {3.755521767127169*^9, 3.7555217972041793`*^9}, { 3.755522561453134*^9, 3.755522564231819*^9}, {3.755522601885935*^9, 3.7555226037287407`*^9}, {3.7555226758687305`*^9, 3.755522678585092*^9}, { 3.7555234832604623`*^9, 3.7555235920444417`*^9}, {3.7555239506007543`*^9, 3.755524013893358*^9}, {3.755524076791689*^9, 3.7555240812793446`*^9}, { 3.7555241238138275`*^9, 3.7555241268985643`*^9}, {3.7555242930449886`*^9, 3.7555243378577013`*^9}, {3.7555256673767824`*^9, 3.7555256808205338`*^9}, {3.7555258588384123`*^9, 3.755525900317296*^9}, { 3.755525930708299*^9, 3.7555260436531134`*^9}, {3.755607147401991*^9, 3.7556071504143705`*^9}, {3.755607992884314*^9, 3.7556080025382996`*^9}, { 3.7556094344057455`*^9, 3.7556094348690443`*^9}, {3.7559613653116636`*^9, 3.755961445097105*^9}, 3.755961484246889*^9, {3.7559618979231987`*^9, 3.755961939470047*^9}, {3.7559620323724904`*^9, 3.7559620330864005`*^9}, { 3.755962155557907*^9, 3.7559621601593847`*^9}, {3.755962303755834*^9, 3.755962343830135*^9}, {3.7559624058018165`*^9, 3.7559624450501757`*^9}, 3.756002186674869*^9, 3.7560029626855392`*^9, {3.756003222110388*^9, 3.756003295034633*^9}, {3.7560056331492863`*^9, 3.7560056663855457`*^9}, { 3.7560057813555765`*^9, 3.7560057863836613`*^9}, {3.7560058917172394`*^9, 3.756005927847292*^9}, 3.756006092376186*^9, 3.756009112317705*^9, { 3.756091886039587*^9, 3.756091887764086*^9}, {3.756092005435152*^9, 3.7560920727337685`*^9}, {3.75609212911592*^9, 3.7560921293252516`*^9}, { 3.756092262958163*^9, 3.756092263157668*^9}, {3.756092342487877*^9, 3.756092347894502*^9}, {3.7560929036769304`*^9, 3.7560929278911004`*^9}, { 3.7560930741522417`*^9, 3.756093083420331*^9}, {3.7560932986236534`*^9, 3.7560933139459305`*^9}, {3.756093449985523*^9, 3.7560934874491863`*^9}, { 3.756093592694581*^9, 3.7560936019456573`*^9}, {3.756093634438078*^9, 3.756093673866626*^9}, {3.756093873069885*^9, 3.756093897964734*^9}, { 3.7560940650109406`*^9, 3.756094078056768*^9}, {3.756442536546026*^9, 3.756442607904289*^9}, {3.7564436397451363`*^9, 3.7564436403231254`*^9}, { 3.7636034984570236`*^9, 3.7636034989933815`*^9}, {3.763603551051456*^9, 3.7636035527617817`*^9}, {3.7636036049384193`*^9, 3.7636036392233057`*^9}, {3.7636036850937223`*^9, 3.763603692587598*^9}, { 3.7636037258272257`*^9, 3.7636037459031096`*^9}, {3.7636037792254367`*^9, 3.76360387572289*^9}, {3.763603971837229*^9, 3.7636040341423655`*^9}, { 3.763604066526084*^9, 3.7636040756798687`*^9}, {3.7636041452118535`*^9, 3.763604278007333*^9}, {3.763604317710966*^9, 3.7636043271387568`*^9}, { 3.7636043584877644`*^9, 3.763604415561053*^9}, {3.763604445680462*^9, 3.7636044504114943`*^9}, {3.763604615444647*^9, 3.7636048082554193`*^9}, 3.763604854904996*^9, {3.7636133594095488`*^9, 3.7636133618464766`*^9}, { 3.7636136063756704`*^9, 3.7636136315671196`*^9}, {3.7636990373827705`*^9, 3.7636990431157646`*^9}, {3.763699090332087*^9, 3.763699110952259*^9}, { 3.763699227420497*^9, 3.7636993642943506`*^9}, {3.763700085627533*^9, 3.763700088329999*^9}, {3.7637001721125274`*^9, 3.763700181422837*^9}, { 3.763700248063385*^9, 3.7637003918630466`*^9}, {3.763700591783223*^9, 3.7637006017496295`*^9}, {3.7637007583576717`*^9, 3.7637007603074865`*^9}, {3.7637137795793185`*^9, 3.7637137822587233`*^9}, {3.7637148704355187`*^9, 3.763714870624051*^9}, { 3.763727592158518*^9, 3.7637275933445053`*^9}, {3.7637276688363667`*^9, 3.7637276694756594`*^9}, 3.763803448896332*^9, {3.76380349501632*^9, 3.7638036835067654`*^9}, {3.763804829093463*^9, 3.7638048385675254`*^9}, 3.7638051033646154`*^9, 3.7638053924528885`*^9, {3.763805557684454*^9, 3.763805634255308*^9}, {3.763806843847647*^9, 3.763806847966059*^9}, { 3.763806942652097*^9, 3.7638071770752254`*^9}, {3.7638141184594107`*^9, 3.763814134133461*^9}, {3.7638146808628216`*^9, 3.7638146925645113`*^9}, { 3.7638147709278784`*^9, 3.7638147811883087`*^9}, {3.7638148155281043`*^9, 3.763814819843194*^9}, {3.7638150259647446`*^9, 3.763815028601293*^9}, { 3.7638151529595194`*^9, 3.763815155849978*^9}, {3.7638163770262136`*^9, 3.763816380851597*^9}, {3.7638164181856327`*^9, 3.7638164950537987`*^9}, 3.763816568304102*^9, {3.7638166173645625`*^9, 3.763816618808757*^9}, { 3.7638167204462805`*^9, 3.763816721012859*^9}, {3.763857602253485*^9, 3.7638579604183645`*^9}, {3.7638580038507566`*^9, 3.7638580060526443`*^9}, {3.763858082269992*^9, 3.7638581746835337`*^9}, { 3.7638582163351564`*^9, 3.7638582415275116`*^9}, {3.7638582983238*^9, 3.763858907503306*^9}, {3.763858941318697*^9, 3.763858956626134*^9}, { 3.7638602435602536`*^9, 3.763860245408451*^9}, {3.7638694636456347`*^9, 3.7638694647177277`*^9}, {3.7638708199536576`*^9, 3.763870829436488*^9}, { 3.763871287170555*^9, 3.7638712876184006`*^9}, {3.763943214376035*^9, 3.7639432984591475`*^9}, {3.763943418832348*^9, 3.7639434335508127`*^9}, { 3.76394347113767*^9, 3.7639435187320576`*^9}, {3.763943585908682*^9, 3.7639436125255404`*^9}, {3.763951722152746*^9, 3.76395172989299*^9}, { 3.7639517863423367`*^9, 3.7639519945900664`*^9}, {3.763952081515512*^9, 3.7639521530710773`*^9}, {3.763952353248129*^9, 3.763952357026309*^9}, { 3.7639524211903834`*^9, 3.7639524243979177`*^9}, {3.7639527174925117`*^9, 3.7639527180252266`*^9}, {3.7641265625745993`*^9, 3.7641265632314167`*^9}, {3.764126605555829*^9, 3.7641266075095396`*^9}, { 3.7641268313964133`*^9, 3.7641268543573804`*^9}, {3.764127044657903*^9, 3.7641270479422092`*^9}, {3.7641271442332697`*^9, 3.7641271469362774`*^9}, {3.764127227626192*^9, 3.7641272592640233`*^9}, { 3.764127335707515*^9, 3.7641273386484756`*^9}, {3.764127429843852*^9, 3.7641274364304185`*^9}, {3.7641275071859307`*^9, 3.764127516803895*^9}, 3.7641276043548007`*^9, {3.7641276925365753`*^9, 3.764127697080591*^9}, 3.764127798472331*^9, 3.764127853631323*^9, 3.764127908496078*^9, { 3.7641280050343323`*^9, 3.764128022046494*^9}, {3.764128128597419*^9, 3.764128154116727*^9}, {3.7641286864636617`*^9, 3.764128701643106*^9}, { 3.7641289910924444`*^9, 3.7641290126680794`*^9}, {3.7641290672285347`*^9, 3.7641290737798567`*^9}, {3.7641325425120363`*^9, 3.764132565390477*^9}, { 3.7641327425004654`*^9, 3.764132750040793*^9}, 3.7641327968340364`*^9, { 3.764133146776842*^9, 3.764133204874522*^9}, {3.7641333488187037`*^9, 3.7641333525577593`*^9}, {3.764413145593136*^9, 3.7644131471236105`*^9}, { 3.764413201645049*^9, 3.7644132349609704`*^9}, {3.764413325008136*^9, 3.7644133748980193`*^9}, {3.7644134113425665`*^9, 3.7644135151187*^9}, { 3.764413554409053*^9, 3.7644136160674934`*^9}, {3.76441371984758*^9, 3.764413730103909*^9}, 3.764419641962368*^9, {3.7644198522879405`*^9, 3.764419879249356*^9}, 3.764419909536559*^9, {3.764419991012162*^9, 3.764420000171088*^9}, {3.7644200798862047`*^9, 3.7644200950961914`*^9}, { 3.7644201529471693`*^9, 3.764420153715966*^9}, {3.764420210346301*^9, 3.764420255343707*^9}, {3.764420296178318*^9, 3.7644203000939393`*^9}, { 3.7644203803359275`*^9, 3.7644203931390867`*^9}, 3.7644204418727274`*^9, { 3.7647259720700207`*^9, 3.7647261047260523`*^9}, {3.7647263483375626`*^9, 3.76472635879602*^9}, 3.764726656736601*^9, {3.764727009127914*^9, 3.764727020100875*^9}, {3.7647270591828785`*^9, 3.7647270819631023`*^9}, { 3.7647272109090505`*^9, 3.764727227846332*^9}, {3.76473247809907*^9, 3.7647324813925114`*^9}, {3.7647349484962797`*^9, 3.7647349979358416`*^9}, {3.7647351097258167`*^9, 3.764735124772463*^9}, { 3.7647352810674453`*^9, 3.7647352901139917`*^9}, {3.7647353746429515`*^9, 3.764735379550926*^9}, {3.7647354596539807`*^9, 3.764735507677454*^9}, { 3.7647355546341*^9, 3.764735728811817*^9}, {3.764735837449795*^9, 3.76473584132898*^9}, {3.76473603649269*^9, 3.7647360592982664`*^9}, { 3.7647360998228803`*^9, 3.76473621551197*^9}, {3.7647362545599003`*^9, 3.764736286430997*^9}, {3.7647364592833533`*^9, 3.764736464019006*^9}, { 3.764736566167658*^9, 3.7647365918958225`*^9}, {3.764764761680134*^9, 3.7647648482473745`*^9}, 3.764764917763693*^9, {3.764764964821686*^9, 3.764765090741813*^9}, {3.7647651742140284`*^9, 3.7647652517335076`*^9}, { 3.764765341266399*^9, 3.7647653614173465`*^9}, 3.764765400284145*^9, { 3.764765691384389*^9, 3.764765708710143*^9}, 3.7647657454275875`*^9, { 3.76476578351686*^9, 3.764765871262255*^9}, {3.7647661045180917`*^9, 3.76476612822571*^9}, {3.7647661964223824`*^9, 3.764766239375331*^9}, { 3.764766330361228*^9, 3.764766338297905*^9}, {3.764767015060799*^9, 3.7647670193029037`*^9}, {3.764767076590926*^9, 3.7647671160277977`*^9}, { 3.7647671493139205`*^9, 3.7647672079236426`*^9}, {3.764767458938404*^9, 3.7647674608323865`*^9}, {3.764810938444873*^9, 3.7648109399353456`*^9}, { 3.7648118616019874`*^9, 3.7648118695079126`*^9}, {3.7648120589477816`*^9, 3.7648124600413237`*^9}, {3.76481250476682*^9, 3.7648125259602103`*^9}, { 3.764812601341893*^9, 3.7648126577763243`*^9}, {3.7648126944039307`*^9, 3.7648128855627623`*^9}, {3.764812924923909*^9, 3.764812926481821*^9}, { 3.764813041485982*^9, 3.764813131254232*^9}, {3.7648134679328885`*^9, 3.7648136479313235`*^9}, {3.7648136917777314`*^9, 3.764813697753367*^9}, { 3.7648137297570653`*^9, 3.764813747862262*^9}, 3.764813784221693*^9, { 3.7648138370678406`*^9, 3.7648141387969923`*^9}, {3.764814321050164*^9, 3.764814422489184*^9}, {3.764814461366684*^9, 3.7648145835728483`*^9}, { 3.764814614769511*^9, 3.7648147525825167`*^9}, {3.764815363375289*^9, 3.7648153644907384`*^9}, {3.764815451671169*^9, 3.7648154601533747`*^9}, { 3.7648175917802963`*^9, 3.7648176401910563`*^9}, {3.765885491237231*^9, 3.765885501131465*^9}, {3.766572999289345*^9, 3.7665729996020145`*^9}, { 3.7665730613126965`*^9, 3.7665730616706066`*^9}, {3.7840103262125545`*^9, 3.7840103546413517`*^9}, {3.784011309725755*^9, 3.7840113197719574`*^9}, { 3.784013374800973*^9, 3.7840133842981763`*^9}, {3.7840238533665447`*^9, 3.78402395932942*^9}, {3.784024091276659*^9, 3.784024112209529*^9}, { 3.7840242793219643`*^9, 3.784024296655184*^9}, {3.7840290670892677`*^9, 3.7840291348388853`*^9}, {3.784029222997594*^9, 3.784029542926179*^9}, { 3.784375172285057*^9, 3.784375319701829*^9}, {3.7843753678421807`*^9, 3.7843753788103914`*^9}, {3.7843754844339557`*^9, 3.784375827494117*^9}, { 3.784375862317687*^9, 3.7843759567563844`*^9}, {3.784376004941759*^9, 3.7843760080157185`*^9}, {3.784376101918992*^9, 3.7843761244332943`*^9}, { 3.784376181191763*^9, 3.7843762145091863`*^9}, {3.7843792489960337`*^9, 3.78437926273014*^9}, {3.7843793293934345`*^9, 3.784379368676588*^9}, { 3.7843796529835215`*^9, 3.7843796858862267`*^9}, {3.784450863324359*^9, 3.7844508986076546`*^9}, {3.7844510208392324`*^9, 3.784451027915551*^9}, { 3.7844511176315613`*^9, 3.7844511673791957`*^9}, {3.784451235055628*^9, 3.78445132575735*^9}, {3.784451995615477*^9, 3.7844520110330954`*^9}, { 3.7844522907551537`*^9, 3.7844523421551*^9}, {3.784700119490345*^9, 3.7847001627913013`*^9}, {3.7847004221290607`*^9, 3.7847004380767317`*^9}, 3.7847007913506136`*^9, {3.784781955129138*^9, 3.784781977787957*^9}, { 3.78488170216677*^9, 3.784881704210422*^9}, 3.784882130557441*^9, { 3.78488220347418*^9, 3.7848822064697027`*^9}, {3.784883393455822*^9, 3.784883458551924*^9}, 3.7848835306495824`*^9, {3.7848836822092113`*^9, 3.7848837303696923`*^9}, 3.7848838199009576`*^9, {3.7848842507527857`*^9, 3.7848842836585226`*^9}, 3.7848843847882996`*^9, {3.784884461405264*^9, 3.7848844645041113`*^9}, {3.784884559404122*^9, 3.7848845656634912`*^9}, { 3.7848852409944844`*^9, 3.7848852740337477`*^9}, {3.7848854548929386`*^9, 3.7848854893046365`*^9}, {3.7848856741783943`*^9, 3.784885691704702*^9}, { 3.784885809660874*^9, 3.784885811424426*^9}, {3.7848860031948376`*^9, 3.784886020570098*^9}, 3.7848861057105627`*^9, {3.7848861627726107`*^9, 3.7848862212876124`*^9}, {3.784886306497995*^9, 3.7848863509322224`*^9}, 3.784886472690192*^9, {3.7848866596243*^9, 3.784886664116289*^9}, { 3.7848866987282944`*^9, 3.7848867077911897`*^9}, {3.78488676128524*^9, 3.7848868667029366`*^9}, {3.7848869381224003`*^9, 3.7848869414281464`*^9}, {3.7848870104508753`*^9, 3.784887039889447*^9}, { 3.7848871795058794`*^9, 3.7848871976746817`*^9}, {3.7848872311446314`*^9, 3.78488724075662*^9}, 3.784887405188785*^9, {3.784887591926689*^9, 3.7848876119305134`*^9}, {3.784887676620901*^9, 3.7848876786672792`*^9}, { 3.78488771054331*^9, 3.784887714354906*^9}, {3.7848877625809546`*^9, 3.7848878103041153`*^9}, 3.7848878862881575`*^9, {3.787717235155089*^9, 3.787717269464238*^9}, {3.7877174592607603`*^9, 3.7877174674038067`*^9}, { 3.7877271032841845`*^9, 3.787727136247201*^9}, 3.787727355369296*^9, 3.7877274973278403`*^9, {3.787727855959008*^9, 3.78772792141208*^9}, 3.787728113487193*^9, {3.7877281704571557`*^9, 3.7877281735077004`*^9}, 3.7877282789827795`*^9, {3.7877286510229864`*^9, 3.787728665729192*^9}, { 3.7877287942225084`*^9, 3.787728807671986*^9}, {3.787729044867985*^9, 3.787729045536916*^9}, {3.787729589732438*^9, 3.7877296062090626`*^9}, { 3.787729794037467*^9, 3.7877297950347877`*^9}, {3.787729855548402*^9, 3.7877299039179935`*^9}, {3.7877300373241186`*^9, 3.787730068136018*^9}, { 3.7877301999859333`*^9, 3.7877302014150777`*^9}, {3.787732033225385*^9, 3.7877320471634016`*^9}, {3.787732077195259*^9, 3.7877320780358667`*^9}, 3.787732189759206*^9, {3.78773231889835*^9, 3.787732327710633*^9}, { 3.7877324857166643`*^9, 3.787732496655479*^9}, {3.7877325848303585`*^9, 3.78773258503596*^9}, {3.7877328504631166`*^9, 3.7877328625892415`*^9}, { 3.7877330254884944`*^9, 3.7877330271019044`*^9}, {3.787733136128061*^9, 3.7877331422258835`*^9}, {3.787733243513567*^9, 3.78773324558677*^9}, 3.787733310555999*^9, 3.7877334085329347`*^9, {3.7877337955932293`*^9, 3.7877337970498257`*^9}, {3.787733867727028*^9, 3.7877338687324905`*^9}, { 3.7877352224369583`*^9, 3.787735224161746*^9}, {3.787735343322833*^9, 3.787735348772827*^9}, {3.787735422704711*^9, 3.7877354268945775`*^9}, { 3.7877355100355635`*^9, 3.787735514671461*^9}, {3.7877356541994534`*^9, 3.7877356632141013`*^9}, 3.7877357913476543`*^9, 3.787736261837074*^9, { 3.7882542159043374`*^9, 3.7882542747998285`*^9}, {3.788254310967661*^9, 3.788254318430212*^9}, {3.788254585790197*^9, 3.7882545888318524`*^9}, { 3.7882547349987383`*^9, 3.788254735940298*^9}, 3.788254830063775*^9, 3.7882549155286837`*^9, {3.7882550121437798`*^9, 3.788255037735396*^9}, { 3.7882551764404287`*^9, 3.78825518352113*^9}, {3.7882552540030313`*^9, 3.788255290224329*^9}, {3.7882553843544893`*^9, 3.788255423248046*^9}, { 3.78825567982127*^9, 3.7882556852479534`*^9}, {3.7882557908576803`*^9, 3.7882558029800806`*^9}, {3.7882560240494256`*^9, 3.7882560388846164`*^9}, 3.788256102343512*^9, {3.788256161397396*^9, 3.7882561626372194`*^9}, { 3.7882562304311895`*^9, 3.78825629590362*^9}, {3.7882563614677362`*^9, 3.7882563620189795`*^9}, {3.7882564138122153`*^9, 3.7882564294158382`*^9}, {3.788256467457189*^9, 3.7882564889521217`*^9}, { 3.7882565883311844`*^9, 3.788256591497148*^9}, {3.7882568409513097`*^9, 3.7882568724526567`*^9}, {3.788256965258837*^9, 3.788256966444976*^9}, { 3.7882570073831463`*^9, 3.7882570497349973`*^9}, {3.7882570992487097`*^9, 3.788257144206352*^9}, {3.78825721252205*^9, 3.788257307277931*^9}, { 3.788257350410209*^9, 3.7882573617262745`*^9}, {3.788257424936472*^9, 3.788257434118204*^9}, {3.788276311330668*^9, 3.788276311647092*^9}, { 3.7882765465512347`*^9, 3.788276608568333*^9}, {3.7882767715851693`*^9, 3.7882768045752783`*^9}, {3.7882769342607436`*^9, 3.7882769409894867`*^9}, {3.7882770202208567`*^9, 3.7882770424485188`*^9}, {3.7882770760040703`*^9, 3.788277077341468*^9}, { 3.788277147336176*^9, 3.788277150397852*^9}, {3.7882772069909*^9, 3.7882772101572385`*^9}, {3.7882772503366175`*^9, 3.7882772773759403`*^9}, {3.7882773922958755`*^9, 3.7882773927832017`*^9}, {3.788277450684473*^9, 3.788277482126852*^9}, { 3.78827754293396*^9, 3.788277545027956*^9}, {3.7883214550230436`*^9, 3.7883214742097826`*^9}, {3.788321520104019*^9, 3.788321685390153*^9}, { 3.788321717307153*^9, 3.788321801831746*^9}, {3.788321836768508*^9, 3.788322037754008*^9}, {3.7883220686363816`*^9, 3.788322220085001*^9}, { 3.7883255906192427`*^9, 3.788325646609389*^9}, {3.7883257976991563`*^9, 3.788325804097658*^9}, {3.788325969279187*^9, 3.7883259830028267`*^9}, { 3.788326975877249*^9, 3.788326979070017*^9}, {3.788328539286415*^9, 3.788328618410488*^9}, {3.788328648595448*^9, 3.788328762662589*^9}, { 3.7883288060890923`*^9, 3.7883288805716724`*^9}, {3.7883319188300047`*^9, 3.78833193230753*^9}, {3.7883321144947567`*^9, 3.788332115050151*^9}, { 3.7883333680456443`*^9, 3.7883333686272163`*^9}, 3.7883336421611414`*^9, { 3.788333691323177*^9, 3.7883336916362*^9}, {3.788333797629262*^9, 3.7883338348662343`*^9}, {3.7883339555470386`*^9, 3.7883339660305166`*^9}, {3.7883340291758356`*^9, 3.788334031484354*^9}, { 3.788334368484807*^9, 3.7883343918754945`*^9}, {3.7883345963739557`*^9, 3.788334645315611*^9}, {3.788411405608647*^9, 3.788411409092114*^9}, { 3.7884115644712825`*^9, 3.7884115911998663`*^9}, {3.7884116673998833`*^9, 3.788411758799066*^9}, {3.788411985303985*^9, 3.788412002701314*^9}, { 3.78841218266156*^9, 3.788412217652734*^9}, {3.788412679618697*^9, 3.78841268296084*^9}, {3.788412968920223*^9, 3.7884129782039633`*^9}, { 3.7884155241723013`*^9, 3.7884155243798914`*^9}, 3.7884156619519596`*^9, { 3.7884162343262696`*^9, 3.788416236013459*^9}, {3.789022054245319*^9, 3.7890221116154556`*^9}, {3.7890222001685014`*^9, 3.789022205961149*^9}, { 3.789094077050009*^9, 3.7890940781167436`*^9}, {3.7890941254883175`*^9, 3.7890942919861226`*^9}, {3.789094340508856*^9, 3.789094543716852*^9}, { 3.789094583794143*^9, 3.7890947278803444`*^9}, {3.7890947714417076`*^9, 3.7890948342626343`*^9}, {3.789095197615344*^9, 3.789095215073329*^9}, { 3.789095256390032*^9, 3.78909525710861*^9}, {3.7890954241290827`*^9, 3.78909583987399*^9}, {3.789096056032333*^9, 3.7890960602768464`*^9}, { 3.7890960928429904`*^9, 3.789096098149865*^9}, {3.789096721918685*^9, 3.789096734998893*^9}, {3.7890967741973257`*^9, 3.78909683859006*^9}, { 3.789096947653244*^9, 3.789097122315098*^9}, {3.7890971528708224`*^9, 3.789097530683948*^9}, {3.7890975852885656`*^9, 3.7890975882562447`*^9}, { 3.7890976430709224`*^9, 3.789097656213524*^9}, {3.789107592314107*^9, 3.7891076537760305`*^9}, {3.789107685160589*^9, 3.789107760590632*^9}, { 3.7891078105008087`*^9, 3.789107846610609*^9}, {3.789107989236459*^9, 3.7891080001561875`*^9}, {3.7891082032172785`*^9, 3.7891082064574785`*^9}, {3.7891083013630204`*^9, 3.789108444864075*^9}, { 3.7891084751958127`*^9, 3.7891085010044174`*^9}, {3.7891085322441816`*^9, 3.7891085353767447`*^9}, {3.789108620037199*^9, 3.789108662297584*^9}, 3.7891087252471294`*^9, {3.789108773507248*^9, 3.7891088501491203`*^9}, { 3.7891088829987*^9, 3.789108918319019*^9}, {3.7891089606286983`*^9, 3.7891090044788837`*^9}, {3.789109048556943*^9, 3.7891091177554493`*^9}, { 3.7891091628149347`*^9, 3.7891092922346783`*^9}, {3.789109382870388*^9, 3.789109402625166*^9}, {3.7891111380334797`*^9, 3.7891113582877145`*^9}, { 3.789111396694514*^9, 3.7891114221541777`*^9}, {3.7891114539845037`*^9, 3.7891114952359962`*^9}, {3.789112929457416*^9, 3.7891129318274393`*^9}, { 3.789112963290578*^9, 3.7891131302196255`*^9}, {3.789113202949188*^9, 3.789113203379569*^9}, {3.7891144371217365`*^9, 3.789114518411393*^9}, { 3.789114638487608*^9, 3.78911468069436*^9}, {3.789114763918976*^9, 3.789114777923211*^9}, {3.789114809301983*^9, 3.7891148392057247`*^9}, { 3.7891148923150015`*^9, 3.789114904054755*^9}, {3.7891149560740595`*^9, 3.7891150071774015`*^9}, {3.789115109642312*^9, 3.7891151147637*^9}, { 3.7891185439211864`*^9, 3.789118561569729*^9}, {3.7891187834106455`*^9, 3.7891187854068985`*^9}, {3.7891188764873776`*^9, 3.7891188767373095`*^9}, {3.789121799028477*^9, 3.789121806719482*^9}, { 3.7891222627163153`*^9, 3.7891222774782734`*^9}, {3.7891223914541044`*^9, 3.7891224006004095`*^9}, {3.789122431773783*^9, 3.7891224422816577`*^9}, { 3.7891224731160736`*^9, 3.789122501042121*^9}, {3.7891226653529224`*^9, 3.7891226664045706`*^9}, 3.789122819901965*^9, {3.789122893844426*^9, 3.7891229543768473`*^9}, {3.7891229964274464`*^9, 3.7891231044294157`*^9}, {3.789123228485856*^9, 3.789123374714591*^9}, { 3.789124218156231*^9, 3.789124220106046*^9}, {3.789124254593116*^9, 3.7891242583777695`*^9}, {3.7891243156014767`*^9, 3.789124326373148*^9}, { 3.789125154499303*^9, 3.7891252228031907`*^9}, {3.8200454708911095`*^9, 3.8200454840718527`*^9}, {3.8509666497276897`*^9, 3.8509666516620097`*^9}, {3.850966717721876*^9, 3.8509667189933705`*^9}, 3.8509667763101106`*^9, {3.8509668228841643`*^9, 3.850966844061469*^9}, { 3.8509668794855585`*^9, 3.8509669485542307`*^9}, {3.850966982527851*^9, 3.8509670397380314`*^9}}, CellLabel-> "In[207]:=",ExpressionUUID->"8fbb140a-f217-4c97-b25a-f0ab664d5b0f"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["SOLID MODEL", "Section", CellChangeTimes->{ 3.4430806364968*^9, {3.4453166713873997`*^9, 3.4453166747414*^9}, { 3.447462264275*^9, 3.4474622644154*^9}, {3.4695731321116*^9, 3.4695731359491997`*^9}, 3.473055186341*^9, {3.4730552472860003`*^9, 3.47305524884*^9}, {3.473055399782*^9, 3.473055419801*^9}, { 3.4734696760778*^9, 3.4734697047349997`*^9}, {3.4770537891542*^9, 3.4770537950354*^9}, {3.4932799754514*^9, 3.4932799779161997`*^9}, { 3.4945558951644*^9, 3.4945558957416*^9}, {3.4957646303032*^9, 3.4957646329084*^9}, {3.497581602118*^9, 3.4975816042552*^9}, { 3.500960505817*^9, 3.5009605094206*^9}, {3.556623836083009*^9, 3.5566238462386265`*^9}, {3.5568725055395393`*^9, 3.5568725163821597`*^9}, {3.556872678728445*^9, 3.5568726810485783`*^9}, { 3.7323376045620503`*^9, 3.7323376086812124`*^9}, {3.7335630623483887`*^9, 3.733563072583865*^9}, {3.733563130246215*^9, 3.733563131355714*^9}, { 3.817531746848799*^9, 3.817531749407099*^9}},ExpressionUUID->"63ada71e-dde0-461f-a58e-\ 67224f0ae52e"], Cell[CellGroupData[{ Cell["SOLID ELEMENT (disp) defs ", "Subsection", CellChangeTimes->{{3.629430162287647*^9, 3.6294301631768484`*^9}, { 3.7575037777673283`*^9, 3.7575037833217053`*^9}, {3.7884237836971426`*^9, 3.7884237842050157`*^9}},ExpressionUUID->"a049ace8-7330-4df1-8b56-\ 0697f104fbba"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"MEC", "-", "E1050"}], "|", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "ns", ",", "NN", ",", "r", ",", "FF", ",", "PP", ",", "uvw", ",", "\[Phi]\[Theta]\[Psi]", ",", "Duvw", ",", "\[Sigma]\[Sigma]", ",", "\[Sigma]", ",", "\[Rho]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "EEEE", ",", "\[Delta]w\[Sigma]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "e", ",", "ee", ",", "\[Epsilon]", ",", "EM", ",", "GM", ",", "GG", ",", "nl", ",", "jac", ",", "FFINV"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]", "-", "\[Gamma]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"assuming", " ", "a", " ", "linear", " ", "mapping"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"Transpose", "[", RowBox[{"D", "[", RowBox[{"r", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}], "}"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "approximations", "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", " ", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"displacement", " ", "gradient"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{"FFINV", ".", RowBox[{"Transpose", "[", RowBox[{"D", "[", RowBox[{"uvw", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}], "}"}]}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"IdentityMatrix", "[", "3", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", " ", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "GG"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "/", "GG"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"1", "/", "GG"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TET5", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], "}"}], ",", RowBox[{"Hexahedron", "[", RowBox[{"{", RowBox[{ "n1_", ",", "n2_", ",", "n3_", ",", "n4_", ",", "n5_", ",", "n6_", ",", "n7_", ",", "n8_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Hexahedron", "[", RowBox[{"{", RowBox[{ "n1", ",", "n2", ",", "n3", ",", "n4", ",", "n5", ",", "n6", ",", "n7", ",", "n8"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Hexahedron", "[", RowBox[{"{", RowBox[{ "n1_", ",", "n2_", ",", "n3_", ",", "n4_", ",", "n5_", ",", "n6_", ",", "n7_", ",", "n8_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "NN", ",", "r", ",", "FF", ",", "PP", ",", "uvw", ",", "\[Sigma]", ",", "EEEE", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "GG", ",", "jac", ",", "FFINV", ",", "\[Epsilon]", ",", "\[Delta]wext", ",", "\[Delta]wint"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{ "n1", ",", "n2", ",", "n3", ",", "n4", ",", "n5", ",", "n6", ",", "n7", ",", "n8"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Gamma]"}], ")"}]}], ",", RowBox[{"\[Alpha]", RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Gamma]"}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]", RowBox[{"(", RowBox[{"1", "-", "\[Gamma]"}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", "\[Beta]", RowBox[{"(", RowBox[{"1", "-", "\[Gamma]"}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}], "\[Gamma]"}], ",", RowBox[{"\[Alpha]", RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}], "\[Gamma]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]", " ", "\[Gamma]"}], ",", RowBox[{"\[Alpha]", " ", "\[Beta]", " ", "\[Gamma]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"assuming", " ", "a", " ", "linear", " ", "mapping"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{ RowBox[{"Transpose", "[", RowBox[{"D", "[", RowBox[{"r", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}], "}"}]}], "]"}], "]"}], "/.", " ", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", " ", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Gamma]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"displacement", " ", "gradient"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{"FFINV", ".", RowBox[{"Transpose", "[", RowBox[{"D", "[", RowBox[{"uvw", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}], "}"}]}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"IdentityMatrix", "[", "3", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "GG"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "/", "GG"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"1", "/", "GG"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"HEX27", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"non", "-", RowBox[{"symmetric", " ", "formulation"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "ns", ",", "NN", ",", "r", ",", "FF", ",", "FFINV", ",", "jac", ",", "PP", ",", "uvw", ",", "\[Phi]\[Theta]\[Psi]", ",", "Duvw", ",", "\[Sigma]\[Sigma]", ",", "\[Sigma]", ",", "\[Rho]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "EEEE", ",", "\[Delta]w\[Sigma]", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "GG", ",", "nl", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Epsilon]"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]", "-", "\[Gamma]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"Transpose", "[", RowBox[{"D", "[", RowBox[{"r", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}], "}"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", "=", RowBox[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"PP", "=", RowBox[{"LeviCivitaTensor", "[", "3", "]"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]\[Theta]\[Psi]", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"displacement", " ", "gradient"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{ RowBox[{"FFINV", ".", RowBox[{"Transpose", "[", RowBox[{"D", "[", RowBox[{"uvw", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}], "}"}]}], "]"}], "]"}]}], "-", RowBox[{"PP", ".", "\[Phi]\[Theta]\[Psi]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"IdentityMatrix", "[", "3", "]"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{ RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "+", "\[Nu]\[Nu]"}], ")"}]}], "*", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], "]"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}]}], "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"nonsymmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", "\[Phi]\[Theta]\[Psi]", "]"}], ".", RowBox[{"{", RowBox[{"mX", ",", "mY", ",", "mZ"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TET5", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.4426474258030453`*^9, {3.4444401255942*^9, 3.4444401388073997`*^9}, { 3.4444401803034*^9, 3.4444401844062*^9}, 3.4444402418922*^9, { 3.4444402805022*^9, 3.4444403134026003`*^9}, {3.4444403443062*^9, 3.4444404484049997`*^9}, {3.444483267101*^9, 3.444483267335*^9}, { 3.4444833136046*^9, 3.4444835622998*^9}, {3.4444836421094*^9, 3.4444837777981997`*^9}, {3.444483920429*^9, 3.4444839412237997`*^9}, 3.4444842905546*^9, {3.4444843207406*^9, 3.4444844162282*^9}, { 3.4444844465078*^9, 3.4444844624354*^9}, {3.4444845255998*^9, 3.4444845894505997`*^9}, {3.4444846290746*^9, 3.444484933025*^9}, { 3.4444849790917997`*^9, 3.4444851148742*^9}, {3.444534936054*^9, 3.4445349675348*^9}, {3.4445355821731997`*^9, 3.44453585174*^9}, { 3.4445372162198*^9, 3.4445372264378*^9}, 3.444537384731*^9, { 3.4445377585382*^9, 3.4445377605818*^9}, {3.4445379733658*^9, 3.4445379736934*^9}, {3.4445380176762*^9, 3.444538032777*^9}, { 3.4445381079222*^9, 3.4445381581386003`*^9}, {3.4445382726456003`*^9, 3.4445382910067997`*^9}, {3.4445383401312*^9, 3.4445383475880003`*^9}, { 3.444538438458*^9, 3.4445384464608*^9}, {3.4445385680783997`*^9, 3.4445385687648*^9}, {3.4445389411991997`*^9, 3.4445389431024*^9}, { 3.444539746605*^9, 3.4445397807846003`*^9}, {3.4445408839765997`*^9, 3.4445409234133997`*^9}, {3.4445409681698*^9, 3.4445409932702*^9}, { 3.4445415452906*^9, 3.4445415706717997`*^9}, {3.4445416647242002`*^9, 3.4445416909477997`*^9}, {3.4445417660150003`*^9, 3.444541788557*^9}, { 3.4445420906977997`*^9, 3.444542104847*^9}, {3.4445421885878*^9, 3.4445421941414003`*^9}, {3.4445422252166*^9, 3.4445422386014*^9}, { 3.444542280425*^9, 3.4445423014538*^9}, {3.444542455769*^9, 3.4445424578282003`*^9}, {3.4445431739214*^9, 3.444543175809*^9}, { 3.4445647020962*^9, 3.4445648405618*^9}, {3.4445648825414*^9, 3.4445648858486*^9}, {3.4445649382646*^9, 3.4445651882702*^9}, { 3.4446164822206*^9, 3.4446165344494*^9}, {3.4446166121842003`*^9, 3.4446166738822002`*^9}, {3.4446167223046*^9, 3.4446168047974*^9}, { 3.444616843033*^9, 3.444616906447*^9}, {3.4446444694708*^9, 3.4446444700948*^9}, {3.4446477738310003`*^9, 3.4446477939862003`*^9}, { 3.4446478467298*^9, 3.4446478681018*^9}, 3.4446480456142*^9, { 3.4446487557418003`*^9, 3.4446487636198*^9}, 3.4446488179974003`*^9, { 3.4446488971205997`*^9, 3.4446489152478*^9}, {3.4446490003458*^9, 3.4446490008294*^9}, {3.4447042728942003`*^9, 3.4447042751562*^9}, { 3.4447044703278*^9, 3.4447044865362*^9}, 3.4447046475282*^9, 3.4447047993786*^9, {3.444704908329*^9, 3.4447049292642*^9}, { 3.4447049861926003`*^9, 3.4447049877214003`*^9}, {3.4447050279296*^9, 3.4447050419695997`*^9}, {3.4447053486656*^9, 3.4447053739376*^9}, 3.4447054561963997`*^9, 3.44470561612*^9, {3.4472133996876*^9, 3.4472134108571997`*^9}, {3.4472134470179996`*^9, 3.4472134648332*^9}, { 3.4472135032872*^9, 3.4472135245344*^9}, {3.4472136963059998`*^9, 3.4472137794384003`*^9}, {3.4472138235708*^9, 3.4472138388900003`*^9}, { 3.4472139099792*^9, 3.4472141367096*^9}, {3.447214202682*^9, 3.4472142975924*^9}, {3.4472144187732*^9, 3.4472145910284*^9}, { 3.4472146560492*^9, 3.4472147023968*^9}, {3.447214803594*^9, 3.4472148728736*^9}, {3.4472149156956*^9, 3.447214940484*^9}, { 3.447216227284*^9, 3.4472162419948*^9}, {3.4472163068908*^9, 3.4472163720832*^9}, {3.4472164665880003`*^9, 3.447216530392*^9}, { 3.4472166237268*^9, 3.4472167058452*^9}, 3.4472167362808*^9, { 3.4472171394658003`*^9, 3.4472171532874002`*^9}, {3.4472172028993998`*^9, 3.4472172216661997`*^9}, {3.4472172524606*^9, 3.4472172690278*^9}, { 3.4472173209133997`*^9, 3.4472173334245996`*^9}, {3.4472173920846*^9, 3.447217404861*^9}, {3.4472179572548*^9, 3.4472180351456003`*^9}, { 3.4472509764091997`*^9, 3.4472511017396*^9}, {3.4473910422216*^9, 3.4473912901524*^9}, 3.4473918688344*^9, {3.447392021185*^9, 3.4473920346633997`*^9}, {3.4473921383304*^9, 3.4473921479088*^9}, { 3.4473923024112*^9, 3.4473923734379997`*^9}, {3.4473928098168*^9, 3.4473928648691998`*^9}, {3.4473931872432003`*^9, 3.4473932461800003`*^9}, {3.4473933026675997`*^9, 3.4473934579812*^9}, { 3.4473935755271997`*^9, 3.447393742572*^9}, {3.4473939032676*^9, 3.4473939384144*^9}, {3.447395257644*^9, 3.4473953141628*^9}, { 3.4473954231132*^9, 3.4473954756384*^9}, {3.4473955348716*^9, 3.4473955723272*^9}, {3.447395648502*^9, 3.4473957588876*^9}, { 3.4473957903996*^9, 3.4473958488372*^9}, 3.4473962894154*^9, { 3.447396350817*^9, 3.447396352611*^9}, {3.4474625379146*^9, 3.4474625637326*^9}, {3.558360651728078*^9, 3.558360652102478*^9}, { 3.5619791319820857`*^9, 3.561979135788492*^9}, 3.561979369382504*^9, { 3.5619794930439215`*^9, 3.5619795010155354`*^9}, {3.561979569218855*^9, 3.56197960614412*^9}, {3.5619797417551584`*^9, 3.5619797448751636`*^9}, { 3.618719065033702*^9, 3.618719075426296*^9}, {3.6187194011669273`*^9, 3.6187194449454317`*^9}, {3.6187196998040085`*^9, 3.6187197102436056`*^9}, {3.618719902254588*^9, 3.6187199711455283`*^9}, { 3.618722365406472*^9, 3.6187225412555304`*^9}, {3.6187226885009522`*^9, 3.6187227109872384`*^9}, {3.618722756922866*^9, 3.6187231317203026`*^9}, { 3.618723424250035*^9, 3.6187234267291765`*^9}, {3.6187235105259695`*^9, 3.6187236491028957`*^9}, {3.618723691580325*^9, 3.618723745975436*^9}, { 3.618723778837316*^9, 3.6187238310002995`*^9}, {3.6187239055875654`*^9, 3.618723940035536*^9}, {3.6187239782667227`*^9, 3.6187240219352207`*^9}, { 3.618724166762504*^9, 3.618724177411113*^9}, {3.618729321696159*^9, 3.618729328067523*^9}, 3.618729374058154*^9, {3.6187294379838104`*^9, 3.618729708464281*^9}, {3.6187297631904106`*^9, 3.618729773195983*^9}, { 3.618729822648812*^9, 3.6187299321490746`*^9}, {3.618729984399063*^9, 3.61873000654133*^9}, {3.6187300746012225`*^9, 3.6187300860458775`*^9}, { 3.618731390835507*^9, 3.6187315116174154`*^9}, {3.618731747324897*^9, 3.6187318214091344`*^9}, {3.6187318769243097`*^9, 3.618732065297084*^9}, { 3.6187321012351394`*^9, 3.618732157420353*^9}, {3.618732188384124*^9, 3.6187322435542793`*^9}, {3.6187322786112847`*^9, 3.6187325478446836`*^9}, {3.6187325819856367`*^9, 3.6187326817653437`*^9}, {3.618732810863728*^9, 3.61873282594359*^9}, { 3.6187336474335766`*^9, 3.618733754678711*^9}, {3.618733827497876*^9, 3.61873396201257*^9}, {3.6187342020362988`*^9, 3.618734236455267*^9}, 3.618734298201799*^9, {3.618734712498495*^9, 3.618734712716508*^9}, 3.6187347739640107`*^9, {3.618738817361748*^9, 3.6187388333816643`*^9}, { 3.6187391349349127`*^9, 3.6187391457955337`*^9}, {3.618739376900752*^9, 3.618739397023903*^9}, {3.618739528394417*^9, 3.618739534809784*^9}, { 3.618739972366811*^9, 3.61873997340687*^9}, {3.6187400416617737`*^9, 3.618740043022852*^9}, {3.6187400971579485`*^9, 3.618740107902563*^9}, { 3.6187401713671927`*^9, 3.6187401723312483`*^9}, {3.6187402613443394`*^9, 3.618740268819767*^9}, {3.6187403697625403`*^9, 3.6187404057615995`*^9}, { 3.618740488277319*^9, 3.618740516244919*^9}, {3.618740647782442*^9, 3.6187406551668644`*^9}, 3.6187407823021364`*^9, {3.6187418050786357`*^9, 3.618741805749674*^9}, {3.6187418557605343`*^9, 3.6187419895921893`*^9}, { 3.618742022944097*^9, 3.61874204379729*^9}, {3.6187420836395683`*^9, 3.618742103384698*^9}, {3.620462440882641*^9, 3.6204624460519366`*^9}, { 3.6204624990259666`*^9, 3.620462576450395*^9}, {3.620463682857678*^9, 3.620463713336421*^9}, 3.6204637901188126`*^9, {3.620464238835478*^9, 3.62046424411378*^9}, 3.628912429385081*^9, {3.6289135207155013`*^9, 3.6289135210805225`*^9}, 3.6289497746958513`*^9, 3.6289498371774254`*^9, { 3.62894988410911*^9, 3.6289500319795675`*^9}, {3.6289501333883677`*^9, 3.628950183744248*^9}, {3.6289503323017445`*^9, 3.628950390181055*^9}, { 3.6289505050536256`*^9, 3.6289505113579865`*^9}, {3.62895070863527*^9, 3.6289507095043197`*^9}, {3.628951013180689*^9, 3.62895101407374*^9}, { 3.629190743153632*^9, 3.629190816645361*^9}, {3.6291909709608326`*^9, 3.629190981678051*^9}, {3.629191034624544*^9, 3.6291910410049553`*^9}, { 3.6293846391370816`*^9, 3.629384641102685*^9}, 3.6294302231277533`*^9, 3.629430298397886*^9, {3.6294304452097435`*^9, 3.6294304461769457`*^9}, 3.629430512991863*^9, {3.629430631630071*^9, 3.6294306397264853`*^9}, { 3.629430697477787*^9, 3.629430801373969*^9}, {3.6294470005483365`*^9, 3.629447006658345*^9}, {3.6294476264402127`*^9, 3.62944766022026*^9}, { 3.629455940543494*^9, 3.6294559434734983`*^9}, {3.6294560037335825`*^9, 3.6294560722536783`*^9}, {3.6294561182137423`*^9, 3.629456154053793*^9}, { 3.6294562173438816`*^9, 3.629456291433985*^9}, 3.629456575994384*^9, { 3.6294571194161444`*^9, 3.629457325936434*^9}, {3.6294573681664925`*^9, 3.629457469696635*^9}, {3.630830822369603*^9, 3.630830833380233*^9}, { 3.6308308916105633`*^9, 3.630830892690625*^9}, {3.630830934683027*^9, 3.6308309652587757`*^9}, {3.630831001140828*^9, 3.6308310302394924`*^9}, { 3.6308311286591215`*^9, 3.6308311872784743`*^9}, {3.6308312724803476`*^9, 3.630831331484722*^9}, {3.630831362277484*^9, 3.630831473963872*^9}, { 3.6308315048656397`*^9, 3.6308315251297984`*^9}, {3.6308500199956975`*^9, 3.630850092130224*^9}, {3.6308926160699577`*^9, 3.630892648580415*^9}, { 3.6308926904976883`*^9, 3.6308930396419015`*^9}, {3.6308931926157703`*^9, 3.6308932605850897`*^9}, {3.630893319631193*^9, 3.6308933413620315`*^9}, { 3.630893371735285*^9, 3.6308933746056895`*^9}, {3.630893484195882*^9, 3.630893495552702*^9}, {3.6308935513072*^9, 3.6308937035322676`*^9}, { 3.630893900966214*^9, 3.630893903165818*^9}, {3.63089401261561*^9, 3.6308940229584284`*^9}, {3.630894084734537*^9, 3.630894141612237*^9}, { 3.6308941732958927`*^9, 3.63089421168756*^9}, {3.6308943234305563`*^9, 3.6308945706597905`*^9}, {3.630894732057674*^9, 3.6308948540342884`*^9}, { 3.6308949175576*^9, 3.6308950352130065`*^9}, {3.6308963280663238`*^9, 3.6308964339281096`*^9}, {3.630896483785797*^9, 3.6308965147216516`*^9}, { 3.630995110764593*^9, 3.6309952194788113`*^9}, 3.631017673702475*^9, 3.6339410343181667`*^9, {3.6339411434394083`*^9, 3.6339413336822896`*^9}, { 3.6339414012381535`*^9, 3.6339415162277308`*^9}, {3.633941550612697*^9, 3.6339415854086876`*^9}, {3.633941898820614*^9, 3.633941918825758*^9}, { 3.633942028814049*^9, 3.6339421351881332`*^9}, 3.6339421753194284`*^9, { 3.6339527595260005`*^9, 3.633952797347164*^9}, {3.6339528326231813`*^9, 3.6339528434568014`*^9}, 3.63395311337924*^9, {3.633953318391966*^9, 3.633953320104064*^9}, {3.6339533894880323`*^9, 3.633953398914572*^9}, { 3.6339534904578075`*^9, 3.6339534909158335`*^9}, {3.6339544324266853`*^9, 3.633954436992946*^9}, {3.633955355536484*^9, 3.633955361782841*^9}, { 3.634613015576932*^9, 3.63461301623897*^9}, {3.6346130510409603`*^9, 3.634613077198457*^9}, 3.634613188324813*^9, {3.6878638635768104`*^9, 3.6878639724170356`*^9}, 3.687864019557732*^9, 3.6878641001403413`*^9, { 3.687864195050747*^9, 3.6878641958857946`*^9}, {3.6878642401333256`*^9, 3.68786426136654*^9}, 3.687864352036726*^9, {3.687864450280345*^9, 3.6878644606039357`*^9}, {3.6878646809015083`*^9, 3.6878646814075365`*^9}, {3.687864779357139*^9, 3.6878648062606783`*^9}, { 3.6878651827021837`*^9, 3.687865213182927*^9}, {3.6878652461998158`*^9, 3.6878652992218485`*^9}, {3.687865350343772*^9, 3.687865355912091*^9}, { 3.687865609571577*^9, 3.6878656309137974`*^9}, {3.687865671576123*^9, 3.6878656918812847`*^9}, 3.687865733639673*^9, {3.6878657691897063`*^9, 3.6878657965562716`*^9}, {3.687865834375435*^9, 3.6878658387066827`*^9}, { 3.687865912326894*^9, 3.6878659163341227`*^9}, {3.6878659782786655`*^9, 3.687866006047254*^9}, {3.6878660595832973`*^9, 3.6878660659666624`*^9}, { 3.6878661218058558`*^9, 3.6878661872325983`*^9}, {3.687866245499931*^9, 3.687866274822608*^9}, 3.687866805421936*^9, {3.6879301815930185`*^9, 3.6879301828630204`*^9}, {3.687930277763153*^9, 3.6879302977631817`*^9}, { 3.6879303280532236`*^9, 3.687930399193323*^9}, {3.6879304307033677`*^9, 3.6879304862434454`*^9}, {3.6879305350435133`*^9, 3.6879306368336563`*^9}, {3.6879308629839725`*^9, 3.6879309443840866`*^9}, {3.6880225059517603`*^9, 3.688022695772026*^9}, { 3.6880227285420723`*^9, 3.688022739402087*^9}, 3.688124666129181*^9, { 3.6882843273150387`*^9, 3.6882845888454046`*^9}, {3.688285837009152*^9, 3.6882858406491575`*^9}, {3.688286818441526*^9, 3.688286844251562*^9}, { 3.6882870165218034`*^9, 3.688287041201838*^9}, {3.68828707122188*^9, 3.68828709261191*^9}, 3.68828714986199*^9, {3.688287467572435*^9, 3.6882874756924467`*^9}, {3.6882875215825105`*^9, 3.688287521962511*^9}, { 3.6924976946811843`*^9, 3.6924978409113894`*^9}, {3.692497927801511*^9, 3.6924979661015644`*^9}, {3.692498035281661*^9, 3.6924981004717526`*^9}, { 3.6924981611518373`*^9, 3.692498164851843*^9}, {3.692498211401908*^9, 3.6924983125120497`*^9}, {3.692502435097616*^9, 3.692502447592331*^9}, { 3.692502485821518*^9, 3.6925024860295296`*^9}, 3.6925027340347147`*^9, { 3.6940858758564043`*^9, 3.6940858848364167`*^9}, {3.6940859944465704`*^9, 3.6940860158966007`*^9}, {3.6940861169567423`*^9, 3.694086419977166*^9}, { 3.6940872923193874`*^9, 3.6940872938293896`*^9}, {3.6940873646994886`*^9, 3.694087369319495*^9}, 3.694087530509721*^9, {3.6945281161723194`*^9, 3.694528128442337*^9}, {3.6945281951824303`*^9, 3.694528217482462*^9}, { 3.694528268612533*^9, 3.694528649083066*^9}, {3.694528693523128*^9, 3.6945286979031343`*^9}, {3.6945781605358806`*^9, 3.6945782254759717`*^9}, {3.6945782921660647`*^9, 3.694578304996083*^9}, { 3.694578337066128*^9, 3.6945783532861505`*^9}, {3.6945783849061947`*^9, 3.6945783866561975`*^9}, {3.6945784400462723`*^9, 3.694578482566332*^9}, 3.694578713616655*^9, {3.7511979506411643`*^9, 3.751197960841903*^9}, { 3.755352558606639*^9, 3.7553526159830475`*^9}, {3.774071654702608*^9, 3.7740716613755894`*^9}, {3.774071748661003*^9, 3.7740718483755345`*^9}, { 3.7740718923844557`*^9, 3.774071983649667*^9}, 3.774072057837844*^9, { 3.774072100100342*^9, 3.774072136005568*^9}, {3.774072187780233*^9, 3.7740722037066555`*^9}, {3.774072323322257*^9, 3.7740724309500237`*^9}, { 3.7740724933285646`*^9, 3.774072635753066*^9}, {3.774072687249714*^9, 3.7740727925054007`*^9}, {3.7740728598637686`*^9, 3.7740728945968986`*^9}, 3.774072979683737*^9, {3.774172222258683*^9, 3.7741722646358166`*^9}, { 3.7741723702318573`*^9, 3.7741723746656275`*^9}, {3.7741725406355767`*^9, 3.7741725730793257`*^9}, 3.7741726613919673`*^9, {3.7741727284394493`*^9, 3.774172868506016*^9}, {3.7741729101771226`*^9, 3.774173007341322*^9}, { 3.774173102959459*^9, 3.7741731324499664`*^9}, 3.774236409887308*^9, { 3.7742365098127813`*^9, 3.7742365393429565`*^9}, {3.7830787204505596`*^9, 3.783078728236431*^9}, {3.7830788333789034`*^9, 3.783078891201686*^9}, { 3.7830789381996555`*^9, 3.7830789386494493`*^9}, 3.783078981596484*^9, { 3.783137965886668*^9, 3.7831381275811653`*^9}, {3.7831382197652965`*^9, 3.7831382711318674`*^9}, {3.7831383021548166`*^9, 3.783138316699332*^9}, { 3.7831384156346865`*^9, 3.7831384387677746`*^9}, {3.7831385999718432`*^9, 3.7831386289162683`*^9}, {3.783138703438572*^9, 3.7831388313574543`*^9}, { 3.7831388726832438`*^9, 3.7831389799876423`*^9}, {3.783139114486741*^9, 3.7831391207657857`*^9}, {3.7831392058372374`*^9, 3.7831392347077627`*^9}, {3.7831392881204815`*^9, 3.783139298414276*^9}, { 3.783139379567049*^9, 3.7831394938819885`*^9}, 3.7831396004671617`*^9, { 3.7831412786243258`*^9, 3.7831412860913258`*^9}, {3.7831414844000688`*^9, 3.7831415377807136`*^9}, {3.7831416766317453`*^9, 3.7831416816557817`*^9}, {3.7831417135337715`*^9, 3.7831417541137705`*^9}, {3.783141785061674*^9, 3.78314188080105*^9}, 3.783142056404602*^9, {3.7834133193911924`*^9, 3.783413370443163*^9}, { 3.7884238054537177`*^9, 3.788423817167117*^9}, {3.7884238549377203`*^9, 3.7884238763673477`*^9}, {3.788423922628934*^9, 3.7884239232207956`*^9}, { 3.788423982788879*^9, 3.7884239842015057`*^9}, {3.7884240163856163`*^9, 3.7884240253516703`*^9}, {3.8200253398852043`*^9, 3.8200254773530717`*^9}, 3.8411959691970887`*^9, {3.84318199280597*^9, 3.8431820660833826`*^9}}, CellLabel-> "In[209]:=",ExpressionUUID->"2765c3d3-7e63-4a4d-b27a-8d8791bb3da0"] }, Closed]], Cell[CellGroupData[{ Cell["SOLID ELEMENT (evnt) defs", "Subsection", InitializationCell->True, CellChangeTimes->{{3.753018875511382*^9, 3.7530188786265306`*^9}, { 3.781589886623744*^9, 3.7815898932426767`*^9}, {3.7878947601549573`*^9, 3.787894760728943*^9}, 3.7878948945295725`*^9, {3.817439343565061*^9, 3.8174393448082724`*^9}, {3.817439544553817*^9, 3.8174395452236648`*^9}, { 3.817439659219601*^9, 3.8174396600345135`*^9}, 3.817439764967313*^9, { 3.8174398145177484`*^9, 3.8174398153738604`*^9}, 3.8431829457768335`*^9},ExpressionUUID->"8e3e71c8-83f5-4e3c-9c4a-\ 4edb840e08a2"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"EVNT", ",", RowBox[{"{", RowBox[{"s0_", ",", "sol0_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"SOLID", ",", "anya_", ",", "anyb_"}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SOLID", ",", "anya", ",", "anyb"}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.4426466268192453`*^9, 3.4426467788544455`*^9}, { 3.443680046807*^9, 3.443680117163*^9}, {3.4436945929248*^9, 3.4436946334536*^9}, 3.4436946653087997`*^9, 3.4436947104396*^9, { 3.4461861532916*^9, 3.446186153744*^9}, {3.4461862231328*^9, 3.4461862553468*^9}, {3.446186292506*^9, 3.4461863473556004`*^9}, { 3.4461863827988*^9, 3.4461864352304*^9}, {3.446186572526*^9, 3.4461865777052*^9}, {3.451263479283*^9, 3.451263479751*^9}, { 3.4938807027527814`*^9, 3.4938807074171515`*^9}, {3.493880800287371*^9, 3.4938808523754373`*^9}, 3.4938809479786386`*^9, 3.4938811002466917`*^9, { 3.4938811515079627`*^9, 3.4938811517107615`*^9}, {3.4941655092594*^9, 3.4941656750562*^9}, {3.4941657353501997`*^9, 3.4941657435246*^9}, { 3.4941657779382*^9, 3.4941658634418*^9}, {3.4957207052706003`*^9, 3.4957207485294*^9}, {3.4957208264826*^9, 3.4957208443914003`*^9}, 3.4957209431258*^9, {3.4957210322642*^9, 3.4957210490341997`*^9}, 3.4957211815324*^9, {3.4957212363352003`*^9, 3.4957212456328*^9}, { 3.4957212942609997`*^9, 3.495721324993*^9}, {3.4975823349274*^9, 3.4975823545366*^9}, {3.4975824057046003`*^9, 3.4975824948898*^9}, { 3.4975825327354*^9, 3.4975825337650003`*^9}, {3.4975826475076*^9, 3.4975826545744*^9}, {3.4993509657212*^9, 3.499350971072*^9}, { 3.4993510472623997`*^9, 3.4993510481828003`*^9}, {3.4993511463536*^9, 3.4993512159764*^9}, {3.4993512745699997`*^9, 3.4993512754748*^9}, { 3.4994811051716003`*^9, 3.4994811663392*^9}, {3.4994811996452*^9, 3.4994813495144*^9}, {3.4994814548164*^9, 3.4994814597148*^9}, { 3.4994815491963997`*^9, 3.4994815501324*^9}, 3.5007041508297997`*^9, { 3.5007041887066*^9, 3.5007042038073997`*^9}, {3.5007042395938*^9, 3.5007042409978*^9}, {3.5007043421602*^9, 3.5007043514421997`*^9}, { 3.5007044087455997`*^9, 3.5007044250632*^9}, {3.5007044934178*^9, 3.5007045024034*^9}, {3.5007046824406*^9, 3.500704999808*^9}, { 3.5007050353234*^9, 3.5007050451202*^9}, {3.5007052587142*^9, 3.5007052605706*^9}, {3.5007053328766003`*^9, 3.5007054596577997`*^9}, { 3.5007159735338*^9, 3.5007161853984003`*^9}, {3.5007162280332003`*^9, 3.5007163483716*^9}, {3.5007163981823997`*^9, 3.5007164168244*^9}, { 3.5007164654028*^9, 3.5007167457036*^9}, {3.5007176771076*^9, 3.5007176863896*^9}, {3.5007177671352*^9, 3.500717783874*^9}, { 3.5007179049924*^9, 3.50071796265*^9}, {3.5009579544962*^9, 3.5009579659934*^9}, {3.5009580383814*^9, 3.5009581011401997`*^9}, { 3.5009581956988*^9, 3.5009582131864*^9}, {3.5009583928048*^9, 3.5009583930388002`*^9}, {3.5009587458640003`*^9, 3.5009587595296*^9}, { 3.5009592634954*^9, 3.5009592736354*^9}, {3.500959331527*^9, 3.5009593527897997`*^9}, {3.5625699941459312`*^9, 3.5625700053623505`*^9}, {3.5625701202721524`*^9, 3.562570128836568*^9}, { 3.6293860977240434`*^9, 3.629386104244855*^9}, {3.629386199327022*^9, 3.629386220496259*^9}, {3.6296431182972393`*^9, 3.62964311889004*^9}, { 3.629777573965969*^9, 3.629777733585449*^9}, {3.6297779641070547`*^9, 3.6297781672591486`*^9}, {3.6297782105906267`*^9, 3.6297787648833303`*^9}, {3.6297788067577257`*^9, 3.6297788473980503`*^9}, {3.6297790116215076`*^9, 3.629779171927389*^9}, { 3.6297795741584954`*^9, 3.629779653484635*^9}, {3.6297818984505787`*^9, 3.6297819210082183`*^9}, {3.629782000178357*^9, 3.6297820021907606`*^9}, { 3.629782216020336*^9, 3.629782224319551*^9}, 3.6297823407737556`*^9, { 3.629783163862401*^9, 3.6297832496313515`*^9}, {3.629870677773334*^9, 3.6298707174286036`*^9}, {3.6298707896411304`*^9, 3.6298709878862786`*^9}, {3.6306592122375627`*^9, 3.6306592151235676`*^9}, {3.6306598443506727`*^9, 3.630659875316727*^9}, 3.63065995660847*^9, 3.630670566864462*^9, {3.63083558537886*^9, 3.6308359887799683`*^9}, {3.6308362111739593`*^9, 3.6308362148243656`*^9}, {3.630836286288091*^9, 3.6308363606378217`*^9}, 3.6308364233343315`*^9, {3.631888358317337*^9, 3.631888434445471*^9}, { 3.6318884656455255`*^9, 3.6318885138028097`*^9}, {3.6318886621590705`*^9, 3.6318886772754974`*^9}, {3.631888745837618*^9, 3.6318888213573503`*^9}, { 3.6318890221765027`*^9, 3.6318890526121564`*^9}, 3.631889169159961*^9, 3.6318894033631725`*^9, {3.631889517414973*^9, 3.6318895524526343`*^9}, { 3.6318896836488647`*^9, 3.631889698765291*^9}, {3.6321898139439125`*^9, 3.632189856272333*^9}, {3.6321898953545685`*^9, 3.6321900355675883`*^9}, { 3.6321900697005405`*^9, 3.6321903203378763`*^9}, {3.6321903691376677`*^9, 3.632190388074751*^9}, {3.632190466145216*^9, 3.6321904844272614`*^9}, { 3.632190625107308*^9, 3.6321907202867517`*^9}, {3.632190835720354*^9, 3.6321908837511015`*^9}, {3.632190986102956*^9, 3.6321910052410507`*^9}, { 3.6321927997536907`*^9, 3.6321928025258493`*^9}, {3.6321941664038568`*^9, 3.632194191948318*^9}, {3.6624544812484736`*^9, 3.662454485084693*^9}, { 3.6624545866345015`*^9, 3.6624546098018265`*^9}, {3.685233396707606*^9, 3.6852334069476204`*^9}, {3.685233673317993*^9, 3.6852336973580265`*^9}, 3.685264712020458*^9, {3.685264780390554*^9, 3.6852648241406155`*^9}, { 3.6852713583430376`*^9, 3.6852714170531197`*^9}, {3.6852718305336986`*^9, 3.6852718842537737`*^9}, {3.6852720012539377`*^9, 3.685272008663948*^9}, { 3.685272070164034*^9, 3.6852720840640535`*^9}, 3.6853404120151405`*^9, { 3.6853405127463226`*^9, 3.685340625313761*^9}, {3.6853410657279515`*^9, 3.685341078722695*^9}, {3.685341189812049*^9, 3.6853411945933223`*^9}, { 3.685341231602439*^9, 3.6853412388978567`*^9}, 3.6853430337255144`*^9, { 3.68585373700861*^9, 3.6858537556736774`*^9}, 3.685853822475498*^9, { 3.68585391622186*^9, 3.6858539266884584`*^9}, {3.685853962796524*^9, 3.685853970925989*^9}, 3.6858541341643257`*^9, {3.685854449069337*^9, 3.685854452354525*^9}, {3.6858544860604534`*^9, 3.6858544933768716`*^9}, { 3.685854943776633*^9, 3.6858549563563523`*^9}, {3.6859534582909718`*^9, 3.685953483154394*^9}, {3.685965935028836*^9, 3.6859660165689497`*^9}, { 3.68596614502913*^9, 3.68596618077918*^9}, {3.6859665004496274`*^9, 3.685966524549661*^9}, {3.6859666104197817`*^9, 3.685966617519791*^9}, { 3.6860123360453115`*^9, 3.6860123945753937`*^9}, {3.6860124484754686`*^9, 3.6860124852555203`*^9}, {3.686012537365593*^9, 3.6860125428256006`*^9}, 3.6860126339057283`*^9, 3.686012710945836*^9, {3.6860128143059807`*^9, 3.6860128145959816`*^9}, {3.6860129183361263`*^9, 3.6860129676061954`*^9}, 3.686013029216282*^9, {3.686019337710574*^9, 3.6860195425908613`*^9}, { 3.686019651761014*^9, 3.6860196633110304`*^9}, 3.6860202343918295`*^9, { 3.6860237604228506`*^9, 3.6860238349729548`*^9}, 3.686023961653132*^9, { 3.68714588472073*^9, 3.687145885140731*^9}, {3.6871460474709578`*^9, 3.687146053790967*^9}, {3.6871460941910233`*^9, 3.6871460981810293`*^9}, { 3.6871461354510813`*^9, 3.687146395471445*^9}, {3.6871464425315113`*^9, 3.687146453221526*^9}, 3.687146604551738*^9, 3.6871466841818495`*^9, { 3.6871470071023016`*^9, 3.687147008182303*^9}, 3.687147048432359*^9, { 3.6871470932524223`*^9, 3.6871471214924617`*^9}, {3.6871471604425163`*^9, 3.6871473693028083`*^9}, {3.6874228236597347`*^9, 3.6874228709898005`*^9}, {3.6874231158501434`*^9, 3.6874232243002954`*^9}, {3.6875189610998473`*^9, 3.687519005537389*^9}, { 3.687519062781663*^9, 3.6875192133922777`*^9}, {3.6875193939396043`*^9, 3.6875193991879044`*^9}, {3.687520128393613*^9, 3.687520238740924*^9}, 3.6875261810306673`*^9, {3.6876715960629864`*^9, 3.6876717494132013`*^9}, { 3.6876718441833344`*^9, 3.6876718768033795`*^9}, {3.6876723915341005`*^9, 3.687672434904161*^9}, 3.688395660193591*^9, 3.6883964158577833`*^9, { 3.692412576581642*^9, 3.6924125803116474`*^9}, {3.6924126302817173`*^9, 3.692412655961754*^9}, {3.692412695731809*^9, 3.6924127074218254`*^9}, { 3.6924127522818885`*^9, 3.6924127586918974`*^9}, {3.69241285349203*^9, 3.6924128539320307`*^9}, {3.692412907092105*^9, 3.692413029772277*^9}, { 3.692413068192331*^9, 3.692413166452468*^9}, {3.692413741305273*^9, 3.6924137594552984`*^9}, {3.6924168804381475`*^9, 3.692416890318161*^9}, { 3.692416926028211*^9, 3.6924169565082536`*^9}, {3.6924169983583126`*^9, 3.692417051860387*^9}, {3.6924171044204607`*^9, 3.6924171568505344`*^9}, { 3.692417194820587*^9, 3.692417195170588*^9}, {3.6924213133305225`*^9, 3.6924213143205233`*^9}, {3.692421353670579*^9, 3.6924213540405793`*^9}, { 3.69277257982156*^9, 3.6927725838615656`*^9}, {3.692855931835436*^9, 3.692855932875437*^9}, {3.6928567610465965`*^9, 3.6928568324266963`*^9}, { 3.692856901206793*^9, 3.6928569095168047`*^9}, {3.69285698469691*^9, 3.692856993426922*^9}, {3.69285703490698*^9, 3.692857117767096*^9}, { 3.6928573265673885`*^9, 3.6928576414078293`*^9}, {3.6932192279315724`*^9, 3.693219231191577*^9}, 3.6932193482617407`*^9, {3.6932193866617947`*^9, 3.693219399421812*^9}, {3.693220387105195*^9, 3.693220395585207*^9}, { 3.693220619885521*^9, 3.693220622315525*^9}, 3.6932206741055975`*^9, { 3.6937158692541003`*^9, 3.693715869654101*^9}, {3.6937159892942686`*^9, 3.693716052294357*^9}, {3.693716084724402*^9, 3.6937165234970164`*^9}, { 3.69371656887708*^9, 3.6937167464873285`*^9}, {3.6937167931673937`*^9, 3.693716881127517*^9}, {3.6937174784783535`*^9, 3.6937174801583557`*^9}, { 3.6937209970340457`*^9, 3.693721056784129*^9}, {3.6940658253906527`*^9, 3.69406583796067*^9}, {3.694065981390871*^9, 3.6940660285909367`*^9}, { 3.69406631676134*^9, 3.694066328431357*^9}, {3.6940663845914354`*^9, 3.69406638788144*^9}, {3.6940667791219873`*^9, 3.6940668111720324`*^9}, { 3.694067197922574*^9, 3.694067205792585*^9}, {3.694230787618657*^9, 3.6942308443987365`*^9}, {3.694230880048786*^9, 3.6942309310488577`*^9}, { 3.6942309647089047`*^9, 3.6942310590790367`*^9}, {3.6942311817392087`*^9, 3.6942313193904014`*^9}, {3.6942313582004557`*^9, 3.6942317436109953`*^9}, {3.694232100401495*^9, 3.694232179791606*^9}, { 3.694232591252182*^9, 3.694232606942204*^9}, 3.694265123583295*^9, 3.6943208649568324`*^9, {3.6944241392570753`*^9, 3.694424146417085*^9}, { 3.72541924301532*^9, 3.7254192468679457`*^9}, {3.725431584796835*^9, 3.725431637535695*^9}, 3.725432095606172*^9, {3.749695458974357*^9, 3.7496954653226786`*^9}, {3.749695629209482*^9, 3.7496957170177097`*^9}, { 3.749695766766241*^9, 3.7496959409872313`*^9}, {3.749696586402536*^9, 3.7496965868288536`*^9}, {3.7496969375048475`*^9, 3.749696939543347*^9}, { 3.7496975602512183`*^9, 3.749697622751583*^9}, {3.7496976733864603`*^9, 3.749697733500789*^9}, 3.749698076456645*^9, {3.7496981179531765`*^9, 3.749698128232212*^9}, {3.7496982428286314`*^9, 3.749698362156461*^9}, { 3.7496984682622967`*^9, 3.7496985284496694`*^9}, {3.7496992170188684`*^9, 3.7496992868619986`*^9}, {3.7496993728466873`*^9, 3.749699375486853*^9}, { 3.7530189177531705`*^9, 3.753018918350237*^9}, {3.753018991800671*^9, 3.753019041865839*^9}, {3.7530191095313196`*^9, 3.7530191100576744`*^9}, 3.753019155952956*^9, {3.7530192458219423`*^9, 3.753019353286773*^9}, { 3.773986323215969*^9, 3.7739864366876383`*^9}, {3.7739864700193005`*^9, 3.7739865885966825`*^9}, {3.7739869332783327`*^9, 3.7739870501829805`*^9}, 3.773987085528166*^9, {3.7739872536160583`*^9, 3.773987270466986*^9}, { 3.773987482712697*^9, 3.7739875221812735`*^9}, {3.773987740298462*^9, 3.7739877466065903`*^9}, {3.7739878599976892`*^9, 3.7739878861137896`*^9}, {3.773987965425336*^9, 3.7739879715632877`*^9}, 3.773988098774023*^9, 3.7739883193781385`*^9, {3.7739884099852057`*^9, 3.7739885862960095`*^9}, {3.773988628922502*^9, 3.773988632767228*^9}, { 3.7739891227568517`*^9, 3.77398915009042*^9}, {3.7739892774900556`*^9, 3.773989291800435*^9}, {3.7739896060525217`*^9, 3.773989635013425*^9}, { 3.7751890832095585`*^9, 3.7751890882413054`*^9}, {3.7751894923762302`*^9, 3.7751895008441906`*^9}, {3.7751911834227276`*^9, 3.775191222686661*^9}, 3.7751912606478214`*^9, {3.7751943412188396`*^9, 3.775194461553982*^9}, { 3.775194496052539*^9, 3.7751945353727713`*^9}, {3.7751945737174063`*^9, 3.775194621343042*^9}, {3.775194667862669*^9, 3.7751947598351893`*^9}, { 3.7751948235734253`*^9, 3.7751949415953684`*^9}, {3.775195100078847*^9, 3.77519512113822*^9}, {3.7751954506873007`*^9, 3.775195467864645*^9}, { 3.775270786870551*^9, 3.775270796325161*^9}, {3.7752708274391947`*^9, 3.775270839737406*^9}, {3.7752709283091574`*^9, 3.7752709474534383`*^9}, { 3.7752710502850266`*^9, 3.7752711744130797`*^9}, {3.7752712273079033`*^9, 3.7752713060364757`*^9}, {3.775271448825513*^9, 3.7752714699277525`*^9}, { 3.775271509321142*^9, 3.775271585609558*^9}, {3.775271620653377*^9, 3.77527180192237*^9}, {3.781589928213842*^9, 3.781590052438653*^9}, { 3.7815900898176003`*^9, 3.781590109307678*^9}, {3.781590201383393*^9, 3.7815902433873234`*^9}, {3.7815905445265956`*^9, 3.781590569573782*^9}, { 3.7815906952864275`*^9, 3.781590715680611*^9}, {3.7815908323678637`*^9, 3.781590881239719*^9}, {3.7815911048122363`*^9, 3.781591119274813*^9}, { 3.817439386305109*^9, 3.8174394287787733`*^9}, {3.8174395552770724`*^9, 3.8174395603447847`*^9}, {3.8174396709099665`*^9, 3.817439676294123*^9}, { 3.8174397747716293`*^9, 3.8174397780717535`*^9}, {3.8174398318697805`*^9, 3.817439837879761*^9}, 3.8175213595144067`*^9, 3.8431829500234118`*^9}, CellLabel-> "In[214]:=",ExpressionUUID->"4181ac41-3f39-4509-9d69-0ecf763e44c4"] }, Closed]], Cell[CellGroupData[{ Cell["SOLID ELEMENT (vibr) defs ", "Subsection", CellChangeTimes->{{3.629430162287647*^9, 3.6294301631768484`*^9}, { 3.7575037777673283`*^9, 3.7575037970958652`*^9}, 3.788423792328411*^9},ExpressionUUID->"78fbdbaa-de20-48de-9ab2-\ 0b9c998c4e2c"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"I1_", ",", "I2_", ",", "I3_", ",", "I4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "ns", ",", "NN", ",", "r", ",", "FF", ",", "PP", ",", "uvw", ",", "uvw0", ",", "uvw2", ",", "Duvw", ",", "\[Epsilon]", ",", "\[Sigma]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "EEEE", ",", "\[Delta]w\[Sigma]", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "GG", ",", "nl", ",", "jac", ",", "FFINV", ",", "\[Delta]wext", ",", "\[Delta]wint", ",", "\[Delta]wine"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"I1", ",", "I2", ",", "I3", ",", "I4"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]", "-", "\[Gamma]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"assuming", " ", "a", " ", "linear", " ", "mapping"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "r"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"uvw0", "=", " ", RowBox[{"uvw", "/.", " ", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"uvw2", "=", " ", RowBox[{"uvw", " ", "/.", " ", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"displacement", " ", "gradient"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "uvw0"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "uvw0"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "uvw0"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "GG"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "/", "GG"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"1", "/", "GG"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uvw0", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wine", "=", RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "uvw0", "]"}], ".", RowBox[{"(", RowBox[{"\[Rho]\[Rho]", " ", "uvw2"}], ")"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TET5", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wext", "+", "\[Delta]wint", "+", "\[Delta]wine"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], "}"}], ",", RowBox[{"Hexahedron", "[", RowBox[{"{", RowBox[{ "n1_", ",", "n2_", ",", "n3_", ",", "n4_", ",", "n5_", ",", "n6_", ",", "n7_", ",", "n8_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Hexahedron", "[", RowBox[{"{", RowBox[{ "n1", ",", "n2", ",", "n3", ",", "n4", ",", "n5", ",", "n6", ",", "n7", ",", "n8"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Hexahedron", "[", RowBox[{"{", RowBox[{ "n1_", ",", "n2_", ",", "n3_", ",", "n4_", ",", "n5_", ",", "n6_", ",", "n7_", ",", "n8_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "NN", ",", "r", ",", "FF", ",", "PP", ",", "uvw0", ",", "uvw2", ",", "\[Sigma]", ",", "EEEE", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "GG", ",", "jac", ",", "FFINV", ",", "\[Epsilon]", ",", "\[Delta]wext", ",", "\[Delta]wint", ",", "\[Delta]wine"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{ "n1", ",", "n2", ",", "n3", ",", "n4", ",", "n5", ",", "n6", ",", "n7", ",", "n8"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Gamma]"}], ")"}]}], ",", RowBox[{"\[Alpha]", RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Gamma]"}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]", RowBox[{"(", RowBox[{"1", "-", "\[Gamma]"}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", "\[Beta]", RowBox[{"(", RowBox[{"1", "-", "\[Gamma]"}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}], "\[Gamma]"}], ",", RowBox[{"\[Alpha]", RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}], "\[Gamma]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]", " ", "\[Gamma]"}], ",", RowBox[{"\[Alpha]", " ", "\[Beta]", " ", "\[Gamma]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"assuming", " ", "a", " ", "linear", " ", "mapping"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{ RowBox[{"Transpose", "[", RowBox[{"D", "[", RowBox[{"r", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}], "}"}]}], "]"}], "]"}], "/.", " ", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", " ", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Gamma]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw0", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}], " ", "/.", " ", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"uvw2", "=", RowBox[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}], " ", "/.", " ", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"displacement", " ", "gradient"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{"FFINV", ".", RowBox[{"Transpose", "[", RowBox[{"D", "[", RowBox[{"uvw0", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}], "}"}]}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"IdentityMatrix", "[", "3", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "GG"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "/", "GG"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"1", "/", "GG"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uvw0", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wine", "=", RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "uvw0", "]"}], ".", RowBox[{"(", RowBox[{"\[Rho]\[Rho]", " ", "uvw2"}], ")"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"HEX27", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wext", "+", "\[Delta]wint", "+", "\[Delta]wine"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.4426474258030453`*^9, {3.4444401255942*^9, 3.4444401388073997`*^9}, { 3.4444401803034*^9, 3.4444401844062*^9}, 3.4444402418922*^9, { 3.4444402805022*^9, 3.4444403134026003`*^9}, {3.4444403443062*^9, 3.4444404484049997`*^9}, {3.444483267101*^9, 3.444483267335*^9}, { 3.4444833136046*^9, 3.4444835622998*^9}, {3.4444836421094*^9, 3.4444837777981997`*^9}, {3.444483920429*^9, 3.4444839412237997`*^9}, 3.4444842905546*^9, {3.4444843207406*^9, 3.4444844162282*^9}, { 3.4444844465078*^9, 3.4444844624354*^9}, {3.4444845255998*^9, 3.4444845894505997`*^9}, {3.4444846290746*^9, 3.444484933025*^9}, { 3.4444849790917997`*^9, 3.4444851148742*^9}, {3.444534936054*^9, 3.4445349675348*^9}, {3.4445355821731997`*^9, 3.44453585174*^9}, { 3.4445372162198*^9, 3.4445372264378*^9}, 3.444537384731*^9, { 3.4445377585382*^9, 3.4445377605818*^9}, {3.4445379733658*^9, 3.4445379736934*^9}, {3.4445380176762*^9, 3.444538032777*^9}, { 3.4445381079222*^9, 3.4445381581386003`*^9}, {3.4445382726456003`*^9, 3.4445382910067997`*^9}, {3.4445383401312*^9, 3.4445383475880003`*^9}, { 3.444538438458*^9, 3.4445384464608*^9}, {3.4445385680783997`*^9, 3.4445385687648*^9}, {3.4445389411991997`*^9, 3.4445389431024*^9}, { 3.444539746605*^9, 3.4445397807846003`*^9}, {3.4445408839765997`*^9, 3.4445409234133997`*^9}, {3.4445409681698*^9, 3.4445409932702*^9}, { 3.4445415452906*^9, 3.4445415706717997`*^9}, {3.4445416647242002`*^9, 3.4445416909477997`*^9}, {3.4445417660150003`*^9, 3.444541788557*^9}, { 3.4445420906977997`*^9, 3.444542104847*^9}, {3.4445421885878*^9, 3.4445421941414003`*^9}, {3.4445422252166*^9, 3.4445422386014*^9}, { 3.444542280425*^9, 3.4445423014538*^9}, {3.444542455769*^9, 3.4445424578282003`*^9}, {3.4445431739214*^9, 3.444543175809*^9}, { 3.4445647020962*^9, 3.4445648405618*^9}, {3.4445648825414*^9, 3.4445648858486*^9}, {3.4445649382646*^9, 3.4445651882702*^9}, { 3.4446164822206*^9, 3.4446165344494*^9}, {3.4446166121842003`*^9, 3.4446166738822002`*^9}, {3.4446167223046*^9, 3.4446168047974*^9}, { 3.444616843033*^9, 3.444616906447*^9}, {3.4446444694708*^9, 3.4446444700948*^9}, {3.4446477738310003`*^9, 3.4446477939862003`*^9}, { 3.4446478467298*^9, 3.4446478681018*^9}, 3.4446480456142*^9, { 3.4446487557418003`*^9, 3.4446487636198*^9}, 3.4446488179974003`*^9, { 3.4446488971205997`*^9, 3.4446489152478*^9}, {3.4446490003458*^9, 3.4446490008294*^9}, {3.4447042728942003`*^9, 3.4447042751562*^9}, { 3.4447044703278*^9, 3.4447044865362*^9}, 3.4447046475282*^9, 3.4447047993786*^9, {3.444704908329*^9, 3.4447049292642*^9}, { 3.4447049861926003`*^9, 3.4447049877214003`*^9}, {3.4447050279296*^9, 3.4447050419695997`*^9}, {3.4447053486656*^9, 3.4447053739376*^9}, 3.4447054561963997`*^9, 3.44470561612*^9, {3.4472133996876*^9, 3.4472134108571997`*^9}, {3.4472134470179996`*^9, 3.4472134648332*^9}, { 3.4472135032872*^9, 3.4472135245344*^9}, {3.4472136963059998`*^9, 3.4472137794384003`*^9}, {3.4472138235708*^9, 3.4472138388900003`*^9}, { 3.4472139099792*^9, 3.4472141367096*^9}, {3.447214202682*^9, 3.4472142975924*^9}, {3.4472144187732*^9, 3.4472145910284*^9}, { 3.4472146560492*^9, 3.4472147023968*^9}, {3.447214803594*^9, 3.4472148728736*^9}, {3.4472149156956*^9, 3.447214940484*^9}, { 3.447216227284*^9, 3.4472162419948*^9}, {3.4472163068908*^9, 3.4472163720832*^9}, {3.4472164665880003`*^9, 3.447216530392*^9}, { 3.4472166237268*^9, 3.4472167058452*^9}, 3.4472167362808*^9, { 3.4472171394658003`*^9, 3.4472171532874002`*^9}, {3.4472172028993998`*^9, 3.4472172216661997`*^9}, {3.4472172524606*^9, 3.4472172690278*^9}, { 3.4472173209133997`*^9, 3.4472173334245996`*^9}, {3.4472173920846*^9, 3.447217404861*^9}, {3.4472179572548*^9, 3.4472180351456003`*^9}, { 3.4472509764091997`*^9, 3.4472511017396*^9}, {3.4473910422216*^9, 3.4473912901524*^9}, 3.4473918688344*^9, {3.447392021185*^9, 3.4473920346633997`*^9}, {3.4473921383304*^9, 3.4473921479088*^9}, { 3.4473923024112*^9, 3.4473923734379997`*^9}, {3.4473928098168*^9, 3.4473928648691998`*^9}, {3.4473931872432003`*^9, 3.4473932461800003`*^9}, {3.4473933026675997`*^9, 3.4473934579812*^9}, { 3.4473935755271997`*^9, 3.447393742572*^9}, {3.4473939032676*^9, 3.4473939384144*^9}, {3.447395257644*^9, 3.4473953141628*^9}, { 3.4473954231132*^9, 3.4473954756384*^9}, {3.4473955348716*^9, 3.4473955723272*^9}, {3.447395648502*^9, 3.4473957588876*^9}, { 3.4473957903996*^9, 3.4473958488372*^9}, 3.4473962894154*^9, { 3.447396350817*^9, 3.447396352611*^9}, {3.4474625379146*^9, 3.4474625637326*^9}, {3.558360651728078*^9, 3.558360652102478*^9}, { 3.5619791319820857`*^9, 3.561979135788492*^9}, 3.561979369382504*^9, { 3.5619794930439215`*^9, 3.5619795010155354`*^9}, {3.561979569218855*^9, 3.56197960614412*^9}, {3.5619797417551584`*^9, 3.5619797448751636`*^9}, { 3.618719065033702*^9, 3.618719075426296*^9}, {3.6187194011669273`*^9, 3.6187194449454317`*^9}, {3.6187196998040085`*^9, 3.6187197102436056`*^9}, {3.618719902254588*^9, 3.6187199711455283`*^9}, { 3.618722365406472*^9, 3.6187225412555304`*^9}, {3.6187226885009522`*^9, 3.6187227109872384`*^9}, {3.618722756922866*^9, 3.6187231317203026`*^9}, { 3.618723424250035*^9, 3.6187234267291765`*^9}, {3.6187235105259695`*^9, 3.6187236491028957`*^9}, {3.618723691580325*^9, 3.618723745975436*^9}, { 3.618723778837316*^9, 3.6187238310002995`*^9}, {3.6187239055875654`*^9, 3.618723940035536*^9}, {3.6187239782667227`*^9, 3.6187240219352207`*^9}, { 3.618724166762504*^9, 3.618724177411113*^9}, {3.618729321696159*^9, 3.618729328067523*^9}, 3.618729374058154*^9, {3.6187294379838104`*^9, 3.618729708464281*^9}, {3.6187297631904106`*^9, 3.618729773195983*^9}, { 3.618729822648812*^9, 3.6187299321490746`*^9}, {3.618729984399063*^9, 3.61873000654133*^9}, {3.6187300746012225`*^9, 3.6187300860458775`*^9}, { 3.618731390835507*^9, 3.6187315116174154`*^9}, {3.618731747324897*^9, 3.6187318214091344`*^9}, {3.6187318769243097`*^9, 3.618732065297084*^9}, { 3.6187321012351394`*^9, 3.618732157420353*^9}, {3.618732188384124*^9, 3.6187322435542793`*^9}, {3.6187322786112847`*^9, 3.6187325478446836`*^9}, {3.6187325819856367`*^9, 3.6187326817653437`*^9}, {3.618732810863728*^9, 3.61873282594359*^9}, { 3.6187336474335766`*^9, 3.618733754678711*^9}, {3.618733827497876*^9, 3.61873396201257*^9}, {3.6187342020362988`*^9, 3.618734236455267*^9}, 3.618734298201799*^9, {3.618734712498495*^9, 3.618734712716508*^9}, 3.6187347739640107`*^9, {3.618738817361748*^9, 3.6187388333816643`*^9}, { 3.6187391349349127`*^9, 3.6187391457955337`*^9}, {3.618739376900752*^9, 3.618739397023903*^9}, {3.618739528394417*^9, 3.618739534809784*^9}, { 3.618739972366811*^9, 3.61873997340687*^9}, {3.6187400416617737`*^9, 3.618740043022852*^9}, {3.6187400971579485`*^9, 3.618740107902563*^9}, { 3.6187401713671927`*^9, 3.6187401723312483`*^9}, {3.6187402613443394`*^9, 3.618740268819767*^9}, {3.6187403697625403`*^9, 3.6187404057615995`*^9}, { 3.618740488277319*^9, 3.618740516244919*^9}, {3.618740647782442*^9, 3.6187406551668644`*^9}, 3.6187407823021364`*^9, {3.6187418050786357`*^9, 3.618741805749674*^9}, {3.6187418557605343`*^9, 3.6187419895921893`*^9}, { 3.618742022944097*^9, 3.61874204379729*^9}, {3.6187420836395683`*^9, 3.618742103384698*^9}, {3.620462440882641*^9, 3.6204624460519366`*^9}, { 3.6204624990259666`*^9, 3.620462576450395*^9}, {3.620463682857678*^9, 3.620463713336421*^9}, 3.6204637901188126`*^9, {3.620464238835478*^9, 3.62046424411378*^9}, 3.628912429385081*^9, {3.6289135207155013`*^9, 3.6289135210805225`*^9}, 3.6289497746958513`*^9, 3.6289498371774254`*^9, { 3.62894988410911*^9, 3.6289500319795675`*^9}, {3.6289501333883677`*^9, 3.628950183744248*^9}, {3.6289503323017445`*^9, 3.628950390181055*^9}, { 3.6289505050536256`*^9, 3.6289505113579865`*^9}, {3.62895070863527*^9, 3.6289507095043197`*^9}, {3.628951013180689*^9, 3.62895101407374*^9}, { 3.629190743153632*^9, 3.629190816645361*^9}, {3.6291909709608326`*^9, 3.629190981678051*^9}, {3.629191034624544*^9, 3.6291910410049553`*^9}, { 3.6293846391370816`*^9, 3.629384641102685*^9}, 3.6294302231277533`*^9, 3.629430298397886*^9, {3.6294304452097435`*^9, 3.6294304461769457`*^9}, 3.629430512991863*^9, {3.629430631630071*^9, 3.6294306397264853`*^9}, { 3.629430697477787*^9, 3.629430801373969*^9}, {3.6294470005483365`*^9, 3.629447006658345*^9}, {3.6294476264402127`*^9, 3.62944766022026*^9}, { 3.629455940543494*^9, 3.6294559434734983`*^9}, {3.6294560037335825`*^9, 3.6294560722536783`*^9}, {3.6294561182137423`*^9, 3.629456154053793*^9}, { 3.6294562173438816`*^9, 3.629456291433985*^9}, 3.629456575994384*^9, { 3.6294571194161444`*^9, 3.629457325936434*^9}, {3.6294573681664925`*^9, 3.629457469696635*^9}, {3.630830822369603*^9, 3.630830833380233*^9}, { 3.6308308916105633`*^9, 3.630830892690625*^9}, {3.630830934683027*^9, 3.6308309652587757`*^9}, {3.630831001140828*^9, 3.6308310302394924`*^9}, { 3.6308311286591215`*^9, 3.6308311872784743`*^9}, {3.6308312724803476`*^9, 3.630831331484722*^9}, {3.630831362277484*^9, 3.630831473963872*^9}, { 3.6308315048656397`*^9, 3.6308315251297984`*^9}, {3.6308500199956975`*^9, 3.630850092130224*^9}, {3.6308926160699577`*^9, 3.630892648580415*^9}, { 3.6308926904976883`*^9, 3.6308930396419015`*^9}, {3.6308931926157703`*^9, 3.6308932605850897`*^9}, {3.630893319631193*^9, 3.6308933413620315`*^9}, { 3.630893371735285*^9, 3.6308933746056895`*^9}, {3.630893484195882*^9, 3.630893495552702*^9}, {3.6308935513072*^9, 3.6308937035322676`*^9}, { 3.630893900966214*^9, 3.630893903165818*^9}, {3.63089401261561*^9, 3.6308940229584284`*^9}, {3.630894084734537*^9, 3.630894141612237*^9}, { 3.6308941732958927`*^9, 3.63089421168756*^9}, {3.6308943234305563`*^9, 3.6308945706597905`*^9}, {3.630894732057674*^9, 3.6308948540342884`*^9}, { 3.6308949175576*^9, 3.6308950352130065`*^9}, {3.6308963280663238`*^9, 3.6308964339281096`*^9}, {3.630896483785797*^9, 3.6308965147216516`*^9}, { 3.630995110764593*^9, 3.6309952194788113`*^9}, 3.631017673702475*^9, 3.6339410343181667`*^9, {3.6339411434394083`*^9, 3.6339413336822896`*^9}, { 3.6339414012381535`*^9, 3.6339415162277308`*^9}, {3.633941550612697*^9, 3.6339415854086876`*^9}, {3.633941898820614*^9, 3.633941918825758*^9}, { 3.633942028814049*^9, 3.6339421351881332`*^9}, 3.6339421753194284`*^9, { 3.6339527595260005`*^9, 3.633952797347164*^9}, {3.6339528326231813`*^9, 3.6339528434568014`*^9}, 3.63395311337924*^9, {3.633953318391966*^9, 3.633953320104064*^9}, {3.6339533894880323`*^9, 3.633953398914572*^9}, { 3.6339534904578075`*^9, 3.6339534909158335`*^9}, {3.6339544324266853`*^9, 3.633954436992946*^9}, {3.633955355536484*^9, 3.633955361782841*^9}, { 3.634613015576932*^9, 3.63461301623897*^9}, {3.6346130510409603`*^9, 3.634613077198457*^9}, 3.634613188324813*^9, {3.6878638635768104`*^9, 3.6878639724170356`*^9}, 3.687864019557732*^9, 3.6878641001403413`*^9, { 3.687864195050747*^9, 3.6878641958857946`*^9}, {3.6878642401333256`*^9, 3.68786426136654*^9}, 3.687864352036726*^9, {3.687864450280345*^9, 3.6878644606039357`*^9}, {3.6878646809015083`*^9, 3.6878646814075365`*^9}, {3.687864779357139*^9, 3.6878648062606783`*^9}, { 3.6878651827021837`*^9, 3.687865213182927*^9}, {3.6878652461998158`*^9, 3.6878652992218485`*^9}, {3.687865350343772*^9, 3.687865355912091*^9}, { 3.687865609571577*^9, 3.6878656309137974`*^9}, {3.687865671576123*^9, 3.6878656918812847`*^9}, 3.687865733639673*^9, {3.6878657691897063`*^9, 3.6878657965562716`*^9}, {3.687865834375435*^9, 3.6878658387066827`*^9}, { 3.687865912326894*^9, 3.6878659163341227`*^9}, {3.6878659782786655`*^9, 3.687866006047254*^9}, {3.6878660595832973`*^9, 3.6878660659666624`*^9}, { 3.6878661218058558`*^9, 3.6878661872325983`*^9}, {3.687866245499931*^9, 3.687866274822608*^9}, 3.687866805421936*^9, {3.6879301815930185`*^9, 3.6879301828630204`*^9}, {3.687930277763153*^9, 3.6879302977631817`*^9}, { 3.6879303280532236`*^9, 3.687930399193323*^9}, {3.6879304307033677`*^9, 3.6879304862434454`*^9}, {3.6879305350435133`*^9, 3.6879306368336563`*^9}, {3.6879308629839725`*^9, 3.6879309443840866`*^9}, {3.6880225059517603`*^9, 3.688022695772026*^9}, { 3.6880227285420723`*^9, 3.688022739402087*^9}, 3.688124666129181*^9, { 3.6882843273150387`*^9, 3.6882845888454046`*^9}, {3.688285837009152*^9, 3.6882858406491575`*^9}, {3.688286818441526*^9, 3.688286844251562*^9}, { 3.6882870165218034`*^9, 3.688287041201838*^9}, {3.68828707122188*^9, 3.68828709261191*^9}, 3.68828714986199*^9, {3.688287467572435*^9, 3.6882874756924467`*^9}, {3.6882875215825105`*^9, 3.688287521962511*^9}, { 3.6924976946811843`*^9, 3.6924978409113894`*^9}, {3.692497927801511*^9, 3.6924979661015644`*^9}, {3.692498035281661*^9, 3.6924981004717526`*^9}, { 3.6924981611518373`*^9, 3.692498164851843*^9}, {3.692498211401908*^9, 3.6924983125120497`*^9}, {3.692502435097616*^9, 3.692502447592331*^9}, { 3.692502485821518*^9, 3.6925024860295296`*^9}, 3.6925027340347147`*^9, { 3.6940858758564043`*^9, 3.6940858848364167`*^9}, {3.6940859944465704`*^9, 3.6940860158966007`*^9}, {3.6940861169567423`*^9, 3.694086419977166*^9}, { 3.6940872923193874`*^9, 3.6940872938293896`*^9}, {3.6940873646994886`*^9, 3.694087369319495*^9}, 3.694087530509721*^9, {3.6945281161723194`*^9, 3.694528128442337*^9}, {3.6945281951824303`*^9, 3.694528217482462*^9}, { 3.694528268612533*^9, 3.694528649083066*^9}, {3.694528693523128*^9, 3.6945286979031343`*^9}, {3.6945781605358806`*^9, 3.6945782254759717`*^9}, {3.6945782921660647`*^9, 3.694578304996083*^9}, { 3.694578337066128*^9, 3.6945783532861505`*^9}, {3.6945783849061947`*^9, 3.6945783866561975`*^9}, {3.6945784400462723`*^9, 3.694578482566332*^9}, 3.694578713616655*^9, {3.7511979506411643`*^9, 3.751197960841903*^9}, { 3.755352558606639*^9, 3.7553526159830475`*^9}, 3.7575038949254227`*^9, { 3.7884241022211647`*^9, 3.788424103002448*^9}, {3.788424158557418*^9, 3.7884241691882877`*^9}, {3.788424255454542*^9, 3.788424261482607*^9}, { 3.78842429669483*^9, 3.788424433254586*^9}, {3.8200255168660507`*^9, 3.820025546496957*^9}, {3.8200255872523527`*^9, 3.8200255963085623`*^9}, { 3.820025628744812*^9, 3.8200257952584977`*^9}, {3.8200260474034243`*^9, 3.820026053432946*^9}}, CellLabel-> "In[215]:=",ExpressionUUID->"1549c103-2862-4066-aa0b-ab54b37c9133"] }, Closed]], Cell[CellGroupData[{ Cell["SOLID ELEMENT (nonl) defs ", "Subsection", CellChangeTimes->{{3.629430162287647*^9, 3.6294301631768484`*^9}, { 3.7575037777673283`*^9, 3.7575038085600357`*^9}, 3.7575039711454515`*^9, 3.790129876602686*^9},ExpressionUUID->"64dc96c6-9d02-4fcd-855a-\ 21396312acb3"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", "E8001"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "NN", ",", "r", ",", "FF", ",", "uvw", ",", "DG", ",", "GL", ",", "\[Delta]GL", ",", "SS", ",", "\[Delta]wext", ",", "\[Delta]wint", ",", "EEEE", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "GG", ",", "jac", ",", "FFINV"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]", "-", "\[Gamma]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"assuming", " ", "a", " ", "linear", " ", "mapping"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "r"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"displacement", " ", "gradient"}], "*)"}], "\[IndentingNewLine]", RowBox[{"DG", "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "uvw"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"GL", "=", RowBox[{ RowBox[{"(", RowBox[{"DG", "+", RowBox[{"Transpose", "[", "DG", "]"}], "+", RowBox[{"DG", ".", RowBox[{"Transpose", "[", "DG", "]"}]}]}], ")"}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]GL", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]", "[", "DG", "]"}], "+", RowBox[{"Transpose", "[", RowBox[{"\[Delta]", "[", "DG", "]"}], "]"}], "+", RowBox[{ RowBox[{"\[Delta]", "[", "DG", "]"}], ".", RowBox[{"Transpose", "[", "DG", "]"}]}], "+", RowBox[{"DG", ".", RowBox[{"Transpose", "[", RowBox[{"\[Delta]", "[", "DG", "]"}], "]"}]}]}], ")"}], "/", "2"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "GG"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "/", "GG"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"1", "/", "GG"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"PK2", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"SS", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"GL", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", "\[Delta]GL", "]"}], ".", RowBox[{"Flatten", "[", "SS", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TET5", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.4426474258030453`*^9, {3.4444401255942*^9, 3.4444401388073997`*^9}, { 3.4444401803034*^9, 3.4444401844062*^9}, 3.4444402418922*^9, { 3.4444402805022*^9, 3.4444403134026003`*^9}, {3.4444403443062*^9, 3.4444404484049997`*^9}, {3.444483267101*^9, 3.444483267335*^9}, { 3.4444833136046*^9, 3.4444835622998*^9}, {3.4444836421094*^9, 3.4444837777981997`*^9}, {3.444483920429*^9, 3.4444839412237997`*^9}, 3.4444842905546*^9, {3.4444843207406*^9, 3.4444844162282*^9}, { 3.4444844465078*^9, 3.4444844624354*^9}, {3.4444845255998*^9, 3.4444845894505997`*^9}, {3.4444846290746*^9, 3.444484933025*^9}, { 3.4444849790917997`*^9, 3.4444851148742*^9}, {3.444534936054*^9, 3.4445349675348*^9}, {3.4445355821731997`*^9, 3.44453585174*^9}, { 3.4445372162198*^9, 3.4445372264378*^9}, 3.444537384731*^9, { 3.4445377585382*^9, 3.4445377605818*^9}, {3.4445379733658*^9, 3.4445379736934*^9}, {3.4445380176762*^9, 3.444538032777*^9}, { 3.4445381079222*^9, 3.4445381581386003`*^9}, {3.4445382726456003`*^9, 3.4445382910067997`*^9}, {3.4445383401312*^9, 3.4445383475880003`*^9}, { 3.444538438458*^9, 3.4445384464608*^9}, {3.4445385680783997`*^9, 3.4445385687648*^9}, {3.4445389411991997`*^9, 3.4445389431024*^9}, { 3.444539746605*^9, 3.4445397807846003`*^9}, {3.4445408839765997`*^9, 3.4445409234133997`*^9}, {3.4445409681698*^9, 3.4445409932702*^9}, { 3.4445415452906*^9, 3.4445415706717997`*^9}, {3.4445416647242002`*^9, 3.4445416909477997`*^9}, {3.4445417660150003`*^9, 3.444541788557*^9}, { 3.4445420906977997`*^9, 3.444542104847*^9}, {3.4445421885878*^9, 3.4445421941414003`*^9}, {3.4445422252166*^9, 3.4445422386014*^9}, { 3.444542280425*^9, 3.4445423014538*^9}, {3.444542455769*^9, 3.4445424578282003`*^9}, {3.4445431739214*^9, 3.444543175809*^9}, { 3.4445647020962*^9, 3.4445648405618*^9}, {3.4445648825414*^9, 3.4445648858486*^9}, {3.4445649382646*^9, 3.4445651882702*^9}, { 3.4446164822206*^9, 3.4446165344494*^9}, {3.4446166121842003`*^9, 3.4446166738822002`*^9}, {3.4446167223046*^9, 3.4446168047974*^9}, { 3.444616843033*^9, 3.444616906447*^9}, {3.4446444694708*^9, 3.4446444700948*^9}, {3.4446477738310003`*^9, 3.4446477939862003`*^9}, { 3.4446478467298*^9, 3.4446478681018*^9}, 3.4446480456142*^9, { 3.4446487557418003`*^9, 3.4446487636198*^9}, 3.4446488179974003`*^9, { 3.4446488971205997`*^9, 3.4446489152478*^9}, {3.4446490003458*^9, 3.4446490008294*^9}, {3.4447042728942003`*^9, 3.4447042751562*^9}, { 3.4447044703278*^9, 3.4447044865362*^9}, 3.4447046475282*^9, 3.4447047993786*^9, {3.444704908329*^9, 3.4447049292642*^9}, { 3.4447049861926003`*^9, 3.4447049877214003`*^9}, {3.4447050279296*^9, 3.4447050419695997`*^9}, {3.4447053486656*^9, 3.4447053739376*^9}, 3.4447054561963997`*^9, 3.44470561612*^9, {3.4472133996876*^9, 3.4472134108571997`*^9}, {3.4472134470179996`*^9, 3.4472134648332*^9}, { 3.4472135032872*^9, 3.4472135245344*^9}, {3.4472136963059998`*^9, 3.4472137794384003`*^9}, {3.4472138235708*^9, 3.4472138388900003`*^9}, { 3.4472139099792*^9, 3.4472141367096*^9}, {3.447214202682*^9, 3.4472142975924*^9}, {3.4472144187732*^9, 3.4472145910284*^9}, { 3.4472146560492*^9, 3.4472147023968*^9}, {3.447214803594*^9, 3.4472148728736*^9}, {3.4472149156956*^9, 3.447214940484*^9}, { 3.447216227284*^9, 3.4472162419948*^9}, {3.4472163068908*^9, 3.4472163720832*^9}, {3.4472164665880003`*^9, 3.447216530392*^9}, { 3.4472166237268*^9, 3.4472167058452*^9}, 3.4472167362808*^9, { 3.4472171394658003`*^9, 3.4472171532874002`*^9}, {3.4472172028993998`*^9, 3.4472172216661997`*^9}, {3.4472172524606*^9, 3.4472172690278*^9}, { 3.4472173209133997`*^9, 3.4472173334245996`*^9}, {3.4472173920846*^9, 3.447217404861*^9}, {3.4472179572548*^9, 3.4472180351456003`*^9}, { 3.4472509764091997`*^9, 3.4472511017396*^9}, {3.4473910422216*^9, 3.4473912901524*^9}, 3.4473918688344*^9, {3.447392021185*^9, 3.4473920346633997`*^9}, {3.4473921383304*^9, 3.4473921479088*^9}, { 3.4473923024112*^9, 3.4473923734379997`*^9}, {3.4473928098168*^9, 3.4473928648691998`*^9}, {3.4473931872432003`*^9, 3.4473932461800003`*^9}, {3.4473933026675997`*^9, 3.4473934579812*^9}, { 3.4473935755271997`*^9, 3.447393742572*^9}, {3.4473939032676*^9, 3.4473939384144*^9}, {3.447395257644*^9, 3.4473953141628*^9}, { 3.4473954231132*^9, 3.4473954756384*^9}, {3.4473955348716*^9, 3.4473955723272*^9}, {3.447395648502*^9, 3.4473957588876*^9}, { 3.4473957903996*^9, 3.4473958488372*^9}, 3.4473962894154*^9, { 3.447396350817*^9, 3.447396352611*^9}, {3.4474625379146*^9, 3.4474625637326*^9}, {3.558360651728078*^9, 3.558360652102478*^9}, { 3.5619791319820857`*^9, 3.561979135788492*^9}, 3.561979369382504*^9, { 3.5619794930439215`*^9, 3.5619795010155354`*^9}, {3.561979569218855*^9, 3.56197960614412*^9}, {3.5619797417551584`*^9, 3.5619797448751636`*^9}, { 3.618719065033702*^9, 3.618719075426296*^9}, {3.6187194011669273`*^9, 3.6187194449454317`*^9}, {3.6187196998040085`*^9, 3.6187197102436056`*^9}, {3.618719902254588*^9, 3.6187199711455283`*^9}, { 3.618722365406472*^9, 3.6187225412555304`*^9}, {3.6187226885009522`*^9, 3.6187227109872384`*^9}, {3.618722756922866*^9, 3.6187231317203026`*^9}, { 3.618723424250035*^9, 3.6187234267291765`*^9}, {3.6187235105259695`*^9, 3.6187236491028957`*^9}, {3.618723691580325*^9, 3.618723745975436*^9}, { 3.618723778837316*^9, 3.6187238310002995`*^9}, {3.6187239055875654`*^9, 3.618723940035536*^9}, {3.6187239782667227`*^9, 3.6187240219352207`*^9}, { 3.618724166762504*^9, 3.618724177411113*^9}, {3.618729321696159*^9, 3.618729328067523*^9}, 3.618729374058154*^9, {3.6187294379838104`*^9, 3.618729708464281*^9}, {3.6187297631904106`*^9, 3.618729773195983*^9}, { 3.618729822648812*^9, 3.6187299321490746`*^9}, {3.618729984399063*^9, 3.61873000654133*^9}, {3.6187300746012225`*^9, 3.6187300860458775`*^9}, { 3.618731390835507*^9, 3.6187315116174154`*^9}, {3.618731747324897*^9, 3.6187318214091344`*^9}, {3.6187318769243097`*^9, 3.618732065297084*^9}, { 3.6187321012351394`*^9, 3.618732157420353*^9}, {3.618732188384124*^9, 3.6187322435542793`*^9}, {3.6187322786112847`*^9, 3.6187325478446836`*^9}, {3.6187325819856367`*^9, 3.6187326817653437`*^9}, {3.618732810863728*^9, 3.61873282594359*^9}, { 3.6187336474335766`*^9, 3.618733754678711*^9}, {3.618733827497876*^9, 3.61873396201257*^9}, {3.6187342020362988`*^9, 3.618734236455267*^9}, 3.618734298201799*^9, {3.618734712498495*^9, 3.618734712716508*^9}, 3.6187347739640107`*^9, {3.618738817361748*^9, 3.6187388333816643`*^9}, { 3.6187391349349127`*^9, 3.6187391457955337`*^9}, {3.618739376900752*^9, 3.618739397023903*^9}, {3.618739528394417*^9, 3.618739534809784*^9}, { 3.618739972366811*^9, 3.61873997340687*^9}, {3.6187400416617737`*^9, 3.618740043022852*^9}, {3.6187400971579485`*^9, 3.618740107902563*^9}, { 3.6187401713671927`*^9, 3.6187401723312483`*^9}, {3.6187402613443394`*^9, 3.618740268819767*^9}, {3.6187403697625403`*^9, 3.6187404057615995`*^9}, { 3.618740488277319*^9, 3.618740516244919*^9}, {3.618740647782442*^9, 3.6187406551668644`*^9}, 3.6187407823021364`*^9, {3.6187418050786357`*^9, 3.618741805749674*^9}, {3.6187418557605343`*^9, 3.6187419895921893`*^9}, { 3.618742022944097*^9, 3.61874204379729*^9}, {3.6187420836395683`*^9, 3.618742103384698*^9}, {3.620462440882641*^9, 3.6204624460519366`*^9}, { 3.6204624990259666`*^9, 3.620462576450395*^9}, {3.620463682857678*^9, 3.620463713336421*^9}, 3.6204637901188126`*^9, {3.620464238835478*^9, 3.62046424411378*^9}, 3.628912429385081*^9, {3.6289135207155013`*^9, 3.6289135210805225`*^9}, 3.6289497746958513`*^9, 3.6289498371774254`*^9, { 3.62894988410911*^9, 3.6289500319795675`*^9}, {3.6289501333883677`*^9, 3.628950183744248*^9}, {3.6289503323017445`*^9, 3.628950390181055*^9}, { 3.6289505050536256`*^9, 3.6289505113579865`*^9}, {3.62895070863527*^9, 3.6289507095043197`*^9}, {3.628951013180689*^9, 3.62895101407374*^9}, { 3.629190743153632*^9, 3.629190816645361*^9}, {3.6291909709608326`*^9, 3.629190981678051*^9}, {3.629191034624544*^9, 3.6291910410049553`*^9}, { 3.6293846391370816`*^9, 3.629384641102685*^9}, 3.6294302231277533`*^9, 3.629430298397886*^9, {3.6294304452097435`*^9, 3.6294304461769457`*^9}, 3.629430512991863*^9, {3.629430631630071*^9, 3.6294306397264853`*^9}, { 3.629430697477787*^9, 3.629430801373969*^9}, {3.6294470005483365`*^9, 3.629447006658345*^9}, {3.6294476264402127`*^9, 3.62944766022026*^9}, { 3.629455940543494*^9, 3.6294559434734983`*^9}, {3.6294560037335825`*^9, 3.6294560722536783`*^9}, {3.6294561182137423`*^9, 3.629456154053793*^9}, { 3.6294562173438816`*^9, 3.629456291433985*^9}, 3.629456575994384*^9, { 3.6294571194161444`*^9, 3.629457325936434*^9}, {3.6294573681664925`*^9, 3.629457469696635*^9}, {3.630830822369603*^9, 3.630830833380233*^9}, { 3.6308308916105633`*^9, 3.630830892690625*^9}, {3.630830934683027*^9, 3.6308309652587757`*^9}, {3.630831001140828*^9, 3.6308310302394924`*^9}, { 3.6308311286591215`*^9, 3.6308311872784743`*^9}, {3.6308312724803476`*^9, 3.630831331484722*^9}, {3.630831362277484*^9, 3.630831473963872*^9}, { 3.6308315048656397`*^9, 3.6308315251297984`*^9}, {3.6308500199956975`*^9, 3.630850092130224*^9}, {3.6308926160699577`*^9, 3.630892648580415*^9}, { 3.6308926904976883`*^9, 3.6308930396419015`*^9}, {3.6308931926157703`*^9, 3.6308932605850897`*^9}, {3.630893319631193*^9, 3.6308933413620315`*^9}, { 3.630893371735285*^9, 3.6308933746056895`*^9}, {3.630893484195882*^9, 3.630893495552702*^9}, {3.6308935513072*^9, 3.6308937035322676`*^9}, { 3.630893900966214*^9, 3.630893903165818*^9}, {3.63089401261561*^9, 3.6308940229584284`*^9}, {3.630894084734537*^9, 3.630894141612237*^9}, { 3.6308941732958927`*^9, 3.63089421168756*^9}, {3.6308943234305563`*^9, 3.6308945706597905`*^9}, {3.630894732057674*^9, 3.6308948540342884`*^9}, { 3.6308949175576*^9, 3.6308950352130065`*^9}, {3.6308963280663238`*^9, 3.6308964339281096`*^9}, {3.630896483785797*^9, 3.6308965147216516`*^9}, { 3.630995110764593*^9, 3.6309952194788113`*^9}, 3.631017673702475*^9, 3.6339410343181667`*^9, {3.6339411434394083`*^9, 3.6339413336822896`*^9}, { 3.6339414012381535`*^9, 3.6339415162277308`*^9}, {3.633941550612697*^9, 3.6339415854086876`*^9}, {3.633941898820614*^9, 3.633941918825758*^9}, { 3.633942028814049*^9, 3.6339421351881332`*^9}, 3.6339421753194284`*^9, { 3.6339527595260005`*^9, 3.633952797347164*^9}, {3.6339528326231813`*^9, 3.6339528434568014`*^9}, 3.63395311337924*^9, {3.633953318391966*^9, 3.633953320104064*^9}, {3.6339533894880323`*^9, 3.633953398914572*^9}, { 3.6339534904578075`*^9, 3.6339534909158335`*^9}, {3.6339544324266853`*^9, 3.633954436992946*^9}, {3.633955355536484*^9, 3.633955361782841*^9}, { 3.634613015576932*^9, 3.63461301623897*^9}, {3.6346130510409603`*^9, 3.634613077198457*^9}, 3.634613188324813*^9, {3.6878638635768104`*^9, 3.6878639724170356`*^9}, 3.687864019557732*^9, 3.6878641001403413`*^9, { 3.687864195050747*^9, 3.6878641958857946`*^9}, {3.6878642401333256`*^9, 3.68786426136654*^9}, 3.687864352036726*^9, {3.687864450280345*^9, 3.6878644606039357`*^9}, {3.6878646809015083`*^9, 3.6878646814075365`*^9}, {3.687864779357139*^9, 3.6878648062606783`*^9}, { 3.6878651827021837`*^9, 3.687865213182927*^9}, {3.6878652461998158`*^9, 3.6878652992218485`*^9}, {3.687865350343772*^9, 3.687865355912091*^9}, { 3.687865609571577*^9, 3.6878656309137974`*^9}, {3.687865671576123*^9, 3.6878656918812847`*^9}, 3.687865733639673*^9, {3.6878657691897063`*^9, 3.6878657965562716`*^9}, {3.687865834375435*^9, 3.6878658387066827`*^9}, { 3.687865912326894*^9, 3.6878659163341227`*^9}, {3.6878659782786655`*^9, 3.687866006047254*^9}, {3.6878660595832973`*^9, 3.6878660659666624`*^9}, { 3.6878661218058558`*^9, 3.6878661872325983`*^9}, {3.687866245499931*^9, 3.687866274822608*^9}, 3.687866805421936*^9, {3.6879301815930185`*^9, 3.6879301828630204`*^9}, {3.687930277763153*^9, 3.6879302977631817`*^9}, { 3.6879303280532236`*^9, 3.687930399193323*^9}, {3.6879304307033677`*^9, 3.6879304862434454`*^9}, {3.6879305350435133`*^9, 3.6879306368336563`*^9}, {3.6879308629839725`*^9, 3.6879309443840866`*^9}, {3.6880225059517603`*^9, 3.688022695772026*^9}, { 3.6880227285420723`*^9, 3.688022739402087*^9}, 3.688124666129181*^9, { 3.6882843273150387`*^9, 3.6882845888454046`*^9}, {3.688285837009152*^9, 3.6882858406491575`*^9}, {3.688286818441526*^9, 3.688286844251562*^9}, { 3.6882870165218034`*^9, 3.688287041201838*^9}, {3.68828707122188*^9, 3.68828709261191*^9}, 3.68828714986199*^9, {3.688287467572435*^9, 3.6882874756924467`*^9}, {3.6882875215825105`*^9, 3.688287521962511*^9}, { 3.6924976946811843`*^9, 3.6924978409113894`*^9}, {3.692497927801511*^9, 3.6924979661015644`*^9}, {3.692498035281661*^9, 3.6924981004717526`*^9}, { 3.6924981611518373`*^9, 3.692498164851843*^9}, {3.692498211401908*^9, 3.6924983125120497`*^9}, {3.692502435097616*^9, 3.692502447592331*^9}, { 3.692502485821518*^9, 3.6925024860295296`*^9}, 3.6925027340347147`*^9, { 3.6940858758564043`*^9, 3.6940858848364167`*^9}, {3.6940859944465704`*^9, 3.6940860158966007`*^9}, {3.6940861169567423`*^9, 3.694086419977166*^9}, { 3.6940872923193874`*^9, 3.6940872938293896`*^9}, {3.6940873646994886`*^9, 3.694087369319495*^9}, 3.694087530509721*^9, {3.6945281161723194`*^9, 3.694528128442337*^9}, {3.6945281951824303`*^9, 3.694528217482462*^9}, { 3.694528268612533*^9, 3.694528649083066*^9}, {3.694528693523128*^9, 3.6945286979031343`*^9}, {3.6945781605358806`*^9, 3.6945782254759717`*^9}, {3.6945782921660647`*^9, 3.694578304996083*^9}, { 3.694578337066128*^9, 3.6945783532861505`*^9}, {3.6945783849061947`*^9, 3.6945783866561975`*^9}, {3.6945784400462723`*^9, 3.694578482566332*^9}, 3.694578713616655*^9, {3.7511979506411643`*^9, 3.751197960841903*^9}, { 3.755352558606639*^9, 3.7553526159830475`*^9}, {3.7575040694816446`*^9, 3.757504093838356*^9}, {3.7901321001392207`*^9, 3.7901321234170127`*^9}, { 3.8216149607895*^9, 3.821615019490923*^9}, {3.8532118261808352`*^9, 3.8532118691811304`*^9}}, CellLabel-> "In[219]:=",ExpressionUUID->"07155f4e-e4f1-47a1-aae9-b3e711a4a89c"] }, Closed]], Cell[CellGroupData[{ Cell["SOLID ELEMENT (tmec) defs ", "Subsection", CellChangeTimes->{{3.629430162287647*^9, 3.6294301631768484`*^9}, { 3.7575037777673283`*^9, 3.7575038085600357`*^9}, 3.757503967837716*^9, { 3.790129869617339*^9, 3.790129870017767*^9}},ExpressionUUID->"a5ff34d6-b1dc-4e8d-8a6c-\ d1fd929002ae"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", "E8001"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"TMEC", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE_", ",", "\[Nu]\[Nu]_", ",", "\[Alpha]\[Alpha]_", ",", "kk_"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"ss_", ",", "\[CurlyTheta]0_"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"TMEC", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE", ",", "\[Nu]\[Nu]", ",", "\[Alpha]\[Alpha]", ",", "kk"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"ss", ",", "\[CurlyTheta]0"}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"TMEC", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE_", ",", "\[Nu]\[Nu]_", ",", "\[Alpha]\[Alpha]_", ",", "kk_"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}], ",", RowBox[{"{", RowBox[{"ss_", ",", "\[CurlyTheta]0_"}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "NN", ",", "r", ",", "FF", ",", "uvw", ",", "\[CurlyTheta]\[CurlyTheta]", ",", "Duvw", ",", "D\[CurlyTheta]\[CurlyTheta]", ",", "\[Sigma]", ",", "\[Rho]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "EEEE", ",", "\[Delta]w\[Sigma]", ",", "\[Epsilon]", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "GG", ",", "jac", ",", "FFINV", ",", "\[Delta]wext", ",", "\[Delta]wint", ",", "\[Delta]pext", ",", "\[Delta]pint"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{"\[Xi]", ",", "\[Eta]", ",", "\[Zeta]", ",", RowBox[{"1", "-", "\[Xi]", "-", "\[Eta]", "-", "\[Zeta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"assuming", " ", "a", " ", "linear", " ", "mapping"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Eta]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Zeta]"], "r"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CurlyTheta]\[CurlyTheta]", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "4"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "gradients", "*)"}], "\[IndentingNewLine]", RowBox[{"Duvw", "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Eta]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Zeta]"], "uvw"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"D\[CurlyTheta]\[CurlyTheta]", "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "\[CurlyTheta]\[CurlyTheta]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Eta]"], "\[CurlyTheta]\[CurlyTheta]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Zeta]"], "\[CurlyTheta]\[CurlyTheta]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "GG"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "/", "GG"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"1", "/", "GG"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"nonsymmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{"Duvw", "-", RowBox[{ RowBox[{"IdentityMatrix", "[", "3", "]"}], "*", "\[Alpha]\[Alpha]", "*", RowBox[{"(", RowBox[{"\[CurlyTheta]\[CurlyTheta]", "-", "\[CurlyTheta]0"}], ")"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]\[Delta]", "[", "Duvw", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]pint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{ "\[Delta]\[Delta]", "[", "D\[CurlyTheta]\[CurlyTheta]", "]"}], ".", "D\[CurlyTheta]\[CurlyTheta]"}]}], "*", "kk"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]pext", "=", " ", RowBox[{ RowBox[{ "\[Delta]\[Delta]", "[", "\[CurlyTheta]\[CurlyTheta]", "]"}], "*", "ss"}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TET5", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wext", "+", "\[Delta]wint", "+", "\[Delta]pext", "+", "\[Delta]pint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Xi]", ",", "\[Eta]", ",", "\[Zeta]"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.4426474258030453`*^9, {3.4444401255942*^9, 3.4444401388073997`*^9}, { 3.4444401803034*^9, 3.4444401844062*^9}, 3.4444402418922*^9, { 3.4444402805022*^9, 3.4444403134026003`*^9}, {3.4444403443062*^9, 3.4444404484049997`*^9}, {3.444483267101*^9, 3.444483267335*^9}, { 3.4444833136046*^9, 3.4444835622998*^9}, {3.4444836421094*^9, 3.4444837777981997`*^9}, {3.444483920429*^9, 3.4444839412237997`*^9}, 3.4444842905546*^9, {3.4444843207406*^9, 3.4444844162282*^9}, { 3.4444844465078*^9, 3.4444844624354*^9}, {3.4444845255998*^9, 3.4444845894505997`*^9}, {3.4444846290746*^9, 3.444484933025*^9}, { 3.4444849790917997`*^9, 3.4444851148742*^9}, {3.444534936054*^9, 3.4445349675348*^9}, {3.4445355821731997`*^9, 3.44453585174*^9}, { 3.4445372162198*^9, 3.4445372264378*^9}, 3.444537384731*^9, { 3.4445377585382*^9, 3.4445377605818*^9}, {3.4445379733658*^9, 3.4445379736934*^9}, {3.4445380176762*^9, 3.444538032777*^9}, { 3.4445381079222*^9, 3.4445381581386003`*^9}, {3.4445382726456003`*^9, 3.4445382910067997`*^9}, {3.4445383401312*^9, 3.4445383475880003`*^9}, { 3.444538438458*^9, 3.4445384464608*^9}, {3.4445385680783997`*^9, 3.4445385687648*^9}, {3.4445389411991997`*^9, 3.4445389431024*^9}, { 3.444539746605*^9, 3.4445397807846003`*^9}, {3.4445408839765997`*^9, 3.4445409234133997`*^9}, {3.4445409681698*^9, 3.4445409932702*^9}, { 3.4445415452906*^9, 3.4445415706717997`*^9}, {3.4445416647242002`*^9, 3.4445416909477997`*^9}, {3.4445417660150003`*^9, 3.444541788557*^9}, { 3.4445420906977997`*^9, 3.444542104847*^9}, {3.4445421885878*^9, 3.4445421941414003`*^9}, {3.4445422252166*^9, 3.4445422386014*^9}, { 3.444542280425*^9, 3.4445423014538*^9}, {3.444542455769*^9, 3.4445424578282003`*^9}, {3.4445431739214*^9, 3.444543175809*^9}, { 3.4445647020962*^9, 3.4445648405618*^9}, {3.4445648825414*^9, 3.4445648858486*^9}, {3.4445649382646*^9, 3.4445651882702*^9}, { 3.4446164822206*^9, 3.4446165344494*^9}, {3.4446166121842003`*^9, 3.4446166738822002`*^9}, {3.4446167223046*^9, 3.4446168047974*^9}, { 3.444616843033*^9, 3.444616906447*^9}, {3.4446444694708*^9, 3.4446444700948*^9}, {3.4446477738310003`*^9, 3.4446477939862003`*^9}, { 3.4446478467298*^9, 3.4446478681018*^9}, 3.4446480456142*^9, { 3.4446487557418003`*^9, 3.4446487636198*^9}, 3.4446488179974003`*^9, { 3.4446488971205997`*^9, 3.4446489152478*^9}, {3.4446490003458*^9, 3.4446490008294*^9}, {3.4447042728942003`*^9, 3.4447042751562*^9}, { 3.4447044703278*^9, 3.4447044865362*^9}, 3.4447046475282*^9, 3.4447047993786*^9, {3.444704908329*^9, 3.4447049292642*^9}, { 3.4447049861926003`*^9, 3.4447049877214003`*^9}, {3.4447050279296*^9, 3.4447050419695997`*^9}, {3.4447053486656*^9, 3.4447053739376*^9}, 3.4447054561963997`*^9, 3.44470561612*^9, {3.4472133996876*^9, 3.4472134108571997`*^9}, {3.4472134470179996`*^9, 3.4472134648332*^9}, { 3.4472135032872*^9, 3.4472135245344*^9}, {3.4472136963059998`*^9, 3.4472137794384003`*^9}, {3.4472138235708*^9, 3.4472138388900003`*^9}, { 3.4472139099792*^9, 3.4472141367096*^9}, {3.447214202682*^9, 3.4472142975924*^9}, {3.4472144187732*^9, 3.4472145910284*^9}, { 3.4472146560492*^9, 3.4472147023968*^9}, {3.447214803594*^9, 3.4472148728736*^9}, {3.4472149156956*^9, 3.447214940484*^9}, { 3.447216227284*^9, 3.4472162419948*^9}, {3.4472163068908*^9, 3.4472163720832*^9}, {3.4472164665880003`*^9, 3.447216530392*^9}, { 3.4472166237268*^9, 3.4472167058452*^9}, 3.4472167362808*^9, { 3.4472171394658003`*^9, 3.4472171532874002`*^9}, {3.4472172028993998`*^9, 3.4472172216661997`*^9}, {3.4472172524606*^9, 3.4472172690278*^9}, { 3.4472173209133997`*^9, 3.4472173334245996`*^9}, {3.4472173920846*^9, 3.447217404861*^9}, {3.4472179572548*^9, 3.4472180351456003`*^9}, { 3.4472509764091997`*^9, 3.4472511017396*^9}, {3.4473910422216*^9, 3.4473912901524*^9}, 3.4473918688344*^9, {3.447392021185*^9, 3.4473920346633997`*^9}, {3.4473921383304*^9, 3.4473921479088*^9}, { 3.4473923024112*^9, 3.4473923734379997`*^9}, {3.4473928098168*^9, 3.4473928648691998`*^9}, {3.4473931872432003`*^9, 3.4473932461800003`*^9}, {3.4473933026675997`*^9, 3.4473934579812*^9}, { 3.4473935755271997`*^9, 3.447393742572*^9}, {3.4473939032676*^9, 3.4473939384144*^9}, {3.447395257644*^9, 3.4473953141628*^9}, { 3.4473954231132*^9, 3.4473954756384*^9}, {3.4473955348716*^9, 3.4473955723272*^9}, {3.447395648502*^9, 3.4473957588876*^9}, { 3.4473957903996*^9, 3.4473958488372*^9}, 3.4473962894154*^9, { 3.447396350817*^9, 3.447396352611*^9}, {3.4474625379146*^9, 3.4474625637326*^9}, {3.558360651728078*^9, 3.558360652102478*^9}, { 3.5619791319820857`*^9, 3.561979135788492*^9}, 3.561979369382504*^9, { 3.5619794930439215`*^9, 3.5619795010155354`*^9}, {3.561979569218855*^9, 3.56197960614412*^9}, {3.5619797417551584`*^9, 3.5619797448751636`*^9}, { 3.618719065033702*^9, 3.618719075426296*^9}, {3.6187194011669273`*^9, 3.6187194449454317`*^9}, {3.6187196998040085`*^9, 3.6187197102436056`*^9}, {3.618719902254588*^9, 3.6187199711455283`*^9}, { 3.618722365406472*^9, 3.6187225412555304`*^9}, {3.6187226885009522`*^9, 3.6187227109872384`*^9}, {3.618722756922866*^9, 3.6187231317203026`*^9}, { 3.618723424250035*^9, 3.6187234267291765`*^9}, {3.6187235105259695`*^9, 3.6187236491028957`*^9}, {3.618723691580325*^9, 3.618723745975436*^9}, { 3.618723778837316*^9, 3.6187238310002995`*^9}, {3.6187239055875654`*^9, 3.618723940035536*^9}, {3.6187239782667227`*^9, 3.6187240219352207`*^9}, { 3.618724166762504*^9, 3.618724177411113*^9}, {3.618729321696159*^9, 3.618729328067523*^9}, 3.618729374058154*^9, {3.6187294379838104`*^9, 3.618729708464281*^9}, {3.6187297631904106`*^9, 3.618729773195983*^9}, { 3.618729822648812*^9, 3.6187299321490746`*^9}, {3.618729984399063*^9, 3.61873000654133*^9}, {3.6187300746012225`*^9, 3.6187300860458775`*^9}, { 3.618731390835507*^9, 3.6187315116174154`*^9}, {3.618731747324897*^9, 3.6187318214091344`*^9}, {3.6187318769243097`*^9, 3.618732065297084*^9}, { 3.6187321012351394`*^9, 3.618732157420353*^9}, {3.618732188384124*^9, 3.6187322435542793`*^9}, {3.6187322786112847`*^9, 3.6187325478446836`*^9}, {3.6187325819856367`*^9, 3.6187326817653437`*^9}, {3.618732810863728*^9, 3.61873282594359*^9}, { 3.6187336474335766`*^9, 3.618733754678711*^9}, {3.618733827497876*^9, 3.61873396201257*^9}, {3.6187342020362988`*^9, 3.618734236455267*^9}, 3.618734298201799*^9, {3.618734712498495*^9, 3.618734712716508*^9}, 3.6187347739640107`*^9, {3.618738817361748*^9, 3.6187388333816643`*^9}, { 3.6187391349349127`*^9, 3.6187391457955337`*^9}, {3.618739376900752*^9, 3.618739397023903*^9}, {3.618739528394417*^9, 3.618739534809784*^9}, { 3.618739972366811*^9, 3.61873997340687*^9}, {3.6187400416617737`*^9, 3.618740043022852*^9}, {3.6187400971579485`*^9, 3.618740107902563*^9}, { 3.6187401713671927`*^9, 3.6187401723312483`*^9}, {3.6187402613443394`*^9, 3.618740268819767*^9}, {3.6187403697625403`*^9, 3.6187404057615995`*^9}, { 3.618740488277319*^9, 3.618740516244919*^9}, {3.618740647782442*^9, 3.6187406551668644`*^9}, 3.6187407823021364`*^9, {3.6187418050786357`*^9, 3.618741805749674*^9}, {3.6187418557605343`*^9, 3.6187419895921893`*^9}, { 3.618742022944097*^9, 3.61874204379729*^9}, {3.6187420836395683`*^9, 3.618742103384698*^9}, {3.620462440882641*^9, 3.6204624460519366`*^9}, { 3.6204624990259666`*^9, 3.620462576450395*^9}, {3.620463682857678*^9, 3.620463713336421*^9}, 3.6204637901188126`*^9, {3.620464238835478*^9, 3.62046424411378*^9}, 3.628912429385081*^9, {3.6289135207155013`*^9, 3.6289135210805225`*^9}, 3.6289497746958513`*^9, 3.6289498371774254`*^9, { 3.62894988410911*^9, 3.6289500319795675`*^9}, {3.6289501333883677`*^9, 3.628950183744248*^9}, {3.6289503323017445`*^9, 3.628950390181055*^9}, { 3.6289505050536256`*^9, 3.6289505113579865`*^9}, {3.62895070863527*^9, 3.6289507095043197`*^9}, {3.628951013180689*^9, 3.62895101407374*^9}, { 3.629190743153632*^9, 3.629190816645361*^9}, {3.6291909709608326`*^9, 3.629190981678051*^9}, {3.629191034624544*^9, 3.6291910410049553`*^9}, { 3.6293846391370816`*^9, 3.629384641102685*^9}, 3.6294302231277533`*^9, 3.629430298397886*^9, {3.6294304452097435`*^9, 3.6294304461769457`*^9}, 3.629430512991863*^9, {3.629430631630071*^9, 3.6294306397264853`*^9}, { 3.629430697477787*^9, 3.629430801373969*^9}, {3.6294470005483365`*^9, 3.629447006658345*^9}, {3.6294476264402127`*^9, 3.62944766022026*^9}, { 3.629455940543494*^9, 3.6294559434734983`*^9}, {3.6294560037335825`*^9, 3.6294560722536783`*^9}, {3.6294561182137423`*^9, 3.629456154053793*^9}, { 3.6294562173438816`*^9, 3.629456291433985*^9}, 3.629456575994384*^9, { 3.6294571194161444`*^9, 3.629457325936434*^9}, {3.6294573681664925`*^9, 3.629457469696635*^9}, {3.630830822369603*^9, 3.630830833380233*^9}, { 3.6308308916105633`*^9, 3.630830892690625*^9}, {3.630830934683027*^9, 3.6308309652587757`*^9}, {3.630831001140828*^9, 3.6308310302394924`*^9}, { 3.6308311286591215`*^9, 3.6308311872784743`*^9}, {3.6308312724803476`*^9, 3.630831331484722*^9}, {3.630831362277484*^9, 3.630831473963872*^9}, { 3.6308315048656397`*^9, 3.6308315251297984`*^9}, {3.6308500199956975`*^9, 3.630850092130224*^9}, {3.6308926160699577`*^9, 3.630892648580415*^9}, { 3.6308926904976883`*^9, 3.6308930396419015`*^9}, {3.6308931926157703`*^9, 3.6308932605850897`*^9}, {3.630893319631193*^9, 3.6308933413620315`*^9}, { 3.630893371735285*^9, 3.6308933746056895`*^9}, {3.630893484195882*^9, 3.630893495552702*^9}, {3.6308935513072*^9, 3.6308937035322676`*^9}, { 3.630893900966214*^9, 3.630893903165818*^9}, {3.63089401261561*^9, 3.6308940229584284`*^9}, {3.630894084734537*^9, 3.630894141612237*^9}, { 3.6308941732958927`*^9, 3.63089421168756*^9}, {3.6308943234305563`*^9, 3.6308945706597905`*^9}, {3.630894732057674*^9, 3.6308948540342884`*^9}, { 3.6308949175576*^9, 3.6308950352130065`*^9}, {3.6308963280663238`*^9, 3.6308964339281096`*^9}, {3.630896483785797*^9, 3.6308965147216516`*^9}, { 3.630995110764593*^9, 3.6309952194788113`*^9}, 3.631017673702475*^9, 3.6339410343181667`*^9, {3.6339411434394083`*^9, 3.6339413336822896`*^9}, { 3.6339414012381535`*^9, 3.6339415162277308`*^9}, {3.633941550612697*^9, 3.6339415854086876`*^9}, {3.633941898820614*^9, 3.633941918825758*^9}, { 3.633942028814049*^9, 3.6339421351881332`*^9}, 3.6339421753194284`*^9, { 3.6339527595260005`*^9, 3.633952797347164*^9}, {3.6339528326231813`*^9, 3.6339528434568014`*^9}, 3.63395311337924*^9, {3.633953318391966*^9, 3.633953320104064*^9}, {3.6339533894880323`*^9, 3.633953398914572*^9}, { 3.6339534904578075`*^9, 3.6339534909158335`*^9}, {3.6339544324266853`*^9, 3.633954436992946*^9}, {3.633955355536484*^9, 3.633955361782841*^9}, { 3.634613015576932*^9, 3.63461301623897*^9}, {3.6346130510409603`*^9, 3.634613077198457*^9}, 3.634613188324813*^9, {3.6878638635768104`*^9, 3.6878639724170356`*^9}, 3.687864019557732*^9, 3.6878641001403413`*^9, { 3.687864195050747*^9, 3.6878641958857946`*^9}, {3.6878642401333256`*^9, 3.68786426136654*^9}, 3.687864352036726*^9, {3.687864450280345*^9, 3.6878644606039357`*^9}, {3.6878646809015083`*^9, 3.6878646814075365`*^9}, {3.687864779357139*^9, 3.6878648062606783`*^9}, { 3.6878651827021837`*^9, 3.687865213182927*^9}, {3.6878652461998158`*^9, 3.6878652992218485`*^9}, {3.687865350343772*^9, 3.687865355912091*^9}, { 3.687865609571577*^9, 3.6878656309137974`*^9}, {3.687865671576123*^9, 3.6878656918812847`*^9}, 3.687865733639673*^9, {3.6878657691897063`*^9, 3.6878657965562716`*^9}, {3.687865834375435*^9, 3.6878658387066827`*^9}, { 3.687865912326894*^9, 3.6878659163341227`*^9}, {3.6878659782786655`*^9, 3.687866006047254*^9}, {3.6878660595832973`*^9, 3.6878660659666624`*^9}, { 3.6878661218058558`*^9, 3.6878661872325983`*^9}, {3.687866245499931*^9, 3.687866274822608*^9}, 3.687866805421936*^9, {3.6879301815930185`*^9, 3.6879301828630204`*^9}, {3.687930277763153*^9, 3.6879302977631817`*^9}, { 3.6879303280532236`*^9, 3.687930399193323*^9}, {3.6879304307033677`*^9, 3.6879304862434454`*^9}, {3.6879305350435133`*^9, 3.6879306368336563`*^9}, {3.6879308629839725`*^9, 3.6879309443840866`*^9}, {3.6880225059517603`*^9, 3.688022695772026*^9}, { 3.6880227285420723`*^9, 3.688022739402087*^9}, 3.688124666129181*^9, { 3.6882843273150387`*^9, 3.6882845888454046`*^9}, {3.688285837009152*^9, 3.6882858406491575`*^9}, {3.688286818441526*^9, 3.688286844251562*^9}, { 3.6882870165218034`*^9, 3.688287041201838*^9}, {3.68828707122188*^9, 3.68828709261191*^9}, 3.68828714986199*^9, {3.688287467572435*^9, 3.6882874756924467`*^9}, {3.6882875215825105`*^9, 3.688287521962511*^9}, { 3.6924976946811843`*^9, 3.6924978409113894`*^9}, {3.692497927801511*^9, 3.6924979661015644`*^9}, {3.692498035281661*^9, 3.6924981004717526`*^9}, { 3.6924981611518373`*^9, 3.692498164851843*^9}, {3.692498211401908*^9, 3.6924983125120497`*^9}, {3.692502435097616*^9, 3.692502447592331*^9}, { 3.692502485821518*^9, 3.6925024860295296`*^9}, 3.6925027340347147`*^9, { 3.6940858758564043`*^9, 3.6940858848364167`*^9}, {3.6940859944465704`*^9, 3.6940860158966007`*^9}, {3.6940861169567423`*^9, 3.694086419977166*^9}, { 3.6940872923193874`*^9, 3.6940872938293896`*^9}, {3.6940873646994886`*^9, 3.694087369319495*^9}, 3.694087530509721*^9, {3.6945281161723194`*^9, 3.694528128442337*^9}, {3.6945281951824303`*^9, 3.694528217482462*^9}, { 3.694528268612533*^9, 3.694528649083066*^9}, {3.694528693523128*^9, 3.6945286979031343`*^9}, {3.6945781605358806`*^9, 3.6945782254759717`*^9}, {3.6945782921660647`*^9, 3.694578304996083*^9}, { 3.694578337066128*^9, 3.6945783532861505`*^9}, {3.6945783849061947`*^9, 3.6945783866561975`*^9}, {3.6945784400462723`*^9, 3.694578482566332*^9}, 3.694578713616655*^9, {3.7511979506411643`*^9, 3.751197960841903*^9}, { 3.755352558606639*^9, 3.7553526159830475`*^9}, {3.7901319321297035`*^9, 3.790131942849823*^9}, {3.790132020952048*^9, 3.790132043231386*^9}, 3.7901320781631036`*^9, {3.8223695908336563`*^9, 3.8223695921212144`*^9}, { 3.8532115763306246`*^9, 3.853211679754381*^9}, {3.853211717157551*^9, 3.8532117537860675`*^9}, 3.85321180626235*^9}, CellLabel-> "In[221]:=",ExpressionUUID->"95a35a51-fd58-4aaf-9734-dc4e0b34c7b6"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", "node_", "]"}]}], "}"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"MODE", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", "node_", "]"}]}], "}"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"MODE", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "mX", ",", "mY", ",", "mZ"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"I1_", ",", "I2_", ",", "I3_", ",", "I4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "ns", ",", "NN", ",", "r", ",", "FF", ",", "PP", ",", "uvw", ",", "\[Phi]\[Theta]\[Psi]", ",", "Duvw", ",", "\[Sigma]\[Sigma]", ",", "\[Sigma]", ",", "\[Rho]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "EEEE", ",", "\[Delta]w\[Sigma]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "e", ",", "ee", ",", "\[Epsilon]", ",", "EM", ",", "GM", ",", "GG", ",", "nl", ",", "jac", ",", "FFINV"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"I1", ",", "I2", ",", "I3", ",", "I4"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]", "-", "\[Gamma]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"assuming", " ", "a", " ", "linear", " ", "mapping"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "r"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"displacement", " ", "gradient"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "uvw"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "GG"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "/", "GG"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"1", "/", "GG"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"nonsymmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TET5", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Hexahedron", "[", "node_", "]"}]}], "}"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"MODE", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]"}], "}"}], ",", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "}"}], ",", RowBox[{"Hexahedron", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Hexahedron", "[", RowBox[{"{", RowBox[{ "I1_", ",", "I2_", ",", "I3_", ",", "I4_", ",", "I5_", ",", "I6_", ",", "I7_", ",", "I8_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "ns", ",", "NN", ",", "r", ",", "FF", ",", "PP", ",", "uvw", ",", "\[Phi]\[Theta]\[Psi]", ",", "Duvw", ",", "\[Sigma]\[Sigma]", ",", "\[Sigma]", ",", "\[Rho]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "EEEE", ",", "\[Delta]w\[Sigma]", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "GG", ",", "nl", ",", "jac", ",", "FFINV", ",", "\[Epsilon]", ",", "\[Delta]wext", ",", "\[Delta]wint"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{ "I1", ",", "I2", ",", "I3", ",", "I4", ",", "I5", ",", "I6", ",", "I7", ",", "I8"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Gamma]"}], ")"}]}], ",", RowBox[{"\[Alpha]", RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Gamma]"}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]", RowBox[{"(", RowBox[{"1", "-", "\[Gamma]"}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", "\[Beta]", RowBox[{"(", RowBox[{"1", "-", "\[Gamma]"}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}], "\[Gamma]"}], ",", RowBox[{"\[Alpha]", RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}], "\[Gamma]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]", " ", "\[Gamma]"}], ",", RowBox[{"\[Alpha]", " ", "\[Beta]", " ", "\[Gamma]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"assuming", " ", "a", " ", "linear", " ", "mapping"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "r"}]}], "}"}], " ", "/.", " ", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", " ", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Gamma]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"displacement", " ", "gradient"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "uvw"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "GG"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "/", "GG"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"1", "/", "GG"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"nonsymmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"HEX27", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"I1_", ",", "I2_", ",", "I3_", ",", "I4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "ns", ",", "NN", ",", "r", ",", "FF", ",", "FFINV", ",", "jac", ",", "PP", ",", "uvw", ",", "\[Phi]\[Theta]\[Psi]", ",", "Duvw", ",", "\[Sigma]\[Sigma]", ",", "\[Sigma]", ",", "\[Rho]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "EEEE", ",", "\[Delta]w\[Sigma]", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "GG", ",", "nl", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Epsilon]"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"I1", ",", "I2", ",", "I3", ",", "I4"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]", "-", "\[Gamma]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "r"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", "=", RowBox[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"PP", "=", RowBox[{"LeviCivitaTensor", "[", "3", "]"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]\[Theta]\[Psi]", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"displacement", " ", "gradient"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{ RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "uvw"}]}], "}"}]}], "-", RowBox[{"PP", ".", "\[Phi]\[Theta]\[Psi]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "GG"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "/", "GG"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"1", "/", "GG"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], "]"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}]}], "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"nonsymmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", "\[Phi]\[Theta]\[Psi]", "]"}], ".", RowBox[{"{", RowBox[{"mX", ",", "mY", ",", "mZ"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TET5", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"SOLIDB", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"I1_", ",", "I2_", ",", "I3_", ",", "I4_"}], "}"}], "]"}]}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]", ",", "ns", ",", "NN", ",", "r", ",", "FF", ",", "FFINV", ",", "PP", ",", "jac", ",", "uvw", ",", "\[Phi]\[Theta]\[Psi]", ",", "Duvw", ",", "\[Delta]uvw", ",", "\[Delta]Duvw", ",", "\[Delta]\[Lambda]\[Lambda]", ",", "\[Sigma]\[Sigma]", ",", "\[Sigma]", ",", "\[Rho]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "e1", ",", "e2", ",", "e3", ",", "EEEE", ",", "IIII", ",", "II", ",", "IIII1", ",", "IIII2", ",", "\[Delta]w\[Sigma]"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]", "-", "\[Gamma]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"assuming", " ", "a", " ", "linear", " ", "mapping"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "r"}]}], "}"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"\[Gamma]", "\[Rule]", RowBox[{"1", "/", "3"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"PP", "=", RowBox[{"LeviCivitaTensor", "[", "3", "]"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]\[Theta]\[Psi]", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "nonsymmetric", " ", "strain", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{ RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "uvw"}]}], "}"}]}], "-", RowBox[{"PP", ".", "\[Phi]\[Theta]\[Psi]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"nonsymmetric", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"II", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIII1", "=", RowBox[{"Outer", "[", RowBox[{"Times", ",", "II", ",", "II"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIII2", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "i", ",", "j", ",", "j", ",", "i"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "II"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "II"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{ RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "+", "\[Nu]\[Nu]"}], ")"}]}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Nu]\[Nu]", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}], "*", "IIII1"}], "+", "IIII2"}], ")"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"nonsymmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", "\[Phi]\[Theta]\[Psi]", "]"}], ".", RowBox[{"{", RowBox[{"mX", ",", "mY", ",", "mZ"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"TET5", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}]}], "]"}]}]}]}], "\[IndentingNewLine]", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"ELEMENT", "[", "node_", "]"}]}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]", ",", "n\[Alpha]", ",", "n\[Beta]", ",", "n\[Gamma]", ",", "enode", ",", "\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "NN", ",", "r", ",", "FF", ",", "FFINV", ",", "PP", ",", "jac", ",", "uvw", ",", "\[Phi]\[Theta]\[Psi]", ",", "\[Epsilon]", ",", "\[Sigma]", ",", "EEEE", ",", "IIII", ",", "II", ",", "IIII1", ",", "IIII2", ",", "\[Delta]wint", ",", "\[Delta]wext"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", "u_", "]"}], ":=", RowBox[{"u", "/.", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"a", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]a", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"b", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]b", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"c", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]c", "[", "any", "]"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "nodes", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"n\[Gamma]", ",", "n\[Beta]", ",", "n\[Alpha]"}], "}"}], "=", RowBox[{"Dimensions", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"enode", "=", RowBox[{"Flatten", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"Flatten", "[", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n\[Alpha]", ",", "\[Alpha]"}], "}"}], ",", RowBox[{"{", RowBox[{"n\[Beta]", ",", "\[Beta]"}], "}"}], ",", RowBox[{"{", RowBox[{"n\[Gamma]", ",", "\[Gamma]"}], "}"}]}], "}"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"assuming", " ", "a", " ", "linear", " ", "mapping"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "r"}]}], "}"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Gamma]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"PP", "=", RowBox[{"LeviCivitaTensor", "[", "3", "]"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]\[Theta]\[Psi]", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "nonsymmetric", " ", "strain", " ", "in", " ", "the", " ", "structural", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{ RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "uvw"}]}], "}"}]}], "-", RowBox[{"PP", ".", "\[Phi]\[Theta]\[Psi]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"nonsymmetric", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"II", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIII1", "=", RowBox[{"Outer", "[", RowBox[{"Times", ",", "II", ",", "II"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIII2", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "i", ",", "j", ",", "j", ",", "i"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "II"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "II"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{ RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "+", "\[Nu]\[Nu]"}], ")"}]}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Nu]\[Nu]", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}], "*", "IIII1"}], "+", "IIII2"}], ")"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"nonsymmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", "\[Alpha]", "}"}]}], "]"}], ",", RowBox[{"{", "\[Beta]", "}"}]}], "]"}], ",", RowBox[{"{", "\[Gamma]", "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", "node_", "]"}]}], "}"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "\[Nu]\[Nu]", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"I1_", ",", "I2_", ",", "I3_", ",", "I4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "ns", ",", "NN", ",", "r", ",", "FF", ",", "PP", ",", "uvw", ",", "uvw0", ",", "uvw2", ",", "Duvw", ",", "\[Epsilon]", ",", "\[Sigma]", ",", "\[Delta]ww", ",", "\[Delta]WW", ",", "EEEE", ",", "\[Delta]w\[Sigma]", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "GG", ",", "nl", ",", "jac", ",", "FFINV", ",", "\[Delta]wext", ",", "\[Delta]wint", ",", "\[Delta]wine"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"I1", ",", "I2", ",", "I3", ",", "I4"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]", "-", "\[Gamma]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"assuming", " ", "a", " ", "linear", " ", "mapping"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "r"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"uvw0", "=", " ", RowBox[{"uvw", "/.", RowBox[{"{", " ", RowBox[{ RowBox[{"anya_", "[", "any_", "]"}], " ", "\[Rule]", " ", RowBox[{"anya", "[", RowBox[{"any", ",", "0"}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"uvw2", "=", " ", RowBox[{"uvw", " ", "/.", RowBox[{"{", " ", RowBox[{ RowBox[{"anya_", "[", "any_", "]"}], " ", "\[Rule]", RowBox[{"anya", "[", RowBox[{"any", ",", "2"}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"displacement", " ", "gradient"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "uvw0"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "uvw0"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "uvw0"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "GG"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "/", "GG"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"1", "/", "GG"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uvw0", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wine", "=", RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", "uvw0", "]"}], ".", RowBox[{"(", RowBox[{"\[Rho]\[Rho]", " ", "uvw2"}], ")"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TET5", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wext", "+", "\[Delta]wint", "+", "\[Delta]wine"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"I1_", ",", "I2_", ",", "I3_", ",", "I4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "NN", ",", "r", ",", "FF", ",", "uvw", ",", "DG", ",", "GL", ",", "\[Delta]GL", ",", "SS", ",", "\[Delta]wext", ",", "\[Delta]wint", ",", "EEEE", ",", "e", ",", "ee", ",", "EM", ",", "GM", ",", "GG", ",", "jac", ",", "FFINV"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"I1", ",", "I2", ",", "I3", ",", "I4"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]", "-", "\[Gamma]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"assuming", " ", "a", " ", "linear", " ", "mapping"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "r"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "approximations", " ", "in", " ", "structural", " ", "system"}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"uvw", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"displacement", " ", "gradient"}], "*)"}], "\[IndentingNewLine]", RowBox[{"DG", "=", RowBox[{"FFINV", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "uvw"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Gamma]"], "uvw"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"GL", "=", RowBox[{ RowBox[{"(", RowBox[{"DG", "+", RowBox[{"Transpose", "[", "DG", "]"}], "+", RowBox[{"DG", ".", RowBox[{"Transpose", "[", "DG", "]"}]}]}], ")"}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]GL", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]", "[", "DG", "]"}], "+", RowBox[{"Transpose", "[", RowBox[{"\[Delta]", "[", "DG", "]"}], "]"}], "+", RowBox[{ RowBox[{"\[Delta]", "[", "DG", "]"}], ".", RowBox[{"Transpose", "[", "DG", "]"}]}], "+", RowBox[{"DG", ".", RowBox[{"Transpose", "[", RowBox[{"\[Delta]", "[", "DG", "]"}], "]"}]}]}], ")"}], "/", "2"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"symmetric", " ", "elasticity", " ", "dyad"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"ee", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "e1", ",", "e2"}], "]"}], ",", RowBox[{"{", RowBox[{"e1", ",", "e"}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", "e"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EM", "=", RowBox[{"Inverse", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{ RowBox[{"-", "\[Nu]\[Nu]"}], "/", "EE"}], ",", RowBox[{"1", "/", "EE"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"GM", "=", RowBox[{"Inverse", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "GG"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "/", "GG"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"1", "/", "GG"}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"EEEE", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EM", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"j", ",", "j"}], "]"}], "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"2", ",", "3"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"GM", "[", RowBox[{"[", RowBox[{"3", ",", "3"}], "]"}], "]"}], "*", RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}], ",", RowBox[{ RowBox[{"ee", "[", RowBox[{"[", RowBox[{"3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ee", "[", RowBox[{"[", RowBox[{"1", ",", "3"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"PK2", " ", "stress"}], "*)"}], "\[IndentingNewLine]", RowBox[{"SS", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"GL", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", "\[Delta]GL", "]"}], ".", RowBox[{"Flatten", "[", "SS", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "uvw", "]"}], ".", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"TET5", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{ 3.4426474258030453`*^9, {3.4444401255942*^9, 3.4444401388073997`*^9}, { 3.4444401803034*^9, 3.4444401844062*^9}, 3.4444402418922*^9, { 3.4444402805022*^9, 3.4444403134026003`*^9}, {3.4444403443062*^9, 3.4444404484049997`*^9}, {3.444483267101*^9, 3.444483267335*^9}, { 3.4444833136046*^9, 3.4444835622998*^9}, {3.4444836421094*^9, 3.4444837777981997`*^9}, {3.444483920429*^9, 3.4444839412237997`*^9}, 3.4444842905546*^9, {3.4444843207406*^9, 3.4444844162282*^9}, { 3.4444844465078*^9, 3.4444844624354*^9}, {3.4444845255998*^9, 3.4444845894505997`*^9}, {3.4444846290746*^9, 3.444484933025*^9}, { 3.4444849790917997`*^9, 3.4444851148742*^9}, {3.444534936054*^9, 3.4445349675348*^9}, {3.4445355821731997`*^9, 3.44453585174*^9}, { 3.4445372162198*^9, 3.4445372264378*^9}, 3.444537384731*^9, { 3.4445377585382*^9, 3.4445377605818*^9}, {3.4445379733658*^9, 3.4445379736934*^9}, {3.4445380176762*^9, 3.444538032777*^9}, { 3.4445381079222*^9, 3.4445381581386003`*^9}, {3.4445382726456003`*^9, 3.4445382910067997`*^9}, {3.4445383401312*^9, 3.4445383475880003`*^9}, { 3.444538438458*^9, 3.4445384464608*^9}, {3.4445385680783997`*^9, 3.4445385687648*^9}, {3.4445389411991997`*^9, 3.4445389431024*^9}, { 3.444539746605*^9, 3.4445397807846003`*^9}, {3.4445408839765997`*^9, 3.4445409234133997`*^9}, {3.4445409681698*^9, 3.4445409932702*^9}, { 3.4445415452906*^9, 3.4445415706717997`*^9}, {3.4445416647242002`*^9, 3.4445416909477997`*^9}, {3.4445417660150003`*^9, 3.444541788557*^9}, { 3.4445420906977997`*^9, 3.444542104847*^9}, {3.4445421885878*^9, 3.4445421941414003`*^9}, {3.4445422252166*^9, 3.4445422386014*^9}, { 3.444542280425*^9, 3.4445423014538*^9}, {3.444542455769*^9, 3.4445424578282003`*^9}, {3.4445431739214*^9, 3.444543175809*^9}, { 3.4445647020962*^9, 3.4445648405618*^9}, {3.4445648825414*^9, 3.4445648858486*^9}, {3.4445649382646*^9, 3.4445651882702*^9}, { 3.4446164822206*^9, 3.4446165344494*^9}, {3.4446166121842003`*^9, 3.4446166738822002`*^9}, {3.4446167223046*^9, 3.4446168047974*^9}, { 3.444616843033*^9, 3.444616906447*^9}, {3.4446444694708*^9, 3.4446444700948*^9}, {3.4446477738310003`*^9, 3.4446477939862003`*^9}, { 3.4446478467298*^9, 3.4446478681018*^9}, 3.4446480456142*^9, { 3.4446487557418003`*^9, 3.4446487636198*^9}, 3.4446488179974003`*^9, { 3.4446488971205997`*^9, 3.4446489152478*^9}, {3.4446490003458*^9, 3.4446490008294*^9}, {3.4447042728942003`*^9, 3.4447042751562*^9}, { 3.4447044703278*^9, 3.4447044865362*^9}, 3.4447046475282*^9, 3.4447047993786*^9, {3.444704908329*^9, 3.4447049292642*^9}, { 3.4447049861926003`*^9, 3.4447049877214003`*^9}, {3.4447050279296*^9, 3.4447050419695997`*^9}, {3.4447053486656*^9, 3.4447053739376*^9}, 3.4447054561963997`*^9, 3.44470561612*^9, {3.4472133996876*^9, 3.4472134108571997`*^9}, {3.4472134470179996`*^9, 3.4472134648332*^9}, { 3.4472135032872*^9, 3.4472135245344*^9}, {3.4472136963059998`*^9, 3.4472137794384003`*^9}, {3.4472138235708*^9, 3.4472138388900003`*^9}, { 3.4472139099792*^9, 3.4472141367096*^9}, {3.447214202682*^9, 3.4472142975924*^9}, {3.4472144187732*^9, 3.4472145910284*^9}, { 3.4472146560492*^9, 3.4472147023968*^9}, {3.447214803594*^9, 3.4472148728736*^9}, {3.4472149156956*^9, 3.447214940484*^9}, { 3.447216227284*^9, 3.4472162419948*^9}, {3.4472163068908*^9, 3.4472163720832*^9}, {3.4472164665880003`*^9, 3.447216530392*^9}, { 3.4472166237268*^9, 3.4472167058452*^9}, 3.4472167362808*^9, { 3.4472171394658003`*^9, 3.4472171532874002`*^9}, {3.4472172028993998`*^9, 3.4472172216661997`*^9}, {3.4472172524606*^9, 3.4472172690278*^9}, { 3.4472173209133997`*^9, 3.4472173334245996`*^9}, {3.4472173920846*^9, 3.447217404861*^9}, {3.4472179572548*^9, 3.4472180351456003`*^9}, { 3.4472509764091997`*^9, 3.4472511017396*^9}, {3.4473910422216*^9, 3.4473912901524*^9}, 3.4473918688344*^9, {3.447392021185*^9, 3.4473920346633997`*^9}, {3.4473921383304*^9, 3.4473921479088*^9}, { 3.4473923024112*^9, 3.4473923734379997`*^9}, {3.4473928098168*^9, 3.4473928648691998`*^9}, {3.4473931872432003`*^9, 3.4473932461800003`*^9}, {3.4473933026675997`*^9, 3.4473934579812*^9}, { 3.4473935755271997`*^9, 3.447393742572*^9}, {3.4473939032676*^9, 3.4473939384144*^9}, {3.447395257644*^9, 3.4473953141628*^9}, { 3.4473954231132*^9, 3.4473954756384*^9}, {3.4473955348716*^9, 3.4473955723272*^9}, {3.447395648502*^9, 3.4473957588876*^9}, { 3.4473957903996*^9, 3.4473958488372*^9}, 3.4473962894154*^9, { 3.447396350817*^9, 3.447396352611*^9}, {3.4474625379146*^9, 3.4474625637326*^9}, {3.558360651728078*^9, 3.558360652102478*^9}, { 3.5619791319820857`*^9, 3.561979135788492*^9}, 3.561979369382504*^9, { 3.5619794930439215`*^9, 3.5619795010155354`*^9}, {3.561979569218855*^9, 3.56197960614412*^9}, {3.5619797417551584`*^9, 3.5619797448751636`*^9}, { 3.618719065033702*^9, 3.618719075426296*^9}, {3.6187194011669273`*^9, 3.6187194449454317`*^9}, {3.6187196998040085`*^9, 3.6187197102436056`*^9}, {3.618719902254588*^9, 3.6187199711455283`*^9}, { 3.618722365406472*^9, 3.6187225412555304`*^9}, {3.6187226885009522`*^9, 3.6187227109872384`*^9}, {3.618722756922866*^9, 3.6187231317203026`*^9}, { 3.618723424250035*^9, 3.6187234267291765`*^9}, {3.6187235105259695`*^9, 3.6187236491028957`*^9}, {3.618723691580325*^9, 3.618723745975436*^9}, { 3.618723778837316*^9, 3.6187238310002995`*^9}, {3.6187239055875654`*^9, 3.618723940035536*^9}, {3.6187239782667227`*^9, 3.6187240219352207`*^9}, { 3.618724166762504*^9, 3.618724177411113*^9}, {3.618729321696159*^9, 3.618729328067523*^9}, 3.618729374058154*^9, {3.6187294379838104`*^9, 3.618729708464281*^9}, {3.6187297631904106`*^9, 3.618729773195983*^9}, { 3.618729822648812*^9, 3.6187299321490746`*^9}, {3.618729984399063*^9, 3.61873000654133*^9}, {3.6187300746012225`*^9, 3.6187300860458775`*^9}, { 3.618731390835507*^9, 3.6187315116174154`*^9}, {3.618731747324897*^9, 3.6187318214091344`*^9}, {3.6187318769243097`*^9, 3.618732065297084*^9}, { 3.6187321012351394`*^9, 3.618732157420353*^9}, {3.618732188384124*^9, 3.6187322435542793`*^9}, {3.6187322786112847`*^9, 3.6187325478446836`*^9}, {3.6187325819856367`*^9, 3.6187326817653437`*^9}, {3.618732810863728*^9, 3.61873282594359*^9}, { 3.6187336474335766`*^9, 3.618733754678711*^9}, {3.618733827497876*^9, 3.61873396201257*^9}, {3.6187342020362988`*^9, 3.618734236455267*^9}, 3.618734298201799*^9, {3.618734712498495*^9, 3.618734712716508*^9}, 3.6187347739640107`*^9, {3.618738817361748*^9, 3.6187388333816643`*^9}, { 3.6187391349349127`*^9, 3.6187391457955337`*^9}, {3.618739376900752*^9, 3.618739397023903*^9}, {3.618739528394417*^9, 3.618739534809784*^9}, { 3.618739972366811*^9, 3.61873997340687*^9}, {3.6187400416617737`*^9, 3.618740043022852*^9}, {3.6187400971579485`*^9, 3.618740107902563*^9}, { 3.6187401713671927`*^9, 3.6187401723312483`*^9}, {3.6187402613443394`*^9, 3.618740268819767*^9}, {3.6187403697625403`*^9, 3.6187404057615995`*^9}, { 3.618740488277319*^9, 3.618740516244919*^9}, {3.618740647782442*^9, 3.6187406551668644`*^9}, 3.6187407823021364`*^9, {3.6187418050786357`*^9, 3.618741805749674*^9}, {3.6187418557605343`*^9, 3.6187419895921893`*^9}, { 3.618742022944097*^9, 3.61874204379729*^9}, {3.6187420836395683`*^9, 3.618742103384698*^9}, {3.620462440882641*^9, 3.6204624460519366`*^9}, { 3.6204624990259666`*^9, 3.620462576450395*^9}, {3.620463682857678*^9, 3.620463713336421*^9}, 3.6204637901188126`*^9, {3.620464238835478*^9, 3.62046424411378*^9}, 3.628912429385081*^9, {3.6289135207155013`*^9, 3.6289135210805225`*^9}, 3.6289497746958513`*^9, 3.6289498371774254`*^9, { 3.62894988410911*^9, 3.6289500319795675`*^9}, {3.6289501333883677`*^9, 3.628950183744248*^9}, {3.6289503323017445`*^9, 3.628950390181055*^9}, { 3.6289505050536256`*^9, 3.6289505113579865`*^9}, {3.62895070863527*^9, 3.6289507095043197`*^9}, {3.628951013180689*^9, 3.62895101407374*^9}, { 3.629190743153632*^9, 3.629190816645361*^9}, {3.6291909709608326`*^9, 3.629190981678051*^9}, {3.629191034624544*^9, 3.6291910410049553`*^9}, { 3.6293846391370816`*^9, 3.629384641102685*^9}, 3.6294302231277533`*^9, 3.629430298397886*^9, {3.6294304452097435`*^9, 3.6294304461769457`*^9}, 3.629430512991863*^9, {3.629430631630071*^9, 3.6294306397264853`*^9}, { 3.629430697477787*^9, 3.629430801373969*^9}, {3.6294470005483365`*^9, 3.629447006658345*^9}, {3.6294476264402127`*^9, 3.62944766022026*^9}, { 3.629455940543494*^9, 3.6294559434734983`*^9}, {3.6294560037335825`*^9, 3.6294560722536783`*^9}, {3.6294561182137423`*^9, 3.629456154053793*^9}, { 3.6294562173438816`*^9, 3.629456291433985*^9}, 3.629456575994384*^9, { 3.6294571194161444`*^9, 3.629457325936434*^9}, {3.6294573681664925`*^9, 3.629457469696635*^9}, {3.630830822369603*^9, 3.630830833380233*^9}, { 3.6308308916105633`*^9, 3.630830892690625*^9}, {3.630830934683027*^9, 3.6308309652587757`*^9}, {3.630831001140828*^9, 3.6308310302394924`*^9}, { 3.6308311286591215`*^9, 3.6308311872784743`*^9}, {3.6308312724803476`*^9, 3.630831331484722*^9}, {3.630831362277484*^9, 3.630831473963872*^9}, { 3.6308315048656397`*^9, 3.6308315251297984`*^9}, {3.6308500199956975`*^9, 3.630850092130224*^9}, {3.6308926160699577`*^9, 3.630892648580415*^9}, { 3.6308926904976883`*^9, 3.6308930396419015`*^9}, {3.6308931926157703`*^9, 3.6308932605850897`*^9}, {3.630893319631193*^9, 3.6308933413620315`*^9}, { 3.630893371735285*^9, 3.6308933746056895`*^9}, {3.630893484195882*^9, 3.630893495552702*^9}, {3.6308935513072*^9, 3.6308937035322676`*^9}, { 3.630893900966214*^9, 3.630893903165818*^9}, {3.63089401261561*^9, 3.6308940229584284`*^9}, {3.630894084734537*^9, 3.630894141612237*^9}, { 3.6308941732958927`*^9, 3.63089421168756*^9}, {3.6308943234305563`*^9, 3.6308945706597905`*^9}, {3.630894732057674*^9, 3.6308948540342884`*^9}, { 3.6308949175576*^9, 3.6308950352130065`*^9}, {3.6308963280663238`*^9, 3.6308964339281096`*^9}, {3.630896483785797*^9, 3.6308965147216516`*^9}, { 3.630995110764593*^9, 3.6309952194788113`*^9}, 3.631017673702475*^9, 3.6339410343181667`*^9, {3.6339411434394083`*^9, 3.6339413336822896`*^9}, { 3.6339414012381535`*^9, 3.6339415162277308`*^9}, {3.633941550612697*^9, 3.6339415854086876`*^9}, {3.633941898820614*^9, 3.633941918825758*^9}, { 3.633942028814049*^9, 3.6339421351881332`*^9}, 3.6339421753194284`*^9, { 3.6339527595260005`*^9, 3.633952797347164*^9}, {3.6339528326231813`*^9, 3.6339528434568014`*^9}, 3.63395311337924*^9, {3.633953318391966*^9, 3.633953320104064*^9}, {3.6339533894880323`*^9, 3.633953398914572*^9}, { 3.6339534904578075`*^9, 3.6339534909158335`*^9}, {3.6339544324266853`*^9, 3.633954436992946*^9}, {3.633955355536484*^9, 3.633955361782841*^9}, { 3.634613015576932*^9, 3.63461301623897*^9}, {3.6346130510409603`*^9, 3.634613077198457*^9}, 3.634613188324813*^9, {3.6878638635768104`*^9, 3.6878639724170356`*^9}, 3.687864019557732*^9, 3.6878641001403413`*^9, { 3.687864195050747*^9, 3.6878641958857946`*^9}, {3.6878642401333256`*^9, 3.68786426136654*^9}, 3.687864352036726*^9, {3.687864450280345*^9, 3.6878644606039357`*^9}, {3.6878646809015083`*^9, 3.6878646814075365`*^9}, {3.687864779357139*^9, 3.6878648062606783`*^9}, { 3.6878651827021837`*^9, 3.687865213182927*^9}, {3.6878652461998158`*^9, 3.6878652992218485`*^9}, {3.687865350343772*^9, 3.687865355912091*^9}, { 3.687865609571577*^9, 3.6878656309137974`*^9}, {3.687865671576123*^9, 3.6878656918812847`*^9}, 3.687865733639673*^9, {3.6878657691897063`*^9, 3.6878657965562716`*^9}, {3.687865834375435*^9, 3.6878658387066827`*^9}, { 3.687865912326894*^9, 3.6878659163341227`*^9}, {3.6878659782786655`*^9, 3.687866006047254*^9}, {3.6878660595832973`*^9, 3.6878660659666624`*^9}, { 3.6878661218058558`*^9, 3.6878661872325983`*^9}, {3.687866245499931*^9, 3.687866274822608*^9}, 3.687866805421936*^9, {3.6879301815930185`*^9, 3.6879301828630204`*^9}, {3.687930277763153*^9, 3.6879302977631817`*^9}, { 3.6879303280532236`*^9, 3.687930399193323*^9}, {3.6879304307033677`*^9, 3.6879304862434454`*^9}, {3.6879305350435133`*^9, 3.6879306368336563`*^9}, {3.6879308629839725`*^9, 3.6879309443840866`*^9}, {3.6880225059517603`*^9, 3.688022695772026*^9}, { 3.6880227285420723`*^9, 3.688022739402087*^9}, 3.688124666129181*^9, { 3.6882843273150387`*^9, 3.6882845888454046`*^9}, {3.688285837009152*^9, 3.6882858406491575`*^9}, {3.688286818441526*^9, 3.688286844251562*^9}, { 3.6882870165218034`*^9, 3.688287041201838*^9}, {3.68828707122188*^9, 3.68828709261191*^9}, 3.68828714986199*^9, {3.688287467572435*^9, 3.6882874756924467`*^9}, {3.6882875215825105`*^9, 3.688287521962511*^9}, { 3.6924976946811843`*^9, 3.6924978409113894`*^9}, {3.692497927801511*^9, 3.6924979661015644`*^9}, {3.692498035281661*^9, 3.6924981004717526`*^9}, { 3.6924981611518373`*^9, 3.692498164851843*^9}, {3.692498211401908*^9, 3.6924983125120497`*^9}, {3.692502435097616*^9, 3.692502447592331*^9}, { 3.692502485821518*^9, 3.6925024860295296`*^9}, 3.6925027340347147`*^9, { 3.6940858758564043`*^9, 3.6940858848364167`*^9}, {3.6940859944465704`*^9, 3.6940860158966007`*^9}, {3.6940861169567423`*^9, 3.694086419977166*^9}, { 3.6940872923193874`*^9, 3.6940872938293896`*^9}, {3.6940873646994886`*^9, 3.694087369319495*^9}, 3.694087530509721*^9, {3.6945281161723194`*^9, 3.694528128442337*^9}, {3.6945281951824303`*^9, 3.694528217482462*^9}, { 3.694528268612533*^9, 3.694528649083066*^9}, {3.694528693523128*^9, 3.6945286979031343`*^9}, {3.6945781605358806`*^9, 3.6945782254759717`*^9}, {3.6945782921660647`*^9, 3.694578304996083*^9}, { 3.694578337066128*^9, 3.6945783532861505`*^9}, {3.6945783849061947`*^9, 3.6945783866561975`*^9}, {3.6945784400462723`*^9, 3.694578482566332*^9}, 3.694578713616655*^9, {3.7511979506411643`*^9, 3.751197960841903*^9}, { 3.755352558606639*^9, 3.7553526159830475`*^9}, {3.7901319321297035`*^9, 3.790131942849823*^9}, {3.790132020952048*^9, 3.790132068764365*^9}},ExpressionUUID->"ff0f4c3e-24c9-4ccb-bc86-\ 287a006d781e"] }, Closed]], Cell[CellGroupData[{ Cell["Element needs 1005", "Subsection", CellChangeTimes->{{3.6337757022685537`*^9, 3.6337757351784363`*^9}, { 3.734064727558645*^9, 3.7340647333030305`*^9}, {3.746150005514146*^9, 3.7461500076701665`*^9}},ExpressionUUID->"fabe559d-d45e-4c99-bb7b-\ a29e3c28074c"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"force", " ", "element"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[Rho]_", "}"}], ",", RowBox[{"{", RowBox[{"lx_", ",", "ly_", ",", "lz_", ",", "ix_", ",", "iy_"}], "}"}], ",", RowBox[{"{", RowBox[{ "FX_", ",", "FY_", ",", "FZ_", ",", "MX_", ",", "MY_", ",", "MZ_"}], "}"}]}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "I1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"m", ",", "J", ",", "ux", ",", "uy", ",", "uz", ",", "T"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"m", "=", RowBox[{"\[Rho]", "*", "lx", "*", "ly", "*", "lz"}]}], ";", "\[IndentingNewLine]", RowBox[{"J", "=", RowBox[{"m", "*", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"lx", "^", "2"}], "+", RowBox[{"lz", "^", "2"}]}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"ly", "^", "2"}], "+", RowBox[{"lz", "^", "2"}]}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"lx", "^", "2"}], "+", RowBox[{"ly", "^", "2"}]}]}], "}"}]}], "}"}], "/", "12"}]}]}], ";", "\[IndentingNewLine]", StyleBox[ RowBox[{"T", "=", RowBox[{"{", RowBox[{"ix", ",", "iy", ",", RowBox[{"ix", "\[Cross]", "iy"}]}], "}"}]}], "OperatorCharacter"], StyleBox[";", "OperatorCharacter"], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ"}], "}"}], "-", RowBox[{"m", " ", "*", " ", RowBox[{"T", ".", " ", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "2"}], "]"}], "]"}]}]}]}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}], ")"}], ".", " ", RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"T", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "2"}], "]"}], "]"}]}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"MX", ",", "MY", ",", "MZ"}], "}"}], "-", RowBox[{"J", ".", " ", "T", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "3"}], "]"}], "]"}]}]}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}], ")"}], ".", RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"T", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "3"}], "]"}], "]"}]}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}]}]}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"RIGID", ",", RowBox[{"{", "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"I1_", ",", "I2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I2", ",", "2"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "2"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}], ".", RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"FX", "[", RowBox[{"{", RowBox[{"I2", ",", "I1"}], "}"}], "]"}], ",", RowBox[{"FY", "[", RowBox[{"{", RowBox[{"I2", ",", "I1"}], "}"}], "]"}], ",", RowBox[{"FZ", "[", RowBox[{"{", RowBox[{"I2", ",", "I1"}], "}"}], "]"}]}], "}"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], ")"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I2", ",", "2"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "2"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], ")"}], ".", RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"FX", "[", RowBox[{"{", RowBox[{"I2", ",", "I1"}], "}"}], "]"}], ",", RowBox[{"FY", "[", RowBox[{"{", RowBox[{"I2", ",", "I1"}], "}"}], "]"}], ",", RowBox[{"FZ", "[", RowBox[{"{", RowBox[{"I2", ",", "I1"}], "}"}], "]"}]}], "}"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}]}], "+", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I2", ",", "3"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}], ".", RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"MX", "[", RowBox[{"{", RowBox[{"I2", ",", "I1"}], "}"}], "]"}], ",", RowBox[{"MY", "[", RowBox[{"{", RowBox[{"I2", ",", "I1"}], "}"}], "]"}], ",", RowBox[{"MZ", "[", RowBox[{"{", RowBox[{"I2", ",", "I1"}], "}"}], "]"}]}], "}"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], ")"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I2", ",", "3"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], ")"}], ".", RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"MX", "[", RowBox[{"{", RowBox[{"I2", ",", "I1"}], "}"}], "]"}], ",", RowBox[{"MY", "[", RowBox[{"{", RowBox[{"I2", ",", "I1"}], "}"}], "]"}], ",", RowBox[{"MZ", "[", RowBox[{"{", RowBox[{"I2", ",", "I1"}], "}"}], "]"}]}], "}"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}]}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"m_", ",", "J_"}], "}"}], ",", RowBox[{"{", RowBox[{ "FX_", ",", "FY_", ",", "FZ_", ",", "MX_", ",", "MY_", ",", "MZ_"}], "}"}]}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "I1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ"}], "}"}], "-", RowBox[{"m", " ", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "2"}], "]"}], "]"}]}]}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}], ")"}], ".", " ", RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "2"}], "]"}], "]"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}]}], " ", "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"MX", ",", "MY", ",", "MZ"}], "}"}], "-", RowBox[{"J", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "3"}], "]"}], "]"}]}]}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}], ")"}], ".", RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "3"}], "]"}], "]"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}]}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Kappa]\[Kappa]_"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"d_", ",", "t_"}], "}"}], ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG", ",", "\[Kappa]\[Kappa]"}], "}"}], ",", RowBox[{"{", " ", RowBox[{ RowBox[{"d", " ", "\[Pi]", " ", "t"}], ",", " ", RowBox[{"d", " ", "\[Pi]", " ", "t", " ", RowBox[{ RowBox[{"(", RowBox[{ SuperscriptBox["d", "2"], "+", SuperscriptBox["t", "2"]}], ")"}], "/", "8"}]}], ",", " ", RowBox[{"d", " ", "\[Pi]", " ", "t", " ", RowBox[{ RowBox[{"(", RowBox[{ SuperscriptBox["d", "2"], "+", SuperscriptBox["t", "2"]}], ")"}], "/", "8"}]}], ",", "iy0"}], "}"}], ",", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fz"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Kappa]\[Kappa]_"}], "}"}], ",", RowBox[{"{", RowBox[{"d_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG", ",", "\[Kappa]\[Kappa]"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Pi", "*", RowBox[{ RowBox[{"d", "^", "2"}], "/", "4"}]}], ",", RowBox[{"Pi", "*", RowBox[{ RowBox[{"d", "^", "4"}], "/", "64"}]}], ",", RowBox[{"Pi", "*", RowBox[{ RowBox[{"d", "^", "4"}], "/", "64"}]}], ",", "iy0"}], "}"}], ",", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fz"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Kappa]\[Kappa]_"}], "}"}], ",", RowBox[{"{", RowBox[{"hy_", ",", "hz_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG", ",", "\[Kappa]\[Kappa]"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"hy", "*", "hz"}], ",", RowBox[{ RowBox[{"hz", "^", "3"}], "*", RowBox[{"hy", "/", "12"}]}], ",", RowBox[{ RowBox[{"hy", "^", "3"}], "*", RowBox[{"hz", "/", "12"}]}], ",", "iy0"}], "}"}], ",", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fz"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Kappa]\[Kappa]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "h", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "ix0", ",", "iz0", ",", "ux", ",", "uy", " ", ",", "uz", " ", ",", "\[Theta]x", " ", ",", "\[Theta]y", " ", ",", "\[Theta]z", " ", ",", "\[Delta]ux", " ", ",", "\[Delta]uy", ",", "\[Delta]uz", ",", "\[Delta]\[Theta]x", ",", "\[Delta]\[Theta]y", ",", "\[Delta]\[Theta]z"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "mapping", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"h", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz0", "=", RowBox[{"ix0", "\[Cross]", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"ux", "[", "1", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "ix0"}]}], ";", " ", RowBox[{ RowBox[{"ux", "[", "2", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"uy", "[", "1", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iy0"}]}], ";", " ", RowBox[{ RowBox[{"uy", "[", "2", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"uz", "[", "1", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iz0"}]}], ";", " ", RowBox[{ RowBox[{"uz", "[", "2", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Theta]x", "[", "1", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "ix0"}]}], ";", " ", RowBox[{ RowBox[{"\[Theta]x", "[", "2", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Theta]y", "[", "1", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iy0"}]}], ";", " ", RowBox[{ RowBox[{"\[Theta]y", "[", "2", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Theta]z", "[", "1", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iz0"}]}], ";", " ", RowBox[{ RowBox[{"\[Theta]z", "[", "2", "]"}], "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "]"}], ".", "ix0"}]}], ";", " ", RowBox[{ RowBox[{"\[Delta]ux", "[", "2", "]"}], "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "]"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]uy", "[", "1", "]"}], "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "]"}], ".", "iy0"}]}], ";", " ", RowBox[{ RowBox[{"\[Delta]uy", "[", "2", "]"}], "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "]"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]uz", "[", "1", "]"}], "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "]"}], ".", "iz0"}]}], ";", " ", RowBox[{ RowBox[{"\[Delta]uz", "[", "2", "]"}], "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "]"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], "]"}], ".", "ix0"}]}], ";", " ", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "]"}], ".", "ix0"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], "]"}], ".", "iy0"}]}], ";", " ", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}], "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "]"}], ".", "iy0"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], "]"}], ".", "iz0"}]}], ";", " ", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}], "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "]"}], ".", "iz0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["AA", "2"], " ", SuperscriptBox["GG", "2"], " ", SuperscriptBox["h", "4"], " ", SuperscriptBox["\[Kappa]\[Kappa]", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "fx", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"6", " ", "fz", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"6", " ", "fz", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "-", RowBox[{"fz", " ", SuperscriptBox["h", "3"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"fz", " ", SuperscriptBox["h", "3"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"fy", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "+", RowBox[{"6", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"h", " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"h", " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}]}], ")"}]}], "-", RowBox[{"12", " ", "GG", " ", "Iyy", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], " ", RowBox[{"\[Theta]x", "[", "1", "]"}]}], "-", RowBox[{"12", " ", "GG", " ", "Izz", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], " ", RowBox[{"\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"12", " ", "GG", " ", "Iyy", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], " ", RowBox[{"\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"12", " ", "GG", " ", "Izz", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], " ", RowBox[{"\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"12", " ", "GG", " ", "Iyy", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], " ", RowBox[{"\[Theta]x", "[", "2", "]"}]}], "+", RowBox[{"12", " ", "GG", " ", "Izz", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], " ", RowBox[{"\[Theta]x", "[", "2", "]"}]}], "-", RowBox[{"12", " ", "GG", " ", "Iyy", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], " ", RowBox[{"\[Theta]x", "[", "2", "]"}]}], "-", RowBox[{"12", " ", "GG", " ", "Izz", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], " ", RowBox[{"\[Theta]x", "[", "2", "]"}]}]}], ")"}]}], "-", RowBox[{"1728", " ", SuperscriptBox["EE", "3"], " ", "Iyy", " ", "Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"AA", " ", RowBox[{"(", RowBox[{ RowBox[{"ux", "[", "1", "]"}], "-", RowBox[{"ux", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "-", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], "-", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]y", "[", "1", "]"}], "-", RowBox[{"\[Theta]y", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], "-", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]z", "[", "1", "]"}], "-", RowBox[{"\[Theta]z", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"144", " ", SuperscriptBox["EE", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["AA", "2"]}], " ", "GG", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"Iyy", "+", "Izz"}], ")"}], " ", "\[Kappa]\[Kappa]", " ", RowBox[{"(", RowBox[{ RowBox[{"ux", "[", "1", "]"}], "-", RowBox[{"ux", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "-", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"6", " ", "fx", " ", SuperscriptBox["h", "2"], " ", "Iyy", " ", "Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"Iyy", " ", "Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"fz", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"6", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "-", RowBox[{"h", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"h", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}]}], ")"}]}], "+", RowBox[{"fy", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "+", RowBox[{"6", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"h", " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"h", " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}]}], ")"}]}], "-", RowBox[{"12", " ", "GG", " ", RowBox[{"(", RowBox[{"Iyy", "+", "Izz"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], "-", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]x", "[", "1", "]"}], "-", RowBox[{"\[Theta]x", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"AA", " ", "GG", " ", "\[Kappa]\[Kappa]", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["h", "2"], " ", SuperscriptBox["Izz", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], "-", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]y", "[", "1", "]"}], "-", RowBox[{"\[Theta]y", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", SuperscriptBox["Iyy", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], "-", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]z", "[", "1", "]"}], "-", RowBox[{"\[Theta]z", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"2", " ", "Iyy", " ", "Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", RowBox[{"uz", "[", "1", "]"}], " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "-", RowBox[{"6", " ", RowBox[{"uz", "[", "2", "]"}], " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "-", RowBox[{"6", " ", RowBox[{"uz", "[", "1", "]"}], " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "+", RowBox[{"6", " ", RowBox[{"uz", "[", "2", "]"}], " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "-", RowBox[{"3", " ", "h", " ", RowBox[{"uz", "[", "1", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"3", " ", "h", " ", RowBox[{"uz", "[", "2", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"3", " ", "h", " ", RowBox[{"uz", "[", "1", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"3", " ", "h", " ", RowBox[{"uz", "[", "2", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"3", " ", RowBox[{"uy", "[", "1", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "-", RowBox[{"2", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"3", " ", RowBox[{"uy", "[", "2", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "-", RowBox[{"2", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"3", " ", "h", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"3", " ", "h", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"3", " ", "h", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"3", " ", "h", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"3", " ", "h", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"3", " ", "h", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"3", " ", "h", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"3", " ", "h", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"12", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "\[Kappa]\[Kappa]", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["AA", "2"], " ", "GG", " ", SuperscriptBox["h", "2"], " ", "\[Kappa]\[Kappa]", " ", RowBox[{"(", RowBox[{ RowBox[{"ux", "[", "1", "]"}], "-", RowBox[{"ux", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "-", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "-", RowBox[{"6", " ", "fx", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{"Iyy", "+", "Izz"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{"Iyy", "+", "Izz"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"fz", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"6", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "-", RowBox[{"h", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"h", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}]}], ")"}]}], "+", RowBox[{"fy", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "+", RowBox[{"6", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"h", " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"h", " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}]}], ")"}]}], "-", RowBox[{"12", " ", "GG", " ", RowBox[{"(", RowBox[{"Iyy", "+", "Izz"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], "-", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]x", "[", "1", "]"}], "-", RowBox[{"\[Theta]x", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"2", " ", "AA", " ", "GG", " ", "\[Kappa]\[Kappa]", " ", RowBox[{"(", RowBox[{ RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", RowBox[{"uz", "[", "1", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"3", " ", RowBox[{"uz", "[", "2", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", RowBox[{"\[Delta]uz", "[", "1", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]y", "[", "1", "]"}], "+", RowBox[{"\[Theta]y", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"3", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]y", "[", "1", "]"}], "+", RowBox[{"\[Theta]y", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"\[Theta]y", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]y", "[", "1", "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", RowBox[{"uy", "[", "1", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "-", RowBox[{"2", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"3", " ", RowBox[{"uy", "[", "2", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "-", RowBox[{"2", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]z", "[", "1", "]"}], "+", RowBox[{"\[Theta]z", "[", "2", "]"}]}], ")"}]}], "-", RowBox[{"3", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]z", "[", "1", "]"}], "+", RowBox[{"\[Theta]z", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"\[Theta]z", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]z", "[", "1", "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}], "/", RowBox[{"(", RowBox[{"12", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", "Iyy"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "\[Kappa]\[Kappa]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", "Izz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h", "2"], " ", "\[Kappa]\[Kappa]"}]}], ")"}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"d_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Pi", "*", RowBox[{ RowBox[{"d", "^", "2"}], "/", "4"}]}], ",", RowBox[{"Pi", "*", RowBox[{ RowBox[{"d", "^", "4"}], "/", "64"}]}], ",", RowBox[{"Pi", "*", RowBox[{ RowBox[{"d", "^", "4"}], "/", "64"}]}], ",", "iy0"}], "}"}], ",", RowBox[{"{", RowBox[{ "fx", ",", "fy", ",", "fz", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"hy_", ",", "hz_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", ",", "GG", ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"hy", "*", "hz"}], ",", RowBox[{ RowBox[{"hz", "^", "3"}], "*", RowBox[{"hy", "/", "12"}]}], ",", RowBox[{ RowBox[{"hy", "^", "3"}], "*", RowBox[{"hz", "/", "12"}]}], ",", "iy0"}], "}"}], ",", RowBox[{"{", RowBox[{ "fx", ",", "fy", ",", "fz", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fx_", ",", "fy_", ",", "fz_", ",", "mx_", ",", "my_", ",", "mz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "h", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "ix0", ",", "iz0", ",", "ux", ",", "uy", " ", ",", "uz", " ", ",", "\[Theta]x", " ", ",", "\[Theta]y", " ", ",", "\[Theta]z", " ", ",", "\[Delta]ux", " ", ",", "\[Delta]uy", ",", "\[Delta]uz", ",", "\[Delta]\[Theta]x", ",", "\[Delta]\[Theta]y", ",", "\[Delta]\[Theta]z"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "mapping", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"h", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"r0", ".", "r0"}], "]"}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"ix0", "=", RowBox[{"r0", "/", "h0"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz0", "=", RowBox[{"ix0", "\[Cross]", "iy0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"2", ",", "2"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "}"}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"ix0", ",", "iy0", ",", "iz0"}], "}"}], ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"uy", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "=", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], ",", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"-", FractionBox["1", RowBox[{"420", " ", SuperscriptBox["h", "3"]}]]}], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "210"}], " ", "fx", " ", SuperscriptBox["h", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"AA", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"420", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"ux", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["h", "2"], " ", "\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"70", " ", RowBox[{"ux", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"70", " ", RowBox[{"ux", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]ux", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}], "+", RowBox[{"156", " ", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"54", " ", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"54", " ", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"156", " ", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"156", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"54", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"54", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"156", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"22", " ", "h", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"13", " ", "h", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"13", " ", "h", " ", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"22", " ", "h", " ", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"22", " ", "h", " ", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"13", " ", "h", " ", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "-", RowBox[{"13", " ", "h", " ", RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"22", " ", "h", " ", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], "-", RowBox[{"22", " ", "h", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"13", " ", "h", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"4", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"3", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"13", " ", "h", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"22", " ", "h", " ", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"3", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"4", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"22", " ", "h", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"13", " ", "h", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"4", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"3", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{"13", " ", "h", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"22", " ", "h", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "-", RowBox[{"3", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"4", " ", SuperscriptBox["h", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"7", " ", RowBox[{"(", RowBox[{ RowBox[{"720", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"5", " ", "fz", " ", SuperscriptBox["h", "5"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{"5", " ", "fy", " ", SuperscriptBox["h", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"6", " ", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], "+", RowBox[{"h", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"360", " ", "EE", " ", "h", " ", RowBox[{"(", RowBox[{ RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"uz", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{ RowBox[{"uz", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"uy", "[", RowBox[{"1", ",", "0"}], "]"}]}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"uy", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"12", " ", SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}], "-", RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"5", " ", RowBox[{"(", RowBox[{ RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"2", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], "-", RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"5", " ", RowBox[{"(", RowBox[{ RowBox[{"GG", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"2", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}]}], "+", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"2", " ", SuperscriptBox["h", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"15", " ", "fz", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"15", " ", "mx", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{"\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{"5", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}]}], "+", RowBox[{"5", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{"4", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"4", " ", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"5", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}]}], "+", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}]}], "+", RowBox[{"5", " ", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]x", "[", RowBox[{"1", ",", "2"}], "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Theta]x", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}], "+", RowBox[{"4", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}]}], "-", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], "+", RowBox[{"4", " ", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}], " ", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"6", " ", SuperscriptBox["h", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"10", " ", "mz", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{"10", " ", "my", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{"\[Rho]\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"Iyy", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"uz", "[", RowBox[{"1", ",", "2"}], "]"}]}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"uz", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uz", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]y", "[", RowBox[{"1", ",", "2"}], "]"}], "+", RowBox[{"\[Theta]y", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"Izz", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"uy", "[", RowBox[{"1", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "-", RowBox[{ RowBox[{"uy", "[", RowBox[{"2", ",", "2"}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"1", ",", "0"}], "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", RowBox[{"1", ",", "0"}], "]"}], "-", RowBox[{"\[Delta]uy", "[", RowBox[{"2", ",", "0"}], "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Theta]z", "[", RowBox[{"1", ",", "2"}], "]"}], "+", RowBox[{"\[Theta]z", "[", RowBox[{"2", ",", "2"}], "]"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"ELEMENT", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "n\[Alpha]", ",", "n\[Beta]", ",", "nne", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "enode", ",", "NN", ",", "r", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "rn", ",", "jac", ",", "h\[Alpha]", ",", "e\[Alpha]", ",", "h\[Beta]", ",", "e\[Beta]", ",", "en", ",", "FF", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "u0", ",", "v0", ",", "w0", ",", "\[Phi]0", ",", "\[Theta]0", ",", "\[Psi]0", ",", "u2", ",", "v2", ",", "w2", ",", "\[Phi]2", ",", "\[Theta]2", ",", "\[Psi]2", ",", "f\[Alpha]", ",", "f\[Beta]", ",", "fn", ",", "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]", ",", "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]", ",", "\[Gamma]\[Alpha]", ",", "\[Gamma]\[Beta]", ",", "GG", ",", "N\[Alpha]\[Alpha]", ",", "N\[Beta]\[Beta]", ",", "N\[Alpha]\[Beta]", ",", "N\[Beta]\[Alpha]", ",", "M\[Alpha]\[Alpha]", ",", "M\[Beta]\[Beta]", ",", "M\[Alpha]\[Beta]", ",", "Q\[Alpha]", ",", "Q\[Beta]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wine"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "nodes", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"n\[Alpha]", ",", "n\[Beta]"}], "}"}], "=", RowBox[{"Dimensions", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"nne", " ", "=", RowBox[{"n\[Alpha]", "*", "n\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"enode", "=", RowBox[{"Flatten", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n\[Alpha]", ",", "\[Alpha]"}], "}"}], ",", RowBox[{"{", RowBox[{"n\[Beta]", ",", "\[Beta]"}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "mapping", " ", "to", " ", "orthonormal", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Alpha]", "=", RowBox[{"Norm", "[", "r\[Alpha]", "]"}]}], ";", RowBox[{"e\[Alpha]", "=", RowBox[{"r\[Alpha]", "/", "h\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Beta]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Beta]", "=", RowBox[{"r\[Beta]", "-", RowBox[{ RowBox[{"(", RowBox[{"r\[Beta]", ".", "e\[Alpha]"}], ")"}], "*", "e\[Alpha]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]", "=", RowBox[{"Norm", "[", "r\[Beta]", "]"}]}], ";", RowBox[{"e\[Beta]", "=", RowBox[{"r\[Beta]", "/", "h\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{"e\[Alpha]", "\[Cross]", "e\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", " ", "=", RowBox[{"h\[Alpha]", "*", "h\[Beta]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"in", " ", "flat", " ", "geometry"}], "*)"}], "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e\[Alpha]", ",", "e\[Beta]", ",", "en"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "transform", " ", "into", " ", "the", " ", "material", " ", "\[Alpha]\[Beta]n"}], "-", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"(", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "2"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"(", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "3"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u0", ",", "v0", ",", "w0"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]0", ",", "\[Theta]0", ",", "\[Psi]0"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u2", ",", "v2", ",", "w2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]2", ",", "\[Theta]2", ",", "\[Psi]2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], " ", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fz"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"strain", " ", "measures", " ", "with", " ", "non"}], "-", RowBox[{"symmetric", " ", "\[Epsilon]"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u0"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v0"}], "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v0"}], "/", "h\[Alpha]"}], "-", "\[Psi]0"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u0"}], "/", "h\[Beta]"}], "+", "\[Psi]0"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Theta]0"}], "/", "h\[Alpha]"}], ",", RowBox[{ RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]0"}]}], "/", "h\[Beta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Theta]0"}], "/", "h\[Beta]"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]0"}], "/", "h\[Alpha]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Beta]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w0"}], "/", "h\[Alpha]"}], "+", "\[Theta]0"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w0"}], "/", "h\[Beta]"}], "-", "\[Phi]0"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"GG", "=", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", "*", "\[Nu]\[Nu]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "stress", " ", "resultants", " ", "with", " ", "a", " ", "nonsymmetric", " ", "N"}], "-", "part"}], "*)"}], "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Alpha]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Beta]\[Beta]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Beta]\[Beta]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Epsilon]\[Beta]\[Beta]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Epsilon]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Alpha]\[Beta]", "=", RowBox[{"tt", "*", "GG", "*", "\[Epsilon]\[Alpha]\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Beta]\[Alpha]", "=", RowBox[{"tt", "*", "GG", "*", "\[Epsilon]\[Beta]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Alpha]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Alpha]\[Alpha]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Beta]\[Beta]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Beta]\[Beta]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"\[Kappa]\[Beta]\[Beta]", "+", RowBox[{"\[Nu]\[Nu]", "*", "\[Kappa]\[Alpha]\[Alpha]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M\[Alpha]\[Beta]", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "*", "GG", "*", "\[Kappa]\[Alpha]\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Alpha]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Beta]", "=", RowBox[{ RowBox[{"5", "/", "6"}], "*", "GG", "*", "tt", "*", "\[Gamma]\[Beta]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "N\[Alpha]\[Alpha]", ",", "N\[Beta]\[Beta]", ",", "N\[Alpha]\[Beta]", ",", "N\[Beta]\[Alpha]"}], "}"}]}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Beta]\[Beta]", ",", "M\[Alpha]\[Beta]"}], "}"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Gamma]\[Alpha]", ",", "\[Gamma]\[Beta]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Beta]"}], "}"}]}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u0", ",", "v0", ",", "w0"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wine", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"u0", ",", "v0", ",", "w0"}], "}"}], "]"}], ".", RowBox[{"(", RowBox[{"\[Rho]\[Rho]", "*", "tt", "*", RowBox[{"{", RowBox[{"u2", ",", "v2", ",", "w2"}], "}"}]}], ")"}]}]}], "-", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Phi]0", ",", "\[Theta]0", ",", "\[Psi]0"}], "}"}], "]"}], ".", RowBox[{"(", RowBox[{"\[Rho]\[Rho]", "*", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", RowBox[{"{", RowBox[{"\[Phi]2", ",", "\[Theta]2", ",", "\[Psi]2"}], "}"}]}], ")"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{"QUAD", "[", RowBox[{"LIN7", ",", RowBox[{ RowBox[{"(", RowBox[{ "\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wine"}], ")"}], "*", "jac"}], ",", "\[Alpha]"}], "]"}], ",", "\[Beta]"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.633673923685915*^9, 3.6336739535006204`*^9}, { 3.633674155068149*^9, 3.6336741996717005`*^9}, {3.6336745049841633`*^9, 3.6336745219741354`*^9}, {3.6336919593939404`*^9, 3.6336919775979815`*^9}, 3.633692380551029*^9, {3.6336927116599674`*^9, 3.633692727194856*^9}, { 3.635310826749509*^9, 3.6353108343419433`*^9}, {3.635311461613821*^9, 3.6353114619508405`*^9}, {3.7326759806780663`*^9, 3.7326760008674326`*^9}, {3.7326760331212645`*^9, 3.7326760385677853`*^9}, {3.732684137201784*^9, 3.73268419404665*^9}, { 3.732684306221466*^9, 3.7326843382153635`*^9}, 3.7326844699232764`*^9, { 3.7326845133861027`*^9, 3.73268452322455*^9}, {3.732759973190983*^9, 3.7327599776758347`*^9}, {3.7327613720703106`*^9, 3.7327614888170295`*^9}, {3.732761535853627*^9, 3.7327615404943867`*^9}, { 3.7327615972663317`*^9, 3.7327616122832594`*^9}, {3.7327616693361855`*^9, 3.73276183332095*^9}, {3.732761876700554*^9, 3.7327618790133*^9}, { 3.732761909063363*^9, 3.732761910469795*^9}, {3.73276200508918*^9, 3.732762006042756*^9}, {3.7327620750344048`*^9, 3.732762101490326*^9}, 3.7327688007102947`*^9, {3.7327705695330524`*^9, 3.7327705708254137`*^9}, { 3.732788507552166*^9, 3.7327885085870132`*^9}, {3.732788681344634*^9, 3.7327887090994544`*^9}, {3.732788743287696*^9, 3.73278879848213*^9}, { 3.732788922306119*^9, 3.7327889462731514`*^9}, {3.732789012151597*^9, 3.732789028200858*^9}, {3.7327890791192408`*^9, 3.732789086999034*^9}, { 3.732789135698248*^9, 3.7327891358892384`*^9}, {3.7327891989507074`*^9, 3.7327891993104925`*^9}, {3.733116709198372*^9, 3.733116731638229*^9}, { 3.7334931331412554`*^9, 3.7334932071522064`*^9}, {3.733493353668892*^9, 3.7334934953404007`*^9}, {3.733493581610343*^9, 3.733493589891471*^9}, { 3.7334936319789553`*^9, 3.7334936623392687`*^9}, {3.7334936935401745`*^9, 3.733493716917615*^9}, {3.7334937687375154`*^9, 3.733493799379287*^9}, { 3.7335602963276734`*^9, 3.7335603891038685`*^9}, {3.7337039222525787`*^9, 3.733703929721642*^9}, {3.7337040222462597`*^9, 3.7337040262631474`*^9}, { 3.733710121070121*^9, 3.733710122358057*^9}, 3.7337110885786676`*^9, 3.733711184948838*^9, {3.733711259729956*^9, 3.733711278366322*^9}, 3.7337113240271106`*^9, {3.733711384581702*^9, 3.733711436236964*^9}, 3.7337114809469175`*^9, {3.7337115173918333`*^9, 3.733711518879483*^9}, 3.733711560439453*^9, {3.733711609599924*^9, 3.7337116342722664`*^9}, { 3.733711689751358*^9, 3.7337116969119487`*^9}, {3.7337129879879694`*^9, 3.7337130014112797`*^9}, {3.733713172835663*^9, 3.733713173913886*^9}, { 3.7337132483436465`*^9, 3.7337132496094065`*^9}, {3.733713283003566*^9, 3.7337134200180254`*^9}, {3.733713464428997*^9, 3.7337135191222897`*^9}, { 3.7337135777847366`*^9, 3.73371367154463*^9}, {3.7337140009857264`*^9, 3.7337140458967295`*^9}, {3.733714091198394*^9, 3.7337141070440063`*^9}, { 3.733714143813529*^9, 3.733714146610505*^9}, {3.733721976862414*^9, 3.7337219813629093`*^9}, {3.733722281191476*^9, 3.7337222944429536`*^9}, { 3.733722382186266*^9, 3.7337223828425617`*^9}, {3.7337224624293957`*^9, 3.7337224858690815`*^9}, 3.7337225537825146`*^9, {3.733722654230641*^9, 3.733722661731436*^9}, {3.733722818999301*^9, 3.7337228267499514`*^9}, { 3.733723144924486*^9, 3.733723159691375*^9}, {3.733723196273369*^9, 3.733723198695795*^9}, {3.7337232377777586`*^9, 3.7337232408874655`*^9}, { 3.73372435111442*^9, 3.733724354067712*^9}, {3.7337244099801674`*^9, 3.733724433076069*^9}, {3.7337245236325226`*^9, 3.733724524679802*^9}, { 3.7337873724058084`*^9, 3.7337873841879997`*^9}, {3.7337879154409466`*^9, 3.7337879158316607`*^9}, {3.734065101190684*^9, 3.734065109945911*^9}, 3.734071634767725*^9, {3.734219464256485*^9, 3.734219489352889*^9}, { 3.734219525211231*^9, 3.7342195715720572`*^9}, 3.73421973141712*^9, { 3.7348415845456142`*^9, 3.7348415857332087`*^9}, {3.7440202929533424`*^9, 3.7440202932363644`*^9}, {3.746150119112222*^9, 3.7461501205962443`*^9}, { 3.7650873052252254`*^9, 3.765087311647415*^9}},ExpressionUUID->"03e80675-88b3-491b-9b61-\ 7f27fb007711"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["SOLVER", "Section", CellChangeTimes->{ 3.4430806364968*^9, {3.4453166713873997`*^9, 3.4453166747414*^9}, { 3.447462264275*^9, 3.4474622644154*^9}, {3.4695731321116*^9, 3.4695731359491997`*^9}, 3.473055186341*^9, {3.4730552472860003`*^9, 3.47305524884*^9}, {3.473055399782*^9, 3.473055419801*^9}, { 3.4734696760778*^9, 3.4734697047349997`*^9}, {3.4770537891542*^9, 3.4770537950354*^9}, {3.4932799754514*^9, 3.4932799779161997`*^9}, { 3.4945558951644*^9, 3.4945558957416*^9}, {3.4957646303032*^9, 3.4957646329084*^9}, {3.497581602118*^9, 3.4975816042552*^9}, { 3.500960505817*^9, 3.5009605094206*^9}, {3.556623836083009*^9, 3.5566238462386265`*^9}, {3.5568725055395393`*^9, 3.5568725163821597`*^9}, {3.556872678728445*^9, 3.5568726810485783`*^9}, { 3.7323376045620503`*^9, 3.7323376086812124`*^9}, {3.7335630623483887`*^9, 3.733563072583865*^9}, {3.733563159827469*^9, 3.7335631629996696`*^9}, { 3.7335632161458936`*^9, 3.733563217193006*^9}},ExpressionUUID->"d8ffbf13-27a0-4328-9a21-\ be6a7e8473f4"], Cell[CellGroupData[{ Cell["DISP defs", "Subsection", CellChangeTimes->{{3.7582531074375505`*^9, 3.7582531288543863`*^9}, { 3.787892825419589*^9, 3.7878928340449758`*^9}, 3.8223696918276553`*^9},ExpressionUUID->"06a9dfe0-2adc-4915-94ed-\ 87c3071c4eb7"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"MEC", "-", "E1050"}], "|", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}], "]"}], ":=", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", ",", "\[Delta]dof", ",", "equ", ",", "sol", ",", "\[Delta]WT"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WT", "=", RowBox[{"ParallelMap", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WT", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WT", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"D", "[", RowBox[{"\[Delta]WT", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"Solve", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"equ", "\[Equal]", "0"}], "]"}], ",", "dof"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"First", "[", "sol", "]"}], "]"}]}]}], "]"}]}], ";"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"large", " ", "scale", " ", "defs"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "CLASSIC", "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", " ", ",", "\[Delta]dof", ",", "sol", ",", "\[Delta]We", ",", "DOF", ",", "\[Delta]DOF", ",", "MAP", ",", "\[Delta]MAP", ",", "ABL", ",", "nequ", ",", "ndof", ",", "A", ",", "B", ",", "dofe", ",", "\[Delta]dofe", ",", "eque", ",", "Le", ",", "LA", ",", "LB", ",", "tt"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"tt", "=", RowBox[{"TimeUsed", "[", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "element", " ", "contributions", " ", "in", " ", "parallel"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"ABL", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]We", " ", "=", " ", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", "#"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dofe", " ", "=", RowBox[{"Union", "[", RowBox[{"Cases", "[", RowBox[{"\[Delta]We", ",", RowBox[{ RowBox[{"a", "[", "__", "]"}], "|", RowBox[{"b", "[", "__", "]"}]}], ",", "Infinity"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]dofe", " ", "=", RowBox[{"Union", "[", RowBox[{"Cases", "[", RowBox[{"\[Delta]We", ",", RowBox[{ RowBox[{"\[Delta]a", "[", "__", "]"}], "|", RowBox[{"\[Delta]b", "[", "__", "]"}]}], ",", "Infinity"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"eque", "=", RowBox[{"D", "[", RowBox[{"\[Delta]We", ",", RowBox[{"{", "\[Delta]dofe", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Join", "[", RowBox[{ RowBox[{"CoefficientArrays", "[", RowBox[{"eque", ",", "dofe"}], "]"}], ",", RowBox[{"{", RowBox[{"dofe", ",", "\[Delta]dofe"}], "}"}]}], "]"}]}], ")"}], "&"}], ",", "\[IndentingNewLine]", "ele"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"\"\\"", ",", RowBox[{ RowBox[{"TimeUsed", "[", "]"}], "-", "tt"}], ",", "\"\<): nele = \>\"", ",", RowBox[{"Length", "[", "ele", "]"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"tt", "=", RowBox[{"TimeUsed", "[", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"dof", " ", "mapping"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"DOF", "=", RowBox[{"Union", "[", RowBox[{"Flatten", "[", RowBox[{"ABL", "[", RowBox[{"[", RowBox[{"All", ",", "3"}], "]"}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]DOF", "=", RowBox[{"Union", "[", RowBox[{"Flatten", "[", RowBox[{"ABL", "[", RowBox[{"[", RowBox[{"All", ",", "4"}], "]"}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ndof", "=", RowBox[{"Length", "[", "DOF", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"nequ", "=", RowBox[{"Length", "[", "\[Delta]DOF", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"MAP", "=", " ", RowBox[{"Dispatch", "[", RowBox[{"Thread", "[", RowBox[{"DOF", "->", RowBox[{"Array", "[", RowBox[{ RowBox[{"#", "&"}], ",", "ndof"}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]MAP", "=", " ", RowBox[{"Dispatch", "[", RowBox[{"Thread", "[", RowBox[{"\[Delta]DOF", "->", RowBox[{"Array", "[", RowBox[{ RowBox[{"#", "&"}], ",", "nequ"}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ABL", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], ",", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "3", "]"}], "]"}], "/.", " ", "MAP"}], ",", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "4", "]"}], "]"}], "/.", " ", "\[Delta]MAP"}]}], "}"}], "&"}], ",", "ABL"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"A", " ", "=", RowBox[{"SparseArray", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "->", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"nequ", ",", "ndof"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"B", " ", "=", RowBox[{"SparseArray", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "1", "}"}], "->", "0"}], "}"}], ",", RowBox[{"{", "nequ", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"\"\\"", ",", RowBox[{ RowBox[{"TimeUsed", "[", "]"}], "-", "tt"}], ",", "\"\<): {nequ,ndof} = \>\"", ",", RowBox[{"{", RowBox[{"nequ", ",", "ndof"}], "}"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"parallel", " ", "build"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"tt", "=", RowBox[{"TimeUsed", "[", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Do", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"LA", " ", "=", " ", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"List", ",", RowBox[{"ec", "[", RowBox[{"[", "4", "]"}], "]"}], ",", RowBox[{"ec", "[", RowBox[{"[", "3", "]"}], "]"}]}], "]"}], ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"LB", " ", "=", " ", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"{", "#", "}"}], "&"}], ",", RowBox[{"ec", "[", RowBox[{"[", "4", "]"}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"A", "+=", RowBox[{"SparseArray", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"LA", "\[Rule]", RowBox[{"Flatten", "[", RowBox[{"ec", "[", RowBox[{"[", "2", "]"}], "]"}], "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"nequ", ",", "ndof"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"B", "+=", RowBox[{"SparseArray", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"LB", "\[Rule]", RowBox[{"Flatten", "[", RowBox[{"ec", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}]}], "]"}], ",", RowBox[{"{", "nequ", "}"}]}], "]"}]}]}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"ec", ",", "ABL"}], "}"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"\"\\"", ",", RowBox[{ RowBox[{"TimeUsed", "[", "]"}], "-", "tt"}], ",", "\"\<): nele = \>\"", ",", RowBox[{"Length", "[", "ele", "]"}]}], "]"}], ";", " ", "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"solve", " ", "with", " ", "default", " ", "method"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"tt", "=", RowBox[{"TimeUsed", "[", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"Thread", "[", RowBox[{"DOF", "->", RowBox[{"LinearSolve", "[", RowBox[{"A", ",", RowBox[{"-", "B"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"\"\\"", ",", RowBox[{ RowBox[{"TimeUsed", "[", "]"}], "-", "tt"}], ",", "\"\<)\>\""}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", "sol", "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "CLASSICP", "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", " ", ",", "\[Delta]dof", ",", "sol", ",", "\[Delta]We", ",", "DOF", ",", "\[Delta]DOF", ",", "MAP", ",", "\[Delta]MAP", ",", "ABL", ",", "nequ", ",", "ndof", ",", "A", ",", "B", ",", "dofe", ",", "\[Delta]dofe", ",", "eque", ",", "Le", ",", "LA", ",", "LB", ",", "tt", ",", "ec"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"tt", "=", RowBox[{"TimeUsed", "[", "]"}]}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"element", " ", "contributions", " ", "in", " ", "parallel"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ABL", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"\[Delta]We", " ", "=", " ", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", "#"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dofe", " ", "=", RowBox[{"Union", "[", RowBox[{"Cases", "[", RowBox[{"\[Delta]We", ",", RowBox[{ RowBox[{"a", "[", "__", "]"}], "|", RowBox[{"b", "[", "__", "]"}], "|", RowBox[{"c", "[", "__", "]"}]}], ",", "Infinity"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]dofe", " ", "=", RowBox[{"Union", "[", RowBox[{"Cases", "[", RowBox[{"\[Delta]We", ",", RowBox[{ RowBox[{"\[Delta]a", "[", "__", "]"}], "|", RowBox[{"\[Delta]b", "[", "__", "]"}], "|", RowBox[{"\[Delta]c", "[", "__", "]"}]}], ",", "Infinity"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"for", " ", "load", " ", "elements"}], "*)"}], "\[IndentingNewLine]", RowBox[{"dofe", "=", RowBox[{"If", "[", RowBox[{ RowBox[{"dofe", "\[Equal]", RowBox[{"{", "}"}]}], ",", RowBox[{"(", RowBox[{"\[Delta]dofe", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Delta]a", "\[Rule]", "a"}], ",", RowBox[{"\[Delta]b", "->", "b"}], ",", RowBox[{"\[Delta]c", "\[Rule]", "c"}]}], "}"}]}], ")"}], ",", "dofe"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"eque", "=", RowBox[{"D", "[", RowBox[{"\[Delta]We", ",", RowBox[{"{", "\[Delta]dofe", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"coff", "=", RowBox[{"CoefficientArrays", "[", RowBox[{"eque", ",", "dofe"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"coff", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Length", "[", "coff", "]"}], "\[Equal]", "1"}], ",", RowBox[{"Append", "[", RowBox[{"coff", ",", RowBox[{"SparseArray", "[", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Length", "[", "\[Delta]dofe", "]"}], ",", RowBox[{"Length", "[", "\[Delta]dofe", "]"}]}], "}"}]}], "]"}]}], "]"}], ",", "coff"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Join", "[", RowBox[{"coff", ",", RowBox[{"{", RowBox[{"dofe", ",", "\[Delta]dofe"}], "}"}]}], "]"}]}], ")"}], "&"}], ",", "\[IndentingNewLine]", "ele"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"Print", "[", RowBox[{"\"\\"", ",", RowBox[{ RowBox[{"TimeUsed", "[", "]"}], "-", "tt"}], ",", "\"\<): nele = \>\"", ",", RowBox[{"Length", "[", "ele", "]"}]}], "]"}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"tt", "=", RowBox[{"TimeUsed", "[", "]"}]}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"dof", " ", "mapping"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"DOF", "=", RowBox[{"Union", "[", RowBox[{"Flatten", "[", RowBox[{"ABL", "[", RowBox[{"[", RowBox[{"All", ",", "3"}], "]"}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]DOF", "=", RowBox[{"Union", "[", RowBox[{"Flatten", "[", RowBox[{"ABL", "[", RowBox[{"[", RowBox[{"All", ",", "4"}], "]"}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ndof", "=", RowBox[{"Length", "[", "DOF", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"nequ", "=", RowBox[{"Length", "[", "\[Delta]DOF", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"MAP", "=", " ", RowBox[{"Dispatch", "[", RowBox[{"Thread", "[", RowBox[{"DOF", "->", RowBox[{"Array", "[", RowBox[{ RowBox[{"#", "&"}], ",", "ndof"}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]MAP", "=", " ", RowBox[{"Dispatch", "[", RowBox[{"Thread", "[", RowBox[{"\[Delta]DOF", "->", RowBox[{"Array", "[", RowBox[{ RowBox[{"#", "&"}], ",", "nequ"}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ABL", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], ",", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "3", "]"}], "]"}], "/.", " ", "MAP"}], ",", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "4", "]"}], "]"}], "/.", " ", "\[Delta]MAP"}]}], "}"}], "&"}], ",", "ABL"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"A", " ", "=", RowBox[{"SparseArray", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "->", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"nequ", ",", "ndof"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"B", " ", "=", RowBox[{"SparseArray", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "1", "}"}], "->", "0"}], "}"}], ",", RowBox[{"{", "nequ", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{"Print", "[", RowBox[{"\"\\"", ",", RowBox[{ RowBox[{"TimeUsed", "[", "]"}], "-", "tt"}], ",", "\"\<): {nequ,ndof} = \>\"", ",", RowBox[{"{", RowBox[{"nequ", ",", "ndof"}], "}"}]}], "]"}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"parallel", " ", "build"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{"tt", "=", RowBox[{"TimeUsed", "[", "]"}]}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{"A", "=", RowBox[{"ParallelSum", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"LA", " ", "=", " ", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"List", ",", RowBox[{"ec", "[", RowBox[{"[", "4", "]"}], "]"}], ",", RowBox[{"ec", "[", RowBox[{"[", "3", "]"}], "]"}]}], "]"}], ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"SparseArray", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"LA", "\[Rule]", RowBox[{"Flatten", "[", RowBox[{"ec", "[", RowBox[{"[", "2", "]"}], "]"}], "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"nequ", ",", "ndof"}], "}"}]}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"ec", ",", "ABL"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"B", "=", RowBox[{"ParallelSum", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"LB", " ", "=", " ", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"{", "#", "}"}], "&"}], ",", RowBox[{"ec", "[", RowBox[{"[", "4", "]"}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"SparseArray", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"LB", "\[Rule]", RowBox[{"Flatten", "[", RowBox[{"ec", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}]}], "]"}], ",", RowBox[{"{", "nequ", "}"}]}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"ec", ",", "ABL"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"Print", "[", RowBox[{"\"\\"", ",", RowBox[{ RowBox[{"TimeUsed", "[", "]"}], "-", "tt"}], ",", "\"\<): nele = \>\"", ",", RowBox[{"Length", "[", "ele", "]"}]}], "]"}], ";"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"solve", " ", "with", " ", "default", " ", "method"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"tt", "=", RowBox[{"TimeUsed", "[", "]"}]}], ";"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"Thread", "[", RowBox[{"DOF", "->", RowBox[{"LinearSolve", "[", RowBox[{"A", ",", RowBox[{"-", "B"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{"Print", "[", RowBox[{"\"\\"", ",", RowBox[{ RowBox[{"TimeUsed", "[", "]"}], "-", "tt"}], ",", "\"\<)\>\""}], "]"}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{"Return", "[", "sol", "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", "\[Delta]WW_", "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"equ", ",", "sol"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"equ", "=", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"Solve", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"equ", "\[Equal]", "0"}], "]"}], ",", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"First", "[", "sol", "]"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.445098179109*^9, 3.4450982721786003`*^9, {3.451279000619*^9, 3.4512790074518003`*^9}, {3.4512864298050003`*^9, 3.4512864368094*^9}, { 3.4706476335011683`*^9, 3.4706476477283683`*^9}, {3.4770540063998003`*^9, 3.4770540103154*^9}, {3.4818115795696*^9, 3.481811581816*^9}, { 3.4820252104592*^9, 3.4820252549035997`*^9}, {3.4820583880738*^9, 3.4820584077454*^9}, {3.4822351571716003`*^9, 3.4822351901188*^9}, { 3.4823004164308*^9, 3.4823004243712*^9}, {3.493344815723*^9, 3.4933448166745996`*^9}, {3.4933448517122*^9, 3.4933448763445997`*^9}, { 3.4933449778422003`*^9, 3.4933449867342*^9}, {3.4942053389948*^9, 3.4942053532688*^9}, {3.495099886848*^9, 3.4950998935959997`*^9}, { 3.495099958993*^9, 3.495099969426*^9}, 3.495100042671*^9, { 3.495100076422*^9, 3.495100110413*^9}, {3.49510016601*^9, 3.4951001814849997`*^9}, 3.4951002189040003`*^9, {3.495100255352*^9, 3.495100257927*^9}, {3.495100455098*^9, 3.4951004564449997`*^9}, { 3.495100515517*^9, 3.4951005243059998`*^9}, {3.495100586*^9, 3.4951006116359997`*^9}, {3.496055002618*^9, 3.496055006674*^9}, { 3.5007168179316*^9, 3.5007168299904003`*^9}, {3.557657331191841*^9, 3.5576573613778934`*^9}, {3.557658058371518*^9, 3.5576580893531723`*^9}, { 3.6204640425822525`*^9, 3.620464043896328*^9}, {3.629448441451354*^9, 3.6294484425113554`*^9}, {3.632027966812848*^9, 3.63202808169145*^9}, { 3.632028112439104*^9, 3.632028231997714*^9}, {3.632028264944972*^9, 3.632028286223409*^9}, 3.6320284618641176`*^9, 3.6320284928925724`*^9, { 3.6321887622237573`*^9, 3.6321887797107573`*^9}, {3.6321888300516367`*^9, 3.6321888552960806`*^9}, 3.6321889475563574`*^9, {3.63218903764051*^9, 3.6321890646730566`*^9}, {3.632189114899929*^9, 3.63218912051025*^9}, { 3.632189363344139*^9, 3.632189368985462*^9}, {3.65933624669765*^9, 3.6593362536240625`*^9}, {3.659336346288225*^9, 3.6593363466002254`*^9}, { 3.685234016837945*^9, 3.6852340690569315`*^9}, {3.6852341853385825`*^9, 3.6852342255038795`*^9}, {3.6852342700224257`*^9, 3.685234275388733*^9}, 3.685260724724876*^9, {3.685271245062879*^9, 3.685271273442919*^9}, { 3.685340120474733*^9, 3.6853401228547363`*^9}, {3.6873488134786153`*^9, 3.6873488145086164`*^9}, {3.687348848548664*^9, 3.6873488495686655`*^9}, { 3.6873489495588055`*^9, 3.687348976528844*^9}, {3.6873490107688913`*^9, 3.6873490208289056`*^9}, {3.6873490736689796`*^9, 3.6873490997690163`*^9}, {3.6873491395590715`*^9, 3.6873491721791177`*^9}, {3.6873493303593388`*^9, 3.687349336179347*^9}, { 3.687521139333435*^9, 3.687521232626771*^9}, {3.687526828204684*^9, 3.6875268662258587`*^9}, {3.687744603751021*^9, 3.687744621651046*^9}, { 3.687744782441271*^9, 3.687744793141286*^9}, {3.687744898361433*^9, 3.687744900871437*^9}, {3.687828873646782*^9, 3.6878288977768154`*^9}, { 3.6893872627070065`*^9, 3.6893872737370224`*^9}, {3.689388189828305*^9, 3.689388190108305*^9}, {3.6924132329925613`*^9, 3.692413234362563*^9}, { 3.6924133951727886`*^9, 3.6924134472928615`*^9}, {3.692413504072941*^9, 3.6924135542830114`*^9}, {3.6924138300453973`*^9, 3.692413892645485*^9}, { 3.6924150151235356`*^9, 3.692415019653542*^9}, {3.6924150955736485`*^9, 3.692415151833727*^9}, {3.6924152984639325`*^9, 3.692415397454071*^9}, { 3.6924155440942764`*^9, 3.6924155997043543`*^9}, {3.6924163099373484`*^9, 3.692416448987543*^9}, {3.6924164799875865`*^9, 3.692416520217643*^9}, { 3.6926047241829367`*^9, 3.6926047936630344`*^9}, {3.692694606764871*^9, 3.6926946080948734`*^9}, {3.6926946485549297`*^9, 3.6926946848649807`*^9}, {3.692694726505039*^9, 3.6926947795951133`*^9}, { 3.6926948533452168`*^9, 3.6926948903052683`*^9}, {3.692695016775445*^9, 3.6926950466854873`*^9}, {3.6926951047455683`*^9, 3.6926952014557037`*^9}, {3.692695400025982*^9, 3.6926954007959833`*^9}, { 3.692699088631146*^9, 3.6926990917611504`*^9}, {3.692699130701205*^9, 3.692699150701233*^9}, {3.6926992111213174`*^9, 3.692699243221362*^9}, { 3.692767928345048*^9, 3.6927679342250557`*^9}, {3.692768078185258*^9, 3.692768090845275*^9}, {3.692768583705965*^9, 3.6927686080859995`*^9}, { 3.692768652936062*^9, 3.6927686668160815`*^9}, {3.6927686975061245`*^9, 3.692768721766158*^9}, {3.6927687546262045`*^9, 3.692768807796279*^9}, { 3.6927688439663296`*^9, 3.692768846666333*^9}, {3.6927689511864796`*^9, 3.6927690097565613`*^9}, {3.692769047276614*^9, 3.6927692269968657`*^9}, { 3.692769260096912*^9, 3.6927692611369133`*^9}, {3.692769508057259*^9, 3.6927695324672937`*^9}, {3.692769570707347*^9, 3.692769719217555*^9}, { 3.6927698159576902`*^9, 3.6927698318077126`*^9}, 3.6927699552978854`*^9, { 3.6927701375081406`*^9, 3.6927701495781574`*^9}, {3.692772614961609*^9, 3.692772638701642*^9}, {3.692782982318822*^9, 3.6927829888081927`*^9}, { 3.6927830390960693`*^9, 3.692783045068411*^9}, {3.692783125046985*^9, 3.6927831273591175`*^9}, {3.692784897481363*^9, 3.6927849907176957`*^9}, 3.6927851596043553`*^9, {3.692786968327264*^9, 3.6927869691872644`*^9}, { 3.6927917561302457`*^9, 3.6927918079203186`*^9}, {3.6927918834304237`*^9, 3.692791893050438*^9}, 3.692791931280491*^9, {3.692791999660587*^9, 3.692792026840625*^9}, {3.6927921455307913`*^9, 3.6927921655908194`*^9}, { 3.692792200960869*^9, 3.692792228630907*^9}, {3.692792265330959*^9, 3.6927922938409986`*^9}, {3.6927923374910593`*^9, 3.6927923700511055`*^9}, {3.6927924565012264`*^9, 3.692792499271286*^9}, { 3.692792553391362*^9, 3.6927925860314074`*^9}, {3.692792731971612*^9, 3.6927927381216207`*^9}, {3.692792820381736*^9, 3.692792853021782*^9}, { 3.6927928932518377`*^9, 3.6927929516419196`*^9}, {3.6927929886919713`*^9, 3.6927930024219904`*^9}, {3.69279305234206*^9, 3.6927930715320873`*^9}, { 3.6927932237223005`*^9, 3.692793224982302*^9}, 3.6927932572523475`*^9, { 3.6927934421826067`*^9, 3.6927934498726172`*^9}, {3.692793484652666*^9, 3.6927935029226913`*^9}, {3.6927954180780883`*^9, 3.692795446828129*^9}, { 3.6928535571114936`*^9, 3.692853577521522*^9}, {3.692854825823887*^9, 3.692854837063903*^9}, {3.692854874433955*^9, 3.6928548775639596`*^9}, { 3.6928579822683063`*^9, 3.6928579955883245`*^9}, {3.6929656707917795`*^9, 3.692965795661954*^9}, {3.6929658426120195`*^9, 3.6929658536320353`*^9}, { 3.6929659138621197`*^9, 3.6929659218321304`*^9}, {3.692965990142226*^9, 3.6929660268822775`*^9}, {3.692966066362333*^9, 3.692966192182509*^9}, 3.69296637876277*^9, {3.6929669253235354`*^9, 3.692966936273551*^9}, { 3.6929669714336*^9, 3.692966971953601*^9}, 3.6929670139636593`*^9, 3.692967433554247*^9, {3.6929675634944286`*^9, 3.6929676911746073`*^9}, { 3.6929677832047367`*^9, 3.6929678068347692`*^9}, {3.6929678599332247`*^9, 3.6929678711132402`*^9}, 3.692967908543293*^9, {3.693017052482854*^9, 3.6930171392429757`*^9}, {3.6930174027243443`*^9, 3.6930175965956163`*^9}, {3.6930184697368383`*^9, 3.6930185654269724`*^9}, {3.6930186942971525`*^9, 3.6930188354373503`*^9}, {3.6930188926684303`*^9, 3.6930189600095253`*^9}, {3.693018990869568*^9, 3.693018991349569*^9}, { 3.693019036009631*^9, 3.693019041239639*^9}, {3.6930190980797186`*^9, 3.693019098629719*^9}, {3.693019130059763*^9, 3.6930192205398893`*^9}, { 3.693020315081422*^9, 3.693020326351438*^9}, {3.6930205415560236`*^9, 3.6930206058761134`*^9}, {3.6931381375028915`*^9, 3.693138137902892*^9}, { 3.693138677303647*^9, 3.693138683263655*^9}, {3.693139600730257*^9, 3.6931396288802967`*^9}, {3.6932135226775846`*^9, 3.6932135229775853`*^9}, {3.693219312471691*^9, 3.69321932632171*^9}, { 3.6932194762919197`*^9, 3.6932194879419365`*^9}, 3.6932195481520205`*^9, { 3.693220303405078*^9, 3.6932203178550987`*^9}, {3.693220688975618*^9, 3.693220698955632*^9}, {3.6933024593938713`*^9, 3.6933024657438803`*^9}, { 3.693302603694073*^9, 3.693302604214074*^9}, {3.6933103950923057`*^9, 3.693310399082311*^9}, {3.6933104528223867`*^9, 3.693310456172391*^9}, { 3.693380733755448*^9, 3.693380746175465*^9}, {3.6936247413492084`*^9, 3.6936247436692114`*^9}, {3.69362490643944*^9, 3.6936249099894447`*^9}, { 3.6937175435584445`*^9, 3.6937175579984646`*^9}, {3.693717708199675*^9, 3.6937177268707013`*^9}, {3.6937178194508305`*^9, 3.6937178401008596`*^9}, {3.693717934550992*^9, 3.6937179428310037`*^9}, { 3.6937180305511265`*^9, 3.693718060841169*^9}, {3.693718198801362*^9, 3.6937182028213673`*^9}, {3.693723123415037*^9, 3.6937231809651175`*^9}, { 3.693723252275217*^9, 3.69372327580525*^9}, {3.6937233347053328`*^9, 3.693723337655337*^9}, {3.693723689337829*^9, 3.6937237730079465`*^9}, { 3.6937240089782767`*^9, 3.6937240113382797`*^9}, {3.6938202843684807`*^9, 3.6938203172553616`*^9}, {3.6938203482121134`*^9, 3.6938203495041876`*^9}, 3.6938204448556414`*^9, {3.693826654370701*^9, 3.693826713082033*^9}, 3.6938269274112916`*^9, {3.69384095960849*^9, 3.6938409879385295`*^9}, { 3.6938967427518525`*^9, 3.6938967457718563`*^9}, {3.693896818211958*^9, 3.6938968234619656`*^9}, {3.6940917346582804`*^9, 3.6940917372882843`*^9}, {3.6949174720509205`*^9, 3.6949174781309295`*^9}, {3.69491751432098*^9, 3.6949175560810385`*^9}, { 3.697770949307855*^9, 3.697770962227873*^9}, {3.723799262336609*^9, 3.723799262645475*^9}, 3.7239435284061375`*^9, {3.7239436460810485`*^9, 3.72394364668592*^9}, {3.7254330838452635`*^9, 3.72543315169353*^9}, { 3.7254331912947936`*^9, 3.7254332075936446`*^9}, {3.725433705009429*^9, 3.7254337902858543`*^9}, {3.72543382083533*^9, 3.7254339260782228`*^9}, { 3.7254341992826924`*^9, 3.725434210286269*^9}, {3.7254342875818415`*^9, 3.7254342880778885`*^9}, {3.725443796293885*^9, 3.7254438161441803`*^9}, { 3.725756614481497*^9, 3.725756618125969*^9}, {3.7257914023599677`*^9, 3.7257914032179613`*^9}, {3.725791548301742*^9, 3.7257915491082635`*^9}, { 3.7257916547512665`*^9, 3.725791656837747*^9}, {3.725891883570933*^9, 3.7258919550235353`*^9}, {3.7258922912790194`*^9, 3.725892303666605*^9}, { 3.7258923638013153`*^9, 3.7258923917562647`*^9}, {3.732781849897335*^9, 3.732781851740935*^9}, {3.756128796258463*^9, 3.756128808101935*^9}, { 3.7561289636033297`*^9, 3.7561289674012337`*^9}, {3.7561291581496544`*^9, 3.756129161730915*^9}, {3.756168228209236*^9, 3.7561682921182303`*^9}, { 3.756168336119172*^9, 3.7561683422817945`*^9}, {3.7561687588268995`*^9, 3.756168760043317*^9}, {3.756168790608805*^9, 3.7561688096838417`*^9}, { 3.7562669791923923`*^9, 3.7562669871894484`*^9}, {3.7562671345571966`*^9, 3.7562671514185095`*^9}, {3.756267238618904*^9, 3.75626728245811*^9}, { 3.7562673231127896`*^9, 3.756267369934089*^9}, {3.7562679132987003`*^9, 3.7562679378330235`*^9}, {3.7562686403059607`*^9, 3.75626865150496*^9}, 3.756268910964476*^9, 3.756268975347582*^9, {3.756291635829771*^9, 3.756291670714565*^9}, {3.7562970292001624`*^9, 3.7562971110957913`*^9}, { 3.756354727514307*^9, 3.7563547516317015`*^9}, {3.756354849442463*^9, 3.7563548962495594`*^9}, {3.7563549974812*^9, 3.7563550014513693`*^9}, { 3.756355080997491*^9, 3.756355089151907*^9}, {3.7563551640676885`*^9, 3.756355171626652*^9}, {3.756355203033866*^9, 3.7563553257026477`*^9}, { 3.7563554337406178`*^9, 3.7563554593890176`*^9}, {3.756355541718184*^9, 3.756355546747837*^9}, {3.7563557326318254`*^9, 3.7563557465035677`*^9}, { 3.7563558550458755`*^9, 3.7563558609196053`*^9}, {3.756355910283166*^9, 3.75635593869836*^9}, {3.7563560087797346`*^9, 3.7563560102950015`*^9}, { 3.756797773170301*^9, 3.7567978192689314`*^9}, {3.756798047305444*^9, 3.7567980844374113`*^9}, {3.7567981179139524`*^9, 3.756798154780326*^9}, { 3.7568139377944374`*^9, 3.756813941735011*^9}, {3.7578171254549913`*^9, 3.7578171982352457`*^9}, {3.75781775424854*^9, 3.7578177761870728`*^9}, { 3.75781956271533*^9, 3.757819566308566*^9}, 3.7878930157969465`*^9, 3.7878931876970196`*^9, {3.7890171909617825`*^9, 3.789017212740966*^9}, { 3.8152685002967186`*^9, 3.815268678285927*^9}, {3.815269201087903*^9, 3.815269223194291*^9}}, CellLabel-> "In[223]:=",ExpressionUUID->"0c482183-6ef6-4cc4-9461-c4c6b57fa359"] }, Closed]], Cell[CellGroupData[{ Cell["EVNT defs", "Subsection", CellChangeTimes->{{3.7582531074375505`*^9, 3.7582531288543863`*^9}, { 3.787892825419589*^9, 3.7878928340449758`*^9}, {3.8175215825088205`*^9, 3.8175215865117702`*^9}, {3.8223696966597366`*^9, 3.822369704047408*^9}},ExpressionUUID->"e15916b1-3f71-49e0-bf31-\ 6ecab0c9b0b3"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"EVNT", ",", RowBox[{"{", RowBox[{"s0_", ",", "sol0_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", ",", "\[Delta]dof", ",", "equ", ",", "sol", ",", "\[Delta]WT", ",", "\[CapitalDelta]s"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WT", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"EVNT", ",", RowBox[{"{", RowBox[{"s0", ",", "sol0"}], "}"}]}], "}"}], ",", "#", " ", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WT", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WT", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"D", "[", RowBox[{"\[Delta]WT", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"First", "[", RowBox[{"Solve", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"equ", "\[Equal]", "0"}], "]"}], ",", "dof"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", "sol", "]"}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "find", " ", "\[CapitalDelta]s", " ", "for", " ", "the", " ", "next", " ", "event"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[CapitalDelta]s", "=", RowBox[{"Min", "[", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"EVNTPOST", ",", RowBox[{"{", RowBox[{"s0", ",", "sol"}], "}"}]}], "}"}], ",", "#", ",", "fun"}], "]"}], "&"}], ",", RowBox[{"Select", "[", RowBox[{"ele", ",", RowBox[{ RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], "\[Equal]", "CONTACT"}], "&"}]}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "solution", " ", "at", " ", "the", " ", "next", " ", "event", " ", "U"}], "=", RowBox[{ RowBox[{"0", " ", "or", " ", "F"}], "=", RowBox[{"0", " ", "or", " ", "both"}]}]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{ RowBox[{"s0", "+", "\[CapitalDelta]s"}], ",", RowBox[{"sol", " ", "/.", RowBox[{"s", "\[Rule]", RowBox[{"s0", "+", "\[CapitalDelta]s"}]}]}]}], "}"}], "]"}]}]}], "]"}]}], ";"}], " "}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.445098179109*^9, 3.4450982721786003`*^9, {3.451279000619*^9, 3.4512790074518003`*^9}, {3.4512864298050003`*^9, 3.4512864368094*^9}, { 3.4706476335011683`*^9, 3.4706476477283683`*^9}, {3.4770540063998003`*^9, 3.4770540103154*^9}, {3.4818115795696*^9, 3.481811581816*^9}, { 3.4820252104592*^9, 3.4820252549035997`*^9}, {3.4820583880738*^9, 3.4820584077454*^9}, {3.4822351571716003`*^9, 3.4822351901188*^9}, { 3.4823004164308*^9, 3.4823004243712*^9}, {3.493344815723*^9, 3.4933448166745996`*^9}, {3.4933448517122*^9, 3.4933448763445997`*^9}, { 3.4933449778422003`*^9, 3.4933449867342*^9}, {3.4942053389948*^9, 3.4942053532688*^9}, {3.495099886848*^9, 3.4950998935959997`*^9}, { 3.495099958993*^9, 3.495099969426*^9}, 3.495100042671*^9, { 3.495100076422*^9, 3.495100110413*^9}, {3.49510016601*^9, 3.4951001814849997`*^9}, 3.4951002189040003`*^9, {3.495100255352*^9, 3.495100257927*^9}, {3.495100455098*^9, 3.4951004564449997`*^9}, { 3.495100515517*^9, 3.4951005243059998`*^9}, {3.495100586*^9, 3.4951006116359997`*^9}, {3.496055002618*^9, 3.496055006674*^9}, { 3.5007168179316*^9, 3.5007168299904003`*^9}, {3.557657331191841*^9, 3.5576573613778934`*^9}, {3.557658058371518*^9, 3.5576580893531723`*^9}, { 3.6204640425822525`*^9, 3.620464043896328*^9}, {3.629448441451354*^9, 3.6294484425113554`*^9}, {3.632027966812848*^9, 3.63202808169145*^9}, { 3.632028112439104*^9, 3.632028231997714*^9}, {3.632028264944972*^9, 3.632028286223409*^9}, 3.6320284618641176`*^9, 3.6320284928925724`*^9, { 3.6321887622237573`*^9, 3.6321887797107573`*^9}, {3.6321888300516367`*^9, 3.6321888552960806`*^9}, 3.6321889475563574`*^9, {3.63218903764051*^9, 3.6321890646730566`*^9}, {3.632189114899929*^9, 3.63218912051025*^9}, { 3.632189363344139*^9, 3.632189368985462*^9}, {3.65933624669765*^9, 3.6593362536240625`*^9}, {3.659336346288225*^9, 3.6593363466002254`*^9}, { 3.685234016837945*^9, 3.6852340690569315`*^9}, {3.6852341853385825`*^9, 3.6852342255038795`*^9}, {3.6852342700224257`*^9, 3.685234275388733*^9}, 3.685260724724876*^9, {3.685271245062879*^9, 3.685271273442919*^9}, { 3.685340120474733*^9, 3.6853401228547363`*^9}, {3.6873488134786153`*^9, 3.6873488145086164`*^9}, {3.687348848548664*^9, 3.6873488495686655`*^9}, { 3.6873489495588055`*^9, 3.687348976528844*^9}, {3.6873490107688913`*^9, 3.6873490208289056`*^9}, {3.6873490736689796`*^9, 3.6873490997690163`*^9}, {3.6873491395590715`*^9, 3.6873491721791177`*^9}, {3.6873493303593388`*^9, 3.687349336179347*^9}, { 3.687521139333435*^9, 3.687521232626771*^9}, {3.687526828204684*^9, 3.6875268662258587`*^9}, {3.687744603751021*^9, 3.687744621651046*^9}, { 3.687744782441271*^9, 3.687744793141286*^9}, {3.687744898361433*^9, 3.687744900871437*^9}, {3.687828873646782*^9, 3.6878288977768154`*^9}, { 3.6893872627070065`*^9, 3.6893872737370224`*^9}, {3.689388189828305*^9, 3.689388190108305*^9}, {3.6924132329925613`*^9, 3.692413234362563*^9}, { 3.6924133951727886`*^9, 3.6924134472928615`*^9}, {3.692413504072941*^9, 3.6924135542830114`*^9}, {3.6924138300453973`*^9, 3.692413892645485*^9}, { 3.6924150151235356`*^9, 3.692415019653542*^9}, {3.6924150955736485`*^9, 3.692415151833727*^9}, {3.6924152984639325`*^9, 3.692415397454071*^9}, { 3.6924155440942764`*^9, 3.6924155997043543`*^9}, {3.6924163099373484`*^9, 3.692416448987543*^9}, {3.6924164799875865`*^9, 3.692416520217643*^9}, { 3.6926047241829367`*^9, 3.6926047936630344`*^9}, {3.692694606764871*^9, 3.6926946080948734`*^9}, {3.6926946485549297`*^9, 3.6926946848649807`*^9}, {3.692694726505039*^9, 3.6926947795951133`*^9}, { 3.6926948533452168`*^9, 3.6926948903052683`*^9}, {3.692695016775445*^9, 3.6926950466854873`*^9}, {3.6926951047455683`*^9, 3.6926952014557037`*^9}, {3.692695400025982*^9, 3.6926954007959833`*^9}, { 3.692699088631146*^9, 3.6926990917611504`*^9}, {3.692699130701205*^9, 3.692699150701233*^9}, {3.6926992111213174`*^9, 3.692699243221362*^9}, { 3.692767928345048*^9, 3.6927679342250557`*^9}, {3.692768078185258*^9, 3.692768090845275*^9}, {3.692768583705965*^9, 3.6927686080859995`*^9}, { 3.692768652936062*^9, 3.6927686668160815`*^9}, {3.6927686975061245`*^9, 3.692768721766158*^9}, {3.6927687546262045`*^9, 3.692768807796279*^9}, { 3.6927688439663296`*^9, 3.692768846666333*^9}, {3.6927689511864796`*^9, 3.6927690097565613`*^9}, {3.692769047276614*^9, 3.6927692269968657`*^9}, { 3.692769260096912*^9, 3.6927692611369133`*^9}, {3.692769508057259*^9, 3.6927695324672937`*^9}, {3.692769570707347*^9, 3.692769719217555*^9}, { 3.6927698159576902`*^9, 3.6927698318077126`*^9}, 3.6927699552978854`*^9, { 3.6927701375081406`*^9, 3.6927701495781574`*^9}, {3.692772614961609*^9, 3.692772638701642*^9}, {3.692782982318822*^9, 3.6927829888081927`*^9}, { 3.6927830390960693`*^9, 3.692783045068411*^9}, {3.692783125046985*^9, 3.6927831273591175`*^9}, {3.692784897481363*^9, 3.6927849907176957`*^9}, 3.6927851596043553`*^9, {3.692786968327264*^9, 3.6927869691872644`*^9}, { 3.6927917561302457`*^9, 3.6927918079203186`*^9}, {3.6927918834304237`*^9, 3.692791893050438*^9}, 3.692791931280491*^9, {3.692791999660587*^9, 3.692792026840625*^9}, {3.6927921455307913`*^9, 3.6927921655908194`*^9}, { 3.692792200960869*^9, 3.692792228630907*^9}, {3.692792265330959*^9, 3.6927922938409986`*^9}, {3.6927923374910593`*^9, 3.6927923700511055`*^9}, {3.6927924565012264`*^9, 3.692792499271286*^9}, { 3.692792553391362*^9, 3.6927925860314074`*^9}, {3.692792731971612*^9, 3.6927927381216207`*^9}, {3.692792820381736*^9, 3.692792853021782*^9}, { 3.6927928932518377`*^9, 3.6927929516419196`*^9}, {3.6927929886919713`*^9, 3.6927930024219904`*^9}, {3.69279305234206*^9, 3.6927930715320873`*^9}, { 3.6927932237223005`*^9, 3.692793224982302*^9}, 3.6927932572523475`*^9, { 3.6927934421826067`*^9, 3.6927934498726172`*^9}, {3.692793484652666*^9, 3.6927935029226913`*^9}, {3.6927954180780883`*^9, 3.692795446828129*^9}, { 3.6928535571114936`*^9, 3.692853577521522*^9}, {3.692854825823887*^9, 3.692854837063903*^9}, {3.692854874433955*^9, 3.6928548775639596`*^9}, { 3.6928579822683063`*^9, 3.6928579955883245`*^9}, {3.6929656707917795`*^9, 3.692965795661954*^9}, {3.6929658426120195`*^9, 3.6929658536320353`*^9}, { 3.6929659138621197`*^9, 3.6929659218321304`*^9}, {3.692965990142226*^9, 3.6929660268822775`*^9}, {3.692966066362333*^9, 3.692966192182509*^9}, 3.69296637876277*^9, {3.6929669253235354`*^9, 3.692966936273551*^9}, { 3.6929669714336*^9, 3.692966971953601*^9}, 3.6929670139636593`*^9, 3.692967433554247*^9, {3.6929675634944286`*^9, 3.6929676911746073`*^9}, { 3.6929677832047367`*^9, 3.6929678068347692`*^9}, {3.6929678599332247`*^9, 3.6929678711132402`*^9}, 3.692967908543293*^9, {3.693017052482854*^9, 3.6930171392429757`*^9}, {3.6930174027243443`*^9, 3.6930175965956163`*^9}, {3.6930184697368383`*^9, 3.6930185654269724`*^9}, {3.6930186942971525`*^9, 3.6930188354373503`*^9}, {3.6930188926684303`*^9, 3.6930189600095253`*^9}, {3.693018990869568*^9, 3.693018991349569*^9}, { 3.693019036009631*^9, 3.693019041239639*^9}, {3.6930190980797186`*^9, 3.693019098629719*^9}, {3.693019130059763*^9, 3.6930192205398893`*^9}, { 3.693020315081422*^9, 3.693020326351438*^9}, {3.6930205415560236`*^9, 3.6930206058761134`*^9}, {3.6931381375028915`*^9, 3.693138137902892*^9}, { 3.693138677303647*^9, 3.693138683263655*^9}, {3.693139600730257*^9, 3.6931396288802967`*^9}, {3.6932135226775846`*^9, 3.6932135229775853`*^9}, {3.693219312471691*^9, 3.69321932632171*^9}, { 3.6932194762919197`*^9, 3.6932194879419365`*^9}, 3.6932195481520205`*^9, { 3.693220303405078*^9, 3.6932203178550987`*^9}, {3.693220688975618*^9, 3.693220698955632*^9}, {3.6933024593938713`*^9, 3.6933024657438803`*^9}, { 3.693302603694073*^9, 3.693302604214074*^9}, {3.6933103950923057`*^9, 3.693310399082311*^9}, {3.6933104528223867`*^9, 3.693310456172391*^9}, { 3.693380733755448*^9, 3.693380746175465*^9}, {3.6936247413492084`*^9, 3.6936247436692114`*^9}, {3.69362490643944*^9, 3.6936249099894447`*^9}, { 3.6937175435584445`*^9, 3.6937175579984646`*^9}, {3.693717708199675*^9, 3.6937177268707013`*^9}, {3.6937178194508305`*^9, 3.6937178401008596`*^9}, {3.693717934550992*^9, 3.6937179428310037`*^9}, { 3.6937180305511265`*^9, 3.693718060841169*^9}, {3.693718198801362*^9, 3.6937182028213673`*^9}, {3.693723123415037*^9, 3.6937231809651175`*^9}, { 3.693723252275217*^9, 3.69372327580525*^9}, {3.6937233347053328`*^9, 3.693723337655337*^9}, {3.693723689337829*^9, 3.6937237730079465`*^9}, { 3.6937240089782767`*^9, 3.6937240113382797`*^9}, {3.6938202843684807`*^9, 3.6938203172553616`*^9}, {3.6938203482121134`*^9, 3.6938203495041876`*^9}, 3.6938204448556414`*^9, {3.693826654370701*^9, 3.693826713082033*^9}, 3.6938269274112916`*^9, {3.69384095960849*^9, 3.6938409879385295`*^9}, { 3.6938967427518525`*^9, 3.6938967457718563`*^9}, {3.693896818211958*^9, 3.6938968234619656`*^9}, {3.6940917346582804`*^9, 3.6940917372882843`*^9}, {3.6949174720509205`*^9, 3.6949174781309295`*^9}, {3.69491751432098*^9, 3.6949175560810385`*^9}, { 3.697770949307855*^9, 3.697770962227873*^9}, {3.723799262336609*^9, 3.723799262645475*^9}, 3.7239435284061375`*^9, {3.7239436460810485`*^9, 3.72394364668592*^9}, {3.7254330838452635`*^9, 3.72543315169353*^9}, { 3.7254331912947936`*^9, 3.7254332075936446`*^9}, {3.725433705009429*^9, 3.7254337902858543`*^9}, {3.72543382083533*^9, 3.7254339260782228`*^9}, { 3.7254341992826924`*^9, 3.725434210286269*^9}, {3.7254342875818415`*^9, 3.7254342880778885`*^9}, {3.725443796293885*^9, 3.7254438161441803`*^9}, { 3.725756614481497*^9, 3.725756618125969*^9}, {3.7257914023599677`*^9, 3.7257914032179613`*^9}, {3.725791548301742*^9, 3.7257915491082635`*^9}, { 3.7257916547512665`*^9, 3.725791656837747*^9}, {3.725891883570933*^9, 3.7258919550235353`*^9}, {3.7258922912790194`*^9, 3.725892303666605*^9}, { 3.7258923638013153`*^9, 3.7258923917562647`*^9}, {3.732781849897335*^9, 3.732781851740935*^9}, {3.756128796258463*^9, 3.756128808101935*^9}, { 3.7561289636033297`*^9, 3.7561289674012337`*^9}, {3.7561291581496544`*^9, 3.756129161730915*^9}, {3.756168228209236*^9, 3.7561682921182303`*^9}, { 3.756168336119172*^9, 3.7561683422817945`*^9}, {3.7561687588268995`*^9, 3.756168760043317*^9}, {3.756168790608805*^9, 3.7561688096838417`*^9}, { 3.7562669791923923`*^9, 3.7562669871894484`*^9}, {3.7562671345571966`*^9, 3.7562671514185095`*^9}, {3.756267238618904*^9, 3.75626728245811*^9}, { 3.7562673231127896`*^9, 3.756267369934089*^9}, {3.7562679132987003`*^9, 3.7562679378330235`*^9}, {3.7562686403059607`*^9, 3.75626865150496*^9}, 3.756268910964476*^9, 3.756268975347582*^9, {3.756291635829771*^9, 3.756291670714565*^9}, {3.7562970292001624`*^9, 3.7562971110957913`*^9}, { 3.756354727514307*^9, 3.7563547516317015`*^9}, {3.756354849442463*^9, 3.7563548962495594`*^9}, {3.7563549974812*^9, 3.7563550014513693`*^9}, { 3.756355080997491*^9, 3.756355089151907*^9}, {3.7563551640676885`*^9, 3.756355171626652*^9}, {3.756355203033866*^9, 3.7563553257026477`*^9}, { 3.7563554337406178`*^9, 3.7563554593890176`*^9}, {3.756355541718184*^9, 3.756355546747837*^9}, {3.7563557326318254`*^9, 3.7563557465035677`*^9}, { 3.7563558550458755`*^9, 3.7563558609196053`*^9}, {3.756355910283166*^9, 3.75635593869836*^9}, {3.7563560087797346`*^9, 3.7563560102950015`*^9}, { 3.756797773170301*^9, 3.7567978192689314`*^9}, {3.756798047305444*^9, 3.7567980844374113`*^9}, {3.7567981179139524`*^9, 3.756798154780326*^9}, { 3.7568139377944374`*^9, 3.756813941735011*^9}, {3.7578171254549913`*^9, 3.7578171982352457`*^9}, {3.75781775424854*^9, 3.7578177761870728`*^9}, { 3.75781956271533*^9, 3.757819566308566*^9}, 3.7878930157969465`*^9, 3.7878931876970196`*^9, {3.7890171909617825`*^9, 3.789017212740966*^9}, { 3.8152685002967186`*^9, 3.815268678285927*^9}, {3.815269201087903*^9, 3.815269223194291*^9}, {3.8175216334258814`*^9, 3.8175216554867306`*^9}, { 3.817608992647215*^9, 3.8176090081319494`*^9}, 3.817609084026562*^9, { 3.8176091236756463`*^9, 3.817609192978817*^9}, {3.8176102671403065`*^9, 3.817610319221841*^9}, {3.817610354806981*^9, 3.8176103596390924`*^9}, { 3.817791293771158*^9, 3.817791414961601*^9}, {3.8177914936598372`*^9, 3.817791499828621*^9}, {3.8177915743263783`*^9, 3.817791574905566*^9}, { 3.8178746728163805`*^9, 3.8178746918171453`*^9}, {3.8178747220729046`*^9, 3.8178747512740507`*^9}, {3.8178747818821955`*^9, 3.817874800317868*^9}, { 3.817874856079772*^9, 3.81787487676381*^9}, {3.843182965086443*^9, 3.8431829731823196`*^9}}, CellLabel-> "In[228]:=",ExpressionUUID->"bbbfdf88-41d3-44a1-ad5a-9c1bd72c7b1b"] }, Closed]], Cell[CellGroupData[{ Cell["VIBR defs", "Subsection", CellChangeTimes->{{3.7582531074375505`*^9, 3.7582531288543863`*^9}, { 3.7878928096029596`*^9, 3.787892817639742*^9}, 3.822369708831148*^9},ExpressionUUID->"80029a0f-ea91-4cfe-9c78-\ 1860aa1e6e10"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", ",", "\[Delta]dof", ",", "dofall", ",", "dof0", " ", ",", "dof2", " ", ",", "equ", ",", "sol", ",", "\[Delta]WW", ",", "KK", ",", "MM", ",", "nn", ",", "val", ",", "vec"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WW", "=", RowBox[{"Simplify", "[", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", " ", "=", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dofall", "=", RowBox[{"Union", "[", RowBox[{"dof", " ", "/.", " ", RowBox[{ RowBox[{"anya_", "[", RowBox[{"anyb_", ",", RowBox[{"0", "|", "2"}]}], "]"}], "\[Rule]", RowBox[{"anya", "[", "anyb", "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof0", " ", "=", RowBox[{"dofall", "/.", " ", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dof2", " ", "=", RowBox[{"dofall", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"KK", " ", "=", RowBox[{"D", "[", RowBox[{"equ", ",", RowBox[{"{", "dof0", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"MM", " ", "=", RowBox[{"D", "[", RowBox[{"equ", ",", RowBox[{"{", "dof2", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"val", ",", "vec"}], "}"}], "=", RowBox[{"Eigensystem", "[", RowBox[{"{", RowBox[{"KK", ",", "MM"}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Table", "[", " ", RowBox[{ RowBox[{"{", " ", RowBox[{ RowBox[{ RowBox[{"\[Omega]", "[", "ii", "]"}], "->", RowBox[{"Sqrt", "[", RowBox[{"val", "[", RowBox[{"[", "ii", "]"}], "]"}], "]"}]}], ",", RowBox[{"Thread", "[", RowBox[{"dofall", "\[Rule]", RowBox[{"vec", "[", RowBox[{"[", RowBox[{"ii", ",", ";;"}], "]"}], "]"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", RowBox[{"Length", "[", "dofall", "]"}]}], "}"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", ",", "\[Delta]dof", ",", "dofall", ",", "dof0", " ", ",", "dof2", " ", ",", "equ", ",", "sol", ",", "\[Delta]WW", ",", "KK", ",", "MM", ",", "nn", ",", "val", ",", "vec"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WW", "=", RowBox[{"Simplify", "[", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", " ", "=", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dofall", "=", RowBox[{"Union", "[", RowBox[{"dof", " ", "/.", " ", RowBox[{ RowBox[{"anya_", "[", RowBox[{"anyb_", ",", RowBox[{"0", "|", "2"}]}], "]"}], "\[Rule]", RowBox[{"anya", "[", "anyb", "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof0", " ", "=", RowBox[{"dofall", "/.", " ", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dof2", " ", "=", RowBox[{"dofall", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"KK", " ", "=", RowBox[{"D", "[", RowBox[{"equ", ",", RowBox[{"{", "dof0", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"MM", " ", "=", RowBox[{"D", "[", RowBox[{"equ", ",", RowBox[{"{", "dof2", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"val", ",", "vec"}], "}"}], "=", RowBox[{"Eigensystem", "[", RowBox[{"{", RowBox[{"KK", ",", "MM"}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Table", "[", " ", RowBox[{ RowBox[{"{", " ", RowBox[{ RowBox[{ RowBox[{"\[Omega]", "[", "ii", "]"}], "->", RowBox[{"Sqrt", "[", RowBox[{"val", "[", RowBox[{"[", "ii", "]"}], "]"}], "]"}]}], ",", RowBox[{"Thread", "[", RowBox[{"dofall", "\[Rule]", RowBox[{"vec", "[", RowBox[{"[", RowBox[{"ii", ",", ";;"}], "]"}], "]"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", RowBox[{"Length", "[", "dofall", "]"}]}], "}"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", "\[Delta]WW_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", ",", "\[Delta]dof", ",", "dofall", ",", "dof0", " ", ",", "dof2", " ", ",", "equ", ",", "sol", ",", "KK", ",", "MM", ",", "nn", ",", "val", ",", "vec"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", " ", "=", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dofall", "=", RowBox[{"Union", "[", RowBox[{"dof", " ", "/.", " ", RowBox[{ RowBox[{"anya_", "[", RowBox[{"anyb_", ",", RowBox[{"0", "|", "2"}]}], "]"}], "\[Rule]", RowBox[{"anya", "[", "anyb", "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof0", " ", "=", RowBox[{"dofall", "/.", " ", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dof2", " ", "=", RowBox[{"dofall", "/.", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"KK", " ", "=", RowBox[{"D", "[", RowBox[{"equ", ",", RowBox[{"{", "dof0", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"MM", " ", "=", RowBox[{"D", "[", RowBox[{"equ", ",", RowBox[{"{", "dof2", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"val", ",", "vec"}], "}"}], "=", RowBox[{"Eigensystem", "[", RowBox[{"{", RowBox[{"KK", ",", "MM"}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Table", "[", " ", RowBox[{ RowBox[{"{", " ", RowBox[{ RowBox[{ RowBox[{"\[Omega]", "[", "ii", "]"}], "->", RowBox[{"Sqrt", "[", RowBox[{"val", "[", RowBox[{"[", "ii", "]"}], "]"}], "]"}]}], ",", RowBox[{"Thread", "[", RowBox[{"dofall", "\[Rule]", RowBox[{"vec", "[", RowBox[{"[", RowBox[{"ii", ",", ";;"}], "]"}], "]"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", RowBox[{"Length", "[", "dofall", "]"}]}], "}"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"MATRIXFUNCTION", "[", RowBox[{"f_", ",", "M_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"val", ",", "vec"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"val", ",", "vec"}], "}"}], "=", RowBox[{"Eigensystem", "[", "M", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"Transpose", "[", "vec", "]"}], ".", RowBox[{"DiagonalMatrix", "[", RowBox[{"Map", "[", RowBox[{"f", ",", "val"}], "]"}], "]"}], ".", RowBox[{"Inverse", "[", RowBox[{"Transpose", "[", "vec", "]"}], "]"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"VIBR", ",", "rule_"}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", ",", "dof0", ",", "dof1", ",", "dof2", ",", "\[Delta]dof", ",", "dofall", ",", "equ", ",", "\[Delta]WW", ",", "KK", ",", "MM", ",", "\[CapitalOmega]"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WW", "=", RowBox[{"Simplify", "[", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", " ", "=", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dofall", "=", RowBox[{"Union", "[", RowBox[{"dof", " ", "/.", " ", RowBox[{ RowBox[{"anya_", "[", RowBox[{"anyb_", ",", RowBox[{"0", "|", "2"}]}], "]"}], "\[Rule]", RowBox[{"anya", "[", "anyb", "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof0", " ", "=", RowBox[{"dofall", "/.", " ", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dof1", " ", "=", RowBox[{"dofall", "/.", " ", RowBox[{"DRULE", "[", "1", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dof2", " ", "=", RowBox[{"dofall", "/.", " ", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"KK", " ", "=", RowBox[{"D", "[", RowBox[{"equ", ",", RowBox[{"{", "dof0", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"MM", " ", "=", RowBox[{"D", "[", RowBox[{"equ", ",", RowBox[{"{", "dof2", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", "=", RowBox[{"MATRIXFUNCTION", "[", RowBox[{ RowBox[{ RowBox[{"Sqrt", "[", "#", "]"}], "&"}], ",", RowBox[{ RowBox[{"Inverse", "[", "MM", "]"}], ".", "KK"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Thread", "[", RowBox[{"dofall", "->", "\[IndentingNewLine]", RowBox[{"Simplify", "[", RowBox[{ RowBox[{ RowBox[{"MATRIXFUNCTION", "[", RowBox[{ RowBox[{ RowBox[{"Cos", "[", RowBox[{"#", "*", "t"}], "]"}], "&"}], ",", "\[CapitalOmega]"}], "]"}], ".", RowBox[{"(", RowBox[{"dof0", "/.", "rule"}], ")"}]}], "+", RowBox[{ RowBox[{"MATRIXFUNCTION", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", RowBox[{"#", "*", "t"}], "]"}], "&"}], ",", "\[CapitalOmega]"}], "]"}], ".", RowBox[{"Inverse", "[", "\[CapitalOmega]", "]"}], ".", RowBox[{"(", RowBox[{"dof1", "/.", "rule"}], ")"}]}]}], "]"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"VIBR", ",", "rule_"}], "}"}], ",", "\[Delta]WW_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", ",", "dof0", ",", "dof1", ",", "dof2", ",", "\[Delta]dof", ",", "dofall", ",", "equ", ",", "KK", ",", "MM", ",", "\[CapitalOmega]"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", " ", "=", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dofall", "=", RowBox[{"Union", "[", RowBox[{"dof", " ", "/.", " ", RowBox[{ RowBox[{"anya_", "[", RowBox[{"anyb_", ",", RowBox[{"0", "|", "2"}]}], "]"}], "\[Rule]", RowBox[{"anya", "[", "anyb", "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof0", " ", "=", RowBox[{"dofall", "/.", " ", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dof1", " ", "=", RowBox[{"dofall", "/.", " ", RowBox[{"DRULE", "[", "1", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dof2", " ", "=", RowBox[{"dofall", "/.", " ", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"KK", " ", "=", RowBox[{"D", "[", RowBox[{"equ", ",", RowBox[{"{", "dof0", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"MM", " ", "=", RowBox[{"D", "[", RowBox[{"equ", ",", RowBox[{"{", "dof2", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", "=", RowBox[{"MATRIXFUNCTION", "[", RowBox[{ RowBox[{ RowBox[{"Sqrt", "[", "#", "]"}], "&"}], ",", RowBox[{ RowBox[{"Inverse", "[", "MM", "]"}], ".", "KK"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Thread", "[", RowBox[{"dofall", "->", "\[IndentingNewLine]", RowBox[{"Simplify", "[", RowBox[{ RowBox[{ RowBox[{"MATRIXFUNCTION", "[", RowBox[{ RowBox[{ RowBox[{"Cos", "[", RowBox[{"#", "*", "t"}], "]"}], "&"}], ",", "\[CapitalOmega]"}], "]"}], ".", RowBox[{"(", RowBox[{"dof0", "/.", "rule"}], ")"}]}], "+", RowBox[{ RowBox[{"MATRIXFUNCTION", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", RowBox[{"#", "*", "t"}], "]"}], "&"}], ",", "\[CapitalOmega]"}], "]"}], ".", RowBox[{"Inverse", "[", "\[CapitalOmega]", "]"}], ".", RowBox[{"(", RowBox[{"dof1", "/.", "rule"}], ")"}]}]}], "]"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}]}], "Input", InitializationCell->True, CellChangeTimes->{ 3.445098179109*^9, 3.4450982721786003`*^9, {3.451279000619*^9, 3.4512790074518003`*^9}, {3.4512864298050003`*^9, 3.4512864368094*^9}, { 3.4706476335011683`*^9, 3.4706476477283683`*^9}, {3.4770540063998003`*^9, 3.4770540103154*^9}, {3.4818115795696*^9, 3.481811581816*^9}, { 3.4820252104592*^9, 3.4820252549035997`*^9}, {3.4820583880738*^9, 3.4820584077454*^9}, {3.4822351571716003`*^9, 3.4822351901188*^9}, { 3.4823004164308*^9, 3.4823004243712*^9}, {3.493344815723*^9, 3.4933448166745996`*^9}, {3.4933448517122*^9, 3.4933448763445997`*^9}, { 3.4933449778422003`*^9, 3.4933449867342*^9}, {3.4942053389948*^9, 3.4942053532688*^9}, {3.495099886848*^9, 3.4950998935959997`*^9}, { 3.495099958993*^9, 3.495099969426*^9}, 3.495100042671*^9, { 3.495100076422*^9, 3.495100110413*^9}, {3.49510016601*^9, 3.4951001814849997`*^9}, 3.4951002189040003`*^9, {3.495100255352*^9, 3.495100257927*^9}, {3.495100455098*^9, 3.4951004564449997`*^9}, { 3.495100515517*^9, 3.4951005243059998`*^9}, {3.495100586*^9, 3.4951006116359997`*^9}, {3.496055002618*^9, 3.496055006674*^9}, { 3.5007168179316*^9, 3.5007168299904003`*^9}, {3.557657331191841*^9, 3.5576573613778934`*^9}, {3.557658058371518*^9, 3.5576580893531723`*^9}, { 3.6204640425822525`*^9, 3.620464043896328*^9}, {3.629448441451354*^9, 3.6294484425113554`*^9}, {3.632027966812848*^9, 3.63202808169145*^9}, { 3.632028112439104*^9, 3.632028231997714*^9}, {3.632028264944972*^9, 3.632028286223409*^9}, 3.6320284618641176`*^9, 3.6320284928925724`*^9, { 3.6321887622237573`*^9, 3.6321887797107573`*^9}, {3.6321888300516367`*^9, 3.6321888552960806`*^9}, 3.6321889475563574`*^9, {3.63218903764051*^9, 3.6321890646730566`*^9}, {3.632189114899929*^9, 3.63218912051025*^9}, { 3.632189363344139*^9, 3.632189368985462*^9}, {3.65933624669765*^9, 3.6593362536240625`*^9}, {3.659336346288225*^9, 3.6593363466002254`*^9}, { 3.685234016837945*^9, 3.6852340690569315`*^9}, {3.6852341853385825`*^9, 3.6852342255038795`*^9}, {3.6852342700224257`*^9, 3.685234275388733*^9}, 3.685260724724876*^9, {3.685271245062879*^9, 3.685271273442919*^9}, { 3.685340120474733*^9, 3.6853401228547363`*^9}, {3.6873488134786153`*^9, 3.6873488145086164`*^9}, {3.687348848548664*^9, 3.6873488495686655`*^9}, { 3.6873489495588055`*^9, 3.687348976528844*^9}, {3.6873490107688913`*^9, 3.6873490208289056`*^9}, {3.6873490736689796`*^9, 3.6873490997690163`*^9}, {3.6873491395590715`*^9, 3.6873491721791177`*^9}, {3.6873493303593388`*^9, 3.687349336179347*^9}, { 3.687521139333435*^9, 3.687521232626771*^9}, {3.687526828204684*^9, 3.6875268662258587`*^9}, {3.687744603751021*^9, 3.687744621651046*^9}, { 3.687744782441271*^9, 3.687744793141286*^9}, {3.687744898361433*^9, 3.687744900871437*^9}, {3.687828873646782*^9, 3.6878288977768154`*^9}, { 3.6893872627070065`*^9, 3.6893872737370224`*^9}, {3.689388189828305*^9, 3.689388190108305*^9}, {3.6924132329925613`*^9, 3.692413234362563*^9}, { 3.6924133951727886`*^9, 3.6924134472928615`*^9}, {3.692413504072941*^9, 3.6924135542830114`*^9}, {3.6924138300453973`*^9, 3.692413892645485*^9}, { 3.6924150151235356`*^9, 3.692415019653542*^9}, {3.6924150955736485`*^9, 3.692415151833727*^9}, {3.6924152984639325`*^9, 3.692415397454071*^9}, { 3.6924155440942764`*^9, 3.6924155997043543`*^9}, {3.6924163099373484`*^9, 3.692416448987543*^9}, {3.6924164799875865`*^9, 3.692416520217643*^9}, { 3.6926047241829367`*^9, 3.6926047936630344`*^9}, {3.692694606764871*^9, 3.6926946080948734`*^9}, {3.6926946485549297`*^9, 3.6926946848649807`*^9}, {3.692694726505039*^9, 3.6926947795951133`*^9}, { 3.6926948533452168`*^9, 3.6926948903052683`*^9}, {3.692695016775445*^9, 3.6926950466854873`*^9}, {3.6926951047455683`*^9, 3.6926952014557037`*^9}, {3.692695400025982*^9, 3.6926954007959833`*^9}, { 3.692699088631146*^9, 3.6926990917611504`*^9}, {3.692699130701205*^9, 3.692699150701233*^9}, {3.6926992111213174`*^9, 3.692699243221362*^9}, { 3.692767928345048*^9, 3.6927679342250557`*^9}, {3.692768078185258*^9, 3.692768090845275*^9}, {3.692768583705965*^9, 3.6927686080859995`*^9}, { 3.692768652936062*^9, 3.6927686668160815`*^9}, {3.6927686975061245`*^9, 3.692768721766158*^9}, {3.6927687546262045`*^9, 3.692768807796279*^9}, { 3.6927688439663296`*^9, 3.692768846666333*^9}, {3.6927689511864796`*^9, 3.6927690097565613`*^9}, {3.692769047276614*^9, 3.6927692269968657`*^9}, { 3.692769260096912*^9, 3.6927692611369133`*^9}, {3.692769508057259*^9, 3.6927695324672937`*^9}, {3.692769570707347*^9, 3.692769719217555*^9}, { 3.6927698159576902`*^9, 3.6927698318077126`*^9}, 3.6927699552978854`*^9, { 3.6927701375081406`*^9, 3.6927701495781574`*^9}, {3.692772614961609*^9, 3.692772638701642*^9}, {3.692782982318822*^9, 3.6927829888081927`*^9}, { 3.6927830390960693`*^9, 3.692783045068411*^9}, {3.692783125046985*^9, 3.6927831273591175`*^9}, {3.692784897481363*^9, 3.6927849907176957`*^9}, 3.6927851596043553`*^9, {3.692786968327264*^9, 3.6927869691872644`*^9}, { 3.6927917561302457`*^9, 3.6927918079203186`*^9}, {3.6927918834304237`*^9, 3.692791893050438*^9}, 3.692791931280491*^9, {3.692791999660587*^9, 3.692792026840625*^9}, {3.6927921455307913`*^9, 3.6927921655908194`*^9}, { 3.692792200960869*^9, 3.692792228630907*^9}, {3.692792265330959*^9, 3.6927922938409986`*^9}, {3.6927923374910593`*^9, 3.6927923700511055`*^9}, {3.6927924565012264`*^9, 3.692792499271286*^9}, { 3.692792553391362*^9, 3.6927925860314074`*^9}, {3.692792731971612*^9, 3.6927927381216207`*^9}, {3.692792820381736*^9, 3.692792853021782*^9}, { 3.6927928932518377`*^9, 3.6927929516419196`*^9}, {3.6927929886919713`*^9, 3.6927930024219904`*^9}, {3.69279305234206*^9, 3.6927930715320873`*^9}, { 3.6927932237223005`*^9, 3.692793224982302*^9}, 3.6927932572523475`*^9, { 3.6927934421826067`*^9, 3.6927934498726172`*^9}, {3.692793484652666*^9, 3.6927935029226913`*^9}, {3.6927954180780883`*^9, 3.692795446828129*^9}, { 3.6928535571114936`*^9, 3.692853577521522*^9}, {3.692854825823887*^9, 3.692854837063903*^9}, {3.692854874433955*^9, 3.6928548775639596`*^9}, { 3.6928579822683063`*^9, 3.6928579955883245`*^9}, {3.6929656707917795`*^9, 3.692965795661954*^9}, {3.6929658426120195`*^9, 3.6929658536320353`*^9}, { 3.6929659138621197`*^9, 3.6929659218321304`*^9}, {3.692965990142226*^9, 3.6929660268822775`*^9}, {3.692966066362333*^9, 3.692966192182509*^9}, 3.69296637876277*^9, {3.6929669253235354`*^9, 3.692966936273551*^9}, { 3.6929669714336*^9, 3.692966971953601*^9}, 3.6929670139636593`*^9, 3.692967433554247*^9, {3.6929675634944286`*^9, 3.6929676911746073`*^9}, { 3.6929677832047367`*^9, 3.6929678068347692`*^9}, {3.6929678599332247`*^9, 3.6929678711132402`*^9}, 3.692967908543293*^9, {3.693017052482854*^9, 3.6930171392429757`*^9}, {3.6930174027243443`*^9, 3.6930175965956163`*^9}, {3.6930184697368383`*^9, 3.6930185654269724`*^9}, {3.6930186942971525`*^9, 3.6930188354373503`*^9}, {3.6930188926684303`*^9, 3.6930189600095253`*^9}, {3.693018990869568*^9, 3.693018991349569*^9}, { 3.693019036009631*^9, 3.693019041239639*^9}, {3.6930190980797186`*^9, 3.693019098629719*^9}, {3.693019130059763*^9, 3.6930192205398893`*^9}, { 3.693020315081422*^9, 3.693020326351438*^9}, {3.6930205415560236`*^9, 3.6930206058761134`*^9}, {3.6931381375028915`*^9, 3.693138137902892*^9}, { 3.693138677303647*^9, 3.693138683263655*^9}, {3.693139600730257*^9, 3.6931396288802967`*^9}, {3.6932135226775846`*^9, 3.6932135229775853`*^9}, {3.693219312471691*^9, 3.69321932632171*^9}, { 3.6932194762919197`*^9, 3.6932194879419365`*^9}, 3.6932195481520205`*^9, { 3.693220303405078*^9, 3.6932203178550987`*^9}, {3.693220688975618*^9, 3.693220698955632*^9}, {3.6933024593938713`*^9, 3.6933024657438803`*^9}, { 3.693302603694073*^9, 3.693302604214074*^9}, {3.6933103950923057`*^9, 3.693310399082311*^9}, {3.6933104528223867`*^9, 3.693310456172391*^9}, { 3.693380733755448*^9, 3.693380746175465*^9}, {3.6936247413492084`*^9, 3.6936247436692114`*^9}, {3.69362490643944*^9, 3.6936249099894447`*^9}, { 3.6937175435584445`*^9, 3.6937175579984646`*^9}, {3.693717708199675*^9, 3.6937177268707013`*^9}, {3.6937178194508305`*^9, 3.6937178401008596`*^9}, {3.693717934550992*^9, 3.6937179428310037`*^9}, { 3.6937180305511265`*^9, 3.693718060841169*^9}, {3.693718198801362*^9, 3.6937182028213673`*^9}, {3.693723123415037*^9, 3.6937231809651175`*^9}, { 3.693723252275217*^9, 3.69372327580525*^9}, {3.6937233347053328`*^9, 3.693723337655337*^9}, {3.693723689337829*^9, 3.6937237730079465`*^9}, { 3.6937240089782767`*^9, 3.6937240113382797`*^9}, {3.6938202843684807`*^9, 3.6938203172553616`*^9}, {3.6938203482121134`*^9, 3.6938203495041876`*^9}, 3.6938204448556414`*^9, {3.693826654370701*^9, 3.693826713082033*^9}, 3.6938269274112916`*^9, {3.69384095960849*^9, 3.6938409879385295`*^9}, { 3.6938967427518525`*^9, 3.6938967457718563`*^9}, {3.693896818211958*^9, 3.6938968234619656`*^9}, {3.6940917346582804`*^9, 3.6940917372882843`*^9}, {3.6949174720509205`*^9, 3.6949174781309295`*^9}, {3.69491751432098*^9, 3.6949175560810385`*^9}, { 3.697770949307855*^9, 3.697770962227873*^9}, {3.723799262336609*^9, 3.723799262645475*^9}, 3.7239435284061375`*^9, {3.7239436460810485`*^9, 3.72394364668592*^9}, {3.7254330838452635`*^9, 3.72543315169353*^9}, { 3.7254331912947936`*^9, 3.7254332075936446`*^9}, {3.725433705009429*^9, 3.7254337902858543`*^9}, {3.72543382083533*^9, 3.7254339260782228`*^9}, { 3.7254341992826924`*^9, 3.725434210286269*^9}, {3.7254342875818415`*^9, 3.7254342880778885`*^9}, {3.725443796293885*^9, 3.7254438161441803`*^9}, { 3.725756614481497*^9, 3.725756618125969*^9}, {3.7257914023599677`*^9, 3.7257914032179613`*^9}, {3.725791548301742*^9, 3.7257915491082635`*^9}, { 3.7257916547512665`*^9, 3.725791656837747*^9}, {3.725891883570933*^9, 3.7258919550235353`*^9}, {3.7258922912790194`*^9, 3.725892303666605*^9}, { 3.7258923638013153`*^9, 3.7258923917562647`*^9}, {3.732781849897335*^9, 3.732781851740935*^9}, {3.756128796258463*^9, 3.756128808101935*^9}, { 3.7561289636033297`*^9, 3.7561289674012337`*^9}, {3.7561291581496544`*^9, 3.756129161730915*^9}, {3.756168228209236*^9, 3.7561682921182303`*^9}, { 3.756168336119172*^9, 3.7561683422817945`*^9}, {3.7561687588268995`*^9, 3.756168760043317*^9}, {3.756168790608805*^9, 3.7561688096838417`*^9}, { 3.7562669791923923`*^9, 3.7562669871894484`*^9}, {3.7562671345571966`*^9, 3.7562671514185095`*^9}, {3.756267238618904*^9, 3.75626728245811*^9}, { 3.7562673231127896`*^9, 3.756267369934089*^9}, {3.7562679132987003`*^9, 3.7562679378330235`*^9}, {3.7562686403059607`*^9, 3.75626865150496*^9}, 3.756268910964476*^9, 3.756268975347582*^9, {3.756291635829771*^9, 3.756291670714565*^9}, {3.7562970292001624`*^9, 3.7562971110957913`*^9}, { 3.756354727514307*^9, 3.7563547516317015`*^9}, {3.756354849442463*^9, 3.7563548962495594`*^9}, {3.7563549974812*^9, 3.7563550014513693`*^9}, { 3.756355080997491*^9, 3.756355089151907*^9}, {3.7563551640676885`*^9, 3.756355171626652*^9}, {3.756355203033866*^9, 3.7563553257026477`*^9}, { 3.7563554337406178`*^9, 3.7563554593890176`*^9}, {3.756355541718184*^9, 3.756355546747837*^9}, {3.7563557326318254`*^9, 3.7563557465035677`*^9}, { 3.7563558550458755`*^9, 3.7563558609196053`*^9}, {3.756355910283166*^9, 3.75635593869836*^9}, {3.7563560087797346`*^9, 3.7563560102950015`*^9}, { 3.756797773170301*^9, 3.7567978192689314`*^9}, {3.756798047305444*^9, 3.7567980844374113`*^9}, {3.7567981179139524`*^9, 3.756798154780326*^9}, { 3.7568139377944374`*^9, 3.756813941735011*^9}, {3.7578171254549913`*^9, 3.7578171982352457`*^9}, {3.75781775424854*^9, 3.7578177761870728`*^9}, { 3.75781956271533*^9, 3.757819566308566*^9}, {3.787892909261981*^9, 3.787892939075147*^9}, 3.787893197839568*^9, {3.7883277627917256`*^9, 3.7883277632122145`*^9}, {3.788327835267661*^9, 3.788327837618348*^9}}, CellLabel-> "In[229]:=",ExpressionUUID->"1582abbd-5e02-4bfd-8ff3-78c5fc645090"] }, Closed]], Cell[CellGroupData[{ Cell["STAB defs", "Subsection", CellChangeTimes->{{3.7582531074375505`*^9, 3.758253144538479*^9}, 3.7878928381949763`*^9, 3.822369712103414*^9},ExpressionUUID->"a68027a3-726d-49a5-bd4f-\ a2b1fb59ecfe"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "p_"}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]WT", ",", "dof", ",", "\[Delta]dof", ",", "equ", ",", "sol", ",", "KK", ",", "KK0", ",", "FF0", ",", "rule0", ",", "KK1", ",", "KK10", ",", "KK11", ",", "val", ",", "vec", ",", "modes", ",", "prule", ",", "list"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WT", "=", RowBox[{"ParallelMap", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WT", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WT", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"D", "[", RowBox[{"\[Delta]WT", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ StyleBox["KK", "OperatorCharacter"], StyleBox["=", "OperatorCharacter"], RowBox[{ StyleBox["D", "OperatorCharacter"], StyleBox["[", "OperatorCharacter"], RowBox[{ StyleBox["equ", "OperatorCharacter"], ",", RowBox[{"{", "dof", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"linearized", " ", "problem"}], "*)"}], "\[IndentingNewLine]", RowBox[{"KK0", "=", RowBox[{"KK", "/.", RowBox[{"Thread", "[", RowBox[{"dof", "\[Rule]", "0"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"FF0", "=", RowBox[{"equ", "/.", RowBox[{"Thread", "[", RowBox[{"dof", "\[Rule]", "0"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"rule0", "=", RowBox[{"Thread", "[", RowBox[{"dof", "->", RowBox[{"LinearSolve", "[", RowBox[{"KK0", ",", RowBox[{"-", "FF0"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", StyleBox["\[IndentingNewLine]", "OperatorCharacter"], RowBox[{"KK1", "=", RowBox[{"KK", "/.", "rule0"}]}], ";", "\[IndentingNewLine]", RowBox[{"KK10", "=", " ", RowBox[{"KK1", " ", "/.", " ", RowBox[{"p", "\[Rule]", "0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"KK11", " ", "=", RowBox[{"D", "[", RowBox[{"KK1", " ", ",", "p"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"list", "=", RowBox[{"Transpose", "[", RowBox[{"Eigensystem", "[", RowBox[{"{", RowBox[{"KK10", ",", "KK11"}], "}"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"pick", " ", "the", " ", "real", " ", "ones"}], "*)"}], "\[IndentingNewLine]", RowBox[{"list", "=", RowBox[{"Select", "[", RowBox[{"list", ",", RowBox[{ RowBox[{"Not", "[", RowBox[{"PossibleZeroQ", "[", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "&"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"list", "=", RowBox[{"Select", "[", RowBox[{"list", ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"Count", "[", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], ",", "\[ImaginaryI]"}], "]"}], "\[Equal]", "0"}], ")"}], "&"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"list", "=", RowBox[{"Select", "[", RowBox[{"list", ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"Count", "[", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"-", "\[ImaginaryI]"}]}], "]"}], "\[Equal]", "0"}], ")"}], "&"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"list", "=", RowBox[{"Select", "[", RowBox[{"list", ",", RowBox[{ RowBox[{"Not", "[", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], "===", "Infinity"}], "]"}], "&"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"p", "[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "\[Rule]", RowBox[{"-", RowBox[{"#1", "[", RowBox[{"[", "1", "]"}], "]"}]}]}], ",", RowBox[{"Thread", "[", RowBox[{"dof", "\[Rule]", RowBox[{"#1", "[", RowBox[{"[", "2", "]"}], "]"}]}], "]"}]}], "}"}], "&"}], ",", "list"}], "]"}]}]}], " ", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "p_"}], "}"}], ",", "\[Delta]WW_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", ",", "\[Delta]dof", ",", "equ", ",", "sol", ",", "KK", ",", "FF0", ",", "KK0", ",", "rule0", ",", "KK1", ",", "KK10", ",", "KK11", ",", "val", ",", "vec", ",", "modes", ",", "prule", ",", "list"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "first", "*)"}], StyleBox["\[IndentingNewLine]", "OperatorCharacter"], RowBox[{ RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", " ", "=", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ StyleBox["KK", "OperatorCharacter"], StyleBox["=", "OperatorCharacter"], RowBox[{ StyleBox["D", "OperatorCharacter"], StyleBox["[", "OperatorCharacter"], RowBox[{ StyleBox["equ", "OperatorCharacter"], ",", RowBox[{"{", "dof", "}"}]}], "]"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"KK0", "=", RowBox[{"KK", "/.", RowBox[{"Thread", "[", RowBox[{"dof", "\[Rule]", "0"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"FF0", "=", RowBox[{"equ", "/.", RowBox[{"Thread", "[", RowBox[{"dof", "\[Rule]", "0"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"rule0", "=", RowBox[{"Thread", "[", RowBox[{"dof", "->", RowBox[{"LinearSolve", "[", RowBox[{"KK0", ",", RowBox[{"-", "FF0"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", StyleBox["\[IndentingNewLine]", "OperatorCharacter"], RowBox[{"KK1", "=", RowBox[{"KK", "/.", "rule0"}]}], ";", "\[IndentingNewLine]", RowBox[{"KK10", "=", " ", RowBox[{"KK1", " ", "/.", " ", RowBox[{"p", "\[Rule]", "0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"KK11", " ", "=", RowBox[{"D", "[", RowBox[{"KK1", " ", ",", "p"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"list", "=", RowBox[{"Transpose", "[", RowBox[{"Eigensystem", "[", RowBox[{"{", RowBox[{"KK10", ",", "KK11"}], "}"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"pick", " ", "the", " ", "real", " ", "ones"}], "*)"}], "\[IndentingNewLine]", RowBox[{"list", "=", RowBox[{"Select", "[", RowBox[{"list", ",", RowBox[{ RowBox[{"Not", "[", RowBox[{"PossibleZeroQ", "[", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "&"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"list", "=", RowBox[{"Select", "[", RowBox[{"list", ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"Count", "[", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], ",", "\[ImaginaryI]"}], "]"}], "\[Equal]", "0"}], ")"}], "&"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"list", "=", RowBox[{"Select", "[", RowBox[{"list", ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"Count", "[", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"-", "\[ImaginaryI]"}]}], "]"}], "\[Equal]", "0"}], ")"}], "&"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"list", "=", RowBox[{"Select", "[", RowBox[{"list", ",", RowBox[{ RowBox[{"Not", "[", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], "===", "Infinity"}], "]"}], "&"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"p", "[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "\[Rule]", RowBox[{"-", RowBox[{"#1", "[", RowBox[{"[", "1", "]"}], "]"}]}]}], ",", RowBox[{"Thread", "[", RowBox[{"dof", "\[Rule]", RowBox[{"#1", "[", RowBox[{"[", "2", "]"}], "]"}]}], "]"}]}], "}"}], "&"}], ",", "list"}], "]"}]}]}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.445098179109*^9, 3.4450982721786003`*^9, {3.451279000619*^9, 3.4512790074518003`*^9}, {3.4512864298050003`*^9, 3.4512864368094*^9}, { 3.4706476335011683`*^9, 3.4706476477283683`*^9}, {3.4770540063998003`*^9, 3.4770540103154*^9}, {3.4818115795696*^9, 3.481811581816*^9}, { 3.4820252104592*^9, 3.4820252549035997`*^9}, {3.4820583880738*^9, 3.4820584077454*^9}, {3.4822351571716003`*^9, 3.4822351901188*^9}, { 3.4823004164308*^9, 3.4823004243712*^9}, {3.493344815723*^9, 3.4933448166745996`*^9}, {3.4933448517122*^9, 3.4933448763445997`*^9}, { 3.4933449778422003`*^9, 3.4933449867342*^9}, {3.4942053389948*^9, 3.4942053532688*^9}, {3.495099886848*^9, 3.4950998935959997`*^9}, { 3.495099958993*^9, 3.495099969426*^9}, 3.495100042671*^9, { 3.495100076422*^9, 3.495100110413*^9}, {3.49510016601*^9, 3.4951001814849997`*^9}, 3.4951002189040003`*^9, {3.495100255352*^9, 3.495100257927*^9}, {3.495100455098*^9, 3.4951004564449997`*^9}, { 3.495100515517*^9, 3.4951005243059998`*^9}, {3.495100586*^9, 3.4951006116359997`*^9}, {3.496055002618*^9, 3.496055006674*^9}, { 3.5007168179316*^9, 3.5007168299904003`*^9}, {3.557657331191841*^9, 3.5576573613778934`*^9}, {3.557658058371518*^9, 3.5576580893531723`*^9}, { 3.6204640425822525`*^9, 3.620464043896328*^9}, {3.629448441451354*^9, 3.6294484425113554`*^9}, {3.632027966812848*^9, 3.63202808169145*^9}, { 3.632028112439104*^9, 3.632028231997714*^9}, {3.632028264944972*^9, 3.632028286223409*^9}, 3.6320284618641176`*^9, 3.6320284928925724`*^9, { 3.6321887622237573`*^9, 3.6321887797107573`*^9}, {3.6321888300516367`*^9, 3.6321888552960806`*^9}, 3.6321889475563574`*^9, {3.63218903764051*^9, 3.6321890646730566`*^9}, {3.632189114899929*^9, 3.63218912051025*^9}, { 3.632189363344139*^9, 3.632189368985462*^9}, {3.65933624669765*^9, 3.6593362536240625`*^9}, {3.659336346288225*^9, 3.6593363466002254`*^9}, { 3.685234016837945*^9, 3.6852340690569315`*^9}, {3.6852341853385825`*^9, 3.6852342255038795`*^9}, {3.6852342700224257`*^9, 3.685234275388733*^9}, 3.685260724724876*^9, {3.685271245062879*^9, 3.685271273442919*^9}, { 3.685340120474733*^9, 3.6853401228547363`*^9}, {3.6873488134786153`*^9, 3.6873488145086164`*^9}, {3.687348848548664*^9, 3.6873488495686655`*^9}, { 3.6873489495588055`*^9, 3.687348976528844*^9}, {3.6873490107688913`*^9, 3.6873490208289056`*^9}, {3.6873490736689796`*^9, 3.6873490997690163`*^9}, {3.6873491395590715`*^9, 3.6873491721791177`*^9}, {3.6873493303593388`*^9, 3.687349336179347*^9}, { 3.687521139333435*^9, 3.687521232626771*^9}, {3.687526828204684*^9, 3.6875268662258587`*^9}, {3.687744603751021*^9, 3.687744621651046*^9}, { 3.687744782441271*^9, 3.687744793141286*^9}, {3.687744898361433*^9, 3.687744900871437*^9}, {3.687828873646782*^9, 3.6878288977768154`*^9}, { 3.6893872627070065`*^9, 3.6893872737370224`*^9}, {3.689388189828305*^9, 3.689388190108305*^9}, {3.6924132329925613`*^9, 3.692413234362563*^9}, { 3.6924133951727886`*^9, 3.6924134472928615`*^9}, {3.692413504072941*^9, 3.6924135542830114`*^9}, {3.6924138300453973`*^9, 3.692413892645485*^9}, { 3.6924150151235356`*^9, 3.692415019653542*^9}, {3.6924150955736485`*^9, 3.692415151833727*^9}, {3.6924152984639325`*^9, 3.692415397454071*^9}, { 3.6924155440942764`*^9, 3.6924155997043543`*^9}, {3.6924163099373484`*^9, 3.692416448987543*^9}, {3.6924164799875865`*^9, 3.692416520217643*^9}, { 3.6926047241829367`*^9, 3.6926047936630344`*^9}, {3.692694606764871*^9, 3.6926946080948734`*^9}, {3.6926946485549297`*^9, 3.6926946848649807`*^9}, {3.692694726505039*^9, 3.6926947795951133`*^9}, { 3.6926948533452168`*^9, 3.6926948903052683`*^9}, {3.692695016775445*^9, 3.6926950466854873`*^9}, {3.6926951047455683`*^9, 3.6926952014557037`*^9}, {3.692695400025982*^9, 3.6926954007959833`*^9}, { 3.692699088631146*^9, 3.6926990917611504`*^9}, {3.692699130701205*^9, 3.692699150701233*^9}, {3.6926992111213174`*^9, 3.692699243221362*^9}, { 3.692767928345048*^9, 3.6927679342250557`*^9}, {3.692768078185258*^9, 3.692768090845275*^9}, {3.692768583705965*^9, 3.6927686080859995`*^9}, { 3.692768652936062*^9, 3.6927686668160815`*^9}, {3.6927686975061245`*^9, 3.692768721766158*^9}, {3.6927687546262045`*^9, 3.692768807796279*^9}, { 3.6927688439663296`*^9, 3.692768846666333*^9}, {3.6927689511864796`*^9, 3.6927690097565613`*^9}, {3.692769047276614*^9, 3.6927692269968657`*^9}, { 3.692769260096912*^9, 3.6927692611369133`*^9}, {3.692769508057259*^9, 3.6927695324672937`*^9}, {3.692769570707347*^9, 3.692769719217555*^9}, { 3.6927698159576902`*^9, 3.6927698318077126`*^9}, 3.6927699552978854`*^9, { 3.6927701375081406`*^9, 3.6927701495781574`*^9}, {3.692772614961609*^9, 3.692772638701642*^9}, {3.692782982318822*^9, 3.6927829888081927`*^9}, { 3.6927830390960693`*^9, 3.692783045068411*^9}, {3.692783125046985*^9, 3.6927831273591175`*^9}, {3.692784897481363*^9, 3.6927849907176957`*^9}, 3.6927851596043553`*^9, {3.692786968327264*^9, 3.6927869691872644`*^9}, { 3.6927917561302457`*^9, 3.6927918079203186`*^9}, {3.6927918834304237`*^9, 3.692791893050438*^9}, 3.692791931280491*^9, {3.692791999660587*^9, 3.692792026840625*^9}, {3.6927921455307913`*^9, 3.6927921655908194`*^9}, { 3.692792200960869*^9, 3.692792228630907*^9}, {3.692792265330959*^9, 3.6927922938409986`*^9}, {3.6927923374910593`*^9, 3.6927923700511055`*^9}, {3.6927924565012264`*^9, 3.692792499271286*^9}, { 3.692792553391362*^9, 3.6927925860314074`*^9}, {3.692792731971612*^9, 3.6927927381216207`*^9}, {3.692792820381736*^9, 3.692792853021782*^9}, { 3.6927928932518377`*^9, 3.6927929516419196`*^9}, {3.6927929886919713`*^9, 3.6927930024219904`*^9}, {3.69279305234206*^9, 3.6927930715320873`*^9}, { 3.6927932237223005`*^9, 3.692793224982302*^9}, 3.6927932572523475`*^9, { 3.6927934421826067`*^9, 3.6927934498726172`*^9}, {3.692793484652666*^9, 3.6927935029226913`*^9}, {3.6927954180780883`*^9, 3.692795446828129*^9}, { 3.6928535571114936`*^9, 3.692853577521522*^9}, {3.692854825823887*^9, 3.692854837063903*^9}, {3.692854874433955*^9, 3.6928548775639596`*^9}, { 3.6928579822683063`*^9, 3.6928579955883245`*^9}, {3.6929656707917795`*^9, 3.692965795661954*^9}, {3.6929658426120195`*^9, 3.6929658536320353`*^9}, { 3.6929659138621197`*^9, 3.6929659218321304`*^9}, {3.692965990142226*^9, 3.6929660268822775`*^9}, {3.692966066362333*^9, 3.692966192182509*^9}, 3.69296637876277*^9, {3.6929669253235354`*^9, 3.692966936273551*^9}, { 3.6929669714336*^9, 3.692966971953601*^9}, 3.6929670139636593`*^9, 3.692967433554247*^9, {3.6929675634944286`*^9, 3.6929676911746073`*^9}, { 3.6929677832047367`*^9, 3.6929678068347692`*^9}, {3.6929678599332247`*^9, 3.6929678711132402`*^9}, 3.692967908543293*^9, {3.693017052482854*^9, 3.6930171392429757`*^9}, {3.6930174027243443`*^9, 3.6930175965956163`*^9}, {3.6930184697368383`*^9, 3.6930185654269724`*^9}, {3.6930186942971525`*^9, 3.6930188354373503`*^9}, {3.6930188926684303`*^9, 3.6930189600095253`*^9}, {3.693018990869568*^9, 3.693018991349569*^9}, { 3.693019036009631*^9, 3.693019041239639*^9}, {3.6930190980797186`*^9, 3.693019098629719*^9}, {3.693019130059763*^9, 3.6930192205398893`*^9}, { 3.693020315081422*^9, 3.693020326351438*^9}, {3.6930205415560236`*^9, 3.6930206058761134`*^9}, {3.6931381375028915`*^9, 3.693138137902892*^9}, { 3.693138677303647*^9, 3.693138683263655*^9}, {3.693139600730257*^9, 3.6931396288802967`*^9}, {3.6932135226775846`*^9, 3.6932135229775853`*^9}, {3.693219312471691*^9, 3.69321932632171*^9}, { 3.6932194762919197`*^9, 3.6932194879419365`*^9}, 3.6932195481520205`*^9, { 3.693220303405078*^9, 3.6932203178550987`*^9}, {3.693220688975618*^9, 3.693220698955632*^9}, {3.6933024593938713`*^9, 3.6933024657438803`*^9}, { 3.693302603694073*^9, 3.693302604214074*^9}, {3.6933103950923057`*^9, 3.693310399082311*^9}, {3.6933104528223867`*^9, 3.693310456172391*^9}, { 3.693380733755448*^9, 3.693380746175465*^9}, {3.6936247413492084`*^9, 3.6936247436692114`*^9}, {3.69362490643944*^9, 3.6936249099894447`*^9}, { 3.6937175435584445`*^9, 3.6937175579984646`*^9}, {3.693717708199675*^9, 3.6937177268707013`*^9}, {3.6937178194508305`*^9, 3.6937178401008596`*^9}, {3.693717934550992*^9, 3.6937179428310037`*^9}, { 3.6937180305511265`*^9, 3.693718060841169*^9}, {3.693718198801362*^9, 3.6937182028213673`*^9}, {3.693723123415037*^9, 3.6937231809651175`*^9}, { 3.693723252275217*^9, 3.69372327580525*^9}, {3.6937233347053328`*^9, 3.693723337655337*^9}, {3.693723689337829*^9, 3.6937237730079465`*^9}, { 3.6937240089782767`*^9, 3.6937240113382797`*^9}, {3.6938202843684807`*^9, 3.6938203172553616`*^9}, {3.6938203482121134`*^9, 3.6938203495041876`*^9}, 3.6938204448556414`*^9, {3.693826654370701*^9, 3.693826713082033*^9}, 3.6938269274112916`*^9, {3.69384095960849*^9, 3.6938409879385295`*^9}, { 3.6938967427518525`*^9, 3.6938967457718563`*^9}, {3.693896818211958*^9, 3.6938968234619656`*^9}, {3.6940917346582804`*^9, 3.6940917372882843`*^9}, {3.6949174720509205`*^9, 3.6949174781309295`*^9}, {3.69491751432098*^9, 3.6949175560810385`*^9}, { 3.697770949307855*^9, 3.697770962227873*^9}, {3.723799262336609*^9, 3.723799262645475*^9}, 3.7239435284061375`*^9, {3.7239436460810485`*^9, 3.72394364668592*^9}, {3.7254330838452635`*^9, 3.72543315169353*^9}, { 3.7254331912947936`*^9, 3.7254332075936446`*^9}, {3.725433705009429*^9, 3.7254337902858543`*^9}, {3.72543382083533*^9, 3.7254339260782228`*^9}, { 3.7254341992826924`*^9, 3.725434210286269*^9}, {3.7254342875818415`*^9, 3.7254342880778885`*^9}, {3.725443796293885*^9, 3.7254438161441803`*^9}, { 3.725756614481497*^9, 3.725756618125969*^9}, {3.7257914023599677`*^9, 3.7257914032179613`*^9}, {3.725791548301742*^9, 3.7257915491082635`*^9}, { 3.7257916547512665`*^9, 3.725791656837747*^9}, {3.725891883570933*^9, 3.7258919550235353`*^9}, {3.7258922912790194`*^9, 3.725892303666605*^9}, { 3.7258923638013153`*^9, 3.7258923917562647`*^9}, {3.732781849897335*^9, 3.732781851740935*^9}, {3.756128796258463*^9, 3.756128808101935*^9}, { 3.7561289636033297`*^9, 3.7561289674012337`*^9}, {3.7561291581496544`*^9, 3.756129161730915*^9}, {3.756168228209236*^9, 3.7561682921182303`*^9}, { 3.756168336119172*^9, 3.7561683422817945`*^9}, {3.7561687588268995`*^9, 3.756168760043317*^9}, {3.756168790608805*^9, 3.7561688096838417`*^9}, { 3.7562669791923923`*^9, 3.7562669871894484`*^9}, {3.7562671345571966`*^9, 3.7562671514185095`*^9}, {3.756267238618904*^9, 3.75626728245811*^9}, { 3.7562673231127896`*^9, 3.756267369934089*^9}, {3.7562679132987003`*^9, 3.7562679378330235`*^9}, {3.7562686403059607`*^9, 3.75626865150496*^9}, 3.756268910964476*^9, 3.756268975347582*^9, {3.756291635829771*^9, 3.756291670714565*^9}, {3.7562970292001624`*^9, 3.7562971110957913`*^9}, { 3.756354727514307*^9, 3.7563547516317015`*^9}, {3.756354849442463*^9, 3.7563548962495594`*^9}, {3.7563549974812*^9, 3.7563550014513693`*^9}, { 3.756355080997491*^9, 3.756355089151907*^9}, {3.7563551640676885`*^9, 3.756355171626652*^9}, {3.756355203033866*^9, 3.7563553257026477`*^9}, { 3.7563554337406178`*^9, 3.7563554593890176`*^9}, {3.756355541718184*^9, 3.756355546747837*^9}, {3.7563557326318254`*^9, 3.7563557465035677`*^9}, { 3.7563558550458755`*^9, 3.7563558609196053`*^9}, {3.756355910283166*^9, 3.75635593869836*^9}, {3.7563560087797346`*^9, 3.7563560102950015`*^9}, { 3.756797773170301*^9, 3.7567978192689314`*^9}, {3.756798047305444*^9, 3.7567980844374113`*^9}, {3.7567981179139524`*^9, 3.756798154780326*^9}, { 3.7568139377944374`*^9, 3.756813941735011*^9}, {3.7578171254549913`*^9, 3.7578171982352457`*^9}, {3.75781775424854*^9, 3.7578177761870728`*^9}, { 3.75781956271533*^9, 3.757819566308566*^9}, {3.758253198275837*^9, 3.7582532020405736`*^9}, {3.7582533756088347`*^9, 3.7582533985722675`*^9}, {3.760670938512352*^9, 3.76067094654175*^9}, { 3.7887482820103493`*^9, 3.7887483199991317`*^9}, {3.7887510286740055`*^9, 3.788751062737857*^9}, {3.788793141413883*^9, 3.788793141695051*^9}, { 3.7888311797760434`*^9, 3.7888312564184446`*^9}, {3.7888312978346624`*^9, 3.7888313137858887`*^9}, {3.788831356407742*^9, 3.7888313933141465`*^9}, { 3.7888314684197545`*^9, 3.7888315368553815`*^9}, {3.7888315954696364`*^9, 3.7888316472186213`*^9}, {3.788831857305335*^9, 3.788831917189584*^9}, { 3.788832255517164*^9, 3.788832334400532*^9}, {3.788832692802744*^9, 3.7888327546283236`*^9}, {3.788832880589661*^9, 3.788832889111374*^9}, { 3.788833325826789*^9, 3.7888333376722994`*^9}, {3.7888334458148613`*^9, 3.7888334462053633`*^9}, {3.7888341360558033`*^9, 3.7888341464830675`*^9}, {3.788834414977331*^9, 3.7888344465268445`*^9}, { 3.7888360737524185`*^9, 3.788836130856104*^9}, {3.7888363421132617`*^9, 3.788836345010672*^9}, {3.7888364482319136`*^9, 3.7888364523480806`*^9}, { 3.7888365732220283`*^9, 3.788836684808531*^9}, {3.7888368167754717`*^9, 3.7888368666444435`*^9}, {3.7888369683341913`*^9, 3.788836976352211*^9}, { 3.788837175638712*^9, 3.7888371869179506`*^9}, {3.788838309650617*^9, 3.788838324612111*^9}, {3.7888530458034954`*^9, 3.7888530623012686`*^9}, { 3.7889364043469267`*^9, 3.7889364238717265`*^9}, {3.7889365367269278`*^9, 3.788936567426444*^9}, {3.7889366124938154`*^9, 3.788936620487116*^9}, { 3.789125410293588*^9, 3.789125420141614*^9}, {3.7891256058149447`*^9, 3.789125607960622*^9}, {3.7891257972104635`*^9, 3.789125797405059*^9}, { 3.7891270413135867`*^9, 3.7891270457560563`*^9}, {3.7891270757650013`*^9, 3.789127077657934*^9}, {3.7891271091340284`*^9, 3.7891271251918364`*^9}, { 3.7891271735278482`*^9, 3.7891271838765836`*^9}, {3.7891272283986025`*^9, 3.7891272986842737`*^9}, 3.789127339177758*^9, {3.850965192080224*^9, 3.850965220988982*^9}, {3.850965564516798*^9, 3.85096556492159*^9}}, CellLabel-> "In[235]:=",ExpressionUUID->"ba787390-fd49-49b1-a24b-6149cb9b7456"] }, Closed]], Cell[CellGroupData[{ Cell["NONL defs", "Subsection", CellChangeTimes->{{3.7582531074375505`*^9, 3.7582531288543863`*^9}, { 3.787892825419589*^9, 3.7878928340449758`*^9}, {3.787893238336218*^9, 3.787893239616878*^9}, {3.822369723252593*^9, 3.822369724343676*^9}},ExpressionUUID->"98b2b612-b5f8-47eb-afd4-\ a2bc79752afc"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", "E8001"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", ",", "dof0", ",", "\[Delta]dof", ",", "equ", ",", "sol", ",", "\[Delta]WT"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WT", "=", RowBox[{"ParallelMap", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WT", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WT", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"D", "[", RowBox[{"\[Delta]WT", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"NSolve", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"equ", "\[Equal]", "0"}], "]"}], ",", "dof", ",", "Reals"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{ RowBox[{"MinimalBy", "[", RowBox[{"sol", ",", RowBox[{ RowBox[{"Norm", "[", RowBox[{"dof", " ", "/.", " ", "#"}], "]"}], "&"}]}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "]"}]}]}], "]"}]}], ";"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"NONL", ",", "ALL"}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", ",", "\[Delta]dof", ",", "equ", ",", "sol", ",", "\[Delta]WT"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WT", "=", RowBox[{"ParallelMap", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WT", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WT", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"D", "[", RowBox[{"\[Delta]WT", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"Solve", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"equ", "\[Equal]", "0"}], "]"}], ",", "dof"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", "sol", "]"}]}]}], "]"}]}], ";"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"NONL", ",", "rule_List"}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", ",", "\[Delta]dof", ",", "dof0", ",", "equ", ",", "sol", ",", "\[Delta]WT"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WT", "=", RowBox[{"ParallelMap", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WT", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WT", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof0", "=", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{"dof", ",", RowBox[{"dof", " ", "/.", "rule"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"D", "[", RowBox[{"\[Delta]WT", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"FindRoot", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"equ", "\[Equal]", "0"}], "]"}], ",", "dof0"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", "sol", "]"}]}]}], "]"}]}], ";"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{ "p_Symbol", ",", "pmin_", ",", "pmax_", ",", "\[CapitalDelta]p_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]WT", ",", "equ", ",", "sol", ",", "sol0", ",", "dof", ",", "\[Delta]dof"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WT", "=", RowBox[{"ParallelMap", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WT", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WT", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"D", "[", RowBox[{"\[Delta]WT", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"Thread", "[", RowBox[{"dof", "\[Rule]", "0"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ReleaseHold", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"sol", "=", RowBox[{"FindRoot", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"equ", "\[Equal]", "0"}], "]"}], ",", RowBox[{"sol", " ", "/.", RowBox[{"Rule", "\[Rule]", "List"}]}]}], "]"}]}], ";", RowBox[{"Prepend", "[", RowBox[{"sol", ",", RowBox[{ RowBox[{"Hold", "[", "p", "]"}], "\[Rule]", "p"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"p", ",", "pmin", ",", "pmax", ",", "\[CapitalDelta]p"}], "}"}]}], "]"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", "\[Delta]WW_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"equ", ",", "sol", ",", "dof", ",", "\[Delta]dof"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"Solve", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"equ", "\[Equal]", "0"}], "]"}], ",", "dof", ",", "Reals"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{ RowBox[{"MinimalBy", "[", RowBox[{"sol", ",", RowBox[{ RowBox[{"Norm", "[", RowBox[{"dof", " ", "/.", " ", "#"}], "]"}], "&"}]}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"NONL", ",", "ALL"}], "}"}], ",", "\[Delta]WW_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"equ", ",", "sol"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"equ", "=", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"Solve", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"equ", "\[Equal]", "0"}], "]"}], ",", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}], ",", "Reals"}], "]"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"NONL", ",", "rule_"}], "}"}], ",", "\[Delta]WW_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", ",", "\[Delta]dof", ",", "dof0", ",", "equ", ",", "sol"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof0", "=", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{"dof", ",", RowBox[{"dof", " ", "/.", "rule"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FindRoot", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"equ", "\[Equal]", "0"}], "]"}], ",", "dof0"}], "]"}]}]}], "]"}]}], ";"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"NONL", ",", "rule0_", ",", "rulen_"}], "}"}], ",", "\[Delta]WW_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", ",", "\[Delta]dof", ",", "dof0", ",", "equ", ",", "sol"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof0", "=", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{"dof", ",", RowBox[{"dof", " ", "/.", "rule"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"FindRoot", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"equ", "\[Equal]", "0"}], "]"}], ",", "dof0", ",", RowBox[{"DampingFactor", "\[Rule]", "4"}], ",", RowBox[{"AccuracyGoal", "\[Rule]", "2"}], ",", RowBox[{"PrecisionGoal", "\[Rule]", "2"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", "sol", "]"}]}]}], "]"}]}], ";"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{ "p_Symbol", ",", "pmin_", ",", "pmax_", ",", "\[CapitalDelta]p_"}], "}"}]}], "}"}], ",", "\[Delta]WW_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "equ", ",", "sol", ",", "sol0", ",", "dof", ",", "\[Delta]dof"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"Thread", "[", RowBox[{"dof", "\[Rule]", "0.0000001"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ReleaseHold", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"sol", "=", RowBox[{"FindRoot", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"equ", "\[Equal]", "0"}], "]"}], ",", RowBox[{"sol", " ", "/.", RowBox[{"Rule", "\[Rule]", "List"}]}]}], "]"}]}], ";", RowBox[{"Prepend", "[", RowBox[{"sol", ",", RowBox[{ RowBox[{"Hold", "[", "p", "]"}], "\[Rule]", "p"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"p", ",", "pmin", ",", "pmax", ",", "\[CapitalDelta]p"}], "}"}]}], "]"}], "]"}]}]}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.445098179109*^9, 3.4450982721786003`*^9, {3.451279000619*^9, 3.4512790074518003`*^9}, {3.4512864298050003`*^9, 3.4512864368094*^9}, { 3.4706476335011683`*^9, 3.4706476477283683`*^9}, {3.4770540063998003`*^9, 3.4770540103154*^9}, {3.4818115795696*^9, 3.481811581816*^9}, { 3.4820252104592*^9, 3.4820252549035997`*^9}, {3.4820583880738*^9, 3.4820584077454*^9}, {3.4822351571716003`*^9, 3.4822351901188*^9}, { 3.4823004164308*^9, 3.4823004243712*^9}, {3.493344815723*^9, 3.4933448166745996`*^9}, {3.4933448517122*^9, 3.4933448763445997`*^9}, { 3.4933449778422003`*^9, 3.4933449867342*^9}, {3.4942053389948*^9, 3.4942053532688*^9}, {3.495099886848*^9, 3.4950998935959997`*^9}, { 3.495099958993*^9, 3.495099969426*^9}, 3.495100042671*^9, { 3.495100076422*^9, 3.495100110413*^9}, {3.49510016601*^9, 3.4951001814849997`*^9}, 3.4951002189040003`*^9, {3.495100255352*^9, 3.495100257927*^9}, {3.495100455098*^9, 3.4951004564449997`*^9}, { 3.495100515517*^9, 3.4951005243059998`*^9}, {3.495100586*^9, 3.4951006116359997`*^9}, {3.496055002618*^9, 3.496055006674*^9}, { 3.5007168179316*^9, 3.5007168299904003`*^9}, {3.557657331191841*^9, 3.5576573613778934`*^9}, {3.557658058371518*^9, 3.5576580893531723`*^9}, { 3.6204640425822525`*^9, 3.620464043896328*^9}, {3.629448441451354*^9, 3.6294484425113554`*^9}, {3.632027966812848*^9, 3.63202808169145*^9}, { 3.632028112439104*^9, 3.632028231997714*^9}, {3.632028264944972*^9, 3.632028286223409*^9}, 3.6320284618641176`*^9, 3.6320284928925724`*^9, { 3.6321887622237573`*^9, 3.6321887797107573`*^9}, {3.6321888300516367`*^9, 3.6321888552960806`*^9}, 3.6321889475563574`*^9, {3.63218903764051*^9, 3.6321890646730566`*^9}, {3.632189114899929*^9, 3.63218912051025*^9}, { 3.632189363344139*^9, 3.632189368985462*^9}, {3.65933624669765*^9, 3.6593362536240625`*^9}, {3.659336346288225*^9, 3.6593363466002254`*^9}, { 3.685234016837945*^9, 3.6852340690569315`*^9}, {3.6852341853385825`*^9, 3.6852342255038795`*^9}, {3.6852342700224257`*^9, 3.685234275388733*^9}, 3.685260724724876*^9, {3.685271245062879*^9, 3.685271273442919*^9}, { 3.685340120474733*^9, 3.6853401228547363`*^9}, {3.6873488134786153`*^9, 3.6873488145086164`*^9}, {3.687348848548664*^9, 3.6873488495686655`*^9}, { 3.6873489495588055`*^9, 3.687348976528844*^9}, {3.6873490107688913`*^9, 3.6873490208289056`*^9}, {3.6873490736689796`*^9, 3.6873490997690163`*^9}, {3.6873491395590715`*^9, 3.6873491721791177`*^9}, {3.6873493303593388`*^9, 3.687349336179347*^9}, { 3.687521139333435*^9, 3.687521232626771*^9}, {3.687526828204684*^9, 3.6875268662258587`*^9}, {3.687744603751021*^9, 3.687744621651046*^9}, { 3.687744782441271*^9, 3.687744793141286*^9}, {3.687744898361433*^9, 3.687744900871437*^9}, {3.687828873646782*^9, 3.6878288977768154`*^9}, { 3.6893872627070065`*^9, 3.6893872737370224`*^9}, {3.689388189828305*^9, 3.689388190108305*^9}, {3.6924132329925613`*^9, 3.692413234362563*^9}, { 3.6924133951727886`*^9, 3.6924134472928615`*^9}, {3.692413504072941*^9, 3.6924135542830114`*^9}, {3.6924138300453973`*^9, 3.692413892645485*^9}, { 3.6924150151235356`*^9, 3.692415019653542*^9}, {3.6924150955736485`*^9, 3.692415151833727*^9}, {3.6924152984639325`*^9, 3.692415397454071*^9}, { 3.6924155440942764`*^9, 3.6924155997043543`*^9}, {3.6924163099373484`*^9, 3.692416448987543*^9}, {3.6924164799875865`*^9, 3.692416520217643*^9}, { 3.6926047241829367`*^9, 3.6926047936630344`*^9}, {3.692694606764871*^9, 3.6926946080948734`*^9}, {3.6926946485549297`*^9, 3.6926946848649807`*^9}, {3.692694726505039*^9, 3.6926947795951133`*^9}, { 3.6926948533452168`*^9, 3.6926948903052683`*^9}, {3.692695016775445*^9, 3.6926950466854873`*^9}, {3.6926951047455683`*^9, 3.6926952014557037`*^9}, {3.692695400025982*^9, 3.6926954007959833`*^9}, { 3.692699088631146*^9, 3.6926990917611504`*^9}, {3.692699130701205*^9, 3.692699150701233*^9}, {3.6926992111213174`*^9, 3.692699243221362*^9}, { 3.692767928345048*^9, 3.6927679342250557`*^9}, {3.692768078185258*^9, 3.692768090845275*^9}, {3.692768583705965*^9, 3.6927686080859995`*^9}, { 3.692768652936062*^9, 3.6927686668160815`*^9}, {3.6927686975061245`*^9, 3.692768721766158*^9}, {3.6927687546262045`*^9, 3.692768807796279*^9}, { 3.6927688439663296`*^9, 3.692768846666333*^9}, {3.6927689511864796`*^9, 3.6927690097565613`*^9}, {3.692769047276614*^9, 3.6927692269968657`*^9}, { 3.692769260096912*^9, 3.6927692611369133`*^9}, {3.692769508057259*^9, 3.6927695324672937`*^9}, {3.692769570707347*^9, 3.692769719217555*^9}, { 3.6927698159576902`*^9, 3.6927698318077126`*^9}, 3.6927699552978854`*^9, { 3.6927701375081406`*^9, 3.6927701495781574`*^9}, {3.692772614961609*^9, 3.692772638701642*^9}, {3.692782982318822*^9, 3.6927829888081927`*^9}, { 3.6927830390960693`*^9, 3.692783045068411*^9}, {3.692783125046985*^9, 3.6927831273591175`*^9}, {3.692784897481363*^9, 3.6927849907176957`*^9}, 3.6927851596043553`*^9, {3.692786968327264*^9, 3.6927869691872644`*^9}, { 3.6927917561302457`*^9, 3.6927918079203186`*^9}, {3.6927918834304237`*^9, 3.692791893050438*^9}, 3.692791931280491*^9, {3.692791999660587*^9, 3.692792026840625*^9}, {3.6927921455307913`*^9, 3.6927921655908194`*^9}, { 3.692792200960869*^9, 3.692792228630907*^9}, {3.692792265330959*^9, 3.6927922938409986`*^9}, {3.6927923374910593`*^9, 3.6927923700511055`*^9}, {3.6927924565012264`*^9, 3.692792499271286*^9}, { 3.692792553391362*^9, 3.6927925860314074`*^9}, {3.692792731971612*^9, 3.6927927381216207`*^9}, {3.692792820381736*^9, 3.692792853021782*^9}, { 3.6927928932518377`*^9, 3.6927929516419196`*^9}, {3.6927929886919713`*^9, 3.6927930024219904`*^9}, {3.69279305234206*^9, 3.6927930715320873`*^9}, { 3.6927932237223005`*^9, 3.692793224982302*^9}, 3.6927932572523475`*^9, { 3.6927934421826067`*^9, 3.6927934498726172`*^9}, {3.692793484652666*^9, 3.6927935029226913`*^9}, {3.6927954180780883`*^9, 3.692795446828129*^9}, { 3.6928535571114936`*^9, 3.692853577521522*^9}, {3.692854825823887*^9, 3.692854837063903*^9}, {3.692854874433955*^9, 3.6928548775639596`*^9}, { 3.6928579822683063`*^9, 3.6928579955883245`*^9}, {3.6929656707917795`*^9, 3.692965795661954*^9}, {3.6929658426120195`*^9, 3.6929658536320353`*^9}, { 3.6929659138621197`*^9, 3.6929659218321304`*^9}, {3.692965990142226*^9, 3.6929660268822775`*^9}, {3.692966066362333*^9, 3.692966192182509*^9}, 3.69296637876277*^9, {3.6929669253235354`*^9, 3.692966936273551*^9}, { 3.6929669714336*^9, 3.692966971953601*^9}, 3.6929670139636593`*^9, 3.692967433554247*^9, {3.6929675634944286`*^9, 3.6929676911746073`*^9}, { 3.6929677832047367`*^9, 3.6929678068347692`*^9}, {3.6929678599332247`*^9, 3.6929678711132402`*^9}, 3.692967908543293*^9, {3.693017052482854*^9, 3.6930171392429757`*^9}, {3.6930174027243443`*^9, 3.6930175965956163`*^9}, {3.6930184697368383`*^9, 3.6930185654269724`*^9}, {3.6930186942971525`*^9, 3.6930188354373503`*^9}, {3.6930188926684303`*^9, 3.6930189600095253`*^9}, {3.693018990869568*^9, 3.693018991349569*^9}, { 3.693019036009631*^9, 3.693019041239639*^9}, {3.6930190980797186`*^9, 3.693019098629719*^9}, {3.693019130059763*^9, 3.6930192205398893`*^9}, { 3.693020315081422*^9, 3.693020326351438*^9}, {3.6930205415560236`*^9, 3.6930206058761134`*^9}, {3.6931381375028915`*^9, 3.693138137902892*^9}, { 3.693138677303647*^9, 3.693138683263655*^9}, {3.693139600730257*^9, 3.6931396288802967`*^9}, {3.6932135226775846`*^9, 3.6932135229775853`*^9}, {3.693219312471691*^9, 3.69321932632171*^9}, { 3.6932194762919197`*^9, 3.6932194879419365`*^9}, 3.6932195481520205`*^9, { 3.693220303405078*^9, 3.6932203178550987`*^9}, {3.693220688975618*^9, 3.693220698955632*^9}, {3.6933024593938713`*^9, 3.6933024657438803`*^9}, { 3.693302603694073*^9, 3.693302604214074*^9}, {3.6933103950923057`*^9, 3.693310399082311*^9}, {3.6933104528223867`*^9, 3.693310456172391*^9}, { 3.693380733755448*^9, 3.693380746175465*^9}, {3.6936247413492084`*^9, 3.6936247436692114`*^9}, {3.69362490643944*^9, 3.6936249099894447`*^9}, { 3.6937175435584445`*^9, 3.6937175579984646`*^9}, {3.693717708199675*^9, 3.6937177268707013`*^9}, {3.6937178194508305`*^9, 3.6937178401008596`*^9}, {3.693717934550992*^9, 3.6937179428310037`*^9}, { 3.6937180305511265`*^9, 3.693718060841169*^9}, {3.693718198801362*^9, 3.6937182028213673`*^9}, {3.693723123415037*^9, 3.6937231809651175`*^9}, { 3.693723252275217*^9, 3.69372327580525*^9}, {3.6937233347053328`*^9, 3.693723337655337*^9}, {3.693723689337829*^9, 3.6937237730079465`*^9}, { 3.6937240089782767`*^9, 3.6937240113382797`*^9}, {3.6938202843684807`*^9, 3.6938203172553616`*^9}, {3.6938203482121134`*^9, 3.6938203495041876`*^9}, 3.6938204448556414`*^9, {3.693826654370701*^9, 3.693826713082033*^9}, 3.6938269274112916`*^9, {3.69384095960849*^9, 3.6938409879385295`*^9}, { 3.6938967427518525`*^9, 3.6938967457718563`*^9}, {3.693896818211958*^9, 3.6938968234619656`*^9}, {3.6940917346582804`*^9, 3.6940917372882843`*^9}, {3.6949174720509205`*^9, 3.6949174781309295`*^9}, {3.69491751432098*^9, 3.6949175560810385`*^9}, { 3.697770949307855*^9, 3.697770962227873*^9}, {3.723799262336609*^9, 3.723799262645475*^9}, 3.7239435284061375`*^9, {3.7239436460810485`*^9, 3.72394364668592*^9}, {3.7254330838452635`*^9, 3.72543315169353*^9}, { 3.7254331912947936`*^9, 3.7254332075936446`*^9}, {3.725433705009429*^9, 3.7254337902858543`*^9}, {3.72543382083533*^9, 3.7254339260782228`*^9}, { 3.7254341992826924`*^9, 3.725434210286269*^9}, {3.7254342875818415`*^9, 3.7254342880778885`*^9}, {3.725443796293885*^9, 3.7254438161441803`*^9}, { 3.725756614481497*^9, 3.725756618125969*^9}, {3.7257914023599677`*^9, 3.7257914032179613`*^9}, {3.725791548301742*^9, 3.7257915491082635`*^9}, { 3.7257916547512665`*^9, 3.725791656837747*^9}, {3.725891883570933*^9, 3.7258919550235353`*^9}, {3.7258922912790194`*^9, 3.725892303666605*^9}, { 3.7258923638013153`*^9, 3.7258923917562647`*^9}, {3.732781849897335*^9, 3.732781851740935*^9}, {3.756128796258463*^9, 3.756128808101935*^9}, { 3.7561289636033297`*^9, 3.7561289674012337`*^9}, {3.7561291581496544`*^9, 3.756129161730915*^9}, {3.756168228209236*^9, 3.7561682921182303`*^9}, { 3.756168336119172*^9, 3.7561683422817945`*^9}, {3.7561687588268995`*^9, 3.756168760043317*^9}, {3.756168790608805*^9, 3.7561688096838417`*^9}, { 3.7562669791923923`*^9, 3.7562669871894484`*^9}, {3.7562671345571966`*^9, 3.7562671514185095`*^9}, {3.756267238618904*^9, 3.75626728245811*^9}, { 3.7562673231127896`*^9, 3.756267369934089*^9}, {3.7562679132987003`*^9, 3.7562679378330235`*^9}, {3.7562686403059607`*^9, 3.75626865150496*^9}, 3.756268910964476*^9, 3.756268975347582*^9, {3.756291635829771*^9, 3.756291670714565*^9}, {3.7562970292001624`*^9, 3.7562971110957913`*^9}, { 3.756354727514307*^9, 3.7563547516317015`*^9}, {3.756354849442463*^9, 3.7563548962495594`*^9}, {3.7563549974812*^9, 3.7563550014513693`*^9}, { 3.756355080997491*^9, 3.756355089151907*^9}, {3.7563551640676885`*^9, 3.756355171626652*^9}, {3.756355203033866*^9, 3.7563553257026477`*^9}, { 3.7563554337406178`*^9, 3.7563554593890176`*^9}, {3.756355541718184*^9, 3.756355546747837*^9}, {3.7563557326318254`*^9, 3.7563557465035677`*^9}, { 3.7563558550458755`*^9, 3.7563558609196053`*^9}, {3.756355910283166*^9, 3.75635593869836*^9}, {3.7563560087797346`*^9, 3.7563560102950015`*^9}, { 3.756797773170301*^9, 3.7567978192689314`*^9}, {3.756798047305444*^9, 3.7567980844374113`*^9}, {3.7567981179139524`*^9, 3.756798154780326*^9}, { 3.7568139377944374`*^9, 3.756813941735011*^9}, {3.7578171254549913`*^9, 3.7578171982352457`*^9}, {3.75781775424854*^9, 3.7578177761870728`*^9}, { 3.75781956271533*^9, 3.757819566308566*^9}, 3.7878930157969465`*^9, { 3.7878932625371447`*^9, 3.787893293562251*^9}, {3.789011658828579*^9, 3.789011685106179*^9}, {3.7890117693402524`*^9, 3.789011778591201*^9}, { 3.7890118169046745`*^9, 3.789011856496833*^9}, {3.789011916734619*^9, 3.7890119176130137`*^9}, {3.7890120044003463`*^9, 3.7890120790499506`*^9}, {3.7890170225675735`*^9, 3.7890170409915233`*^9}, {3.789137822804145*^9, 3.789137840140971*^9}, { 3.789138830369392*^9, 3.789138831966152*^9}, {3.7891389641705704`*^9, 3.7891389664011173`*^9}, {3.7891390002011633`*^9, 3.7891390083921847`*^9}, {3.7891390613275332`*^9, 3.789139181303717*^9}, { 3.7891788441595936`*^9, 3.7891788709933996`*^9}, {3.789197516887492*^9, 3.7891975292926593`*^9}, {3.789197640603428*^9, 3.7891976690423317`*^9}, { 3.7891980332343006`*^9, 3.789198036543322*^9}, {3.7894414019567575`*^9, 3.7894414188832755`*^9}, {3.7894415106536922`*^9, 3.7894415689767485`*^9}, {3.7894417279374404`*^9, 3.7894417609320536`*^9}, {3.7894418267668767`*^9, 3.789441867240697*^9}, { 3.7894419854165044`*^9, 3.7894419959085493`*^9}, {3.7894812275884027`*^9, 3.789481229196883*^9}, {3.789565208967163*^9, 3.789565222891079*^9}, { 3.7895652677339725`*^9, 3.789565310260277*^9}, {3.7897242364891343`*^9, 3.7897242407177544`*^9}, {3.8524287719473324`*^9, 3.852428794640484*^9}, { 3.852439296064255*^9, 3.8524393135928726`*^9}, {3.8524396227849884`*^9, 3.8524396273158197`*^9}, {3.8524399109547606`*^9, 3.8524399119152737`*^9}, {3.852441403168058*^9, 3.852441440998828*^9}, { 3.852955456548892*^9, 3.852955462666407*^9}, {3.852958622336733*^9, 3.852958622702162*^9}, {3.8530378998165426`*^9, 3.8530379193339243`*^9}, { 3.853037953502244*^9, 3.8530379856109133`*^9}, {3.85303807352728*^9, 3.853038096110407*^9}, {3.8530381808829203`*^9, 3.853038216537428*^9}}, CellLabel-> "In[237]:=",ExpressionUUID->"93f8f26c-cc52-4815-b9c5-8e8d29ab34ca"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"NONL", ",", "rule0_"}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", ",", "\[Delta]dof", ",", "equ", ",", "sol", ",", "\[Delta]WT"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WT", "=", RowBox[{"ParallelMap", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"NONL", ",", "rule0"}], "}"}], ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WT", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WT", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"D", "[", RowBox[{"\[Delta]WT", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"Solve", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"equ", "\[Equal]", "0"}], "]"}], ",", "dof"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"First", "[", "sol", "]"}], "]"}]}]}], "]"}]}], ";"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"NONL", ",", "rule0_", ",", "rule1_"}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", ",", "\[Delta]dof", ",", "equ", ",", "sol", ",", "\[Delta]WT"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WT", "=", RowBox[{"ParallelMap", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"NONL", ",", "rule0", ",", "rule1"}], "}"}], ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WT", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WT", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"D", "[", RowBox[{"\[Delta]WT", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"Solve", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"equ", "\[Equal]", "0"}], "]"}], ",", "dof"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"First", "[", "sol", "]"}], "]"}]}]}], "]"}]}], ";"}], " "}]}], "Input",ExpressionUUID->"8c0972a6-d0bf-4366-bd28-6830262bc5aa"] }, Closed]], Cell[CellGroupData[{ Cell["TMEC defs", "Subsection", CellChangeTimes->{{3.7582531074375505`*^9, 3.7582531288543863`*^9}, { 3.787892825419589*^9, 3.7878928340449758`*^9}, {3.822369175023527*^9, 3.8223691834150925`*^9}, {3.8223697280437837`*^9, 3.8223697285388823`*^9}},ExpressionUUID->"68b5c243-34c4-4245-a1bc-\ 2f082a71a9f7"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", ",", "\[Delta]dof", ",", "equ", ",", "sol", ",", "\[Delta]WT"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WT", "=", RowBox[{"ParallelMap", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"TMEC", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WT", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WT", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"D", "[", RowBox[{"\[Delta]WT", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"Solve", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"equ", "\[Equal]", "0"}], "]"}], ",", "dof"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"First", "[", "sol", "]"}], "]"}]}]}], "]"}]}], ";"}], " ", ";"}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.445098179109*^9, 3.4450982721786003`*^9, {3.451279000619*^9, 3.4512790074518003`*^9}, {3.4512864298050003`*^9, 3.4512864368094*^9}, { 3.4706476335011683`*^9, 3.4706476477283683`*^9}, {3.4770540063998003`*^9, 3.4770540103154*^9}, {3.4818115795696*^9, 3.481811581816*^9}, { 3.4820252104592*^9, 3.4820252549035997`*^9}, {3.4820583880738*^9, 3.4820584077454*^9}, {3.4822351571716003`*^9, 3.4822351901188*^9}, { 3.4823004164308*^9, 3.4823004243712*^9}, {3.493344815723*^9, 3.4933448166745996`*^9}, {3.4933448517122*^9, 3.4933448763445997`*^9}, { 3.4933449778422003`*^9, 3.4933449867342*^9}, {3.4942053389948*^9, 3.4942053532688*^9}, {3.495099886848*^9, 3.4950998935959997`*^9}, { 3.495099958993*^9, 3.495099969426*^9}, 3.495100042671*^9, { 3.495100076422*^9, 3.495100110413*^9}, {3.49510016601*^9, 3.4951001814849997`*^9}, 3.4951002189040003`*^9, {3.495100255352*^9, 3.495100257927*^9}, {3.495100455098*^9, 3.4951004564449997`*^9}, { 3.495100515517*^9, 3.4951005243059998`*^9}, {3.495100586*^9, 3.4951006116359997`*^9}, {3.496055002618*^9, 3.496055006674*^9}, { 3.5007168179316*^9, 3.5007168299904003`*^9}, {3.557657331191841*^9, 3.5576573613778934`*^9}, {3.557658058371518*^9, 3.5576580893531723`*^9}, { 3.6204640425822525`*^9, 3.620464043896328*^9}, {3.629448441451354*^9, 3.6294484425113554`*^9}, {3.632027966812848*^9, 3.63202808169145*^9}, { 3.632028112439104*^9, 3.632028231997714*^9}, {3.632028264944972*^9, 3.632028286223409*^9}, 3.6320284618641176`*^9, 3.6320284928925724`*^9, { 3.6321887622237573`*^9, 3.6321887797107573`*^9}, {3.6321888300516367`*^9, 3.6321888552960806`*^9}, 3.6321889475563574`*^9, {3.63218903764051*^9, 3.6321890646730566`*^9}, {3.632189114899929*^9, 3.63218912051025*^9}, { 3.632189363344139*^9, 3.632189368985462*^9}, {3.65933624669765*^9, 3.6593362536240625`*^9}, {3.659336346288225*^9, 3.6593363466002254`*^9}, { 3.685234016837945*^9, 3.6852340690569315`*^9}, {3.6852341853385825`*^9, 3.6852342255038795`*^9}, {3.6852342700224257`*^9, 3.685234275388733*^9}, 3.685260724724876*^9, {3.685271245062879*^9, 3.685271273442919*^9}, { 3.685340120474733*^9, 3.6853401228547363`*^9}, {3.6873488134786153`*^9, 3.6873488145086164`*^9}, {3.687348848548664*^9, 3.6873488495686655`*^9}, { 3.6873489495588055`*^9, 3.687348976528844*^9}, {3.6873490107688913`*^9, 3.6873490208289056`*^9}, {3.6873490736689796`*^9, 3.6873490997690163`*^9}, {3.6873491395590715`*^9, 3.6873491721791177`*^9}, {3.6873493303593388`*^9, 3.687349336179347*^9}, { 3.687521139333435*^9, 3.687521232626771*^9}, {3.687526828204684*^9, 3.6875268662258587`*^9}, {3.687744603751021*^9, 3.687744621651046*^9}, { 3.687744782441271*^9, 3.687744793141286*^9}, {3.687744898361433*^9, 3.687744900871437*^9}, {3.687828873646782*^9, 3.6878288977768154`*^9}, { 3.6893872627070065`*^9, 3.6893872737370224`*^9}, {3.689388189828305*^9, 3.689388190108305*^9}, {3.6924132329925613`*^9, 3.692413234362563*^9}, { 3.6924133951727886`*^9, 3.6924134472928615`*^9}, {3.692413504072941*^9, 3.6924135542830114`*^9}, {3.6924138300453973`*^9, 3.692413892645485*^9}, { 3.6924150151235356`*^9, 3.692415019653542*^9}, {3.6924150955736485`*^9, 3.692415151833727*^9}, {3.6924152984639325`*^9, 3.692415397454071*^9}, { 3.6924155440942764`*^9, 3.6924155997043543`*^9}, {3.6924163099373484`*^9, 3.692416448987543*^9}, {3.6924164799875865`*^9, 3.692416520217643*^9}, { 3.6926047241829367`*^9, 3.6926047936630344`*^9}, {3.692694606764871*^9, 3.6926946080948734`*^9}, {3.6926946485549297`*^9, 3.6926946848649807`*^9}, {3.692694726505039*^9, 3.6926947795951133`*^9}, { 3.6926948533452168`*^9, 3.6926948903052683`*^9}, {3.692695016775445*^9, 3.6926950466854873`*^9}, {3.6926951047455683`*^9, 3.6926952014557037`*^9}, {3.692695400025982*^9, 3.6926954007959833`*^9}, { 3.692699088631146*^9, 3.6926990917611504`*^9}, {3.692699130701205*^9, 3.692699150701233*^9}, {3.6926992111213174`*^9, 3.692699243221362*^9}, { 3.692767928345048*^9, 3.6927679342250557`*^9}, {3.692768078185258*^9, 3.692768090845275*^9}, {3.692768583705965*^9, 3.6927686080859995`*^9}, { 3.692768652936062*^9, 3.6927686668160815`*^9}, {3.6927686975061245`*^9, 3.692768721766158*^9}, {3.6927687546262045`*^9, 3.692768807796279*^9}, { 3.6927688439663296`*^9, 3.692768846666333*^9}, {3.6927689511864796`*^9, 3.6927690097565613`*^9}, {3.692769047276614*^9, 3.6927692269968657`*^9}, { 3.692769260096912*^9, 3.6927692611369133`*^9}, {3.692769508057259*^9, 3.6927695324672937`*^9}, {3.692769570707347*^9, 3.692769719217555*^9}, { 3.6927698159576902`*^9, 3.6927698318077126`*^9}, 3.6927699552978854`*^9, { 3.6927701375081406`*^9, 3.6927701495781574`*^9}, {3.692772614961609*^9, 3.692772638701642*^9}, {3.692782982318822*^9, 3.6927829888081927`*^9}, { 3.6927830390960693`*^9, 3.692783045068411*^9}, {3.692783125046985*^9, 3.6927831273591175`*^9}, {3.692784897481363*^9, 3.6927849907176957`*^9}, 3.6927851596043553`*^9, {3.692786968327264*^9, 3.6927869691872644`*^9}, { 3.6927917561302457`*^9, 3.6927918079203186`*^9}, {3.6927918834304237`*^9, 3.692791893050438*^9}, 3.692791931280491*^9, {3.692791999660587*^9, 3.692792026840625*^9}, {3.6927921455307913`*^9, 3.6927921655908194`*^9}, { 3.692792200960869*^9, 3.692792228630907*^9}, {3.692792265330959*^9, 3.6927922938409986`*^9}, {3.6927923374910593`*^9, 3.6927923700511055`*^9}, {3.6927924565012264`*^9, 3.692792499271286*^9}, { 3.692792553391362*^9, 3.6927925860314074`*^9}, {3.692792731971612*^9, 3.6927927381216207`*^9}, {3.692792820381736*^9, 3.692792853021782*^9}, { 3.6927928932518377`*^9, 3.6927929516419196`*^9}, {3.6927929886919713`*^9, 3.6927930024219904`*^9}, {3.69279305234206*^9, 3.6927930715320873`*^9}, { 3.6927932237223005`*^9, 3.692793224982302*^9}, 3.6927932572523475`*^9, { 3.6927934421826067`*^9, 3.6927934498726172`*^9}, {3.692793484652666*^9, 3.6927935029226913`*^9}, {3.6927954180780883`*^9, 3.692795446828129*^9}, { 3.6928535571114936`*^9, 3.692853577521522*^9}, {3.692854825823887*^9, 3.692854837063903*^9}, {3.692854874433955*^9, 3.6928548775639596`*^9}, { 3.6928579822683063`*^9, 3.6928579955883245`*^9}, {3.6929656707917795`*^9, 3.692965795661954*^9}, {3.6929658426120195`*^9, 3.6929658536320353`*^9}, { 3.6929659138621197`*^9, 3.6929659218321304`*^9}, {3.692965990142226*^9, 3.6929660268822775`*^9}, {3.692966066362333*^9, 3.692966192182509*^9}, 3.69296637876277*^9, {3.6929669253235354`*^9, 3.692966936273551*^9}, { 3.6929669714336*^9, 3.692966971953601*^9}, 3.6929670139636593`*^9, 3.692967433554247*^9, {3.6929675634944286`*^9, 3.6929676911746073`*^9}, { 3.6929677832047367`*^9, 3.6929678068347692`*^9}, {3.6929678599332247`*^9, 3.6929678711132402`*^9}, 3.692967908543293*^9, {3.693017052482854*^9, 3.6930171392429757`*^9}, {3.6930174027243443`*^9, 3.6930175965956163`*^9}, {3.6930184697368383`*^9, 3.6930185654269724`*^9}, {3.6930186942971525`*^9, 3.6930188354373503`*^9}, {3.6930188926684303`*^9, 3.6930189600095253`*^9}, {3.693018990869568*^9, 3.693018991349569*^9}, { 3.693019036009631*^9, 3.693019041239639*^9}, {3.6930190980797186`*^9, 3.693019098629719*^9}, {3.693019130059763*^9, 3.6930192205398893`*^9}, { 3.693020315081422*^9, 3.693020326351438*^9}, {3.6930205415560236`*^9, 3.6930206058761134`*^9}, {3.6931381375028915`*^9, 3.693138137902892*^9}, { 3.693138677303647*^9, 3.693138683263655*^9}, {3.693139600730257*^9, 3.6931396288802967`*^9}, {3.6932135226775846`*^9, 3.6932135229775853`*^9}, {3.693219312471691*^9, 3.69321932632171*^9}, { 3.6932194762919197`*^9, 3.6932194879419365`*^9}, 3.6932195481520205`*^9, { 3.693220303405078*^9, 3.6932203178550987`*^9}, {3.693220688975618*^9, 3.693220698955632*^9}, {3.6933024593938713`*^9, 3.6933024657438803`*^9}, { 3.693302603694073*^9, 3.693302604214074*^9}, {3.6933103950923057`*^9, 3.693310399082311*^9}, {3.6933104528223867`*^9, 3.693310456172391*^9}, { 3.693380733755448*^9, 3.693380746175465*^9}, {3.6936247413492084`*^9, 3.6936247436692114`*^9}, {3.69362490643944*^9, 3.6936249099894447`*^9}, { 3.6937175435584445`*^9, 3.6937175579984646`*^9}, {3.693717708199675*^9, 3.6937177268707013`*^9}, {3.6937178194508305`*^9, 3.6937178401008596`*^9}, {3.693717934550992*^9, 3.6937179428310037`*^9}, { 3.6937180305511265`*^9, 3.693718060841169*^9}, {3.693718198801362*^9, 3.6937182028213673`*^9}, {3.693723123415037*^9, 3.6937231809651175`*^9}, { 3.693723252275217*^9, 3.69372327580525*^9}, {3.6937233347053328`*^9, 3.693723337655337*^9}, {3.693723689337829*^9, 3.6937237730079465`*^9}, { 3.6937240089782767`*^9, 3.6937240113382797`*^9}, {3.6938202843684807`*^9, 3.6938203172553616`*^9}, {3.6938203482121134`*^9, 3.6938203495041876`*^9}, 3.6938204448556414`*^9, {3.693826654370701*^9, 3.693826713082033*^9}, 3.6938269274112916`*^9, {3.69384095960849*^9, 3.6938409879385295`*^9}, { 3.6938967427518525`*^9, 3.6938967457718563`*^9}, {3.693896818211958*^9, 3.6938968234619656`*^9}, {3.6940917346582804`*^9, 3.6940917372882843`*^9}, {3.6949174720509205`*^9, 3.6949174781309295`*^9}, {3.69491751432098*^9, 3.6949175560810385`*^9}, { 3.697770949307855*^9, 3.697770962227873*^9}, {3.723799262336609*^9, 3.723799262645475*^9}, 3.7239435284061375`*^9, {3.7239436460810485`*^9, 3.72394364668592*^9}, {3.7254330838452635`*^9, 3.72543315169353*^9}, { 3.7254331912947936`*^9, 3.7254332075936446`*^9}, {3.725433705009429*^9, 3.7254337902858543`*^9}, {3.72543382083533*^9, 3.7254339260782228`*^9}, { 3.7254341992826924`*^9, 3.725434210286269*^9}, {3.7254342875818415`*^9, 3.7254342880778885`*^9}, {3.725443796293885*^9, 3.7254438161441803`*^9}, { 3.725756614481497*^9, 3.725756618125969*^9}, {3.7257914023599677`*^9, 3.7257914032179613`*^9}, {3.725791548301742*^9, 3.7257915491082635`*^9}, { 3.7257916547512665`*^9, 3.725791656837747*^9}, {3.725891883570933*^9, 3.7258919550235353`*^9}, {3.7258922912790194`*^9, 3.725892303666605*^9}, { 3.7258923638013153`*^9, 3.7258923917562647`*^9}, {3.732781849897335*^9, 3.732781851740935*^9}, {3.756128796258463*^9, 3.756128808101935*^9}, { 3.7561289636033297`*^9, 3.7561289674012337`*^9}, {3.7561291581496544`*^9, 3.756129161730915*^9}, {3.756168228209236*^9, 3.7561682921182303`*^9}, { 3.756168336119172*^9, 3.7561683422817945`*^9}, {3.7561687588268995`*^9, 3.756168760043317*^9}, {3.756168790608805*^9, 3.7561688096838417`*^9}, { 3.7562669791923923`*^9, 3.7562669871894484`*^9}, {3.7562671345571966`*^9, 3.7562671514185095`*^9}, {3.756267238618904*^9, 3.75626728245811*^9}, { 3.7562673231127896`*^9, 3.756267369934089*^9}, {3.7562679132987003`*^9, 3.7562679378330235`*^9}, {3.7562686403059607`*^9, 3.75626865150496*^9}, 3.756268910964476*^9, 3.756268975347582*^9, {3.756291635829771*^9, 3.756291670714565*^9}, {3.7562970292001624`*^9, 3.7562971110957913`*^9}, { 3.756354727514307*^9, 3.7563547516317015`*^9}, {3.756354849442463*^9, 3.7563548962495594`*^9}, {3.7563549974812*^9, 3.7563550014513693`*^9}, { 3.756355080997491*^9, 3.756355089151907*^9}, {3.7563551640676885`*^9, 3.756355171626652*^9}, {3.756355203033866*^9, 3.7563553257026477`*^9}, { 3.7563554337406178`*^9, 3.7563554593890176`*^9}, {3.756355541718184*^9, 3.756355546747837*^9}, {3.7563557326318254`*^9, 3.7563557465035677`*^9}, { 3.7563558550458755`*^9, 3.7563558609196053`*^9}, {3.756355910283166*^9, 3.75635593869836*^9}, {3.7563560087797346`*^9, 3.7563560102950015`*^9}, { 3.756797773170301*^9, 3.7567978192689314`*^9}, {3.756798047305444*^9, 3.7567980844374113`*^9}, {3.7567981179139524`*^9, 3.756798154780326*^9}, { 3.7568139377944374`*^9, 3.756813941735011*^9}, {3.7578171254549913`*^9, 3.7578171982352457`*^9}, {3.75781775424854*^9, 3.7578177761870728`*^9}, { 3.75781956271533*^9, 3.757819566308566*^9}, 3.7878930157969465`*^9, 3.7878931876970196`*^9, {3.7890171909617825`*^9, 3.789017212740966*^9}, { 3.8152685002967186`*^9, 3.815268678285927*^9}, {3.815269201087903*^9, 3.815269223194291*^9}, {3.8223692003538074`*^9, 3.822369210700147*^9}, { 3.822369272776178*^9, 3.822369299587499*^9}, 3.8223697355995836`*^9, { 3.822370335148969*^9, 3.8223703474091916`*^9}}, CellLabel-> "In[246]:=",ExpressionUUID->"f9ea8ad7-d4e3-4408-a24d-b067e7bee725"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["PRE-POST", "Section", CellChangeTimes->{ 3.4430806364968*^9, {3.4453166713873997`*^9, 3.4453166747414*^9}, { 3.447462264275*^9, 3.4474622644154*^9}, {3.4695731321116*^9, 3.4695731359491997`*^9}, 3.473055186341*^9, {3.4730552472860003`*^9, 3.47305524884*^9}, {3.473055399782*^9, 3.473055419801*^9}, { 3.4734696760778*^9, 3.4734697047349997`*^9}, {3.4770537891542*^9, 3.4770537950354*^9}, {3.4932799754514*^9, 3.4932799779161997`*^9}, { 3.4945558951644*^9, 3.4945558957416*^9}, {3.4957646303032*^9, 3.4957646329084*^9}, {3.497581602118*^9, 3.4975816042552*^9}, { 3.500960505817*^9, 3.5009605094206*^9}, {3.556623836083009*^9, 3.5566238462386265`*^9}, {3.5568725055395393`*^9, 3.5568725163821597`*^9}, {3.556872678728445*^9, 3.5568726810485783`*^9}, { 3.7323376045620503`*^9, 3.7323376086812124`*^9}, {3.7335630623483887`*^9, 3.733563072583865*^9}, {3.733563159827469*^9, 3.7335631629996696`*^9}},ExpressionUUID->"af367fee-9121-44e2-ad23-\ 5df36af01ac8"], Cell[CellGroupData[{ Cell["LINK-TIE defs", "Subsection", CellChangeTimes->{{3.632187277028809*^9, 3.63218727949695*^9}, 3.632188602208605*^9, {3.632189487917265*^9, 3.6321894914104643`*^9}, { 3.68532054956944*^9, 3.6853205513594418`*^9}, {3.685326992341719*^9, 3.685326999819147*^9}, {3.685327113810607*^9, 3.685327116900611*^9}, { 3.76060719416889*^9, 3.760607206352191*^9}},ExpressionUUID->"25e4566d-0b26-45f6-becc-\ 777d07235552"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"LINK", "[", RowBox[{"{", RowBox[{"I1_Integer", ",", "I2_Integer"}], "}"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"DeleteCases", "[", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"{", RowBox[{ RowBox[{"Thread", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I2", ",", "3"}], "]"}], "]"}], "\[Rule]", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "3"}], "]"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Thread", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I2", ",", "2"}], "]"}], "]"}], "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "2"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "3"}], "]"}], "]"}], StyleBox["\[Cross]", "OperatorCharacter"], RowBox[{ StyleBox["(", "OperatorCharacter"], RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "1"}], "]"}], "]"}]}], ")"}]}]}], ")"}]}], "]"}]}], "}"}], "]"}], ",", RowBox[{"0", "\[Rule]", "0"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"rigid", " ", "link"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"LINK", "[", RowBox[{"lnk_", ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", " ", RowBox[{ RowBox[{"{", RowBox[{"funout", ",", "n1", ",", "n2"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"funout", " ", "=", "fun"}], ";", "\[IndentingNewLine]", RowBox[{"Do", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "=", RowBox[{"lnk", "[", RowBox[{"[", "i", "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", "n1", "]"}], "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], ",", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], StyleBox["\[Cross]", "OperatorCharacter"], RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}]}], ")"}]}]}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}]}], "}"}]}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", RowBox[{"Length", "[", "lnk", "]"}]}], "}"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", "funout", "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "one", " ", "node", " ", "tie", " ", "with", " ", "any", " ", "element"}], "*)"}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"could", " ", "be", " ", "generalized"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"TIE", "[", RowBox[{"n0_", ",", "nodes_", ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", " ", RowBox[{ RowBox[{"{", RowBox[{ "funout", ",", "n\[Xi]", ",", "n\[Eta]", ",", "\[Xi]", ",", "\[Eta]", ",", "NN", ",", "x", ",", "y", ",", "z", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"funout", " ", "=", "fun"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"n\[Xi]", ",", "n\[Eta]"}], "}"}], "=", RowBox[{"Dimensions", "[", "nodes", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n\[Xi]", ",", "\[Xi]"}], "}"}], ",", RowBox[{"{", RowBox[{"n\[Eta]", ",", "\[Eta]"}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"Flatten", "[", "nodes", "]"}], ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Xi]", ",", "\[Eta]"}], "}"}], "=", RowBox[{ RowBox[{"MinimalBy", "[", RowBox[{ RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"\[Xi]", ",", "\[Eta]", ",", " ", RowBox[{"Norm", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n0", ",", "1"}], "]"}], "]"}], "-", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Xi]", ",", "0", ",", "1", ",", RowBox[{"1", "/", "20"}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Eta]", ",", "0", ",", "1", ",", RowBox[{"1", "/", "20"}]}], "}"}]}], "]"}], ",", "1"}], "]"}], ",", "Last"}], "]"}], "[", RowBox[{"[", RowBox[{"1", ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"Flatten", "[", "nodes", "]"}], ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"Flatten", "[", "nodes", "]"}], ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", "n0", "]"}], "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n0", ",", "1"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", "funout", "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "one", " ", "node", " ", "tie", " ", "with", " ", "any", " ", "element"}], "*)"}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{"could", " ", "be", " ", "generalized", "\[IndentingNewLine]", RowBox[{"TIE", "[", RowBox[{"n0_", ",", "nodes_", ",", "fun_"}], "]"}]}], ":=", RowBox[{"Module", "[", " ", RowBox[{ RowBox[{"{", RowBox[{ "funout", ",", "n\[Xi]", ",", "n\[Eta]", ",", "\[Xi]", ",", "\[Eta]", ",", "NN", ",", "x", ",", "y", ",", "z", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"funout", " ", "=", "fun"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"n\[Xi]", ",", "n\[Eta]"}], "}"}], "=", RowBox[{"Dimensions", "[", "nodes", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n\[Xi]", ",", "\[Xi]"}], "}"}], ",", RowBox[{"{", RowBox[{"n\[Eta]", ",", "\[Eta]"}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"Flatten", "[", "nodes", "]"}], ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Xi]", ",", "\[Eta]"}], "}"}], "=", RowBox[{ RowBox[{"MinimalBy", "[", RowBox[{ RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"\[Xi]", ",", "\[Eta]", ",", " ", RowBox[{"Norm", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n0", ",", "1"}], "]"}], "]"}], "-", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Xi]", ",", "0", ",", "1", ",", RowBox[{"1", "/", "20"}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Eta]", ",", "0", ",", "1", ",", RowBox[{"1", "/", "20"}]}], "}"}]}], "]"}], ",", "1"}], "]"}], ",", "Last"}], "]"}], "[", RowBox[{"[", RowBox[{"1", ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"Flatten", "[", "nodes", "]"}], ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"Flatten", "[", "nodes", "]"}], ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", "n0", "]"}], "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n0", ",", "1"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", "funout", "]"}]}]}], "]"}]}], ";"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{ "one", " ", "node", " ", "tie", " ", "with", " ", "any", " ", "element", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"could", " ", "be", " ", "generalized"}], "*)"}], "\[IndentingNewLine]", RowBox[{"TIE", "[", RowBox[{"n0_", ",", "nodes_", ",", "fun_"}], "]"}]}], ":=", RowBox[{"Module", "[", " ", RowBox[{ RowBox[{"{", RowBox[{ "funout", ",", "n\[Xi]", ",", "n\[Eta]", ",", "\[Xi]", ",", "\[Eta]", ",", "NN", ",", "x", ",", "y", ",", "z", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"funout", " ", "=", "fun"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"n\[Xi]", ",", "n\[Eta]"}], "}"}], "=", RowBox[{"Dimensions", "[", "nodes", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n\[Xi]", ",", "\[Xi]"}], "}"}], ",", RowBox[{"{", RowBox[{"n\[Eta]", ",", "\[Eta]"}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"Flatten", "[", "nodes", "]"}], ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Xi]", ",", "\[Eta]"}], "}"}], "=", RowBox[{ RowBox[{"MinimalBy", "[", RowBox[{ RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"\[Xi]", ",", "\[Eta]", ",", " ", RowBox[{"Norm", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n0", ",", "1"}], "]"}], "]"}], "-", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Xi]", ",", "0", ",", "1", ",", RowBox[{"1", "/", "20"}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Eta]", ",", "0", ",", "1", ",", RowBox[{"1", "/", "20"}]}], "}"}]}], "]"}], ",", "1"}], "]"}], ",", "Last"}], "]"}], "[", RowBox[{"[", RowBox[{"1", ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"Flatten", "[", "nodes", "]"}], ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"Flatten", "[", "nodes", "]"}], ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", "n0", "]"}], "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n0", ",", "1"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", "funout", "]"}]}]}], "]"}]}], ";"}], "*)"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.496939383309*^9, 3.4969394213417997`*^9}, { 3.559961640310264*^9, 3.559961656783893*^9}, {3.5599617303692226`*^9, 3.5599617392300377`*^9}, {3.5601312763250604`*^9, 3.5601312794606657`*^9}, {3.5601313134219255`*^9, 3.560131324388745*^9}, { 3.560132497854006*^9, 3.5601324981348066`*^9}, {3.63023183959678*^9, 3.630231884758859*^9}, {3.630649684386073*^9, 3.630649712146661*^9}, { 3.630649747889705*^9, 3.6306497780604305`*^9}, {3.630649843969201*^9, 3.6306501496326838`*^9}, {3.6306501928641567`*^9, 3.630650252234552*^9}, { 3.630650308727783*^9, 3.6306503113519335`*^9}, {3.630650349614122*^9, 3.630650420974203*^9}, {3.630650474367257*^9, 3.630650601725542*^9}, { 3.630651184910898*^9, 3.630651194788463*^9}, {3.6306517131931143`*^9, 3.6306517167213163`*^9}, {3.6306573863011556`*^9, 3.6306574164092083`*^9}, {3.6306574511192694`*^9, 3.630657474862511*^9}, { 3.6306575678542747`*^9, 3.6306576670080485`*^9}, {3.6306577117645273`*^9, 3.6306579038944645`*^9}, {3.630658012221055*^9, 3.630658091874795*^9}, { 3.6306581291432605`*^9, 3.630658226440631*^9}, {3.63065827139991*^9, 3.6306582739115143`*^9}, 3.630658635254949*^9, {3.6306586682178073`*^9, 3.6306586813998303`*^9}, {3.6306590619156985`*^9, 3.630659069606512*^9}, { 3.6321872976489887`*^9, 3.6321873151349883`*^9}, 3.6321874056671667`*^9, { 3.632187463194457*^9, 3.6321878547998557`*^9}, {3.632187889913864*^9, 3.6321878942471123`*^9}, {3.632187976697828*^9, 3.632187979874009*^9}, { 3.6321886111201143`*^9, 3.63218861505834*^9}, {3.632188654528598*^9, 3.6321886640741434`*^9}, {3.632189320010661*^9, 3.632189331931343*^9}, { 3.6853206095995235`*^9, 3.685320631309554*^9}, {3.6853206843496284`*^9, 3.685320754049726*^9}, {3.685320792059779*^9, 3.685320823639823*^9}, { 3.685321020360099*^9, 3.6853211351402597`*^9}, {3.6853211801403227`*^9, 3.685321665981003*^9}, {3.6853216989010487`*^9, 3.6853217094910636`*^9}, { 3.6853217810511637`*^9, 3.6853220138814898`*^9}, {3.6853225388622246`*^9, 3.6853226020023127`*^9}, {3.6853270065604563`*^9, 3.685327020590476*^9}, { 3.685327067740542*^9, 3.6853271904307137`*^9}, {3.6853272344507756`*^9, 3.685327367150961*^9}, {3.685327539861203*^9, 3.685327565421239*^9}, { 3.6853276026012907`*^9, 3.685327613201306*^9}, 3.685327846481632*^9, { 3.7606071666879735`*^9, 3.760607186226157*^9}, {3.7606081322359104`*^9, 3.7606081444875402`*^9}, {3.7831752763351398`*^9, 3.783175293210803*^9}, { 3.783175332699009*^9, 3.783175341729051*^9}, {3.7888532050250206`*^9, 3.7888532418332033`*^9}}, CellLabel-> "In[247]:=",ExpressionUUID->"c7b010b8-6fe0-4bb5-9e12-73bc81e245cb"] }, Closed]], Cell[CellGroupData[{ Cell["TOOL defs", "Subsection",ExpressionUUID->"aed2bdbf-0063-4f44-a187-438df80d0c2c"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"EX", "[", RowBox[{"M_", ",", "K_", ",", "alist_", ",", "rule_", ",", "time_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "t0", ",", "A", ",", "fun", ",", "dfun", ",", "out", ",", "alist0", ",", "alist1", ",", "a0", ",", "a1"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"alist0", " ", "=", RowBox[{"(", RowBox[{"alist", " ", "/.", RowBox[{"{", " ", RowBox[{ RowBox[{"a", "[", "b_", "]"}], " ", "\[Rule]", " ", RowBox[{"a", "[", RowBox[{"b", ",", "0"}], "]"}]}], "}"}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"alist1", " ", "=", RowBox[{"(", RowBox[{"alist", " ", "/.", RowBox[{"{", " ", RowBox[{ RowBox[{"a", "[", "b_", "]"}], " ", "\[Rule]", " ", RowBox[{"a", "[", RowBox[{"b", ",", "1"}], "]"}]}], "}"}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"a0", " ", "=", RowBox[{"(", RowBox[{"alist0", " ", "/.", " ", "rule"}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"a1", " ", "=", RowBox[{"(", RowBox[{"alist1", " ", "/.", " ", "rule"}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"t0", " ", "=", " ", RowBox[{"First", "[", "time", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"A", " ", "=", " ", RowBox[{ RowBox[{"Inverse", "[", "M", "]"}], ".", "K"}]}], ";", "\[IndentingNewLine]", RowBox[{"fun", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{ RowBox[{"MATRIXFUN", "[", RowBox[{"A", ",", RowBox[{ RowBox[{"Cos", "[", RowBox[{ RowBox[{"Sqrt", "[", "#", "]"}], "*", RowBox[{"(", RowBox[{"t", "-", "t0"}], ")"}]}], "]"}], "&"}]}], "]"}], ".", "a0"}], "+", RowBox[{ RowBox[{"MATRIXFUN", "[", RowBox[{"A", ",", RowBox[{ RowBox[{ RowBox[{"Sin", "[", RowBox[{ RowBox[{"Sqrt", "[", "#", "]"}], "*", RowBox[{"(", RowBox[{"t", "-", "t0"}], ")"}]}], "]"}], "/", RowBox[{"Sqrt", "[", "#", "]"}]}], "&"}]}], "]"}], ".", "a1"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dfun", " ", "=", " ", RowBox[{"D", "[", RowBox[{"fun", ",", "t"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"out", " ", "=", " ", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"Join", "[", RowBox[{"fun", ",", "dfun"}], "]"}], " ", "/.", " ", RowBox[{"t", "->", "#"}]}], ")"}], "&"}], ",", "time"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"alist0", " ", "=", RowBox[{"(", RowBox[{"alist", " ", "/.", RowBox[{"{", " ", RowBox[{ RowBox[{"a", "[", "b_", "]"}], " ", "\[Rule]", " ", RowBox[{"a", "[", RowBox[{"b", ",", "0"}], "]"}]}], "}"}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"alist1", " ", "=", RowBox[{"(", RowBox[{"alist", " ", "/.", RowBox[{"{", " ", RowBox[{ RowBox[{"a", "[", "b_", "]"}], " ", "\[Rule]", " ", RowBox[{"a", "[", RowBox[{"b", ",", "1"}], "]"}]}], "}"}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"MAKERULE", "[", RowBox[{ RowBox[{"Join", "[", RowBox[{"alist0", ",", "alist1"}], "]"}], ",", "#"}], "]"}], "&"}], " ", ",", "out"}], "]"}]}]}], "]"}]}], ";"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"CR", "[", RowBox[{"M_", ",", "K_", ",", "alist_", ",", "rule_", ",", "time_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nn", ",", "\[CapitalDelta]t", ",", "A", ",", "II", ",", "AA", ",", "out", ",", "alist0", ",", "alist1", ",", "a0", ",", "a1"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"alist0", " ", "=", RowBox[{"(", RowBox[{"alist", " ", "/.", RowBox[{"{", " ", RowBox[{ RowBox[{"a", "[", "b_", "]"}], " ", "\[Rule]", " ", RowBox[{"a", "[", RowBox[{"b", ",", "0"}], "]"}]}], "}"}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"alist1", " ", "=", RowBox[{"(", RowBox[{"alist", " ", "/.", RowBox[{"{", " ", RowBox[{ RowBox[{"a", "[", "b_", "]"}], " ", "\[Rule]", " ", RowBox[{"a", "[", RowBox[{"b", ",", "1"}], "]"}]}], "}"}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"a0", " ", "=", RowBox[{"(", RowBox[{"alist0", " ", "/.", " ", "rule"}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"a1", " ", "=", RowBox[{"(", RowBox[{"alist1", " ", "/.", " ", "rule"}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"nn", " ", "=", RowBox[{ RowBox[{"Length", "[", "time", "]"}], "-", "1"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalDelta]t", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"Last", "[", "time", "]"}], "-", RowBox[{"First", "[", "time", "]"}]}], ")"}], "/", "nn"}]}], ";", "\[IndentingNewLine]", RowBox[{"A", " ", "=", " ", RowBox[{ RowBox[{"Inverse", "[", "M", "]"}], ".", "K"}]}], ";", "\[IndentingNewLine]", RowBox[{"II", " ", "=", " ", RowBox[{"IdentityMatrix", "[", RowBox[{"Length", "[", "a0", "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"AA", " ", "=", " ", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"ArrayFlatten", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"II", ",", RowBox[{ RowBox[{ RowBox[{"-", "II"}], "/", "2"}], "*", "\[CapitalDelta]t"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"A", "*", RowBox[{ RowBox[{"\[CapitalDelta]t", "^", "2"}], "/", "2"}]}], ",", RowBox[{"II", "*", "\[CapitalDelta]t"}]}], "}"}]}], "}"}], "]"}], "]"}], ".", RowBox[{"ArrayFlatten", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"II", ",", RowBox[{ RowBox[{"II", "/", "2"}], "*", "\[CapitalDelta]t"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "A"}], "*", RowBox[{ RowBox[{"\[CapitalDelta]t", "^", "2"}], "/", "2"}]}], ",", RowBox[{"II", "*", "\[CapitalDelta]t"}]}], "}"}]}], "}"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"out", " ", "=", RowBox[{"NestList", "[", RowBox[{ RowBox[{ RowBox[{"AA", ".", "#"}], "&"}], ",", RowBox[{"Flatten", "[", RowBox[{"{", RowBox[{"a0", ",", "a1"}], "}"}], "]"}], ",", "nn"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"MAKERULE", "[", RowBox[{ RowBox[{"Join", "[", RowBox[{"alist0", ",", "alist1"}], "]"}], ",", "#"}], "]"}], "&"}], " ", ",", "out"}], "]"}]}]}], "]"}]}], ";"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"DG", "[", RowBox[{"M_", ",", "K_", ",", "alist_", ",", "rule_", ",", "time_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nn", ",", "\[CapitalDelta]t", ",", "A", ",", "II", " ", ",", "AA", " ", ",", "out", ",", "alist0", ",", "alist1", ",", "a0", ",", "a1"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"alist0", " ", "=", RowBox[{"(", RowBox[{"alist", " ", "/.", RowBox[{"{", " ", RowBox[{ RowBox[{"a", "[", "b_", "]"}], " ", "\[Rule]", " ", RowBox[{"a", "[", RowBox[{"b", ",", "0"}], "]"}]}], "}"}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"alist1", " ", "=", RowBox[{"(", RowBox[{"alist", " ", "/.", RowBox[{"{", " ", RowBox[{ RowBox[{"a", "[", "b_", "]"}], " ", "\[Rule]", " ", RowBox[{"a", "[", RowBox[{"b", ",", "1"}], "]"}]}], "}"}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"a0", " ", "=", RowBox[{"(", RowBox[{"alist0", " ", "/.", " ", "rule"}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"a1", " ", "=", RowBox[{"(", RowBox[{"alist1", " ", "/.", " ", "rule"}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"nn", " ", "=", RowBox[{ RowBox[{"Length", "[", "time", "]"}], "-", "1"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalDelta]t", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"Last", "[", "time", "]"}], "-", RowBox[{"First", "[", "time", "]"}]}], ")"}], "/", "nn"}]}], ";", "\[IndentingNewLine]", RowBox[{"A", " ", "=", " ", RowBox[{ RowBox[{"Inverse", "[", "M", "]"}], ".", "K"}]}], ";", "\[IndentingNewLine]", RowBox[{"II", " ", "=", " ", RowBox[{"IdentityMatrix", "[", RowBox[{"Length", "[", "a0", "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"AA", " ", "=", " ", RowBox[{ RowBox[{"Inverse", "[", RowBox[{"ArrayFlatten", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"A", "*", RowBox[{"\[CapitalDelta]t", "^", "2"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"II", "-", RowBox[{"A", "*", RowBox[{ RowBox[{"\[CapitalDelta]t", "^", "2"}], "/", "2"}]}]}], ")"}], "*", "\[CapitalDelta]t"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "II"}], "-", RowBox[{"A", "*", RowBox[{ RowBox[{"\[CapitalDelta]t", "^", "2"}], "/", "2"}]}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"A", "*", RowBox[{ RowBox[{"\[CapitalDelta]t", "^", "2"}], "/", "3"}]}], ")"}], "*", "\[CapitalDelta]t"}]}], "}"}]}], "}"}], "]"}], "]"}], ".", RowBox[{"ArrayFlatten", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"0", "*", "II"}], ",", RowBox[{"II", "*", "\[CapitalDelta]t"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "II"}], ",", RowBox[{ RowBox[{"-", "II"}], "*", "\[CapitalDelta]t"}]}], "}"}]}], "}"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"out", " ", "=", RowBox[{"NestList", "[", RowBox[{ RowBox[{ RowBox[{"AA", ".", "#"}], "&"}], ",", RowBox[{"Flatten", "[", RowBox[{"{", RowBox[{"a0", ",", "a1"}], "}"}], "]"}], ",", "nn"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"MAKERULE", "[", RowBox[{ RowBox[{"Join", "[", RowBox[{"alist0", ",", "alist1"}], "]"}], ",", "#"}], "]"}], "&"}], " ", ",", "out"}], "]"}]}]}], "]"}]}], ";"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"NEWTON", "[", RowBox[{"equ_", ",", "var_", ",", "rule_", ",", RowBox[{"{", RowBox[{"\[CurlyEpsilon]_", ",", "m_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"Dequ", ",", "sol", ",", "dsol", ",", "K", ",", "F", ",", RowBox[{"ii", "=", "m"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"Dequ", "=", RowBox[{"Transpose", "[", RowBox[{"D", "[", RowBox[{"equ", ",", RowBox[{"{", "var", "}"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sol", " ", "=", RowBox[{"var", " ", "/.", " ", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", RowBox[{ RowBox[{"ii", ">", "0"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"K", "=", RowBox[{"Dequ", " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "->", "sol"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"F", "=", RowBox[{"equ", " ", "/.", RowBox[{"Thread", "[", RowBox[{"var", "->", "sol"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dsol", "=", RowBox[{"-", RowBox[{"LinearSolve", "[", RowBox[{"K", ",", "F"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", "dsol", "]"}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"sol", "+", "dsol"}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Norm", "[", "dsol", "]"}], "<", RowBox[{"\[CurlyEpsilon]", "*", RowBox[{"Norm", "[", "sol", "]"}]}]}], ",", RowBox[{"Break", "[", "]"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"ii", "=", RowBox[{"ii", "-", "1"}]}]}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"Thread", "[", RowBox[{"var", "->", "sol"}], "]"}]}]}], "]"}]}], ";"}], " "}]}], "Input", InitializationCell->True, CellChangeTimes->{{3.4941679835598*^9, 3.4941680104542*^9}, { 3.7258920393300085`*^9, 3.725892047236313*^9}, {3.7258921328118224`*^9, 3.725892185576483*^9}}, CellLabel-> "In[250]:=",ExpressionUUID->"9310e4cd-2b6b-41c8-8c04-6144ef4a2da3"] }, Closed]], Cell[CellGroupData[{ Cell["REFINE defs", "Subsection", CellChangeTimes->{{3.7555369693812027`*^9, 3.7555369706487265`*^9}},ExpressionUUID->"57ef130e-2ec6-4c2e-82c4-\ e3084f15fed5"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"left", " ", ":=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"a1_", ",", "a2_", ",", "a3_"}], "}"}], "->", RowBox[{"{", RowBox[{"a1", ",", " ", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"3", " ", "a1"}], "+", RowBox[{"6", " ", "a2"}], "-", "a3"}], ")"}], "/", "8"}], ",", "a2"}], "}"}]}], ",", RowBox[{ RowBox[{"{", RowBox[{"a1_", ",", "a2_"}], "}"}], "->", RowBox[{"{", RowBox[{"a1", ",", RowBox[{ RowBox[{"(", RowBox[{"a1", "+", "a2"}], ")"}], "/", "2"}]}], "}"}]}], ",", RowBox[{"a1_", "->", "a1"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"right", " ", ":=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"a1_", ",", "a2_", ",", "a3_"}], "}"}], "->", RowBox[{"{", RowBox[{"a2", ",", " ", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "a1"}], "+", RowBox[{"6", " ", "a2"}], "+", RowBox[{"3", " ", "a3"}]}], ")"}], "/", "8"}], ",", "a3"}], "}"}]}], ",", RowBox[{ RowBox[{"{", RowBox[{"a1_", ",", "a2_"}], "}"}], "->", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"a1", "+", "a2"}], ")"}], "/", "2"}], ",", "a2"}], "}"}]}], ",", RowBox[{"a1_", "->", "a1"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"RIGID", ",", "mat_", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"RIGID", ",", "mat", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n3", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"RIGID", ",", "mat", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n3", ",", "n2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"FORCE", ",", "mat_", ",", RowBox[{"Point", "[", RowBox[{"{", "a1_", "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{"{", RowBox[{"FORCE", ",", "mat", ",", RowBox[{"Point", "[", RowBox[{"{", "a1", "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"fX", " ", "/.", "left"}], ",", RowBox[{"fY", "/.", "left"}], ",", RowBox[{"fZ", "/.", "left"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n3", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"fX", " ", "/.", "right"}], ",", RowBox[{"fY", "/.", "right"}], ",", RowBox[{"fZ", "/.", "right"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n3", ",", "n2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", "AA_", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", " ", "/.", "left"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", "/.", "left"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n3", "=", RowBox[{"NEWNODE", "[", RowBox[{"BAR", ",", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", " ", "/.", "right"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", "/.", "right"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n3", ",", "n2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", "AA_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", " ", "/.", "left"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", "/.", "left"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"fX", "/.", "left"}], ",", RowBox[{"fY", "/.", "left"}], ",", RowBox[{"fZ", "/.", "left"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n3", "=", RowBox[{"NEWNODE", "[", RowBox[{"BAR", ",", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", " ", "/.", "right"}], "}"}], ",", RowBox[{"{", RowBox[{"AA", "/.", "right"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"fX", "/.", "right"}], ",", RowBox[{"fY", "/.", "right"}], ",", RowBox[{"fZ", "/.", "right"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n3", ",", "n2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "AA_", "}"}], ",", RowBox[{"{", "ff_", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EE", " ", "/.", "left"}], ",", RowBox[{"\[Rho]\[Rho]", "/.", "left"}]}], "}"}], ",", RowBox[{"{", RowBox[{"AA", "/.", "left"}], "}"}], ",", RowBox[{"{", RowBox[{"ff", "/.", "left"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n3", "=", RowBox[{"NEWNODE", "[", RowBox[{"BAR", ",", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EE", " ", "/.", "right"}], ",", RowBox[{"\[Rho]\[Rho]", "/.", "right"}]}], "}"}], ",", RowBox[{"{", RowBox[{"AA", "/.", "right"}], "}"}], ",", RowBox[{"{", RowBox[{"ff", "/.", "right"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n3", ",", "n2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "iy_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", " ", "/.", "left"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"AA", "/.", "left"}], ",", "iy"}], " ", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"fX", "/.", "left"}], ",", RowBox[{"fY", "/.", "left"}], ",", RowBox[{"fZ", "/.", "left"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n3", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", " ", "/.", "right"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"AA", "/.", "right"}], ",", "iy"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"fX", "/.", "right"}], ",", RowBox[{"fY", "/.", "right"}], ",", RowBox[{"fZ", "/.", "right"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n3", ",", "n2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Alpha]\[Alpha]_", ",", "kk_"}], "}"}], ",", RowBox[{"{", "AA_", "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "ss_", ",", "\[CurlyTheta]\[CurlyTheta]_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EE", " ", "/.", "left"}], ",", RowBox[{"\[Alpha]\[Alpha]", "/.", "left"}], ",", RowBox[{"kk", "/.", "left"}]}], " ", "}"}], ",", RowBox[{"{", RowBox[{"AA", "/.", "left"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"fx", "/.", "left"}], ",", RowBox[{"ss", "/.", "left"}], ",", RowBox[{"\[CurlyTheta]\[CurlyTheta]", "/.", "left"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n3", "=", RowBox[{"NEWNODET", "[", RowBox[{"BAR", ",", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EE", " ", "/.", "right"}], ",", RowBox[{"\[Alpha]\[Alpha]", "/.", "right"}], ",", RowBox[{"kk", "/.", "right"}]}], " ", "}"}], ",", RowBox[{"{", RowBox[{"AA", "/.", "right"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"fx", "/.", "right"}], ",", RowBox[{"ss", "/.", "right"}], ",", RowBox[{"\[CurlyTheta]\[CurlyTheta]", "/.", "right"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n3", ",", "n2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "GG_", "}"}], ",", RowBox[{"{", "JJ_", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"GG", "/.", "left"}], "}"}], ",", RowBox[{"{", RowBox[{"JJ", "/.", "left"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n3", "=", RowBox[{"NEWNODE", "[", RowBox[{"BAR", ",", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"GG", " ", "/.", "right"}], "}"}], ",", RowBox[{"{", RowBox[{"JJ", "/.", "right"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n3", ",", "n2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "GG_", "}"}], ",", RowBox[{"{", "JJ_", "}"}], ",", RowBox[{"{", RowBox[{"mX_", ",", "mY_", ",", "mZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"GG", "/.", "left"}], "}"}], ",", RowBox[{"{", RowBox[{"JJ", "/.", "left"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"mX", "/.", "left"}], ",", RowBox[{"mY", "/.", "left"}], ",", RowBox[{"mZ", "/.", "left"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n3", "=", RowBox[{"NEWNODE", "[", RowBox[{"BAR", ",", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"GG", " ", "/.", "right"}], "}"}], ",", RowBox[{"{", RowBox[{"JJ", "/.", "right"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"mX", "/.", "right"}], ",", RowBox[{"mY", "/.", "right"}], ",", RowBox[{"mZ", "/.", "right"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n3", ",", "n2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "JJ_", "}"}], ",", RowBox[{"{", "mm_", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"GG", " ", "/.", "left"}], ",", RowBox[{"\[Rho]\[Rho]", "/.", "left"}]}], "}"}], ",", RowBox[{"{", RowBox[{"JJ", "/.", "left"}], "}"}], ",", RowBox[{"{", RowBox[{"mm", "/.", "left"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n3", "=", RowBox[{"NEWNODE", "[", RowBox[{"BAR", ",", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"GG", " ", "/.", "right"}], ",", RowBox[{"\[Rho]\[Rho]", "/.", "right"}]}], "}"}], ",", RowBox[{"{", RowBox[{"JJ", "/.", "right"}], "}"}], ",", RowBox[{"{", RowBox[{"mm", "/.", "right"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n3", ",", "n2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", "\[Kappa]0_"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", RowBox[{"Ln_", ",", "Lb_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", "\[Kappa]0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE", "}"}], ",", RowBox[{"{", RowBox[{"Ln", " ", ",", "Lb"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n3", "=", RowBox[{"NEWNODE", "[", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", "\[Kappa]0"}], "}"}], ",", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", "\[Kappa]0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE", "}"}], ",", RowBox[{"{", RowBox[{"Ln", ",", "Lb"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n3", ",", "n2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"BEAM", ",", "pro_", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", "pro", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n3", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", "pro", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n3", ",", "n2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EE", " ", "/.", "left"}], ",", RowBox[{"GG", " ", "/.", "left"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"AA", " ", "/.", "left"}], ",", RowBox[{"Iyy", " ", "/.", "left"}], ",", RowBox[{"Izz", " ", "/.", "left"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"fx", " ", "/.", "left"}], ",", RowBox[{"fy", " ", "/.", "left"}], ",", RowBox[{"fz", " ", "/.", "left"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n3", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EE", " ", "/.", "right"}], ",", RowBox[{"GG", " ", "/.", "right"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"AA", " ", "/.", "right"}], ",", RowBox[{"Iyy", " ", "/.", "right"}], ",", RowBox[{"Izz", " ", "/.", "right"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"fx", " ", "/.", "right"}], ",", RowBox[{"fy", " ", "/.", "right"}], ",", RowBox[{"fz", " ", "/.", "right"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n3", ",", "n2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_", ",", "Ip_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EE", " ", "/.", "left"}], ",", RowBox[{"GG", " ", "/.", "left"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"AA", " ", "/.", "left"}], ",", RowBox[{"Iyy", " ", "/.", "left"}], ",", RowBox[{"Izz", " ", "/.", "left"}], ",", "Ip"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"fx", " ", "/.", "left"}], ",", RowBox[{"fy", " ", "/.", "left"}], ",", RowBox[{"fz", " ", "/.", "left"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n3", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EE", " ", "/.", "right"}], ",", RowBox[{"GG", " ", "/.", "right"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"AA", " ", "/.", "right"}], ",", RowBox[{"Iyy", " ", "/.", "right"}], ",", RowBox[{"Izz", " ", "/.", "right"}], ",", "Ip"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"fx", " ", "/.", "right"}], ",", RowBox[{"fy", " ", "/.", "right"}], ",", RowBox[{"fz", " ", "/.", "right"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n3", ",", "n2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EE", " ", "/.", "left"}], ",", RowBox[{"GG", " ", "/.", "left"}], ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"AA", " ", "/.", "left"}], ",", RowBox[{"Iyy", " ", "/.", "left"}], ",", RowBox[{"Izz", " ", "/.", "left"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"fx", " ", "/.", "left"}], ",", RowBox[{"fy", " ", "/.", "left"}], ",", RowBox[{"fz", " ", "/.", "left"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n3", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EE", " ", "/.", "right"}], ",", RowBox[{"GG", " ", "/.", "right"}], ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"AA", " ", "/.", "right"}], ",", RowBox[{"Iyy", " ", "/.", "right"}], ",", RowBox[{"Izz", " ", "/.", "right"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"fx", " ", "/.", "right"}], ",", RowBox[{"fy", " ", "/.", "right"}], ",", RowBox[{"fz", " ", "/.", "right"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n3", ",", "n2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_", ",", "Ip_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EE", " ", "/.", "left"}], ",", RowBox[{"GG", " ", "/.", "left"}], ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"AA", " ", "/.", "left"}], ",", RowBox[{"Iyy", " ", "/.", "left"}], ",", RowBox[{"Izz", " ", "/.", "left"}], ",", "Ip"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"fx", " ", "/.", "left"}], ",", RowBox[{"fy", " ", "/.", "left"}], ",", RowBox[{"fz", " ", "/.", "left"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n3", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EE", " ", "/.", "right"}], ",", RowBox[{"GG", " ", "/.", "right"}], ",", "\[Rho]\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"AA", " ", "/.", "right"}], ",", RowBox[{"Iyy", " ", "/.", "right"}], ",", RowBox[{"Izz", " ", "/.", "right"}], ",", "Ip"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"fx", " ", "/.", "right"}], ",", RowBox[{"fy", " ", "/.", "right"}], ",", RowBox[{"fz", " ", "/.", "right"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n3", ",", "n2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"TWODIM", ",", "mat_", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"TWODIM", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n4", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"TWODIM", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n4", ",", "n2", ",", RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"TWODIM", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n6", ",", "n5", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"TWODIM", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n4", ",", "n5", ",", "n6"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"PLANE", ",", "mat_", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n4", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n4", ",", "n2", ",", RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n6", ",", "n5", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n4", ",", "n5", ",", "n6"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"PLANE", ",", "mat_", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n4", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n4", ",", "n2", ",", RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n6", ",", "n5", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n4", ",", "n5", ",", "n6"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"SOLID1", ",", "mat_", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"SOLID1", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n4", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID1", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n4", ",", "n2", ",", RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID1", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n6", ",", "n5", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID1", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n4", ",", "n5", ",", "n6"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"SOLID2", ",", "mat_", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"SOLID2", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n4", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID2", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n4", ",", "n2", ",", RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID2", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n6", ",", "n5", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID2", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n4", ",", "n5", ",", "n6"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"EMS", ",", "mat_", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"EMS", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n8", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n3"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n9", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"EMS", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n5", ",", "n2", ",", "n9", ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n4"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"EMS", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n8", ",", "n9", ",", "n3", ",", RowBox[{"n7", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n4"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"EMS", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n9", ",", "n6", ",", "n7", ",", "n4"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"PLANE", ",", "mat_", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"n9", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n8", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n4"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n5", ",", "n2", ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}], ",", "n9"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n8", ",", "n9", ",", RowBox[{"n7", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n4"}], "}"}], "]"}], "]"}]}], ",", "n4"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n9", ",", "n6", ",", "n3", ",", "n7"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"PLATE", ",", "mat_", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLATE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n4", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n4", ",", "n2", ",", RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n6", ",", "n5", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n4", ",", "n5", ",", "n6"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"PLATE", ",", "mat_", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLATE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n9", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n8", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n4"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n5", ",", "n2", ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}], ",", "n9"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n8", ",", "n9", ",", RowBox[{"n7", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n4"}], "}"}], "]"}], "]"}]}], ",", "n4"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n9", ",", "n6", ",", "n3", ",", "n7"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"PLATE", ",", "mat_", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], ",", RowBox[{"{", RowBox[{"n3_", ",", "n4_"}], "}"}]}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLATE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"n8", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n3"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n9", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}], "]"}]}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n5", ",", "n2"}], "}"}], ",", RowBox[{"{", RowBox[{"n9", ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n4"}], "}"}], "]"}], "]"}]}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n8", ",", "n9"}], "}"}], ",", RowBox[{"{", RowBox[{"n3", ",", RowBox[{"n7", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n4"}], "}"}], "]"}], "]"}]}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n9", ",", "n6"}], "}"}], ",", RowBox[{"{", RowBox[{"n7", ",", "n4"}], "}"}]}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"SHELL", ",", "mat_", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"SHELL", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n4", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SHELL", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n4", ",", "n2", ",", RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SHELL", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n6", ",", "n5", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SHELL", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n4", ",", "n5", ",", "n6"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"SOLID", ",", "mat_", ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"SOLID", ",", "mat", ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{ RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n8", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n4"}], "}"}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"n7", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n3"}], "}"}], "]"}], "]"}]}], ",", "n1"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID", ",", "mat", ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n5", ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"n9", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n4"}], "}"}], "]"}], "]"}]}], ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID", ",", "mat", ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n8", ",", "n9", ",", RowBox[{"n10", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n4"}], "}"}], "]"}], "]"}]}], ",", "n4"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID", ",", "mat", ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n7", ",", "n10", ",", "n6", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID", ",", "mat", ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n8", ",", "n6", ",", "n10", ",", "n9"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID", ",", "mat", ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n8", ",", "n6", ",", "n5", ",", "n9"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID", ",", "mat", ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n8", ",", "n6", ",", "n10", ",", "n7"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID", ",", "mat", ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n8", ",", "n6", ",", "n5", ",", "n7"}], "}"}], "]"}]}], "}"}]}], "\[IndentingNewLine]", " ", "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"SOLID", ",", "mat_", ",", RowBox[{"Hexahedron", "[", RowBox[{"{", RowBox[{ "n1_", ",", "n2_", ",", "n3_", ",", "n4_", ",", "n5_", ",", "n6_", ",", "n7_", ",", "n8_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"SOLID", ",", "mat", ",", RowBox[{"Hexahedron", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n9", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"n13", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n12", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n4"}], "}"}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"n14", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n5"}], "}"}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"n18", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n6", ",", "n5"}], "}"}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"n22", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{ "n1", ",", "n2", ",", "n3", ",", "n4", ",", "n5", ",", "n6", ",", "n7", ",", "n8"}], "}"}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"n21", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n4", ",", "n5", ",", "n8"}], "}"}], "]"}], "]"}]}]}], " ", "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID", ",", "mat", ",", RowBox[{"Hexahedron", "[", RowBox[{"{", RowBox[{"n9", ",", "n2", ",", "\[IndentingNewLine]", RowBox[{"n10", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}], ",", "n13", ",", "n18", ",", "\[IndentingNewLine]", RowBox[{"n15", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n6"}], "}"}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"n19", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3", ",", "n7", ",", "n6"}], "}"}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", "n22"}], " ", "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID", ",", "mat", ",", RowBox[{"Hexahedron", "[", RowBox[{"{", RowBox[{"n13", ",", "n10", ",", "n3", ",", "\[IndentingNewLine]", RowBox[{"n11", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n4"}], "}"}], "]"}], "]"}]}], ",", "n22", ",", "n19", ",", "\[IndentingNewLine]", RowBox[{"n16", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n7"}], "}"}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"n20", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n4", ",", "n3", ",", "n7", ",", "n8"}], "}"}], "]"}], "]"}]}]}], " ", "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID", ",", "mat", ",", RowBox[{"Hexahedron", "[", RowBox[{"{", RowBox[{ "n12", ",", "n13", ",", "n11", ",", "n4", ",", "\[IndentingNewLine]", "n21", ",", "n22", ",", "n20", ",", "\[IndentingNewLine]", RowBox[{"n17", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n4", ",", "n8"}], "}"}], "]"}], "]"}]}]}], " ", "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID", ",", "mat", ",", RowBox[{"Hexahedron", "[", RowBox[{"{", RowBox[{ "n14", ",", "n18", ",", "n22", ",", "n21", ",", "n5", ",", "\[IndentingNewLine]", RowBox[{"n23", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n6", ",", "n5"}], "}"}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"n27", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n5", ",", "n6", ",", "n7", ",", "n8"}], "}"}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"n26", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n5", ",", "n8"}], "}"}], "]"}], "]"}]}]}], " ", "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID", ",", "mat", ",", RowBox[{"Hexahedron", "[", RowBox[{"{", RowBox[{ "n18", ",", "n15", ",", "n19", ",", "n22", ",", "n23", ",", "n6", ",", "\[IndentingNewLine]", RowBox[{"n24", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n6", ",", "n7"}], "}"}], "]"}], "]"}]}], ",", "n27"}], " ", "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID", ",", "mat", ",", RowBox[{"Hexahedron", "[", RowBox[{"{", RowBox[{ "n22", ",", "n19", ",", "n16", ",", "n20", ",", "n27", ",", "n24", ",", "n7", ",", "\[IndentingNewLine]", RowBox[{"n25", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n7", ",", "n8"}], "}"}], "]"}], "]"}]}]}], " ", "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID", ",", "mat", ",", RowBox[{"Hexahedron", "[", RowBox[{"{", RowBox[{ "n21", ",", "n22", ",", "n20", ",", "n17", ",", "n26", ",", "n27", ",", "n25", ",", "\[IndentingNewLine]", "n8"}], " ", "}"}], "]"}]}], "}"}]}], "\[IndentingNewLine]", " ", "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"if", " ", "nothing", " ", "applies"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"typ_", ",", "mat_", ",", "nod_"}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{"{", RowBox[{"typ", ",", "mat", ",", "nod"}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REFINE", "[", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"funout", "=", "fun"}], ",", RowBox[{"eleout", "=", "ele"}], ",", "ii", ",", "rule", ",", "a1", ",", "a2", ",", "a3", ",", "a4", ",", "a5", ",", "a6", ",", "left", ",", "right"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "refinement", " ", "inherits", " ", "conditions", " ", "and", " ", "has", " ", "memory"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ii", " ", "=", RowBox[{ RowBox[{"Length", "[", "funout", "]"}], "+", "1"}]}], ";", "\[IndentingNewLine]", RowBox[{"Clear", "[", RowBox[{"NEWNODE", ",", "NEWNODET"}], "]"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"NEWNODET", "[", RowBox[{"{", RowBox[{"a1_", ",", "a2_"}], "}"}], "]"}], ":=", RowBox[{ RowBox[{"NEWNODET", "[", RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], "]"}], "=", RowBox[{"CompoundExpression", "[", RowBox[{ RowBox[{"funout", "=", RowBox[{"Join", "[", RowBox[{"funout", ",", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a2", ",", "1"}], "]"}], "]"}]}], ")"}], "/", "2"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"uX", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"uY", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", "ii", "]"}]}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]X", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Z", "[", "ii", "]"}]}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", " ", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "4"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[CurlyTheta]", "[", "ii", "]"}]}], "]"}]}], "}"}], "}"}]}], "]"}]}], ";", RowBox[{"ii", "++"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"a1_", ",", "a2_"}], "}"}], "]"}], ":=", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], "]"}], "=", RowBox[{"CompoundExpression", "[", RowBox[{ RowBox[{"funout", "=", RowBox[{"Join", "[", RowBox[{"funout", ",", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a2", ",", "1"}], "]"}], "]"}]}], ")"}], "/", "2"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"uX", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"uY", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", "ii", "]"}]}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]X", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Z", "[", "ii", "]"}]}], "]"}]}], "}"}]}], "}"}], "}"}]}], "]"}]}], ";", RowBox[{"ii", "++"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"offset", "[", RowBox[{"\[Kappa]_", ",", "n1_", ",", "n2_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"r12", ",", "L"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"\[Kappa]", "\[Equal]", "0"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"r12", "=", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"L", "=", RowBox[{"Sqrt", "[", RowBox[{"r12", ".", "r12"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}], StyleBox["\[Cross]", "OperatorCharacter"], "r12"}]}], "/", "L"}], "*", RowBox[{"(", RowBox[{ RowBox[{"1.", "/", "\[Kappa]"}], "-", RowBox[{"Sqrt", "[", RowBox[{ RowBox[{"1.", "/", RowBox[{"\[Kappa]", "^", "2"}]}], "-", RowBox[{ RowBox[{"L", "^", "2"}], "/", "4"}]}], "]"}]}], ")"}]}]}]}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", "\[Kappa]_"}], "}"}], ",", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}]}], "]"}], ":=", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", "\[Kappa]"}], "}"}], ",", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}]}], "]"}], "=", RowBox[{"CompoundExpression", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"funout", "=", RowBox[{"Join", "[", RowBox[{"funout", ",", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}]}], ")"}], "/", "2"}], "+", RowBox[{"offset", "[", RowBox[{"\[Kappa]", ",", "n1", ",", "n2"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"uX", "[", RowBox[{"ii", ",", "0"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"uY", "[", RowBox[{"ii", ",", "0"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"ii", ",", "0"}], "]"}]}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"uX", "[", RowBox[{"ii", ",", "1"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"uY", "[", RowBox[{"ii", ",", "1"}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "3", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", "3", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", RowBox[{"ii", ",", "1"}], "]"}]}], "]"}]}], "}"}]}], " ", "}"}], "}"}]}], "]"}]}], ";", RowBox[{"ii", "++"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"a1_", ",", "a2_", ",", "a3_", ",", "a4_"}], "}"}], "]"}], ":=", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3", ",", "a4"}], "}"}], "]"}], "=", RowBox[{"CompoundExpression", "[", RowBox[{ RowBox[{"funout", "=", RowBox[{"Join", "[", RowBox[{"funout", ",", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a2", ",", "1"}], "]"}], "]"}], "+", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a3", ",", "1"}], "]"}], "]"}], "+", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a4", ",", "1"}], "]"}], "]"}]}], ")"}], "/", "4"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3", ",", "a4"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3", ",", "a4"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"uX", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3", ",", "a4"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3", ",", "a4"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"uY", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3", ",", "a4"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3", ",", "a4"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", "ii", "]"}]}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3", ",", "a4"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3", ",", "a4"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]X", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3", ",", "a4"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3", ",", "a4"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3", ",", "a4"}], "}"}], ",", "3", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2", ",", "a3", ",", "a4"}], "}"}], ",", "3", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Z", "[", "ii", "]"}]}], "]"}]}], "}"}]}], " ", " ", "}"}], "}"}]}], "]"}]}], ";", RowBox[{"ii", "++"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{ "a1_", ",", "a2_", ",", "a3_", ",", "a4_", ",", "a5_", ",", "a6_", ",", "a7_", ",", "a8_"}], "}"}], "]"}], ":=", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{ "a1", ",", "a2", ",", "a3", ",", "a4", ",", "a5", ",", "a6", ",", "a7", ",", "a8"}], "}"}], "]"}], "=", RowBox[{"CompoundExpression", "[", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{ "a1", ",", "a2", ",", "a3", ",", "a4", ",", "a5", ",", "a6", ",", "a7", ",", "a8"}], "}"}]}], ";", RowBox[{"funout", "=", RowBox[{"Join", "[", RowBox[{"funout", ",", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"uX", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"uY", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"nl", ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", "ii", "]"}]}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]X", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"nl", ",", "3", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Z", "[", "ii", "]"}]}], "]"}]}], "}"}]}], " ", " ", "}"}], "}"}]}], "]"}]}], ";", RowBox[{"ii", "++"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{"a1_", ",", "a2_"}], "}"}]}], "]"}], ":=", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"a2", ",", "a1"}], "}"}], "]"}], "=", RowBox[{"CompoundExpression", "[", RowBox[{ RowBox[{"funout", "=", RowBox[{"Join", "[", RowBox[{"funout", ",", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a2", ",", "1"}], "]"}], "]"}]}], ")"}], "/", "2"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"ux", "[", "ii", "]"}], "*", RowBox[{"Simplify", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a1", ",", "1"}], "]"}], "]"}]}], ")"}], "/", "\[IndentingNewLine]", RowBox[{"Sqrt", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a1", ",", "1"}], "]"}], "]"}]}], ")"}], ".", RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a1", ",", "1"}], "]"}], "]"}]}], ")"}]}], "]"}]}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], "}"}]}], "]"}]}], ";", RowBox[{"ii", "++"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"NEWNODET", "[", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{"a1_", ",", "a2_"}], "}"}]}], "]"}], ":=", RowBox[{ RowBox[{"NEWNODET", "[", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{"a2", ",", "a1"}], "}"}]}], "]"}], "=", RowBox[{"CompoundExpression", "[", RowBox[{ RowBox[{"funout", "=", RowBox[{"Join", "[", RowBox[{"funout", ",", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a2", ",", "1"}], "]"}], "]"}]}], ")"}], "/", "2"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"ux", "[", "ii", "]"}], "*", RowBox[{"Simplify", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a1", ",", "1"}], "]"}], "]"}]}], ")"}], "/", "\[IndentingNewLine]", RowBox[{"Sqrt", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a1", ",", "1"}], "]"}], "]"}]}], ")"}], ".", RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a1", ",", "1"}], "]"}], "]"}]}], ")"}]}], "]"}]}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", " ", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "4"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[CurlyTheta]", "[", "ii", "]"}]}], "]"}]}], "}"}], "}"}]}], "]"}]}], ";", RowBox[{"ii", "++"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"DO", " ", "IT"}], "*)"}], "\[IndentingNewLine]", RowBox[{"eleout", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"REF", "[", "#", "]"}], "&"}], ",", "eleout"}], "]"}], ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{"eleout", ",", "funout"}], "}"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REFINE", "[", RowBox[{"{", RowBox[{"ele_", ",", "fun_", ",", "lnk_"}], "}"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"funout", "=", "fun"}], ",", RowBox[{"eleout", "=", "ele"}], ",", RowBox[{"lnkout", "=", "lnk"}], ",", "ii", ",", "rule", ",", "a1", ",", "a2", ",", "a3", ",", "a4", ",", "a5", ",", "a6", ",", "left", ",", "right"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "refinement", " ", "inherits", " ", "conditions", " ", "and", " ", "has", " ", "memory"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ii", " ", "=", RowBox[{ RowBox[{"Length", "[", "funout", "]"}], "+", "1"}]}], ";", "\[IndentingNewLine]", RowBox[{"Clear", "[", "NEWNODE", "]"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"a1_", ",", "a2_"}], "}"}], "]"}], ":=", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], "]"}], "=", RowBox[{"CompoundExpression", "[", RowBox[{ RowBox[{"funout", "=", RowBox[{"Join", "[", RowBox[{"funout", ",", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a2", ",", "1"}], "]"}], "]"}]}], ")"}], "/", "2"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"uX", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"uY", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", "ii", "]"}]}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]X", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Z", "[", "ii", "]"}]}], "]"}]}], "}"}]}], "}"}], "}"}]}], "]"}]}], ";", RowBox[{"ii", "++"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{"a1_", ",", "a2_"}], "}"}]}], "]"}], ":=", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"a2", ",", "a1"}], "}"}], "]"}], "=", RowBox[{"CompoundExpression", "[", RowBox[{ RowBox[{"funout", "=", RowBox[{"Join", "[", RowBox[{"funout", ",", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a2", ",", "1"}], "]"}], "]"}]}], ")"}], "/", "2"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"ux", "[", "ii", "]"}], "*", RowBox[{"Simplify", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a1", ",", "1"}], "]"}], "]"}]}], ")"}], "/", "\[IndentingNewLine]", RowBox[{"Sqrt", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a1", ",", "1"}], "]"}], "]"}]}], ")"}], ".", RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a1", ",", "1"}], "]"}], "]"}]}], ")"}]}], "]"}]}], ",", RowBox[{"L", ">", "0"}]}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], "}"}]}], "]"}]}], ";", RowBox[{"ii", "++"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"driven", " ", "by", " ", "this"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"rule", ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", "mat_", ",", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], "\[RuleDelayed]", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n4", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"n4", ",", "n2", ",", RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"n6", ",", "n5", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"n4", ",", "n5", ",", "n6"}], "}"}], "]"}]}], "}"}]}], "}"}]}], "\[IndentingNewLine]", "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"eleout", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"(", RowBox[{"eleout", " ", "/.", " ", "rule"}], ")"}], ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{"eleout", ",", "funout"}], "}"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REFINE", "[", RowBox[{"{", RowBox[{"ele_", ",", "fun_", ",", "elnk_"}], "}"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"funout", "=", "fun"}], ",", RowBox[{"eleout", "=", "ele"}], ",", RowBox[{"elnkout", "=", "elnk"}], ",", "ii", ",", "rule", ",", "a1", ",", "a2", ",", "a3", ",", "a4", ",", "a5", ",", "a6", ",", "left", ",", "right", ",", "NEWNODE"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "refinement", " ", "inherits", " ", "conditions", " ", "and", " ", "has", " ", "memory"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ii", " ", "=", RowBox[{ RowBox[{"Length", "[", "funout", "]"}], "+", "1"}]}], ";", "\[IndentingNewLine]", RowBox[{"Clear", "[", "NEWNODE", "]"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"a1_", ",", "a2_"}], "}"}], "]"}], ":=", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], "]"}], "=", RowBox[{"CompoundExpression", "[", RowBox[{ RowBox[{"funout", "=", RowBox[{"Join", "[", RowBox[{"funout", ",", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a2", ",", "1"}], "]"}], "]"}]}], ")"}], "/", "2"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"uX", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"uY", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", "ii", "]"}]}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]X", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Z", "[", "ii", "]"}]}], "]"}]}], "}"}]}], "}"}], "}"}]}], "]"}]}], ";", RowBox[{"ii", "++"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"driven", " ", "by", " ", "this"}], "*)"}], "\[IndentingNewLine]", RowBox[{"rule", ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", "mat_", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], "\[RuleDelayed]", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n4", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n4", ",", "n2", ",", RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n6", ",", "n5", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n4", ",", "n5", ",", "n6"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"FACE", ",", "mat_", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], "\[RuleDelayed]", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"FACE", ",", "mat", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n3", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FACE", ",", "mat", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n3", ",", "n2"}], "}"}], "]"}]}], "}"}]}], "}"}]}]}], "\[IndentingNewLine]", "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "refined", " ", "edges", " ", "should", " ", "be", " ", "removed"}], "*)"}], "\[IndentingNewLine]", RowBox[{"elnkout", "=", RowBox[{"DeleteDuplicates", "[", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"#", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], ",", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"#", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}], ",", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], "]"}], "]"}]}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], ",", RowBox[{"#", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], "]"}], "]"}], ",", RowBox[{"#", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}]}], "}"}]}], "}"}]}], "}"}], "&"}], ",", "elnk"}], "]"}], ",", "1"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"eleout", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"(", RowBox[{"eleout", " ", "/.", " ", "rule"}], ")"}], ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{"eleout", ",", "funout", ",", "elnkout"}], "}"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "*)"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.443930973126174*^9, {3.4771023549018*^9, 3.4771023808445997`*^9}, { 3.4771024577682*^9, 3.4771025046618*^9}, {3.4771063565654*^9, 3.4771063705898*^9}, 3.4771089762209997`*^9, 3.477109006645*^9, { 3.4771109395810003`*^9, 3.4771109526226*^9}, {3.477110989427*^9, 3.4771110302522*^9}, {3.4771110800372*^9, 3.4771111191308002`*^9}, { 3.4771220486066*^9, 3.4771220663286*^9}, {3.4771317865394*^9, 3.4771318192214003`*^9}, {3.4771323345362*^9, 3.477132377639*^9}, { 3.630489883760623*^9, 3.630489885414226*^9}, {3.631409232246135*^9, 3.631409318077486*^9}, {3.6314094294772816`*^9, 3.631409430304083*^9}, { 3.6314095931215687`*^9, 3.6314095963195744`*^9}, {3.6314105089523773`*^9, 3.631410515504389*^9}, 3.631435133305333*^9, {3.631435355203025*^9, 3.6314353561500793`*^9}, 3.6314356018121305`*^9, 3.631435754368856*^9, 3.631435796315255*^9, {3.63143606319652*^9, 3.631436069549884*^9}, { 3.6347884698816414`*^9, 3.63478847685104*^9}, {3.6347954098385844`*^9, 3.6347954141598315`*^9}, {3.6347956603329115`*^9, 3.634795675947805*^9}, { 3.634796217815798*^9, 3.6347962287334223`*^9}, {3.6347962930030985`*^9, 3.6347963097820582`*^9}, {3.63479634495407*^9, 3.6347963538665795`*^9}, { 3.6347967044436316`*^9, 3.6347967222076473`*^9}, {3.6348910182399282`*^9, 3.6348910703229065`*^9}, {3.634891202082443*^9, 3.63489120569665*^9}, { 3.635129073304618*^9, 3.6351290927607307`*^9}, {3.6351291514160852`*^9, 3.6351291562713633`*^9}, {3.6351296027379*^9, 3.635129640630067*^9}, { 3.6351296766311264`*^9, 3.6351296770091476`*^9}, {3.635133864772954*^9, 3.6351340703167105`*^9}, {3.635134178738912*^9, 3.635134204883407*^9}, { 3.6351532590142465`*^9, 3.6351534908115044`*^9}, {3.6353108694909534`*^9, 3.635310875829316*^9}, {3.657768370048919*^9, 3.6577683714841213`*^9}, { 3.6853593982958508`*^9, 3.6853593994858527`*^9}, 3.685359462505941*^9, { 3.685359541326051*^9, 3.685359573806097*^9}, {3.6874387445294027`*^9, 3.687438822019511*^9}, 3.6874389450596833`*^9, {3.6874389956197543`*^9, 3.6874390405998173`*^9}, {3.6874391238499336`*^9, 3.6874391937200317`*^9}, {3.6874392244700747`*^9, 3.687439453750396*^9}, { 3.687439572800562*^9, 3.68743958546058*^9}, {3.68743962102063*^9, 3.687439653600675*^9}, {3.6874397535808153`*^9, 3.6874397667108335`*^9}, 3.6874457948947306`*^9, {3.6874461481952252`*^9, 3.6874461564952374`*^9}, { 3.6876686346644025`*^9, 3.6876686478844213`*^9}, {3.6876686911644816`*^9, 3.687668823124666*^9}, {3.687668960604859*^9, 3.6876691302750964`*^9}, { 3.687669356755413*^9, 3.6876695631957026`*^9}, {3.68766976165598*^9, 3.687669770715993*^9}, {3.6876724948642445`*^9, 3.687672495474246*^9}, { 3.687672580794365*^9, 3.6876727153745537`*^9}, {3.687672853854748*^9, 3.6876729332848587`*^9}, {3.6876729722949133`*^9, 3.6876731124151096`*^9}, {3.687673280685345*^9, 3.687673411335528*^9}, 3.6879313344746327`*^9, {3.687931387314707*^9, 3.6879314004147253`*^9}, { 3.6879314569548044`*^9, 3.6879314600748086`*^9}, {3.687931618845031*^9, 3.687931690255131*^9}, {3.687931744255206*^9, 3.6879317511352158`*^9}, { 3.6879317991852837`*^9, 3.6879318101552987`*^9}, {3.6879318528753586`*^9, 3.687931875785391*^9}, {3.6880321738474593`*^9, 3.688032324857671*^9}, { 3.68811073769691*^9, 3.68811083105704*^9}, {3.688182194807842*^9, 3.6881822090088615`*^9}, {3.6881823158700113`*^9, 3.6881824932602596`*^9}, {3.6881827603406334`*^9, 3.688182807210699*^9}, { 3.6881829158708515`*^9, 3.68818292930087*^9}, {3.688182999800969*^9, 3.6881831324711547`*^9}, {3.688183628661849*^9, 3.6881836750819144`*^9}, { 3.688211059016615*^9, 3.6882111198466997`*^9}, {3.6882111896067977`*^9, 3.6882112272568502`*^9}, {3.688211687127494*^9, 3.688211814657673*^9}, { 3.688211854527728*^9, 3.6882118603977365`*^9}, {3.6882139698004313`*^9, 3.68821399050046*^9}, {3.68821420020687*^9, 3.688214201756872*^9}, 3.6882144390772047`*^9, {3.6882146560475082`*^9, 3.6882146684575257`*^9}, { 3.688214751567642*^9, 3.6882147680976653`*^9}, {3.688214804297716*^9, 3.6882149595979333`*^9}, {3.6882150203480186`*^9, 3.6882152133382883`*^9}, {3.6882152437383313`*^9, 3.688215312948428*^9}, 3.6882155446087523`*^9, {3.688540867416464*^9, 3.688540868276465*^9}, { 3.688540923456542*^9, 3.688540987616632*^9}, {3.689509628603777*^9, 3.6895096840119457`*^9}, 3.6895097148397093`*^9, {3.689568676097738*^9, 3.689568771827872*^9}, {3.689737582567273*^9, 3.689737610517312*^9}, { 3.689738148338065*^9, 3.689738254678214*^9}, {3.689738292788267*^9, 3.689738346768343*^9}, {3.6897387257888737`*^9, 3.6897388179090023`*^9}, { 3.6898585271206756`*^9, 3.689858545170701*^9}, {3.6898585824607525`*^9, 3.689858769851015*^9}, {3.6940970096156654`*^9, 3.6940970747057567`*^9}, 3.6941413988145113`*^9, {3.694354094868929*^9, 3.6943541832790527`*^9}, { 3.694920239046096*^9, 3.694920319576208*^9}, {3.6949203962063155`*^9, 3.694920412426338*^9}, {3.6949204882764444`*^9, 3.6949204937164516`*^9}, 3.6949205606465454`*^9, {3.695100444594348*^9, 3.6951004570843654`*^9}, { 3.6973395634474907`*^9, 3.69733958428752*^9}, {3.697985422771953*^9, 3.6979855230120935`*^9}, {3.697985573722165*^9, 3.697985597992199*^9}, { 3.6979856429622617`*^9, 3.6979856711723013`*^9}, {3.7244643325478783`*^9, 3.724464348643357*^9}, {3.724467403856756*^9, 3.724467437838467*^9}, { 3.7244675479335804`*^9, 3.724467563230343*^9}, 3.7244676966368866`*^9, { 3.724467772264612*^9, 3.724467824163081*^9}, {3.7244678625415535`*^9, 3.724467863396864*^9}, {3.724468018783759*^9, 3.72446802144991*^9}, { 3.7244681559004545`*^9, 3.7244681850540376`*^9}, {3.724468459327367*^9, 3.724468483652465*^9}, {3.7244686219080153`*^9, 3.7244687024486265`*^9}, { 3.7244712391235456`*^9, 3.7244712430734224`*^9}, {3.7244712821065245`*^9, 3.724471282307459*^9}, {3.7244718283139167`*^9, 3.724471852982109*^9}, { 3.7245109260422964`*^9, 3.7245109717411103`*^9}, {3.7254180257070103`*^9, 3.725418132591786*^9}, {3.725418186497287*^9, 3.725418198564393*^9}, { 3.725418240702896*^9, 3.7254182427078333`*^9}, 3.7254182729821267`*^9, { 3.7254183742147875`*^9, 3.72541838162965*^9}, {3.7254184135842233`*^9, 3.7254184150237846`*^9}, {3.725418877464322*^9, 3.7254189569953265`*^9}, { 3.725418994143058*^9, 3.725419023781932*^9}, {3.7254193126441193`*^9, 3.725419396185589*^9}, {3.725432214366968*^9, 3.725432235836476*^9}, { 3.7254322894678383`*^9, 3.725432377695853*^9}, {3.726401253407773*^9, 3.7264012633218203`*^9}, {3.726401405512204*^9, 3.7264014071162825`*^9}, { 3.7264014439323297`*^9, 3.7264014462981124`*^9}, {3.726401485648699*^9, 3.7264016429140606`*^9}, {3.726401682872032*^9, 3.726401718837957*^9}, { 3.726401899357152*^9, 3.7264019010212574`*^9}, {3.7264019889732013`*^9, 3.726401991903804*^9}, {3.7264021595991826`*^9, 3.7264021616913195`*^9}, { 3.726402447890601*^9, 3.726402463475356*^9}, {3.747040699533342*^9, 3.7470408363290567`*^9}, {3.7471061663693695`*^9, 3.747106214420479*^9}, { 3.7471067469638214`*^9, 3.747106834372692*^9}, {3.7471068959871335`*^9, 3.747106915079779*^9}, {3.7471069588898473`*^9, 3.747106998742816*^9}, 3.747107044736511*^9, {3.747107087544964*^9, 3.7471070893575435`*^9}, { 3.7471138002489843`*^9, 3.747113811418234*^9}, {3.7471138500028563`*^9, 3.747113892211589*^9}, 3.747114310142033*^9, {3.7471143424625273`*^9, 3.747114343868453*^9}, {3.7471148744458303`*^9, 3.747114931572899*^9}, { 3.74711503534515*^9, 3.747115041218787*^9}, {3.7471156330947733`*^9, 3.7471156387028475`*^9}, {3.747116431240279*^9, 3.7471164335522423`*^9}, { 3.7471164808222904`*^9, 3.7471166104321785`*^9}, {3.747116647876696*^9, 3.7471167102835293`*^9}, {3.74865997476248*^9, 3.7486600101981816`*^9}, { 3.748660042393119*^9, 3.748660069138746*^9}, {3.748660177148834*^9, 3.748660251952998*^9}, {3.7486604981713724`*^9, 3.748660508798976*^9}, { 3.7486929231374454`*^9, 3.7486929342382526`*^9}, {3.7486929737776747`*^9, 3.7486929903337507`*^9}, {3.7486930264117804`*^9, 3.7486931799453707`*^9}, {3.748693249361241*^9, 3.7486932724173203`*^9}, 3.7486933276281357`*^9, 3.7486939237519407`*^9, {3.7486939698417687`*^9, 3.7486939700127883`*^9}, {3.748694008103215*^9, 3.7486940757142344`*^9}, { 3.7486942326282196`*^9, 3.748694304005413*^9}, {3.748695188924658*^9, 3.748695190701332*^9}, {3.7486952252639275`*^9, 3.7486953104760585`*^9}, { 3.748695384723056*^9, 3.748695811151685*^9}, {3.7486958766029434`*^9, 3.7486959097256002`*^9}, {3.7486964229653544`*^9, 3.7486964578684864`*^9}, 3.7487454821763644`*^9, {3.754056041592442*^9, 3.754056060140006*^9}, { 3.754056347029888*^9, 3.754056351327733*^9}, {3.754056854382514*^9, 3.754056862089791*^9}, {3.7540569630968127`*^9, 3.7540569674225426`*^9}, { 3.7540570759551015`*^9, 3.7540570801772118`*^9}, {3.754057135076915*^9, 3.754057152630065*^9}, {3.7540571929041653`*^9, 3.754057236529367*^9}, { 3.754057397662035*^9, 3.7540574231277227`*^9}, {3.7540574560189123`*^9, 3.754057472695193*^9}, {3.754057518721182*^9, 3.754057583163235*^9}, 3.754057631189864*^9, {3.7540576696626444`*^9, 3.754057832330846*^9}, { 3.7540578903947163`*^9, 3.7540579289766736`*^9}, {3.7540580507949033`*^9, 3.7540580513826957`*^9}, {3.7540978904321117`*^9, 3.7540979191340885`*^9}, {3.7540979931579046`*^9, 3.7540979999909244`*^9}, {3.7540980363245296`*^9, 3.754098095196913*^9}, { 3.7540981279820137`*^9, 3.75409817510705*^9}, {3.7540983080840054`*^9, 3.7540983887416687`*^9}, {3.754098433086689*^9, 3.7540984487715254`*^9}, { 3.754098518107086*^9, 3.7540985418746586`*^9}, {3.7540985740895276`*^9, 3.7540985855956683`*^9}, {3.7540986329334645`*^9, 3.754098651832582*^9}, 3.754098694943287*^9, {3.7540987996641817`*^9, 3.7540988293199515`*^9}, { 3.754098922368672*^9, 3.754098946956335*^9}, {3.7541009656118875`*^9, 3.754100966064907*^9}, {3.7541260794470377`*^9, 3.754126112298939*^9}, { 3.7541261993178277`*^9, 3.7541263394250636`*^9}, {3.7541264153576813`*^9, 3.754126455276905*^9}, {3.7541264972202415`*^9, 3.754126628008542*^9}, { 3.7541266613158674`*^9, 3.754126719835323*^9}, 3.7541267961648273`*^9, { 3.754126828833903*^9, 3.754126890819979*^9}, {3.754126943227796*^9, 3.754127112269927*^9}, {3.7541271553116074`*^9, 3.7541271992360067`*^9}, { 3.754127253229822*^9, 3.754127273225658*^9}, {3.754127329226965*^9, 3.7541273643065696`*^9}, {3.7541277175880594`*^9, 3.754127721159455*^9}, { 3.754127900093892*^9, 3.754127900428954*^9}, {3.7555365688081875`*^9, 3.7555368169423947`*^9}, {3.7566194252966633`*^9, 3.756619503340211*^9}, { 3.7606073727611165`*^9, 3.7606074044677906`*^9}, {3.7639037635827665`*^9, 3.7639039669013567`*^9}, {3.7639040036658916`*^9, 3.7639040352749486`*^9}, {3.7639041491982164`*^9, 3.7639041498420076`*^9}, {3.7641295066295767`*^9, 3.7641296291063385`*^9}, 3.7641297671450467`*^9, {3.764129842917159*^9, 3.76412986403855*^9}, { 3.7641299539495287`*^9, 3.7641299638308244`*^9}, {3.764130242057335*^9, 3.764130264998592*^9}, {3.7641304121561837`*^9, 3.764130517277567*^9}, { 3.764905400658563*^9, 3.764905448073204*^9}, {3.7661917992707295`*^9, 3.7661918111029887`*^9}, {3.7661937058475633`*^9, 3.7661937308527126`*^9}, {3.766288732159727*^9, 3.7662887421574078`*^9}, 3.7741665150318885`*^9, {3.774166583333705*^9, 3.7741666346924067`*^9}, { 3.7741666777885046`*^9, 3.7741667276801615`*^9}, {3.7741681843844967`*^9, 3.774168277409542*^9}, {3.774237957645171*^9, 3.7742379961381702`*^9}, { 3.774238228752078*^9, 3.7742383203485446`*^9}, {3.7742384167748957`*^9, 3.774238438885627*^9}, {3.774238499096892*^9, 3.7742385555597315`*^9}, { 3.7742385931019473`*^9, 3.774238669464537*^9}, {3.774239332037335*^9, 3.774239458024664*^9}, {3.7742396127858567`*^9, 3.7742396524321165`*^9}, { 3.774239693440149*^9, 3.774239749194436*^9}, {3.774239781513965*^9, 3.7742399183443785`*^9}, {3.774239993088747*^9, 3.7742399984000196`*^9}, { 3.774240080591405*^9, 3.7742403502486305`*^9}, {3.7742403925474215`*^9, 3.7742406200754595`*^9}, {3.7742406536016474`*^9, 3.774240771836528*^9}, { 3.774240802985832*^9, 3.7742408207850018`*^9}, {3.7742408510511465`*^9, 3.7742409420304427`*^9}, 3.7742409770366917`*^9, {3.7742410127101192`*^9, 3.774241115672659*^9}, {3.7742411489763308`*^9, 3.7742412065999565`*^9}, { 3.7751895563614497`*^9, 3.775189557474781*^9}, {3.7751896076191764`*^9, 3.7751897799276996`*^9}, {3.777096408797056*^9, 3.7770964403195615`*^9}, { 3.777096485036745*^9, 3.7770965029912896`*^9}, {3.7956770978646717`*^9, 3.7956772181619654`*^9}, {3.8146735876267333`*^9, 3.814673589766639*^9}, { 3.8146739729339857`*^9, 3.8146740117645845`*^9}, {3.8146740671049843`*^9, 3.8146741049177666`*^9}, {3.8146741507745976`*^9, 3.8146741804277105`*^9}, {3.814674251422745*^9, 3.8146743106812353`*^9}, 3.814674726159151*^9, 3.814674968815707*^9, 3.814675018726674*^9, { 3.820993565028139*^9, 3.8209935658103247`*^9}, {3.8209936225592756`*^9, 3.8209937079555244`*^9}, {3.8209937406519527`*^9, 3.820993799726659*^9}, { 3.8449114536299915`*^9, 3.8449114597094784`*^9}, 3.844911489750399*^9, { 3.844911524811378*^9, 3.8449116115216727`*^9}, {3.8449116508263726`*^9, 3.8449118900319576`*^9}, {3.8449119415999355`*^9, 3.8449119426680517`*^9}, {3.8449119732971334`*^9, 3.8449120379798584`*^9}, {3.8449120825540514`*^9, 3.84491208370156*^9}, { 3.8449131304497786`*^9, 3.84491313620944*^9}, {3.844913600565547*^9, 3.844913684928097*^9}, {3.8449138096165752`*^9, 3.8449138945019174`*^9}, { 3.8469121733333035`*^9, 3.846912212029579*^9}, {3.846912263742777*^9, 3.846912264841491*^9}, {3.846913863799194*^9, 3.8469138819214835`*^9}, { 3.8518356301432843`*^9, 3.851835652475341*^9}, {3.853032777958458*^9, 3.853032812072734*^9}}, CellLabel-> "In[254]:=",ExpressionUUID->"797ad8d2-c1f3-436b-bcf0-ab6a58e6258f"] }, Closed]], Cell[CellGroupData[{ Cell["ENRICH defs", "Subsection", CellChangeTimes->{{3.7555369693812027`*^9, 3.7555369706487265`*^9}, { 3.7594889422016716`*^9, 3.759488944733738*^9}},ExpressionUUID->"24f0f609-0d0a-432d-be7b-\ 5b7e02cf05fb"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"(*", RowBox[{"enrich", " ", "triangle"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"ENRICH", "[", RowBox[{"{", RowBox[{"crd_", ",", "nod_"}], "}"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"ii", ",", "FN", ",", "rule", ",", "crdnew", ",", "nodnew"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"crdnew", " ", "=", "crd"}], ";", " ", "\[IndentingNewLine]", RowBox[{"ii", "=", RowBox[{ RowBox[{"Length", "[", "crdnew", "]"}], "+", "1"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"FN", "[", RowBox[{"{", RowBox[{"a_", ",", "b_"}], "}"}], "]"}], ":=", RowBox[{ RowBox[{"FN", "[", RowBox[{"{", RowBox[{"b", ",", "a"}], "}"}], "]"}], "=", RowBox[{ RowBox[{"FN", "[", RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}], "]"}], "=", RowBox[{"CompoundExpression", "[", RowBox[{ RowBox[{"crdnew", "=", RowBox[{"Append", "[", RowBox[{"crdnew", ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"crdnew", "[", RowBox[{"[", "a", "]"}], "]"}], "+", RowBox[{"crdnew", "[", RowBox[{"[", "b", "]"}], "]"}]}], ")"}], "/", "2"}]}], "]"}]}], ";", RowBox[{"ii", "++"}]}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"rule", ":=", RowBox[{ RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"a_", ",", "b_", ",", "c_"}], "}"}], "]"}], "\[RuleDelayed]", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"a", ",", "b", ",", "c", ",", RowBox[{"FN", "[", RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}], "]"}], ",", RowBox[{"FN", "[", RowBox[{"{", RowBox[{"b", ",", "c"}], "}"}], "]"}], ",", RowBox[{"FN", "[", RowBox[{"{", RowBox[{"c", ",", "a"}], "}"}], "]"}]}], "}"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"nodnew", "=", RowBox[{"nod", " ", "/.", " ", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{"crdnew", ",", "nodnew"}], " ", "}"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{"ENRICH", "[", RowBox[{"{", RowBox[{"nod_", ",", "crd_"}], "}"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"FN", ",", "ii", ",", "rule", ",", "nodout", ",", "crdout"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"crdout", " ", "=", "crd"}], ";", RowBox[{"nodout", "=", "nod"}], ";", "\[IndentingNewLine]", RowBox[{"ii", "=", RowBox[{ RowBox[{"Length", "[", "crdout", "]"}], "+", "1"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"FN", "[", RowBox[{"{", RowBox[{"a_", ",", "b_"}], "}"}], "]"}], ":=", RowBox[{ RowBox[{"FN", "[", RowBox[{"{", RowBox[{"b", ",", "a"}], "}"}], "]"}], "=", RowBox[{"CompoundExpression", "[", RowBox[{ RowBox[{"crdout", "=", RowBox[{"Join", "[", RowBox[{"crdout", ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2", RowBox[{"crdout", "[", RowBox[{"[", "a", "]"}], "]"}]}], "+", RowBox[{"crdout", "[", RowBox[{"[", "b", "]"}], "]"}]}], ")"}], "/", "3"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"crdout", "[", RowBox[{"[", "a", "]"}], "]"}], "+", RowBox[{"2", RowBox[{"crdout", "[", RowBox[{"[", "b", "]"}], "]"}]}]}], ")"}], "/", "3"}]}], "}"}]}], "]"}]}], ";", RowBox[{"{", RowBox[{ RowBox[{"ii", "++"}], ",", RowBox[{"ii", "++"}]}], "}"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"rule", ":=", RowBox[{ RowBox[{"Line", "[", RowBox[{"{", RowBox[{"a_", ",", "b_"}], "}"}], "]"}], "\[RuleDelayed]", RowBox[{"Line", "[", RowBox[{"Flatten", "[", RowBox[{"{", RowBox[{"a", ",", RowBox[{"FN", "[", RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}], "]"}], ",", "b"}], "}"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"nodout", "=", RowBox[{"(", RowBox[{"nodout", "/.", " ", "rule"}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{"nodout", ",", "crdout"}], "}"}], "]"}]}]}], "]"}]}], ";"}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ENRICH", "[", RowBox[{"{", RowBox[{"ele_", ",", "fun_", ",", "elnk_"}], "}"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"funout", "=", "fun"}], ",", RowBox[{"eleout", "=", "ele"}], ",", RowBox[{"elnkout", "=", "elnk"}], ",", "ii", ",", "rule", ",", "a1", ",", "a2", ",", "a3", ",", "a4", ",", "a5", ",", "a6", ",", "left", ",", "right", ",", "NEWNODE", ",", "edg", ",", "lnkrule"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "refinement", " ", "inherits", " ", "conditions", " ", "and", " ", "has", " ", "memory"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ii", " ", "=", RowBox[{ RowBox[{"Length", "[", "funout", "]"}], "+", "1"}]}], ";", "\[IndentingNewLine]", RowBox[{"Clear", "[", "NEWNODE", "]"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"a1_", ",", "a2_"}], "}"}], "]"}], ":=", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], "]"}], "=", RowBox[{"CompoundExpression", "[", RowBox[{ RowBox[{"funout", "=", RowBox[{"Join", "[", RowBox[{"funout", ",", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"funout", "[", RowBox[{"[", RowBox[{"a2", ",", "1"}], "]"}], "]"}]}], ")"}], "/", "2"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"uX", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"uY", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"uZ", "[", "ii", "]"}]}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]X", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "2"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Y", "[", "ii", "]"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"AllTrue", "[", RowBox[{ RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "3"}], "]"}], "]"}], ",", "NumberQ"}], "]"}], ",", RowBox[{"Mean", "[", RowBox[{"funout", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], ",", "3", ",", "3"}], "]"}], "]"}], "]"}], ",", RowBox[{"\[Theta]Z", "[", "ii", "]"}]}], "]"}]}], "}"}]}], "}"}], "}"}]}], "]"}]}], ";", RowBox[{"ii", "++"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"driven", " ", "by", " ", "this"}], "*)"}], "\[IndentingNewLine]", RowBox[{"rule", ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", "mat_", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], "\[RuleDelayed]", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}], ",", "n2", ",", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}], ",", "n3", ",", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}], " ", "}"}], "]"}]}], "}"}], "}"}]}], "\[IndentingNewLine]", "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"elnkout", "=", RowBox[{"Join", "[", RowBox[{"elnk", ",", RowBox[{"DeleteDuplicates", "[", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"#", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], ",", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"#", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}], ",", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], "]"}], "]"}]}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], ",", RowBox[{"#", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], "]"}], "]"}], ",", RowBox[{"#", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}]}], "}"}]}], "}"}]}], "}"}], "&"}], ",", "elnk"}], "]"}], ",", "1"}], "]"}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"eleout", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"(", RowBox[{"eleout", " ", "/.", " ", "rule"}], ")"}], ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{"eleout", ",", "funout", ",", "elnkout"}], "}"}], "]"}]}]}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.697985830982525*^9, 3.6979858329925275`*^9}, { 3.698414463543007*^9, 3.698414476843025*^9}, {3.6984148090934906`*^9, 3.6984148464035425`*^9}, {3.6984149699237156`*^9, 3.6984149730637197`*^9}, {3.698415039563813*^9, 3.6984150501038275`*^9}, { 3.698415130973941*^9, 3.6984151547039742`*^9}, {3.6984151857740173`*^9, 3.6984152096340513`*^9}, {3.6984152435240984`*^9, 3.698415255934116*^9}, 3.6984153434742384`*^9, {3.698415428614358*^9, 3.6984155528645315`*^9}, { 3.698415650334668*^9, 3.6984156957947316`*^9}, {3.6984971216481996`*^9, 3.6984971440082307`*^9}, {3.698497256408388*^9, 3.6984972586283913`*^9}, { 3.698497324188483*^9, 3.698497334418497*^9}, {3.6984974231086216`*^9, 3.69849751476875*^9}, {3.699107129086978*^9, 3.69910719511707*^9}, { 3.6994220214505434`*^9, 3.699422023570546*^9}, 3.6994224722011747`*^9, { 3.700296892213687*^9, 3.7002969404537544`*^9}, {3.700297153924053*^9, 3.700297154704054*^9}, {3.700298036047288*^9, 3.7002980600173216`*^9}, { 3.7002981562074566`*^9, 3.7002981872574997`*^9}, {3.7129791718840046`*^9, 3.7129791800257635`*^9}, {3.712979232875139*^9, 3.712979252111267*^9}, { 3.7129794197387886`*^9, 3.712979525828207*^9}, {3.7129795809903307`*^9, 3.712979590413209*^9}, {3.7129796478565316`*^9, 3.7129796809538364`*^9}, { 3.7129804673191423`*^9, 3.7129804748198795`*^9}, {3.712980610928114*^9, 3.712980622210312*^9}, {3.7129807144235544`*^9, 3.712980726627682*^9}, { 3.7129807741799045`*^9, 3.7129807809461966`*^9}, {3.7129811406876945`*^9, 3.7129811475474696`*^9}, 3.7129820013233137`*^9, 3.712982092129925*^9, { 3.7129824843276033`*^9, 3.7129825137528653`*^9}, {3.71298256627383*^9, 3.712982670207111*^9}, {3.7129827678737044`*^9, 3.712982856273471*^9}, { 3.7129829454548435`*^9, 3.712983022932089*^9}, {3.712983202325946*^9, 3.7129832392986393`*^9}, {3.712983366989815*^9, 3.712983388023601*^9}, { 3.7129834186205378`*^9, 3.7129835372579465`*^9}, {3.712983834758374*^9, 3.712983894467859*^9}, {3.7129840417335854`*^9, 3.712984063673375*^9}, 3.7129841515267477`*^9, {3.7129844471207294`*^9, 3.7129845210814824`*^9}, { 3.712984569477442*^9, 3.7129845739623785`*^9}, {3.712984641406767*^9, 3.712984648032766*^9}, {3.712985039824218*^9, 3.71298523890793*^9}, 3.7129853718321877`*^9, {3.7129854137561316`*^9, 3.7129854179438295`*^9}, { 3.712985449603707*^9, 3.7129854556822214`*^9}, {3.7129855201112256`*^9, 3.712985525768077*^9}, {3.712985625231479*^9, 3.7129857027712817`*^9}, { 3.7129857629336724`*^9, 3.712985769059338*^9}, {3.7129858314881444`*^9, 3.712985835050726*^9}, {3.7129860602431355`*^9, 3.712986064853248*^9}, { 3.7129862394499397`*^9, 3.712986242887823*^9}, {3.7129866297240076`*^9, 3.7129866397563314`*^9}, {3.71298680167982*^9, 3.712986860763974*^9}, { 3.7129869813135347`*^9, 3.7129869942367897`*^9}, {3.712987135892788*^9, 3.712987136814763*^9}, {3.7129950311602526`*^9, 3.7129950408646345`*^9}, { 3.7129950854940643`*^9, 3.712995128842733*^9}, {3.712995161470902*^9, 3.712995164018298*^9}, {3.712995233556699*^9, 3.712995253965371*^9}, 3.712995343491997*^9, {3.7129953798398485`*^9, 3.712995411374176*^9}, { 3.712996268059813*^9, 3.712996279264394*^9}, {3.712996332785453*^9, 3.7129963339887047`*^9}, {3.7129963699143753`*^9, 3.7129965642163386`*^9}, {3.7129967399069395`*^9, 3.7129967825364337`*^9}, {3.7130023714774327`*^9, 3.713002390011431*^9}, { 3.7130024555486317`*^9, 3.713002456033061*^9}, {3.7130096859044127`*^9, 3.713009698562335*^9}, {3.713009785977857*^9, 3.7130098720964165`*^9}, { 3.7138474164601574`*^9, 3.713847460605017*^9}, {3.713848647902732*^9, 3.7138486952205644`*^9}, {3.7140410034418354`*^9, 3.71404102099051*^9}, { 3.7140410516813707`*^9, 3.7140410571662374`*^9}, {3.7500561163492336`*^9, 3.750056118309679*^9}, {3.75005644772439*^9, 3.750056460364983*^9}, { 3.750418955819368*^9, 3.750418991955581*^9}, {3.7504190504328346`*^9, 3.7504191179118333`*^9}, {3.750419148990396*^9, 3.7504192971886773`*^9}, { 3.7504193704776974`*^9, 3.750419371460817*^9}, {3.750419622202434*^9, 3.7504196274570265`*^9}, {3.750419676396184*^9, 3.7504197005232496`*^9}, { 3.7504199014205647`*^9, 3.7504199105731564`*^9}, 3.7504199674269505`*^9, { 3.75042000580826*^9, 3.7504200179820857`*^9}, {3.7504200623902054`*^9, 3.7504200725254693`*^9}, {3.7594891152396383`*^9, 3.759489154065875*^9}, { 3.7606073008309183`*^9, 3.7606073145514975`*^9}, {3.7606073578977823`*^9, 3.760607359417551*^9}, {3.7606074424144297`*^9, 3.760607457401692*^9}, { 3.844827354234421*^9, 3.8448273760220327`*^9}, {3.8448275231364627`*^9, 3.8448275266575537`*^9}, 3.8448276238320646`*^9, {3.8448277812192287`*^9, 3.8448277848034983`*^9}, {3.844827829780749*^9, 3.8448278559054637`*^9}, { 3.844828686628151*^9, 3.8448286878814173`*^9}}, CellLabel-> "In[289]:=",ExpressionUUID->"1975a601-4da2-46da-a032-7825d595170e"] }, Closed]], Cell[CellGroupData[{ Cell["GREFINE defs", "Subsection", CellChangeTimes->{{3.7555369693812027`*^9, 3.7555369706487265`*^9}, { 3.7594889422016716`*^9, 3.759488944733738*^9}, {3.7597145150982075`*^9, 3.759714542190567*^9}, {3.7597145828965845`*^9, 3.7597145848583384`*^9}},ExpressionUUID->"2a69b2ad-4531-4e5a-ae19-\ d98593b19786"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"GREF", "[", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"n4", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], ",", "n2", ",", RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n5", ",", "n3", ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n6", ",", "n1", ",", "n4"}], "}"}], "]"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n4", ",", "n5", ",", "n6"}], "}"}], "]"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GREF", "[", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n8", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n3"}], "}"}], "]"}], "]"}]}], ",", RowBox[{"n9", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n5", ",", "n2", ",", "n9", ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n4"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n8", ",", "n9", ",", "n3", ",", RowBox[{"n7", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n4"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n9", ",", "n6", ",", "n7", ",", "n4"}], "}"}], "]"}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GREFINE", "[", RowBox[{"{", RowBox[{"crd_", ",", "nod_"}], "}"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"crdout", "=", "crd"}], ",", RowBox[{"nodout", "=", "nod"}], ",", "ii"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"ii", " ", "=", RowBox[{ RowBox[{"Length", "[", "crdout", "]"}], "+", "1"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Clear", "[", "NEWNODE", "]"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"a1_", ",", "a2_"}], "}"}], "]"}], ":=", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], "]"}], "=", RowBox[{"CompoundExpression", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"crdout", "=", RowBox[{"Join", "[", RowBox[{"crdout", ",", RowBox[{"{", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"crdout", "[", RowBox[{"[", "a1", "]"}], "]"}], "+", RowBox[{"crdout", "[", RowBox[{"[", "a2", "]"}], "]"}]}], ")"}], "/", "2"}], "}"}]}], "]"}]}], ",", RowBox[{"ii", "++"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"nodout", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"GREF", "[", "#", "]"}], "&"}], ",", "nodout"}], "]"}], ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{"crdout", ",", "nodout"}], "}"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GENR", "[", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}], "]"}], ":=", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}], "]"}], ",", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}], ",", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n1"}], "}"}], "]"}], "]"}]}], "}"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{"GENR", "[", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], ",", RowBox[{"n8", "=", RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"n1", ",", "n3"}], "}"}], "]"}]}], ",", RowBox[{"n9", "=", RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}]}]}], "}"}], "]"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n5", ",", "n2", ",", "n9", ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"n2", ",", "n4"}], "}"}], "]"}]}]}], "}"}], "]"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n8", ",", "n9", ",", "n3", ",", RowBox[{"n7", "=", RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"n3", ",", "n4"}], "}"}], "]"}]}]}], "}"}], "]"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n9", ",", "n6", ",", "n7", ",", "n4"}], "}"}], "]"}], "}"}]}], "}"}]}], ";"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GENRICH", "[", RowBox[{"{", RowBox[{"crd_", ",", "nod_"}], "}"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"ii", ",", "FN", ",", "rule", ",", RowBox[{"crdout", "=", "crd"}], ",", RowBox[{"nodout", "=", "nod"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"ii", "=", RowBox[{ RowBox[{"Length", "[", "crdout", "]"}], "+", "1"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Clear", "[", "NEWNODE", "]"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"a1_", ",", "a2_"}], "}"}], "]"}], ":=", RowBox[{ RowBox[{"NEWNODE", "[", RowBox[{"{", RowBox[{"a1", ",", "a2"}], "}"}], "]"}], "=", RowBox[{"CompoundExpression", "[", RowBox[{ RowBox[{"crdout", "=", RowBox[{"Join", "[", RowBox[{"crdout", ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"crdout", "[", RowBox[{"[", "a1", "]"}], "]"}], "+", RowBox[{"crdout", "[", RowBox[{"[", "a2", "]"}], "]"}]}], ")"}], "/", "2"}], "}"}]}], "]"}]}], ",", RowBox[{"ii", "++"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"nodout", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"GENR", "[", "#", "]"}], "&"}], ",", "nodout"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{"crdout", ",", "nodout"}], "}"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.697985830982525*^9, 3.6979858329925275`*^9}, { 3.698414463543007*^9, 3.698414476843025*^9}, {3.6984148090934906`*^9, 3.6984148464035425`*^9}, {3.6984149699237156`*^9, 3.6984149730637197`*^9}, {3.698415039563813*^9, 3.6984150501038275`*^9}, { 3.698415130973941*^9, 3.6984151547039742`*^9}, {3.6984151857740173`*^9, 3.6984152096340513`*^9}, {3.6984152435240984`*^9, 3.698415255934116*^9}, 3.6984153434742384`*^9, {3.698415428614358*^9, 3.6984155528645315`*^9}, { 3.698415650334668*^9, 3.6984156957947316`*^9}, {3.6984971216481996`*^9, 3.6984971440082307`*^9}, {3.698497256408388*^9, 3.6984972586283913`*^9}, { 3.698497324188483*^9, 3.698497334418497*^9}, {3.6984974231086216`*^9, 3.69849751476875*^9}, {3.699107129086978*^9, 3.69910719511707*^9}, { 3.6994220214505434`*^9, 3.699422023570546*^9}, 3.6994224722011747`*^9, { 3.700296892213687*^9, 3.7002969404537544`*^9}, {3.700297153924053*^9, 3.700297154704054*^9}, {3.700298036047288*^9, 3.7002980600173216`*^9}, { 3.7002981562074566`*^9, 3.7002981872574997`*^9}, {3.7129791718840046`*^9, 3.7129791800257635`*^9}, {3.712979232875139*^9, 3.712979252111267*^9}, { 3.7129794197387886`*^9, 3.712979525828207*^9}, {3.7129795809903307`*^9, 3.712979590413209*^9}, {3.7129796478565316`*^9, 3.7129796809538364`*^9}, { 3.7129804673191423`*^9, 3.7129804748198795`*^9}, {3.712980610928114*^9, 3.712980622210312*^9}, {3.7129807144235544`*^9, 3.712980726627682*^9}, { 3.7129807741799045`*^9, 3.7129807809461966`*^9}, {3.7129811406876945`*^9, 3.7129811475474696`*^9}, 3.7129820013233137`*^9, 3.712982092129925*^9, { 3.7129824843276033`*^9, 3.7129825137528653`*^9}, {3.71298256627383*^9, 3.712982670207111*^9}, {3.7129827678737044`*^9, 3.712982856273471*^9}, { 3.7129829454548435`*^9, 3.712983022932089*^9}, {3.712983202325946*^9, 3.7129832392986393`*^9}, {3.712983366989815*^9, 3.712983388023601*^9}, { 3.7129834186205378`*^9, 3.7129835372579465`*^9}, {3.712983834758374*^9, 3.712983894467859*^9}, {3.7129840417335854`*^9, 3.712984063673375*^9}, 3.7129841515267477`*^9, {3.7129844471207294`*^9, 3.7129845210814824`*^9}, { 3.712984569477442*^9, 3.7129845739623785`*^9}, {3.712984641406767*^9, 3.712984648032766*^9}, {3.712985039824218*^9, 3.71298523890793*^9}, 3.7129853718321877`*^9, {3.7129854137561316`*^9, 3.7129854179438295`*^9}, { 3.712985449603707*^9, 3.7129854556822214`*^9}, {3.7129855201112256`*^9, 3.712985525768077*^9}, {3.712985625231479*^9, 3.7129857027712817`*^9}, { 3.7129857629336724`*^9, 3.712985769059338*^9}, {3.7129858314881444`*^9, 3.712985835050726*^9}, {3.7129860602431355`*^9, 3.712986064853248*^9}, { 3.7129862394499397`*^9, 3.712986242887823*^9}, {3.7129866297240076`*^9, 3.7129866397563314`*^9}, {3.71298680167982*^9, 3.712986860763974*^9}, { 3.7129869813135347`*^9, 3.7129869942367897`*^9}, {3.712987135892788*^9, 3.712987136814763*^9}, {3.7129950311602526`*^9, 3.7129950408646345`*^9}, { 3.7129950854940643`*^9, 3.712995128842733*^9}, {3.712995161470902*^9, 3.712995164018298*^9}, {3.712995233556699*^9, 3.712995253965371*^9}, 3.712995343491997*^9, {3.7129953798398485`*^9, 3.712995411374176*^9}, { 3.712996268059813*^9, 3.712996279264394*^9}, {3.712996332785453*^9, 3.7129963339887047`*^9}, {3.7129963699143753`*^9, 3.7129965642163386`*^9}, {3.7129967399069395`*^9, 3.7129967825364337`*^9}, {3.7130023714774327`*^9, 3.713002390011431*^9}, { 3.7130024555486317`*^9, 3.713002456033061*^9}, {3.7130096859044127`*^9, 3.713009698562335*^9}, {3.713009785977857*^9, 3.7130098720964165`*^9}, { 3.7138474164601574`*^9, 3.713847460605017*^9}, {3.713848647902732*^9, 3.7138486952205644`*^9}, {3.7140410034418354`*^9, 3.71404102099051*^9}, { 3.7140410516813707`*^9, 3.7140410571662374`*^9}, {3.7500561163492336`*^9, 3.750056118309679*^9}, {3.75005644772439*^9, 3.750056460364983*^9}, { 3.750418955819368*^9, 3.750418991955581*^9}, {3.7504190504328346`*^9, 3.7504191179118333`*^9}, {3.750419148990396*^9, 3.7504192971886773`*^9}, { 3.7504193704776974`*^9, 3.750419371460817*^9}, {3.750419622202434*^9, 3.7504196274570265`*^9}, {3.750419676396184*^9, 3.7504197005232496`*^9}, { 3.7504199014205647`*^9, 3.7504199105731564`*^9}, 3.7504199674269505`*^9, { 3.75042000580826*^9, 3.7504200179820857`*^9}, {3.7504200623902054`*^9, 3.7504200725254693`*^9}, {3.7594891152396383`*^9, 3.759489154065875*^9}, { 3.7597145916194983`*^9, 3.759714665591065*^9}, {3.75971472891543*^9, 3.759714824916602*^9}, {3.7597148706987467`*^9, 3.759714947478797*^9}, { 3.7597150349307227`*^9, 3.7597151634794807`*^9}, {3.759715246935138*^9, 3.7597153062491665`*^9}, {3.7597153377190075`*^9, 3.7597153870577526`*^9}, {3.7597154590071197`*^9, 3.759715500272478*^9}, { 3.7597155491240797`*^9, 3.7597155760904846`*^9}, {3.7597156273541317`*^9, 3.75971569203012*^9}, {3.759715739514512*^9, 3.7597157580149326`*^9}, { 3.7597158013411117`*^9, 3.75971588340364*^9}, {3.759715927490775*^9, 3.7597160612515965`*^9}, {3.759716123477256*^9, 3.759716134998943*^9}, { 3.7597192931263885`*^9, 3.7597193363351936`*^9}, {3.7597193773167334`*^9, 3.759719404125424*^9}, {3.7597244593792834`*^9, 3.759724529395421*^9}, { 3.7597247902250433`*^9, 3.759724797335229*^9}, {3.7597248368354387`*^9, 3.7597248400493813`*^9}, {3.759727702871601*^9, 3.7597277380976105`*^9}, { 3.759727774307602*^9, 3.759727786273531*^9}, {3.759727871612993*^9, 3.7597278889996324`*^9}, 3.7597279993022413`*^9, {3.75973165307685*^9, 3.7597316585755997`*^9}, {3.7597317206705837`*^9, 3.759731738556853*^9}, { 3.759731825620432*^9, 3.759731856878929*^9}, {3.759735536137723*^9, 3.7597356755580835`*^9}, {3.759743445765726*^9, 3.759743450812235*^9}, 3.7597442184489155`*^9}, CellLabel-> "In[291]:=",ExpressionUUID->"0283d983-d817-46a5-b74b-efb5cf0d716b"] }, Closed]], Cell[CellGroupData[{ Cell["EXTRUDE defs", "Subsection", CellChangeTimes->{{3.6337757022685537`*^9, 3.6337757351784363`*^9}, { 3.734064727558645*^9, 3.73406474989952*^9}, {3.7451438105166326`*^9, 3.745143811840375*^9}, {3.7606070835401344`*^9, 3.760607098895162*^9}, { 3.760607554619519*^9, 3.7606075611760683`*^9}},ExpressionUUID->"e0a2ce5b-c393-42b9-ad19-\ 4b155e375583"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"extrude", " ", "a", " ", "cross"}], "-", RowBox[{"section", " ", "in", " ", "z"}], "-", "direction"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"EXTRUDE", "[", RowBox[{ RowBox[{"{", RowBox[{"nod_", ",", "crd_"}], "}"}], ",", RowBox[{"{", RowBox[{"ns_", ",", "np_"}], "}"}], ",", "L_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"nodout", ",", "crdout", ",", "offset", ",", "nnod"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"crdout", "=", RowBox[{"Table", "[", " ", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Append", "[", RowBox[{"#", ",", RowBox[{"L", "*", RowBox[{"ii", "/", RowBox[{"(", RowBox[{"np", "*", "ns"}], ")"}]}]}]}], "]"}], "&"}], ",", "crd"}], "]"}], ",", RowBox[{"{", RowBox[{"ii", ",", "0", ",", RowBox[{"np", "*", "ns"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"nnod", "=", RowBox[{"Max", "[", RowBox[{"Flatten", "[", RowBox[{"nod", " ", "/.", " ", RowBox[{ RowBox[{"Line", "[", "a_", "]"}], "\[Rule]", "a"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"offset", " ", "=", RowBox[{"Partition", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{"ii", ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", " ", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"np", "+", "1"}], ")"}], "*", "ns"}], "-", RowBox[{"(", RowBox[{"ns", "-", "1"}], ")"}]}]}], "}"}]}], "]"}], ",", RowBox[{"np", "+", "1"}], ",", "np"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"nodout", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"nod", " ", "/.", RowBox[{ RowBox[{"Line", "[", "a_", "]"}], "\[Rule]", RowBox[{"ELEMENT", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"a", "+", RowBox[{ RowBox[{"(", RowBox[{"ii", "-", "1"}], ")"}], "*", "nnod"}]}], ",", RowBox[{"{", RowBox[{"ii", ",", "off"}], "}"}]}], "]"}], "]"}]}]}], ",", RowBox[{"{", RowBox[{"off", ",", "offset"}], "}"}]}], "]"}], ",", "1"}], "]"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{"nodout", ",", "crdout"}], "}"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"extrude", " ", "a", " ", "cross"}], "-", RowBox[{"section", " ", "in", " ", "z"}], "-", "direction"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"EXTRUDE", "[", RowBox[{ RowBox[{"{", RowBox[{"nod_", ",", "crd_"}], "}"}], ",", "np_", ",", "z_List"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nodout", ",", "crdout", ",", "offset", ",", "nnod", ",", "ns"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"ns", "=", RowBox[{ RowBox[{"Length", "[", "z", "]"}], "-", "1"}]}], ";", "\[IndentingNewLine]", RowBox[{"crdout", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"Table", "[", " ", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Append", "[", RowBox[{"#", ",", RowBox[{ RowBox[{"z", "[", RowBox[{"[", "is", "]"}], "]"}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"z", "[", RowBox[{"[", RowBox[{"is", "+", "1"}], "]"}], "]"}], "-", RowBox[{"z", "[", RowBox[{"[", "is", "]"}], "]"}]}], ")"}], "*", RowBox[{"ii", "/", "np"}]}]}]}], "]"}], "&"}], ",", "crd"}], "]"}], ",", RowBox[{"{", RowBox[{"ii", ",", RowBox[{"If", "[", RowBox[{ RowBox[{"is", "==", "1"}], ",", "0", ",", "1"}], "]"}], ",", "np"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"is", ",", "1", ",", "ns"}], "}"}]}], "]"}], ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"nnod", "=", RowBox[{"Max", "[", RowBox[{"Flatten", "[", RowBox[{"nod", " ", "/.", " ", RowBox[{ RowBox[{"Line", "[", "a_", "]"}], "\[Rule]", "a"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"offset", " ", "=", RowBox[{"Partition", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{"ii", ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", " ", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"np", "+", "1"}], ")"}], "*", "ns"}], "-", RowBox[{"(", RowBox[{"ns", "-", "1"}], ")"}]}]}], "}"}]}], "]"}], ",", RowBox[{"np", "+", "1"}], ",", "np"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"nodout", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"nod", " ", "/.", RowBox[{ RowBox[{"Line", "[", "a_", "]"}], "\[Rule]", RowBox[{"ELEMENT", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"a", "+", RowBox[{ RowBox[{"(", RowBox[{"ii", "-", "1"}], ")"}], "*", "nnod"}]}], ",", RowBox[{"{", RowBox[{"ii", ",", "off"}], "}"}]}], "]"}], "]"}]}]}], ",", RowBox[{"{", RowBox[{"off", ",", "offset"}], "}"}]}], "]"}], ",", "1"}], "]"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{"nodout", ",", "crdout"}], "}"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.633673923685915*^9, 3.6336739535006204`*^9}, { 3.633674155068149*^9, 3.6336741996717005`*^9}, {3.6336745049841633`*^9, 3.6336745219741354`*^9}, {3.6336919593939404`*^9, 3.6336919775979815`*^9}, 3.633692380551029*^9, {3.6336927116599674`*^9, 3.633692727194856*^9}, { 3.635310826749509*^9, 3.6353108343419433`*^9}, {3.635311461613821*^9, 3.6353114619508405`*^9}, {3.7326759806780663`*^9, 3.7326760008674326`*^9}, {3.7326760331212645`*^9, 3.7326760385677853`*^9}, {3.732684137201784*^9, 3.73268419404665*^9}, { 3.732684306221466*^9, 3.7326843382153635`*^9}, 3.7326844699232764`*^9, { 3.7326845133861027`*^9, 3.73268452322455*^9}, {3.732759973190983*^9, 3.7327599776758347`*^9}, {3.7327613720703106`*^9, 3.7327614888170295`*^9}, {3.732761535853627*^9, 3.7327615404943867`*^9}, { 3.7327615972663317`*^9, 3.7327616122832594`*^9}, {3.7327616693361855`*^9, 3.73276183332095*^9}, {3.732761876700554*^9, 3.7327618790133*^9}, { 3.732761909063363*^9, 3.732761910469795*^9}, {3.73276200508918*^9, 3.732762006042756*^9}, {3.7327620750344048`*^9, 3.732762101490326*^9}, 3.7327688007102947`*^9, {3.7327705695330524`*^9, 3.7327705708254137`*^9}, { 3.732788507552166*^9, 3.7327885085870132`*^9}, {3.732788681344634*^9, 3.7327887090994544`*^9}, {3.732788743287696*^9, 3.73278879848213*^9}, { 3.732788922306119*^9, 3.7327889462731514`*^9}, {3.732789012151597*^9, 3.732789028200858*^9}, {3.7327890791192408`*^9, 3.732789086999034*^9}, { 3.732789135698248*^9, 3.7327891358892384`*^9}, {3.7327891989507074`*^9, 3.7327891993104925`*^9}, {3.733116709198372*^9, 3.733116731638229*^9}, { 3.7334931331412554`*^9, 3.7334932071522064`*^9}, {3.733493353668892*^9, 3.7334934953404007`*^9}, {3.733493581610343*^9, 3.733493589891471*^9}, { 3.7334936319789553`*^9, 3.7334936623392687`*^9}, {3.7334936935401745`*^9, 3.733493716917615*^9}, {3.7334937687375154`*^9, 3.733493799379287*^9}, { 3.7335602963276734`*^9, 3.7335603891038685`*^9}, {3.7337039222525787`*^9, 3.733703929721642*^9}, {3.7337040222462597`*^9, 3.7337040262631474`*^9}, { 3.733710121070121*^9, 3.733710122358057*^9}, 3.7337110885786676`*^9, 3.733711184948838*^9, {3.733711259729956*^9, 3.733711278366322*^9}, 3.7337113240271106`*^9, {3.733711384581702*^9, 3.733711436236964*^9}, 3.7337114809469175`*^9, {3.7337115173918333`*^9, 3.733711518879483*^9}, 3.733711560439453*^9, {3.733711609599924*^9, 3.7337116342722664`*^9}, { 3.733711689751358*^9, 3.7337116969119487`*^9}, {3.7337129879879694`*^9, 3.7337130014112797`*^9}, {3.733713172835663*^9, 3.733713173913886*^9}, { 3.7337132483436465`*^9, 3.7337132496094065`*^9}, {3.733713283003566*^9, 3.7337134200180254`*^9}, {3.733713464428997*^9, 3.7337135191222897`*^9}, { 3.7337135777847366`*^9, 3.73371367154463*^9}, {3.7337140009857264`*^9, 3.7337140458967295`*^9}, {3.733714091198394*^9, 3.7337141070440063`*^9}, { 3.733714143813529*^9, 3.733714146610505*^9}, {3.733721976862414*^9, 3.7337219813629093`*^9}, {3.733722281191476*^9, 3.7337222944429536`*^9}, { 3.733722382186266*^9, 3.7337223828425617`*^9}, {3.7337224624293957`*^9, 3.7337224858690815`*^9}, 3.7337225537825146`*^9, {3.733722654230641*^9, 3.733722661731436*^9}, {3.733722818999301*^9, 3.7337228267499514`*^9}, { 3.733723144924486*^9, 3.733723159691375*^9}, {3.733723196273369*^9, 3.733723198695795*^9}, {3.7337232377777586`*^9, 3.7337232408874655`*^9}, { 3.73372435111442*^9, 3.733724354067712*^9}, {3.7337244099801674`*^9, 3.733724433076069*^9}, {3.7337245236325226`*^9, 3.733724524679802*^9}, { 3.7337873724058084`*^9, 3.7337873841879997`*^9}, {3.7337879154409466`*^9, 3.7337879158316607`*^9}, {3.7340647908247976`*^9, 3.73406479426425*^9}, { 3.7340650184820967`*^9, 3.7340650196896086`*^9}, {3.7340717757289314`*^9, 3.734071783044138*^9}, 3.760607155346615*^9, {3.7606075704439325`*^9, 3.76060759034247*^9}}, CellLabel-> "In[296]:=",ExpressionUUID->"a5793423-1f61-46c4-b427-822da44b0f71"] }, Closed]], Cell[CellGroupData[{ Cell["TRIANGULATE defs", "Subsection", CellChangeTimes->{{3.7555369693812027`*^9, 3.7555369706487265`*^9}, { 3.784699941516708*^9, 3.7846999469147763`*^9}},ExpressionUUID->"a3eec395-d0e8-4965-9dc2-\ 7cbf7329b094"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"Needs", "[", "\"\\"", "]"}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"TRIANGULATE", "[", RowBox[{ RowBox[{"{", RowBox[{"seg_", ",", "crd_", ",", "mrk_"}], "}"}], ",", RowBox[{"{", RowBox[{"dms_", ",", "atr_", ",", "cns_"}], "}"}], ",", "a_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "inInst", ",", "outInst", ",", "crdout", ",", "polout", ",", "typout", ",", "segout", ",", "mrkout", ",", "str"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"set", " ", "it"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"inInst", "=", RowBox[{"TriangleCreate", "[", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetPoints", "[", RowBox[{"inInst", ",", "crd"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetSegments", "[", RowBox[{"inInst", ",", "seg"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetSegmentMarkers", "[", RowBox[{"inInst", ",", "mrk"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetRegions", "[", RowBox[{"inInst", ",", "dms", ",", " ", "atr", ",", " ", "cns"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"do", " ", "it"}], "*)"}], "\[IndentingNewLine]", RowBox[{"str", "=", RowBox[{"\"\\"", StyleBox["<>", "OperatorCharacter"], RowBox[{"ToString", "[", RowBox[{"1.", "*", "a"}], "]"}], StyleBox["<>", "OperatorCharacter"], "\"\\""}]}], ";", "\[IndentingNewLine]", RowBox[{"outInst", " ", "=", " ", RowBox[{"TriangleTriangulate", "[", RowBox[{"inInst", ",", "str"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", "extract", "*)"}], "\[IndentingNewLine]", RowBox[{"crdout", "=", " ", RowBox[{"TriangleGetPoints", "[", "outInst", "]"}]}], ";", RowBox[{"polout", "=", RowBox[{"TriangleGetElements", "[", "outInst", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"segout", "=", RowBox[{"TriangleGetSegments", "[", "outInst", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"mrkout", "=", RowBox[{"TriangleGetSegmentMarkers", "[", "outInst", "]"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"typout", "=", RowBox[{"Flatten", "[", RowBox[{"Round", "[", RowBox[{"TriangleGetElementAttributes", "[", "outInst", "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{ "crdout", ",", "polout", ",", "typout", ",", "segout", ",", "mrkout"}], "}"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"TRIANGULATE", "[", RowBox[{ RowBox[{"{", RowBox[{"seg_", ",", "mrk_"}], "}"}], ",", "crd_", ",", "a_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "inInst", ",", "outInst", ",", "crdout", ",", "eleout", ",", "segout", ",", "mrkout"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"set", " ", "it"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"inInst", "=", RowBox[{"TriangleCreate", "[", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetPoints", "[", RowBox[{"inInst", ",", "crd"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetSegments", "[", RowBox[{"inInst", ",", "seg"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetSegmentMarkers", "[", RowBox[{"inInst", ",", "mrk"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"do", " ", "it"}], "*)"}], "\[IndentingNewLine]", RowBox[{"str", "=", RowBox[{"\"\\"", StyleBox["<>", "OperatorCharacter"], RowBox[{"ToString", "[", RowBox[{"1.", "*", "a"}], "]"}], StyleBox["<>", "OperatorCharacter"], "\"\\""}]}], ";", "\[IndentingNewLine]", RowBox[{"outInst", " ", "=", " ", RowBox[{"TriangleTriangulate", "[", RowBox[{"inInst", ",", "str"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", "extract", "*)"}], "\[IndentingNewLine]", RowBox[{"crdout", "=", " ", RowBox[{"TriangleGetPoints", "[", "outInst", "]"}]}], ";", RowBox[{"eleout", "=", RowBox[{"TriangleGetElements", "[", "outInst", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"segout", "=", RowBox[{"TriangleGetSegments", "[", "outInst", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"mrkout", "=", RowBox[{"TriangleGetSegmentMarkers", "[", "outInst", "]"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"eleout", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Polygon", "[", "#", "]"}], "&"}], ",", "eleout"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{"crdout", ",", "eleout", ",", "segout", ",", "mrkout"}], "}"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"TRIANGULATE", "[", RowBox[{"{", RowBox[{"crd_", ",", "nod_"}], "}"}], "]"}], ":=", RowBox[{"TRIANGULATE", "[", RowBox[{ RowBox[{"nod", " ", "/.", RowBox[{ RowBox[{"Line", "[", "any_", "]"}], "\[Rule]", "any"}]}], ",", "crd"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"TRIANGULATE", "[", RowBox[{"seg_", ",", "crd_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"inInst", ",", "outInst", ",", "crdout", ",", "eleout"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"set", " ", "it"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"inInst", "=", RowBox[{"TriangleCreate", "[", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetPoints", "[", RowBox[{"inInst", ",", "crd"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetSegments", "[", RowBox[{"inInst", ",", "seg"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"do", " ", "it"}], "*)"}], "\[IndentingNewLine]", RowBox[{"outInst", " ", "=", " ", RowBox[{"TriangleTriangulate", "[", RowBox[{"inInst", ",", "\"\\""}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", "extract", "*)"}], "\[IndentingNewLine]", RowBox[{"crdout", "=", " ", RowBox[{"TriangleGetPoints", "[", "outInst", "]"}]}], ";", RowBox[{"eleout", "=", RowBox[{"TriangleGetElements", "[", "outInst", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"eleout", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Polygon", "[", "#", "]"}], "&"}], ",", "eleout"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{"crdout", ",", "eleout"}], "}"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"TRIANGULATE", "[", RowBox[{ RowBox[{"{", RowBox[{"crd_", ",", "nod_"}], "}"}], ",", "a_"}], "]"}], ":=", RowBox[{"TRIANGULATE", "[", RowBox[{ RowBox[{"nod", " ", "/.", RowBox[{ RowBox[{"Line", "[", "any_", "]"}], "\[Rule]", "any"}]}], ",", "crd", ",", "a"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"TRIANGULATE", "[", RowBox[{"seg_", ",", "crd_", ",", "a_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "inInst", ",", "outInst", ",", "crdout", ",", "eleout", ",", "str"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"set", " ", "it"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"inInst", "=", RowBox[{"TriangleCreate", "[", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetPoints", "[", RowBox[{"inInst", ",", "crd"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetSegments", "[", RowBox[{"inInst", ",", "seg"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"do", " ", "it"}], "*)"}], "\[IndentingNewLine]", RowBox[{"str", "=", RowBox[{"\"\\"", StyleBox["<>", "OperatorCharacter"], RowBox[{"ToString", "[", RowBox[{"1.", "*", "a"}], "]"}], StyleBox["<>", "OperatorCharacter"], "\"\\""}]}], ";", "\[IndentingNewLine]", RowBox[{"outInst", " ", "=", " ", RowBox[{"TriangleTriangulate", "[", RowBox[{"inInst", ",", "str"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", "extract", "*)"}], "\[IndentingNewLine]", RowBox[{"crdout", "=", " ", RowBox[{"TriangleGetPoints", "[", "outInst", "]"}]}], ";", RowBox[{"eleout", "=", RowBox[{"TriangleGetElements", "[", "outInst", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"eleout", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Polygon", "[", "#", "]"}], "&"}], ",", "eleout"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{"crdout", ",", "eleout"}], "}"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"TRIANGULATE", "[", RowBox[{ RowBox[{"{", RowBox[{"crd_", ",", "nod_"}], "}"}], ",", RowBox[{"{", RowBox[{"dms_", ",", "atr_", ",", "cns_"}], "}"}]}], "]"}], ":=", RowBox[{"TRIANGULATE", "[", RowBox[{ RowBox[{"nod", " ", "/.", RowBox[{ RowBox[{"Line", "[", "any_", "]"}], "\[Rule]", "any"}]}], ",", "crd", ",", RowBox[{"{", RowBox[{"dms", ",", "atr", ",", "cns"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"TRIANGULATE", "[", RowBox[{"seg_", ",", "crd_", ",", RowBox[{"{", RowBox[{"dms_", ",", "atr_", ",", "cns_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "inInst", ",", "outInst", ",", "crdout", ",", "polout", ",", "typout"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"set", " ", "it"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"inInst", "=", RowBox[{"TriangleCreate", "[", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetPoints", "[", RowBox[{"inInst", ",", "crd"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetSegments", "[", RowBox[{"inInst", ",", "seg"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetRegions", "[", RowBox[{"inInst", ",", "dms", ",", " ", "atr", ",", " ", "cns"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"do", " ", "it"}], "*)"}], "\[IndentingNewLine]", RowBox[{"outInst", " ", "=", " ", RowBox[{"TriangleTriangulate", "[", RowBox[{"inInst", ",", "\"\\""}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", "extract", "*)"}], "\[IndentingNewLine]", RowBox[{"crdout", "=", " ", RowBox[{"TriangleGetPoints", "[", "outInst", "]"}]}], ";", RowBox[{"polout", "=", RowBox[{"TriangleGetElements", "[", "outInst", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"polout", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Polygon", "[", "#", "]"}], "&"}], ",", "polout"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"typout", "=", RowBox[{"Flatten", "[", RowBox[{"Round", "[", RowBox[{"TriangleGetElementAttributes", "[", "outInst", "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{"crdout", ",", "polout", ",", "typout"}], "}"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"TRIANGULATE", "[", RowBox[{ RowBox[{"{", RowBox[{"crd_", ",", "nod_"}], "}"}], ",", RowBox[{"{", RowBox[{"dms_", ",", "atr_", ",", "cns_"}], "}"}], ",", "a_"}], "]"}], ":=", RowBox[{"TRIANGULATE", "[", RowBox[{ RowBox[{"nod", " ", "/.", RowBox[{ RowBox[{"Line", "[", "any_", "]"}], "\[Rule]", "any"}]}], ",", "crd", ",", RowBox[{"{", RowBox[{"dms", ",", "atr", ",", "cns"}], "}"}], ",", "a"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"TRIANGULATE", "[", RowBox[{"seg_", ",", "crd_", ",", RowBox[{"{", RowBox[{"dms_", ",", "atr_", ",", "cns_"}], "}"}], ",", "a_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "inInst", ",", "outInst", ",", "crdout", ",", "polout", ",", "typout", ",", "str"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"set", " ", "it"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"inInst", "=", RowBox[{"TriangleCreate", "[", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetPoints", "[", RowBox[{"inInst", ",", "crd"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetSegments", "[", RowBox[{"inInst", ",", "seg"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetRegions", "[", RowBox[{"inInst", ",", "dms", ",", " ", "atr", ",", " ", "cns"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"do", " ", "it"}], "*)"}], "\[IndentingNewLine]", RowBox[{"str", "=", RowBox[{"\"\\"", StyleBox["<>", "OperatorCharacter"], RowBox[{"ToString", "[", RowBox[{"1.", "*", "a"}], "]"}], StyleBox["<>", "OperatorCharacter"], "\"\\""}]}], ";", "\[IndentingNewLine]", RowBox[{"outInst", " ", "=", " ", RowBox[{"TriangleTriangulate", "[", RowBox[{"inInst", ",", "str"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", "extract", "*)"}], "\[IndentingNewLine]", RowBox[{"crdout", "=", " ", RowBox[{"TriangleGetPoints", "[", "outInst", "]"}]}], ";", RowBox[{"polout", "=", RowBox[{"TriangleGetElements", "[", "outInst", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"polout", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Polygon", "[", "#", "]"}], "&"}], ",", "polout"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"typout", "=", RowBox[{"Flatten", "[", RowBox[{"Round", "[", RowBox[{"TriangleGetElementAttributes", "[", "outInst", "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{"crdout", ",", "polout", ",", "typout"}], "}"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"TRIANGULATE", "[", RowBox[{"seg_", ",", "crd_", ",", RowBox[{"{", RowBox[{"dms_", ",", "atr_", ",", "cns_", ",", "hls_"}], "}"}], ",", "a_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "inInst", ",", "outInst", ",", "crdout", ",", "polout", ",", "typout", ",", "str"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"set", " ", "it"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"inInst", "=", RowBox[{"TriangleCreate", "[", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetPoints", "[", RowBox[{"inInst", ",", "crd"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetSegments", "[", RowBox[{"inInst", ",", "seg"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetRegions", "[", RowBox[{"inInst", ",", "dms", ",", " ", "atr", ",", " ", "cns"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"TriangleSetHoles", "[", RowBox[{"inInst", ",", " ", "hls"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"do", " ", "it"}], "*)"}], "\[IndentingNewLine]", RowBox[{"str", "=", RowBox[{"\"\\"", StyleBox["<>", "OperatorCharacter"], RowBox[{"ToString", "[", RowBox[{"1.", "*", "a"}], "]"}], StyleBox["<>", "OperatorCharacter"], "\"\\""}]}], ";", "\[IndentingNewLine]", RowBox[{"outInst", " ", "=", " ", RowBox[{"TriangleTriangulate", "[", RowBox[{"inInst", ",", "str"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", "extract", "*)"}], "\[IndentingNewLine]", RowBox[{"crdout", "=", " ", RowBox[{"TriangleGetPoints", "[", "outInst", "]"}]}], ";", RowBox[{"polout", "=", RowBox[{"TriangleGetElements", "[", "outInst", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"polout", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Polygon", "[", "#", "]"}], "&"}], ",", "polout"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"typout", "=", RowBox[{"Flatten", "[", RowBox[{"Round", "[", RowBox[{"TriangleGetElementAttributes", "[", "outInst", "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{"polout", ",", "crdout", ",", "typout"}], "}"}], "]"}]}]}], "]"}]}], ";"}]}], "Input", InitializationCell->True, CellChangeTimes->{ 3.443930973126174*^9, {3.4771023549018*^9, 3.4771023808445997`*^9}, { 3.4771024577682*^9, 3.4771025046618*^9}, {3.4771063565654*^9, 3.4771063705898*^9}, 3.4771089762209997`*^9, 3.477109006645*^9, { 3.4771109395810003`*^9, 3.4771109526226*^9}, {3.477110989427*^9, 3.4771110302522*^9}, {3.4771110800372*^9, 3.4771111191308002`*^9}, { 3.4771220486066*^9, 3.4771220663286*^9}, {3.4771317865394*^9, 3.4771318192214003`*^9}, {3.4771323345362*^9, 3.477132377639*^9}, { 3.630489883760623*^9, 3.630489885414226*^9}, {3.631409232246135*^9, 3.631409318077486*^9}, {3.6314094294772816`*^9, 3.631409430304083*^9}, { 3.6314095931215687`*^9, 3.6314095963195744`*^9}, {3.6314105089523773`*^9, 3.631410515504389*^9}, 3.631435133305333*^9, {3.631435355203025*^9, 3.6314353561500793`*^9}, 3.6314356018121305`*^9, 3.631435754368856*^9, 3.631435796315255*^9, {3.63143606319652*^9, 3.631436069549884*^9}, { 3.6347884698816414`*^9, 3.63478847685104*^9}, {3.6347954098385844`*^9, 3.6347954141598315`*^9}, {3.6347956603329115`*^9, 3.634795675947805*^9}, { 3.634796217815798*^9, 3.6347962287334223`*^9}, {3.6347962930030985`*^9, 3.6347963097820582`*^9}, {3.63479634495407*^9, 3.6347963538665795`*^9}, { 3.6347967044436316`*^9, 3.6347967222076473`*^9}, {3.6348910182399282`*^9, 3.6348910703229065`*^9}, {3.634891202082443*^9, 3.63489120569665*^9}, { 3.635129073304618*^9, 3.6351290927607307`*^9}, {3.6351291514160852`*^9, 3.6351291562713633`*^9}, {3.6351296027379*^9, 3.635129640630067*^9}, { 3.6351296766311264`*^9, 3.6351296770091476`*^9}, {3.635133864772954*^9, 3.6351340703167105`*^9}, {3.635134178738912*^9, 3.635134204883407*^9}, { 3.6351532590142465`*^9, 3.6351534908115044`*^9}, {3.6353108694909534`*^9, 3.635310875829316*^9}, {3.657768370048919*^9, 3.6577683714841213`*^9}, { 3.6853593982958508`*^9, 3.6853593994858527`*^9}, 3.685359462505941*^9, { 3.685359541326051*^9, 3.685359573806097*^9}, {3.6874387445294027`*^9, 3.687438822019511*^9}, 3.6874389450596833`*^9, {3.6874389956197543`*^9, 3.6874390405998173`*^9}, {3.6874391238499336`*^9, 3.6874391937200317`*^9}, {3.6874392244700747`*^9, 3.687439453750396*^9}, { 3.687439572800562*^9, 3.68743958546058*^9}, {3.68743962102063*^9, 3.687439653600675*^9}, {3.6874397535808153`*^9, 3.6874397667108335`*^9}, 3.6874457948947306`*^9, {3.6874461481952252`*^9, 3.6874461564952374`*^9}, { 3.6876686346644025`*^9, 3.6876686478844213`*^9}, {3.6876686911644816`*^9, 3.687668823124666*^9}, {3.687668960604859*^9, 3.6876691302750964`*^9}, { 3.687669356755413*^9, 3.6876695631957026`*^9}, {3.68766976165598*^9, 3.687669770715993*^9}, {3.6876724948642445`*^9, 3.687672495474246*^9}, { 3.687672580794365*^9, 3.6876727153745537`*^9}, {3.687672853854748*^9, 3.6876729332848587`*^9}, {3.6876729722949133`*^9, 3.6876731124151096`*^9}, {3.687673280685345*^9, 3.687673411335528*^9}, 3.6879313344746327`*^9, {3.687931387314707*^9, 3.6879314004147253`*^9}, { 3.6879314569548044`*^9, 3.6879314600748086`*^9}, {3.687931618845031*^9, 3.687931690255131*^9}, {3.687931744255206*^9, 3.6879317511352158`*^9}, { 3.6879317991852837`*^9, 3.6879318101552987`*^9}, {3.6879318528753586`*^9, 3.687931875785391*^9}, {3.6880321738474593`*^9, 3.688032324857671*^9}, { 3.68811073769691*^9, 3.68811083105704*^9}, {3.688182194807842*^9, 3.6881822090088615`*^9}, {3.6881823158700113`*^9, 3.6881824932602596`*^9}, {3.6881827603406334`*^9, 3.688182807210699*^9}, { 3.6881829158708515`*^9, 3.68818292930087*^9}, {3.688182999800969*^9, 3.6881831324711547`*^9}, {3.688183628661849*^9, 3.6881836750819144`*^9}, { 3.688211059016615*^9, 3.6882111198466997`*^9}, {3.6882111896067977`*^9, 3.6882112272568502`*^9}, {3.688211687127494*^9, 3.688211814657673*^9}, { 3.688211854527728*^9, 3.6882118603977365`*^9}, {3.6882139698004313`*^9, 3.68821399050046*^9}, {3.68821420020687*^9, 3.688214201756872*^9}, 3.6882144390772047`*^9, {3.6882146560475082`*^9, 3.6882146684575257`*^9}, { 3.688214751567642*^9, 3.6882147680976653`*^9}, {3.688214804297716*^9, 3.6882149595979333`*^9}, {3.6882150203480186`*^9, 3.6882152133382883`*^9}, {3.6882152437383313`*^9, 3.688215312948428*^9}, 3.6882155446087523`*^9, {3.688540867416464*^9, 3.688540868276465*^9}, { 3.688540923456542*^9, 3.688540987616632*^9}, {3.689509628603777*^9, 3.6895096840119457`*^9}, 3.6895097148397093`*^9, {3.689568676097738*^9, 3.689568771827872*^9}, {3.689737582567273*^9, 3.689737610517312*^9}, { 3.689738148338065*^9, 3.689738254678214*^9}, {3.689738292788267*^9, 3.689738346768343*^9}, {3.6897387257888737`*^9, 3.6897388179090023`*^9}, { 3.6898585271206756`*^9, 3.689858545170701*^9}, {3.6898585824607525`*^9, 3.689858769851015*^9}, {3.6940970096156654`*^9, 3.6940970747057567`*^9}, 3.6941413988145113`*^9, {3.694354094868929*^9, 3.6943541832790527`*^9}, { 3.694920239046096*^9, 3.694920319576208*^9}, {3.6949203962063155`*^9, 3.694920412426338*^9}, {3.6949204882764444`*^9, 3.6949204937164516`*^9}, 3.6949205606465454`*^9, {3.695100444594348*^9, 3.6951004570843654`*^9}, { 3.6973395634474907`*^9, 3.69733958428752*^9}, {3.697985422771953*^9, 3.6979855230120935`*^9}, {3.697985573722165*^9, 3.697985597992199*^9}, { 3.6979856429622617`*^9, 3.6979856711723013`*^9}, {3.7244643325478783`*^9, 3.724464348643357*^9}, {3.724467403856756*^9, 3.724467437838467*^9}, { 3.7244675479335804`*^9, 3.724467563230343*^9}, 3.7244676966368866`*^9, { 3.724467772264612*^9, 3.724467824163081*^9}, {3.7244678625415535`*^9, 3.724467863396864*^9}, {3.724468018783759*^9, 3.72446802144991*^9}, { 3.7244681559004545`*^9, 3.7244681850540376`*^9}, {3.724468459327367*^9, 3.724468483652465*^9}, {3.7244686219080153`*^9, 3.7244687024486265`*^9}, { 3.7244712391235456`*^9, 3.7244712430734224`*^9}, {3.7244712821065245`*^9, 3.724471282307459*^9}, {3.7244718283139167`*^9, 3.724471852982109*^9}, { 3.7245109260422964`*^9, 3.7245109717411103`*^9}, {3.7254180257070103`*^9, 3.725418132591786*^9}, {3.725418186497287*^9, 3.725418198564393*^9}, { 3.725418240702896*^9, 3.7254182427078333`*^9}, 3.7254182729821267`*^9, { 3.7254183742147875`*^9, 3.72541838162965*^9}, {3.7254184135842233`*^9, 3.7254184150237846`*^9}, {3.725418877464322*^9, 3.7254189569953265`*^9}, { 3.725418994143058*^9, 3.725419023781932*^9}, {3.7254193126441193`*^9, 3.725419396185589*^9}, {3.725432214366968*^9, 3.725432235836476*^9}, { 3.7254322894678383`*^9, 3.725432377695853*^9}, {3.726401253407773*^9, 3.7264012633218203`*^9}, {3.726401405512204*^9, 3.7264014071162825`*^9}, { 3.7264014439323297`*^9, 3.7264014462981124`*^9}, {3.726401485648699*^9, 3.7264016429140606`*^9}, {3.726401682872032*^9, 3.726401718837957*^9}, { 3.726401899357152*^9, 3.7264019010212574`*^9}, {3.7264019889732013`*^9, 3.726401991903804*^9}, {3.7264021595991826`*^9, 3.7264021616913195`*^9}, { 3.726402447890601*^9, 3.726402463475356*^9}, {3.747040699533342*^9, 3.7470408363290567`*^9}, {3.7471061663693695`*^9, 3.747106214420479*^9}, { 3.7471067469638214`*^9, 3.747106834372692*^9}, {3.7471068959871335`*^9, 3.747106915079779*^9}, {3.7471069588898473`*^9, 3.747106998742816*^9}, 3.747107044736511*^9, {3.747107087544964*^9, 3.7471070893575435`*^9}, { 3.7471138002489843`*^9, 3.747113811418234*^9}, {3.7471138500028563`*^9, 3.747113892211589*^9}, 3.747114310142033*^9, {3.7471143424625273`*^9, 3.747114343868453*^9}, {3.7471148744458303`*^9, 3.747114931572899*^9}, { 3.74711503534515*^9, 3.747115041218787*^9}, {3.7471156330947733`*^9, 3.7471156387028475`*^9}, {3.747116431240279*^9, 3.7471164335522423`*^9}, { 3.7471164808222904`*^9, 3.7471166104321785`*^9}, {3.747116647876696*^9, 3.7471167102835293`*^9}, {3.74865997476248*^9, 3.7486600101981816`*^9}, { 3.748660042393119*^9, 3.748660069138746*^9}, {3.748660177148834*^9, 3.748660251952998*^9}, {3.7486604981713724`*^9, 3.748660508798976*^9}, { 3.7486929231374454`*^9, 3.7486929342382526`*^9}, {3.7486929737776747`*^9, 3.7486929903337507`*^9}, {3.7486930264117804`*^9, 3.7486931799453707`*^9}, {3.748693249361241*^9, 3.7486932724173203`*^9}, 3.7486933276281357`*^9, 3.7486939237519407`*^9, {3.7486939698417687`*^9, 3.7486939700127883`*^9}, {3.748694008103215*^9, 3.7486940757142344`*^9}, { 3.7486942326282196`*^9, 3.748694304005413*^9}, {3.748695188924658*^9, 3.748695190701332*^9}, {3.7486952252639275`*^9, 3.7486953104760585`*^9}, { 3.748695384723056*^9, 3.748695811151685*^9}, {3.7486958766029434`*^9, 3.7486959097256002`*^9}, {3.7486964229653544`*^9, 3.7486964578684864`*^9}, 3.7487454821763644`*^9, {3.754056041592442*^9, 3.754056060140006*^9}, { 3.754056347029888*^9, 3.754056351327733*^9}, {3.754056854382514*^9, 3.754056862089791*^9}, {3.7540569630968127`*^9, 3.7540569674225426`*^9}, { 3.7540570759551015`*^9, 3.7540570801772118`*^9}, {3.754057135076915*^9, 3.754057152630065*^9}, {3.7540571929041653`*^9, 3.754057236529367*^9}, { 3.754057397662035*^9, 3.7540574231277227`*^9}, {3.7540574560189123`*^9, 3.754057472695193*^9}, {3.754057518721182*^9, 3.754057583163235*^9}, 3.754057631189864*^9, {3.7540576696626444`*^9, 3.754057832330846*^9}, { 3.7540578903947163`*^9, 3.7540579289766736`*^9}, {3.7540580507949033`*^9, 3.7540580513826957`*^9}, {3.7540978904321117`*^9, 3.7540979191340885`*^9}, {3.7540979931579046`*^9, 3.7540979999909244`*^9}, {3.7540980363245296`*^9, 3.754098095196913*^9}, { 3.7540981279820137`*^9, 3.75409817510705*^9}, {3.7540983080840054`*^9, 3.7540983887416687`*^9}, {3.754098433086689*^9, 3.7540984487715254`*^9}, { 3.754098518107086*^9, 3.7540985418746586`*^9}, {3.7540985740895276`*^9, 3.7540985855956683`*^9}, {3.7540986329334645`*^9, 3.754098651832582*^9}, 3.754098694943287*^9, {3.7540987996641817`*^9, 3.7540988293199515`*^9}, { 3.754098922368672*^9, 3.754098946956335*^9}, {3.7541009656118875`*^9, 3.754100966064907*^9}, {3.7541260794470377`*^9, 3.754126112298939*^9}, { 3.7541261993178277`*^9, 3.7541263394250636`*^9}, {3.7541264153576813`*^9, 3.754126455276905*^9}, {3.7541264972202415`*^9, 3.754126628008542*^9}, { 3.7541266613158674`*^9, 3.754126719835323*^9}, 3.7541267961648273`*^9, { 3.754126828833903*^9, 3.754126890819979*^9}, {3.754126943227796*^9, 3.754127112269927*^9}, {3.7541271553116074`*^9, 3.7541271992360067`*^9}, { 3.754127253229822*^9, 3.754127273225658*^9}, {3.754127329226965*^9, 3.7541273643065696`*^9}, {3.7541277175880594`*^9, 3.754127721159455*^9}, { 3.754127900093892*^9, 3.754127900428954*^9}, {3.7555365688081875`*^9, 3.7555368169423947`*^9}, {3.7566194252966633`*^9, 3.756619503340211*^9}, { 3.7606073727611165`*^9, 3.7606074044677906`*^9}, {3.7639037635827665`*^9, 3.7639039669013567`*^9}, {3.7639040036658916`*^9, 3.7639040352749486`*^9}, {3.7639041491982164`*^9, 3.7639041498420076`*^9}, {3.7641295066295767`*^9, 3.7641296291063385`*^9}, 3.7641297671450467`*^9, {3.764129842917159*^9, 3.76412986403855*^9}, { 3.7641299539495287`*^9, 3.7641299638308244`*^9}, {3.764130242057335*^9, 3.764130264998592*^9}, {3.7641304121561837`*^9, 3.764130517277567*^9}, { 3.764905400658563*^9, 3.764905448073204*^9}, {3.7661917992707295`*^9, 3.7661918111029887`*^9}, {3.7661937058475633`*^9, 3.7661937308527126`*^9}, {3.766288732159727*^9, 3.7662887421574078`*^9}, 3.7741665150318885`*^9, {3.774166583333705*^9, 3.7741666346924067`*^9}, { 3.7741666777885046`*^9, 3.7741667276801615`*^9}, {3.7741681843844967`*^9, 3.774168277409542*^9}, {3.774237957645171*^9, 3.7742379961381702`*^9}, { 3.774238228752078*^9, 3.7742383203485446`*^9}, {3.7742384167748957`*^9, 3.774238438885627*^9}, {3.774238499096892*^9, 3.7742385555597315`*^9}, { 3.7742385931019473`*^9, 3.774238669464537*^9}, {3.774239332037335*^9, 3.774239458024664*^9}, {3.7742396127858567`*^9, 3.7742396524321165`*^9}, { 3.774239693440149*^9, 3.774239749194436*^9}, {3.774239781513965*^9, 3.7742399183443785`*^9}, {3.774239993088747*^9, 3.7742399984000196`*^9}, { 3.774240080591405*^9, 3.7742403502486305`*^9}, {3.7742403925474215`*^9, 3.7742406200754595`*^9}, {3.7742406536016474`*^9, 3.774240771836528*^9}, { 3.774240802985832*^9, 3.7742408207850018`*^9}, {3.7742408510511465`*^9, 3.7742409420304427`*^9}, 3.7742409770366917`*^9, {3.7742410127101192`*^9, 3.774241115672659*^9}, {3.7742411489763308`*^9, 3.7742412065999565`*^9}, { 3.7751895563614497`*^9, 3.775189557474781*^9}, {3.7751896076191764`*^9, 3.7751897799276996`*^9}, {3.777096408797056*^9, 3.7770964403195615`*^9}, { 3.777096485036745*^9, 3.7770965029912896`*^9}, 3.7847000290779285`*^9, { 3.7866769257536707`*^9, 3.7866769613037777`*^9}, {3.7873053599413404`*^9, 3.7873054240368595`*^9}, {3.78730664769903*^9, 3.7873066512662177`*^9}, { 3.7873066825368905`*^9, 3.787306955112986*^9}, {3.787307227184967*^9, 3.787307234638444*^9}, {3.787307265472159*^9, 3.787307267764142*^9}, { 3.7873080496920834`*^9, 3.7873080627577534`*^9}, {3.787313297531843*^9, 3.787313308431161*^9}, 3.7873133927244625`*^9, 3.787628244885955*^9, 3.787651422801089*^9, {3.787651471253007*^9, 3.787651471569529*^9}, { 3.7876536890179644`*^9, 3.7876536899407806`*^9}, {3.843283788165268*^9, 3.8432838872123113`*^9}, {3.843283923901783*^9, 3.843283925305036*^9}, { 3.8432839713240523`*^9, 3.8432840064768605`*^9}, {3.8432847051109915`*^9, 3.8432847055104575`*^9}}, CellLabel-> "In[298]:=",ExpressionUUID->"f52ed36f-c8fe-4fa7-9a38-2db375a610e7"] }, Closed]], Cell[CellGroupData[{ Cell["STANDARDFORM ETC. defs", "Subsection", CellChangeTimes->{{3.687518097184434*^9, 3.687518099119545*^9}, { 3.8223704779241266`*^9, 3.8223704849224677`*^9}, {3.847105064772148*^9, 3.8471050666839848`*^9}},ExpressionUUID->"1a20d09c-0a54-45c1-8947-\ 5b7037e80b9a"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"MEC", "-", "E1050", "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"STANDARDFORM", "[", "\[Delta]W_", "]"}], ":=", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", "\[Delta]W"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", "\[Delta]W_"}], "]"}], ":=", " ", RowBox[{"Print", "[", RowBox[{"\"\<\[Delta]W = -\>\"", ",", SuperscriptBox[ RowBox[{"MatrixForm", "[", RowBox[{"\[Delta]DOFS", "[", "\[Delta]W", "]"}], "]"}], "T"], ",", "\"\<(\>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{"-", RowBox[{"D", "[", RowBox[{ RowBox[{"D", "[", RowBox[{"\[Delta]W", ",", RowBox[{"{", RowBox[{"\[Delta]DOFS", "[", "\[Delta]W", "]"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"DOFS", "[", "\[Delta]W", "]"}], "}"}]}], "]"}]}], "]"}], "]"}], ",", "\[IndentingNewLine]", "\"\<\>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"DOFS", "[", "\[Delta]W", "]"}], "]"}], ",", "\"\<-\>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"D", "[", RowBox[{"\[Delta]W", ",", RowBox[{"{", RowBox[{"\[Delta]DOFS", "[", "\[Delta]W", "]"}], "}"}]}], "]"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{ RowBox[{"DOFS", "[", "\[Delta]W", "]"}], "\[Rule]", "0"}], "]"}]}], "]"}], "]"}], ",", "\"\<)\>\""}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}], "]"}], ":=", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ELEMENTFORM", "[", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}], "]"}], ":=", RowBox[{"ELEMENTFORM", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ELEMENTFORM", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]WW", ",", "dof", ",", "\[Delta]dof", ",", "equ", ",", "frule", ",", "ind", ",", "\[Delta]ind"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WW", "=", RowBox[{"Simplify", "[", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"ind", " ", "=", RowBox[{"Union", "[", RowBox[{"dof", " ", "/.", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"uX", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"ux", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"uY", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"uy", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"uZ", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"uz", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Theta]X", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Theta]x", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Theta]Y", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Theta]y", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Theta]Z", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Theta]z", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"Flatten", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", " ", RowBox[{ RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"uX", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"ux", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"uY", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"uy", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"uZ", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"uz", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"\[Theta]X", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"\[Theta]x", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"\[Theta]Y", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"\[Theta]y", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"\[Theta]Z", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"\[Theta]z", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "ind"}], "}"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]ind", " ", "=", RowBox[{"Union", "[", RowBox[{"\[Delta]dof", " ", "/.", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"\[Delta]uX", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]ux", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]uY", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]uy", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]uZ", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]uz", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]\[Theta]X", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]\[Theta]Y", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]\[Theta]Z", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]dof", "=", RowBox[{"Flatten", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", " ", RowBox[{ RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]uX", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]ux", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]uY", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]uy", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]uZ", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]uz", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]\[Theta]X", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]\[Theta]Y", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]\[Theta]Z", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "\[Delta]ind"}], "}"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"frule", " ", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"\[Delta]uX", "[", "any__", "]"}], "\[Rule]", RowBox[{"FX", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"\[Delta]ux", "[", "any__", "]"}], "\[Rule]", RowBox[{"Fx", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"\[Delta]uY", "[", "any__", "]"}], "\[Rule]", RowBox[{"FY", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"\[Delta]uy", "[", "any__", "]"}], "\[Rule]", RowBox[{"Fy", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"\[Delta]uZ", "[", "any__", "]"}], "\[Rule]", RowBox[{"FZ", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"\[Delta]uz", "[", "any__", "]"}], "\[Rule]", RowBox[{"Fz", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"\[Delta]\[Theta]X", "[", "any__", "]"}], "\[Rule]", RowBox[{"MX", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", "any__", "]"}], "\[Rule]", RowBox[{"Mx", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"\[Delta]\[Theta]Y", "[", "any__", "]"}], "\[Rule]", RowBox[{"MY", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "any__", "]"}], "\[Rule]", RowBox[{"My", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"\[Delta]\[Theta]Z", "[", "any__", "]"}], "\[Rule]", RowBox[{"MZ", "[", "any", "]"}]}], ",", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "any__", "]"}], "\[Rule]", RowBox[{"Mz", "[", "any", "]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{ RowBox[{"MatrixForm", "[", RowBox[{"\[Delta]dof", " ", "/.", "frule"}], "]"}], ",", "\"\< = \>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{"-", RowBox[{"D", "[", RowBox[{ RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}], ",", RowBox[{"{", "dof", "}"}]}], "]"}]}], "]"}], "]"}], ",", "\[IndentingNewLine]", "\"\<\>\"", ",", RowBox[{"MatrixForm", "[", "dof", "]"}], ",", "\"\<-\>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"dof", "\[Rule]", "0"}], "]"}]}], "]"}], "]"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]WW", ",", "dof", ",", "\[Delta]dof", ",", "equ", ",", "ind", ",", "\[Delta]ind"}], " ", "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WW", "=", RowBox[{"Simplify", "[", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"ind", " ", "=", RowBox[{"Union", "[", RowBox[{"dof", " ", "/.", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"uX", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"ux", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"uY", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"uy", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"uZ", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"uz", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Theta]X", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Theta]x", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Theta]Y", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Theta]y", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Theta]Z", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Theta]z", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"Flatten", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", " ", RowBox[{ RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"uX", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"ux", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"uY", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"uy", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"uZ", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"uz", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"\[Theta]X", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"\[Theta]x", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"\[Theta]Y", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"\[Theta]y", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"\[Theta]Z", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Cases", "[", RowBox[{"dof", ",", RowBox[{"\[Theta]z", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "ind"}], "}"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]ind", " ", "=", RowBox[{"Union", "[", RowBox[{"\[Delta]dof", " ", "/.", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"\[Delta]uX", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]ux", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]uY", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]uy", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]uZ", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]uz", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]\[Theta]X", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]\[Theta]x", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]\[Theta]Y", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]\[Theta]Z", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}], ",", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "any__", "]"}], "\[Rule]", RowBox[{"{", "any", "}"}]}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]dof", "=", RowBox[{"Flatten", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", " ", RowBox[{ RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]uX", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]ux", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]uY", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]uy", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]uZ", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]uz", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]\[Theta]X", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]\[Theta]x", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]\[Theta]Y", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]\[Theta]y", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]\[Theta]Z", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Cases", "[", RowBox[{"\[Delta]dof", ",", RowBox[{"\[Delta]\[Theta]z", "[", RowBox[{"i", " ", "/.", RowBox[{"List", "\[Rule]", "Sequence"}]}], "]"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "\[Delta]ind"}], "}"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"\"\<\[Delta]W = -\>\"", ",", SuperscriptBox[ RowBox[{"MatrixForm", "[", "\[Delta]dof", "]"}], "T"], ",", "\"\<(\>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{"-", RowBox[{"D", "[", RowBox[{ RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}], ",", RowBox[{"{", "dof", "}"}]}], "]"}]}], "]"}], "]"}], ",", "\[IndentingNewLine]", "\"\<\>\"", ",", RowBox[{"MatrixForm", "[", "dof", "]"}], ",", "\"\<-\>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"dof", "\[Rule]", "0"}], "]"}]}], "]"}], "]"}], ",", "\"\<)\>\""}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]WW", ",", "dof", ",", "\[Delta]dof", ",", "equ", ",", "ind", ",", "\[Delta]ind"}], " ", "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WW", "=", RowBox[{"Simplify", "[", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"\"\<\[Delta]W = -\>\"", ",", SuperscriptBox[ RowBox[{"MatrixForm", "[", "\[Delta]dof", "]"}], "T"], ",", "\"\<(\>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{"-", RowBox[{"D", "[", RowBox[{ RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}], ",", RowBox[{"{", "dof", "}"}]}], "]"}]}], "]"}], "]"}], ",", "\[IndentingNewLine]", "\"\<\>\"", ",", RowBox[{"MatrixForm", "[", "dof", "]"}], ",", "\"\<-\>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"dof", "\[Rule]", "0"}], "]"}]}], "]"}], "]"}], ",", "\"\<)\>\""}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]WW", ",", "dof", ",", "\[Delta]dof", ",", "equ", ",", "ind", ",", "\[Delta]ind"}], " ", "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WW", "=", RowBox[{"Simplify", "[", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"TMEC", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"\"\<\[Delta]W = -\>\"", ",", SuperscriptBox[ RowBox[{"MatrixForm", "[", "\[Delta]dof", "]"}], "T"], ",", "\"\<(\>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{"-", RowBox[{"D", "[", RowBox[{ RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}], ",", RowBox[{"{", "dof", "}"}]}], "]"}]}], "]"}], "]"}], ",", "\[IndentingNewLine]", "\"\<\>\"", ",", RowBox[{"MatrixForm", "[", "dof", "]"}], ",", "\"\<-\>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{"dof", "\[Rule]", "0"}], "]"}]}], "]"}], "]"}], ",", "\"\<)\>\""}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", RowBox[{"EVENT", ",", RowBox[{"{", RowBox[{"s0_", ",", "sol0_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"\[Delta]WW", ",", "dof", ",", "\[Delta]dof", ",", "equ"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WW", "=", RowBox[{"Simplify", "[", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"Simplify", "[", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"\"\<\[Delta]W = -\>\"", ",", SuperscriptBox[ RowBox[{"MatrixForm", "[", "\[Delta]dof", "]"}], "T"], ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", "equ", "]"}], "]"}]}], " ", "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", "\[Delta]WW_"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"dof", ",", "\[Delta]dof", ",", "equ"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"Simplify", "[", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"\"\<\[Delta]W = -\>\"", ",", SuperscriptBox[ RowBox[{"MatrixForm", "[", "\[Delta]dof", "]"}], "T"], ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", "equ", "]"}], "]"}]}], " ", "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"\[Delta]WW", ",", "dof", ",", "\[Delta]dof", ",", "equ"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WW", "=", RowBox[{"Simplify", "[", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"Simplify", "[", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"\"\<\[Delta]W = -\>\"", ",", SuperscriptBox[ RowBox[{"MatrixForm", "[", "\[Delta]dof", "]"}], "T"], ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{"-", "equ"}], "]"}], "]"}]}], " ", "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", RowBox[{"NONL", ",", "rule0_"}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"\[Delta]WW", ",", "dof", ",", "\[Delta]dof", ",", "equ"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WW", "=", RowBox[{"Simplify", "[", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"NONL", ",", "rule0"}], "}"}], ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"Simplify", "[", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"\"\<\[Delta]W = -\>\"", ",", SuperscriptBox[ RowBox[{"MatrixForm", "[", "\[Delta]dof", "]"}], "T"], ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{"-", "equ"}], "]"}], "]"}]}], " ", "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", RowBox[{"NONL", ",", "rule0_"}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"\[Delta]WW", ",", "dof", ",", "\[Delta]dof", ",", "equ"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WW", "=", RowBox[{"Simplify", "[", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"NONL", ",", "rule0"}], "}"}], ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", "=", RowBox[{"Simplify", "[", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"\"\<\[Delta]W = -\>\"", ",", SuperscriptBox[ RowBox[{"MatrixForm", "[", "\[Delta]dof", "]"}], "T"], ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{"-", "equ"}], "]"}], "]"}]}], " ", "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", "\[Delta]W_"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "dof", ",", "\[Delta]dof", ",", "equ", ",", "dofall", ",", "dof0", ",", "dof2", ",", "KK", ",", "MM"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]W", "]"}]}], ";", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]W", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", " ", "=", RowBox[{"D", "[", RowBox[{"\[Delta]W", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dofall", "=", RowBox[{"Union", "[", RowBox[{"dof", " ", "/.", " ", RowBox[{ RowBox[{"anya_", "[", RowBox[{"anyb__", ",", RowBox[{"0", "|", "2"}]}], "]"}], "\[Rule]", RowBox[{"anya", "[", "anyb", "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof0", " ", "=", RowBox[{"dofall", " ", "/.", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dof2", " ", "=", RowBox[{"dofall", "/.", " ", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"KK", " ", "=", RowBox[{"D", "[", RowBox[{"equ", ",", RowBox[{"{", "dof0", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"MM", " ", "=", RowBox[{"D", "[", RowBox[{"equ", ",", RowBox[{"{", "dof2", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"\"\<\[Delta]W = -\>\"", ",", SuperscriptBox[ RowBox[{"MatrixForm", "[", "\[Delta]dof", "]"}], "T"], ",", "\"\<(\>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{"-", "KK"}], "]"}], "]"}], ",", "\[IndentingNewLine]", "\"\<\>\"", ",", RowBox[{"MatrixForm", "[", "dof0", "]"}], ",", "\"\<+\>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{"-", "MM"}], "]"}], "]"}], ",", "\[IndentingNewLine]", "\"\<\>\"", ",", RowBox[{"MatrixForm", "[", "dof2", "]"}], ",", "\"\<-\>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"equ", " ", "/.", RowBox[{"Thread", "[", RowBox[{"dof", "\[Rule]", "0"}], "]"}]}], "]"}], ",", "\"\<)\>\""}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]WW", ",", "dof", ",", "\[Delta]dof", ",", "equ", ",", "dofall", ",", "dof0", ",", "dof2", ",", "KK", ",", "MM"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]WW", "=", RowBox[{"Simplify", "[", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"VIBR", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof", "=", RowBox[{"DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]dof", "=", RowBox[{"\[Delta]DOFS", "[", "\[Delta]WW", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"equ", " ", "=", RowBox[{"D", "[", RowBox[{"\[Delta]WW", ",", RowBox[{"{", "\[Delta]dof", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dofall", "=", RowBox[{"Union", "[", RowBox[{"dof", " ", "/.", " ", RowBox[{ RowBox[{"anya_", "[", RowBox[{"anyb_", ",", RowBox[{"0", "|", "2"}]}], "]"}], "\[Rule]", RowBox[{"anya", "[", "anyb", "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"dof0", " ", "=", RowBox[{"dofall", " ", "/.", " ", RowBox[{"DRULE", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dof2", " ", "=", RowBox[{"dofall", "/.", " ", RowBox[{"DRULE", "[", "2", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"KK", " ", "=", RowBox[{"D", "[", RowBox[{"equ", ",", RowBox[{"{", "dof0", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"MM", " ", "=", RowBox[{"D", "[", RowBox[{"equ", ",", RowBox[{"{", "dof2", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"\"\<\[Delta]W = -\>\"", ",", SuperscriptBox[ RowBox[{"MatrixForm", "[", "\[Delta]dof", "]"}], "T"], ",", "\"\<(\>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{"-", "KK"}], "]"}], "]"}], ",", "\[IndentingNewLine]", "\"\<\>\"", ",", RowBox[{"MatrixForm", "[", "dof0", "]"}], ",", "\"\<+\>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{"-", "MM"}], "]"}], "]"}], ",", "\[IndentingNewLine]", "\"\<\>\"", ",", RowBox[{"MatrixForm", "[", "dof2", "]"}], ",", "\"\<-\>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"equ", " ", "/.", RowBox[{"Thread", "[", RowBox[{"dof", "\[Rule]", "0"}], "]"}]}], "]"}], ",", "\"\<)\>\""}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}], "]"}], ":=", RowBox[{"Grid", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"TableForm", "[", RowBox[{"ele", ",", RowBox[{"TableDepth", "\[Rule]", "2"}], ",", RowBox[{"TableHeadings", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"Array", "[", RowBox[{ RowBox[{"#", "&"}], ",", RowBox[{"Length", "[", "ele", "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{ "\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}]}], "}"}]}]}], "]"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"TableForm", "[", RowBox[{"fun", ",", RowBox[{"TableDepth", "\[Rule]", "2"}], ",", RowBox[{"TableHeadings", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"Array", "[", RowBox[{ RowBox[{"#", "&"}], ",", RowBox[{"Length", "[", "fun", "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{ "\"\<{X,Y,Z}\>\"", ",", "\"\<{\!\(\*SubscriptBox[\(u\), \(X\)]\),\!\(\*SubscriptBox[\ \(u\), \(Y\)]\),\!\(\*SubscriptBox[\(u\), \(Z\)]\)}\>\"", ",", "\"\<{\!\(\*SubscriptBox[\(\[Theta]\), \ \(X\)]\),\!\(\*SubscriptBox[\(\[Theta]\), \(Y\)]\),\!\(\*SubscriptBox[\(\ \[Theta]\), \(Z\)]\)}\>\"", ",", "\"\<\[CurlyTheta]\>\""}], "}"}]}], "}"}]}]}], "]"}], "}"}]}], "}"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"MESH", "[", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"pick", ",", "labs", ",", "crds", ",", "\[ScriptCapitalR]"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"pick", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Not", "[", RowBox[{"AllTrue", "[", RowBox[{"#", ",", "PossibleZeroQ"}], "]"}], "]"}], "&"}], ",", RowBox[{"Transpose", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{";;", ",", "1"}], "]"}], "]"}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"crds", "=", RowBox[{"Pick", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], ",", "pick"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"labs", "=", RowBox[{"Pick", "[", RowBox[{ RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}], ",", "pick"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[ScriptCapitalR]", "=", RowBox[{"MeshRegion", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{";;", ",", "1", ",", "crds"}], "]"}], "]"}], ",", RowBox[{"ele", "[", RowBox[{"[", RowBox[{";;", ",", "3"}], "]"}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{ RowBox[{"HighlightMesh", "[", RowBox[{"\[ScriptCapitalR]", ",", RowBox[{"Style", "[", RowBox[{"1", ",", "Thin"}], "]"}]}], "]"}], ",", RowBox[{"HighlightMesh", "[", RowBox[{"\[ScriptCapitalR]", ",", "0"}], "]"}], ",", RowBox[{"AxesLabel", "\[Rule]", "labs"}], ",", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"SphericalRegion", "\[Rule]", "True"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"DISP", "[", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "pick", ",", "labs", ",", "crds", ",", "\[ScriptCapitalR]", ",", "range", ",", "off"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"pick", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Not", "[", RowBox[{"AllTrue", "[", RowBox[{"#", ",", "PossibleZeroQ"}], "]"}], "]"}], "&"}], ",", RowBox[{"Transpose", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{";;", ",", "1"}], "]"}], "]"}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"crds", "=", RowBox[{"Pick", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], ",", "pick"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"labs", "=", RowBox[{"Pick", "[", RowBox[{ RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}], ",", "pick"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"range", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"MinMax", "[", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{";;", ",", "1", ",", "#"}], "]"}], "]"}], "+", RowBox[{"fun", "[", RowBox[{"[", RowBox[{";;", ",", "2", ",", "#"}], "]"}], "]"}]}], ")"}], "]"}], "&"}], ",", "crds"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"off", "=", RowBox[{"Norm", "[", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], "-", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}]}], "&"}], ",", "range"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"range", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], "-", RowBox[{"off", "/", "5"}]}], ",", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], "+", RowBox[{"off", "/", "5"}]}]}], "}"}], "&"}], ",", "range"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[ScriptCapitalR]", "=", RowBox[{"MeshRegion", "[", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{";;", ",", "1", ",", "crds"}], "]"}], "]"}], "+", RowBox[{"fun", "[", RowBox[{"[", RowBox[{";;", ",", "2", ",", "crds"}], "]"}], "]"}]}], ",", RowBox[{"ele", "[", RowBox[{"[", RowBox[{";;", ",", "3"}], "]"}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{ RowBox[{"HighlightMesh", "[", RowBox[{"\[ScriptCapitalR]", ",", RowBox[{"Style", "[", RowBox[{"1", ",", "Thin"}], "]"}]}], "]"}], ",", RowBox[{"HighlightMesh", "[", RowBox[{"\[ScriptCapitalR]", ",", "0"}], "]"}], ",", RowBox[{"AxesLabel", "\[Rule]", "labs"}], ",", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"Boxed", "\[Rule]", "True"}], ",", RowBox[{"PlotRange", "\[Rule]", "range"}], ",", RowBox[{"SphericalRegion", "\[Rule]", "True"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STRESS", "[", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}], "]"}], ":=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], "===", "PLANE"}], ")"}], "||", RowBox[{"(", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], "===", "TWODIM"}], ")"}]}], ",", RowBox[{"\[Delta]W", "[", RowBox[{"STRES", ",", "#", ",", "fun"}], "]"}], ",", "None"}], "]"}], "&"}], ",", "ele"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"COLORFUNCTION", "[", RowBox[{"min_", ",", "max_"}], "]"}], ":=", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"#", "<", "0"}], ",", RowBox[{"Blend", "[", RowBox[{ RowBox[{"{", RowBox[{"Blue", ",", "LightGray"}], "}"}], ",", RowBox[{ RowBox[{"(", RowBox[{"#", "-", "min"}], ")"}], "/", RowBox[{"(", RowBox[{"0", "-", "min"}], ")"}]}]}], "]"}], ",", RowBox[{"Blend", "[", RowBox[{ RowBox[{"{", RowBox[{"LightGray", ",", "Red"}], "}"}], ",", RowBox[{ RowBox[{"(", RowBox[{"#", "-", "0"}], ")"}], "/", RowBox[{"(", RowBox[{"max", "-", "0"}], ")"}]}]}], "]"}]}], "]"}], "&"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "calculations"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"DISP", "[", RowBox[{ RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}], ",", "exp_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "pick", ",", "labs", ",", "crds", ",", "srule", ",", "val", ",", "min", ",", "max", ",", "grule"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"pick", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Not", "[", RowBox[{"AllTrue", "[", RowBox[{"#", ",", "PossibleZeroQ"}], "]"}], "]"}], "&"}], ",", RowBox[{"Transpose", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{";;", ",", "1"}], "]"}], "]"}], "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"crds", "=", RowBox[{"Pick", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], ",", "pick"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"labs", "=", RowBox[{"Pick", "[", RowBox[{ RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}], ",", "pick"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"srule", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STRES", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"val", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"exp", " ", "/.", "#"}], "&"}], ",", "srule"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", "val", "]"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"min", ",", "max"}], "}"}], "=", RowBox[{"MinMax", "[", "val", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"grule", " ", ":=", RowBox[{ RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "\[RuleDelayed]", " ", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "1", ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}], "+", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], ",", "2", ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{ RowBox[{"Graphics", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"COLORFUNCTION", "[", RowBox[{"min", ",", "max"}], "]"}], "[", RowBox[{"val", "[", RowBox[{"[", "e", "]"}], "]"}], "]"}], ",", RowBox[{ RowBox[{"ele", "[", RowBox[{"[", RowBox[{"e", ",", "3"}], "]"}], "]"}], "/.", "grule"}]}], "}"}], ",", RowBox[{"{", RowBox[{"e", ",", "1", ",", RowBox[{"Length", "[", "ele", "]"}]}], "}"}]}], "]"}], "]"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"FrameLabel", "\[Rule]", "labs"}]}], "]"}]}]}], " ", "\[IndentingNewLine]", "]"}]}], ";"}], " ", "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{ 3.443930973126174*^9, {3.4771023549018*^9, 3.4771023808445997`*^9}, { 3.4771024577682*^9, 3.4771025046618*^9}, {3.4771063565654*^9, 3.4771063705898*^9}, 3.4771089762209997`*^9, 3.477109006645*^9, { 3.4771109395810003`*^9, 3.4771109526226*^9}, {3.477110989427*^9, 3.4771110302522*^9}, {3.4771110800372*^9, 3.4771111191308002`*^9}, { 3.4771220486066*^9, 3.4771220663286*^9}, {3.4771317865394*^9, 3.4771318192214003`*^9}, {3.4771323345362*^9, 3.477132377639*^9}, { 3.630489883760623*^9, 3.630489885414226*^9}, {3.631409232246135*^9, 3.631409318077486*^9}, {3.6314094294772816`*^9, 3.631409430304083*^9}, { 3.6314095931215687`*^9, 3.6314095963195744`*^9}, {3.6314105089523773`*^9, 3.631410515504389*^9}, 3.631435133305333*^9, {3.631435355203025*^9, 3.6314353561500793`*^9}, 3.6314356018121305`*^9, 3.631435754368856*^9, 3.631435796315255*^9, {3.63143606319652*^9, 3.631436069549884*^9}, { 3.6347884698816414`*^9, 3.63478847685104*^9}, {3.6347954098385844`*^9, 3.6347954141598315`*^9}, {3.6347956603329115`*^9, 3.634795675947805*^9}, { 3.634796217815798*^9, 3.6347962287334223`*^9}, {3.6347962930030985`*^9, 3.6347963097820582`*^9}, {3.63479634495407*^9, 3.6347963538665795`*^9}, { 3.6347967044436316`*^9, 3.6347967222076473`*^9}, {3.6348910182399282`*^9, 3.6348910703229065`*^9}, {3.634891202082443*^9, 3.63489120569665*^9}, { 3.635129073304618*^9, 3.6351290927607307`*^9}, {3.6351291514160852`*^9, 3.6351291562713633`*^9}, {3.6351296027379*^9, 3.635129640630067*^9}, { 3.6351296766311264`*^9, 3.6351296770091476`*^9}, {3.635133864772954*^9, 3.6351340703167105`*^9}, {3.635134178738912*^9, 3.635134204883407*^9}, { 3.6351532590142465`*^9, 3.6351534908115044`*^9}, {3.6353108694909534`*^9, 3.635310875829316*^9}, {3.657768370048919*^9, 3.6577683714841213`*^9}, { 3.6853593982958508`*^9, 3.6853593994858527`*^9}, 3.685359462505941*^9, { 3.685359541326051*^9, 3.685359573806097*^9}, {3.6874387445294027`*^9, 3.687438822019511*^9}, 3.6874389450596833`*^9, {3.6874389956197543`*^9, 3.6874390405998173`*^9}, {3.6874391238499336`*^9, 3.6874391937200317`*^9}, {3.6874392244700747`*^9, 3.687439453750396*^9}, { 3.687439572800562*^9, 3.68743958546058*^9}, {3.68743962102063*^9, 3.687439653600675*^9}, {3.6874397535808153`*^9, 3.6874397667108335`*^9}, 3.6874457948947306`*^9, {3.6874461481952252`*^9, 3.6874461564952374`*^9}, { 3.6875181522405834`*^9, 3.68751815568078*^9}, {3.6875204157420483`*^9, 3.687520416720104*^9}, 3.68752138033622*^9, {3.687521416058263*^9, 3.687521421832593*^9}, {3.688053601494135*^9, 3.688053602544136*^9}, { 3.688053924504587*^9, 3.688053958964635*^9}, {3.6882157502790403`*^9, 3.6882158044791164`*^9}, {3.6882622853518825`*^9, 3.6882623772920113`*^9}, {3.688262410942058*^9, 3.688262438992098*^9}, { 3.6883055547978315`*^9, 3.6883055581478367`*^9}, 3.6885556940086794`*^9, { 3.6887891056829405`*^9, 3.688789118792959*^9}, {3.689569235320521*^9, 3.6895692415105295`*^9}, {3.6895692890105963`*^9, 3.6895693069106207`*^9}, 3.6895693822507267`*^9, {3.689569427000789*^9, 3.6895694482508187`*^9}, 3.6895694919908876`*^9, {3.6895695387109528`*^9, 3.689569578131008*^9}, { 3.689569627301077*^9, 3.689569645991103*^9}, {3.6895697401912346`*^9, 3.6895697702212768`*^9}, 3.6895698011213202`*^9, {3.689744714260333*^9, 3.6897447652504044`*^9}, {3.689744965010684*^9, 3.689744999060732*^9}, { 3.689745080870846*^9, 3.6897450850308523`*^9}, {3.689931309632269*^9, 3.6899314628124833`*^9}, {3.6899315289025755`*^9, 3.6899315295525765`*^9}, 3.6899317777829237`*^9, {3.6899318153929768`*^9, 3.6899319421931543`*^9}, { 3.6899320773633437`*^9, 3.6899320881033583`*^9}, {3.689932151873448*^9, 3.6899321525034485`*^9}, {3.690167105883365*^9, 3.690167146283422*^9}, { 3.6902010125655856`*^9, 3.6902010371956205`*^9}, {3.690201134205756*^9, 3.6902011393057632`*^9}, {3.6902012251758833`*^9, 3.6902012529259224`*^9}, {3.690201324926023*^9, 3.690201330666031*^9}, { 3.690201373796091*^9, 3.6902013758560944`*^9}, {3.692601858964926*^9, 3.692601979185094*^9}, {3.692602032125168*^9, 3.692602087355245*^9}, { 3.692602118515289*^9, 3.6926021393253183`*^9}, {3.6926022282954426`*^9, 3.6926022417854614`*^9}, {3.6926023345055914`*^9, 3.6926024870358047`*^9}, {3.692602578835933*^9, 3.692602643676024*^9}, { 3.692602680546076*^9, 3.6926027938862343`*^9}, {3.6926033898490686`*^9, 3.69260341914911*^9}, {3.6926034700191813`*^9, 3.6926034970292187`*^9}, { 3.692603554029299*^9, 3.692603577969332*^9}, 3.692603688499487*^9, { 3.6926038593097258`*^9, 3.692603862659731*^9}, {3.692604812853061*^9, 3.692604831743088*^9}, {3.6926231439402156`*^9, 3.6926232412303514`*^9}, { 3.692690175958668*^9, 3.692690189128687*^9}, {3.6926902468687677`*^9, 3.692690268088797*^9}, {3.6926903035588465`*^9, 3.692690322168873*^9}, { 3.692690954409758*^9, 3.6926910022098246`*^9}, {3.6927712759197345`*^9, 3.6927713146397886`*^9}, {3.6931903688317842`*^9, 3.693190412011845*^9}, { 3.693190453611903*^9, 3.693190645072171*^9}, {3.693190734522297*^9, 3.6931907666223416`*^9}, {3.6931908229324207`*^9, 3.69319083728244*^9}, { 3.6931909707526274`*^9, 3.693190977632637*^9}, {3.693191099552808*^9, 3.693191167062902*^9}, {3.693380931925725*^9, 3.6933809742257843`*^9}, { 3.693381048845889*^9, 3.6933810491658893`*^9}, {3.6937172796980753`*^9, 3.6937172962480984`*^9}, 3.6940830696432643`*^9, {3.694265186313383*^9, 3.6942652017534046`*^9}, {3.6943214452576447`*^9, 3.694321472597683*^9}, { 3.694321554517798*^9, 3.6943215869878435`*^9}, {3.694321622098892*^9, 3.6943216224888935`*^9}, 3.6994204614383593`*^9, {3.699421287129515*^9, 3.6994212950795264`*^9}, {3.6994213310795765`*^9, 3.6994213778796425`*^9}, 3.6994215436398745`*^9, {3.7242984497704906`*^9, 3.7242984923330016`*^9}, { 3.72441256854047*^9, 3.7244125884060483`*^9}, {3.724423663595652*^9, 3.7244236935801315`*^9}, {3.7244238000272264`*^9, 3.724423808981761*^9}, { 3.724423851341444*^9, 3.72442385406735*^9}, 3.7531742584901376`*^9, { 3.75317433551407*^9, 3.753174346315694*^9}, {3.7531744883509235`*^9, 3.7531745210492754`*^9}, {3.753174634967907*^9, 3.7531746472931037`*^9}, { 3.753175721657942*^9, 3.7531757255294914`*^9}, {3.7557182025229635`*^9, 3.7557182030038967`*^9}, {3.756297307135029*^9, 3.756297308897887*^9}, { 3.7606708035908995`*^9, 3.7606708139790516`*^9}, {3.760670898506214*^9, 3.760670900521375*^9}, {3.7739914305755105`*^9, 3.7739914316320434`*^9}, { 3.7821126248524623`*^9, 3.7821126618917875`*^9}, {3.7821128287376575`*^9, 3.782113058088851*^9}, 3.7821131332211285`*^9, {3.78230654015934*^9, 3.782306645788203*^9}, {3.7823084511158514`*^9, 3.7823084719170256`*^9}, { 3.7823089681411147`*^9, 3.782309014159138*^9}, {3.7823090529903145`*^9, 3.782309098299096*^9}, {3.7834165730387535`*^9, 3.783416574885394*^9}, { 3.7834177206360197`*^9, 3.7834177235800114`*^9}, {3.7834178083523865`*^9, 3.783417811301102*^9}, {3.78341790496704*^9, 3.7834179579660645`*^9}, { 3.7834205477524905`*^9, 3.783420592682665*^9}, {3.7834206239423256`*^9, 3.783420694447334*^9}, {3.783420731072624*^9, 3.7834207678524528`*^9}, { 3.783420801192772*^9, 3.7834208184926167`*^9}, {3.7834208900921984`*^9, 3.7834208997123528`*^9}, {3.7834209626227193`*^9, 3.783420995272684*^9}, 3.783421034482338*^9, {3.7834210681022635`*^9, 3.7834210798275776`*^9}, { 3.783421113532735*^9, 3.7834211771988773`*^9}, {3.783421696697568*^9, 3.7834216971028566`*^9}, {3.7834218696329055`*^9, 3.783421906748032*^9}, { 3.7883262853435993`*^9, 3.7883263022151365`*^9}, {3.7883263694714775`*^9, 3.788326373049384*^9}, 3.788326407340768*^9, {3.788326462030433*^9, 3.7883264759465675`*^9}, {3.7883266381172643`*^9, 3.7883266752530084`*^9}, {3.78832683682738*^9, 3.788326853529421*^9}, { 3.788327257534025*^9, 3.7883272687062693`*^9}, {3.788575008576598*^9, 3.7885750852092667`*^9}, {3.7885752039321165`*^9, 3.7885752254012146`*^9}, {3.788677105989899*^9, 3.7886771563854265`*^9}, { 3.788677419098531*^9, 3.7886776914502583`*^9}, {3.788677863953772*^9, 3.788677873982659*^9}, {3.788677972296945*^9, 3.7886779751198874`*^9}, { 3.788678104512977*^9, 3.788678132702388*^9}, {3.788678229588771*^9, 3.7886782311665745`*^9}, {3.7886782945295157`*^9, 3.7886783636952543`*^9}, {3.7886784043995614`*^9, 3.788678410344158*^9}, { 3.788678513776554*^9, 3.7886785139327545`*^9}, {3.7887492506266127`*^9, 3.788749271502985*^9}, {3.7887494537067327`*^9, 3.7887494576578264`*^9}, { 3.7888494712317395`*^9, 3.788849476626989*^9}, {3.7890121503559027`*^9, 3.7890121818326073`*^9}, 3.789567712832692*^9, {3.790128896256201*^9, 3.790128897703824*^9}, {3.7901289319915466`*^9, 3.790128937645911*^9}, { 3.790128972298277*^9, 3.790128973869923*^9}, {3.8146823682070165`*^9, 3.814682369609891*^9}, {3.8146824749880943`*^9, 3.8146825013459005`*^9}, { 3.8146825650091476`*^9, 3.814682574936365*^9}, {3.814682678090005*^9, 3.8146827094381466`*^9}, {3.8146827427363567`*^9, 3.8146827504312325`*^9}, {3.814682781533187*^9, 3.814682798049752*^9}, { 3.814683865904718*^9, 3.814683921031538*^9}, {3.817549572368679*^9, 3.817549648245356*^9}, {3.8223698040336294`*^9, 3.8223698883671684`*^9}, { 3.822370507521001*^9, 3.8223705081203985`*^9}, {3.822370624230193*^9, 3.8223706400618677`*^9}}, CellLabel-> "In[310]:=",ExpressionUUID->"890883ed-125f-4947-8651-685e9ea67989"] }, Closed]], Cell[CellGroupData[{ Cell["POST defs", "Subsection",ExpressionUUID->"86c035c4-399f-40a3-9748-ab2d70534b08"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Clear", "[", RowBox[{"SHOW", ",", "GRAPH"}], "]"}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"box", " ", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}], "*", "1.5"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"jointsize", " ", "=", "0.02"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"scale", " ", "=", "1."}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"aspectratio", "=", RowBox[{"1", "/", "4"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"PRINT", "[", RowBox[{"label_", ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], " ", ":=", " ", RowBox[{"Print", "[", RowBox[{"label", ",", "\"\< \>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"ele", ",", RowBox[{"TableDepth", "\[Rule]", "2"}]}], "]"}], ",", "\"\< \>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"fun", ",", RowBox[{"TableDepth", "\[Rule]", "2"}]}], "]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"PRINT", "[", RowBox[{"label_", ",", RowBox[{"{", "tab_", "}"}]}], "]"}], " ", ":=", " ", RowBox[{"Print", "[", RowBox[{"label", ",", "\"\< \>\"", ",", RowBox[{"MatrixForm", "[", RowBox[{"tab", ",", RowBox[{"TableDepth", "\[Rule]", "2"}]}], "]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SHOW", "[", RowBox[{"var_", ",", "rule_", ",", "time_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"nn", ",", "ne", ",", "sol"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"nn", "=", RowBox[{"Length", "[", "time", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ne", " ", "=", RowBox[{"Length", "[", "var", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"sol", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"time", "[", RowBox[{"[", "ii", "]"}], "]"}], ",", RowBox[{"(", RowBox[{ RowBox[{"var", "[", RowBox[{"[", "jj", "]"}], "]"}], " ", "/.", " ", RowBox[{"rule", "[", RowBox[{"[", "ii", "]"}], "]"}]}], ")"}]}], "}"}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", "nn"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ListPlot", "[", RowBox[{"sol", ",", RowBox[{"Joined", "\[Rule]", "True"}], ",", RowBox[{"Frame", "\[Rule]", " ", "True"}], ",", RowBox[{"PlotRange", "\[Rule]", " ", "All"}], ",", RowBox[{"AspectRatio", "\[Rule]", "aspectratio"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"jj", ",", "1", ",", "ne"}], "}"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SHOW", "[", RowBox[{ RowBox[{"{", RowBox[{"MODE", ",", "step_", ",", "time_"}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "funin_"}], "}"}]}], "]"}], ":=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", " ", "=", " ", RowBox[{"funin", " ", "/.", " ", RowBox[{"t", " ", "\[Rule]", " ", "#"}]}]}], ";", " ", RowBox[{"SHOW", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}], ")"}], "&"}], ",", "time"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SHOW", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "rule_"}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "funin_"}], "}"}]}], "]"}], ":=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", " ", "=", " ", RowBox[{"funin", " ", "/.", " ", "#"}]}], ";", " ", RowBox[{"SHOW", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}], ")"}], "&"}], ",", "rule"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SHOW", "[", RowBox[{ RowBox[{"{", RowBox[{"DG", ",", "rule_", ",", "time_"}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "funin_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", "localrule", "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"localrule", " ", "=", RowBox[{"rule", " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"a", "[", RowBox[{"b_", ",", "0"}], "]"}], "\[Rule]", " ", RowBox[{"a", "[", "b", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", " ", RowBox[{"(", RowBox[{"funin", " ", "/.", RowBox[{"localrule", "[", RowBox[{"[", "ii", "]"}], "]"}]}], ")"}]}], ";", " ", RowBox[{"SHOW", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", RowBox[{"Length", "[", "rule", "]"}]}], "}"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SHOW", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Show", "[", RowBox[{ RowBox[{"Graphics3D", "[", RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], ",", RowBox[{"Axes", "\[Rule]", " ", "True"}], ",", RowBox[{"Boxed", "\[Rule]", "True"}], ",", RowBox[{"SphericalRegion", " ", "\[Rule]", " ", "True"}], ",", RowBox[{"Lighting", "\[Rule]", "Automatic"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}], ",", RowBox[{"PlotRange", "\[Rule]", "box"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SHOW", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "rule_"}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Show", "[", RowBox[{ RowBox[{"Graphics3D", "[", RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{"{", RowBox[{"ele", ",", RowBox[{"fun", " ", "/.", "rule"}]}], "}"}], "]"}], ",", RowBox[{"Axes", "\[Rule]", " ", "True"}], ",", RowBox[{"Boxed", "\[Rule]", "True"}], ",", RowBox[{"SphericalRegion", " ", "\[Rule]", " ", "True"}], ",", RowBox[{"Lighting", "\[Rule]", "None"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}], ",", RowBox[{"PlotRange", "\[Rule]", "box"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}], "]"}], ":=", RowBox[{"Flatten", "[", RowBox[{"Join", "[", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"GRAPH", "[", "#", "]"}], "&"}], ",", "ele"}], "]"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPH", "[", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ "FX_", ",", "FY_", ",", "FZ_", ",", "MX_", ",", "MY_", ",", "MZ_"}], "}"}], ",", RowBox[{"{", "I1_", "}"}]}], "}"}], "]"}], ":=", RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPH", "[", RowBox[{"{", RowBox[{"GLUE", ",", RowBox[{"{", RowBox[{"{", RowBox[{"kx_", ",", "ky_"}], "}"}], "}"}], ",", RowBox[{"{", RowBox[{"I1_", ",", "I2_"}], "}"}]}], "}"}], "]"}], ":=", RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPH", "[", RowBox[{"{", RowBox[{"GLUE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"kx_", ",", "ky_", ",", "kz_"}], "}"}], ",", RowBox[{"{", RowBox[{"z1_", ",", "z2_", ",", "iy_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"I1_", ",", "I2_", ",", "I3_", ",", "I4_"}], "}"}]}], "}"}], "]"}], ":=", RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPH", "[", RowBox[{"{", RowBox[{"GLUE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"kx_", ",", "ky_", ",", "kz_"}], "}"}], ",", RowBox[{"{", RowBox[{"z1_", ",", "z2_", ",", "ty_", ",", "iy_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ "I1_", ",", "I2_", ",", "I3_", ",", "I4_", ",", "I5_", ",", "I6_"}], "}"}]}], "}"}], "]"}], ":=", RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPH", "[", RowBox[{"{", RowBox[{"GLUET", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"kx_", ",", "ky_", ",", "kz_"}], "}"}], ",", RowBox[{"{", RowBox[{"z1_", ",", "z2_", ",", "ty_", ",", "iy_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ "I1_", ",", "I2_", ",", "I3_", ",", "I4_", ",", "I5_", ",", "I6_"}], "}"}]}], "}"}], "]"}], ":=", RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPH", "[", RowBox[{"{", RowBox[{"RIGID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "mm_", ",", "Ixx_", ",", "Iyy_", ",", "Izz_", ",", "ix_", ",", "iy_"}], "}"}], ",", RowBox[{"{", RowBox[{ "Fx_", ",", "Fy_", ",", "Fz_", ",", "Mx_", ",", "My_", ",", "Mz_"}], "}"}]}], "}"}], ",", RowBox[{"{", "I1_", "}"}]}], "}"}], "]"}], ":=", RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPH", "[", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "AA_", "}"}], ",", RowBox[{"{", "fx_", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"I1_", ",", "I2_"}], "}"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"Thickness", "[", "0.005", "]"}], ",", "Black", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"XYZ", "[", "I1", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I1", "]"}], "*", "scale"}]}], ",", RowBox[{ RowBox[{"XYZ", "[", "I2", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I2", "]"}], "*", "scale"}]}]}], " ", "}"}], "]"}], ",", "Blue", ",", RowBox[{"PointSize", "[", "jointsize", "]"}], ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"XYZ", "[", "I1", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I1", "]"}], "*", "scale"}]}], "]"}], ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"XYZ", "[", "I2", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I2", "]"}], "*", "scale"}]}], "]"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPH", "[", RowBox[{"{", RowBox[{"BAR", ",", "list_", ",", RowBox[{"{", RowBox[{"I1_", ",", "I2_"}], "}"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"Thickness", "[", "0.005", "]"}], ",", "Black", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"XYZ", "[", "I1", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I1", "]"}], "*", "scale"}]}], ",", RowBox[{ RowBox[{"XYZ", "[", "I2", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I2", "]"}], "*", "scale"}]}]}], " ", "}"}], "]"}], ",", "Blue", ",", RowBox[{"PointSize", "[", "jointsize", "]"}], ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"XYZ", "[", "I1", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I1", "]"}], "*", "scale"}]}], "]"}], ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"XYZ", "[", "I2", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I2", "]"}], "*", "scale"}]}], "]"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPH", "[", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Irr_", ",", "Iyy_", ",", "Izz_", ",", "iy_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"I1_", ",", "I2_"}], "}"}]}], "}"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "ix", ",", "hx", ",", "iz", ",", "ty", ",", "tz", ",", "\[CapitalOmega]", ",", "NL", ",", "NC", ",", "XX", ",", "YY", ",", "ZZ", ",", "uu", ",", "vv", ",", "ww", ",", "\[Phi]\[Phi]", ",", "\[CapitalTheta]\[CapitalTheta]", ",", "\[Psi]\[Psi]", ",", "XYZN"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ix", ",", "hx"}], "}"}], "=", RowBox[{"UNIT", "[", RowBox[{ RowBox[{"XYZ", "[", "I2", "]"}], "-", RowBox[{"XYZ", "[", "I1", "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz", "=", RowBox[{"CROSS", "[", RowBox[{"ix", ",", "iy"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ty", " ", "=", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"12", "*", RowBox[{"Iyy", "/", "AA"}]}], "]"}], "/", "2"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"tz", " ", "=", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"12", "*", RowBox[{"Izz", "/", "AA"}]}], "]"}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "hx", "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NL", "=", " ", RowBox[{"SHAPES1", "[", " ", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "x"}], "}"}], ",", "\[CapitalOmega]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NC", "=", " ", RowBox[{"SHAPES11", "[", " ", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "x", ",", RowBox[{"x", "^", "2"}], ",", RowBox[{"x", "^", "3"}]}], "}"}], ",", "\[CapitalOmega]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"XX", "=", " ", RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"X", "[", "I1", "]"}], ",", RowBox[{"X", "[", "I2", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"YY", "=", " ", RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"Y", "[", "I1", "]"}], ",", RowBox[{"Y", "[", "I2", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"ZZ", "=", " ", RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"Z", "[", "I1", "]"}], ",", RowBox[{"Z", "[", "I2", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"uu", "=", " ", RowBox[{ RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"ix", ".", RowBox[{"UVW", "[", "I1", "]"}]}], ",", RowBox[{"ix", ".", RowBox[{"UVW", "[", "I2", "]"}]}]}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"vv", "=", " ", RowBox[{ RowBox[{"NC", ".", RowBox[{"{", RowBox[{ RowBox[{"iy", ".", RowBox[{"UVW", "[", "I1", "]"}]}], ",", RowBox[{"iz", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I1", "]"}]}], ",", RowBox[{"iy", ".", RowBox[{"UVW", "[", "I2", "]"}]}], ",", RowBox[{"iz", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I2", "]"}]}]}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"ww", "=", " ", RowBox[{ RowBox[{"NC", ".", RowBox[{"{", RowBox[{ RowBox[{"iz", ".", RowBox[{"UVW", "[", "I1", "]"}]}], ",", RowBox[{"-", RowBox[{"iy", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I1", "]"}]}]}], ",", RowBox[{"iz", ".", RowBox[{"UVW", "[", "I2", "]"}]}], ",", RowBox[{"-", RowBox[{"iy", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I2", "]"}]}]}]}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]\[Phi]", "=", " ", RowBox[{ RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"ix", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I1", "]"}]}], ",", RowBox[{"ix", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I2", "]"}]}]}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalTheta]\[CapitalTheta]", "=", RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "x"], "ww"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]\[Psi]", "=", " ", RowBox[{ SubscriptBox["\[PartialD]", "x"], "vv"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"XYZN", "[", RowBox[{"y_", ",", "z_"}], "]"}], "=", RowBox[{ RowBox[{"{", RowBox[{"XX", ",", "YY", ",", "ZZ"}], "}"}], "+", RowBox[{"ix", "*", "uu"}], "+", RowBox[{"iy", "*", RowBox[{"(", RowBox[{"y", "+", "vv"}], ")"}]}], "+", RowBox[{"iz", "*", RowBox[{"(", RowBox[{"z", "+", "ww"}], ")"}]}], "+", RowBox[{"CROSS", "[", RowBox[{ RowBox[{ RowBox[{"ix", "*", "\[Phi]\[Phi]"}], "+", RowBox[{"iy", "*", "\[CapitalTheta]\[CapitalTheta]"}], "+", RowBox[{"iz", "*", "\[Psi]\[Psi]"}]}], ",", RowBox[{ RowBox[{"iy", "*", "y"}], "+", RowBox[{"iz", "*", "z"}]}]}], "]"}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"Join", "[", " ", RowBox[{ RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"FaceForm", "[", "Gray", "]"}], ",", RowBox[{ RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"XYZN", "[", RowBox[{"ty", ",", "tz"}], "]"}], ",", RowBox[{"XYZN", "[", RowBox[{ RowBox[{"-", "ty"}], ",", "tz"}], "]"}], ",", RowBox[{"XYZN", "[", RowBox[{ RowBox[{"-", "ty"}], ",", RowBox[{"-", "tz"}]}], "]"}], ",", RowBox[{"XYZN", "[", RowBox[{"ty", ",", RowBox[{"-", "tz"}]}], "]"}]}], "}"}], " ", "]"}], "/.", RowBox[{"x", "\[Rule]", "xr"}]}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"xr", ",", "0", ",", "hx", ",", RowBox[{"hx", "/", "20"}]}], "}"}]}], "]"}], " ", ",", RowBox[{"{", "Gray", "}"}], ",", RowBox[{"{", RowBox[{"Line", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"XYZN", "[", RowBox[{"0", ",", "0"}], "]"}], "/.", RowBox[{"x", "\[Rule]", "xr"}]}], ",", RowBox[{"{", RowBox[{"xr", ",", "0", ",", "hx", ",", RowBox[{"hx", "/", "50"}]}], "}"}]}], "]"}], " ", "]"}], "}"}], " ", ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Blue", ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"XYZ", "[", "I1", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I1", "]"}], "*", "scale"}]}], "]"}], ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"XYZ", "[", "I2", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I2", "]"}], "*", "scale"}]}], "]"}]}], "}"}]}], " ", "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPH", "[", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Irr_", ",", "Iyy_", ",", "Izz_", ",", "iy_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"I1_", ",", "I2_", ",", "I3_"}], "}"}]}], "}"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "ix", ",", "hx", ",", "iz", ",", "ty", ",", "tz", ",", "\[CapitalOmega]", ",", "NL", ",", "NC", ",", "XX", ",", "YY", ",", "ZZ", ",", "uu", ",", "vv", ",", "ww", ",", "\[Phi]\[Phi]", ",", "\[CapitalTheta]\[CapitalTheta]", ",", "\[Psi]\[Psi]", ",", "XYZN"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ix", ",", "hx"}], "}"}], "=", RowBox[{"UNIT", "[", RowBox[{ RowBox[{"XYZ", "[", "I3", "]"}], "-", RowBox[{"XYZ", "[", "I1", "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz", "=", RowBox[{"CROSS", "[", RowBox[{"ix", ",", "iy"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ty", " ", "=", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"12", "*", RowBox[{"Iyy", "/", "AA"}]}], "]"}], "/", "2"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"tz", " ", "=", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"12", "*", RowBox[{"Izz", "/", "AA"}]}], "]"}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "hx", "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NL", "=", " ", RowBox[{"SHAPES1", "[", " ", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "x"}], "}"}], ",", "\[CapitalOmega]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NQ", "=", " ", RowBox[{"SHAPES1", "[", " ", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "x", ",", RowBox[{"x", "^", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{ RowBox[{"{", "hx", "}"}], "/", "2"}], ",", RowBox[{"{", "hx", "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NC", "=", " ", RowBox[{"SHAPES11", "[", " ", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "x", ",", RowBox[{"x", "^", "2"}], ",", RowBox[{"x", "^", "3"}]}], "}"}], ",", "\[CapitalOmega]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"XX", "=", " ", RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"X", "[", "I1", "]"}], ",", RowBox[{"X", "[", "I3", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"YY", "=", " ", RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"Y", "[", "I1", "]"}], ",", RowBox[{"Y", "[", "I3", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"ZZ", "=", " ", RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"Z", "[", "I1", "]"}], ",", RowBox[{"Z", "[", "I3", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"uu", "=", " ", RowBox[{ RowBox[{"NQ", ".", RowBox[{"{", RowBox[{ RowBox[{"ix", ".", RowBox[{"UVW", "[", "I1", "]"}]}], ",", RowBox[{"ix", ".", RowBox[{"UVW", "[", "I2", "]"}]}], ",", RowBox[{"ix", ".", RowBox[{"UVW", "[", "I3", "]"}]}]}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"vv", "=", " ", RowBox[{ RowBox[{"NC", ".", RowBox[{"{", RowBox[{ RowBox[{"iy", ".", RowBox[{"UVW", "[", "I1", "]"}]}], ",", RowBox[{"iz", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I1", "]"}]}], ",", RowBox[{"iy", ".", RowBox[{"UVW", "[", "I3", "]"}]}], ",", RowBox[{"iz", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I3", "]"}]}]}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"ww", "=", " ", RowBox[{ RowBox[{"NC", ".", RowBox[{"{", RowBox[{ RowBox[{"iz", ".", RowBox[{"UVW", "[", "I1", "]"}]}], ",", RowBox[{"-", RowBox[{"iy", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I1", "]"}]}]}], ",", RowBox[{"iz", ".", RowBox[{"UVW", "[", "I3", "]"}]}], ",", RowBox[{"-", RowBox[{"iy", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I3", "]"}]}]}]}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]\[Phi]", "=", " ", RowBox[{ RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"ix", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I1", "]"}]}], ",", RowBox[{"ix", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I3", "]"}]}]}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalTheta]\[CapitalTheta]", "=", RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "x"], "ww"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]\[Psi]", "=", " ", RowBox[{ SubscriptBox["\[PartialD]", "x"], "vv"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"XYZN", "[", RowBox[{"y_", ",", "z_"}], "]"}], "=", RowBox[{ RowBox[{"{", RowBox[{"XX", ",", "YY", ",", "ZZ"}], "}"}], "+", RowBox[{"ix", "*", "uu"}], "+", RowBox[{"iy", "*", RowBox[{"(", RowBox[{"y", "+", "vv"}], ")"}]}], "+", RowBox[{"iz", "*", RowBox[{"(", RowBox[{"z", "+", "ww"}], ")"}]}], "+", RowBox[{"CROSS", "[", RowBox[{ RowBox[{ RowBox[{"ix", "*", "\[Phi]\[Phi]"}], "+", RowBox[{"iy", "*", "\[CapitalTheta]\[CapitalTheta]"}], "+", RowBox[{"iz", "*", "\[Psi]\[Psi]"}]}], ",", RowBox[{ RowBox[{"iy", "*", "y"}], "+", RowBox[{"iz", "*", "z"}]}]}], "]"}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"Join", "[", " ", RowBox[{ RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"FaceForm", "[", "Gray", "]"}], ",", RowBox[{ RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"XYZN", "[", RowBox[{"ty", ",", "tz"}], "]"}], ",", RowBox[{"XYZN", "[", RowBox[{ RowBox[{"-", "ty"}], ",", "tz"}], "]"}], ",", RowBox[{"XYZN", "[", RowBox[{ RowBox[{"-", "ty"}], ",", RowBox[{"-", "tz"}]}], "]"}], ",", RowBox[{"XYZN", "[", RowBox[{"ty", ",", RowBox[{"-", "tz"}]}], "]"}]}], "}"}], " ", "]"}], "/.", RowBox[{"x", "\[Rule]", "xr"}]}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"xr", ",", "0", ",", "hx", ",", RowBox[{"hx", "/", "20"}]}], "}"}]}], "]"}], " ", ",", RowBox[{"{", "Gray", "}"}], ",", RowBox[{"{", RowBox[{"Line", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"XYZN", "[", RowBox[{"0", ",", "0"}], "]"}], "/.", RowBox[{"x", "\[Rule]", "xr"}]}], ",", RowBox[{"{", RowBox[{"xr", ",", "0", ",", "hx", ",", RowBox[{"hx", "/", "50"}]}], "}"}]}], "]"}], " ", "]"}], "}"}], " ", ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Blue", ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"XYZ", "[", "I1", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I1", "]"}], "*", "scale"}]}], "]"}], ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"XYZ", "[", "I2", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I2", "]"}], "*", "scale"}]}], "]"}]}], "}"}]}], " ", "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPH", "[", RowBox[{"{", RowBox[{"BEAMT", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Irr_", ",", "Iyy_", ",", "Izz_", ",", "iy_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"I1_", ",", "I2_", ",", "I3_"}], "}"}]}], "}"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "ix", ",", "hx", ",", "iz", ",", "ty", ",", "tz", ",", "\[CapitalOmega]", ",", "NL", ",", "NC", ",", "XX", ",", "YY", ",", "ZZ", ",", "uu", ",", "vv", ",", "ww", ",", "\[Phi]\[Phi]", ",", "\[CapitalTheta]\[CapitalTheta]", ",", "\[Psi]\[Psi]", ",", "XYZN"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ix", ",", "hx"}], "}"}], "=", RowBox[{"UNIT", "[", RowBox[{ RowBox[{"XYZ", "[", "I3", "]"}], "-", RowBox[{"XYZ", "[", "I1", "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz", "=", RowBox[{"CROSS", "[", RowBox[{"ix", ",", "iy"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ty", " ", "=", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"12", "*", RowBox[{"Iyy", "/", "AA"}]}], "]"}], "/", "2"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"tz", " ", "=", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"12", "*", RowBox[{"Izz", "/", "AA"}]}], "]"}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "hx", "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NQ", "=", " ", RowBox[{"SHAPES1", "[", " ", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "x", ",", RowBox[{"x", "^", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{ RowBox[{"{", "hx", "}"}], "/", "2"}], ",", RowBox[{"{", "hx", "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"XX", "=", " ", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{ RowBox[{"X", "[", "I1", "]"}], ",", RowBox[{"X", "[", "I2", "]"}], ",", RowBox[{"X", "[", "I3", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"YY", "=", " ", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{ RowBox[{"Y", "[", "I1", "]"}], ",", RowBox[{"Y", "[", "I2", "]"}], ",", RowBox[{"Y", "[", "I3", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"ZZ", "=", " ", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{ RowBox[{"Z", "[", "I1", "]"}], ",", RowBox[{"Z", "[", "I2", "]"}], ",", RowBox[{"Z", "[", "I3", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"uu", "=", " ", RowBox[{ RowBox[{"NQ", ".", RowBox[{"{", RowBox[{ RowBox[{"ix", ".", RowBox[{"UVW", "[", "I1", "]"}]}], ",", RowBox[{"ix", ".", RowBox[{"UVW", "[", "I2", "]"}]}], ",", RowBox[{"ix", ".", RowBox[{"UVW", "[", "I3", "]"}]}]}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"vv", "=", " ", RowBox[{ RowBox[{"NQ", ".", RowBox[{"{", RowBox[{ RowBox[{"iy", ".", RowBox[{"UVW", "[", "I1", "]"}]}], ",", RowBox[{"iy", ".", RowBox[{"UVW", "[", "I2", "]"}]}], ",", RowBox[{"iy", ".", RowBox[{"UVW", "[", "I3", "]"}]}]}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"ww", "=", " ", RowBox[{ RowBox[{"NQ", ".", RowBox[{"{", RowBox[{ RowBox[{"iz", ".", RowBox[{"UVW", "[", "I1", "]"}]}], ",", RowBox[{"iz", ".", RowBox[{"UVW", "[", "I2", "]"}]}], ",", RowBox[{"iz", ".", RowBox[{"UVW", "[", "I3", "]"}]}]}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]\[Phi]", "=", " ", RowBox[{ RowBox[{"NQ", ".", RowBox[{"{", RowBox[{ RowBox[{"ix", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I1", "]"}]}], ",", RowBox[{"ix", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I2", "]"}]}], ",", RowBox[{"ix", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I3", "]"}]}]}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalTheta]\[CapitalTheta]", "=", " ", RowBox[{ RowBox[{"NQ", ".", RowBox[{"{", RowBox[{ RowBox[{"iy", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I1", "]"}]}], ",", RowBox[{"iy", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I2", "]"}]}], ",", RowBox[{"iy", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I3", "]"}]}]}], "}"}]}], "*", "scale"}]}], ";"}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]\[Psi]", "=", " ", RowBox[{ RowBox[{"NQ", ".", RowBox[{"{", RowBox[{ RowBox[{"iz", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I1", "]"}]}], ",", RowBox[{"iz", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I2", "]"}]}], ",", RowBox[{"iz", ".", RowBox[{"\[Phi]\[CapitalTheta]\[Psi]", "[", "I3", "]"}]}]}], "}"}]}], "*", "scale"}]}], ";"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"XYZN", "[", RowBox[{"y_", ",", "z_"}], "]"}], "=", RowBox[{ RowBox[{"{", RowBox[{"XX", ",", "YY", ",", "ZZ"}], "}"}], "+", RowBox[{"ix", "*", "uu"}], "+", RowBox[{"iy", "*", RowBox[{"(", RowBox[{"y", "+", "vv"}], ")"}]}], "+", RowBox[{"iz", "*", RowBox[{"(", RowBox[{"z", "+", "ww"}], ")"}]}], "+", RowBox[{"CROSS", "[", RowBox[{ RowBox[{ RowBox[{"ix", "*", "\[Phi]\[Phi]"}], "+", RowBox[{"iy", "*", "\[CapitalTheta]\[CapitalTheta]"}], "+", RowBox[{"iz", "*", "\[Psi]\[Psi]"}]}], ",", RowBox[{ RowBox[{"iy", "*", "y"}], "+", RowBox[{"iz", "*", "z"}]}]}], "]"}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"Join", "[", " ", RowBox[{ RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"FaceForm", "[", "Gray", "]"}], ",", RowBox[{ RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"XYZN", "[", RowBox[{"ty", ",", "tz"}], "]"}], ",", RowBox[{"XYZN", "[", RowBox[{ RowBox[{"-", "ty"}], ",", "tz"}], "]"}], ",", RowBox[{"XYZN", "[", RowBox[{ RowBox[{"-", "ty"}], ",", RowBox[{"-", "tz"}]}], "]"}], ",", RowBox[{"XYZN", "[", RowBox[{"ty", ",", RowBox[{"-", "tz"}]}], "]"}]}], "}"}], " ", "]"}], "/.", RowBox[{"x", "\[Rule]", "xr"}]}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"xr", ",", "0", ",", "hx", ",", RowBox[{"hx", "/", "20"}]}], "}"}]}], "]"}], " ", ",", RowBox[{"{", "Gray", "}"}], ",", RowBox[{"{", RowBox[{"Line", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"XYZN", "[", RowBox[{"0", ",", "0"}], "]"}], "/.", RowBox[{"x", "\[Rule]", "xr"}]}], ",", RowBox[{"{", RowBox[{"xr", ",", "0", ",", "hx", ",", RowBox[{"hx", "/", "50"}]}], "}"}]}], "]"}], " ", "]"}], "}"}], " ", ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Blue", ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"XYZ", "[", "I1", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I1", "]"}], "*", "scale"}]}], "]"}], ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"XYZ", "[", "I2", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I2", "]"}], "*", "scale"}]}], "]"}]}], "}"}]}], " ", "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPH", "[", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"I1_", ",", "I2_", ",", "I3_"}], "}"}]}], "}"}], "]"}], ":=", "\n", RowBox[{"{", RowBox[{"Gray", ",", RowBox[{"Polygon", "[", " ", RowBox[{ RowBox[{"XYZ", "[", RowBox[{"{", RowBox[{"I1", ",", "I2", ",", "I3", ",", "I1"}], "}"}], "]"}], "+", " ", RowBox[{ RowBox[{"UVW", "[", RowBox[{"{", RowBox[{"I1", ",", "I2", ",", "I3", ",", "I1"}], "}"}], "]"}], "*", "scale"}]}], "]"}], ",", "Blue", ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"XYZ", "[", "I1", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I1", "]"}], "*", "scale"}]}], "]"}], ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"XYZ", "[", "I2", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I2", "]"}], "*", "scale"}]}], "]"}], ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"XYZ", "[", "I3", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I3", "]"}], "*", "scale"}]}], "]"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPH", "[", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"I1_", ",", "I2_", ",", "I3_", ",", "I4_"}], "}"}]}], "}"}], "]"}], ":=", "\n", RowBox[{"{", RowBox[{"Gray", ",", RowBox[{"Polygon", "[", " ", RowBox[{ RowBox[{"XYZ", "[", RowBox[{"{", RowBox[{"I1", ",", "I2", ",", "I4", ",", "I3", ",", "I1"}], "}"}], "]"}], "+", " ", RowBox[{ RowBox[{"UVW", "[", RowBox[{"{", RowBox[{"I1", ",", "I2", ",", "I4", ",", "I3", ",", "I1"}], "}"}], "]"}], "*", "scale"}]}], "]"}], ",", "Blue", ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"XYZ", "[", "I1", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I1", "]"}], "*", "scale"}]}], "]"}], ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"XYZ", "[", "I2", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I2", "]"}], "*", "scale"}]}], "]"}], ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"XYZ", "[", "I3", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I3", "]"}], "*", "scale"}]}], "]"}], ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"XYZ", "[", "I4", "]"}], "+", RowBox[{ RowBox[{"UVW", "[", "I4", "]"}], "*", "scale"}]}], "]"}]}], "}"}]}], ";"}]}]}]], "Input", CellChangeTimes->{{3.443928906918974*^9, 3.443928929991374*^9}, { 3.443929321457774*^9, 3.443929366962974*^9}, {3.443929418474174*^9, 3.4439294203773737`*^9}, {3.443929488800974*^9, 3.4439294898461742`*^9}, { 3.443930075892174*^9, 3.4439300788405743`*^9}, {3.443930455096974*^9, 3.4439304595273743`*^9}, {3.443930823241374*^9, 3.443930856126174*^9}, { 3.443931095008974*^9, 3.443931111997374*^9}, {3.443931155724174*^9, 3.4439311829461737`*^9}, {3.443931237046974*^9, 3.443931263410974*^9}, 3.4439313163885736`*^9, {3.4439313583057737`*^9, 3.443931361909374*^9}, 3.4439314336509743`*^9, {3.443931519341774*^9, 3.4439315263773737`*^9}, { 3.443931599338574*^9, 3.4439315999157743`*^9}, {3.443931654312974*^9, 3.443931663626174*^9}, {3.443931727149374*^9, 3.4439317436853743`*^9}, { 3.443931775712174*^9, 3.443931903195374*^9}, {3.443932055919374*^9, 3.443932087025774*^9}, {3.4439321180697737`*^9, 3.4439322133857737`*^9}, { 3.443932558437174*^9, 3.443932580074374*^9}, {3.443932636171974*^9, 3.443932669587174*^9}, {3.4439327043127737`*^9, 3.443932734670374*^9}, { 3.4439327953075743`*^9, 3.443932797023574*^9}, {3.443933058434774*^9, 3.443933059136774*^9}, {3.443933108214374*^9, 3.4439331098211737`*^9}, 3.443933204232374*^9, 3.443933238567974*^9, {3.443933324492774*^9, 3.4439333252727737`*^9}, {3.443933359343174*^9, 3.4439334752043743`*^9}, 3.443933509758374*^9, {3.443933589006374*^9, 3.443933589786374*^9}, { 3.443933864798774*^9, 3.443933872177574*^9}, {3.443933907417974*^9, 3.443933934561974*^9}, 3.443934011001974*^9, {3.443934148547174*^9, 3.4439341545999737`*^9}, {3.443934196688774*^9, 3.443934199559174*^9}, 3.443934615985574*^9, {3.443934665562374*^9, 3.443934690335174*^9}, { 3.4439348709051743`*^9, 3.443934878829974*^9}, {3.443934986984774*^9, 3.443934989371574*^9}, {3.4439362770051737`*^9, 3.443936288673974*^9}, 3.443937073322974*^9, {3.4439453557081738`*^9, 3.443945414722974*^9}, { 3.4439454486685743`*^9, 3.443945493908574*^9}, {3.443945592813574*^9, 3.443945602610374*^9}, {3.444042647998565*^9, 3.444042677045765*^9}, 3.4444395736456003`*^9, {3.4444396926112003`*^9, 3.4444397018152*^9}, { 3.4464299717019997`*^9, 3.4464299849308*^9}, {3.4466049799505997`*^9, 3.4466049833514*^9}, {3.4466050206822*^9, 3.4466050890257998`*^9}, { 3.4466051204286003`*^9, 3.4466052301902*^9}, 3.4771131915032*^9, { 3.5007268004706*^9, 3.5007268065234003`*^9}, {3.5007272402033997`*^9, 3.5007272528238*^9}, 3.5007273148494*^9, {3.6880535892141175`*^9, 3.6880535907041197`*^9}},ExpressionUUID->"6c784c18-cbe7-41d4-9317-\ 3394ef19b985"] }, Closed]], Cell[CellGroupData[{ Cell["GRAPHICS defs", "Subsection", CellChangeTimes->{{3.6337757022685537`*^9, 3.6337757351784363`*^9}, { 3.734064727558645*^9, 3.73406474989952*^9}, {3.734064825975355*^9, 3.734064828569765*^9}, {3.7451438050875483`*^9, 3.7451438075158496`*^9}, { 3.750748347033251*^9, 3.750748355529561*^9}, {3.78956792066949*^9, 3.789567926782812*^9}, 3.7895679585556145`*^9},ExpressionUUID->"773b4adc-8178-438d-9847-\ 2e15a35aa106"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"beam", " ", "graphics"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{"MESH", ",", RowBox[{"{", RowBox[{"BEAM", ",", "pro_", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"{", RowBox[{"Gray", ",", RowBox[{"Cylinder", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}]}], "}"}], ",", "0.003"}], "]"}], ",", "Blue", ",", RowBox[{"PointSize", "[", "Medium", "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}]}], "}"}], "]"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"d_", ",", "t_"}], "}"}], ",", "iy_"}], "}"}], ",", "for_"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Rho]", ",", "h", ",", "NL", ",", "NQ", ",", "ix", ",", "iz", ",", "T"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Rho]", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"\[Rho]", ".", "\[Rho]"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"h", ">", "0"}], ",", RowBox[{"L", ">", "0"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NL", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Xi]"}], ",", "\[Xi]"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NQ", "=", RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "\[Xi]"}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", "\[Xi]"}]}], ")"}]}], ",", RowBox[{"h", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "\[Xi]"}], ")"}], "2"], " ", "\[Xi]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{"2", " ", "\[Xi]"}]}], ")"}], " ", SuperscriptBox["\[Xi]", "2"]}], ",", RowBox[{"h", " ", SuperscriptBox["\[Xi]", "2"], " ", RowBox[{"(", RowBox[{"\[Xi]", "-", "1"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix", "=", RowBox[{"\[Rho]", "/", "h"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz", "=", RowBox[{"ix", "\[Cross]", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"T", "=", RowBox[{"{", RowBox[{"ix", ",", "iy", ",", "iz"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"ux1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "ix"}]}], ";", " ", RowBox[{"ux2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "ix"}]}], ";", "\[IndentingNewLine]", RowBox[{"uy1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iy"}]}], ";", " ", RowBox[{"uy2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"uz1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iz"}]}], ";", " ", RowBox[{"uz2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iz"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]x1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "ix"}]}], ";", " ", RowBox[{"\[Theta]x2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "ix"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]y1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iy"}]}], ";", " ", RowBox[{"\[Theta]y2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]z1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iz"}]}], ";", " ", RowBox[{"\[Theta]z2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iz"}]}], ";", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{ RowBox[{"NL", ".", RowBox[{"{", RowBox[{"ux1", ",", "ux2"}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{ RowBox[{"NQ", ".", RowBox[{"{", RowBox[{"uy1", ",", RowBox[{"-", "\[Theta]z1"}], ",", "uy2", ",", RowBox[{"-", "\[Theta]z2"}]}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"NQ", ".", RowBox[{"{", RowBox[{"uz1", ",", RowBox[{"-", "\[Theta]y1"}], ",", "uz2", ",", RowBox[{"-", "\[Theta]y2"}]}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"pp", "=", RowBox[{"Partition", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ix", "*", "h", "*", "\[Xi]"}], "+", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], ".", "T"}]}], ",", RowBox[{"{", RowBox[{"\[Xi]", ",", "0", ",", "1", ",", RowBox[{"1", "/", "10"}]}], "}"}]}], "]"}], ",", "2", ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"pp", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ix", "*", "h", "*", "\[Xi]"}], "+", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], ".", "T"}]}], ",", RowBox[{"{", RowBox[{"\[Xi]", ",", "0", ",", "1", ",", RowBox[{"1", "/", "10"}]}], "}"}]}], "]"}]}], ";", RowBox[{"{", RowBox[{"Gray", ",", RowBox[{"CapForm", "[", "\"\\"", "]"}], ",", RowBox[{"Tube", "[", RowBox[{"pp", ",", RowBox[{"d", "/", "2"}]}], " ", "]"}], ",", "Blue", ",", RowBox[{"PointSize", "[", "Medium", "]"}], ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "*", "scale"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "*", "scale"}]}], "]"}]}], "}"}]}]}], " ", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", RowBox[{"ly_", ",", "lz_", ",", "iy_"}], "}"}], ",", "for_"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Rho]", ",", "h", ",", "x", ",", "y", ",", "z", ",", "NL", ",", "NQ", ",", "ix", ",", "iz", ",", "T", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Rho]", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"\[Rho]", ".", "\[Rho]"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"h", ">", "0"}], ",", RowBox[{"L", ">", "0"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix", "=", RowBox[{"\[Rho]", "/", "h"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz", "=", RowBox[{"ix", "\[Cross]", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Rho]", "=", RowBox[{ RowBox[{"x", " ", "ix"}], "+", RowBox[{"y", " ", "iy"}], "+", RowBox[{"z", " ", "iz"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"T", "=", RowBox[{"{", RowBox[{"ix", ",", "iy", ",", "iz"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NL", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ",", RowBox[{"x", "/", "h"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NQ", "=", RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", RowBox[{"x", "/", "h"}]}]}], ")"}]}], ",", RowBox[{"h", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ")"}], "2"], " ", RowBox[{"x", "/", "h"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{"2", " ", RowBox[{"x", "/", "h"}]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}], "2"]}], ",", RowBox[{"h", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"x", "/", "h"}], "-", "1"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"ux1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "ix"}]}], ";", " ", RowBox[{"ux2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "ix"}]}], ";", "\[IndentingNewLine]", RowBox[{"uy1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iy"}]}], ";", " ", RowBox[{"uy2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"uz1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iz"}]}], ";", " ", RowBox[{"uz2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iz"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]x1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "ix"}]}], ";", " ", RowBox[{"\[Theta]x2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "ix"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]y1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iy"}]}], ";", " ", RowBox[{"\[Theta]y2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]z1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iz"}]}], ";", " ", RowBox[{"\[Theta]z2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iz"}]}], ";", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{"ux1", ",", "ux2"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{"uy1", ",", RowBox[{"-", "\[Theta]z1"}], ",", "uy2", ",", RowBox[{"-", "\[Theta]z2"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{"uz1", ",", RowBox[{"-", "\[Theta]y1"}], ",", "uz2", ",", RowBox[{"-", "\[Theta]y2"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{"\[Theta]x1", ",", "\[Theta]x2"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}]}], ";", "\[IndentingNewLine]", RowBox[{"ux", "=", RowBox[{ RowBox[{"(", RowBox[{"u", "+", RowBox[{"\[Theta]", " ", "z"}], "-", RowBox[{"\[Psi]", " ", "y"}]}], ")"}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"uy", "=", RowBox[{ RowBox[{"(", RowBox[{"v", "-", RowBox[{"\[Phi]", " ", "z"}]}], ")"}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"uz", "=", RowBox[{ RowBox[{"(", RowBox[{"w", "+", RowBox[{"\[Phi]", " ", "y"}]}], ")"}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"pp", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", "\[Rho]", "+", RowBox[{ RowBox[{"{", RowBox[{"ux", ",", "uy", ",", "uz"}], "}"}], ".", "T"}]}], ")"}], "/.", RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{"y", ",", "z"}], "}"}], "\[Rule]", "yz"}], "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "h", ",", RowBox[{"h", "/", "10"}]}], "}"}], ",", RowBox[{"{", RowBox[{"yz", ",", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"ly", ",", "lz"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "ly"}], ",", "lz"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "ly"}], ",", RowBox[{"-", "lz"}]}], "}"}], ",", RowBox[{"{", RowBox[{"ly", ",", RowBox[{"-", "lz"}]}], "}"}]}], "}"}], "/", "2"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Join", "[", RowBox[{ RowBox[{"{", RowBox[{"Gray", ",", RowBox[{"EdgeForm", "[", "]"}]}], "}"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"pp", "[", RowBox[{"[", RowBox[{"ii", ",", "1"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{"ii", ",", "2"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", "2"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", "1"}], "]"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"pp", "[", RowBox[{"[", RowBox[{"ii", ",", "2"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{"ii", ",", "3"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", "3"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", "2"}], "]"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"pp", "[", RowBox[{"[", RowBox[{"ii", ",", "4"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{"ii", ",", "3"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", "3"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", "4"}], "]"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"pp", "[", RowBox[{"[", RowBox[{"ii", ",", "1"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{"ii", ",", "4"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", "4"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", "1"}], "]"}], "]"}]}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", RowBox[{ RowBox[{"Length", "[", "pp", "]"}], "-", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"Blue", ",", RowBox[{"PointSize", "[", "Medium", "]"}], ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "*", "scale"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "*", "scale"}]}], "]"}]}], "}"}]}], " ", "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{"MESH", ",", RowBox[{"{", RowBox[{"RIGID", ",", "pro_", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"{", RowBox[{"Black", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}]}], "}"}], "]"}], ",", "Blue", ",", RowBox[{"PointSize", "[", "Medium", "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}]}], "}"}], "]"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"RIGID", ",", "pro_", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"crd1", ",", "crd2"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"crd1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "*", "scale"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"crd2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "*", "scale"}]}]}], ";", RowBox[{"{", RowBox[{"Black", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"crd1", ",", "crd2"}], "}"}], "]"}], ",", "Blue", ",", RowBox[{"PointSize", "[", "Medium", "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"crd1", ",", "crd2"}], "}"}], "]"}]}], "}"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"RIGID", ",", RowBox[{"{", RowBox[{"d_", ",", "b_", ",", "iy_"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"crd1", ",", "crd2"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"crd1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "-", RowBox[{"iy", "*", RowBox[{"b", "/", "2"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"crd2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "+", RowBox[{"iy", "*", RowBox[{"b", "/", "2"}]}]}]}], ";", RowBox[{"{", RowBox[{"Black", ",", RowBox[{"Cylinder", "[", RowBox[{ RowBox[{"{", RowBox[{"crd1", ",", "crd2"}], "}"}], ",", RowBox[{"d", "/", "2"}]}], "]"}], ",", "Blue", ",", RowBox[{"PointSize", "[", "Medium", "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"crd1", ",", "crd2"}], "}"}], "]"}]}], "}"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[Rho]_", "}"}], ",", RowBox[{"{", RowBox[{"lx_", ",", "ly_", ",", "lz_", ",", "ix_", ",", "iy_"}], "}"}], ",", RowBox[{"{", RowBox[{ "FX_", ",", "FY_", ",", "FZ_", ",", "MX_", ",", "MY_", ",", "MZ_"}], "}"}]}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"r", ",", "T"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"pnt", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "lx"}], ",", RowBox[{"-", "ly"}], ",", RowBox[{"-", "lz"}]}], "}"}], ",", RowBox[{"{", RowBox[{"lx", ",", RowBox[{"-", "ly"}], ",", RowBox[{"-", "lz"}]}], "}"}], ",", RowBox[{"{", RowBox[{"lx", ",", "ly", ",", RowBox[{"-", "lz"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "lx"}], ",", "ly", ",", RowBox[{"-", "lz"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"-", "lx"}], ",", RowBox[{"-", "ly"}], ",", "lz"}], "}"}], ",", RowBox[{"{", RowBox[{"lx", ",", RowBox[{"-", "ly"}], ",", "lz"}], "}"}], ",", RowBox[{"{", RowBox[{"lx", ",", "ly", ",", "lz"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "lx"}], ",", "ly", ",", "lz"}], "}"}]}], "}"}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"crd", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ix", ",", "iy", ",", RowBox[{"ix", StyleBox["\[Cross]", "OperatorCharacter"], "iy"}]}], "}"}], ".", "#"}], "&"}], ",", "pnt"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", "#", "+", RowBox[{"scale", "*", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{"scale", "*", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], StyleBox["\[Cross]", "OperatorCharacter"], RowBox[{ StyleBox["(", "OperatorCharacter"], RowBox[{ StyleBox["#", "OperatorCharacter"], StyleBox["-", "OperatorCharacter"], RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}], ")"}]}]}]}], "&"}], ",", "crd"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Gray", ",", RowBox[{"Opacity", "[", "0.5", "]"}], ",", "\[IndentingNewLine]", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"r", "[", RowBox[{"[", "4", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "3", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "2", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}], "]"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"r", "[", RowBox[{"[", "5", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "6", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "7", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "8", "]"}], "]"}]}], "}"}], "]"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"r", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "2", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "6", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "5", "]"}], "]"}]}], "}"}], "]"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"r", "[", RowBox[{"[", "3", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "4", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "8", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "7", "]"}], "]"}]}], "}"}], "]"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"r", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "5", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "8", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "4", "]"}], "]"}]}], "}"}], "]"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"r", "[", RowBox[{"[", "2", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "3", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "7", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "6", "]"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "Blue", ",", RowBox[{"PointSize", "[", "Medium", "]"}], ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"scale", "*", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}]}], "]"}]}], "}"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", "t_", "}"}], ",", "for_"}], "}"}], ",", RowBox[{"ELEMENT", "[", "nodes_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "node", ",", "n\[Alpha]", ",", "n\[Beta]", ",", "\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Rho]", ",", "r\[Alpha]", ",", "r\[Beta]", ",", "rn", ",", "r0", ",", "n", ",", "NN", ",", "en", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "pp", ",", "face1", ",", "face2", ",", "face3", ",", "face4", ",", "face5", ",", "face6"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"n\[Alpha]", ",", "n\[Beta]"}], "}"}], "=", RowBox[{"Dimensions", "[", "nodes", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n\[Alpha]", ",", "\[Alpha]"}], "}"}], ",", RowBox[{"{", RowBox[{"n\[Beta]", ",", "\[Beta]"}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"node", "=", RowBox[{"Flatten", "[", "nodes", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Alpha]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r0"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Beta]", "=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r0"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"rn", "=", RowBox[{"r\[Alpha]", "\[Cross]", "r\[Beta]"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{"rn", "/", RowBox[{"Norm", "[", "rn", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Rho]", "=", RowBox[{"en", "*", "\[Gamma]"}]}], ";", "\[IndentingNewLine]", RowBox[{"n", "=", "5"}], ";", "\[IndentingNewLine]", RowBox[{"pp", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"r0", "+", "\[Rho]", "+", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "*", "scale"}], "+", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "\[Cross]", "\[Rho]"}], "*", "scale"}]}], ")"}], " ", "/.", " ", RowBox[{"\[Gamma]", "->", RowBox[{"t", "/", "2"}]}]}], ",", RowBox[{"{", RowBox[{"\[Beta]", ",", "0", ",", "1", ",", RowBox[{"1", "/", "n"}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "0", ",", "1", ",", RowBox[{"1", "/", "n"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"face1", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"pp", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"i", "+", "1"}], ",", "j"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"i", "+", "1"}], ",", RowBox[{"j", "+", "1"}]}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{"i", ",", RowBox[{"j", "+", "1"}]}], "]"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "n"}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "n"}], "}"}]}], "]"}], ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"pp", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"r0", "+", "\[Rho]", "+", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "*", "scale"}], "+", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "\[Cross]", "\[Rho]"}], "*", "scale"}]}], ")"}], " ", "/.", " ", RowBox[{"\[Gamma]", "\[Rule]", RowBox[{ RowBox[{"-", "t"}], "/", "2"}]}]}], " ", ",", RowBox[{"{", RowBox[{"\[Beta]", ",", "0", ",", "1", ",", RowBox[{"1", "/", "n"}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "0", ",", "1", ",", RowBox[{"1", "/", "n"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"face2", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"Reverse", "[", RowBox[{"{", RowBox[{ RowBox[{"pp", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"i", "+", "1"}], ",", "j"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"i", "+", "1"}], ",", RowBox[{"j", "+", "1"}]}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{"i", ",", RowBox[{"j", "+", "1"}]}], "]"}], "]"}]}], "}"}], "]"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "n"}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "n"}], "}"}]}], "]"}], ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"pp", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"r0", "+", "\[Rho]", "+", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "*", "scale"}], "+", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "\[Cross]", "\[Rho]"}], "*", "scale"}]}], ")"}], " ", "/.", " ", RowBox[{"\[Beta]", "\[Rule]", "1"}]}], ",", RowBox[{"{", RowBox[{"\[Gamma]", ",", RowBox[{ RowBox[{"-", "t"}], "/", "2"}], ",", RowBox[{"t", "/", "2"}], ",", RowBox[{"t", "/", "n"}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "0", ",", "1", ",", RowBox[{"1", "/", "n"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"n", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"face3", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"pp", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"i", "+", "1"}], ",", "j"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"i", "+", "1"}], ",", RowBox[{"j", "+", "1"}]}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{"i", ",", RowBox[{"j", "+", "1"}]}], "]"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "n"}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "n"}], "}"}]}], "]"}], ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"pp", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"r0", "+", "\[Rho]", "+", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "*", "scale"}], "+", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "\[Cross]", "\[Rho]"}], "*", "scale"}]}], ")"}], " ", "/.", " ", RowBox[{"\[Beta]", "\[Rule]", "0"}]}], ",", RowBox[{"{", RowBox[{"\[Gamma]", ",", RowBox[{ RowBox[{"-", "t"}], "/", "2"}], ",", RowBox[{"t", "/", "2"}], ",", RowBox[{"t", "/", "n"}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "0", ",", "1", ",", RowBox[{"1", "/", "n"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"face4", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"Reverse", "[", RowBox[{"{", RowBox[{ RowBox[{"pp", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"i", "+", "1"}], ",", "j"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"i", "+", "1"}], ",", RowBox[{"j", "+", "1"}]}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{"i", ",", RowBox[{"j", "+", "1"}]}], "]"}], "]"}]}], "}"}], "]"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "n"}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "n"}], "}"}]}], "]"}], ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"pp", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"r0", "+", "\[Rho]", "+", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "*", "scale"}], "+", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "\[Cross]", "\[Rho]"}], "*", "scale"}]}], ")"}], " ", "/.", " ", RowBox[{"\[Alpha]", "\[Rule]", "1"}]}], ",", RowBox[{"{", RowBox[{"\[Gamma]", ",", RowBox[{ RowBox[{"-", "t"}], "/", "2"}], ",", RowBox[{"t", "/", "2"}], ",", RowBox[{"t", "/", "n"}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Beta]", ",", "0", ",", "1", ",", RowBox[{"1", "/", "n"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"face5", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"pp", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"i", "+", "1"}], ",", "j"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"i", "+", "1"}], ",", RowBox[{"j", "+", "1"}]}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{"i", ",", RowBox[{"j", "+", "1"}]}], "]"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "n"}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "n"}], "}"}]}], "]"}], ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"pp", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"r0", "+", "\[Rho]", "+", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "*", "scale"}], "+", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "\[Cross]", "\[Rho]"}], "*", "scale"}]}], ")"}], " ", "/.", " ", RowBox[{"\[Alpha]", "\[Rule]", "0"}]}], ",", RowBox[{"{", RowBox[{"\[Gamma]", ",", RowBox[{ RowBox[{"-", "t"}], "/", "2"}], ",", RowBox[{"t", "/", "2"}], ",", RowBox[{"t", "/", "n"}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Beta]", ",", "0", ",", "1", ",", RowBox[{"1", "/", "n"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"face6", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"Reverse", "[", RowBox[{"{", RowBox[{ RowBox[{"pp", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"i", "+", "1"}], ",", "j"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"i", "+", "1"}], ",", RowBox[{"j", "+", "1"}]}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{"i", ",", RowBox[{"j", "+", "1"}]}], "]"}], "]"}]}], "}"}], "]"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "n"}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "n"}], "}"}]}], "]"}], ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Gray", ",", RowBox[{"Opacity", "[", "0.5", "]"}], ",", RowBox[{"EdgeForm", "[", "]"}], ",", RowBox[{"Polygon", "[", "face1", "]"}], ",", RowBox[{"Polygon", "[", "face2", "]"}], ",", RowBox[{"Polygon", "[", "face3", "]"}], ",", RowBox[{"Polygon", "[", "face4", "]"}], ",", RowBox[{"Polygon", "[", "face5", "]"}], ",", RowBox[{"Polygon", "[", "face6", "]"}], ",", "Blue", ",", RowBox[{"PointSize", "[", "Tiny", "]"}], ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"node", ",", "2"}], "]"}], "]"}], "*", "scale"}]}], "]"}]}], "}"}]}]}], " ", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", RowBox[{"d_", ",", "iy_"}], "}"}], ",", "for_"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Rho]", ",", "h", ",", "NL", ",", "NQ", ",", "ix", ",", "iz", ",", "T"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Rho]", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"\[Rho]", ".", "\[Rho]"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"h", ">", "0"}], ",", RowBox[{"L", ">", "0"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NL", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Xi]"}], ",", "\[Xi]"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NQ", "=", RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "\[Xi]"}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", "\[Xi]"}]}], ")"}]}], ",", RowBox[{"h", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "\[Xi]"}], ")"}], "2"], " ", "\[Xi]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{"2", " ", "\[Xi]"}]}], ")"}], " ", SuperscriptBox["\[Xi]", "2"]}], ",", RowBox[{"h", " ", SuperscriptBox["\[Xi]", "2"], " ", RowBox[{"(", RowBox[{"\[Xi]", "-", "1"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix", "=", RowBox[{"\[Rho]", "/", "h"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz", "=", RowBox[{"ix", "\[Cross]", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"T", "=", RowBox[{"{", RowBox[{"ix", ",", "iy", ",", "iz"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"ux1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "ix"}]}], ";", " ", RowBox[{"ux2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "ix"}]}], ";", "\[IndentingNewLine]", RowBox[{"uy1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iy"}]}], ";", " ", RowBox[{"uy2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"uz1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iz"}]}], ";", " ", RowBox[{"uz2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iz"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]x1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "ix"}]}], ";", " ", RowBox[{"\[Theta]x2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "ix"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]y1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iy"}]}], ";", " ", RowBox[{"\[Theta]y2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]z1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iz"}]}], ";", " ", RowBox[{"\[Theta]z2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iz"}]}], ";", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{ RowBox[{"NL", ".", RowBox[{"{", RowBox[{"ux1", ",", "ux2"}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{ RowBox[{"NQ", ".", RowBox[{"{", RowBox[{"uy1", ",", RowBox[{"-", "\[Theta]z1"}], ",", "uy2", ",", RowBox[{"-", "\[Theta]z2"}]}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"NQ", ".", RowBox[{"{", RowBox[{"uz1", ",", RowBox[{"-", "\[Theta]y1"}], ",", "uz2", ",", RowBox[{"-", "\[Theta]y2"}]}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"pp", "=", RowBox[{"Partition", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ix", "*", "h", "*", "\[Xi]"}], "+", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], ".", "T"}]}], ",", RowBox[{"{", RowBox[{"\[Xi]", ",", "0", ",", "1", ",", RowBox[{"1", "/", "10"}]}], "}"}]}], "]"}], ",", "2", ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"pp", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ix", "*", "h", "*", "\[Xi]"}], "+", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], ".", "T"}]}], ",", RowBox[{"{", RowBox[{"\[Xi]", ",", "0", ",", "1", ",", RowBox[{"1", "/", "10"}]}], "}"}]}], "]"}]}], ";", RowBox[{"{", RowBox[{"Gray", ",", RowBox[{"Tube", "[", RowBox[{"pp", ",", RowBox[{"d", "/", "2"}]}], " ", "]"}], ",", "Blue", ",", RowBox[{"PointSize", "[", "Medium", "]"}], ",", RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "*", "scale"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "+", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}]}], "]"}], "*", "scale"}]}], "}"}]}]}], " ", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"nonlinear", " ", "beam", " ", "graphics"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iy_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[CapitalDelta]h", ",", "h0", ",", "NN", ",", "r0", ",", "u", ",", "w"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "*", RowBox[{"(", RowBox[{"1", "-", "\[Xi]"}], ")"}]}], "+", RowBox[{"\[Xi]", "*", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h0", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", " ", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "r0"}], ".", RowBox[{ SubscriptBox["\[PartialD]", "\[Xi]"], "r0"}]}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"h", ">", "0"}]}]}], "]"}]}], ";", StyleBox["\[IndentingNewLine]", "OperatorCharacter"], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "\[Xi]"}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", "\[Xi]"}]}], ")"}]}], ",", RowBox[{"h0", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "\[Xi]"}], ")"}], "2"], " ", "\[Xi]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{"2", " ", "\[Xi]"}]}], ")"}], " ", SuperscriptBox["\[Xi]", "2"]}], ",", RowBox[{"h0", " ", SuperscriptBox["\[Xi]", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Xi]"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NN", ".", RowBox[{"Flatten", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", RowBox[{"2", ";;", "3"}], ",", "1"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"NN", ".", RowBox[{"Flatten", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], ",", RowBox[{"2", ";;", "3"}], ",", "3"}], "]"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"r0", "+", RowBox[{"{", RowBox[{"u", ",", "0", ",", "w"}], "}"}]}], ",", RowBox[{"{", RowBox[{"\[Xi]", ",", "0", ",", "1", ",", "0.05"}], "}"}]}], "]"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"FX_Real", ",", "FY_Real", ",", "FZ_Real"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "r0"}], "}"}], ",", RowBox[{ RowBox[{"L", "=", RowBox[{"Max", "[", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], "-", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}]}], "&"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"MinMax", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{";;", ",", "1", ",", "i"}], "]"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}]}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"scale", "*", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Black", ",", "Thick", ",", RowBox[{"Arrowheads", "[", "Medium", "]"}], ",", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{"r0", ",", RowBox[{"r0", "+", RowBox[{ RowBox[{"L", "/", "10"}], "*", RowBox[{ RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ"}], "}"}], "/", RowBox[{"Max", "[", RowBox[{ RowBox[{"Norm", "[", RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ"}], "}"}], "]"}], ",", RowBox[{"1", "/", "100"}]}], "]"}]}]}]}]}], "}"}], "]"}]}], "}"}]}]}], "]"}]}], ";"}], "*)"}], "\[IndentingNewLine]"}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.633673923685915*^9, 3.6336739535006204`*^9}, { 3.633674155068149*^9, 3.6336741996717005`*^9}, {3.6336745049841633`*^9, 3.6336745219741354`*^9}, {3.6336919593939404`*^9, 3.6336919775979815`*^9}, 3.633692380551029*^9, {3.6336927116599674`*^9, 3.633692727194856*^9}, { 3.635310826749509*^9, 3.6353108343419433`*^9}, {3.635311461613821*^9, 3.6353114619508405`*^9}, {3.7326759806780663`*^9, 3.7326760008674326`*^9}, {3.7326760331212645`*^9, 3.7326760385677853`*^9}, {3.732684137201784*^9, 3.73268419404665*^9}, { 3.732684306221466*^9, 3.7326843382153635`*^9}, 3.7326844699232764`*^9, { 3.7326845133861027`*^9, 3.73268452322455*^9}, {3.732759973190983*^9, 3.7327599776758347`*^9}, {3.7327613720703106`*^9, 3.7327614888170295`*^9}, {3.732761535853627*^9, 3.7327615404943867`*^9}, { 3.7327615972663317`*^9, 3.7327616122832594`*^9}, {3.7327616693361855`*^9, 3.73276183332095*^9}, {3.732761876700554*^9, 3.7327618790133*^9}, { 3.732761909063363*^9, 3.732761910469795*^9}, {3.73276200508918*^9, 3.732762006042756*^9}, {3.7327620750344048`*^9, 3.732762101490326*^9}, 3.7327688007102947`*^9, {3.7327705695330524`*^9, 3.7327705708254137`*^9}, { 3.732788507552166*^9, 3.7327885085870132`*^9}, {3.732788681344634*^9, 3.7327887090994544`*^9}, {3.732788743287696*^9, 3.73278879848213*^9}, { 3.732788922306119*^9, 3.7327889462731514`*^9}, {3.732789012151597*^9, 3.732789028200858*^9}, {3.7327890791192408`*^9, 3.732789086999034*^9}, { 3.732789135698248*^9, 3.7327891358892384`*^9}, {3.7327891989507074`*^9, 3.7327891993104925`*^9}, {3.733116709198372*^9, 3.733116731638229*^9}, { 3.7334931331412554`*^9, 3.7334932071522064`*^9}, {3.733493353668892*^9, 3.7334934953404007`*^9}, {3.733493581610343*^9, 3.733493589891471*^9}, { 3.7334936319789553`*^9, 3.7334936623392687`*^9}, {3.7334936935401745`*^9, 3.733493716917615*^9}, {3.7334937687375154`*^9, 3.733493799379287*^9}, { 3.7335602963276734`*^9, 3.7335603891038685`*^9}, {3.7337039222525787`*^9, 3.733703929721642*^9}, {3.7337040222462597`*^9, 3.7337040262631474`*^9}, { 3.733710121070121*^9, 3.733710122358057*^9}, 3.7337110885786676`*^9, 3.733711184948838*^9, {3.733711259729956*^9, 3.733711278366322*^9}, 3.7337113240271106`*^9, {3.733711384581702*^9, 3.733711436236964*^9}, 3.7337114809469175`*^9, {3.7337115173918333`*^9, 3.733711518879483*^9}, 3.733711560439453*^9, {3.733711609599924*^9, 3.7337116342722664`*^9}, { 3.733711689751358*^9, 3.7337116969119487`*^9}, {3.7337129879879694`*^9, 3.7337130014112797`*^9}, {3.733713172835663*^9, 3.733713173913886*^9}, { 3.7337132483436465`*^9, 3.7337132496094065`*^9}, {3.733713283003566*^9, 3.7337134200180254`*^9}, {3.733713464428997*^9, 3.7337135191222897`*^9}, { 3.7337135777847366`*^9, 3.73371367154463*^9}, {3.7337140009857264`*^9, 3.7337140458967295`*^9}, {3.733714091198394*^9, 3.7337141070440063`*^9}, { 3.733714143813529*^9, 3.733714146610505*^9}, {3.733721976862414*^9, 3.7337219813629093`*^9}, {3.733722281191476*^9, 3.7337222944429536`*^9}, { 3.733722382186266*^9, 3.7337223828425617`*^9}, {3.7337224624293957`*^9, 3.7337224858690815`*^9}, 3.7337225537825146`*^9, {3.733722654230641*^9, 3.733722661731436*^9}, {3.733722818999301*^9, 3.7337228267499514`*^9}, { 3.733723144924486*^9, 3.733723159691375*^9}, {3.733723196273369*^9, 3.733723198695795*^9}, {3.7337232377777586`*^9, 3.7337232408874655`*^9}, { 3.73372435111442*^9, 3.733724354067712*^9}, {3.7337244099801674`*^9, 3.733724433076069*^9}, {3.7337245236325226`*^9, 3.733724524679802*^9}, { 3.7337873724058084`*^9, 3.7337873841879997`*^9}, {3.7337879154409466`*^9, 3.7337879158316607`*^9}, {3.7340647908247976`*^9, 3.73406479426425*^9}, 3.734064961166012*^9, {3.7340649924958353`*^9, 3.7340650071121197`*^9}, { 3.734065080806053*^9, 3.7340651183371983`*^9}, {3.7340717082263236`*^9, 3.7340717106541834`*^9}, {3.7340733640961533`*^9, 3.734073544150256*^9}, { 3.734073575450083*^9, 3.7340736415768323`*^9}, {3.7340736917524757`*^9, 3.7340736979070516`*^9}, {3.7340738227246733`*^9, 3.734073837462171*^9}, { 3.7340739034480777`*^9, 3.734073926441464*^9}, {3.7340739810895205`*^9, 3.734073989147008*^9}, {3.7340742070861125`*^9, 3.7340742176873407`*^9}, { 3.7340743130118575`*^9, 3.7340743136367188`*^9}, 3.734147513058416*^9, { 3.734147568916667*^9, 3.7341475939306383`*^9}, {3.734147807211531*^9, 3.7341478287481747`*^9}, {3.734147861578357*^9, 3.7341478856653595`*^9}, 3.73414797622887*^9, {3.734148333604216*^9, 3.7341483447645597`*^9}, { 3.734148391271126*^9, 3.734148430462343*^9}, {3.7341486538224015`*^9, 3.734148655872754*^9}, {3.734780635679473*^9, 3.7347806548690386`*^9}, { 3.734780765771411*^9, 3.7347807803670073`*^9}, {3.7347809996713924`*^9, 3.734781008203253*^9}, {3.7348427053556232`*^9, 3.7348427411876764`*^9}, { 3.7348427811917715`*^9, 3.7348428157425947`*^9}, {3.7352741876350036`*^9, 3.735274188984682*^9}, {3.744334694805724*^9, 3.744334695602414*^9}, { 3.7443347269076095`*^9, 3.7443347277042484`*^9}, {3.7443708556292257`*^9, 3.744370857925562*^9}, {3.7443710360558863`*^9, 3.7443710373681135`*^9}, { 3.7443728681474504`*^9, 3.7443728796447964`*^9}, {3.744372944801361*^9, 3.7443729465196667`*^9}, 3.7444272378898153`*^9, {3.7450269816449513`*^9, 3.745026983254672*^9}, {3.7461503454492016`*^9, 3.7461503964527383`*^9}, { 3.7461504977259088`*^9, 3.7461505005843096`*^9}, {3.7461505589454737`*^9, 3.7461506157760525`*^9}, {3.746150984703903*^9, 3.74615099456116*^9}, { 3.750748457386656*^9, 3.75074846753214*^9}, {3.750748881443331*^9, 3.7507488854690557`*^9}, {3.750749005058874*^9, 3.750749023499106*^9}, { 3.7507501792180104`*^9, 3.750750248150975*^9}, {3.7507502795426817`*^9, 3.750750280787862*^9}, {3.7507503174292965`*^9, 3.7507503665913057`*^9}, { 3.7507503972457952`*^9, 3.7507504187333727`*^9}, {3.7507505335852304`*^9, 3.750750827854561*^9}, {3.7507508607353168`*^9, 3.7507508749873066`*^9}, { 3.750750906727187*^9, 3.750750925222521*^9}, {3.7507511964801655`*^9, 3.7507512498091383`*^9}, {3.760607688544195*^9, 3.7606077135130415`*^9}, 3.7606087463370066`*^9, {3.765086128848972*^9, 3.765086135973978*^9}, { 3.765086334880218*^9, 3.765086340797302*^9}, {3.8532058197692585`*^9, 3.8532058295626307`*^9}, {3.853205931683282*^9, 3.8532059509132338`*^9}, { 3.853206459482326*^9, 3.8532064976587143`*^9}, 3.8532069619654517`*^9}, CellLabel-> "In[333]:=",ExpressionUUID->"1b3236c8-2377-4f6a-97a6-8ea6af071442"] }, Open ]], Cell[CellGroupData[{ Cell["SHOW3D GRAPHICS defs", "Subsection", CellChangeTimes->{{3.6337757022685537`*^9, 3.6337757351784363`*^9}, { 3.734064727558645*^9, 3.73406474989952*^9}, {3.7451438105166326`*^9, 3.745143811840375*^9}, {3.7606070835401344`*^9, 3.760607098895162*^9}, { 3.760607741638811*^9, 3.760607749187194*^9}, {3.760608900875217*^9, 3.7606089113767295`*^9}},ExpressionUUID->"f00aec32-f5de-4e85-88aa-\ 4ceffa8f1e09"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"POSTFORM", "=", RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SHOW3D", "[", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}], "]"}], ":=", RowBox[{"SHOW3D", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SHOW3D", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{ RowBox[{"Graphics3D", "[", RowBox[{"Join", "[", " ", RowBox[{ RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", "#", ",", "fun"}], " ", "]"}], "&"}], ",", "ele"}], "]"}], ",", "1"}], "]"}], ",", "POSTFORM"}], "]"}], "]"}], ",", RowBox[{"SphericalRegion", "\[Rule]", "True"}], ",", RowBox[{"Axes", "->", "True"}], ",", RowBox[{"Lighting", "\[Rule]", "\"\\""}]}], "]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SHOW3D", "[", RowBox[{"MESH", ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"SHOW3D", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"MEC", "-", RowBox[{"E1050", " ", "and", " ", "MEC"}], "-", RowBox[{"E8001", " ", "defs"}]}], "*)"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"typ_", ",", "pro_", ",", "nod_"}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"LINK", ",", "typ_", ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"FX_", ",", "FY_", ",", "FZ_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "r0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"L", "=", RowBox[{"Max", "[", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], "-", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}]}], "&"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"MinMax", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{";;", ",", "1", ",", "i"}], "]"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}]}], "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"scale", "*", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Black", ",", "Thick", ",", RowBox[{"Arrowheads", "[", "Medium", "]"}], ",", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{"r0", ",", RowBox[{"r0", "+", RowBox[{ RowBox[{"L", "/", "10"}], "*", RowBox[{ RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ"}], "}"}], "/", RowBox[{"Max", "[", RowBox[{ RowBox[{"Norm", "[", RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ"}], "}"}], "]"}], ",", RowBox[{"1", "/", "100"}]}], "]"}]}]}]}]}], "}"}], "]"}]}], "}"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"RIGID", ",", RowBox[{"{", "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"m_", ",", "J_"}], "}"}], ",", RowBox[{"{", RowBox[{"ix_", ",", "iy_"}], "}"}], ",", RowBox[{"{", RowBox[{"xyz_", ",", "mc_"}], "}"}]}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"r", ",", "crd"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"crd", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ix", ",", "iy", ",", RowBox[{"ix", StyleBox["\[Cross]", "OperatorCharacter"], "iy"}]}], "}"}], ".", "#"}], "&"}], ",", "xyz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", "#", "+", RowBox[{"scale", "*", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{"scale", "*", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], StyleBox["\[Cross]", "OperatorCharacter"], RowBox[{ StyleBox["(", "OperatorCharacter"], RowBox[{ StyleBox["#", "OperatorCharacter"], StyleBox["-", "OperatorCharacter"], RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}], ")"}]}]}]}], "&"}], ",", "crd"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Join", "[", RowBox[{"FORCEFORM", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Polygon", "[", RowBox[{"r", "[", RowBox[{"[", "#", "]"}], "]"}], "]"}], "&"}], ",", "mc"}], "]"}], ",", "\[IndentingNewLine]", "POINTFORM", ",", RowBox[{"{", RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"scale", "*", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}]}], "]"}], "}"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"AA_", ",", "Iy_", ",", "Iz_"}], "}"}], ",", "iy_", ",", RowBox[{"{", RowBox[{"yz_", ",", "mc_"}], "}"}]}], "}"}], ",", "for_"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"AA", ",", "Iy", ",", "Iz", ",", "iy"}], "}"}], ",", RowBox[{"{", RowBox[{"yz", ",", "mc"}], "}"}]}], "}"}], ",", "for"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"AA_", ",", "Iy_", ",", "Iz_", ",", "iy_"}], "}"}], ",", RowBox[{"{", RowBox[{"crd_", ",", "nod_"}], "}"}]}], "}"}], ",", "for_"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r1", ",", "\[CapitalDelta]r", ",", "r", ",", "h", ",", "x", ",", "y", ",", "z", ",", "NL", ",", "NQ", ",", "ix", ",", "iz", ",", "T", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "ux1", ",", "ux2", ",", "uz1", ",", "uz2", ",", "uy1", ",", "uy2", ",", "\[Theta]x1", ",", "\[Theta]x2", ",", "\[Theta]y1", ",", "\[Theta]y2", ",", "\[Theta]z1", ",", "\[Theta]z2", ",", "ux", ",", "uy", ",", "uz", ",", "pp", ",", "nn"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"r1", "=", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalDelta]r", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h", "=", RowBox[{"Sqrt", "[", RowBox[{"\[CapitalDelta]r", ".", "\[CapitalDelta]r"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix", "=", RowBox[{"\[CapitalDelta]r", "/", "h"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz", "=", RowBox[{"ix", "\[Cross]", "iy"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"displacements", " ", "and", " ", "rotations"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NL", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ",", RowBox[{"x", "/", "h"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NQ", "=", RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", RowBox[{"x", "/", "h"}]}]}], ")"}]}], ",", RowBox[{"h", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ")"}], "2"], " ", RowBox[{"x", "/", "h"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{"2", " ", RowBox[{"x", "/", "h"}]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}], "2"]}], ",", RowBox[{"h", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"x", "/", "h"}], "-", "1"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"ux1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "ix"}]}], ";", " ", RowBox[{"ux2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "ix"}]}], ";", "\[IndentingNewLine]", RowBox[{"uy1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iy"}]}], ";", " ", RowBox[{"uy2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"uz1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iz"}]}], ";", " ", RowBox[{"uz2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iz"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]x1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "ix"}]}], ";", " ", RowBox[{"\[Theta]x2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "ix"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]y1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iy"}]}], ";", " ", RowBox[{"\[Theta]y2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]z1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iz"}]}], ";", " ", RowBox[{"\[Theta]z2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iz"}]}], ";", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{"ux1", ",", "ux2"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{"uy1", ",", "\[Theta]z1", ",", "uy2", ",", "\[Theta]z2"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{"uz1", ",", RowBox[{"-", "\[Theta]y1"}], ",", "uz2", ",", RowBox[{"-", "\[Theta]y2"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{"\[Theta]x1", ",", "\[Theta]x2"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}]}], ";", "\[IndentingNewLine]", RowBox[{"ux", "=", RowBox[{ RowBox[{"(", RowBox[{"u", "+", RowBox[{"\[Theta]", " ", "z"}], "-", RowBox[{"\[Psi]", " ", "y"}]}], ")"}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"uy", "=", RowBox[{ RowBox[{"(", RowBox[{"v", "-", RowBox[{"\[Phi]", " ", "z"}]}], ")"}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"uz", "=", RowBox[{ RowBox[{"(", RowBox[{"w", "+", RowBox[{"\[Phi]", " ", "y"}]}], ")"}], "*", "scale"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"nn", "=", "10"}], ";", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"ii", " ", "slab", " ", "and", " ", "jj", " ", "nod"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"pp", "[", RowBox[{"ii_", ",", "jj_"}], "]"}], ":=", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"r1", "+", RowBox[{ RowBox[{"(", RowBox[{"x", "+", "ux"}], ")"}], " ", "ix"}], "+", RowBox[{ RowBox[{"(", RowBox[{"y", "+", "uy"}], " ", ")"}], "iy"}], " ", "+", RowBox[{ RowBox[{"(", RowBox[{"z", "+", "uz"}], ")"}], " ", "iz"}]}], ")"}], "/.", RowBox[{"x", "\[Rule]", RowBox[{"(", RowBox[{"ii", "*", RowBox[{"h", "/", "nn"}]}], ")"}]}]}], "/.", RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{"y", ",", "z"}], "}"}], "\[Rule]", RowBox[{"crd", "[", RowBox[{"[", "jj", "]"}], "]"}]}], "]"}]}]}], " ", ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Join", "[", RowBox[{"BEAMFORM", ",", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"pp", "[", RowBox[{"ii", ",", RowBox[{"nod", "[", RowBox[{"[", RowBox[{"ip", ",", "1"}], "]"}], "]"}]}], "]"}], ",", RowBox[{"pp", "[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", RowBox[{"nod", "[", RowBox[{"[", RowBox[{"ip", ",", "1"}], "]"}], "]"}]}], "]"}], ",", RowBox[{"pp", "[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", RowBox[{"nod", "[", RowBox[{"[", RowBox[{"ip", ",", "2"}], "]"}], "]"}]}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"ii", ",", RowBox[{"nod", "[", RowBox[{"[", RowBox[{"ip", ",", "2"}], "]"}], "]"}]}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"ii", ",", "0", ",", RowBox[{"nn", "-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"ip", ",", "1", ",", RowBox[{"Length", "[", "nod", "]"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", "POINTFORM", ",", RowBox[{"{", RowBox[{ RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "*", "scale"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "*", "scale"}]}], "]"}]}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]"}], "Input", InitializationCell->True, CellChangeTimes->{{3.633673923685915*^9, 3.6336739535006204`*^9}, { 3.633674155068149*^9, 3.6336741996717005`*^9}, {3.6336745049841633`*^9, 3.6336745219741354`*^9}, {3.6336919593939404`*^9, 3.6336919775979815`*^9}, 3.633692380551029*^9, {3.6336927116599674`*^9, 3.633692727194856*^9}, { 3.635310826749509*^9, 3.6353108343419433`*^9}, {3.635311461613821*^9, 3.6353114619508405`*^9}, {3.7326759806780663`*^9, 3.7326760008674326`*^9}, {3.7326760331212645`*^9, 3.7326760385677853`*^9}, {3.732684137201784*^9, 3.73268419404665*^9}, { 3.732684306221466*^9, 3.7326843382153635`*^9}, 3.7326844699232764`*^9, { 3.7326845133861027`*^9, 3.73268452322455*^9}, {3.732759973190983*^9, 3.7327599776758347`*^9}, {3.7327613720703106`*^9, 3.7327614888170295`*^9}, {3.732761535853627*^9, 3.7327615404943867`*^9}, { 3.7327615972663317`*^9, 3.7327616122832594`*^9}, {3.7327616693361855`*^9, 3.73276183332095*^9}, {3.732761876700554*^9, 3.7327618790133*^9}, { 3.732761909063363*^9, 3.732761910469795*^9}, {3.73276200508918*^9, 3.732762006042756*^9}, {3.7327620750344048`*^9, 3.732762101490326*^9}, 3.7327688007102947`*^9, {3.7327705695330524`*^9, 3.7327705708254137`*^9}, { 3.732788507552166*^9, 3.7327885085870132`*^9}, {3.732788681344634*^9, 3.7327887090994544`*^9}, {3.732788743287696*^9, 3.73278879848213*^9}, { 3.732788922306119*^9, 3.7327889462731514`*^9}, {3.732789012151597*^9, 3.732789028200858*^9}, {3.7327890791192408`*^9, 3.732789086999034*^9}, { 3.732789135698248*^9, 3.7327891358892384`*^9}, {3.7327891989507074`*^9, 3.7327891993104925`*^9}, {3.733116709198372*^9, 3.733116731638229*^9}, { 3.7334931331412554`*^9, 3.7334932071522064`*^9}, {3.733493353668892*^9, 3.7334934953404007`*^9}, {3.733493581610343*^9, 3.733493589891471*^9}, { 3.7334936319789553`*^9, 3.7334936623392687`*^9}, {3.7334936935401745`*^9, 3.733493716917615*^9}, {3.7334937687375154`*^9, 3.733493799379287*^9}, { 3.7335602963276734`*^9, 3.7335603891038685`*^9}, {3.7337039222525787`*^9, 3.733703929721642*^9}, {3.7337040222462597`*^9, 3.7337040262631474`*^9}, { 3.733710121070121*^9, 3.733710122358057*^9}, 3.7337110885786676`*^9, 3.733711184948838*^9, {3.733711259729956*^9, 3.733711278366322*^9}, 3.7337113240271106`*^9, {3.733711384581702*^9, 3.733711436236964*^9}, 3.7337114809469175`*^9, {3.7337115173918333`*^9, 3.733711518879483*^9}, 3.733711560439453*^9, {3.733711609599924*^9, 3.7337116342722664`*^9}, { 3.733711689751358*^9, 3.7337116969119487`*^9}, {3.7337129879879694`*^9, 3.7337130014112797`*^9}, {3.733713172835663*^9, 3.733713173913886*^9}, { 3.7337132483436465`*^9, 3.7337132496094065`*^9}, {3.733713283003566*^9, 3.7337134200180254`*^9}, {3.733713464428997*^9, 3.7337135191222897`*^9}, { 3.7337135777847366`*^9, 3.73371367154463*^9}, {3.7337140009857264`*^9, 3.7337140458967295`*^9}, {3.733714091198394*^9, 3.7337141070440063`*^9}, { 3.733714143813529*^9, 3.733714146610505*^9}, {3.733721976862414*^9, 3.7337219813629093`*^9}, {3.733722281191476*^9, 3.7337222944429536`*^9}, { 3.733722382186266*^9, 3.7337223828425617`*^9}, {3.7337224624293957`*^9, 3.7337224858690815`*^9}, 3.7337225537825146`*^9, {3.733722654230641*^9, 3.733722661731436*^9}, {3.733722818999301*^9, 3.7337228267499514`*^9}, { 3.733723144924486*^9, 3.733723159691375*^9}, {3.733723196273369*^9, 3.733723198695795*^9}, {3.7337232377777586`*^9, 3.7337232408874655`*^9}, { 3.73372435111442*^9, 3.733724354067712*^9}, {3.7337244099801674`*^9, 3.733724433076069*^9}, {3.7337245236325226`*^9, 3.733724524679802*^9}, { 3.7337873724058084`*^9, 3.7337873841879997`*^9}, {3.7337879154409466`*^9, 3.7337879158316607`*^9}, {3.7340647908247976`*^9, 3.73406479426425*^9}, { 3.7340650184820967`*^9, 3.7340650196896086`*^9}, {3.7340717757289314`*^9, 3.734071783044138*^9}, 3.760607155346615*^9, 3.7606077013285637`*^9, 3.760607753497196*^9, {3.760608088928544*^9, 3.7606081156683984`*^9}, { 3.760608160193988*^9, 3.7606081844316325`*^9}, {3.760608240118147*^9, 3.7606082403257685`*^9}, {3.760608370421237*^9, 3.7606085188738213`*^9}, { 3.7606087505165215`*^9, 3.7606087536075697`*^9}, {3.7606087890680313`*^9, 3.760608797233983*^9}, {3.7606088687210503`*^9, 3.7606088969051304`*^9}, { 3.760608928173344*^9, 3.760608935537922*^9}, 3.760609001847164*^9, 3.760610501819937*^9, {3.7606107473288507`*^9, 3.760610758648224*^9}, 3.760610853832239*^9, {3.7606112396040025`*^9, 3.7606112817332983`*^9}, { 3.760611401222947*^9, 3.76061140197075*^9}, {3.760611673421208*^9, 3.7606117248805995`*^9}, {3.7606118287018495`*^9, 3.7606119921793656`*^9}, {3.760612127470795*^9, 3.760612223396744*^9}, { 3.76061550773096*^9, 3.7606155085119963`*^9}, 3.760615603302456*^9, { 3.760615693062388*^9, 3.760615704512997*^9}, 3.7606158367472205`*^9, { 3.760615988102416*^9, 3.7606160042704983`*^9}, {3.7632524995190973`*^9, 3.7632525737340136`*^9}, {3.763426957870851*^9, 3.763426959053108*^9}, { 3.7634271873253856`*^9, 3.763427188674776*^9}, {3.7634423988211765`*^9, 3.7634424251737814`*^9}, {3.7634426334949675`*^9, 3.7634426560163193`*^9}, {3.763528275706467*^9, 3.7635284013459897`*^9}, { 3.763528705040784*^9, 3.7635287224411435`*^9}, {3.7635289011396055`*^9, 3.763528901842952*^9}, {3.763548522859683*^9, 3.76354854228095*^9}, { 3.7636050270340595`*^9, 3.763605035756063*^9}, {3.763605112705577*^9, 3.763605344908389*^9}, {3.7636054077448673`*^9, 3.7636054326054068`*^9}, { 3.7636054757131557`*^9, 3.7636054979248376`*^9}, {3.763605542706845*^9, 3.763605675311968*^9}, {3.763605884155599*^9, 3.7636058987003956`*^9}, { 3.763606027844756*^9, 3.7636060593519597`*^9}, {3.7636061708042307`*^9, 3.763606210806114*^9}, 3.763606241472248*^9, {3.7636062752072725`*^9, 3.763606340114405*^9}, {3.763606445999727*^9, 3.7636064489171495`*^9}, { 3.763606744287244*^9, 3.7636067648057427`*^9}, 3.7636070601536713`*^9, { 3.763607262857174*^9, 3.763607300007738*^9}, {3.7636074396359158`*^9, 3.7636074830770864`*^9}, {3.7636076263020697`*^9, 3.7636076543842106`*^9}, 3.763607688296667*^9, {3.7636077698636456`*^9, 3.7636077758773165`*^9}, { 3.763607857294286*^9, 3.7636078613443317`*^9}, 3.763608605441226*^9, { 3.7638142471323504`*^9, 3.7638142487803507`*^9}, {3.7638142898908815`*^9, 3.7638143569012723`*^9}, {3.763958140651967*^9, 3.763958153489439*^9}, 3.76395845683808*^9, {3.7639608609270196`*^9, 3.763960872595887*^9}, { 3.764339536191163*^9, 3.7643395373935814`*^9}, {3.764339581142139*^9, 3.7643396307895145`*^9}, {3.7643397270416403`*^9, 3.764339746774886*^9}, { 3.7643759693358665`*^9, 3.764375988525555*^9}, {3.764410286736837*^9, 3.764410291232706*^9}, {3.7649058387052116`*^9, 3.7649058888300486`*^9}, { 3.764905919657881*^9, 3.7649059255708666`*^9}, {3.764906015807353*^9, 3.7649060798935275`*^9}, {3.7649061275007944`*^9, 3.764906182700228*^9}, { 3.7649814310038157`*^9, 3.764981612888131*^9}, {3.764981649845045*^9, 3.764981717214387*^9}, {3.7650095509166293`*^9, 3.7650095663321896`*^9}, { 3.765009596962874*^9, 3.7650096065955095`*^9}, 3.7650098165773335`*^9, { 3.765011173435627*^9, 3.765011180125066*^9}, {3.7650788221318007`*^9, 3.765078823898266*^9}, {3.7650788935676775`*^9, 3.7650789311170053`*^9}, { 3.765085243174881*^9, 3.7650852441096754`*^9}, 3.765085550868559*^9, { 3.7650855978395305`*^9, 3.7650856220925417`*^9}, {3.7650863545547857`*^9, 3.7650863799862742`*^9}, {3.7650865194326468`*^9, 3.765086519785918*^9}, { 3.7650865505251884`*^9, 3.7650865669896946`*^9}, 3.765087372975154*^9, { 3.7650874030551014`*^9, 3.7650874163952713`*^9}, {3.765087536684074*^9, 3.7650876355597906`*^9}, 3.7650877252914543`*^9, {3.765088672041128*^9, 3.7650887019763765`*^9}, {3.765088740411885*^9, 3.765088742455727*^9}, { 3.7650889283353214`*^9, 3.7650889447918415`*^9}, {3.765089035561446*^9, 3.7650890612584443`*^9}, {3.7650891812559137`*^9, 3.765089209061077*^9}, { 3.7650893423167953`*^9, 3.76508943243054*^9}, {3.765090684608432*^9, 3.765090700734714*^9}, 3.7650907477613907`*^9, {3.7650908366428585`*^9, 3.7650908539151096`*^9}, {3.7650908896330676`*^9, 3.765090909940852*^9}, { 3.765091082681374*^9, 3.7650911113055153`*^9}, {3.7650911427516937`*^9, 3.7650911450258894`*^9}, {3.7650912819372005`*^9, 3.765091515369325*^9}, { 3.7650916102443376`*^9, 3.7650917517497134`*^9}, {3.765092443582117*^9, 3.765092498126871*^9}, {3.76509426500305*^9, 3.765094281405676*^9}, 3.765094315674655*^9, {3.7652396904249477`*^9, 3.765239693502611*^9}, 3.765253217258378*^9, {3.7652532852065315`*^9, 3.7652532918614807`*^9}, 3.766189724095389*^9, {3.766190438614527*^9, 3.7661905103848095`*^9}, { 3.76619098699972*^9, 3.766190987925188*^9}, {3.766193820625373*^9, 3.7661938215367756`*^9}, {3.7662041564549007`*^9, 3.7662041841044207`*^9}, {3.766204415112673*^9, 3.766204435514146*^9}, { 3.766204514370674*^9, 3.766204525664904*^9}, 3.766204570014185*^9, { 3.7665714310907745`*^9, 3.76657144559927*^9}, {3.7665725420953245`*^9, 3.7665725423845477`*^9}, {3.7666314737351704`*^9, 3.7666315492489386`*^9}, {3.7740882771256323`*^9, 3.774088312744491*^9}, { 3.774150773834302*^9, 3.774150944718382*^9}, {3.774150975094303*^9, 3.774151054824913*^9}, {3.7741511238761725`*^9, 3.7741512298519745`*^9}, { 3.77415129158794*^9, 3.774151651300989*^9}, {3.774151741892136*^9, 3.774151770064453*^9}, {3.7742415341727543`*^9, 3.7742416306317797`*^9}, { 3.7751898888726125`*^9, 3.775189913786336*^9}, {3.7751899486865563`*^9, 3.7751899522127523`*^9}, {3.7751899989654093`*^9, 3.7751900149868736`*^9}, {3.7751900517928104`*^9, 3.775190066570419*^9}, { 3.7879798676374617`*^9, 3.7879798943206964`*^9}, {3.792287382183713*^9, 3.792287444759338*^9}, {3.792287488992601*^9, 3.7922875432928047`*^9}, { 3.7922886672157793`*^9, 3.7922886764378495`*^9}, {3.792288708660981*^9, 3.7922888810105305`*^9}, {3.792300131730332*^9, 3.7923001501177034`*^9}, { 3.795768609226843*^9, 3.7957686326352005`*^9}, {3.7957686687171*^9, 3.7957686846637707`*^9}, {3.7957688298513894`*^9, 3.795768834915843*^9}, 3.7957688867486525`*^9, {3.795768942098573*^9, 3.795768993537817*^9}, { 3.7957690236098194`*^9, 3.79576902468211*^9}, {3.7957690712421293`*^9, 3.795769275801197*^9}, {3.7957693460703883`*^9, 3.795769349757367*^9}, { 3.79576972202382*^9, 3.7957697714534473`*^9}, {3.795769801653285*^9, 3.795769804711711*^9}, {3.796345941656575*^9, 3.7963459430887594`*^9}, { 3.8298913714361515`*^9, 3.829891372330407*^9}, {3.843728585368825*^9, 3.84372858844851*^9}, {3.8449958679518747`*^9, 3.8449959617306128`*^9}, { 3.845978121229767*^9, 3.845978121586933*^9}, {3.8459781752184176`*^9, 3.845978183704877*^9}, {3.8459783826308093`*^9, 3.8459784254435472`*^9}, { 3.845978956970813*^9, 3.8459791499511595`*^9}, 3.8461289015497713`*^9, 3.846128946122293*^9, {3.846309385225996*^9, 3.846309410347027*^9}, { 3.846309504823522*^9, 3.846309511339752*^9}, {3.8532051618832316`*^9, 3.8532051757582083`*^9}, 3.853205648810899*^9, {3.853205773068694*^9, 3.8532058080261583`*^9}, {3.853206663322813*^9, 3.853206670956298*^9}}, CellLabel-> "In[343]:=",ExpressionUUID->"6da38beb-2bb8-4c31-889a-cf48e67a1a60"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"project", " ", "definitions"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"CORNERE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"d_", ",", "l_"}], "}"}], ",", "i1_", ",", "i2_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"i3", ",", "r0", ",", "dr1", ",", "dr2", ",", "dr3"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"i3", "=", RowBox[{ RowBox[{"i1", StyleBox["\[Cross]", "OperatorCharacter"], "i2"}], "/", RowBox[{"Norm", "[", RowBox[{"i1", StyleBox["\[Cross]", "OperatorCharacter"], "i2"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"scale", "*", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dr1", "=", RowBox[{ RowBox[{"i1", "*", "l"}], "+", RowBox[{"scale", "*", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], StyleBox["\[Cross]", "OperatorCharacter"], "i1"}], "*", "l"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dr2", "=", RowBox[{ RowBox[{"i2", "*", "l"}], "+", RowBox[{"scale", "*", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], StyleBox["\[Cross]", "OperatorCharacter"], "i2"}], "*", "l"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dr3", "=", RowBox[{ RowBox[{"i3", "*", "l"}], "+", RowBox[{"scale", "*", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], StyleBox["\[Cross]", "OperatorCharacter"], "i3"}], "*", "l"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Red", ",", RowBox[{"Sphere", "[", RowBox[{"r0", ",", RowBox[{"d", "/", "2"}]}], "]"}], ",", RowBox[{"Cylinder", "[", RowBox[{ RowBox[{"{", RowBox[{"r0", ",", RowBox[{"r0", "+", "dr1"}]}], "}"}], ",", RowBox[{"d", "/", "2"}]}], "]"}], ",", RowBox[{"Cylinder", "[", RowBox[{ RowBox[{"{", RowBox[{"r0", ",", RowBox[{"r0", "+", "dr2"}]}], "}"}], ",", RowBox[{"d", "/", "2"}]}], "]"}], ",", RowBox[{"Cylinder", "[", RowBox[{ RowBox[{"{", RowBox[{"r0", ",", RowBox[{"r0", "+", "dr3"}]}], "}"}], ",", RowBox[{"d", "/", "2"}]}], "]"}]}], "}"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"PIVOTA", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"d_", ",", "l_"}], "}"}], ",", "i1_", ",", "i2_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"i3", ",", "r0", ",", "dr1", ",", "dr2", ",", "dr3"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"i3", "=", RowBox[{ RowBox[{"i1", StyleBox["\[Cross]", "OperatorCharacter"], "i2"}], "/", RowBox[{"Norm", "[", RowBox[{"i1", StyleBox["\[Cross]", "OperatorCharacter"], "i2"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"scale", "*", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dr1", "=", RowBox[{ RowBox[{"i1", "*", "l"}], "+", RowBox[{"scale", "*", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], StyleBox["\[Cross]", "OperatorCharacter"], "i1"}], "*", "l"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dr2", "=", RowBox[{ RowBox[{"i2", "*", "l"}], "+", RowBox[{"scale", "*", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], StyleBox["\[Cross]", "OperatorCharacter"], "i2"}], "*", "l"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dr3", "=", RowBox[{ RowBox[{"i3", "*", RowBox[{"d", "/", "4"}]}], "+", RowBox[{"scale", "*", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], StyleBox["\[Cross]", "OperatorCharacter"], "i3"}], "*", RowBox[{"d", "/", "4"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Blue", ",", RowBox[{"Cylinder", "[", RowBox[{ RowBox[{"{", RowBox[{"r0", ",", RowBox[{"r0", "+", "dr1"}]}], "}"}], ",", RowBox[{"d", "/", "2"}]}], "]"}], ",", RowBox[{"Cylinder", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"r0", "-", "dr2"}], ",", RowBox[{"r0", "+", "dr2"}]}], "}"}], ",", RowBox[{"d", "/", "2"}]}], "]"}], ",", RowBox[{"Cylinder", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"r0", "-", "dr3"}], ",", RowBox[{"r0", "+", "dr3"}]}], "}"}], ",", "d"}], "]"}]}], "}"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"SLEEVEA", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"d_", ",", "l_"}], "}"}], ",", "i1_", ",", "i2_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "i3", ",", "r0", ",", "r1", ",", "dr1", ",", "dr2", ",", "dr3"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"i3", "=", RowBox[{ RowBox[{"i1", StyleBox["\[Cross]", "OperatorCharacter"], "i2"}], "/", RowBox[{"Norm", "[", RowBox[{"i1", StyleBox["\[Cross]", "OperatorCharacter"], "i2"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"scale", "*", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r1", "=", RowBox[{"r0", "+", RowBox[{"i2", "*", RowBox[{"d", "/", "2"}]}], "+", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], StyleBox["\[Cross]", "OperatorCharacter"], "i2"}], "*", RowBox[{"d", "/", "2"}], "*", "scale"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dr1", "=", RowBox[{ RowBox[{"i1", "*", RowBox[{"l", "/", "2"}]}], "+", RowBox[{"scale", "*", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], StyleBox["\[Cross]", "OperatorCharacter"], "i1"}], "*", RowBox[{"l", "/", "2"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dr3", "=", RowBox[{ RowBox[{"i3", "*", RowBox[{"d", "/", "8"}]}], "+", RowBox[{"scale", "*", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], StyleBox["\[Cross]", "OperatorCharacter"], "i3"}], "*", RowBox[{"d", "/", "8"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Blue", ",", RowBox[{"Cylinder", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"r0", "-", "dr1"}], ",", RowBox[{"r0", "+", "dr1"}]}], "}"}], ",", RowBox[{"d", "/", "2"}]}], "]"}], ",", RowBox[{"Cylinder", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"r1", "-", "dr3"}], ",", RowBox[{"r1", "+", "dr3"}]}], "}"}], ",", "d"}], "]"}]}], "}"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "first", " ", "order", " ", "beam", " ", "model", " ", "graphics"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", RowBox[{"AA_", ",", "Iy_", ",", "Iz_", ",", "Jx_", ",", RowBox[{"{", RowBox[{"iyr_", ",", "\[Alpha]_"}], "}"}], ",", "pol_"}], "}"}], ",", "for_"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r1", ",", "\[CapitalDelta]r", ",", "r", ",", "h", ",", "x", ",", "y", ",", "z", ",", "NL", ",", "NQ", ",", "ixr", ",", "izr", ",", "ix", ",", "iy", ",", "iz", ",", "T", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "ux1", ",", "ux2", ",", "uz1", ",", "uz2", ",", "uy1", ",", "uy2", ",", "\[Theta]x1", ",", "\[Theta]x2", ",", "\[Theta]y1", ",", "\[Theta]y2", ",", "\[Theta]z1", ",", "\[Theta]z2", ",", "ux", ",", "uy", ",", "uz", ",", "pp", ",", "nn"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"r1", "=", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalDelta]r", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h", "=", RowBox[{"Sqrt", "[", RowBox[{"\[CapitalDelta]r", ".", "\[CapitalDelta]r"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ixr", "=", RowBox[{"\[CapitalDelta]r", "/", "h"}]}], ";", "\[IndentingNewLine]", RowBox[{"izr", "=", RowBox[{"ixr", "\[Cross]", "iyr"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix", " ", "=", "ixr"}], ";", "\[IndentingNewLine]", RowBox[{"iy", " ", "=", RowBox[{ RowBox[{ RowBox[{"Cos", "[", "\[Alpha]", "]"}], " ", "iyr"}], "+", RowBox[{ RowBox[{"Sin", "[", "\[Alpha]", "]"}], "izr"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"iz", " ", "=", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"Sin", "[", "\[Alpha]", "]"}]}], " ", "iyr"}], "+", RowBox[{ RowBox[{"Cos", "[", "\[Alpha]", "]"}], "izr"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"displacements", " ", "and", " ", "rotations"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NL", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ",", RowBox[{"x", "/", "h"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NQ", "=", RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", RowBox[{"x", "/", "h"}]}]}], ")"}]}], ",", RowBox[{"h", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ")"}], "2"], " ", RowBox[{"x", "/", "h"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{"2", " ", RowBox[{"x", "/", "h"}]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}], "2"]}], ",", RowBox[{"h", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"x", "/", "h"}], "-", "1"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"ux1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "ix"}]}], ";", " ", RowBox[{"ux2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "ix"}]}], ";", "\[IndentingNewLine]", RowBox[{"uy1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iy"}]}], ";", " ", RowBox[{"uy2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"uz1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iz"}]}], ";", " ", RowBox[{"uz2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iz"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]x1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "ix"}]}], ";", " ", RowBox[{"\[Theta]x2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "ix"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]y1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iy"}]}], ";", " ", RowBox[{"\[Theta]y2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]z1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iz"}]}], ";", " ", RowBox[{"\[Theta]z2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iz"}]}], ";", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{"ux1", ",", "ux2"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{"uy1", ",", "\[Theta]z1", ",", "uy2", ",", "\[Theta]z2"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{"uz1", ",", RowBox[{"-", "\[Theta]y1"}], ",", "uz2", ",", RowBox[{"-", "\[Theta]y2"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{"\[Theta]x1", ",", "\[Theta]x2"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}]}], ";", "\[IndentingNewLine]", RowBox[{"ux", "=", RowBox[{ RowBox[{"(", RowBox[{"u", "+", RowBox[{"\[Theta]", " ", "z"}], "-", RowBox[{"\[Psi]", " ", "y"}]}], ")"}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"uy", "=", RowBox[{ RowBox[{"(", RowBox[{"v", "-", RowBox[{"\[Phi]", " ", "z"}]}], ")"}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"uz", "=", RowBox[{ RowBox[{"(", RowBox[{"w", "+", RowBox[{"\[Phi]", " ", "y"}]}], ")"}], "*", "scale"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"nn", "=", "10"}], ";", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"ii", " ", "slab", " ", "and", " ", "jj", " ", "nod"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"pp", "[", RowBox[{"ii_", ",", "jj_"}], "]"}], ":=", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"r1", "+", RowBox[{ RowBox[{"(", RowBox[{"x", "+", "ux"}], ")"}], " ", "ix"}], "+", RowBox[{ RowBox[{"(", RowBox[{"y", "+", "uy"}], " ", ")"}], "iy"}], " ", "+", RowBox[{ RowBox[{"(", RowBox[{"z", "+", "uz"}], ")"}], " ", "iz"}]}], ")"}], "/.", RowBox[{"x", "\[Rule]", RowBox[{"(", RowBox[{"ii", "*", RowBox[{"h", "/", "nn"}]}], ")"}]}]}], "/.", RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{"y", ",", "z"}], "}"}], "\[Rule]", RowBox[{"pol", "[", RowBox[{"[", "jj", "]"}], "]"}]}], "]"}]}]}], " ", ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Join", "[", RowBox[{"BEAMFORM", ",", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"pp", "[", RowBox[{"ii", ",", "jj"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", "jj"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", RowBox[{"jj", "+", "1"}]}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"ii", ",", RowBox[{"jj", "+", "1"}]}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"ii", ",", "0", ",", RowBox[{"nn", "-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"jj", ",", "1", ",", RowBox[{ RowBox[{"Length", "[", "pol", "]"}], "-", "1"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", "POINTFORM", ",", RowBox[{"{", RowBox[{ RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "*", "scale"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "*", "scale"}]}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"scale", "\[Equal]", "0"}], ",", RowBox[{"{", RowBox[{"Red", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"r1", "+", RowBox[{"\[CapitalDelta]r", "/", "2"}]}], ",", RowBox[{"r1", "+", RowBox[{"\[CapitalDelta]r", "/", "2"}], "+", RowBox[{"ix", "*", RowBox[{"h", "/", "10"}]}]}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "Green", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"r1", "+", RowBox[{"\[CapitalDelta]r", "/", "2"}]}], ",", RowBox[{"r1", "+", RowBox[{"\[CapitalDelta]r", "/", "2"}], "+", RowBox[{"iy", "*", RowBox[{"h", "/", "10"}]}]}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "Blue", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"r1", "+", RowBox[{"\[CapitalDelta]r", "/", "2"}]}], ",", RowBox[{"r1", "+", RowBox[{"\[CapitalDelta]r", "/", "2"}], "+", RowBox[{"iz", "*", RowBox[{"h", "/", "10"}]}]}]}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "]"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", RowBox[{ "AA_", ",", "Iy_", ",", "Iz_", ",", "Jx_", ",", "iy_", ",", "pol_"}], "}"}], ",", "for_"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r1", ",", "\[CapitalDelta]r", ",", "r", ",", "h", ",", "x", ",", "y", ",", "z", ",", "NL", ",", "NQ", ",", "ix", ",", "iz", ",", "T", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "ux1", ",", "ux2", ",", "uz1", ",", "uz2", ",", "uy1", ",", "uy2", ",", "\[Theta]x1", ",", "\[Theta]x2", ",", "\[Theta]y1", ",", "\[Theta]y2", ",", "\[Theta]z1", ",", "\[Theta]z2", ",", "ux", ",", "uy", ",", "uz", ",", "pp", ",", "nn"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"r1", "=", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalDelta]r", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h", "=", RowBox[{"Sqrt", "[", RowBox[{"\[CapitalDelta]r", ".", "\[CapitalDelta]r"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix", "=", RowBox[{"\[CapitalDelta]r", "/", "h"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz", "=", RowBox[{"ix", "\[Cross]", "iy"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"displacements", " ", "and", " ", "rotations"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NL", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ",", RowBox[{"x", "/", "h"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NQ", "=", RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", RowBox[{"x", "/", "h"}]}]}], ")"}]}], ",", RowBox[{"h", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ")"}], "2"], " ", RowBox[{"x", "/", "h"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{"2", " ", RowBox[{"x", "/", "h"}]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}], "2"]}], ",", RowBox[{"h", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"x", "/", "h"}], "-", "1"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"ux1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "ix"}]}], ";", " ", RowBox[{"ux2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "ix"}]}], ";", "\[IndentingNewLine]", RowBox[{"uy1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iy"}]}], ";", " ", RowBox[{"uy2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"uz1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iz"}]}], ";", " ", RowBox[{"uz2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iz"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]x1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "ix"}]}], ";", " ", RowBox[{"\[Theta]x2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "ix"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]y1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iy"}]}], ";", " ", RowBox[{"\[Theta]y2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]z1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iz"}]}], ";", " ", RowBox[{"\[Theta]z2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iz"}]}], ";", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{"ux1", ",", "ux2"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{"uy1", ",", "\[Theta]z1", ",", "uy2", ",", "\[Theta]z2"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{"uz1", ",", RowBox[{"-", "\[Theta]y1"}], ",", "uz2", ",", RowBox[{"-", "\[Theta]y2"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{"\[Theta]x1", ",", "\[Theta]x2"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}]}], ";", "\[IndentingNewLine]", RowBox[{"ux", "=", RowBox[{ RowBox[{"(", RowBox[{"u", "+", RowBox[{"\[Theta]", " ", "z"}], "-", RowBox[{"\[Psi]", " ", "y"}]}], ")"}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"uy", "=", RowBox[{ RowBox[{"(", RowBox[{"v", "-", RowBox[{"\[Phi]", " ", "z"}]}], ")"}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"uz", "=", RowBox[{ RowBox[{"(", RowBox[{"w", "+", RowBox[{"\[Phi]", " ", "y"}]}], ")"}], "*", "scale"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"nn", "=", "10"}], ";", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"ii", " ", "slab", " ", "and", " ", "jj", " ", "nod"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"pp", "[", RowBox[{"ii_", ",", "jj_"}], "]"}], ":=", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"r1", "+", RowBox[{ RowBox[{"(", RowBox[{"x", "+", "ux"}], ")"}], " ", "ix"}], "+", RowBox[{ RowBox[{"(", RowBox[{"y", "+", "uy"}], " ", ")"}], "iy"}], " ", "+", RowBox[{ RowBox[{"(", RowBox[{"z", "+", "uz"}], ")"}], " ", "iz"}]}], ")"}], "/.", RowBox[{"x", "\[Rule]", RowBox[{"(", RowBox[{"ii", "*", RowBox[{"h", "/", "nn"}]}], ")"}]}]}], "/.", RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{"y", ",", "z"}], "}"}], "\[Rule]", RowBox[{"pol", "[", RowBox[{"[", "jj", "]"}], "]"}]}], "]"}]}]}], " ", ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Join", "[", RowBox[{"BEAMFORM", ",", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"pp", "[", RowBox[{"ii", ",", "jj"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", "jj"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", RowBox[{"jj", "+", "1"}]}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"ii", ",", RowBox[{"jj", "+", "1"}]}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"ii", ",", "0", ",", RowBox[{"nn", "-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"jj", ",", "1", ",", RowBox[{ RowBox[{"Length", "[", "pol", "]"}], "-", "1"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", "POINTFORM", ",", RowBox[{"{", RowBox[{ RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "*", "scale"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "*", "scale"}]}], "]"}]}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", "d_", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat", ",", RowBox[{"{", RowBox[{"d", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", RowBox[{"d_", ",", "iy_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat", ",", RowBox[{"{", RowBox[{ RowBox[{"CIRCLE", "[", "d", "]"}], ",", "iy"}], "}"}], ",", "for"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"BEAMFORM", "=", RowBox[{"{", RowBox[{ RowBox[{"FaceForm", "[", "Gray", "]"}], ",", RowBox[{"EdgeForm", "[", "]"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"POINTFORM", "=", RowBox[{"{", RowBox[{"Blue", ",", RowBox[{"PointSize", "[", "Medium", "]"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", RowBox[{"d_", ",", "iy_"}], "}"}], ",", "for_"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Rho]", ",", "h", ",", "x", ",", "y", ",", "z", ",", "NL", ",", "NQ", ",", "ix", ",", "iz", ",", "T", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "ux1", ",", "ux2", ",", "uz1", ",", "uz2", ",", "uy1", ",", "uy2", ",", "\[Theta]x1", ",", "\[Theta]x2", ",", "\[Theta]y1", ",", "\[Theta]y2", ",", "\[Theta]z1", ",", "\[Theta]z2", ",", "ux", ",", "uy", ",", "uz", ",", "pp"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Rho]", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h", "=", RowBox[{"Sqrt", "[", RowBox[{"\[Rho]", ".", "\[Rho]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NL", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ",", RowBox[{"x", "/", "h"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NQ", "=", RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", RowBox[{"x", "/", "h"}]}]}], ")"}]}], ",", RowBox[{"h", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ")"}], "2"], " ", RowBox[{"x", "/", "h"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{"2", " ", RowBox[{"x", "/", "h"}]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}], "2"]}], ",", RowBox[{"h", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"x", "/", "h"}], "-", "1"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix", "=", RowBox[{"\[Rho]", "/", "h"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz", "=", RowBox[{"ix", "\[Cross]", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"T", "=", RowBox[{"{", RowBox[{"ix", ",", "iy", ",", "iz"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"ux1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "ix"}]}], ";", " ", RowBox[{"ux2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "ix"}]}], ";", "\[IndentingNewLine]", RowBox[{"uy1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iy"}]}], ";", " ", RowBox[{"uy2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"uz1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iz"}]}], ";", " ", RowBox[{"uz2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iz"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]x1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "ix"}]}], ";", " ", RowBox[{"\[Theta]x2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "ix"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]y1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iy"}]}], ";", " ", RowBox[{"\[Theta]y2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]z1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iz"}]}], ";", " ", RowBox[{"\[Theta]z2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iz"}]}], ";", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{ RowBox[{"NL", ".", RowBox[{"{", RowBox[{"ux1", ",", "ux2"}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{ RowBox[{"NQ", ".", RowBox[{"{", RowBox[{"uy1", ",", RowBox[{"-", "\[Theta]z1"}], ",", "uy2", ",", RowBox[{"-", "\[Theta]z2"}]}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ RowBox[{"NQ", ".", RowBox[{"{", RowBox[{"uz1", ",", RowBox[{"-", "\[Theta]y1"}], ",", "uz2", ",", RowBox[{"-", "\[Theta]y2"}]}], "}"}]}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"pp", "=", RowBox[{"Partition", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ix", "*", "x"}], "+", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], ".", "T"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "h", ",", RowBox[{"h", "/", "10"}]}], "}"}]}], "]"}], ",", "2", ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"pp", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"ix", "*", "x"}], "+", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], ".", "T"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "h", ",", RowBox[{"h", "/", "10"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Join", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"FaceForm", "[", "Black", "]"}], ",", RowBox[{"EdgeForm", "[", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"Tube", "[", RowBox[{"pp", ",", RowBox[{"d", "/", "2"}]}], "]"}], "}"}], ",", "POINTFORM", ",", RowBox[{"{", RowBox[{ RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "*", "scale"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "*", "scale"}]}], "]"}]}], "}"}]}], " ", "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", RowBox[{ RowBox[{"RECTANGLE", "[", RowBox[{"ly_", ",", "lz_", ",", "t_"}], "]"}], ",", "iy_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat", ",", RowBox[{"{", RowBox[{ RowBox[{"RECTANGLE", "[", RowBox[{"ly", ",", "lz"}], "]"}], ",", "iy"}], "}"}], ",", "for"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", RowBox[{ RowBox[{"RECTANGLE", "[", RowBox[{"ly_", ",", "lz_"}], "]"}], ",", "iy_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat", ",", RowBox[{"{", RowBox[{ RowBox[{"RECTANGLE", "[", RowBox[{"ly", ",", "lz"}], "]"}], ",", "iy"}], "}"}], ",", "for"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", RowBox[{"RECTANGLE", "[", RowBox[{"ly_", ",", "lz_"}], "]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat", ",", RowBox[{"{", RowBox[{ RowBox[{"RECTANGLE", "[", RowBox[{"ly", ",", "lz"}], "]"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", "for"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", RowBox[{"RECTANGLE", "[", RowBox[{"ly_", ",", "lz_"}], "]"}], "}"}], ",", "for_"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat", ",", RowBox[{"{", RowBox[{ RowBox[{"RECTANGLE", "[", RowBox[{"ly", ",", "lz"}], "]"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", "for"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", RowBox[{ RowBox[{"RECTANGLE", "[", RowBox[{"ly_", ",", "lz_"}], "]"}], ",", "iy_"}], "}"}], ",", "for_"}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Rho]", ",", "h", ",", "x", ",", "y", ",", "z", ",", "NL", ",", "NQ", ",", "ix", ",", "iz", ",", "T", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "ux1", ",", "ux2", ",", "uz1", ",", "uz2", ",", "uy1", ",", "uy2", ",", "\[Theta]x1", ",", "\[Theta]x2", ",", "\[Theta]y1", ",", "\[Theta]y2", ",", "\[Theta]z1", ",", "\[Theta]z2", ",", "ux", ",", "uy", ",", "uz", ",", "pp"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Rho]", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"h", "=", RowBox[{"Sqrt", "[", RowBox[{"\[Rho]", ".", "\[Rho]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ix", "=", RowBox[{"\[Rho]", "/", "h"}]}], ";", "\[IndentingNewLine]", RowBox[{"iz", "=", RowBox[{"ix", "\[Cross]", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Rho]", "=", RowBox[{ RowBox[{"x", " ", "ix"}], "+", RowBox[{"y", " ", "iy"}], "+", RowBox[{"z", " ", "iz"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"T", "=", RowBox[{"{", RowBox[{"ix", ",", "iy", ",", "iz"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NL", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ",", RowBox[{"x", "/", "h"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NQ", "=", RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", RowBox[{"x", "/", "h"}]}]}], ")"}]}], ",", RowBox[{"h", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"x", "/", "h"}]}], ")"}], "2"], " ", RowBox[{"x", "/", "h"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{"2", " ", RowBox[{"x", "/", "h"}]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}], "2"]}], ",", RowBox[{"h", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "/", "h"}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"x", "/", "h"}], "-", "1"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"ux1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "ix"}]}], ";", " ", RowBox[{"ux2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "ix"}]}], ";", "\[IndentingNewLine]", RowBox[{"uy1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iy"}]}], ";", " ", RowBox[{"uy2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"uz1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], ".", "iz"}]}], ";", " ", RowBox[{"uz2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], ".", "iz"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]x1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "ix"}]}], ";", " ", RowBox[{"\[Theta]x2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "ix"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]y1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iy"}]}], ";", " ", RowBox[{"\[Theta]y2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iy"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]z1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], ".", "iz"}]}], ";", " ", RowBox[{"\[Theta]z2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], ".", "iz"}]}], ";", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{"ux1", ",", "ux2"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"v", "=", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{"uy1", ",", "\[Theta]z1", ",", "uy2", ",", "\[Theta]z2"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"NQ", ".", RowBox[{"{", RowBox[{"uz1", ",", RowBox[{"-", "\[Theta]y1"}], ",", "uz2", ",", RowBox[{"-", "\[Theta]y2"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{"\[Theta]x1", ",", "\[Theta]x2"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]", "=", RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}]}], ";", "\[IndentingNewLine]", RowBox[{"ux", "=", RowBox[{ RowBox[{"(", RowBox[{"u", "+", RowBox[{"\[Theta]", " ", "z"}], "-", RowBox[{"\[Psi]", " ", "y"}]}], ")"}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"uy", "=", RowBox[{ RowBox[{"(", RowBox[{"v", "-", RowBox[{"\[Phi]", " ", "z"}]}], ")"}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"uz", "=", RowBox[{ RowBox[{"(", RowBox[{"w", "+", RowBox[{"\[Phi]", " ", "y"}]}], ")"}], "*", "scale"}]}], ";", "\[IndentingNewLine]", RowBox[{"pp", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", "\[Rho]", "+", RowBox[{ RowBox[{"{", RowBox[{"ux", ",", "uy", ",", "uz"}], "}"}], ".", "T"}]}], ")"}], "/.", RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{"y", ",", "z"}], "}"}], "\[Rule]", "yz"}], "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "h", ",", RowBox[{"h", "/", "10"}]}], "}"}], ",", RowBox[{"{", RowBox[{"yz", ",", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"ly", ",", "lz"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "ly"}], ",", "lz"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "ly"}], ",", RowBox[{"-", "lz"}]}], "}"}], ",", RowBox[{"{", RowBox[{"ly", ",", RowBox[{"-", "lz"}]}], "}"}]}], "}"}], "/", "2"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Join", "[", RowBox[{"BEAMFORM", ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"pp", "[", RowBox[{"[", RowBox[{"ii", ",", "1"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{"ii", ",", "2"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", "2"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", "1"}], "]"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"pp", "[", RowBox[{"[", RowBox[{"ii", ",", "2"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{"ii", ",", "3"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", "3"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", "2"}], "]"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"pp", "[", RowBox[{"[", RowBox[{"ii", ",", "4"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{"ii", ",", "3"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", "3"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", "4"}], "]"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"pp", "[", RowBox[{"[", RowBox[{"ii", ",", "1"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{"ii", ",", "4"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", "4"}], "]"}], "]"}], ",", RowBox[{"pp", "[", RowBox[{"[", RowBox[{ RowBox[{"ii", "+", "1"}], ",", "1"}], "]"}], "]"}]}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", RowBox[{ RowBox[{"Length", "[", "pp", "]"}], "-", "1"}]}], "}"}]}], "]"}], ",", "POINTFORM", ",", RowBox[{"{", RowBox[{ RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "*", "scale"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "*", "scale"}]}], "]"}]}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"RIGID", ",", "pro_", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"crd1", ",", "crd2"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"crd1", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}], "*", "scale"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"crd2", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "*", "scale"}]}]}], ";", RowBox[{"{", RowBox[{"Black", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"crd1", ",", "crd2"}], "}"}], "]"}], ",", "Blue", ",", RowBox[{"PointSize", "[", "Medium", "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"crd1", ",", "crd2"}], "}"}], "]"}]}], "}"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"FORCEFORM", "=", RowBox[{"{", RowBox[{"Gray", ",", RowBox[{"Opacity", "[", "0.5", "]"}], ",", RowBox[{"EdgeForm", "[", "]"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[Rho]_", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"HEXAHEDRON", "[", RowBox[{"lx_", ",", "ly_", ",", "lz_"}], "]"}], ",", "ix_", ",", "iy_"}], "}"}], ",", RowBox[{"{", RowBox[{ "FX_", ",", "FY_", ",", "FZ_", ",", "MX_", ",", "MY_", ",", "MZ_"}], "}"}]}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"r", ",", "T", ",", "pnt", ",", "crd"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"pnt", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "lx"}], ",", RowBox[{"-", "ly"}], ",", RowBox[{"-", "lz"}]}], "}"}], ",", RowBox[{"{", RowBox[{"lx", ",", RowBox[{"-", "ly"}], ",", RowBox[{"-", "lz"}]}], "}"}], ",", RowBox[{"{", RowBox[{"lx", ",", "ly", ",", RowBox[{"-", "lz"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "lx"}], ",", "ly", ",", RowBox[{"-", "lz"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"-", "lx"}], ",", RowBox[{"-", "ly"}], ",", "lz"}], "}"}], ",", RowBox[{"{", RowBox[{"lx", ",", RowBox[{"-", "ly"}], ",", "lz"}], "}"}], ",", RowBox[{"{", RowBox[{"lx", ",", "ly", ",", "lz"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "lx"}], ",", "ly", ",", "lz"}], "}"}]}], "}"}], "/", "2"}]}], ";", "\[IndentingNewLine]", RowBox[{"crd", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ix", ",", "iy", ",", RowBox[{"ix", StyleBox["\[Cross]", "OperatorCharacter"], "iy"}]}], "}"}], ".", "#"}], "&"}], ",", "pnt"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", "#", "+", RowBox[{"scale", "*", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], "+", RowBox[{"scale", "*", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], StyleBox["\[Cross]", "OperatorCharacter"], RowBox[{ StyleBox["(", "OperatorCharacter"], RowBox[{ StyleBox["#", "OperatorCharacter"], StyleBox["-", "OperatorCharacter"], RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}]}], ")"}]}]}]}], "&"}], ",", "crd"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Join", "[", RowBox[{"FORCEFORM", ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"r", "[", RowBox[{"[", "4", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "3", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "2", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}], "]"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"r", "[", RowBox[{"[", "5", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "6", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "7", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "8", "]"}], "]"}]}], "}"}], "]"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"r", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "2", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "6", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "5", "]"}], "]"}]}], "}"}], "]"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"r", "[", RowBox[{"[", "3", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "4", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "8", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "7", "]"}], "]"}]}], "}"}], "]"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"r", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "5", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "8", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "4", "]"}], "]"}]}], "}"}], "]"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{ RowBox[{"r", "[", RowBox[{"[", "2", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "3", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "7", "]"}], "]"}], ",", RowBox[{"r", "[", RowBox[{"[", "6", "]"}], "]"}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", "POINTFORM", ",", RowBox[{"{", RowBox[{"Point", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "1"}], "]"}], "]"}], "+", RowBox[{"scale", "*", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}]}], "]"}], "}"}]}], "]"}]}]}], "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.633673923685915*^9, 3.6336739535006204`*^9}, { 3.633674155068149*^9, 3.6336741996717005`*^9}, {3.6336745049841633`*^9, 3.6336745219741354`*^9}, {3.6336919593939404`*^9, 3.6336919775979815`*^9}, 3.633692380551029*^9, {3.6336927116599674`*^9, 3.633692727194856*^9}, { 3.635310826749509*^9, 3.6353108343419433`*^9}, {3.635311461613821*^9, 3.6353114619508405`*^9}, {3.7326759806780663`*^9, 3.7326760008674326`*^9}, {3.7326760331212645`*^9, 3.7326760385677853`*^9}, {3.732684137201784*^9, 3.73268419404665*^9}, { 3.732684306221466*^9, 3.7326843382153635`*^9}, 3.7326844699232764`*^9, { 3.7326845133861027`*^9, 3.73268452322455*^9}, {3.732759973190983*^9, 3.7327599776758347`*^9}, {3.7327613720703106`*^9, 3.7327614888170295`*^9}, {3.732761535853627*^9, 3.7327615404943867`*^9}, { 3.7327615972663317`*^9, 3.7327616122832594`*^9}, {3.7327616693361855`*^9, 3.73276183332095*^9}, {3.732761876700554*^9, 3.7327618790133*^9}, { 3.732761909063363*^9, 3.732761910469795*^9}, {3.73276200508918*^9, 3.732762006042756*^9}, {3.7327620750344048`*^9, 3.732762101490326*^9}, 3.7327688007102947`*^9, {3.7327705695330524`*^9, 3.7327705708254137`*^9}, { 3.732788507552166*^9, 3.7327885085870132`*^9}, {3.732788681344634*^9, 3.7327887090994544`*^9}, {3.732788743287696*^9, 3.73278879848213*^9}, { 3.732788922306119*^9, 3.7327889462731514`*^9}, {3.732789012151597*^9, 3.732789028200858*^9}, {3.7327890791192408`*^9, 3.732789086999034*^9}, { 3.732789135698248*^9, 3.7327891358892384`*^9}, {3.7327891989507074`*^9, 3.7327891993104925`*^9}, {3.733116709198372*^9, 3.733116731638229*^9}, { 3.7334931331412554`*^9, 3.7334932071522064`*^9}, {3.733493353668892*^9, 3.7334934953404007`*^9}, {3.733493581610343*^9, 3.733493589891471*^9}, { 3.7334936319789553`*^9, 3.7334936623392687`*^9}, {3.7334936935401745`*^9, 3.733493716917615*^9}, {3.7334937687375154`*^9, 3.733493799379287*^9}, { 3.7335602963276734`*^9, 3.7335603891038685`*^9}, {3.7337039222525787`*^9, 3.733703929721642*^9}, {3.7337040222462597`*^9, 3.7337040262631474`*^9}, { 3.733710121070121*^9, 3.733710122358057*^9}, 3.7337110885786676`*^9, 3.733711184948838*^9, {3.733711259729956*^9, 3.733711278366322*^9}, 3.7337113240271106`*^9, {3.733711384581702*^9, 3.733711436236964*^9}, 3.7337114809469175`*^9, {3.7337115173918333`*^9, 3.733711518879483*^9}, 3.733711560439453*^9, {3.733711609599924*^9, 3.7337116342722664`*^9}, { 3.733711689751358*^9, 3.7337116969119487`*^9}, {3.7337129879879694`*^9, 3.7337130014112797`*^9}, {3.733713172835663*^9, 3.733713173913886*^9}, { 3.7337132483436465`*^9, 3.7337132496094065`*^9}, {3.733713283003566*^9, 3.7337134200180254`*^9}, {3.733713464428997*^9, 3.7337135191222897`*^9}, { 3.7337135777847366`*^9, 3.73371367154463*^9}, {3.7337140009857264`*^9, 3.7337140458967295`*^9}, {3.733714091198394*^9, 3.7337141070440063`*^9}, { 3.733714143813529*^9, 3.733714146610505*^9}, {3.733721976862414*^9, 3.7337219813629093`*^9}, {3.733722281191476*^9, 3.7337222944429536`*^9}, { 3.733722382186266*^9, 3.7337223828425617`*^9}, {3.7337224624293957`*^9, 3.7337224858690815`*^9}, 3.7337225537825146`*^9, {3.733722654230641*^9, 3.733722661731436*^9}, {3.733722818999301*^9, 3.7337228267499514`*^9}, { 3.733723144924486*^9, 3.733723159691375*^9}, {3.733723196273369*^9, 3.733723198695795*^9}, {3.7337232377777586`*^9, 3.7337232408874655`*^9}, { 3.73372435111442*^9, 3.733724354067712*^9}, {3.7337244099801674`*^9, 3.733724433076069*^9}, {3.7337245236325226`*^9, 3.733724524679802*^9}, { 3.7337873724058084`*^9, 3.7337873841879997`*^9}, {3.7337879154409466`*^9, 3.7337879158316607`*^9}, {3.7340647908247976`*^9, 3.73406479426425*^9}, { 3.7340650184820967`*^9, 3.7340650196896086`*^9}, {3.7340717757289314`*^9, 3.734071783044138*^9}, 3.760607155346615*^9, 3.7606077013285637`*^9, 3.760607753497196*^9, {3.760608088928544*^9, 3.7606081156683984`*^9}, { 3.760608160193988*^9, 3.7606081844316325`*^9}, {3.760608240118147*^9, 3.7606082403257685`*^9}, {3.760608370421237*^9, 3.7606085188738213`*^9}, { 3.7606087505165215`*^9, 3.7606087536075697`*^9}, {3.7606087890680313`*^9, 3.760608797233983*^9}, {3.7606088687210503`*^9, 3.7606088969051304`*^9}, { 3.760608928173344*^9, 3.760608935537922*^9}, 3.760609001847164*^9, 3.760610501819937*^9, {3.7606107473288507`*^9, 3.760610758648224*^9}, 3.760610853832239*^9, {3.7606112396040025`*^9, 3.7606112817332983`*^9}, { 3.760611401222947*^9, 3.76061140197075*^9}, {3.760611673421208*^9, 3.7606117248805995`*^9}, {3.7606118287018495`*^9, 3.7606119921793656`*^9}, {3.760612127470795*^9, 3.760612223396744*^9}, { 3.76061550773096*^9, 3.7606155085119963`*^9}, 3.760615603302456*^9, { 3.760615693062388*^9, 3.760615704512997*^9}, 3.7606158367472205`*^9, { 3.760615988102416*^9, 3.7606160042704983`*^9}, {3.7632524995190973`*^9, 3.7632525737340136`*^9}, {3.763426957870851*^9, 3.763426959053108*^9}, { 3.7634271873253856`*^9, 3.763427188674776*^9}, {3.7634423988211765`*^9, 3.7634424251737814`*^9}, {3.7634426334949675`*^9, 3.7634426560163193`*^9}, {3.763528275706467*^9, 3.7635284013459897`*^9}, { 3.763528705040784*^9, 3.7635287224411435`*^9}, {3.7635289011396055`*^9, 3.763528901842952*^9}, {3.763548522859683*^9, 3.76354854228095*^9}, { 3.7636050270340595`*^9, 3.763605035756063*^9}, {3.763605112705577*^9, 3.763605344908389*^9}, {3.7636054077448673`*^9, 3.7636054326054068`*^9}, { 3.7636054757131557`*^9, 3.7636054979248376`*^9}, {3.763605542706845*^9, 3.763605675311968*^9}, {3.763605884155599*^9, 3.7636058987003956`*^9}, { 3.763606027844756*^9, 3.7636060593519597`*^9}, {3.7636061708042307`*^9, 3.763606210806114*^9}, 3.763606241472248*^9, {3.7636062752072725`*^9, 3.763606340114405*^9}, {3.763606445999727*^9, 3.7636064489171495`*^9}, { 3.763606744287244*^9, 3.7636067648057427`*^9}, 3.7636070601536713`*^9, { 3.763607262857174*^9, 3.763607300007738*^9}, {3.7636074396359158`*^9, 3.7636074830770864`*^9}, {3.7636076263020697`*^9, 3.7636076543842106`*^9}, 3.763607688296667*^9, {3.7636077698636456`*^9, 3.7636077758773165`*^9}, { 3.763607857294286*^9, 3.7636078613443317`*^9}, 3.763608605441226*^9, { 3.7638142471323504`*^9, 3.7638142487803507`*^9}, {3.7638142898908815`*^9, 3.7638143569012723`*^9}, {3.763958140651967*^9, 3.763958153489439*^9}, 3.76395845683808*^9, {3.7639608609270196`*^9, 3.763960872595887*^9}, { 3.764339536191163*^9, 3.7643395373935814`*^9}, {3.764339581142139*^9, 3.7643396307895145`*^9}, {3.7643397270416403`*^9, 3.764339746774886*^9}, { 3.7643759693358665`*^9, 3.764375988525555*^9}, {3.764410286736837*^9, 3.764410291232706*^9}, {3.7649058387052116`*^9, 3.7649058888300486`*^9}, { 3.764905919657881*^9, 3.7649059255708666`*^9}, {3.764906015807353*^9, 3.7649060798935275`*^9}, {3.7649061275007944`*^9, 3.764906182700228*^9}, { 3.7649814310038157`*^9, 3.764981612888131*^9}, {3.764981649845045*^9, 3.764981717214387*^9}, {3.7650095509166293`*^9, 3.7650095663321896`*^9}, { 3.765009596962874*^9, 3.7650096065955095`*^9}, 3.7650098165773335`*^9, { 3.765011173435627*^9, 3.765011180125066*^9}, {3.7650788221318007`*^9, 3.765078823898266*^9}, {3.7650788935676775`*^9, 3.7650789311170053`*^9}, { 3.765085243174881*^9, 3.7650852441096754`*^9}, 3.765085550868559*^9, { 3.7650855978395305`*^9, 3.7650856220925417`*^9}, {3.7650863545547857`*^9, 3.7650863799862742`*^9}, {3.7650865194326468`*^9, 3.765086519785918*^9}, { 3.7650865505251884`*^9, 3.7650865669896946`*^9}, 3.765087372975154*^9, { 3.7650874030551014`*^9, 3.7650874163952713`*^9}, {3.765087536684074*^9, 3.7650876355597906`*^9}, 3.7650877252914543`*^9, {3.765088672041128*^9, 3.7650887019763765`*^9}, {3.765088740411885*^9, 3.765088742455727*^9}, { 3.7650889283353214`*^9, 3.7650889447918415`*^9}, {3.765089035561446*^9, 3.7650890612584443`*^9}, {3.7650891812559137`*^9, 3.765089209061077*^9}, { 3.7650893423167953`*^9, 3.76508943243054*^9}, {3.765090684608432*^9, 3.765090700734714*^9}, 3.7650907477613907`*^9, {3.7650908366428585`*^9, 3.7650908539151096`*^9}, {3.7650908896330676`*^9, 3.765090909940852*^9}, { 3.765091082681374*^9, 3.7650911113055153`*^9}, {3.7650911427516937`*^9, 3.7650911450258894`*^9}, {3.7650912819372005`*^9, 3.765091515369325*^9}, { 3.7650916102443376`*^9, 3.7650917517497134`*^9}, {3.765092443582117*^9, 3.765092498126871*^9}, {3.76509426500305*^9, 3.765094281405676*^9}, 3.765094315674655*^9, {3.7652396904249477`*^9, 3.765239693502611*^9}, 3.765253217258378*^9, {3.7652532852065315`*^9, 3.7652532918614807`*^9}, 3.766189724095389*^9, {3.766190438614527*^9, 3.7661905103848095`*^9}, { 3.76619098699972*^9, 3.766190987925188*^9}, {3.766193820625373*^9, 3.7661938215367756`*^9}, {3.7662041564549007`*^9, 3.7662041841044207`*^9}, {3.766204415112673*^9, 3.766204435514146*^9}, { 3.766204514370674*^9, 3.766204525664904*^9}, 3.766204570014185*^9, { 3.7665714310907745`*^9, 3.76657144559927*^9}, {3.7665725420953245`*^9, 3.7665725423845477`*^9}, {3.7666314737351704`*^9, 3.7666315492489386`*^9}, {3.7740882771256323`*^9, 3.774088312744491*^9}, { 3.774150773834302*^9, 3.774150944718382*^9}, {3.774150975094303*^9, 3.774151054824913*^9}, {3.7741511238761725`*^9, 3.7741512298519745`*^9}, { 3.77415129158794*^9, 3.774151651300989*^9}, {3.774151741892136*^9, 3.774151770064453*^9}, {3.7742415341727543`*^9, 3.7742416306317797`*^9}, { 3.7751898888726125`*^9, 3.775189913786336*^9}, {3.7751899486865563`*^9, 3.7751899522127523`*^9}, {3.7751899989654093`*^9, 3.7751900149868736`*^9}, {3.7751900517928104`*^9, 3.775190066570419*^9}, { 3.7879798676374617`*^9, 3.7879798943206964`*^9}, {3.792287382183713*^9, 3.792287444759338*^9}, {3.792287488992601*^9, 3.7922875432928047`*^9}, { 3.7922886672157793`*^9, 3.7922886764378495`*^9}, {3.792288708660981*^9, 3.7922888810105305`*^9}, {3.792300131730332*^9, 3.7923001501177034`*^9}, { 3.795768609226843*^9, 3.7957686326352005`*^9}, {3.7957686687171*^9, 3.7957686846637707`*^9}, {3.7957688298513894`*^9, 3.795768834915843*^9}, 3.7957688867486525`*^9, {3.795768942098573*^9, 3.795768993537817*^9}, { 3.7957690236098194`*^9, 3.79576902468211*^9}, {3.7957690712421293`*^9, 3.795769275801197*^9}, {3.7957693460703883`*^9, 3.795769349757367*^9}, { 3.79576972202382*^9, 3.7957697714534473`*^9}, {3.795769801653285*^9, 3.795769804711711*^9}, {3.796345941656575*^9, 3.7963459430887594`*^9}, { 3.8298913714361515`*^9, 3.829891372330407*^9}, {3.843728585368825*^9, 3.84372858844851*^9}, {3.8449958679518747`*^9, 3.8449959617306128`*^9}, { 3.845978121229767*^9, 3.845978121586933*^9}, {3.8459781752184176`*^9, 3.845978183704877*^9}, {3.8459783826308093`*^9, 3.8459784254435472`*^9}, { 3.845978956970813*^9, 3.8459791499511595`*^9}, 3.8461289015497713`*^9, 3.846128946122293*^9, {3.846309385225996*^9, 3.846309410347027*^9}, { 3.846309504823522*^9, 3.846309511339752*^9}, {3.8532051618832316`*^9, 3.8532051757582083`*^9}, 3.853205648810899*^9, {3.853205773068694*^9, 3.8532058080261583`*^9}, {3.853206663322813*^9, 3.853206670956298*^9}}, CellLabel-> "In[354]:=",ExpressionUUID->"7653a3c0-7297-41d0-9ec9-41ef62c16876"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"plate", " ", "graphics"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", "hn_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{"mat", ",", RowBox[{"{", "hn", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", "hn_", "}"}], ",", "for_"}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{"mat", ",", RowBox[{"{", "hn", "}"}], ",", "for"}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", "hn_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{"mat", ",", RowBox[{"{", "hn", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", "hn_", "}"}], ",", "for_"}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{"mat", ",", RowBox[{"{", "hn", "}"}], ",", "for"}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", "hn_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{"mat", ",", RowBox[{"{", "hn", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", "hn_", "}"}], ",", "for_"}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "NN", ",", "r0", ",", "r0\[Alpha]", ",", "r0\[Beta]", ",", "h\[Alpha]", ",", "h\[Beta]", ",", "e\[Alpha]", ",", "e\[Beta]", ",", "en", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "\[Rho]", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "pp", ",", "pn"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}], ",", "\[Alpha]", ",", "\[Beta]"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r0\[Alpha]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r0"}]}], ";", "\[IndentingNewLine]", RowBox[{"r0\[Beta]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r0"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{ RowBox[{"(", RowBox[{"r0\[Alpha]", StyleBox["\[Cross]", "OperatorCharacter"], "r0\[Beta]"}], ")"}], "/", RowBox[{"Norm", "[", RowBox[{"r0\[Alpha]", StyleBox["\[Cross]", "OperatorCharacter"], "r0\[Beta]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Rho]", "=", RowBox[{"en", "*", "n"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"pp", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"r0", "+", "\[Rho]", "+", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "*", "scale"}], "+", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "\[Cross]", "\[Rho]"}], "*", "scale"}]}], ")"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "n"}], "}"}], "\[Rule]", "#"}], "]"}]}], "&"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"-", "hn"}], "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", RowBox[{ RowBox[{"-", "hn"}], "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{ RowBox[{"-", "hn"}], "/", "2"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"hn", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", RowBox[{"hn", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"hn", "/", "2"}]}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"pn", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"r0", "+", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "*", "scale"}]}], ")"}], "/.", RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "n"}], "}"}], "\[Rule]", "#"}], "]"}]}], "&"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Gray", ",", RowBox[{"Opacity", "[", "0.5", "]"}], ",", RowBox[{"EdgeForm", "[", "]"}], ",", RowBox[{"Prism", "[", "pp", "]"}], ",", "Blue", ",", RowBox[{"PointSize", "[", "Medium", "]"}], ",", RowBox[{"Point", "[", "pn", "]"}]}], "}"}]}]}], " ", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", "hn_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{"mat", ",", RowBox[{"{", "hn", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", "hn_", "}"}], ",", "for_"}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{"mat", ",", RowBox[{"{", "hn", "}"}], ",", "for"}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", "hn_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{"mat", ",", RowBox[{"{", "hn", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", "hn_", "}"}], ",", "for_"}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{"mat", ",", RowBox[{"{", "hn", "}"}], ",", "for"}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", "hn_", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{"mat", ",", RowBox[{"{", "hn", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", "hn_", "}"}], ",", "for_"}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "nl", ",", "NN", ",", "r0", ",", "r0\[Alpha]", ",", "r0\[Beta]", ",", "h\[Alpha]", ",", "h\[Beta]", ",", "e\[Alpha]", ",", "e\[Beta]", ",", "en", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "\[Rho]", ",", "u", ",", "v", ",", "w", ",", "\[Phi]", ",", "\[Theta]", ",", "\[Psi]", ",", "pp", ",", "pn"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"nl", "=", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", RowBox[{"(", RowBox[{"1", "-", "\[Beta]"}], ")"}]}], ",", RowBox[{"\[Alpha]", " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"r0\[Alpha]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "r0"}]}], ";", "\[IndentingNewLine]", RowBox[{"r0\[Beta]", "=", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "r0"}]}], ";", "\[IndentingNewLine]", RowBox[{"en", "=", RowBox[{ RowBox[{"(", RowBox[{"r0\[Alpha]", StyleBox["\[Cross]", "OperatorCharacter"], "r0\[Beta]"}], ")"}], "/", RowBox[{"Norm", "[", RowBox[{"r0\[Alpha]", StyleBox["\[Cross]", "OperatorCharacter"], "r0\[Beta]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Rho]", "=", RowBox[{"en", "*", "n"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"pp", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"r0", "+", "\[Rho]", "+", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "*", "scale"}], "+", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "\[Cross]", "\[Rho]"}], "*", "scale"}]}], ")"}], " ", "/.", RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "n"}], "}"}], "\[Rule]", "#"}], "]"}]}], "&"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"-", "hn"}], "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", RowBox[{ RowBox[{"-", "hn"}], "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{ RowBox[{"-", "hn"}], "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{ RowBox[{"-", "hn"}], "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"hn", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", RowBox[{"hn", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"hn", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"hn", "/", "2"}]}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"pn", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"r0", "+", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "*", "scale"}]}], ")"}], "/.", RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "n"}], "}"}], "\[Rule]", "#"}], "]"}]}], "&"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Gray", ",", RowBox[{"Opacity", "[", "0.5", "]"}], ",", RowBox[{"EdgeForm", "[", "]"}], ",", RowBox[{"Hexahedron", "[", "pp", "]"}], ",", "Blue", ",", RowBox[{"PointSize", "[", "Medium", "]"}], ",", RowBox[{"Point", "[", "pn", "]"}]}], "}"}]}]}], " ", "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.633673923685915*^9, 3.6336739535006204`*^9}, { 3.633674155068149*^9, 3.6336741996717005`*^9}, {3.6336745049841633`*^9, 3.6336745219741354`*^9}, {3.6336919593939404`*^9, 3.6336919775979815`*^9}, 3.633692380551029*^9, {3.6336927116599674`*^9, 3.633692727194856*^9}, { 3.635310826749509*^9, 3.6353108343419433`*^9}, {3.635311461613821*^9, 3.6353114619508405`*^9}, {3.7326759806780663`*^9, 3.7326760008674326`*^9}, {3.7326760331212645`*^9, 3.7326760385677853`*^9}, {3.732684137201784*^9, 3.73268419404665*^9}, { 3.732684306221466*^9, 3.7326843382153635`*^9}, 3.7326844699232764`*^9, { 3.7326845133861027`*^9, 3.73268452322455*^9}, {3.732759973190983*^9, 3.7327599776758347`*^9}, {3.7327613720703106`*^9, 3.7327614888170295`*^9}, {3.732761535853627*^9, 3.7327615404943867`*^9}, { 3.7327615972663317`*^9, 3.7327616122832594`*^9}, {3.7327616693361855`*^9, 3.73276183332095*^9}, {3.732761876700554*^9, 3.7327618790133*^9}, { 3.732761909063363*^9, 3.732761910469795*^9}, {3.73276200508918*^9, 3.732762006042756*^9}, {3.7327620750344048`*^9, 3.732762101490326*^9}, 3.7327688007102947`*^9, {3.7327705695330524`*^9, 3.7327705708254137`*^9}, { 3.732788507552166*^9, 3.7327885085870132`*^9}, {3.732788681344634*^9, 3.7327887090994544`*^9}, {3.732788743287696*^9, 3.73278879848213*^9}, { 3.732788922306119*^9, 3.7327889462731514`*^9}, {3.732789012151597*^9, 3.732789028200858*^9}, {3.7327890791192408`*^9, 3.732789086999034*^9}, { 3.732789135698248*^9, 3.7327891358892384`*^9}, {3.7327891989507074`*^9, 3.7327891993104925`*^9}, {3.733116709198372*^9, 3.733116731638229*^9}, { 3.7334931331412554`*^9, 3.7334932071522064`*^9}, {3.733493353668892*^9, 3.7334934953404007`*^9}, {3.733493581610343*^9, 3.733493589891471*^9}, { 3.7334936319789553`*^9, 3.7334936623392687`*^9}, {3.7334936935401745`*^9, 3.733493716917615*^9}, {3.7334937687375154`*^9, 3.733493799379287*^9}, { 3.7335602963276734`*^9, 3.7335603891038685`*^9}, {3.7337039222525787`*^9, 3.733703929721642*^9}, {3.7337040222462597`*^9, 3.7337040262631474`*^9}, { 3.733710121070121*^9, 3.733710122358057*^9}, 3.7337110885786676`*^9, 3.733711184948838*^9, {3.733711259729956*^9, 3.733711278366322*^9}, 3.7337113240271106`*^9, {3.733711384581702*^9, 3.733711436236964*^9}, 3.7337114809469175`*^9, {3.7337115173918333`*^9, 3.733711518879483*^9}, 3.733711560439453*^9, {3.733711609599924*^9, 3.7337116342722664`*^9}, { 3.733711689751358*^9, 3.7337116969119487`*^9}, {3.7337129879879694`*^9, 3.7337130014112797`*^9}, {3.733713172835663*^9, 3.733713173913886*^9}, { 3.7337132483436465`*^9, 3.7337132496094065`*^9}, {3.733713283003566*^9, 3.7337134200180254`*^9}, {3.733713464428997*^9, 3.7337135191222897`*^9}, { 3.7337135777847366`*^9, 3.73371367154463*^9}, {3.7337140009857264`*^9, 3.7337140458967295`*^9}, {3.733714091198394*^9, 3.7337141070440063`*^9}, { 3.733714143813529*^9, 3.733714146610505*^9}, {3.733721976862414*^9, 3.7337219813629093`*^9}, {3.733722281191476*^9, 3.7337222944429536`*^9}, { 3.733722382186266*^9, 3.7337223828425617`*^9}, {3.7337224624293957`*^9, 3.7337224858690815`*^9}, 3.7337225537825146`*^9, {3.733722654230641*^9, 3.733722661731436*^9}, {3.733722818999301*^9, 3.7337228267499514`*^9}, { 3.733723144924486*^9, 3.733723159691375*^9}, {3.733723196273369*^9, 3.733723198695795*^9}, {3.7337232377777586`*^9, 3.7337232408874655`*^9}, { 3.73372435111442*^9, 3.733724354067712*^9}, {3.7337244099801674`*^9, 3.733724433076069*^9}, {3.7337245236325226`*^9, 3.733724524679802*^9}, { 3.7337873724058084`*^9, 3.7337873841879997`*^9}, {3.7337879154409466`*^9, 3.7337879158316607`*^9}, {3.7340647908247976`*^9, 3.73406479426425*^9}, { 3.7340650184820967`*^9, 3.7340650196896086`*^9}, {3.7340717757289314`*^9, 3.734071783044138*^9}, 3.760607155346615*^9, 3.7606077013285637`*^9, 3.760607753497196*^9, {3.760608088928544*^9, 3.7606081156683984`*^9}, { 3.760608160193988*^9, 3.7606081844316325`*^9}, {3.760608240118147*^9, 3.7606082403257685`*^9}, {3.760608370421237*^9, 3.7606085188738213`*^9}, { 3.7606087505165215`*^9, 3.7606087536075697`*^9}, {3.7606087890680313`*^9, 3.760608797233983*^9}, {3.7606088687210503`*^9, 3.7606088969051304`*^9}, { 3.760608928173344*^9, 3.760608935537922*^9}, 3.760609001847164*^9, 3.760610501819937*^9, {3.7606107473288507`*^9, 3.760610758648224*^9}, 3.760610853832239*^9, {3.7606112396040025`*^9, 3.7606112817332983`*^9}, { 3.760611401222947*^9, 3.76061140197075*^9}, {3.760611673421208*^9, 3.7606117248805995`*^9}, {3.7606118287018495`*^9, 3.7606119921793656`*^9}, {3.760612127470795*^9, 3.760612223396744*^9}, { 3.76061550773096*^9, 3.7606155085119963`*^9}, 3.760615603302456*^9, { 3.760615693062388*^9, 3.760615704512997*^9}, 3.7606158367472205`*^9, { 3.760615988102416*^9, 3.7606160042704983`*^9}, {3.7632524995190973`*^9, 3.7632525737340136`*^9}, {3.763426957870851*^9, 3.763426959053108*^9}, { 3.7634271873253856`*^9, 3.763427188674776*^9}, {3.7634423988211765`*^9, 3.7634424251737814`*^9}, {3.7634426334949675`*^9, 3.7634426560163193`*^9}, {3.763528275706467*^9, 3.7635284013459897`*^9}, { 3.763528705040784*^9, 3.7635287224411435`*^9}, {3.7635289011396055`*^9, 3.763528901842952*^9}, {3.763548522859683*^9, 3.76354854228095*^9}, { 3.7636050270340595`*^9, 3.763605035756063*^9}, {3.763605112705577*^9, 3.763605344908389*^9}, {3.7636054077448673`*^9, 3.7636054326054068`*^9}, { 3.7636054757131557`*^9, 3.7636054979248376`*^9}, {3.763605542706845*^9, 3.763605675311968*^9}, {3.763605884155599*^9, 3.7636058987003956`*^9}, { 3.763606027844756*^9, 3.7636060593519597`*^9}, {3.7636061708042307`*^9, 3.763606210806114*^9}, 3.763606241472248*^9, {3.7636062752072725`*^9, 3.763606340114405*^9}, {3.763606445999727*^9, 3.7636064489171495`*^9}, { 3.763606744287244*^9, 3.7636067648057427`*^9}, 3.7636070601536713`*^9, { 3.763607262857174*^9, 3.763607300007738*^9}, {3.7636074396359158`*^9, 3.7636074830770864`*^9}, {3.7636076263020697`*^9, 3.7636076543842106`*^9}, 3.763607688296667*^9, {3.7636077698636456`*^9, 3.7636077758773165`*^9}, { 3.763607857294286*^9, 3.7636078613443317`*^9}, 3.763608605441226*^9, { 3.7638142471323504`*^9, 3.7638142487803507`*^9}, {3.7638142898908815`*^9, 3.7638143569012723`*^9}, {3.763958140651967*^9, 3.763958153489439*^9}, 3.76395845683808*^9, {3.7639608609270196`*^9, 3.763960872595887*^9}, { 3.764339536191163*^9, 3.7643395373935814`*^9}, {3.764339581142139*^9, 3.7643396307895145`*^9}, {3.7643397270416403`*^9, 3.764339746774886*^9}, { 3.7643759693358665`*^9, 3.764375988525555*^9}, {3.764410286736837*^9, 3.764410291232706*^9}, {3.7649058387052116`*^9, 3.7649058888300486`*^9}, { 3.764905919657881*^9, 3.7649059255708666`*^9}, {3.764906015807353*^9, 3.7649060798935275`*^9}, {3.7649061275007944`*^9, 3.764906182700228*^9}, { 3.7649814310038157`*^9, 3.764981612888131*^9}, {3.764981649845045*^9, 3.764981717214387*^9}, {3.7650095509166293`*^9, 3.7650095663321896`*^9}, { 3.765009596962874*^9, 3.7650096065955095`*^9}, 3.7650098165773335`*^9, { 3.765011173435627*^9, 3.765011180125066*^9}, {3.7650788221318007`*^9, 3.765078823898266*^9}, {3.7650788935676775`*^9, 3.7650789311170053`*^9}, { 3.765085243174881*^9, 3.7650852441096754`*^9}, 3.765085550868559*^9, { 3.7650855978395305`*^9, 3.7650856220925417`*^9}, {3.7650863545547857`*^9, 3.7650863799862742`*^9}, {3.7650865194326468`*^9, 3.765086519785918*^9}, { 3.7650865505251884`*^9, 3.7650865669896946`*^9}, 3.765087372975154*^9, { 3.7650874030551014`*^9, 3.7650874163952713`*^9}, {3.765087536684074*^9, 3.7650876355597906`*^9}, 3.7650877252914543`*^9, {3.765088672041128*^9, 3.7650887019763765`*^9}, {3.765088740411885*^9, 3.765088742455727*^9}, { 3.7650889283353214`*^9, 3.7650889447918415`*^9}, {3.765089035561446*^9, 3.7650890612584443`*^9}, {3.7650891812559137`*^9, 3.765089209061077*^9}, { 3.7650893423167953`*^9, 3.76508943243054*^9}, {3.765090684608432*^9, 3.765090700734714*^9}, 3.7650907477613907`*^9, {3.7650908366428585`*^9, 3.7650908539151096`*^9}, {3.7650908896330676`*^9, 3.765090909940852*^9}, { 3.765091082681374*^9, 3.7650911113055153`*^9}, {3.7650911427516937`*^9, 3.7650911450258894`*^9}, {3.7650912819372005`*^9, 3.765091515369325*^9}, { 3.7650916102443376`*^9, 3.7650917517497134`*^9}, {3.765092443582117*^9, 3.765092498126871*^9}, {3.76509426500305*^9, 3.765094281405676*^9}, 3.765094315674655*^9, {3.7652396904249477`*^9, 3.765239693502611*^9}, 3.765253217258378*^9, {3.7652532852065315`*^9, 3.7652532918614807`*^9}, 3.766189724095389*^9, {3.766190438614527*^9, 3.7661905103848095`*^9}, { 3.76619098699972*^9, 3.766190987925188*^9}, {3.766193820625373*^9, 3.7661938215367756`*^9}, {3.7662041564549007`*^9, 3.7662041841044207`*^9}, {3.766204415112673*^9, 3.766204435514146*^9}, { 3.766204514370674*^9, 3.766204525664904*^9}, 3.766204570014185*^9, { 3.7665714310907745`*^9, 3.76657144559927*^9}, {3.7665725420953245`*^9, 3.7665725423845477`*^9}, {3.7666314737351704`*^9, 3.7666315492489386`*^9}, {3.7740882771256323`*^9, 3.774088312744491*^9}, { 3.774150773834302*^9, 3.774150944718382*^9}, {3.774150975094303*^9, 3.774151054824913*^9}, {3.7741511238761725`*^9, 3.7741512298519745`*^9}, { 3.77415129158794*^9, 3.774151651300989*^9}, {3.774151741892136*^9, 3.774151770064453*^9}, {3.7742415341727543`*^9, 3.7742416306317797`*^9}, { 3.7751898888726125`*^9, 3.775189913786336*^9}, {3.7751899486865563`*^9, 3.7751899522127523`*^9}, {3.7751899989654093`*^9, 3.7751900149868736`*^9}, {3.7751900517928104`*^9, 3.775190066570419*^9}, { 3.7879798676374617`*^9, 3.7879798943206964`*^9}, {3.792287382183713*^9, 3.792287444759338*^9}, {3.792287488992601*^9, 3.7922875432928047`*^9}, { 3.7922886672157793`*^9, 3.7922886764378495`*^9}, {3.792288708660981*^9, 3.7922888810105305`*^9}, {3.792300131730332*^9, 3.7923001501177034`*^9}, { 3.795768609226843*^9, 3.7957686326352005`*^9}, {3.7957686687171*^9, 3.7957686846637707`*^9}, {3.7957688298513894`*^9, 3.795768834915843*^9}, 3.7957688867486525`*^9, {3.795768942098573*^9, 3.795768993537817*^9}, { 3.7957690236098194`*^9, 3.79576902468211*^9}, {3.7957690712421293`*^9, 3.795769275801197*^9}, {3.7957693460703883`*^9, 3.795769349757367*^9}, { 3.79576972202382*^9, 3.7957697714534473`*^9}, {3.795769801653285*^9, 3.795769804711711*^9}, {3.796345941656575*^9, 3.7963459430887594`*^9}, { 3.8298913714361515`*^9, 3.829891372330407*^9}, {3.843728585368825*^9, 3.84372858844851*^9}, {3.8449958679518747`*^9, 3.8449959617306128`*^9}, { 3.845978121229767*^9, 3.845978121586933*^9}, {3.8459781752184176`*^9, 3.845978183704877*^9}, {3.8459783826308093`*^9, 3.8459784254435472`*^9}, { 3.845978956970813*^9, 3.8459791499511595`*^9}, 3.8461289015497713`*^9, { 3.846128946122293*^9, 3.846128968019552*^9}, {3.846129003512868*^9, 3.8461290485155616`*^9}, {3.8461291291837854`*^9, 3.846129173768606*^9}, { 3.8461293216071515`*^9, 3.846129324863345*^9}, {3.846129415192334*^9, 3.846129416208379*^9}, {3.8461294959672627`*^9, 3.8461295654972105`*^9}, { 3.84612986121124*^9, 3.8461298706686964`*^9}}, CellLabel-> "In[372]:=",ExpressionUUID->"9401b9b0-0d65-4f8f-abf7-575cd33ebc44"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"solid", " ", "elements"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{"mat_", ",", "for_"}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", " ", "\[IndentingNewLine]", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", "pn", "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"pn", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], ",", "2"}], "]"}], "]"}], "*", "scale"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Gray", ",", RowBox[{"Opacity", "[", "0.5", "]"}], ",", RowBox[{"EdgeForm", "[", "]"}], ",", RowBox[{"Tetrahedron", "[", "pn", "]"}], ",", "Blue", ",", RowBox[{"PointSize", "[", "Medium", "]"}], ",", RowBox[{"Point", "[", "pn", "]"}]}], "}"}]}]}], " ", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{"mat_", ",", "for_"}], "}"}], ",", RowBox[{"Hexahedron", "[", RowBox[{"{", RowBox[{ "n1_", ",", "n2_", ",", "n3_", ",", "n4_", ",", "n5_", ",", "n6_", ",", "n7_", ",", "n8_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", " ", "\[IndentingNewLine]", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"pn", ",", "nn"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"nn", "=", RowBox[{"{", RowBox[{ "n1", ",", "n2", ",", "n3", ",", "n4", ",", "n5", ",", "n6", ",", "n7", ",", "n8"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"pn", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nn", ",", "1"}], "]"}], "]"}], "+", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nn", ",", "2"}], "]"}], "]"}], "*", "scale"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Gray", ",", RowBox[{"Opacity", "[", "0.5", "]"}], ",", RowBox[{"EdgeForm", "[", "]"}], ",", RowBox[{"Hexahedron", "[", "pn", "]"}], ",", "Blue", ",", RowBox[{"PointSize", "[", "Medium", "]"}], ",", RowBox[{"Point", "[", "pn", "]"}]}], "}"}]}]}], " ", "]"}]}], ";"}]}]}]], "Input", InitializationCell->True, CellChangeTimes->{{3.633673923685915*^9, 3.6336739535006204`*^9}, { 3.633674155068149*^9, 3.6336741996717005`*^9}, {3.6336745049841633`*^9, 3.6336745219741354`*^9}, {3.6336919593939404`*^9, 3.6336919775979815`*^9}, 3.633692380551029*^9, {3.6336927116599674`*^9, 3.633692727194856*^9}, { 3.635310826749509*^9, 3.6353108343419433`*^9}, {3.635311461613821*^9, 3.6353114619508405`*^9}, {3.7326759806780663`*^9, 3.7326760008674326`*^9}, {3.7326760331212645`*^9, 3.7326760385677853`*^9}, {3.732684137201784*^9, 3.73268419404665*^9}, { 3.732684306221466*^9, 3.7326843382153635`*^9}, 3.7326844699232764`*^9, { 3.7326845133861027`*^9, 3.73268452322455*^9}, {3.732759973190983*^9, 3.7327599776758347`*^9}, {3.7327613720703106`*^9, 3.7327614888170295`*^9}, {3.732761535853627*^9, 3.7327615404943867`*^9}, { 3.7327615972663317`*^9, 3.7327616122832594`*^9}, {3.7327616693361855`*^9, 3.73276183332095*^9}, {3.732761876700554*^9, 3.7327618790133*^9}, { 3.732761909063363*^9, 3.732761910469795*^9}, {3.73276200508918*^9, 3.732762006042756*^9}, {3.7327620750344048`*^9, 3.732762101490326*^9}, 3.7327688007102947`*^9, {3.7327705695330524`*^9, 3.7327705708254137`*^9}, { 3.732788507552166*^9, 3.7327885085870132`*^9}, {3.732788681344634*^9, 3.7327887090994544`*^9}, {3.732788743287696*^9, 3.73278879848213*^9}, { 3.732788922306119*^9, 3.7327889462731514`*^9}, {3.732789012151597*^9, 3.732789028200858*^9}, {3.7327890791192408`*^9, 3.732789086999034*^9}, { 3.732789135698248*^9, 3.7327891358892384`*^9}, {3.7327891989507074`*^9, 3.7327891993104925`*^9}, {3.733116709198372*^9, 3.733116731638229*^9}, { 3.7334931331412554`*^9, 3.7334932071522064`*^9}, {3.733493353668892*^9, 3.7334934953404007`*^9}, {3.733493581610343*^9, 3.733493589891471*^9}, { 3.7334936319789553`*^9, 3.7334936623392687`*^9}, {3.7334936935401745`*^9, 3.733493716917615*^9}, {3.7334937687375154`*^9, 3.733493799379287*^9}, { 3.7335602963276734`*^9, 3.7335603891038685`*^9}, {3.7337039222525787`*^9, 3.733703929721642*^9}, {3.7337040222462597`*^9, 3.7337040262631474`*^9}, { 3.733710121070121*^9, 3.733710122358057*^9}, 3.7337110885786676`*^9, 3.733711184948838*^9, {3.733711259729956*^9, 3.733711278366322*^9}, 3.7337113240271106`*^9, {3.733711384581702*^9, 3.733711436236964*^9}, 3.7337114809469175`*^9, {3.7337115173918333`*^9, 3.733711518879483*^9}, 3.733711560439453*^9, {3.733711609599924*^9, 3.7337116342722664`*^9}, { 3.733711689751358*^9, 3.7337116969119487`*^9}, {3.7337129879879694`*^9, 3.7337130014112797`*^9}, {3.733713172835663*^9, 3.733713173913886*^9}, { 3.7337132483436465`*^9, 3.7337132496094065`*^9}, {3.733713283003566*^9, 3.7337134200180254`*^9}, {3.733713464428997*^9, 3.7337135191222897`*^9}, { 3.7337135777847366`*^9, 3.73371367154463*^9}, {3.7337140009857264`*^9, 3.7337140458967295`*^9}, {3.733714091198394*^9, 3.7337141070440063`*^9}, { 3.733714143813529*^9, 3.733714146610505*^9}, {3.733721976862414*^9, 3.7337219813629093`*^9}, {3.733722281191476*^9, 3.7337222944429536`*^9}, { 3.733722382186266*^9, 3.7337223828425617`*^9}, {3.7337224624293957`*^9, 3.7337224858690815`*^9}, 3.7337225537825146`*^9, {3.733722654230641*^9, 3.733722661731436*^9}, {3.733722818999301*^9, 3.7337228267499514`*^9}, { 3.733723144924486*^9, 3.733723159691375*^9}, {3.733723196273369*^9, 3.733723198695795*^9}, {3.7337232377777586`*^9, 3.7337232408874655`*^9}, { 3.73372435111442*^9, 3.733724354067712*^9}, {3.7337244099801674`*^9, 3.733724433076069*^9}, {3.7337245236325226`*^9, 3.733724524679802*^9}, { 3.7337873724058084`*^9, 3.7337873841879997`*^9}, {3.7337879154409466`*^9, 3.7337879158316607`*^9}, {3.7340647908247976`*^9, 3.73406479426425*^9}, { 3.7340650184820967`*^9, 3.7340650196896086`*^9}, {3.7340717757289314`*^9, 3.734071783044138*^9}, 3.760607155346615*^9, 3.7606077013285637`*^9, 3.760607753497196*^9, {3.760608088928544*^9, 3.7606081156683984`*^9}, { 3.760608160193988*^9, 3.7606081844316325`*^9}, {3.760608240118147*^9, 3.7606082403257685`*^9}, {3.760608370421237*^9, 3.7606085188738213`*^9}, { 3.7606087505165215`*^9, 3.7606087536075697`*^9}, {3.7606087890680313`*^9, 3.760608797233983*^9}, {3.7606088687210503`*^9, 3.7606088969051304`*^9}, { 3.760608928173344*^9, 3.760608935537922*^9}, 3.760609001847164*^9, 3.760610501819937*^9, {3.7606107473288507`*^9, 3.760610758648224*^9}, 3.760610853832239*^9, {3.7606112396040025`*^9, 3.7606112817332983`*^9}, { 3.760611401222947*^9, 3.76061140197075*^9}, {3.760611673421208*^9, 3.7606117248805995`*^9}, {3.7606118287018495`*^9, 3.7606119921793656`*^9}, {3.760612127470795*^9, 3.760612223396744*^9}, { 3.76061550773096*^9, 3.7606155085119963`*^9}, 3.760615603302456*^9, { 3.760615693062388*^9, 3.760615704512997*^9}, 3.7606158367472205`*^9, { 3.760615988102416*^9, 3.7606160042704983`*^9}, {3.7632524995190973`*^9, 3.7632525737340136`*^9}, {3.763426957870851*^9, 3.763426959053108*^9}, { 3.7634271873253856`*^9, 3.763427188674776*^9}, {3.7634423988211765`*^9, 3.7634424251737814`*^9}, {3.7634426334949675`*^9, 3.7634426560163193`*^9}, {3.763528275706467*^9, 3.7635284013459897`*^9}, { 3.763528705040784*^9, 3.7635287224411435`*^9}, {3.7635289011396055`*^9, 3.763528901842952*^9}, {3.763548522859683*^9, 3.76354854228095*^9}, { 3.7636050270340595`*^9, 3.763605035756063*^9}, {3.763605112705577*^9, 3.763605344908389*^9}, {3.7636054077448673`*^9, 3.7636054326054068`*^9}, { 3.7636054757131557`*^9, 3.7636054979248376`*^9}, {3.763605542706845*^9, 3.763605675311968*^9}, {3.763605884155599*^9, 3.7636058987003956`*^9}, { 3.763606027844756*^9, 3.7636060593519597`*^9}, {3.7636061708042307`*^9, 3.763606210806114*^9}, 3.763606241472248*^9, {3.7636062752072725`*^9, 3.763606340114405*^9}, {3.763606445999727*^9, 3.7636064489171495`*^9}, { 3.763606744287244*^9, 3.7636067648057427`*^9}, 3.7636070601536713`*^9, { 3.763607262857174*^9, 3.763607300007738*^9}, {3.7636074396359158`*^9, 3.7636074830770864`*^9}, {3.7636076263020697`*^9, 3.7636076543842106`*^9}, 3.763607688296667*^9, {3.7636077698636456`*^9, 3.7636077758773165`*^9}, { 3.763607857294286*^9, 3.7636078613443317`*^9}, 3.763608605441226*^9, { 3.7638142471323504`*^9, 3.7638142487803507`*^9}, {3.7638142898908815`*^9, 3.7638143569012723`*^9}, {3.763958140651967*^9, 3.763958153489439*^9}, 3.76395845683808*^9, {3.7639608609270196`*^9, 3.763960872595887*^9}, { 3.764339536191163*^9, 3.7643395373935814`*^9}, {3.764339581142139*^9, 3.7643396307895145`*^9}, {3.7643397270416403`*^9, 3.764339746774886*^9}, { 3.7643759693358665`*^9, 3.764375988525555*^9}, {3.764410286736837*^9, 3.764410291232706*^9}, {3.7649058387052116`*^9, 3.7649058888300486`*^9}, { 3.764905919657881*^9, 3.7649059255708666`*^9}, {3.764906015807353*^9, 3.7649060798935275`*^9}, {3.7649061275007944`*^9, 3.764906182700228*^9}, { 3.7649814310038157`*^9, 3.764981612888131*^9}, {3.764981649845045*^9, 3.764981717214387*^9}, {3.7650095509166293`*^9, 3.7650095663321896`*^9}, { 3.765009596962874*^9, 3.7650096065955095`*^9}, 3.7650098165773335`*^9, { 3.765011173435627*^9, 3.765011180125066*^9}, {3.7650788221318007`*^9, 3.765078823898266*^9}, {3.7650788935676775`*^9, 3.7650789311170053`*^9}, { 3.765085243174881*^9, 3.7650852441096754`*^9}, 3.765085550868559*^9, { 3.7650855978395305`*^9, 3.7650856220925417`*^9}, {3.7650863545547857`*^9, 3.7650863799862742`*^9}, {3.7650865194326468`*^9, 3.765086519785918*^9}, { 3.7650865505251884`*^9, 3.7650865669896946`*^9}, 3.765087372975154*^9, { 3.7650874030551014`*^9, 3.7650874163952713`*^9}, {3.765087536684074*^9, 3.7650876355597906`*^9}, 3.7650877252914543`*^9, {3.765088672041128*^9, 3.7650887019763765`*^9}, {3.765088740411885*^9, 3.765088742455727*^9}, { 3.7650889283353214`*^9, 3.7650889447918415`*^9}, {3.765089035561446*^9, 3.7650890612584443`*^9}, {3.7650891812559137`*^9, 3.765089209061077*^9}, { 3.7650893423167953`*^9, 3.76508943243054*^9}, {3.765090684608432*^9, 3.765090700734714*^9}, 3.7650907477613907`*^9, {3.7650908366428585`*^9, 3.7650908539151096`*^9}, {3.7650908896330676`*^9, 3.765090909940852*^9}, { 3.765091082681374*^9, 3.7650911113055153`*^9}, {3.7650911427516937`*^9, 3.7650911450258894`*^9}, {3.7650912819372005`*^9, 3.765091515369325*^9}, { 3.7650916102443376`*^9, 3.7650917517497134`*^9}, {3.765092443582117*^9, 3.765092498126871*^9}, {3.76509426500305*^9, 3.765094281405676*^9}, 3.765094315674655*^9, {3.7652396904249477`*^9, 3.765239693502611*^9}, 3.765253217258378*^9, {3.7652532852065315`*^9, 3.7652532918614807`*^9}, 3.766189724095389*^9, {3.766190438614527*^9, 3.7661905103848095`*^9}, { 3.76619098699972*^9, 3.766190987925188*^9}, {3.766193820625373*^9, 3.7661938215367756`*^9}, {3.7662041564549007`*^9, 3.7662041841044207`*^9}, {3.766204415112673*^9, 3.766204435514146*^9}, { 3.766204514370674*^9, 3.766204525664904*^9}, 3.766204570014185*^9, { 3.7665714310907745`*^9, 3.76657144559927*^9}, {3.7665725420953245`*^9, 3.7665725423845477`*^9}, {3.7666314737351704`*^9, 3.7666315492489386`*^9}, {3.7740882771256323`*^9, 3.774088312744491*^9}, { 3.774150773834302*^9, 3.774150944718382*^9}, {3.774150975094303*^9, 3.774151054824913*^9}, {3.7741511238761725`*^9, 3.7741512298519745`*^9}, { 3.77415129158794*^9, 3.774151651300989*^9}, {3.774151741892136*^9, 3.774151770064453*^9}, {3.7742415341727543`*^9, 3.7742416306317797`*^9}, { 3.7751898888726125`*^9, 3.775189913786336*^9}, {3.7751899486865563`*^9, 3.7751899522127523`*^9}, {3.7751899989654093`*^9, 3.7751900149868736`*^9}, {3.7751900517928104`*^9, 3.775190066570419*^9}, { 3.7879798676374617`*^9, 3.7879798943206964`*^9}, {3.792287382183713*^9, 3.792287444759338*^9}, {3.792287488992601*^9, 3.7922875432928047`*^9}, { 3.7922886672157793`*^9, 3.7922886764378495`*^9}, {3.792288708660981*^9, 3.7922888810105305`*^9}, {3.792300131730332*^9, 3.7923001501177034`*^9}, { 3.795768609226843*^9, 3.7957686326352005`*^9}, {3.7957686687171*^9, 3.7957686846637707`*^9}, {3.7957688298513894`*^9, 3.795768834915843*^9}, 3.7957688867486525`*^9, {3.795768942098573*^9, 3.795768993537817*^9}, { 3.7957690236098194`*^9, 3.79576902468211*^9}, {3.7957690712421293`*^9, 3.795769275801197*^9}, {3.7957693460703883`*^9, 3.795769349757367*^9}, { 3.79576972202382*^9, 3.7957697714534473`*^9}, {3.795769801653285*^9, 3.795769804711711*^9}, {3.796345941656575*^9, 3.7963459430887594`*^9}, { 3.8298913714361515`*^9, 3.829891372330407*^9}, {3.843728585368825*^9, 3.84372858844851*^9}, {3.8449958679518747`*^9, 3.8449959617306128`*^9}, { 3.845978121229767*^9, 3.845978121586933*^9}, {3.8459781752184176`*^9, 3.845978183704877*^9}, {3.8459783826308093`*^9, 3.8459784254435472`*^9}, { 3.845978956970813*^9, 3.8459791499511595`*^9}, 3.8461289015497713`*^9}, CellLabel-> "In[384]:=",ExpressionUUID->"bdf0fee5-0f58-42a5-8728-bc93f8964f93"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Building blocks", "Title", CellChangeTimes->{ 3.4430806364968*^9, {3.4453166713873997`*^9, 3.4453166747414*^9}, { 3.447462264275*^9, 3.4474622644154*^9}, {3.4695731321116*^9, 3.4695731359491997`*^9}, {3.473055192524*^9, 3.473055199133*^9}, { 3.47305542959*^9, 3.4730554407939997`*^9}, {3.4734696797594*^9, 3.4734696967634*^9}, {3.4933064685896*^9, 3.493306471148*^9}, { 3.5568725291398897`*^9, 3.5568725438967333`*^9}, 3.5568726929512587`*^9, { 3.5576544837556367`*^9, 3.5576544886852455`*^9}, {3.6852489036101027`*^9, 3.68524892333013*^9}, {3.688455478402707*^9, 3.688455486552718*^9}, { 3.813031714323161*^9, 3.813031718925788*^9}, {3.813031758195632*^9, 3.8130317648033185`*^9}, {3.813032384726508*^9, 3.813032390240255*^9}, { 3.814583256251114*^9, 3.8145832796753936`*^9}, {3.8196005424148855`*^9, 3.8196005483154497`*^9}, {3.819950294085473*^9, 3.8199503065825105`*^9}},ExpressionUUID->"6a385782-eb61-456f-9f91-\ 380d4036a0d8"], Cell[CellGroupData[{ Cell["APPROXIMATIONS", "Subsection", CellChangeTimes->{{3.473055512584*^9, 3.4730555529630003`*^9}, { 3.4730575328269997`*^9, 3.473057539222*^9}, {3.4734691424642*^9, 3.4734691605758*^9}, {3.5681161575453596`*^9, 3.568116161819767*^9}, { 3.59922265025865*^9, 3.599222653363055*^9}, 3.629777520582675*^9, 3.629791653258878*^9, {3.630370559869874*^9, 3.6303705662970853`*^9}, { 3.6618219022583027`*^9, 3.6618219059243093`*^9}, 3.6852488995100965`*^9, 3.685281849223243*^9, {3.6853234590535126`*^9, 3.685323459673514*^9}, { 3.68587640866364*^9, 3.6858764117036448`*^9}, {3.6862101948897667`*^9, 3.6862101984397717`*^9}, {3.686235632357339*^9, 3.6862356325473394`*^9}, { 3.686290377128008*^9, 3.686290380228012*^9}, {3.6863951313545313`*^9, 3.6863951457345514`*^9}, {3.6883646955890894`*^9, 3.6883646971490917`*^9}, 3.7807552452476177`*^9, {3.811316330506975*^9, 3.81131633668452*^9}, 3.8127824542431855`*^9, 3.8127840219912105`*^9, {3.813031734498083*^9, 3.8130317350874367`*^9}, {3.8145817138547506`*^9, 3.8145817395042872`*^9}, {3.814581776238999*^9, 3.814581799742174*^9}, { 3.814581962677523*^9, 3.8145819647221575`*^9}, {3.8145998190246944`*^9, 3.814599846730754*^9}, {3.8153778767843122`*^9, 3.815377881775329*^9}, { 3.8199410957155104`*^9, 3.8199410988195906`*^9}},ExpressionUUID->"0d2913ef-0aef-4ae5-ae1f-\ 42a83bd3e7cd"], Cell[CellGroupData[{ Cell[TextData[{ "LINEAR ", Cell[BoxData[ FormBox[ SuperscriptBox["C", "0"], TraditionalForm]], FormatType->"TraditionalForm",ExpressionUUID-> "c8b3e187-d6d4-4a10-9d91-60e9247e2e5a"] }], "Subsubsection", CellChangeTimes->{{3.8153761102345724`*^9, 3.815376150616532*^9}, { 3.8153778585373697`*^9, 3.8153778611644793`*^9}, {3.8153778930697937`*^9, 3.815377932666324*^9}, {3.819854195004692*^9, 3.819854197490559*^9}, 3.819941078108614*^9, {3.8199476858408775`*^9, 3.8199477222022824`*^9}, { 3.8199479521208344`*^9, 3.8199479622931814`*^9}},ExpressionUUID->"162ac754-d74f-4ca6-80c8-\ d8d961edea19"], Cell[BoxData[{ RowBox[{ RowBox[{"u", ":=", RowBox[{"Tr", "[", RowBox[{ RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"u1"}, {"u2"} }], "\[NoBreak]", ")"}], "\[Transpose]"}], ".", RowBox[{"Inverse", "[", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "1"}, {"x1", "x2"} }], "\[NoBreak]", ")"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1"}, {"x"} }], "\[NoBreak]", ")"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"u", ":=", RowBox[{"Tr", "[", RowBox[{ RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"u1"}, {"u2"}, {"u3"} }], "\[NoBreak]", ")"}], "\[Transpose]"}], ".", RowBox[{"Inverse", "[", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "1", "1"}, {"x1", "x2", "x3"}, {"y1", "y2", "y3"} }], "\[NoBreak]", ")"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1"}, {"x"}, {"y"} }], "\[NoBreak]", ")"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"u", ":=", RowBox[{"Tr", "[", RowBox[{ RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"u1"}, {"u2"}, {"u3"}, {"u4"} }], "\[NoBreak]", ")"}], "\[Transpose]"}], ".", RowBox[{"Inverse", "[", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "1", "1", "1"}, {"x1", "x2", "x3", "x4"}, {"y1", "y2", "y3", "y4"}, {"z1", "z2", "z3", "z4"} }], "\[NoBreak]", ")"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1"}, {"x"}, {"y"}, {"z"} }], "\[NoBreak]", ")"}]}], "]"}]}], ";"}]}], "Input", CellChangeTimes->{{3.8196002881768866`*^9, 3.819600290595418*^9}, { 3.819793832823107*^9, 3.8197939441926823`*^9}, {3.8198542169513407`*^9, 3.819854304992836*^9}, {3.8199401440223775`*^9, 3.8199401451752453`*^9}, { 3.819940216079404*^9, 3.8199402350359707`*^9}, {3.8199402668370905`*^9, 3.819940270118642*^9}, {3.819941117148842*^9, 3.819941292564108*^9}, { 3.819941392926919*^9, 3.819941410180554*^9}, {3.819947320586339*^9, 3.8199473306436195`*^9}, {3.819947369119611*^9, 3.8199476276395407`*^9}}, CellLabel-> "In[461]:=",ExpressionUUID->"667512d3-b54f-4fe9-bb73-3019faaf7bea"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "QUADRATIC ", Cell[BoxData[ FormBox[ SuperscriptBox["C", "0"], TraditionalForm]], FormatType->"TraditionalForm",ExpressionUUID-> "9f431e87-135f-41fb-85e4-ea581823e804"] }], "Subsubsection", CellChangeTimes->{{3.8153761102345724`*^9, 3.815376150616532*^9}, { 3.8153778585373697`*^9, 3.8153778611644793`*^9}, {3.8153778930697937`*^9, 3.815377926338909*^9}, {3.8199479921343904`*^9, 3.819948001552022*^9}, { 3.8199496400756197`*^9, 3.8199496508441324`*^9}},ExpressionUUID->"8b303821-a3bc-4d02-b626-\ 00ac8af3f93c"], Cell[BoxData[ RowBox[{ RowBox[{"u", ":=", RowBox[{"Tr", "[", RowBox[{ RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"u1"}, {"u2"}, {"u3"} }], "\[NoBreak]", ")"}], "\[Transpose]"}], ".", RowBox[{"Inverse", "[", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "1", "1"}, {"x1", "x2", "x3"}, { SuperscriptBox["x1", "2"], SuperscriptBox["x2", "2"], SuperscriptBox["x3", "2"]} }], "\[NoBreak]", ")"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1"}, {"x"}, { SuperscriptBox["x", "2"]} }], "\[NoBreak]", ")"}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.8199483664156747`*^9, 3.8199485493881135`*^9}, { 3.8199485913144693`*^9, 3.8199488450890017`*^9}, {3.819949316406085*^9, 3.819949552511241*^9}, {3.819949588290868*^9, 3.8199495904707317`*^9}, { 3.819949721403361*^9, 3.819949748157431*^9}, 3.8199499668780727`*^9, { 3.8199500738101087`*^9, 3.8199500897824917`*^9}, {3.8199501689926205`*^9, 3.819950173688433*^9}, {3.8199502200208445`*^9, 3.819950224828543*^9}}, CellLabel-> "In[464]:=",ExpressionUUID->"5b39d0a4-4bf4-459f-b04a-9fa6a08b00f4"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "QUBIC ", Cell[BoxData[ FormBox[ SuperscriptBox["C", "1"], TraditionalForm]],ExpressionUUID-> "c01813c7-0c55-4a5c-a2e6-8d68d976fd14"] }], "Subsubsection", CellChangeTimes->{{3.8153761102345724`*^9, 3.815376150616532*^9}, { 3.8153778585373697`*^9, 3.8153778611644793`*^9}, {3.8153778930697937`*^9, 3.815377926338909*^9}, {3.8199479921343904`*^9, 3.819948001552022*^9}},ExpressionUUID->"efb27dda-7a73-487d-b443-\ 3bf17635a222"], Cell[BoxData[ RowBox[{ RowBox[{"u", ":=", RowBox[{"Tr", "[", RowBox[{ RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"u1"}, {"du1"}, {"u2"}, {"du2"} }], "\[NoBreak]", ")"}], "\[Transpose]"}], ".", RowBox[{"Inverse", "[", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "0", "1", "0"}, {"x1", "1", "x2", "1"}, { SuperscriptBox["x1", "2"], RowBox[{"2", "x1"}], SuperscriptBox["x2", "2"], RowBox[{"2", "x2"}]}, { SuperscriptBox["x1", "3"], RowBox[{"3", SuperscriptBox["x1", "2"]}], SuperscriptBox["x2", "3"], RowBox[{"3", SuperscriptBox["x2", "2"]}]} }], "\[NoBreak]", ")"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1"}, {"x"}, { SuperscriptBox["x", "2"]}, { SuperscriptBox["x", "3"]} }], "\[NoBreak]", ")"}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.8199483664156747`*^9, 3.8199485493881135`*^9}, { 3.8199485913144693`*^9, 3.8199488450890017`*^9}, {3.819949316406085*^9, 3.819949552511241*^9}, {3.819949588290868*^9, 3.8199495904707317`*^9}}, CellLabel-> "In[465]:=",ExpressionUUID->"ff1ebdca-191a-4f41-8713-99748a72fee9"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"NN", " ", "=", " ", RowBox[{"a", "+", RowBox[{"b", " ", "x"}], "+", RowBox[{"c", " ", "y"}], "+", RowBox[{"d", " ", "x", " ", "y"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"NN", "/.", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "0"}], ",", RowBox[{"y", "\[Rule]", "0"}]}], "}"}]}], ")"}], "\[Equal]", "0"}], ",", RowBox[{ RowBox[{"(", RowBox[{"NN", "/.", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "L"}], ",", RowBox[{"y", "\[Rule]", "0"}]}], "}"}]}], ")"}], "\[Equal]", "0"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{"NN", "/.", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "L"}], ",", RowBox[{"y", "\[Rule]", "L"}]}], "}"}]}], ")"}], "\[Equal]", "0"}], ",", RowBox[{ RowBox[{"(", RowBox[{"NN", "/.", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "0"}], ",", RowBox[{"y", "\[Rule]", "L"}]}], "}"}]}], ")"}], "\[Equal]", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"a", ",", "b", ",", "c", ",", "d"}], "}"}]}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Simplify", "[", RowBox[{"NN", " ", "/.", "sol"}], "]"}]}]}]], "Input", CellChangeTimes->{{3.8220316101829433`*^9, 3.8220319006269274`*^9}}, CellLabel-> "In[466]:=",ExpressionUUID->"5f613cb9-a9e2-4794-85a6-86c846186544"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"a", "\[Rule]", "0"}], ",", RowBox[{"b", "\[Rule]", "0"}], ",", RowBox[{"c", "\[Rule]", FractionBox["1", "L"]}], ",", RowBox[{"d", "\[Rule]", RowBox[{"-", FractionBox["1", SuperscriptBox["L", "2"]]}]}]}], "}"}]], "Output", CellChangeTimes->{{3.822031789655941*^9, 3.8220319015494275`*^9}, 3.853032924662415*^9}, CellLabel-> "Out[467]=",ExpressionUUID->"84d03451-e88f-406c-9148-b5d4913b09f7"], Cell[BoxData[ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"L", "-", "x"}], ")"}], " ", "y"}], SuperscriptBox["L", "2"]]], "Output", CellChangeTimes->{{3.822031789655941*^9, 3.8220319015494275`*^9}, 3.853032924677374*^9}, CellLabel-> "Out[468]=",ExpressionUUID->"d2fcd6f9-9b75-4a34-97bf-6cbadd9df4e4"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["VIRTUAL WORK DENSITIES", "Subsection", CellChangeTimes->{{3.473055512584*^9, 3.4730555529630003`*^9}, { 3.4730575328269997`*^9, 3.473057539222*^9}, {3.4734691424642*^9, 3.4734691605758*^9}, {3.5681161575453596`*^9, 3.568116161819767*^9}, { 3.59922265025865*^9, 3.599222653363055*^9}, 3.629777520582675*^9, 3.629791653258878*^9, {3.630370559869874*^9, 3.6303705662970853`*^9}, { 3.6618219022583027`*^9, 3.6618219059243093`*^9}, 3.6852488995100965`*^9, 3.685281849223243*^9, {3.6853234590535126`*^9, 3.685323459673514*^9}, { 3.68587640866364*^9, 3.6858764117036448`*^9}, {3.6862101948897667`*^9, 3.6862101984397717`*^9}, {3.686235632357339*^9, 3.6862356325473394`*^9}, { 3.686290377128008*^9, 3.686290380228012*^9}, {3.6863951313545313`*^9, 3.6863951457345514`*^9}, {3.6883646955890894`*^9, 3.6883646971490917`*^9}, 3.7807552452476177`*^9, {3.811316330506975*^9, 3.81131633668452*^9}, 3.8127824542431855`*^9, 3.8127840219912105`*^9, {3.813031734498083*^9, 3.8130317350874367`*^9}, {3.8145817138547506`*^9, 3.8145817395042872`*^9}, {3.814581776238999*^9, 3.814581799742174*^9}, { 3.814581962677523*^9, 3.8145819647221575`*^9}, {3.8145998190246944`*^9, 3.814599846730754*^9}, {3.8146008007283373`*^9, 3.81460080653517*^9}, { 3.8159703504602785`*^9, 3.8159703518851805`*^9}},ExpressionUUID->"afb80a20-e5d9-4db8-bc99-\ 2e402a0d6607"], Cell[CellGroupData[{ Cell["BEAM MODEL", "Subsubsection", CellChangeTimes->{{3.8153761102345724`*^9, 3.815376150616532*^9}, { 3.8155550704278812`*^9, 3.815555097192521*^9}, {3.81597039148044*^9, 3.815970392981469*^9}, {3.8197932900575743`*^9, 3.8197932910084567`*^9}},ExpressionUUID->"b1de8e05-e4e5-4906-a827-\ 733bd6c4e2d5"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"bar", " ", "mode"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", " ", RowBox[{ RowBox[{ RowBox[{"Exx", ":=", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], "+", RowBox[{ FractionBox["1", "2"], SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], ")"}], "2"]}], "+", RowBox[{ FractionBox["1", "2"], SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], ")"}], "2"]}], "+", RowBox[{ FractionBox["1", "2"], SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}], ")"}], "2"]}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wint", ":=", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], "]"}]}], "\[CapitalEpsilon]", " ", "A", " ", RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}]}]}], ";", " ", RowBox[{"\[Delta]wint", ":=", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]\[Delta]", "[", "Exx", "]"}]}], "\[CapitalEpsilon]", " ", "A", " ", "Exx"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wext", ":=", RowBox[{ RowBox[{"\[Delta]", "[", "u", "]"}], " ", "fx"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wine", ":=", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", "u", "]"}]}], " ", "\[Rho]", " ", "A", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"t", ",", "t"}]], "u"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wcpl", ":=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], "]"}], "\[CapitalEpsilon]", " ", "A", " ", "\[Alpha]", " ", "\[CapitalDelta]\[CurlyTheta]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]pint", ":=", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[CurlyTheta]"}], "]"}]}], " ", "k", " ", "A", " ", RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[CurlyTheta]"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]pext", ":=", RowBox[{ RowBox[{"\[Delta]", "[", "\[CurlyTheta]", "]"}], " ", "s"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.8122458946247807`*^9, 3.8122459117806697`*^9}, { 3.81224594830929*^9, 3.8122462868421164`*^9}, {3.81224633207593*^9, 3.8122464535289297`*^9}, {3.812246516009039*^9, 3.812246563090599*^9}, { 3.812246638940317*^9, 3.812246876774053*^9}, {3.8123470486670413`*^9, 3.812347051682555*^9}, {3.8123470966072025`*^9, 3.812347323132008*^9}, { 3.81234741007143*^9, 3.812347415966572*^9}, {3.8123475116907806`*^9, 3.812347520634344*^9}, {3.8123475758734417`*^9, 3.812347579567418*^9}, { 3.8123477492891097`*^9, 3.812347762488459*^9}, {3.8123478282231417`*^9, 3.8123478472209744`*^9}, {3.812348071175949*^9, 3.812348072474114*^9}, { 3.8123481259943905`*^9, 3.8123481287065563`*^9}, {3.8123481606590233`*^9, 3.8123481635272818`*^9}, {3.8129373002804165`*^9, 3.8129374795649176`*^9}, {3.8129375608148932`*^9, 3.8129376841051188`*^9}, {3.8129377388246346`*^9, 3.812937751721712*^9}, { 3.8129378361071234`*^9, 3.8129378848425455`*^9}, {3.812937928137231*^9, 3.8129379634791355`*^9}, {3.8129495347076764`*^9, 3.812949648561287*^9}, { 3.8130317918239193`*^9, 3.8130318138107257`*^9}, {3.8130318491063366`*^9, 3.81303188231655*^9}, {3.8130356475942745`*^9, 3.8130356809995785`*^9}, { 3.813035723222085*^9, 3.8130357590144258`*^9}, {3.8130358624005957`*^9, 3.8130359070572233`*^9}, {3.813035937058835*^9, 3.813035954588526*^9}, { 3.814582008240017*^9, 3.8145820248715706`*^9}, {3.814582096515246*^9, 3.8145820976899586`*^9}, {3.814582222644521*^9, 3.8145822694304285`*^9}, 3.8145823659907265`*^9, {3.8145998741008406`*^9, 3.814600136314242*^9}, { 3.8146008155128937`*^9, 3.8146008175253997`*^9}, {3.814600885570817*^9, 3.8146011063818507`*^9}, {3.8146011515994005`*^9, 3.8146013530398593`*^9}, 3.8146014065154305`*^9, {3.814601537078768*^9, 3.814601632104453*^9}, { 3.8146064870264406`*^9, 3.814606490130829*^9}, 3.814606610960127*^9, { 3.814606651276392*^9, 3.8146066606647425`*^9}, {3.8146067115977106`*^9, 3.814606762494011*^9}, {3.8159703281352887`*^9, 3.8159703402311783`*^9}, { 3.8197933045292535`*^9, 3.819793376237859*^9}, {3.819793427516329*^9, 3.81979374113615*^9}, {3.8198531206708927`*^9, 3.819853318519034*^9}, { 3.8198534731601114`*^9, 3.8198535001782303`*^9}, {3.8220141941955996`*^9, 3.822014290900113*^9}, {3.8220143222350264`*^9, 3.822014371257183*^9}, { 3.822014420871383*^9, 3.82201455714007*^9}, {3.8220147683440943`*^9, 3.822014852498207*^9}, 3.822014890162271*^9, {3.8220186983475323`*^9, 3.8220188522089043`*^9}, {3.8226254483668633`*^9, 3.8226254538325567`*^9}, {3.8226254977692766`*^9, 3.8226255989801593`*^9}, {3.822625660413871*^9, 3.8226257244889565`*^9}, { 3.822625784898554*^9, 3.8226257884059076`*^9}, {3.822625841405484*^9, 3.82262595974108*^9}, {3.822626497029248*^9, 3.8226265279080334`*^9}, { 3.8226265745781474`*^9, 3.822626587819417*^9}, {3.8226266337869635`*^9, 3.8226266353557696`*^9}, {3.822626757328236*^9, 3.8226267614127035`*^9}, { 3.8227937934053507`*^9, 3.822793877446885*^9}, {3.822793932631747*^9, 3.8227939905807443`*^9}, {3.82279402359865*^9, 3.8227940749755487`*^9}}, CellLabel-> "In[469]:=",ExpressionUUID->"61f5f099-228b-4fce-ba92-c0ab305b436c"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"torsion", " ", "mode"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]wint", ":=", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Phi]"}], "]"}]}], " ", "G", " ", "Ip", " ", RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Phi]"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wext", ":=", RowBox[{ RowBox[{"\[Delta]", "[", "\[Phi]", "]"}], " ", "mx"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wine", ":=", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", "\[Phi]", "]"}]}], " ", "\[Rho]", " ", "Irr", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"t", ",", "t"}]], "\[Phi]"}]}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.8122458946247807`*^9, 3.8122459117806697`*^9}, { 3.81224594830929*^9, 3.8122462868421164`*^9}, {3.81224633207593*^9, 3.8122464535289297`*^9}, {3.812246516009039*^9, 3.812246563090599*^9}, { 3.812246638940317*^9, 3.812246876774053*^9}, {3.8123470486670413`*^9, 3.812347051682555*^9}, {3.8123470966072025`*^9, 3.812347323132008*^9}, { 3.81234741007143*^9, 3.812347415966572*^9}, {3.8123475116907806`*^9, 3.812347520634344*^9}, {3.8123475758734417`*^9, 3.812347579567418*^9}, { 3.8123477492891097`*^9, 3.812347762488459*^9}, {3.8123478282231417`*^9, 3.8123478472209744`*^9}, {3.812348071175949*^9, 3.812348072474114*^9}, { 3.8123481259943905`*^9, 3.8123481287065563`*^9}, {3.8123481606590233`*^9, 3.8123481635272818`*^9}, {3.8129373002804165`*^9, 3.8129374795649176`*^9}, {3.8129375608148932`*^9, 3.8129376841051188`*^9}, {3.8129377388246346`*^9, 3.812937751721712*^9}, { 3.8129378361071234`*^9, 3.8129378848425455`*^9}, {3.812937928137231*^9, 3.8129379634791355`*^9}, {3.8129495347076764`*^9, 3.812949648561287*^9}, { 3.8130317918239193`*^9, 3.8130318138107257`*^9}, {3.8130318491063366`*^9, 3.81303188231655*^9}, {3.8130356475942745`*^9, 3.8130356809995785`*^9}, { 3.813035723222085*^9, 3.8130357590144258`*^9}, {3.8130358624005957`*^9, 3.8130359070572233`*^9}, {3.813035937058835*^9, 3.813035954588526*^9}, { 3.814582008240017*^9, 3.8145820248715706`*^9}, {3.814582096515246*^9, 3.8145820976899586`*^9}, {3.814582222644521*^9, 3.8145822694304285`*^9}, 3.8145823659907265`*^9, {3.8145998741008406`*^9, 3.814600136314242*^9}, { 3.8146008155128937`*^9, 3.8146008175253997`*^9}, {3.814600885570817*^9, 3.8146011063818507`*^9}, {3.8146011515994005`*^9, 3.8146013530398593`*^9}, 3.8146014065154305`*^9, {3.814601537078768*^9, 3.814601632104453*^9}, { 3.8146064870264406`*^9, 3.814606490130829*^9}, 3.814606610960127*^9, { 3.814606651276392*^9, 3.8146066606647425`*^9}, {3.8146067115977106`*^9, 3.814606762494011*^9}, {3.8159703281352887`*^9, 3.8159703402311783`*^9}, { 3.8197933045292535`*^9, 3.819793376237859*^9}, {3.819793427516329*^9, 3.81979374113615*^9}, {3.8198531206708927`*^9, 3.819853318519034*^9}, { 3.8198534731601114`*^9, 3.8198535001782303`*^9}, {3.8220141941955996`*^9, 3.822014290900113*^9}, {3.8220143222350264`*^9, 3.822014346401341*^9}, { 3.822014904572884*^9, 3.8220149367236567`*^9}, {3.822794250933531*^9, 3.8227942568646584`*^9}}, CellLabel-> "In[476]:=",ExpressionUUID->"6f10e45f-13a2-4cd5-b8a1-1c9e3ac2ff00"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"bending", " ", RowBox[{"(", "xz", ")"}], " ", "mode"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]wint", ":=", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}], "]"}]}], " ", "\[CapitalEpsilon]", " ", "Iyy", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wext", ":=", RowBox[{ RowBox[{"\[Delta]", "[", "w", "]"}], " ", "fz"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wine", ":=", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", "w", "]"}]}], " ", "\[Rho]", " ", "A", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"t", ",", "t"}]], "w"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}], "]"}], " ", "\[Rho]", " ", "Iyy", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "t", ",", "t"}]], "w"}]}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wsta", ":=", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}], "]"}]}], RowBox[{"(", RowBox[{"\[CapitalEpsilon]", " ", "A", " ", RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}]}], ")"}], RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}]}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.822794101700261*^9, 3.8227941479930334`*^9}, { 3.822794180887678*^9, 3.8227942482556624`*^9}, {3.8227942842341223`*^9, 3.822794309893144*^9}, {3.8227944130550375`*^9, 3.822794429081745*^9}, { 3.8227944653822117`*^9, 3.8227945285611787`*^9}, {3.822794611759951*^9, 3.8227947216944475`*^9}}, CellLabel-> "In[479]:=",ExpressionUUID->"c1bf58ef-f98e-4e6a-9256-3c88e0b79a73"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"bending", " ", RowBox[{"(", "xy", ")"}], " ", "mode"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]wint", ":=", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "v"}], "]"}]}], " ", "\[CapitalEpsilon]", " ", "Iyy", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "v"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wext", ":=", RowBox[{ RowBox[{"\[Delta]", "[", "v", "]"}], " ", "fy"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wine", ":=", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", "v", "]"}]}], " ", "\[Rho]", " ", "A", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"t", ",", "t"}]], "v"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], "]"}], " ", "\[Rho]", " ", "Iyy", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "t", ",", "t"}]], "v"}]}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wsta", ":=", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], "]"}]}], RowBox[{"(", RowBox[{"\[CapitalEpsilon]", " ", "A", " ", RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}]}], ")"}], RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}]}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.822794101700261*^9, 3.8227941479930334`*^9}, { 3.822794180887678*^9, 3.8227942482556624`*^9}, {3.8227942842341223`*^9, 3.822794309893144*^9}, {3.8227944130550375`*^9, 3.822794429081745*^9}, { 3.8227944653822117`*^9, 3.8227945285611787`*^9}, {3.822794611759951*^9, 3.8227947216944475`*^9}, {3.822800306589834*^9, 3.8228003860590916`*^9}}, CellLabel-> "In[483]:=",ExpressionUUID->"f0631ef9-a9cf-4715-8dd7-c748b9f841b0"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"w", " ", "=", " ", RowBox[{ RowBox[{"uZ", "[", "0", "]"}], " ", "4", " ", RowBox[{"(", RowBox[{"x", "/", "L"}], ")"}], RowBox[{"(", RowBox[{"1", "-", RowBox[{"x", "/", "L"}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}], "]"}]}], " ", "\[CapitalEpsilon]", " ", "Iyy", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}], " ", "-", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ FractionBox["1", "2"], SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}], ")"}], "2"]}], "]"}], "\[CapitalEpsilon]", " ", "A", " ", FractionBox["1", "2"], SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}], ")"}], "2"]}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]W", "=", RowBox[{ RowBox[{"Integrate", "[", RowBox[{"\[Delta]wint", ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "L"}], "}"}]}], "]"}], "+", RowBox[{"F", " ", RowBox[{"\[Delta]", "[", RowBox[{"w", " ", "/.", RowBox[{"x", "\[Rule]", RowBox[{"L", "/", "2"}]}]}], "]"}]}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Simplify", "[", "\[Delta]W", "]"}]}]}]], "Input", CellChangeTimes->{{3.82279483009081*^9, 3.822794969956561*^9}, { 3.8227950204702716`*^9, 3.8227951518811617`*^9}, {3.8227953443838997`*^9, 3.822795351564015*^9}, {3.822795991762432*^9, 3.8227960047802234`*^9}}, CellLabel-> "In[487]:=",ExpressionUUID->"19bb77ba-380c-49d2-99b3-5d1a77644648"], Cell[BoxData[ RowBox[{ RowBox[{"F", " ", RowBox[{"\[Delta]uZ", "[", "0", "]"}]}], "-", FractionBox[ RowBox[{"64", " ", "\[CapitalEpsilon]", " ", RowBox[{"(", RowBox[{ RowBox[{"5", " ", "Iyy", " ", RowBox[{"uZ", "[", "0", "]"}]}], "+", RowBox[{"2", " ", "A", " ", SuperscriptBox[ RowBox[{"uZ", "[", "0", "]"}], "3"]}]}], ")"}], " ", RowBox[{"\[Delta]uZ", "[", "0", "]"}]}], RowBox[{"5", " ", SuperscriptBox["L", "3"]}]]}]], "Output", CellChangeTimes->{3.853032925061337*^9}, CellLabel-> "Out[490]=",ExpressionUUID->"a07f3917-4445-4893-bac5-45a1114501cc"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["PLATE MODEL ", "Subsubsection", CellChangeTimes->{{3.8153761102345724`*^9, 3.8153761757169156`*^9}, { 3.8155550612856245`*^9, 3.8155550857667856`*^9}, {3.8159703836711783`*^9, 3.815970385180562*^9}, 3.819793250888075*^9, {3.8220138550915227`*^9, 3.8220138550928526`*^9}},ExpressionUUID->"d7109425-1791-4931-ad0b-\ bad3a9ba7ad1"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"thin", " ", "slab", " ", "mode"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"Exx"}, {"Eyy"}, {"Exy"} }], "\[NoBreak]", ")"}], ":=", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}]}, { RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], "+", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}]}]} }], "\[NoBreak]", ")"}], "+", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], ")"}], "2"], "/", "2"}], "+", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], ")"}], "2"], "/", "2"}]}]}, { RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}], ")"}], "2"], "/", "2"}], "+", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}], ")"}], "2"], "/", "2"}]}]}, { RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], ")"}], RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], ")"}], RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}], ")"}]}]}]} }], "\[NoBreak]", ")"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wint", ":=", RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}]}, { RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], "+", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}]}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"t", " ", "\[CapitalEpsilon]"}], RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}]], RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "\[Nu]", "0"}, {"\[Nu]", "1", "0"}, {"0", "0", FractionBox[ RowBox[{"1", "-", "\[Nu]"}], "2"]} }], "\[NoBreak]", ")"}]}], ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}]}, { RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], "+", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}]}]} }], "\[NoBreak]", ")"}]}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wint0", ":=", RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"Exx"}, {"Eyy"}, {"Exy"} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"t", " ", "\[CapitalEpsilon]"}], RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}]], RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "\[Nu]", "0"}, {"\[Nu]", "1", "0"}, {"0", "0", FractionBox[ RowBox[{"1", "-", "\[Nu]"}], "2"]} }], "\[NoBreak]", ")"}]}], ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"Exx"}, {"Eyy"}, {"Exy"} }], "\[NoBreak]", ")"}]}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wine", ":=", RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"u"}, {"v"} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", RowBox[{"h\[Rho]", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"t", ",", "t"}]], RowBox[{"(", "\[NoBreak]", GridBox[{ {"u"}, {"v"} }], "\[NoBreak]", ")"}]}]}], ")"}]}], " ", "]"}]}]}], " ", ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wext", ":=", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"u"}, {"v"} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"fx"}, {"fy"} }], "\[NoBreak]", ")"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wcpl", ":=", RowBox[{"Tr", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1"}, {"1"} }], "\[NoBreak]", ")"}]}], " ", FractionBox[ RowBox[{"\[Alpha]", " ", "\[CapitalEpsilon]", " "}], RowBox[{"1", "-", "\[Nu]"}]], RowBox[{ SubsuperscriptBox["\[Integral]", RowBox[{ RowBox[{"-", "t"}], "/", "2"}], RowBox[{"t", "/", "2"}]], RowBox[{"\[CapitalDelta]\[CurlyTheta]", RowBox[{"\[DifferentialD]", "z"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]pine", ":=", RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[CurlyTheta]"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "\[CurlyTheta]"}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[CurlyTheta]"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "\[CurlyTheta]"}]} }], "\[NoBreak]", ")"}]}], " ", "t", " ", "k"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]pext", ":=", RowBox[{ RowBox[{"\[Delta]", "[", "\[CurlyTheta]", "]"}], " ", "s"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.815376079275247*^9, 3.815376084074486*^9}, { 3.8153762691761475`*^9, 3.81537637169284*^9}, {3.815376408228937*^9, 3.8153768545545063`*^9}, 3.8153768906625123`*^9, {3.815377226090613*^9, 3.815377243749753*^9}, {3.815377320906008*^9, 3.8153773695372734`*^9}, { 3.815377401490987*^9, 3.8153774339257746`*^9}, 3.815377636067772*^9, { 3.8153777436891727`*^9, 3.8153777579877353`*^9}, {3.815378317503425*^9, 3.8153783297840624`*^9}, {3.815378596102874*^9, 3.8153786641604166`*^9}, { 3.815555236681955*^9, 3.815555256861638*^9}, {3.815970241520693*^9, 3.815970288970612*^9}, {3.8197930288557158`*^9, 3.819793108805518*^9}, { 3.8197931428339415`*^9, 3.8197932600036354`*^9}, {3.8198533334635773`*^9, 3.8198534003721933`*^9}, {3.8209954403224945`*^9, 3.820995464460252*^9}, { 3.8214116021139812`*^9, 3.821411613520486*^9}, {3.8220134664378595`*^9, 3.8220134942125635`*^9}, {3.822013636172348*^9, 3.822013660653085*^9}, { 3.8220136940643253`*^9, 3.8220137095733585`*^9}, {3.8220137400342855`*^9, 3.8220138276621084`*^9}, {3.822013865712245*^9, 3.8220141198601255`*^9}, { 3.8220145897943444`*^9, 3.822014632748041*^9}, {3.8220185536686554`*^9, 3.8220186366280794`*^9}, 3.8222202914316864`*^9, {3.822284129118959*^9, 3.822284130436101*^9}, {3.822285758917274*^9, 3.8222858392220035`*^9}, { 3.8226263917600307`*^9, 3.822626400054607*^9}, {3.8226264713781877`*^9, 3.822626472382482*^9}, {3.8226266959522676`*^9, 3.8226267477762117`*^9}, { 3.822626796327529*^9, 3.8226269739859304`*^9}, {3.8226270696375046`*^9, 3.822627097464016*^9}, {3.82262738419366*^9, 3.8226273848687844`*^9}, { 3.8226275012187433`*^9, 3.8226275136853914`*^9}, {3.8227023828653297`*^9, 3.822702630787526*^9}, {3.8227027245174074`*^9, 3.82270283265123*^9}, { 3.822702868916325*^9, 3.822702874231553*^9}, {3.8227029311094465`*^9, 3.822702940209586*^9}, {3.8227032901656156`*^9, 3.8227033201586447`*^9}, { 3.8228004802034817`*^9, 3.822800485425867*^9}, {3.8228005211618586`*^9, 3.8228005919369607`*^9}, {3.823135482928742*^9, 3.8231354842107*^9}, { 3.851847556164915*^9, 3.8518475972035427`*^9}}, CellLabel-> "In[491]:=",ExpressionUUID->"5530c711-9694-4aec-86f0-257c15d0f1e4"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"bending", " ", "mode"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]wint", ":=", RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", " ", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["t", "3"], " ", "\[CapitalEpsilon]"}], RowBox[{"12", RowBox[{"(", RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}], ")"}]}]], RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "\[Nu]", "0"}, {"\[Nu]", "1", "0"}, {"0", "0", FractionBox[ RowBox[{"1", "-", "\[Nu]"}], "2"]} }], "\[NoBreak]", ")"}]}], ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}]}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wext", ":=", RowBox[{ RowBox[{"\[Delta]", "[", "w", "]"}], " ", "fz"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wine", ":=", RowBox[{ RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["h", "3"], " ", "\[Rho]"}], "12"], RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"t", ",", "t"}]], RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}]} }], "\[NoBreak]", ")"}]}]}], ")"}]}], " ", "]"}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", "w", "]"}], "h", " ", "\[Rho]", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"t", ",", "t"}]], "w"}]}]}]}], " ", ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wsta", ":=", RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"Nxx", "Nxy"}, {"Nxy", "Nyy"} }], "\[NoBreak]", ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}]} }], "\[NoBreak]", ")"}]}], "]"}]}]}], ";", " ", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"Nxx"}, {"Nyy"}, {"Nxy"} }], "\[NoBreak]", ")"}], ":=", RowBox[{ FractionBox[ RowBox[{"t", " ", "\[CapitalEpsilon]"}], RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}]], RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "\[Nu]", "0"}, {"\[Nu]", "1", "0"}, {"0", "0", FractionBox[ RowBox[{"1", "-", "\[Nu]"}], "2"]} }], "\[NoBreak]", ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}]}, { RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], "+", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}]}]} }], "\[NoBreak]", ")"}]}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wcpl", ":=", RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1"}, {"1"} }], "\[NoBreak]", ")"}]}], FractionBox[ RowBox[{" ", RowBox[{"\[Alpha]", " ", "\[CapitalEpsilon]"}]}], RowBox[{"1", "-", "\[Nu]"}]], RowBox[{ SubsuperscriptBox["\[Integral]", RowBox[{ RowBox[{"-", "t"}], "/", "2"}], RowBox[{"t", "/", "2"}]], RowBox[{"z", " ", "\[CapitalDelta]\[CurlyTheta]", RowBox[{"\[DifferentialD]", "z"}]}]}]}], "]"}]}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.815376079275247*^9, 3.815376084074486*^9}, { 3.8153762691761475`*^9, 3.81537637169284*^9}, {3.815376408228937*^9, 3.8153768545545063`*^9}, 3.8153768906625123`*^9, {3.815377226090613*^9, 3.815377243749753*^9}, {3.815377320906008*^9, 3.8153773695372734`*^9}, { 3.815377401490987*^9, 3.8153774339257746`*^9}, 3.815377636067772*^9, { 3.8153777436891727`*^9, 3.8153777579877353`*^9}, {3.815378317503425*^9, 3.8153783297840624`*^9}, {3.815378596102874*^9, 3.8153786641604166`*^9}, { 3.815555236681955*^9, 3.815555256861638*^9}, {3.815970241520693*^9, 3.815970288970612*^9}, {3.8197930288557158`*^9, 3.819793108805518*^9}, { 3.8197931428339415`*^9, 3.8197932600036354`*^9}, {3.8198533334635773`*^9, 3.819853450433564*^9}, {3.8204731596954165`*^9, 3.820473173739369*^9}, { 3.820995119011181*^9, 3.820995126402494*^9}, {3.820995209861804*^9, 3.8209952799743805`*^9}, {3.820995322040347*^9, 3.8209954099942408`*^9}, { 3.82099550430188*^9, 3.8209956033995657`*^9}, {3.8214115972048492`*^9, 3.82141161802429*^9}, {3.8214117784781094`*^9, 3.821411786344531*^9}, { 3.8220122285487475`*^9, 3.822012357613187*^9}, {3.822012424643895*^9, 3.82201242811836*^9}, {3.8220124589303164`*^9, 3.822012572850343*^9}, { 3.822012605546539*^9, 3.822012664677631*^9}, 3.822012703591533*^9, { 3.8220127349053545`*^9, 3.822012736825061*^9}, {3.822012823284993*^9, 3.822012848119725*^9}, {3.822013229620719*^9, 3.822013238456396*^9}, { 3.822013398186573*^9, 3.822013431874333*^9}, {3.822013507516363*^9, 3.8220135520108066`*^9}, {3.8220135845895243`*^9, 3.822013653677226*^9}, { 3.822014131762353*^9, 3.822014171541131*^9}, {3.8220145927934275`*^9, 3.8220145983616686`*^9}, {3.822014638268268*^9, 3.822014661660056*^9}, { 3.822018656159581*^9, 3.82201865956546*^9}, {3.8222830439812937`*^9, 3.822283045885082*^9}, {3.822283084714826*^9, 3.8222832254020443`*^9}, 3.822283404395464*^9, {3.822283436828066*^9, 3.822283551562297*^9}, { 3.8226274700755506`*^9, 3.822627475568598*^9}, 3.822702730887912*^9, { 3.822703037483117*^9, 3.822703093054139*^9}, {3.822703167004958*^9, 3.822703169454815*^9}, {3.822800601333069*^9, 3.822800618058327*^9}, { 3.822800668211516*^9, 3.822800705393556*^9}}, CellLabel-> "In[499]:=",ExpressionUUID->"75e89c8c-d624-4c79-98fc-b38ed11332bf"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"shallow", " ", "nonlinear", " ", "plate"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"Exx"}, {"Eyy"}, {"Exy"} }], "\[NoBreak]", ")"}], ":=", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}]}, { RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], "+", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}]}]} }], "\[NoBreak]", ")"}], "+", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}], ")"}], "2"], "/", "2"}]}, { RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}], ")"}], "2"], "/", "2"}]}, { RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}], ")"}], RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}], ")"}]}]} }], "\[NoBreak]", ")"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wint0", ":=", RowBox[{ RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"Exx"}, {"Eyy"}, {"Exy"} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"t", " ", "\[CapitalEpsilon]"}], RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}]], RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "\[Nu]", "0"}, {"\[Nu]", "1", "0"}, {"0", "0", FractionBox[ RowBox[{"1", "-", "\[Nu]"}], "2"]} }], "\[NoBreak]", ")"}]}], ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"Exx"}, {"Eyy"}, {"Exy"} }], "\[NoBreak]", ")"}]}], "]"}]}], "-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", " ", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["t", "3"], " ", "\[CapitalEpsilon]"}], RowBox[{"12", RowBox[{"(", RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}], ")"}]}]], RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "\[Nu]", "0"}, {"\[Nu]", "1", "0"}, {"0", "0", FractionBox[ RowBox[{"1", "-", "\[Nu]"}], "2"]} }], "\[NoBreak]", ")"}]}], ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}]}], "]"}]}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.815376079275247*^9, 3.815376084074486*^9}, { 3.8153762691761475`*^9, 3.81537637169284*^9}, {3.815376408228937*^9, 3.8153768545545063`*^9}, 3.8153768906625123`*^9, {3.815377226090613*^9, 3.815377243749753*^9}, {3.815377320906008*^9, 3.8153773695372734`*^9}, { 3.815377401490987*^9, 3.8153774339257746`*^9}, 3.815377636067772*^9, { 3.8153777436891727`*^9, 3.8153777579877353`*^9}, {3.815378317503425*^9, 3.8153783297840624`*^9}, {3.815378596102874*^9, 3.8153786641604166`*^9}, { 3.815555236681955*^9, 3.815555256861638*^9}, {3.815970241520693*^9, 3.815970288970612*^9}, {3.8197930288557158`*^9, 3.819793108805518*^9}, { 3.8197931428339415`*^9, 3.8197932600036354`*^9}, {3.8198533334635773`*^9, 3.819853450433564*^9}, {3.8204731596954165`*^9, 3.820473173739369*^9}, { 3.820995119011181*^9, 3.820995126402494*^9}, {3.820995209861804*^9, 3.8209952799743805`*^9}, {3.820995322040347*^9, 3.8209954099942408`*^9}, { 3.82099550430188*^9, 3.8209956033995657`*^9}, {3.8214115972048492`*^9, 3.82141161802429*^9}, {3.8214117784781094`*^9, 3.821411786344531*^9}, { 3.8220122285487475`*^9, 3.822012357613187*^9}, {3.822012424643895*^9, 3.82201242811836*^9}, {3.8220124589303164`*^9, 3.822012572850343*^9}, { 3.822012605546539*^9, 3.822012664677631*^9}, 3.822012703591533*^9, { 3.8220127349053545`*^9, 3.822012736825061*^9}, {3.822012823284993*^9, 3.822012848119725*^9}, {3.822013229620719*^9, 3.822013238456396*^9}, { 3.822013398186573*^9, 3.822013431874333*^9}, {3.822013507516363*^9, 3.8220135520108066`*^9}, {3.8220135845895243`*^9, 3.822013653677226*^9}, { 3.822014131762353*^9, 3.822014171541131*^9}, {3.8220145927934275`*^9, 3.8220145983616686`*^9}, {3.822014638268268*^9, 3.822014661660056*^9}, { 3.822018656159581*^9, 3.82201865956546*^9}, {3.8222830439812937`*^9, 3.822283045885082*^9}, {3.822283084714826*^9, 3.8222832254020443`*^9}, 3.822283404395464*^9, {3.822283436828066*^9, 3.822283551562297*^9}, { 3.8226274700755506`*^9, 3.822627475568598*^9}, 3.822702730887912*^9, { 3.822703037483117*^9, 3.822703093054139*^9}, {3.822703167004958*^9, 3.822703169454815*^9}, {3.822800601333069*^9, 3.822800618058327*^9}, { 3.822800668211516*^9, 3.822800705393556*^9}, {3.853218494706453*^9, 3.853218677855839*^9}, {3.853218715456251*^9, 3.8532187197553587`*^9}, 3.8532187862418203`*^9, {3.8532228638308563`*^9, 3.85322287562099*^9}},ExpressionUUID->"9b14d110-ca4c-4d7c-9f3f-\ 55060cbac994"] }, Closed]], Cell[CellGroupData[{ Cell["SOLID MODEL ", "Subsubsection", CellChangeTimes->{{3.8153761102345724`*^9, 3.8153761757169156`*^9}, { 3.8155550612856245`*^9, 3.8155550857667856`*^9}, {3.8159703836711783`*^9, 3.815970385180562*^9}, 3.819793250888075*^9, {3.819853555422123*^9, 3.8198535571357107`*^9}},ExpressionUUID->"fb5115cb-5c46-462d-b545-\ 09d24c3dbd84"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"\[Epsilon]xx"}, {"\[Epsilon]yy"}, {"\[Epsilon]zz"} }], "\[NoBreak]", ")"}], ":=", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "z"], "w"}]} }], "\[NoBreak]", ")"}]}], ";", " ", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"\[Gamma]xy"}, {"\[Gamma]yz"}, {"\[Gamma]zx"} }], "\[NoBreak]", ")"}], ":=", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}], "+", RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}]}]}, { RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "z"], "v"}], "+", RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}]}]}, { RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}], "+", RowBox[{ SubscriptBox["\[PartialD]", "z"], "u"}]}]} }], "\[NoBreak]", ")"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"\[Epsilon]xx"}, {"\[Epsilon]yy"}, {"\[Epsilon]zz"} }], "\[NoBreak]", ")"}], ":=", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "z"], "w"}]} }], "\[NoBreak]", ")"}], "+", RowBox[{ FractionBox["1", "2"], RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], ")"}], "2"], "+", SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], ")"}], "2"], "+", SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}], ")"}], "2"]}]}, { RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}], ")"}], "2"], "+", SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}], ")"}], "2"], "+", SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}], ")"}], "2"]}]}, { RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "z"], "u"}], ")"}], "2"], "+", SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "z"], "v"}], ")"}], "2"], "+", SuperscriptBox[ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "z"], "w"}], ")"}], "2"]}]} }], "\[NoBreak]", ")"}]}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"\[Gamma]xy"}, {"\[Gamma]yz"}, {"\[Gamma]zx"} }], "\[NoBreak]", ")"}], ":=", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], ")"}], RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], ")"}], RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}], ")"}], RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}], ")"}]}]}]}, { RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}], ")"}], RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "z"], "u"}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}], ")"}], RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "z"], "v"}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}], ")"}], RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "z"], "w"}], ")"}]}]}]}, { RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "z"], "u"}], ")"}], RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "z"], "v"}], ")"}], RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "z"], "w"}], ")"}], RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}], ")"}]}]}]} }], "\[NoBreak]", ")"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"\[Sigma]xx"}, {"\[Sigma]yy"}, {"\[Sigma]zz"} }], "\[NoBreak]", ")"}], ":=", RowBox[{ RowBox[{"(", " ", RowBox[{ FractionBox["\[CapitalEpsilon]", RowBox[{ RowBox[{"(", RowBox[{"1", "+", "\[Nu]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", RowBox[{"2", "\[Nu]"}]}], ")"}]}]], RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"1", "-", "\[Nu]"}], "\[Nu]", "\[Nu]"}, {"\[Nu]", RowBox[{"1", "-", "\[Nu]"}], "\[Nu]"}, {"\[Nu]", "\[Nu]", RowBox[{"1", "-", "\[Nu]"}]} }], "\[NoBreak]", ")"}]}], ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"\[Epsilon]xx"}, {"\[Epsilon]yy"}, {"\[Epsilon]zz"} }], "\[NoBreak]", ")"}]}]}], ";", " ", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"\[Sigma]xy"}, {"\[Sigma]yz"}, {"\[Sigma]zx"} }], "\[NoBreak]", ")"}], ":=", RowBox[{ FractionBox["\[CapitalEpsilon]", RowBox[{"2", "+", RowBox[{"2", "\[Nu]"}]}]], RowBox[{"(", "\[NoBreak]", GridBox[{ {"\[Gamma]xy"}, {"\[Gamma]yz"}, {"\[Gamma]zx"} }], "\[NoBreak]", ")"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wint", ":=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"\[Epsilon]xx"}, {"\[Epsilon]yy"}, {"\[Epsilon]zz"} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"\[Sigma]xx"}, {"\[Sigma]yy"}, {"\[Sigma]zz"} }], "\[NoBreak]", ")"}]}]}], "-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"\[Gamma]xy"}, {"\[Gamma]yz"}, {"\[Gamma]zx"} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"\[Sigma]xy"}, {"\[Sigma]yz"}, {"\[Sigma]zx"} }], "\[NoBreak]", ")"}]}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wext", ":=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"u"}, {"v"}, {"w"} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"fx"}, {"fy"}, {"fz"} }], "\[NoBreak]", ")"}]}]}], ";"}]}]}]], "Input", CellChangeTimes->{{3.815376079275247*^9, 3.815376084074486*^9}, { 3.8153762691761475`*^9, 3.81537637169284*^9}, {3.815376408228937*^9, 3.8153768545545063`*^9}, 3.8153768906625123`*^9, {3.815377226090613*^9, 3.815377243749753*^9}, {3.815377320906008*^9, 3.8153773695372734`*^9}, { 3.815377401490987*^9, 3.8153774339257746`*^9}, 3.815377636067772*^9, { 3.8153777436891727`*^9, 3.8153777579877353`*^9}, {3.815378317503425*^9, 3.8153783297840624`*^9}, {3.815378596102874*^9, 3.8153786641604166`*^9}, { 3.815555236681955*^9, 3.815555256861638*^9}, {3.815970241520693*^9, 3.815970288970612*^9}, {3.8197930288557158`*^9, 3.819793108805518*^9}, { 3.8197931428339415`*^9, 3.8197932600036354`*^9}, {3.8198533334635773`*^9, 3.8198534003721933`*^9}, {3.819853568522805*^9, 3.8198535748574696`*^9}, { 3.8198536434093494`*^9, 3.819853647541463*^9}, {3.8198536777405787`*^9, 3.819853767687767*^9}, {3.8198538156796074`*^9, 3.8198540710650525`*^9}, { 3.8220149705414286`*^9, 3.822014991080544*^9}, {3.822015024732211*^9, 3.822015493649189*^9}, {3.8220155277480507`*^9, 3.8220156511791196`*^9}, 3.8220156900351777`*^9, {3.8220157282408*^9, 3.822015819731036*^9}, { 3.8220184496192317`*^9, 3.8220185243444557`*^9}, {3.822220449505496*^9, 3.822220581738879*^9}}, CellLabel-> "In[504]:=",ExpressionUUID->"b7110b20-43d4-4a4c-bc9d-f2e4dc4a8bf3"], Cell[BoxData[ TemplateBox[{ "SetDelayed", "shape", "\"Lists \\!\\(\\*RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", \\\"\ \[Epsilon]xx\\\", \\\"}\\\"}], \\\",\\\", RowBox[{\\\"{\\\", \\\"\[Epsilon]yy\ \\\", \\\"}\\\"}], \\\",\\\", RowBox[{\\\"{\\\", \\\"\[Epsilon]zz\\\", \ \\\"}\\\"}]}], \\\"}\\\"}]\\) and \\!\\(\\*RowBox[{RowBox[{\\\"{\\\", \ RowBox[{RowBox[{\\\"{\\\", RowBox[{SubscriptBox[\\\"\[PartialD]\\\", RowBox[{\ \\\"x\\\"}]], \\\"u\\\"}], \\\"}\\\"}], \\\",\\\", RowBox[{\\\"{\\\", \ RowBox[{SubscriptBox[\\\"\[PartialD]\\\", RowBox[{\\\"y\\\"}]], \\\"v\\\"}], \ \\\"}\\\"}], \\\",\\\", RowBox[{\\\"{\\\", RowBox[{SubscriptBox[\\\"\ \[PartialD]\\\", RowBox[{\\\"z\\\"}]], \\\"w\\\"}], \\\"}\\\"}]}], \ \\\"}\\\"}], \\\"+\\\", RowBox[{FractionBox[\\\"1\\\", \\\"2\\\"], \\\" \\\", \ RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{SuperscriptBox[RowBox[{\ \\\"(\\\", RowBox[{SubscriptBox[\\\"\[PartialD]\\\", RowBox[{\\\"x\\\"}]], \\\ \"u\\\"}], \\\")\\\"}], \\\"2\\\"], \\\"+\\\", SuperscriptBox[RowBox[{\\\"(\\\ \", RowBox[{SubscriptBox[\\\"\[PartialD]\\\", RowBox[{\\\"x\\\"}]], \ \\\"v\\\"}], \\\")\\\"}], \\\"2\\\"], \\\"+\\\", SuperscriptBox[RowBox[{\\\"(\ \\\", RowBox[{SubscriptBox[\\\"\[PartialD]\\\", RowBox[{\\\"x\\\"}]], \\\"w\\\ \"}], \\\")\\\"}], \\\"2\\\"]}], \\\"}\\\"}], \\\",\\\", RowBox[{\\\"{\\\", \ RowBox[{SuperscriptBox[RowBox[{\\\"(\\\", \ RowBox[{SubscriptBox[\\\"\[PartialD]\\\", RowBox[{\\\"y\\\"}]], \\\"u\\\"}], \ \\\")\\\"}], \\\"2\\\"], \\\"+\\\", SuperscriptBox[RowBox[{\\\"(\\\", \ RowBox[{SubscriptBox[\\\"\[PartialD]\\\", RowBox[{\\\"y\\\"}]], \\\"v\\\"}], \ \\\")\\\"}], \\\"2\\\"], \\\"+\\\", SuperscriptBox[RowBox[{\\\"(\\\", \ RowBox[{SubscriptBox[\\\"\[PartialD]\\\", RowBox[{\\\"y\\\"}]], \\\"w\\\"}], \ \\\")\\\"}], \\\"2\\\"]}], \\\"}\\\"}], \\\",\\\", RowBox[{\\\"{\\\", \ RowBox[{SuperscriptBox[RowBox[{\\\"(\\\", \ RowBox[{SubscriptBox[\\\"\[PartialD]\\\", RowBox[{\\\"z\\\"}]], \\\"u\\\"}], \ \\\")\\\"}], \\\"2\\\"], \\\"+\\\", SuperscriptBox[RowBox[{\\\"(\\\", \ RowBox[{SubscriptBox[\\\"\[PartialD]\\\", RowBox[{\\\"z\\\"}]], \\\"v\\\"}], \ \\\")\\\"}], \\\"2\\\"], \\\"+\\\", SuperscriptBox[RowBox[{\\\"(\\\", \ RowBox[{SubscriptBox[\\\"\[PartialD]\\\", RowBox[{\\\"z\\\"}]], \\\"w\\\"}], \ \\\")\\\"}], \\\"2\\\"]}], \\\"}\\\"}]}], \\\"}\\\"}]}]}]\\) are not the same \ shape.\"", 2, 505, 5, 16193119520414287340, "Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{3.853032925407507*^9}, CellLabel-> "During evaluation of \ In[504]:=",ExpressionUUID->"c7a71a78-70a8-444d-a8cd-eed5443e5d16"], Cell[BoxData[ TemplateBox[{ "SetDelayed", "shape", "\"Lists \\!\\(\\*RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", \\\"\ \[Sigma]xx\\\", \\\"}\\\"}], \\\",\\\", RowBox[{\\\"{\\\", \ \\\"\[Sigma]yy\\\", \\\"}\\\"}], \\\",\\\", RowBox[{\\\"{\\\", \\\"\[Sigma]zz\ \\\", \\\"}\\\"}]}], \\\"}\\\"}]\\) and \\!\\(\\*RowBox[{FractionBox[RowBox[{\ \\\"\[CapitalEpsilon]\\\", \\\" \\\", RowBox[{\\\"{\\\", \ RowBox[{RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"1\\\", \\\"-\\\", \ \\\"\[Nu]\\\"}], \\\",\\\", \\\"\[Nu]\\\", \\\",\\\", \\\"\[Nu]\\\"}], \ \\\"}\\\"}], \\\",\\\", RowBox[{\\\"{\\\", RowBox[{\\\"\[Nu]\\\", \\\",\\\", \ RowBox[{\\\"1\\\", \\\"-\\\", \\\"\[Nu]\\\"}], \\\",\\\", \\\"\[Nu]\\\"}], \\\ \"}\\\"}], \\\",\\\", RowBox[{\\\"{\\\", RowBox[{\\\"\[Nu]\\\", \\\",\\\", \\\ \"\[Nu]\\\", \\\",\\\", RowBox[{\\\"1\\\", \\\"-\\\", \\\"\[Nu]\\\"}]}], \ \\\"}\\\"}]}], \\\"}\\\"}]}], RowBox[{RowBox[{\\\"(\\\", RowBox[{\\\"1\\\", \ \\\"+\\\", \\\"\[Nu]\\\"}], \\\")\\\"}], \\\" \\\", RowBox[{\\\"(\\\", \ RowBox[{\\\"1\\\", \\\"-\\\", RowBox[{\\\"Times\\\", \\\"[\\\", RowBox[{\\\"\ \[LeftSkeleton]\\\", \\\"2\\\", \\\"\[RightSkeleton]\\\"}], \\\"]\\\"}]}], \\\ \")\\\"}]}]], \\\".\\\", RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", \\\"\ \[Epsilon]xx\\\", \\\"}\\\"}], \\\",\\\", RowBox[{\\\"{\\\", \\\"\[Epsilon]yy\ \\\", \\\"}\\\"}], \\\",\\\", RowBox[{\\\"{\\\", \\\"\[Epsilon]zz\\\", \ \\\"}\\\"}]}], \\\"}\\\"}]}]\\) are not the same shape.\"", 2, 507, 6, 16193119520414287340, "Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{3.853032925423025*^9}, CellLabel-> "During evaluation of \ In[504]:=",ExpressionUUID->"00d9d89d-2a8c-45ec-9d5d-f4cb2ec9f2a5"], Cell[BoxData[ TemplateBox[{ "SetDelayed", "shape", "\"Lists \\!\\(\\*RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", \\\"\ \[Sigma]xy\\\", \\\"}\\\"}], \\\",\\\", RowBox[{\\\"{\\\", \ \\\"\[Sigma]yz\\\", \\\"}\\\"}], \\\",\\\", RowBox[{\\\"{\\\", \\\"\[Sigma]zx\ \\\", \\\"}\\\"}]}], \\\"}\\\"}]\\) and \\!\\(\\*FractionBox[RowBox[{\\\"\ \[CapitalEpsilon]\\\", \\\" \\\", RowBox[{\\\"{\\\", \ RowBox[{RowBox[{\\\"{\\\", \\\"\[Gamma]xy\\\", \\\"}\\\"}], \\\",\\\", \ RowBox[{\\\"{\\\", \\\"\[Gamma]yz\\\", \\\"}\\\"}], \\\",\\\", \ RowBox[{\\\"{\\\", \\\"\[Gamma]zx\\\", \\\"}\\\"}]}], \\\"}\\\"}]}], RowBox[{\ \\\"2\\\", \\\"+\\\", RowBox[{\\\"2\\\", \\\" \\\", \\\"\[Nu]\\\"}]}]]\\) are \ not the same shape.\"", 2, 507, 7, 16193119520414287340, "Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{3.853032925562045*^9}, CellLabel-> "During evaluation of \ In[504]:=",ExpressionUUID->"20b8ba8d-1bba-4407-9622-8d359f493c3e"] }, Open ]] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Problems and solutions", "Title", CellChangeTimes->{ 3.4430806364968*^9, {3.4453166713873997`*^9, 3.4453166747414*^9}, { 3.447462264275*^9, 3.4474622644154*^9}, {3.4695731321116*^9, 3.4695731359491997`*^9}, {3.473055192524*^9, 3.473055199133*^9}, { 3.47305542959*^9, 3.4730554407939997`*^9}, {3.4734696797594*^9, 3.4734696967634*^9}, {3.4933064685896*^9, 3.493306471148*^9}, { 3.5568725291398897`*^9, 3.5568725438967333`*^9}, 3.5568726929512587`*^9, { 3.5576544837556367`*^9, 3.5576544886852455`*^9}, {3.6852489036101027`*^9, 3.68524892333013*^9}, {3.688455478402707*^9, 3.688455486552718*^9}},ExpressionUUID->"c094e867-eedb-49ea-81fe-\ 4ac178148a9f"], Cell[CellGroupData[{ Cell["INTRODUCTION (week 2)", "Subsection", CellChangeTimes->{{3.473055512584*^9, 3.4730555529630003`*^9}, { 3.4730575328269997`*^9, 3.473057539222*^9}, {3.4734691424642*^9, 3.4734691605758*^9}, {3.5681161575453596`*^9, 3.568116161819767*^9}, { 3.59922265025865*^9, 3.599222653363055*^9}, 3.629777520582675*^9, 3.629791653258878*^9, {3.630370559869874*^9, 3.6303705662970853`*^9}, { 3.6618219022583027`*^9, 3.6618219059243093`*^9}, 3.6852488995100965`*^9, 3.685281849223243*^9, {3.6853234590535126`*^9, 3.685323459673514*^9}, { 3.68587640866364*^9, 3.6858764117036448`*^9}, {3.6862101948897667`*^9, 3.6862101984397717`*^9}, {3.686235632357339*^9, 3.6862356325473394`*^9}, { 3.686290377128008*^9, 3.686290380228012*^9}, {3.6863951313545313`*^9, 3.6863951457345514`*^9}, {3.6883646955890894`*^9, 3.6883646971490917`*^9}, 3.69079328920778*^9, 3.7530712354565744`*^9, 3.7866746400333786`*^9, { 3.816933130133701*^9, 3.8169331461988688`*^9}, {3.8187683453801126`*^9, 3.8187683495925474`*^9}},ExpressionUUID->"4b032a41-028b-4092-b65a-\ 9e634ae03405"], Cell[CellGroupData[{ Cell["Lecture example 1.1 (structure analysis)", "Subsubsection", CellChangeTimes->{{3.4734694905626*^9, 3.4734694918886003`*^9}, { 3.5992247695247765`*^9, 3.599224771911581*^9}, 3.6862337070346437`*^9, 3.686290215967782*^9, {3.6863951815146017`*^9, 3.6863951817946024`*^9}, { 3.686463495303398*^9, 3.6864634969434004`*^9}, {3.7876248316360073`*^9, 3.787624839161375*^9}, {3.8189037716385527`*^9, 3.818903776541187*^9}},ExpressionUUID->"9aac42a8-292f-4229-ba7a-\ ff683fbe5b47"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "4"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"JOINT", ",", RowBox[{"{", "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "1", "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"JOINT", ",", RowBox[{"{", "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"JOINT", ",", RowBox[{"{", RowBox[{"a", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "4", "}"}], "]"}]}], "}"}]}], "\[IndentingNewLine]", "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "1", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "3", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", " ", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "4", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}], "Input", CellChangeTimes->{{3.4426465840284452`*^9, 3.4426465892856455`*^9}, { 3.442646804859646*^9, 3.442646838774046*^9}, {3.473469518159*^9, 3.473469542105*^9}, {3.567488659560421*^9, 3.567488679996457*^9}, { 3.6293857978759165`*^9, 3.6293858030083256`*^9}, {3.6293859164049253`*^9, 3.629386031689128*^9}, {3.6297796999883165`*^9, 3.629779712249938*^9}, { 3.6297797534184103`*^9, 3.629779757864418*^9}, {3.6297799558131657`*^9, 3.629779994220433*^9}, {3.6297821687834535`*^9, 3.629782179984273*^9}, { 3.6297822711976333`*^9, 3.6297823082320986`*^9}, {3.6297916313252397`*^9, 3.6297916340240445`*^9}, {3.62987105119119*^9, 3.629871103544882*^9}, { 3.630231689415316*^9, 3.6302317303497877`*^9}, {3.6305529893093967`*^9, 3.63055299723485*^9}, {3.6306697846790886`*^9, 3.630669836330779*^9}, { 3.6306698912116756`*^9, 3.6306699292913427`*^9}, 3.6611752627847633`*^9, { 3.68519377703102*^9, 3.6851937863110332`*^9}, 3.685193829331094*^9, { 3.685233503917756*^9, 3.685233516277773*^9}, {3.685233597647887*^9, 3.685233615337912*^9}, {3.6852337344080787`*^9, 3.685233778910141*^9}, { 3.685233822710202*^9, 3.685233869000267*^9}, {3.685234136752804*^9, 3.685234139506961*^9}, 3.685234415812765*^9, {3.685234451830825*^9, 3.6852344677197337`*^9}, 3.6852619909866486`*^9, {3.6852629455979853`*^9, 3.6852629685880175`*^9}, 3.6852672555340195`*^9, {3.685270602011979*^9, 3.685270662762064*^9}, 3.685270775492222*^9, {3.685271434203144*^9, 3.685271439133151*^9}, {3.6853411055772305`*^9, 3.685341119183009*^9}, { 3.6853412984732637`*^9, 3.6853413099869223`*^9}, {3.6853417310800076`*^9, 3.685341741111581*^9}, {3.6853446026382513`*^9, 3.685344638248288*^9}, { 3.685875619502535*^9, 3.685875662152595*^9}, 3.6858757765527554`*^9, { 3.6863576684041834`*^9, 3.6863576792341986`*^9}, {3.69079336330791*^9, 3.690793478888513*^9}, {3.690793512022971*^9, 3.6907935419126234`*^9}, { 3.690793581973494*^9, 3.6907936094451427`*^9}, {3.690795505722073*^9, 3.690795509076079*^9}, {3.7537624520547013`*^9, 3.75376245992811*^9}, { 3.754127553263769*^9, 3.754127567681919*^9}, {3.754127654073234*^9, 3.7541276553706284`*^9}, 3.7553517003717556`*^9, {3.8187685944225264`*^9, 3.818768632979694*^9}, {3.818903903343067*^9, 3.818904167227741*^9}, { 3.818904329868784*^9, 3.818904360696265*^9}, 3.818904432229208*^9, { 3.818932203173953*^9, 3.818932219421686*^9}, 3.8189390550786867`*^9, { 3.8190773835545607`*^9, 3.8190773971877785`*^9}}, CellLabel-> "In[336]:=",ExpressionUUID->"791e3657-2892-4e7f-b01c-e4d90582ccdc"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 1.2 (displacement analysis)", "Subsubsection", CellChangeTimes->{{3.4734694905626*^9, 3.4734694918886003`*^9}, { 3.5992247695247765`*^9, 3.599224771911581*^9}, 3.6862337070346437`*^9, 3.686290215967782*^9, {3.6863951815146017`*^9, 3.6863951817946024`*^9}, { 3.686463495303398*^9, 3.6864634969434004`*^9}, {3.7876248316360073`*^9, 3.787624839161375*^9}, {3.8189037505536313`*^9, 3.818903765919631*^9}},ExpressionUUID->"61bce4a2-2758-460e-9011-\ 10d261d3455b"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", " ", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"a", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}], "Input", CellChangeTimes->{{3.4426465840284452`*^9, 3.4426465892856455`*^9}, { 3.442646804859646*^9, 3.442646838774046*^9}, {3.473469518159*^9, 3.473469542105*^9}, {3.567488659560421*^9, 3.567488679996457*^9}, { 3.6293857978759165`*^9, 3.6293858030083256`*^9}, {3.6293859164049253`*^9, 3.629386031689128*^9}, {3.6297796999883165`*^9, 3.629779712249938*^9}, { 3.6297797534184103`*^9, 3.629779757864418*^9}, {3.6297799558131657`*^9, 3.629779994220433*^9}, {3.6297821687834535`*^9, 3.629782179984273*^9}, { 3.6297822711976333`*^9, 3.6297823082320986`*^9}, {3.6297916313252397`*^9, 3.6297916340240445`*^9}, {3.62987105119119*^9, 3.629871103544882*^9}, { 3.630231689415316*^9, 3.6302317303497877`*^9}, {3.6305529893093967`*^9, 3.63055299723485*^9}, {3.6306697846790886`*^9, 3.630669836330779*^9}, { 3.6306698912116756`*^9, 3.6306699292913427`*^9}, 3.6611752627847633`*^9, { 3.68519377703102*^9, 3.6851937863110332`*^9}, 3.685193829331094*^9, { 3.685233503917756*^9, 3.685233516277773*^9}, {3.685233597647887*^9, 3.685233615337912*^9}, {3.6852337344080787`*^9, 3.685233778910141*^9}, { 3.685233822710202*^9, 3.685233869000267*^9}, {3.685234136752804*^9, 3.685234139506961*^9}, 3.685234415812765*^9, {3.685234451830825*^9, 3.6852344677197337`*^9}, 3.6852619909866486`*^9, {3.6852629455979853`*^9, 3.6852629685880175`*^9}, 3.6852672555340195`*^9, {3.685270602011979*^9, 3.685270662762064*^9}, 3.685270775492222*^9, {3.685271434203144*^9, 3.685271439133151*^9}, {3.6853411055772305`*^9, 3.685341119183009*^9}, { 3.6853412984732637`*^9, 3.6853413099869223`*^9}, {3.6853417310800076`*^9, 3.685341741111581*^9}, {3.6853446026382513`*^9, 3.685344638248288*^9}, { 3.685875619502535*^9, 3.685875662152595*^9}, 3.6858757765527554`*^9, { 3.6863576684041834`*^9, 3.6863576792341986`*^9}, {3.69079336330791*^9, 3.690793478888513*^9}, {3.690793512022971*^9, 3.6907935419126234`*^9}, { 3.690793581973494*^9, 3.6907936094451427`*^9}, {3.690795505722073*^9, 3.690795509076079*^9}, {3.7537624520547013`*^9, 3.75376245992811*^9}, { 3.754127553263769*^9, 3.754127567681919*^9}, {3.754127654073234*^9, 3.7541276553706284`*^9}, 3.7553517003717556`*^9, {3.8187685944225264`*^9, 3.818768632979694*^9}, {3.8189037897896566`*^9, 3.818903891691725*^9}, { 3.8189322784076967`*^9, 3.818932279384528*^9}, 3.8189390383862524`*^9}, CellLabel-> "In[339]:=",ExpressionUUID->"6584dfe0-7603-49d3-94da-5575af117569"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 1.3 (vibration analysis)", "Subsubsection", CellChangeTimes->{{3.4734694905626*^9, 3.4734694918886003`*^9}, { 3.5992247695247765`*^9, 3.599224771911581*^9}, 3.6862337070346437`*^9, 3.686290215967782*^9, {3.6863951815146017`*^9, 3.6863951817946024`*^9}, { 3.686463495303398*^9, 3.6864634969434004`*^9}, {3.7876248316360073`*^9, 3.787624839161375*^9}, {3.8189037505536313`*^9, 3.818903765919631*^9}, { 3.818904453117077*^9, 3.818904455443469*^9}, 3.818905799942091*^9},ExpressionUUID->"5f18722c-d360-4af9-9f52-\ 1aaae1c2afe0"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", " ", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "3", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ini", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"uX", "[", RowBox[{"2", ",", "0"}], "]"}], "\[Rule]", RowBox[{"a", "/", "2"}]}], ",", RowBox[{ RowBox[{"uX", "[", RowBox[{"3", ",", "0"}], "]"}], "\[Rule]", "a"}], ",", RowBox[{ RowBox[{"uX", "[", RowBox[{"_", ",", "1"}], "]"}], "\[Rule]", "0"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"FullSimplify", "[", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"VIBR", ",", "ini"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], " ", "]"}]}], "Input", CellChangeTimes->{{3.4426465840284452`*^9, 3.4426465892856455`*^9}, { 3.442646804859646*^9, 3.442646838774046*^9}, {3.473469518159*^9, 3.473469542105*^9}, {3.567488659560421*^9, 3.567488679996457*^9}, { 3.6293857978759165`*^9, 3.6293858030083256`*^9}, {3.6293859164049253`*^9, 3.629386031689128*^9}, {3.6297796999883165`*^9, 3.629779712249938*^9}, { 3.6297797534184103`*^9, 3.629779757864418*^9}, {3.6297799558131657`*^9, 3.629779994220433*^9}, {3.6297821687834535`*^9, 3.629782179984273*^9}, { 3.6297822711976333`*^9, 3.6297823082320986`*^9}, {3.6297916313252397`*^9, 3.6297916340240445`*^9}, {3.62987105119119*^9, 3.629871103544882*^9}, { 3.630231689415316*^9, 3.6302317303497877`*^9}, {3.6305529893093967`*^9, 3.63055299723485*^9}, {3.6306697846790886`*^9, 3.630669836330779*^9}, { 3.6306698912116756`*^9, 3.6306699292913427`*^9}, 3.6611752627847633`*^9, { 3.68519377703102*^9, 3.6851937863110332`*^9}, 3.685193829331094*^9, { 3.685233503917756*^9, 3.685233516277773*^9}, {3.685233597647887*^9, 3.685233615337912*^9}, {3.6852337344080787`*^9, 3.685233778910141*^9}, { 3.685233822710202*^9, 3.685233869000267*^9}, {3.685234136752804*^9, 3.685234139506961*^9}, 3.685234415812765*^9, {3.685234451830825*^9, 3.6852344677197337`*^9}, 3.6852619909866486`*^9, {3.6852629455979853`*^9, 3.6852629685880175`*^9}, 3.6852672555340195`*^9, {3.685270602011979*^9, 3.685270662762064*^9}, 3.685270775492222*^9, {3.685271434203144*^9, 3.685271439133151*^9}, {3.6853411055772305`*^9, 3.685341119183009*^9}, { 3.6853412984732637`*^9, 3.6853413099869223`*^9}, {3.6853417310800076`*^9, 3.685341741111581*^9}, {3.6853446026382513`*^9, 3.685344638248288*^9}, { 3.685875619502535*^9, 3.685875662152595*^9}, 3.6858757765527554`*^9, { 3.6863576684041834`*^9, 3.6863576792341986`*^9}, {3.69079336330791*^9, 3.690793478888513*^9}, {3.690793512022971*^9, 3.6907935419126234`*^9}, { 3.690793581973494*^9, 3.6907936094451427`*^9}, {3.690795505722073*^9, 3.690795509076079*^9}, {3.7537624520547013`*^9, 3.75376245992811*^9}, { 3.754127553263769*^9, 3.754127567681919*^9}, {3.754127654073234*^9, 3.7541276553706284`*^9}, 3.7553517003717556`*^9, {3.8187685944225264`*^9, 3.818768632979694*^9}, {3.8189037897896566`*^9, 3.818903891691725*^9}, { 3.818904466225399*^9, 3.818904675241041*^9}, {3.8189049237970304`*^9, 3.8189049251199293`*^9}, {3.8189049615108304`*^9, 3.818904961921609*^9}, { 3.818905081334079*^9, 3.8189050897634983`*^9}, {3.8189051305999546`*^9, 3.818905143860015*^9}, {3.8189052185399995`*^9, 3.818905228906042*^9}, { 3.8189053495870695`*^9, 3.8189053888000546`*^9}, {3.8189054670968304`*^9, 3.8189054921455994`*^9}, {3.8189055827614374`*^9, 3.818905626899233*^9}, { 3.8189056807097125`*^9, 3.818905682976835*^9}, 3.818905766358502*^9, { 3.8189324188198233`*^9, 3.818932419716118*^9}, {3.818933917456164*^9, 3.818933953146742*^9}, {3.8189342859506845`*^9, 3.8189343355884323`*^9}}, CellLabel-> "In[342]:=",ExpressionUUID->"0e14e494-89ab-4ad0-b8c0-10a6284cae93"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 1.4 (stability analysis)", "Subsubsection", CellChangeTimes->{{3.4734694905626*^9, 3.4734694918886003`*^9}, { 3.5992247695247765`*^9, 3.599224771911581*^9}, 3.6862337070346437`*^9, 3.686290215967782*^9, {3.6863951815146017`*^9, 3.6863951817946024`*^9}, { 3.686463495303398*^9, 3.6864634969434004`*^9}, {3.7876248316360073`*^9, 3.787624839161375*^9}, {3.8189037505536313`*^9, 3.818903765919631*^9}, { 3.818904453117077*^9, 3.818904455443469*^9}, {3.8189058032326117`*^9, 3.8189058136179996`*^9}},ExpressionUUID->"d5ab2f1f-fe7d-4b0c-b713-\ 7e504f9c030c"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"a", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "a"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}]}], "Input", CellChangeTimes->{{3.4426465840284452`*^9, 3.4426465892856455`*^9}, { 3.442646804859646*^9, 3.442646838774046*^9}, {3.473469518159*^9, 3.473469542105*^9}, {3.567488659560421*^9, 3.567488679996457*^9}, { 3.6293857978759165`*^9, 3.6293858030083256`*^9}, {3.6293859164049253`*^9, 3.629386031689128*^9}, {3.6297796999883165`*^9, 3.629779712249938*^9}, { 3.6297797534184103`*^9, 3.629779757864418*^9}, {3.6297799558131657`*^9, 3.629779994220433*^9}, {3.6297821687834535`*^9, 3.629782179984273*^9}, { 3.6297822711976333`*^9, 3.6297823082320986`*^9}, {3.6297916313252397`*^9, 3.6297916340240445`*^9}, {3.62987105119119*^9, 3.629871103544882*^9}, { 3.630231689415316*^9, 3.6302317303497877`*^9}, {3.6305529893093967`*^9, 3.63055299723485*^9}, {3.6306697846790886`*^9, 3.630669836330779*^9}, { 3.6306698912116756`*^9, 3.6306699292913427`*^9}, 3.6611752627847633`*^9, { 3.68519377703102*^9, 3.6851937863110332`*^9}, 3.685193829331094*^9, { 3.685233503917756*^9, 3.685233516277773*^9}, {3.685233597647887*^9, 3.685233615337912*^9}, {3.6852337344080787`*^9, 3.685233778910141*^9}, { 3.685233822710202*^9, 3.685233869000267*^9}, {3.685234136752804*^9, 3.685234139506961*^9}, 3.685234415812765*^9, {3.685234451830825*^9, 3.6852344677197337`*^9}, 3.6852619909866486`*^9, {3.6852629455979853`*^9, 3.6852629685880175`*^9}, 3.6852672555340195`*^9, {3.685270602011979*^9, 3.685270662762064*^9}, 3.685270775492222*^9, {3.685271434203144*^9, 3.685271439133151*^9}, {3.6853411055772305`*^9, 3.685341119183009*^9}, { 3.6853412984732637`*^9, 3.6853413099869223`*^9}, {3.6853417310800076`*^9, 3.685341741111581*^9}, {3.6853446026382513`*^9, 3.685344638248288*^9}, { 3.685875619502535*^9, 3.685875662152595*^9}, 3.6858757765527554`*^9, { 3.6863576684041834`*^9, 3.6863576792341986`*^9}, {3.69079336330791*^9, 3.690793478888513*^9}, {3.690793512022971*^9, 3.6907935419126234`*^9}, { 3.690793581973494*^9, 3.6907936094451427`*^9}, {3.690795505722073*^9, 3.690795509076079*^9}, {3.7537624520547013`*^9, 3.75376245992811*^9}, { 3.754127553263769*^9, 3.754127567681919*^9}, {3.754127654073234*^9, 3.7541276553706284`*^9}, 3.7553517003717556`*^9, {3.8187685944225264`*^9, 3.818768632979694*^9}, {3.8189037897896566`*^9, 3.818903891691725*^9}, { 3.818904466225399*^9, 3.818904675241041*^9}, {3.8189049237970304`*^9, 3.8189049251199293`*^9}, {3.8189049615108304`*^9, 3.818904961921609*^9}, { 3.818905081334079*^9, 3.8189050897634983`*^9}, {3.8189051305999546`*^9, 3.818905143860015*^9}, {3.8189052185399995`*^9, 3.818905228906042*^9}, { 3.8189053495870695`*^9, 3.8189053888000546`*^9}, {3.8189054670968304`*^9, 3.8189054921455994`*^9}, {3.8189055827614374`*^9, 3.818905626899233*^9}, { 3.8189056807097125`*^9, 3.818905682976835*^9}, 3.818905766358502*^9, { 3.818905911877447*^9, 3.818906001649149*^9}, {3.8189061178251677`*^9, 3.8189061484071755`*^9}, {3.818906243285356*^9, 3.8189062714631653`*^9}, { 3.8189063511758795`*^9, 3.8189063568376904`*^9}, {3.818906585329872*^9, 3.818906591483492*^9}, {3.818906626703429*^9, 3.81890662834041*^9}, { 3.818932589763369*^9, 3.8189325919837103`*^9}}, CellLabel->"In[11]:=",ExpressionUUID->"20359c31-e79a-44dc-9d11-ffe8fcaffa83"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 1.5 (large displacement analysis)", "Subsubsection", CellChangeTimes->{{3.4734694905626*^9, 3.4734694918886003`*^9}, { 3.5992247695247765`*^9, 3.599224771911581*^9}, 3.6862337070346437`*^9, 3.686290215967782*^9, {3.6863951815146017`*^9, 3.6863951817946024`*^9}, { 3.686463495303398*^9, 3.6864634969434004`*^9}, {3.7876248316360073`*^9, 3.787624839161375*^9}, {3.8189037505536313`*^9, 3.818903765919631*^9}, { 3.818904453117077*^9, 3.818904455443469*^9}, {3.8189058032326117`*^9, 3.8189058136179996`*^9}, {3.8189066805326967`*^9, 3.8189067103046494`*^9}, {3.818907219119192*^9, 3.818907222320526*^9}, { 3.8191046090636425`*^9, 3.8191046134938107`*^9}},ExpressionUUID->"3e2f56e3-2eb0-44d4-bbb4-\ 11727f8765cd"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"val", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"A", "->", "0.01"}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"a", "\[Rule]", RowBox[{ RowBox[{"-", "L"}], "/", "10"}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]", " "}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", " ", "L"}], " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"a", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"NONL", ",", "ALL"}], "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "//.", "val"}]}], "]"}]}], "Input", CellChangeTimes->{{3.4426465840284452`*^9, 3.4426465892856455`*^9}, { 3.442646804859646*^9, 3.442646838774046*^9}, {3.473469518159*^9, 3.473469542105*^9}, {3.567488659560421*^9, 3.567488679996457*^9}, { 3.6293857978759165`*^9, 3.6293858030083256`*^9}, {3.6293859164049253`*^9, 3.629386031689128*^9}, {3.6297796999883165`*^9, 3.629779712249938*^9}, { 3.6297797534184103`*^9, 3.629779757864418*^9}, {3.6297799558131657`*^9, 3.629779994220433*^9}, {3.6297821687834535`*^9, 3.629782179984273*^9}, { 3.6297822711976333`*^9, 3.6297823082320986`*^9}, {3.6297916313252397`*^9, 3.6297916340240445`*^9}, {3.62987105119119*^9, 3.629871103544882*^9}, { 3.630231689415316*^9, 3.6302317303497877`*^9}, {3.6305529893093967`*^9, 3.63055299723485*^9}, {3.6306697846790886`*^9, 3.630669836330779*^9}, { 3.6306698912116756`*^9, 3.6306699292913427`*^9}, 3.6611752627847633`*^9, { 3.68519377703102*^9, 3.6851937863110332`*^9}, 3.685193829331094*^9, { 3.685233503917756*^9, 3.685233516277773*^9}, {3.685233597647887*^9, 3.685233615337912*^9}, {3.6852337344080787`*^9, 3.685233778910141*^9}, { 3.685233822710202*^9, 3.685233869000267*^9}, {3.685234136752804*^9, 3.685234139506961*^9}, 3.685234415812765*^9, {3.685234451830825*^9, 3.6852344677197337`*^9}, 3.6852619909866486`*^9, {3.6852629455979853`*^9, 3.6852629685880175`*^9}, 3.6852672555340195`*^9, {3.685270602011979*^9, 3.685270662762064*^9}, 3.685270775492222*^9, {3.685271434203144*^9, 3.685271439133151*^9}, {3.6853411055772305`*^9, 3.685341119183009*^9}, { 3.6853412984732637`*^9, 3.6853413099869223`*^9}, {3.6853417310800076`*^9, 3.685341741111581*^9}, {3.6853446026382513`*^9, 3.685344638248288*^9}, { 3.685875619502535*^9, 3.685875662152595*^9}, 3.6858757765527554`*^9, { 3.6863576684041834`*^9, 3.6863576792341986`*^9}, {3.69079336330791*^9, 3.690793478888513*^9}, {3.690793512022971*^9, 3.6907935419126234`*^9}, { 3.690793581973494*^9, 3.6907936094451427`*^9}, {3.690795505722073*^9, 3.690795509076079*^9}, {3.7537624520547013`*^9, 3.75376245992811*^9}, { 3.754127553263769*^9, 3.754127567681919*^9}, {3.754127654073234*^9, 3.7541276553706284`*^9}, 3.7553517003717556`*^9, {3.8187685944225264`*^9, 3.818768632979694*^9}, {3.8189037897896566`*^9, 3.818903891691725*^9}, { 3.818904466225399*^9, 3.818904675241041*^9}, {3.8189049237970304`*^9, 3.8189049251199293`*^9}, {3.8189049615108304`*^9, 3.818904961921609*^9}, { 3.818905081334079*^9, 3.8189050897634983`*^9}, {3.8189051305999546`*^9, 3.818905143860015*^9}, {3.8189052185399995`*^9, 3.818905228906042*^9}, { 3.8189053495870695`*^9, 3.8189053888000546`*^9}, {3.8189054670968304`*^9, 3.8189054921455994`*^9}, {3.8189055827614374`*^9, 3.818905626899233*^9}, { 3.8189056807097125`*^9, 3.818905682976835*^9}, 3.818905766358502*^9, { 3.818905911877447*^9, 3.818906001649149*^9}, {3.8189061178251677`*^9, 3.8189061484071755`*^9}, {3.818906243285356*^9, 3.8189062714631653`*^9}, { 3.8189063511758795`*^9, 3.8189063568376904`*^9}, {3.818906585329872*^9, 3.818906591483492*^9}, {3.818906626703429*^9, 3.81890662834041*^9}, { 3.8189067855957966`*^9, 3.818906795741164*^9}, {3.818906847646274*^9, 3.8189069265140657`*^9}, {3.8189069660607*^9, 3.8189069751089797`*^9}, { 3.8189070137046757`*^9, 3.818907071690199*^9}, 3.818939166730035*^9, { 3.8189392811217995`*^9, 3.818939308027191*^9}, {3.818939612512598*^9, 3.8189396255546746`*^9}, {3.8189396888230515`*^9, 3.818939690546791*^9}, { 3.818941306347761*^9, 3.8189413069023876`*^9}, {3.8189413536741495`*^9, 3.8189413668673153`*^9}, 3.819104686652321*^9, {3.8506153020981913`*^9, 3.850615307831856*^9}, {3.8506153509571085`*^9, 3.850615422642296*^9}, { 3.8506154564202614`*^9, 3.8506155467512794`*^9}},ExpressionUUID->"8d781f7e-6bba-4547-a9f9-\ dfc08320210e"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 1.6 (thermo-mechanical analysis)", "Subsubsection", CellChangeTimes->{{3.4734694905626*^9, 3.4734694918886003`*^9}, { 3.5992247695247765`*^9, 3.599224771911581*^9}, 3.6862337070346437`*^9, 3.686290215967782*^9, {3.6863951815146017`*^9, 3.6863951817946024`*^9}, { 3.686463495303398*^9, 3.6864634969434004`*^9}, {3.7876248316360073`*^9, 3.787624839161375*^9}, {3.8189037505536313`*^9, 3.818903765919631*^9}, { 3.818904453117077*^9, 3.818904455443469*^9}, {3.8189058032326117`*^9, 3.8189058136179996`*^9}, {3.8189066805326967`*^9, 3.8189067103046494`*^9}, {3.8189071749677935`*^9, 3.8189071840031424`*^9}, {3.818907228710081*^9, 3.818907236014058*^9}, { 3.819104708530879*^9, 3.8191047133780074`*^9}},ExpressionUUID->"5de18652-2348-4485-9982-\ 16fe2124dc17"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]", "[", "2", "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", " ", "L"}], " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"2", " ", "a"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], " "}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4426465840284452`*^9, 3.4426465892856455`*^9}, { 3.442646804859646*^9, 3.442646838774046*^9}, {3.473469518159*^9, 3.473469542105*^9}, {3.567488659560421*^9, 3.567488679996457*^9}, { 3.6293857978759165`*^9, 3.6293858030083256`*^9}, {3.6293859164049253`*^9, 3.629386031689128*^9}, {3.6297796999883165`*^9, 3.629779712249938*^9}, { 3.6297797534184103`*^9, 3.629779757864418*^9}, {3.6297799558131657`*^9, 3.629779994220433*^9}, {3.6297821687834535`*^9, 3.629782179984273*^9}, { 3.6297822711976333`*^9, 3.6297823082320986`*^9}, {3.6297916313252397`*^9, 3.6297916340240445`*^9}, {3.62987105119119*^9, 3.629871103544882*^9}, { 3.630231689415316*^9, 3.6302317303497877`*^9}, {3.6305529893093967`*^9, 3.63055299723485*^9}, {3.6306697846790886`*^9, 3.630669836330779*^9}, { 3.6306698912116756`*^9, 3.6306699292913427`*^9}, 3.6611752627847633`*^9, { 3.68519377703102*^9, 3.6851937863110332`*^9}, 3.685193829331094*^9, { 3.685233503917756*^9, 3.685233516277773*^9}, {3.685233597647887*^9, 3.685233615337912*^9}, {3.6852337344080787`*^9, 3.685233778910141*^9}, { 3.685233822710202*^9, 3.685233869000267*^9}, {3.685234136752804*^9, 3.685234139506961*^9}, 3.685234415812765*^9, {3.685234451830825*^9, 3.6852344677197337`*^9}, 3.6852619909866486`*^9, {3.6852629455979853`*^9, 3.6852629685880175`*^9}, 3.6852672555340195`*^9, {3.685270602011979*^9, 3.685270662762064*^9}, 3.685270775492222*^9, {3.685271434203144*^9, 3.685271439133151*^9}, {3.6853411055772305`*^9, 3.685341119183009*^9}, { 3.6853412984732637`*^9, 3.6853413099869223`*^9}, {3.6853417310800076`*^9, 3.685341741111581*^9}, {3.6853446026382513`*^9, 3.685344638248288*^9}, { 3.685875619502535*^9, 3.685875662152595*^9}, 3.6858757765527554`*^9, { 3.6863576684041834`*^9, 3.6863576792341986`*^9}, {3.69079336330791*^9, 3.690793478888513*^9}, {3.690793512022971*^9, 3.6907935419126234`*^9}, { 3.690793581973494*^9, 3.6907936094451427`*^9}, {3.690795505722073*^9, 3.690795509076079*^9}, {3.7537624520547013`*^9, 3.75376245992811*^9}, { 3.754127553263769*^9, 3.754127567681919*^9}, {3.754127654073234*^9, 3.7541276553706284`*^9}, 3.7553517003717556`*^9, {3.8187685944225264`*^9, 3.818768632979694*^9}, {3.8189037897896566`*^9, 3.818903891691725*^9}, { 3.818904466225399*^9, 3.818904675241041*^9}, {3.8189049237970304`*^9, 3.8189049251199293`*^9}, {3.8189049615108304`*^9, 3.818904961921609*^9}, { 3.818905081334079*^9, 3.8189050897634983`*^9}, {3.8189051305999546`*^9, 3.818905143860015*^9}, {3.8189052185399995`*^9, 3.818905228906042*^9}, { 3.8189053495870695`*^9, 3.8189053888000546`*^9}, {3.8189054670968304`*^9, 3.8189054921455994`*^9}, {3.8189055827614374`*^9, 3.818905626899233*^9}, { 3.8189056807097125`*^9, 3.818905682976835*^9}, 3.818905766358502*^9, { 3.818905911877447*^9, 3.818906001649149*^9}, {3.8189061178251677`*^9, 3.8189061484071755`*^9}, {3.818906243285356*^9, 3.8189062714631653`*^9}, { 3.8189063511758795`*^9, 3.8189063568376904`*^9}, {3.818906585329872*^9, 3.818906591483492*^9}, {3.818906626703429*^9, 3.81890662834041*^9}, { 3.8189067855957966`*^9, 3.818906795741164*^9}, {3.818906847646274*^9, 3.8189069265140657`*^9}, {3.8189069660607*^9, 3.8189069751089797`*^9}, { 3.8189070137046757`*^9, 3.818907071690199*^9}, {3.8190112348088083`*^9, 3.819011267096024*^9}, {3.81901130156429*^9, 3.819011303017789*^9}, { 3.850614543193836*^9, 3.850614549498017*^9}, {3.8506150595049334`*^9, 3.85061507150959*^9}, {3.850615129445158*^9, 3.8506151582241964`*^9}, { 3.8506156789915085`*^9, 3.850615685597824*^9}}, CellLabel->"In[52]:=",ExpressionUUID->"35452574-3b83-4220-8780-2ea80d30e195"] }, Closed]], Cell[CellGroupData[{ Cell["Modelling assignment (Properties [kg,m,s])", "Subsubsection", InitializationCell->True, CellChangeTimes->{{3.473055485005*^9, 3.473055488513*^9}, {3.473057544493*^9, 3.473057567259*^9}, {3.4734691404674*^9, 3.4734691826186*^9}, { 3.5674322230551395`*^9, 3.567432229575951*^9}, {3.5674885568810406`*^9, 3.5674885586126437`*^9}, 3.5986036084199142`*^9, {3.598603673712649*^9, 3.5986036738476562`*^9}, {3.6297775308006935`*^9, 3.629777534217099*^9}, { 3.6611749978437643`*^9, 3.6611750017959766`*^9}, 3.68524888736008*^9, 3.685281845213238*^9, {3.6853234458234944`*^9, 3.685323452933504*^9}, { 3.6858763883636117`*^9, 3.6858763984036255`*^9}, {3.6862356299073353`*^9, 3.6862356300473356`*^9}, {3.6862902438578215`*^9, 3.686290263787849*^9}, { 3.6862903725280013`*^9, 3.686290373378002*^9}, {3.686370549159279*^9, 3.6863705527492843`*^9}, {3.6863950336343946`*^9, 3.6863950375944004`*^9}, {3.688458622114133*^9, 3.688458623034134*^9}, { 3.689506748056718*^9, 3.689506801416793*^9}, {3.68966751764763*^9, 3.689667526267642*^9}, {3.690085875524898*^9, 3.6900859067149415`*^9}, 3.6900866074679227`*^9, {3.7207676560117645`*^9, 3.720767671653473*^9}, { 3.7207779221135454`*^9, 3.7207779514262304`*^9}, 3.7209453296113124`*^9, { 3.720954242518319*^9, 3.7209542483343773`*^9}, {3.720955122676032*^9, 3.720955125376188*^9}, {3.7630157941965237`*^9, 3.763015798709092*^9}, { 3.8187684560290804`*^9, 3.818768486290943*^9}},ExpressionUUID->"612e6103-9000-4ecc-a3de-\ 0c310ea17db1"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"val", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[CapitalEpsilon]", "\[Rule]", RowBox[{"4.22", " ", RowBox[{"10", "^", "9"}]}]}], ",", "\[IndentingNewLine]", RowBox[{"\[Nu]", "\[Rule]", "0.32"}], ",", "\[IndentingNewLine]", RowBox[{"G", "\[Rule]", RowBox[{"\[CapitalEpsilon]", "/", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", " ", "\[Nu]"}]}], ")"}]}]}], ",", "\[IndentingNewLine]", RowBox[{"g", " ", "\[Rule]", " ", "9.81"}], ",", "\[IndentingNewLine]", RowBox[{"Ri", "\[Rule]", RowBox[{"0.03", "/", "2"}]}], ",", "\[IndentingNewLine]", RowBox[{"R", "\[Rule]", RowBox[{"0.49", "/", "2"}]}], ",", "\[IndentingNewLine]", RowBox[{"Ro", "\[Rule]", RowBox[{"0.56", "/", "2"}]}], ",", "\[IndentingNewLine]", RowBox[{"t", "\[Rule]", "0.0041"}], ",", "\[IndentingNewLine]", RowBox[{"m", "\[Rule]", "1"}], ",", "\[IndentingNewLine]", RowBox[{"F", "\[Rule]", RowBox[{ RowBox[{"-", "m"}], "*", "g"}]}], ",", "\[IndentingNewLine]", RowBox[{"q", "\[Rule]", RowBox[{"F", "/", RowBox[{"(", RowBox[{"2", "*", "Pi", "*", "Ri"}], ")"}]}]}], ",", "\[IndentingNewLine]", RowBox[{"p", "\[Rule]", RowBox[{"F", "/", RowBox[{"(", RowBox[{"Pi", "*", RowBox[{"Ri", "^", "2"}]}], ")"}]}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"val", " ", "/.", RowBox[{"Rule", "\[Rule]", "List"}]}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}], ",", RowBox[{"Spacings", "->", RowBox[{"{", RowBox[{"5", ",", "1.2"}], "}"}]}], ",", RowBox[{"Frame", "\[Rule]", "All"}]}], "]"}], "\[IndentingNewLine]"}], "Input", InitializationCell->True, CellChangeTimes->{{3.6863705153692317`*^9, 3.686370679619462*^9}, { 3.6863708350096793`*^9, 3.6863708538497057`*^9}, {3.6863709094197836`*^9, 3.6863710323899555`*^9}, {3.686371148400118*^9, 3.686371156220129*^9}, 3.6863731163828735`*^9, {3.68637357135351*^9, 3.6863735794035215`*^9}, { 3.6863736844536686`*^9, 3.6863738493538995`*^9}, {3.686373881783945*^9, 3.686373973294073*^9}, {3.6863740493241796`*^9, 3.6863741565443296`*^9}, { 3.6863742089844027`*^9, 3.6863742758344965`*^9}, {3.6863897431369877`*^9, 3.6863897520670004`*^9}, 3.6863900699274454`*^9, {3.6863901468075533`*^9, 3.6863902658177195`*^9}, {3.686390319277795*^9, 3.6863903519178405`*^9}, { 3.686390397247904*^9, 3.686390427217946*^9}, {3.686390459497991*^9, 3.6863904761580143`*^9}, {3.6863905276880865`*^9, 3.6863905777781563`*^9}, {3.686390670928287*^9, 3.686390675228293*^9}, { 3.6863907227683597`*^9, 3.686390733498375*^9}, {3.686390804698474*^9, 3.686390827328506*^9}, {3.686390992398737*^9, 3.6863910252587833`*^9}, { 3.6863910641588373`*^9, 3.6863911055488954`*^9}, {3.686391157528968*^9, 3.6863911896790133`*^9}, 3.686395498755046*^9, {3.6892327767790966`*^9, 3.6892327873291116`*^9}, {3.6892328489891977`*^9, 3.689232865399221*^9}, { 3.689232953809345*^9, 3.6892329824393845`*^9}, {3.6893289630314827`*^9, 3.6893291253217096`*^9}, {3.6893358540358973`*^9, 3.6893358835459385`*^9}, {3.6893359746860666`*^9, 3.6893359842060795`*^9}, {3.6894733530870104`*^9, 3.689473444807139*^9}, { 3.689473491927205*^9, 3.689473677627465*^9}, {3.6894737130275145`*^9, 3.689473749107565*^9}, {3.6894745167486396`*^9, 3.6894745323986616`*^9}, { 3.689495259635374*^9, 3.689495317625456*^9}, {3.6894954633666596`*^9, 3.689495555046788*^9}, {3.689495600796852*^9, 3.6894956425879107`*^9}, { 3.6894956961979856`*^9, 3.6894956963179855`*^9}, {3.689504900824132*^9, 3.689505010264285*^9}, {3.6895050462443357`*^9, 3.689505088824395*^9}, { 3.689505122504442*^9, 3.68950513512446*^9}, {3.689505198024548*^9, 3.6895053831748075`*^9}, {3.689505420424859*^9, 3.6895054952049637`*^9}, { 3.689505557185051*^9, 3.6895055590550537`*^9}, {3.6895058207854195`*^9, 3.6895058297254324`*^9}, {3.689506118075836*^9, 3.689506132575856*^9}, { 3.6895065569764504`*^9, 3.6895065784064803`*^9}, {3.6895066955566444`*^9, 3.689506721696681*^9}, 3.689506821346821*^9, {3.6895069502770014`*^9, 3.689506973157033*^9}, {3.6895070091770835`*^9, 3.6895070113770866`*^9}, { 3.6895087483360715`*^9, 3.689508750016074*^9}, {3.6895089739463873`*^9, 3.6895089796763954`*^9}, 3.6895090305364666`*^9, 3.6895093904053044`*^9, { 3.689509753387914*^9, 3.689509771218934*^9}, {3.6895120928205338`*^9, 3.6895120988705425`*^9}, {3.689512232230729*^9, 3.689512258130765*^9}, { 3.6895124899310904`*^9, 3.689512643861305*^9}, {3.68951268258136*^9, 3.6895127391314387`*^9}, {3.6895127730614862`*^9, 3.689512819511551*^9}, 3.6895130996919436`*^9, 3.689513284592202*^9, {3.6895137283728237`*^9, 3.6895137479728513`*^9}, {3.689579593274*^9, 3.689579597023215*^9}, { 3.689585471084192*^9, 3.689585479169654*^9}, {3.6895855726430006`*^9, 3.6895856052878675`*^9}, {3.690085580774485*^9, 3.6900855860744925`*^9}, 3.690086566347865*^9, {3.6900866476679792`*^9, 3.6900867458681164`*^9}, { 3.6900868837003098`*^9, 3.690087003260477*^9}, 3.6900894703679433`*^9, 3.690089514588005*^9, 3.6902684706708283`*^9, {3.716209216071653*^9, 3.716209415805846*^9}, {3.7162094491656237`*^9, 3.716209465600016*^9}, { 3.716209628252907*^9, 3.716209713517415*^9}, {3.7162098822064223`*^9, 3.71620989999518*^9}, 3.7162100333272276`*^9, {3.7162101665349436`*^9, 3.7162101943881416`*^9}, {3.716210384084732*^9, 3.7162103889912677`*^9}, { 3.7162104221909075`*^9, 3.7162104260273495`*^9}, {3.7162104829773674`*^9, 3.7162104838100796`*^9}, {3.716210698510934*^9, 3.716210699011717*^9}, { 3.716210803690628*^9, 3.7162108184535522`*^9}, {3.716210993904647*^9, 3.7162110047134485`*^9}, {3.716211119737378*^9, 3.716211121355849*^9}, { 3.7162112436182027`*^9, 3.7162112550162387`*^9}, {3.7162113895941925`*^9, 3.7162113896959352`*^9}, {3.71621142292785*^9, 3.7162114244609985`*^9}, { 3.7162114940706472`*^9, 3.7162114949395356`*^9}, {3.716211552794401*^9, 3.7162115539953823`*^9}, {3.716211626470986*^9, 3.7162116405695963`*^9}, { 3.7162166287105837`*^9, 3.716216634034197*^9}, {3.7162168268347545`*^9, 3.716216840797591*^9}, {3.7162170523909206`*^9, 3.716217052591113*^9}, { 3.7162171200707817`*^9, 3.7162171229770503`*^9}, {3.716217154723361*^9, 3.7162171566245937`*^9}, {3.716217240869212*^9, 3.716217242987534*^9}, { 3.716217288807726*^9, 3.716217327073721*^9}, {3.716217672639592*^9, 3.7162176748941717`*^9}, {3.716217829860299*^9, 3.7162178329313655`*^9}, { 3.716217924140138*^9, 3.716217949832694*^9}, {3.7162180897198906`*^9, 3.716218152632536*^9}, {3.7162182600891066`*^9, 3.7162183130356874`*^9}, { 3.716218410040044*^9, 3.716218411656926*^9}, 3.7162184627726173`*^9, { 3.7162185232867155`*^9, 3.7162185234023747`*^9}, {3.716218622006528*^9, 3.716218635237047*^9}, {3.716218726860424*^9, 3.716218728278825*^9}, { 3.7162638093432827`*^9, 3.716263860812231*^9}, {3.716263933517833*^9, 3.716263935467373*^9}, {3.716269263511388*^9, 3.7162692750054045`*^9}, { 3.7162693504522424`*^9, 3.716269350636551*^9}, {3.720766254867813*^9, 3.7207662831530857`*^9}, {3.720766487327323*^9, 3.720766526550705*^9}, { 3.7207665580555553`*^9, 3.720766562915493*^9}, {3.720767293010071*^9, 3.7207674154637885`*^9}, {3.720767763788762*^9, 3.720767771112485*^9}, { 3.720767834672716*^9, 3.720767862128559*^9}, {3.7207679324678297`*^9, 3.720767940701857*^9}, {3.7207680234375515`*^9, 3.7207680248963165`*^9}, { 3.720768107597091*^9, 3.7207681083844814`*^9}, {3.720777245874063*^9, 3.7207772467718225`*^9}, {3.720847339872751*^9, 3.720847345616869*^9}, { 3.72094538339188*^9, 3.7209453954447193`*^9}, 3.720954283398532*^9, { 3.7209551419097805`*^9, 3.720955169225294*^9}, {3.72096346731903*^9, 3.7209634955284243`*^9}, {3.7210936347534947`*^9, 3.721093645958805*^9}, { 3.721118015600674*^9, 3.721118016533119*^9}, {3.7211181278057885`*^9, 3.721118129043748*^9}, {3.721118184989329*^9, 3.721118186313213*^9}, { 3.721118228780463*^9, 3.721118230656896*^9}, {3.763549046079115*^9, 3.76354907548849*^9}, {3.7635491974401584`*^9, 3.7635492020076656`*^9}, { 3.7635493210224185`*^9, 3.763549321492321*^9}, {3.7635496822247863`*^9, 3.763549685197352*^9}, {3.7635501876145735`*^9, 3.76355018836583*^9}, { 3.763550328523074*^9, 3.763550328828741*^9}, {3.7635522336928015`*^9, 3.763552234513685*^9}, {3.7638998094611406`*^9, 3.7638998096640997`*^9}, { 3.7639569894916277`*^9, 3.7639570257832017`*^9}, {3.7639571112289886`*^9, 3.7639571114921117`*^9}, {3.7639571683463163`*^9, 3.7639571696509066`*^9}, {3.7639574511536417`*^9, 3.7639574678167944`*^9}, {3.7639575278575845`*^9, 3.7639575603115005`*^9}, 3.763957713386468*^9, 3.7644105244374*^9, {3.7644107301110177`*^9, 3.764410734114828*^9}, {3.7644111255907536`*^9, 3.7644111267476225`*^9}, { 3.764411586595505*^9, 3.764411588044775*^9}, {3.7644117003396435`*^9, 3.764411710048355*^9}, {3.764411794655582*^9, 3.7644117950550694`*^9}, 3.7645576411664743`*^9, 3.764557765225023*^9, {3.7645585460765285`*^9, 3.7645585478827753`*^9}, 3.7645586233382854`*^9, {3.764560026583099*^9, 3.764560081559435*^9}, 3.76456038686705*^9, {3.764560423655078*^9, 3.7645604242801833`*^9}, {3.7645609637992783`*^9, 3.7645609650487413`*^9}, {3.7648188933283696`*^9, 3.764819039124056*^9}, { 3.765705776609866*^9, 3.765705778726362*^9}, 3.765705853972187*^9, { 3.7657063206635413`*^9, 3.7657063535844555`*^9}, 3.765706590251129*^9, { 3.765706680416685*^9, 3.765706707949399*^9}, 3.7657700697584*^9, 3.765770467555976*^9, {3.7658540676518416`*^9, 3.76585412816885*^9}, 3.7658563321802692`*^9, {3.765856838614369*^9, 3.7658568407272882`*^9}, 3.7658572036726866`*^9, {3.766115852555232*^9, 3.766115860290945*^9}, 3.7661158991844587`*^9, {3.7664660816093254`*^9, 3.7664660978619423`*^9}, { 3.7664681287504897`*^9, 3.7664681288598194`*^9}, {3.7664752421356936`*^9, 3.7664752959279666`*^9}, {3.766476415445288*^9, 3.766476416112812*^9}, { 3.766476567491147*^9, 3.766476567607998*^9}, {3.7664767091097374`*^9, 3.7664767213503003`*^9}, 3.7664784950150013`*^9, {3.7664788299753385`*^9, 3.766478839497611*^9}, 3.766478878928746*^9, {3.7664789376597743`*^9, 3.766478952690792*^9}, {3.7664796823241563`*^9, 3.7664796824574904`*^9}, { 3.7664809101609907`*^9, 3.7664809142558203`*^9}, {3.766481857638945*^9, 3.7664818577871895`*^9}, {3.766481897949862*^9, 3.7664819254078355`*^9}, { 3.766482153730875*^9, 3.7664821606765013`*^9}, {3.7664826419676046`*^9, 3.766482648414214*^9}, {3.766482769150177*^9, 3.7664827717136345`*^9}, { 3.7665402885316005`*^9, 3.766540292800579*^9}, {3.7665406523565145`*^9, 3.76654065451227*^9}, {3.7665409826851544`*^9, 3.766540990949094*^9}, { 3.7665423206796193`*^9, 3.7665423443507023`*^9}, {3.766542442924909*^9, 3.7665424473303733`*^9}, {3.766543125137824*^9, 3.766543161535568*^9}, 3.7665433398832865`*^9, {3.7665434541297007`*^9, 3.7665434556607285`*^9}, { 3.7665438301065493`*^9, 3.7665438375735807`*^9}, {3.7665439299802046`*^9, 3.7665439305425596`*^9}, 3.7665440481868963`*^9, {3.7665529775405354`*^9, 3.7665530760958223`*^9}, {3.766554294248799*^9, 3.766554300532671*^9}, { 3.766630628640416*^9, 3.7666306712077837`*^9}, {3.7666321029718156`*^9, 3.7666321044220095`*^9}, {3.76663221736679*^9, 3.766632217683257*^9}, 3.7666323502342677`*^9, 3.766632557770585*^9, {3.766726285264265*^9, 3.766726345062645*^9}, {3.7667271277547398`*^9, 3.7667271517491374`*^9}, { 3.7667358013527913`*^9, 3.7667358277528553`*^9}, {3.766735965611145*^9, 3.76673601619306*^9}, {3.766736237552089*^9, 3.766736237677061*^9}, { 3.7667363437930827`*^9, 3.766736364585148*^9}, {3.766736424789489*^9, 3.7667364250394225`*^9}, {3.7667364662331557`*^9, 3.766736476105855*^9}, 3.7667365616324253`*^9, {3.7667374573761845`*^9, 3.766737477387139*^9}, { 3.766737704802785*^9, 3.7667377124572525`*^9}, {3.7667377639451847`*^9, 3.7667377649137077`*^9}, {3.7667378367093935`*^9, 3.766737840161701*^9}, { 3.7667381644917765`*^9, 3.7667381652417793`*^9}, {3.7667385927994585`*^9, 3.766738593736743*^9}, {3.7667386423657494`*^9, 3.7667386438341465`*^9}, { 3.766738683825314*^9, 3.7667386899020147`*^9}, 3.766741389582658*^9, { 3.766741426699325*^9, 3.7667414511581683`*^9}, {3.766741683381443*^9, 3.7667416878794765`*^9}, {3.7667418032159834`*^9, 3.766741813686798*^9}, { 3.766888334491317*^9, 3.7668883476135297`*^9}, {3.787302769991276*^9, 3.787302775360155*^9}, {3.7876421733427515`*^9, 3.7876421957437563`*^9}, { 3.818587612436021*^9, 3.8185876364056263`*^9}, {3.8185890591581845`*^9, 3.81858906754212*^9}}, CellLabel-> "In[386]:=",ExpressionUUID->"d7c7bfec-f72f-483c-aaac-e4c477a9b7b6"], Cell[BoxData[ TagBox[GridBox[{ {"\[CapitalEpsilon]", "4.2199999999999995`*^9"}, {"\[Nu]", "0.32`"}, {"G", FractionBox["\[CapitalEpsilon]", RowBox[{"2", "+", RowBox[{"2", " ", "\[Nu]"}]}]]}, {"g", "9.81`"}, {"Ri", "0.015`"}, {"R", "0.245`"}, {"Ro", "0.28`"}, {"t", "0.0041`"}, {"m", "1"}, {"F", RowBox[{ RowBox[{"-", "g"}], " ", "m"}]}, {"q", FractionBox["F", RowBox[{"2", " ", "\[Pi]", " ", "Ri"}]]}, {"p", FractionBox["F", RowBox[{"\[Pi]", " ", SuperscriptBox["Ri", "2"]}]]} }, AutoDelete->False, GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxFrame->{"Columns" -> {{True}}, "Rows" -> {{True}}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{5}}, "Rows" -> {{1.2}}}], "Grid"]], "Output", CellChangeTimes->{3.8506303577530274`*^9, 3.850882650027203*^9, 3.850882776291467*^9, 3.850884854382003*^9, 3.8510436809853745`*^9, 3.8511325961582184`*^9, 3.851847759391696*^9, 3.852171371058408*^9, 3.8523580090547457`*^9, 3.8530302091693935`*^9, 3.8530317356564193`*^9, 3.853033041379058*^9, 3.8532087134880404`*^9, 3.8533018854156275`*^9, 3.8533020308853917`*^9, 3.8534600145773897`*^9, 3.8534601412405205`*^9}, CellLabel-> "Out[387]=",ExpressionUUID->"f3230e1b-db94-4add-869d-4daa61d4edd4"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Modelling assignment (Experiment)", "Subsubsection", CellChangeTimes->{{3.473055512584*^9, 3.4730555529630003`*^9}, { 3.4730575328269997`*^9, 3.473057539222*^9}, {3.4734691424642*^9, 3.4734691605758*^9}, {3.4736023142902*^9, 3.4736023273162003`*^9}, { 3.568715518105007*^9, 3.568715523097016*^9}, 3.5994750893663483`*^9, 3.6297916561604834`*^9, {3.63073778491436*^9, 3.630737793931176*^9}, { 3.6624537703648133`*^9, 3.6624537732749796`*^9}, 3.685248933840145*^9, { 3.685267058363743*^9, 3.6852671273738394`*^9}, {3.685323461463516*^9, 3.6853234663335233`*^9}, {3.6858764211836576`*^9, 3.6858764235236607`*^9}, 3.6859482147140565`*^9, {3.686226212775403*^9, 3.6862262151354065`*^9}, { 3.686466369367293*^9, 3.686466390117322*^9}, {3.732333324403823*^9, 3.7323333512571926`*^9}, {3.7330531980857735`*^9, 3.733053222557193*^9}, { 3.7330643803419495`*^9, 3.733064384574917*^9}, {3.764819307824876*^9, 3.7648193089127207`*^9}, {3.765705926317233*^9, 3.765705947708847*^9}, { 3.7664771433740315`*^9, 3.7664771458408413`*^9}, {3.7664804155817566`*^9, 3.766480417312395*^9}, {3.7667263641049314`*^9, 3.766726397862908*^9}, { 3.8185869766098504`*^9, 3.8185869795645185`*^9}, {3.818587134665669*^9, 3.8185871363217373`*^9}, {3.818768492979179*^9, 3.8187685002924805`*^9}},ExpressionUUID->"2a3fdd82-94d7-4d25-86ae-\ 7cd9b8408625"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"exp", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0.90", ",", RowBox[{"1", "*", "g"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1.69", ",", RowBox[{"2", "*", "g"}]}], "}"}], ",", RowBox[{"{", RowBox[{"2.36", ",", RowBox[{"3", "*", "g"}]}], "}"}], ",", RowBox[{"{", RowBox[{"2.95", ",", RowBox[{"4", "*", "g"}]}], "}"}]}], "}"}], " ", "/.", "val"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"FF", "=", RowBox[{"Normal", "[", RowBox[{"Fit", "[", RowBox[{"exp", ",", RowBox[{"{", RowBox[{"1", ",", "w", ",", RowBox[{"w", "^", "2"}]}], "}"}], ",", "w"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{ RowBox[{"ListPlot", "[", RowBox[{"exp", ",", RowBox[{"Frame", "\[Rule]", "True"}]}], "]"}], ",", RowBox[{"Plot", "[", RowBox[{"FF", ",", RowBox[{"{", RowBox[{"w", ",", RowBox[{"Min", "[", RowBox[{"exp", "[", RowBox[{"[", RowBox[{";;", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"Max", "[", RowBox[{"exp", "[", RowBox[{"[", RowBox[{";;", ",", "1"}], "]"}], "]"}], "]"}]}], "}"}]}], "]"}], ",", RowBox[{"FrameLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}], ",", RowBox[{"PlotLabel", "\[Rule]", "\"\\""}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.732963786982458*^9, 3.732963800329712*^9}, { 3.7329638807173033`*^9, 3.7329639838406887`*^9}, {3.7329640219057136`*^9, 3.7329640679494686`*^9}, {3.7329641106095915`*^9, 3.7329641238605337`*^9}, {3.7329641586934195`*^9, 3.7329641775638523`*^9}, {3.7329642131292753`*^9, 3.7329642468139324`*^9}, {3.732964291650645*^9, 3.732964295266472*^9}, { 3.7329643646012278`*^9, 3.7329645915297546`*^9}, {3.732964625547305*^9, 3.732964633879656*^9}, {3.732964682913621*^9, 3.732964776488607*^9}, { 3.732964812880664*^9, 3.7329648406399565`*^9}, {3.7329649084689856`*^9, 3.732965030133172*^9}, {3.732965104873771*^9, 3.7329651443322325`*^9}, { 3.7329651781396537`*^9, 3.73296520770864*^9}, {3.732965254213273*^9, 3.7329652993251047`*^9}, {3.7329653860024896`*^9, 3.7329653897065096`*^9}, {3.7329654581300693`*^9, 3.7329654674851675`*^9}, {3.7329655079892044`*^9, 3.7329655085784197`*^9}, 3.733053175193036*^9, {3.733054323981842*^9, 3.7330543310918913`*^9}, { 3.7330544527768817`*^9, 3.733054457152335*^9}, {3.733054573883443*^9, 3.7330546234511395`*^9}, {3.7330643435838375`*^9, 3.7330643547895327`*^9}, {3.7330643919191055`*^9, 3.7330644303402214`*^9}, {3.7331050956954727`*^9, 3.7331051189053106`*^9}, {3.7331111086485624`*^9, 3.7331111523877835`*^9}, {3.7331116359386663`*^9, 3.733111681037479*^9}, 3.7331466985132923`*^9, {3.733146742189515*^9, 3.7331467425179462`*^9}, { 3.7331882689213552`*^9, 3.7331882705625243`*^9}, {3.733456902620245*^9, 3.7334569073552113`*^9}, 3.7657059051454167`*^9, {3.765706272424467*^9, 3.765706305757754*^9}, {3.7657063874410734`*^9, 3.7657065682529764`*^9}, { 3.7657066048810625`*^9, 3.7657066299581566`*^9}, {3.765857078340946*^9, 3.7658571332338734`*^9}, {3.766475318047246*^9, 3.766475333494685*^9}, { 3.7664803019289956`*^9, 3.766480319352639*^9}, {3.7667264099225736`*^9, 3.766726719444113*^9}, {3.766726750764609*^9, 3.766726781866746*^9}, { 3.7667268230448494`*^9, 3.766726890403782*^9}, {3.766737556915142*^9, 3.7667376461757183`*^9}, {3.7667535576278677`*^9, 3.766753567823385*^9}, { 3.7667536001320033`*^9, 3.7667536651452446`*^9}, {3.7667537160938406`*^9, 3.7667537659916053`*^9}, {3.766753804364827*^9, 3.7667538080234776`*^9}, { 3.7667538880492616`*^9, 3.7667538883438697`*^9}, 3.7683546699256487`*^9, { 3.768354953226757*^9, 3.7683549706983614`*^9}, {3.7683550070952144`*^9, 3.768355024734041*^9}, {3.7866772118625803`*^9, 3.7866772198621316`*^9}, { 3.786677258517625*^9, 3.7866772970973134`*^9}, {3.78667734452592*^9, 3.786677487664295*^9}, {3.7866775183684816`*^9, 3.7866776052090716`*^9}, { 3.7866777170345635`*^9, 3.7866777230196533`*^9}, {3.786677760746047*^9, 3.786677922979863*^9}, 3.7875829483079205`*^9, {3.817522292235844*^9, 3.817522327395365*^9}, {3.8175223667257123`*^9, 3.8175223711802607`*^9}, { 3.8175224288622837`*^9, 3.8175225177920494`*^9}, 3.818589137303688*^9, { 3.850615829178358*^9, 3.85061583665879*^9}, {3.8508826737634134`*^9, 3.8508826804033833`*^9}, {3.850975423241478*^9, 3.8509754467253647`*^9}},ExpressionUUID->"f0883c56-221e-49b0-8337-\ be21b0915171"] }, Closed]], Cell[CellGroupData[{ Cell["Modelling assignment (Analytical method simplified)", "Subsubsection", CellChangeTimes->{{3.473055512584*^9, 3.4730555529630003`*^9}, { 3.4730575328269997`*^9, 3.473057539222*^9}, {3.4734691424642*^9, 3.4734691605758*^9}, {3.4736023142902*^9, 3.4736023273162003`*^9}, { 3.568715518105007*^9, 3.568715523097016*^9}, 3.5994750893663483`*^9, 3.6297916561604834`*^9, {3.63073778491436*^9, 3.630737793931176*^9}, { 3.6624537703648133`*^9, 3.6624537732749796`*^9}, 3.685248933840145*^9, { 3.685267058363743*^9, 3.6852671273738394`*^9}, {3.685323461463516*^9, 3.6853234663335233`*^9}, {3.6858764211836576`*^9, 3.6858764235236607`*^9}, 3.6859482147140565`*^9, {3.686226212775403*^9, 3.6862262151354065`*^9}, { 3.686466369367293*^9, 3.686466390117322*^9}, {3.732333324403823*^9, 3.7323333512571926`*^9}, {3.7330531980857735`*^9, 3.733053222557193*^9}, { 3.7330643803419495`*^9, 3.733064384574917*^9}, {3.764819307824876*^9, 3.7648193089127207`*^9}, {3.765705926317233*^9, 3.765705947708847*^9}, { 3.7664771433740315`*^9, 3.7664771458408413`*^9}, {3.7664804155817566`*^9, 3.766480417312395*^9}, {3.7667263641049314`*^9, 3.766726366745177*^9}, { 3.7866797020276375`*^9, 3.7866797091155815`*^9}, {3.8169349645564723`*^9, 3.816934967437971*^9}, {3.8185871085929155`*^9, 3.8185871120790567`*^9}, { 3.818587147124024*^9, 3.818587150622024*^9}, {3.818768504761609*^9, 3.818768511921299*^9}},ExpressionUUID->"f8eaea5b-7add-4647-9717-\ 93d42ce100ae"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"DD", "=", FractionBox[ RowBox[{"\[CapitalEpsilon]", " ", SuperscriptBox["t", "3"]}], RowBox[{"12", "-", RowBox[{"12", SuperscriptBox["\[Nu]", "2"]}]}]]}], ";"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"w0", ":=", RowBox[{ FractionBox[ RowBox[{"F", " ", SuperscriptBox["R", "2"]}], RowBox[{"16", " ", "Pi", " ", "DD"}]], FractionBox[ RowBox[{"3", "+", "\[Nu]"}], RowBox[{"1", "+", "\[Nu]"}]]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"k", "=", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"F", "/", "w0"}], ")"}], "/", "1000"}], " ", "//.", "val"}]}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.732963786982458*^9, 3.732963800329712*^9}, { 3.7329638807173033`*^9, 3.7329639838406887`*^9}, {3.7329640219057136`*^9, 3.7329640679494686`*^9}, {3.7329641106095915`*^9, 3.7329641238605337`*^9}, {3.7329641586934195`*^9, 3.7329641775638523`*^9}, {3.7329642131292753`*^9, 3.7329642468139324`*^9}, {3.732964291650645*^9, 3.732964295266472*^9}, { 3.7329643646012278`*^9, 3.7329645915297546`*^9}, {3.732964625547305*^9, 3.732964633879656*^9}, {3.732964682913621*^9, 3.732964776488607*^9}, { 3.732964812880664*^9, 3.7329648406399565`*^9}, {3.7329649084689856`*^9, 3.732965030133172*^9}, {3.732965104873771*^9, 3.7329651443322325`*^9}, { 3.7329651781396537`*^9, 3.73296520770864*^9}, {3.732965254213273*^9, 3.7329652993251047`*^9}, {3.7329653860024896`*^9, 3.7329653897065096`*^9}, {3.7329654581300693`*^9, 3.7329654674851675`*^9}, {3.7329655079892044`*^9, 3.7329655085784197`*^9}, 3.733053175193036*^9, {3.733054323981842*^9, 3.7330543310918913`*^9}, { 3.7330544527768817`*^9, 3.733054457152335*^9}, {3.733054573883443*^9, 3.7330546234511395`*^9}, {3.7330643435838375`*^9, 3.7330643547895327`*^9}, {3.7330643919191055`*^9, 3.7330644303402214`*^9}, {3.7331050956954727`*^9, 3.7331051189053106`*^9}, {3.7331111086485624`*^9, 3.7331111523877835`*^9}, {3.7331116359386663`*^9, 3.733111681037479*^9}, 3.7331466985132923`*^9, {3.733146742189515*^9, 3.7331467425179462`*^9}, { 3.7331882689213552`*^9, 3.7331882705625243`*^9}, {3.733456902620245*^9, 3.7334569073552113`*^9}, 3.7657059051454167`*^9, {3.765706272424467*^9, 3.765706305757754*^9}, {3.7657063874410734`*^9, 3.7657065682529764`*^9}, { 3.7657066048810625`*^9, 3.7657066299581566`*^9}, {3.765857078340946*^9, 3.7658571332338734`*^9}, {3.766475318047246*^9, 3.766475333494685*^9}, { 3.7664803019289956`*^9, 3.766480319352639*^9}, {3.766728193630061*^9, 3.76672819508255*^9}, {3.7668226244126663`*^9, 3.766822719296406*^9}, { 3.7668227719268694`*^9, 3.766822786626172*^9}, {3.7668228231264915`*^9, 3.7668228813658266`*^9}, {3.7668229260422144`*^9, 3.7668229380494995`*^9}, {3.7683555758986053`*^9, 3.768355668707209*^9}, { 3.768356902587074*^9, 3.7683570207621355`*^9}, {3.7683570674174614`*^9, 3.768357075346031*^9}, {3.768357275055511*^9, 3.7683572895188885`*^9}, { 3.7684537754941835`*^9, 3.768453813213885*^9}, 3.786684377575962*^9, { 3.7866844122688456`*^9, 3.7866844872632594`*^9}, {3.7866845404915056`*^9, 3.7866845854386406`*^9}, {3.7866846822157893`*^9, 3.7866848827458925`*^9}, {3.786685178950626*^9, 3.786685233195717*^9}, { 3.786685494114931*^9, 3.7866855462458096`*^9}, {3.7866855886652155`*^9, 3.786685700525444*^9}, {3.7875834162983584`*^9, 3.787583421968145*^9}, 3.816935166983514*^9, 3.8185889346088843`*^9}, CellLabel->"In[66]:=",ExpressionUUID->"3b12001d-9df2-4f5a-b356-794dcdd33b58"] }, Closed]], Cell[CellGroupData[{ Cell["Modelling assignment (Analytical method improved)", "Subsubsection", CellChangeTimes->{{3.473055512584*^9, 3.4730555529630003`*^9}, { 3.4730575328269997`*^9, 3.473057539222*^9}, {3.4734691424642*^9, 3.4734691605758*^9}, {3.4736023142902*^9, 3.4736023273162003`*^9}, { 3.568715518105007*^9, 3.568715523097016*^9}, 3.5994750893663483`*^9, 3.6297916561604834`*^9, {3.63073778491436*^9, 3.630737793931176*^9}, { 3.6624537703648133`*^9, 3.6624537732749796`*^9}, 3.685248933840145*^9, { 3.685267058363743*^9, 3.6852671273738394`*^9}, {3.685323461463516*^9, 3.6853234663335233`*^9}, {3.6858764211836576`*^9, 3.6858764235236607`*^9}, 3.6859482147140565`*^9, {3.686226212775403*^9, 3.6862262151354065`*^9}, { 3.686466369367293*^9, 3.686466390117322*^9}, {3.732333324403823*^9, 3.7323333512571926`*^9}, {3.7330531980857735`*^9, 3.733053222557193*^9}, { 3.7330643803419495`*^9, 3.733064384574917*^9}, {3.764819307824876*^9, 3.7648193089127207`*^9}, {3.765705926317233*^9, 3.765705947708847*^9}, { 3.7664771433740315`*^9, 3.7664771458408413`*^9}, {3.7664804155817566`*^9, 3.766480417312395*^9}, {3.7667263641049314`*^9, 3.766726366745177*^9}, { 3.7866797020276375`*^9, 3.7866797091155815`*^9}, {3.8169349720346622`*^9, 3.816934976193177*^9}, {3.8185871182307973`*^9, 3.8185871201829357`*^9}, { 3.818587153796042*^9, 3.8185871553178315`*^9}, {3.8187685159835835`*^9, 3.818768527108595*^9}, 3.8509754018752074`*^9},ExpressionUUID->"b56efb6f-e083-4955-a2a8-\ 0cfd3b4e340c"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"DD", "=", FractionBox[ RowBox[{"\[CapitalEpsilon]", " ", SuperscriptBox["t", "3"]}], RowBox[{"12", "-", RowBox[{"12", SuperscriptBox["\[Nu]", "2"]}]}]]}], ";"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"w0", ":=", RowBox[{ FractionBox[ RowBox[{"F", " ", SuperscriptBox["R", "2"]}], RowBox[{"16", " ", "Pi", " ", "DD"}]], RowBox[{"(", RowBox[{"2", "+", RowBox[{ SuperscriptBox[ RowBox[{"(", FractionBox["R", "Ro"], ")"}], "2"], FractionBox[ RowBox[{"1", "-", "\[Nu]"}], RowBox[{"1", "+", "\[Nu]"}]]}]}], " ", ")"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"k", "=", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"F", "/", "w0"}], ")"}], "/", "1000"}], " ", "//.", "val"}]}]}]}]], "Input", CellChangeTimes->{{3.732963786982458*^9, 3.732963800329712*^9}, { 3.7329638807173033`*^9, 3.7329639838406887`*^9}, {3.7329640219057136`*^9, 3.7329640679494686`*^9}, {3.7329641106095915`*^9, 3.7329641238605337`*^9}, {3.7329641586934195`*^9, 3.7329641775638523`*^9}, {3.7329642131292753`*^9, 3.7329642468139324`*^9}, {3.732964291650645*^9, 3.732964295266472*^9}, { 3.7329643646012278`*^9, 3.7329645915297546`*^9}, {3.732964625547305*^9, 3.732964633879656*^9}, {3.732964682913621*^9, 3.732964776488607*^9}, { 3.732964812880664*^9, 3.7329648406399565`*^9}, {3.7329649084689856`*^9, 3.732965030133172*^9}, {3.732965104873771*^9, 3.7329651443322325`*^9}, { 3.7329651781396537`*^9, 3.73296520770864*^9}, {3.732965254213273*^9, 3.7329652993251047`*^9}, {3.7329653860024896`*^9, 3.7329653897065096`*^9}, {3.7329654581300693`*^9, 3.7329654674851675`*^9}, {3.7329655079892044`*^9, 3.7329655085784197`*^9}, 3.733053175193036*^9, {3.733054323981842*^9, 3.7330543310918913`*^9}, { 3.7330544527768817`*^9, 3.733054457152335*^9}, {3.733054573883443*^9, 3.7330546234511395`*^9}, {3.7330643435838375`*^9, 3.7330643547895327`*^9}, {3.7330643919191055`*^9, 3.7330644303402214`*^9}, {3.7331050956954727`*^9, 3.7331051189053106`*^9}, {3.7331111086485624`*^9, 3.7331111523877835`*^9}, {3.7331116359386663`*^9, 3.733111681037479*^9}, 3.7331466985132923`*^9, {3.733146742189515*^9, 3.7331467425179462`*^9}, { 3.7331882689213552`*^9, 3.7331882705625243`*^9}, {3.733456902620245*^9, 3.7334569073552113`*^9}, 3.7657059051454167`*^9, {3.765706272424467*^9, 3.765706305757754*^9}, {3.7657063874410734`*^9, 3.7657065682529764`*^9}, { 3.7657066048810625`*^9, 3.7657066299581566`*^9}, {3.765857078340946*^9, 3.7658571332338734`*^9}, {3.766475318047246*^9, 3.766475333494685*^9}, { 3.7664803019289956`*^9, 3.766480319352639*^9}, {3.766728193630061*^9, 3.76672819508255*^9}, {3.7668226244126663`*^9, 3.766822719296406*^9}, { 3.7668227719268694`*^9, 3.766822786626172*^9}, {3.7668228231264915`*^9, 3.7668228813658266`*^9}, {3.7668229260422144`*^9, 3.7668229380494995`*^9}, {3.7683555758986053`*^9, 3.768355668707209*^9}, { 3.768356902587074*^9, 3.7683570207621355`*^9}, {3.7683570674174614`*^9, 3.768357075346031*^9}, {3.768357275055511*^9, 3.7683572895188885`*^9}, { 3.7684537754941835`*^9, 3.768453813213885*^9}, 3.786684377575962*^9, { 3.7866844122688456`*^9, 3.7866844872632594`*^9}, {3.7866845404915056`*^9, 3.7866845854386406`*^9}, {3.7866846822157893`*^9, 3.7866848827458925`*^9}, {3.786685178950626*^9, 3.786685233195717*^9}, { 3.786685494114931*^9, 3.7866855462458096`*^9}, {3.7866855886652155`*^9, 3.786685700525444*^9}, {3.7875834162983584`*^9, 3.787583421968145*^9}, { 3.8169351928529873`*^9, 3.816935200154375*^9}, {3.816935269632413*^9, 3.816935271224258*^9}, {3.818588951863042*^9, 3.8185889607419295`*^9}}, CellLabel->"In[69]:=",ExpressionUUID->"1a147b60-e71c-4838-a395-4e9b0c2bdd8d"] }, Closed]], Cell[CellGroupData[{ Cell["Modelling assignment (Analytical method full)", "Subsubsection", CellChangeTimes->{{3.473055512584*^9, 3.4730555529630003`*^9}, { 3.4730575328269997`*^9, 3.473057539222*^9}, {3.4734691424642*^9, 3.4734691605758*^9}, {3.4736023142902*^9, 3.4736023273162003`*^9}, { 3.568715518105007*^9, 3.568715523097016*^9}, 3.5994750893663483`*^9, 3.6297916561604834`*^9, {3.63073778491436*^9, 3.630737793931176*^9}, { 3.6624537703648133`*^9, 3.6624537732749796`*^9}, 3.685248933840145*^9, { 3.685267058363743*^9, 3.6852671273738394`*^9}, {3.685323461463516*^9, 3.6853234663335233`*^9}, {3.6858764211836576`*^9, 3.6858764235236607`*^9}, 3.6859482147140565`*^9, {3.686226212775403*^9, 3.6862262151354065`*^9}, { 3.686466369367293*^9, 3.686466390117322*^9}, {3.732333324403823*^9, 3.7323333512571926`*^9}, {3.7330531980857735`*^9, 3.733053222557193*^9}, { 3.7330643803419495`*^9, 3.733064384574917*^9}, {3.764819307824876*^9, 3.7648193089127207`*^9}, {3.765705926317233*^9, 3.765705947708847*^9}, { 3.7664771433740315`*^9, 3.7664771458408413`*^9}, {3.7664804155817566`*^9, 3.766480417312395*^9}, {3.7667263641049314`*^9, 3.766726366745177*^9}, { 3.7866797020276375`*^9, 3.7866797091155815`*^9}, {3.8169349802152348`*^9, 3.816934983617084*^9}, {3.8185871254882812`*^9, 3.818587126923666*^9}, { 3.818587160674302*^9, 3.818587162370451*^9}, {3.81876853856913*^9, 3.818768547005771*^9}},ExpressionUUID->"d6c09b2d-0060-462f-9e65-\ edce649c8801"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"DD", "=", FractionBox[ RowBox[{"\[CapitalEpsilon]", " ", SuperscriptBox["t", "3"]}], RowBox[{"12", "-", RowBox[{"12", SuperscriptBox["\[Nu]", "2"]}]}]]}], ";"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"w0", ":=", RowBox[{ FractionBox[ RowBox[{"F", " ", SuperscriptBox["R", "2"]}], RowBox[{"16", " ", "Pi", " ", "DD"}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", SuperscriptBox[ RowBox[{"(", FractionBox["Ri", "R"], ")"}], "2"]}], ")"}], RowBox[{"(", RowBox[{"2", "+", RowBox[{ SuperscriptBox[ RowBox[{"(", FractionBox["R", "Ro"], ")"}], "2"], FractionBox[ RowBox[{"1", "-", "\[Nu]"}], RowBox[{"1", "+", "\[Nu]"}]]}]}], " ", ")"}]}], "+", RowBox[{"2", SuperscriptBox[ RowBox[{"(", FractionBox["Ri", "R"], ")"}], "2"], RowBox[{"Log", "[", RowBox[{"(", FractionBox["Ri", "R"], ")"}], "]"}]}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"k", "=", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"F", "/", "w0"}], ")"}], "/", "1000"}], " ", "//.", "val"}]}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.732963786982458*^9, 3.732963800329712*^9}, { 3.7329638807173033`*^9, 3.7329639838406887`*^9}, {3.7329640219057136`*^9, 3.7329640679494686`*^9}, {3.7329641106095915`*^9, 3.7329641238605337`*^9}, {3.7329641586934195`*^9, 3.7329641775638523`*^9}, {3.7329642131292753`*^9, 3.7329642468139324`*^9}, {3.732964291650645*^9, 3.732964295266472*^9}, { 3.7329643646012278`*^9, 3.7329645915297546`*^9}, {3.732964625547305*^9, 3.732964633879656*^9}, {3.732964682913621*^9, 3.732964776488607*^9}, { 3.732964812880664*^9, 3.7329648406399565`*^9}, {3.7329649084689856`*^9, 3.732965030133172*^9}, {3.732965104873771*^9, 3.7329651443322325`*^9}, { 3.7329651781396537`*^9, 3.73296520770864*^9}, {3.732965254213273*^9, 3.7329652993251047`*^9}, {3.7329653860024896`*^9, 3.7329653897065096`*^9}, {3.7329654581300693`*^9, 3.7329654674851675`*^9}, {3.7329655079892044`*^9, 3.7329655085784197`*^9}, 3.733053175193036*^9, {3.733054323981842*^9, 3.7330543310918913`*^9}, { 3.7330544527768817`*^9, 3.733054457152335*^9}, {3.733054573883443*^9, 3.7330546234511395`*^9}, {3.7330643435838375`*^9, 3.7330643547895327`*^9}, {3.7330643919191055`*^9, 3.7330644303402214`*^9}, {3.7331050956954727`*^9, 3.7331051189053106`*^9}, {3.7331111086485624`*^9, 3.7331111523877835`*^9}, {3.7331116359386663`*^9, 3.733111681037479*^9}, 3.7331466985132923`*^9, {3.733146742189515*^9, 3.7331467425179462`*^9}, { 3.7331882689213552`*^9, 3.7331882705625243`*^9}, {3.733456902620245*^9, 3.7334569073552113`*^9}, 3.7657059051454167`*^9, {3.765706272424467*^9, 3.765706305757754*^9}, {3.7657063874410734`*^9, 3.7657065682529764`*^9}, { 3.7657066048810625`*^9, 3.7657066299581566`*^9}, {3.765857078340946*^9, 3.7658571332338734`*^9}, {3.766475318047246*^9, 3.766475333494685*^9}, { 3.7664803019289956`*^9, 3.766480319352639*^9}, {3.766728193630061*^9, 3.76672819508255*^9}, {3.7668226244126663`*^9, 3.766822719296406*^9}, { 3.7668227719268694`*^9, 3.766822786626172*^9}, {3.7668228231264915`*^9, 3.7668228813658266`*^9}, {3.7668229260422144`*^9, 3.7668229380494995`*^9}, {3.7683555758986053`*^9, 3.768355668707209*^9}, { 3.768356902587074*^9, 3.7683570207621355`*^9}, {3.7683570674174614`*^9, 3.768357075346031*^9}, {3.768357275055511*^9, 3.7683572895188885`*^9}, { 3.7684537754941835`*^9, 3.768453813213885*^9}, 3.786684377575962*^9, { 3.7866844122688456`*^9, 3.7866844872632594`*^9}, {3.7866845404915056`*^9, 3.7866845854386406`*^9}, {3.7866846822157893`*^9, 3.7866848827458925`*^9}, {3.786685178950626*^9, 3.786685233195717*^9}, { 3.786685494114931*^9, 3.7866855462458096`*^9}, {3.7866855886652155`*^9, 3.786685700525444*^9}, {3.7875834162983584`*^9, 3.787583421968145*^9}, { 3.816935236292815*^9, 3.816935237444829*^9}, {3.8185889771610513`*^9, 3.818589016841549*^9}, 3.819600866682102*^9}, CellLabel->"In[72]:=",ExpressionUUID->"9418a6e5-055c-43ef-87e1-2c501a162f13"] }, Closed]], Cell[CellGroupData[{ Cell["Modelling assignment (Virtual work expression)", "Subsubsection", CellChangeTimes->{{3.473055512584*^9, 3.4730555529630003`*^9}, { 3.4730575328269997`*^9, 3.473057539222*^9}, {3.4734691424642*^9, 3.4734691605758*^9}, {3.4736023142902*^9, 3.4736023273162003`*^9}, { 3.568715518105007*^9, 3.568715523097016*^9}, 3.5994750893663483`*^9, 3.6297916561604834`*^9, {3.63073778491436*^9, 3.630737793931176*^9}, { 3.6624537703648133`*^9, 3.6624537732749796`*^9}, 3.685248933840145*^9, { 3.685267058363743*^9, 3.6852671273738394`*^9}, {3.685323461463516*^9, 3.6853234663335233`*^9}, {3.6858764211836576`*^9, 3.6858764235236607`*^9}, 3.6859482147140565`*^9, {3.686226212775403*^9, 3.6862262151354065`*^9}, { 3.686466369367293*^9, 3.686466390117322*^9}, {3.732333324403823*^9, 3.7323333512571926`*^9}, {3.7330531980857735`*^9, 3.733053222557193*^9}, { 3.7330643803419495`*^9, 3.733064384574917*^9}, {3.7331064314352827`*^9, 3.733106433686386*^9}, {3.7331849245982533`*^9, 3.7331849405062175`*^9}, { 3.733186311322669*^9, 3.7331863141198373`*^9}, {3.764818735955555*^9, 3.764818757330291*^9}, {3.7657068324597855`*^9, 3.7657068329763837`*^9}, { 3.766476969087038*^9, 3.7664769771360793`*^9}, {3.766477197694624*^9, 3.7664771995413065`*^9}, {3.766555582509639*^9, 3.7665555906854963`*^9}, { 3.786678204834051*^9, 3.786678208360791*^9}, {3.786679720427352*^9, 3.786679727097021*^9}, {3.816934890146792*^9, 3.8169349186885166`*^9}, { 3.818587078690192*^9, 3.8185870823325496`*^9}, {3.8185874901561103`*^9, 3.818587519550008*^9}, {3.8187685546046886`*^9, 3.8187685608450513`*^9}},ExpressionUUID->"30c837b8-77d7-4a14-876c-\ 0bddffc8916f"], Cell[BoxData[ RowBox[{"Block", "[", RowBox[{ RowBox[{"{", RowBox[{ "w", ",", "\[CapitalOmega]", ",", "\[Delta]wint", ",", "\[Delta]Wint", ",", "\[Delta]Wext", ",", "\[Delta]W", ",", "sol"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"w", "=", RowBox[{ RowBox[{ RowBox[{"a", "[", "0", "]"}], " ", RowBox[{"(", RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"], "-", SuperscriptBox["R", "2"]}], ")"}]}], "+", RowBox[{ RowBox[{"a", "[", "1", "]"}], " ", RowBox[{ RowBox[{"(", RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"], "-", SuperscriptBox["R", "2"]}], ")"}], "^", "2"}]}], "+", RowBox[{ RowBox[{"a", "[", "2", "]"}], " ", RowBox[{ RowBox[{"(", RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"], "-", SuperscriptBox["R", "2"]}], ")"}], "^", "3"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}], ",", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}], ",", RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]}], "}"}], "]"}], ".", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["t", "3"], "/", "12"}], "*", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "\[Nu]", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Nu]", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]"}], ")"}], "/", "2"}]}], "}"}]}], "}"}], "*", RowBox[{"\[CapitalEpsilon]", "/", RowBox[{"(", RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}], ")"}]}]}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}], ",", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}], ",", RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]}], "}"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", "=", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", "R"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]Wint", " ", "=", RowBox[{"Integrate", "[", RowBox[{"\[Delta]wint", ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], StyleBox["\[Element]", "OperatorCharacter"], StyleBox["\[CapitalOmega]", "OperatorCharacter"]}], StyleBox[",", "OperatorCharacter"], RowBox[{ StyleBox["Assumptions", "OperatorCharacter"], StyleBox["\[Rule]", "OperatorCharacter"], RowBox[{"R", StyleBox[">", "OperatorCharacter"], StyleBox["0", "OperatorCharacter"]}]}]}], StyleBox["]", "OperatorCharacter"]}]}], StyleBox[";", "OperatorCharacter"], StyleBox["\[IndentingNewLine]", "OperatorCharacter"], RowBox[{"\[Delta]Wext", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", "w", "]"}], "F"}], " ", "/.", " ", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "0"}], ",", RowBox[{"y", "\[Rule]", "0"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "=", RowBox[{"(", RowBox[{"\[Delta]Wint", "+", "\[Delta]Wext"}], ")"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"sol", "=", " ", RowBox[{"SOLVE", "[", "\[Delta]W", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", "sol", "]"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"F", "/", "w"}], ")"}], "/.", "sol"}], "//.", "val"}], " ", "/.", " ", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "0"}], ",", RowBox[{"y", "\[Rule]", "0"}]}], "}"}]}], " ", ")"}], " ", "/", "1000"}]}]}], " ", "]"}]], "Input", CellChangeTimes->{{3.7331065052935543`*^9, 3.7331065455132427`*^9}, { 3.7331065985294237`*^9, 3.7331066038054595`*^9}, {3.7331169427386923`*^9, 3.7331170722995424`*^9}, {3.733117684451476*^9, 3.7331177032503495`*^9}, { 3.7331179347590604`*^9, 3.733118054709407*^9}, {3.7331180944008336`*^9, 3.7331183637373*^9}, {3.7331184294476814`*^9, 3.7331184669670315`*^9}, { 3.7331186831457067`*^9, 3.7331186835208015`*^9}, {3.7331187877505193`*^9, 3.7331188031112776`*^9}, {3.7331189820573163`*^9, 3.7331190570183573`*^9}, {3.7331204383732452`*^9, 3.7331204673922415`*^9}, {3.733120613813942*^9, 3.73312069735923*^9}, { 3.7331207697421885`*^9, 3.733120840437128*^9}, {3.733120897536913*^9, 3.7331208981617327`*^9}, {3.733120950307825*^9, 3.7331209687472754`*^9}, { 3.7331210145021257`*^9, 3.733121019643283*^9}, {3.73312105866333*^9, 3.7331211164194407`*^9}, 3.7331212169925804`*^9, 3.733121511882849*^9, { 3.73313538916969*^9, 3.7331354368934317`*^9}, {3.7331354941964245`*^9, 3.7331354971967516`*^9}, 3.7331356721337495`*^9, {3.73313598594795*^9, 3.733136045626433*^9}, {3.7331360791609364`*^9, 3.733136094912895*^9}, { 3.73313612515032*^9, 3.733136255523641*^9}, {3.733136286980091*^9, 3.733136311373001*^9}, {3.733136365910065*^9, 3.7331363787864265`*^9}, { 3.733136415180851*^9, 3.7331365557116456`*^9}, {3.733136629641155*^9, 3.7331366368608675`*^9}, {3.7331367168846874`*^9, 3.7331367300426655`*^9}, {3.733136761545972*^9, 3.7331367995341597`*^9}, { 3.7331368320220904`*^9, 3.7331368692916746`*^9}, {3.73313695903555*^9, 3.73313701765102*^9}, {3.7331372189690466`*^9, 3.7331372671775126`*^9}, { 3.733137326902588*^9, 3.7331373941594505`*^9}, {3.7331375441517935`*^9, 3.733137628457588*^9}, {3.7331376840728426`*^9, 3.7331377015749903`*^9}, { 3.7331385020500193`*^9, 3.7331385039879985`*^9}, {3.733138561525031*^9, 3.7331385634005165`*^9}, {3.7331457065506525`*^9, 3.733145714629631*^9}, { 3.7331457481800256`*^9, 3.7331457494145594`*^9}, {3.7331457820429187`*^9, 3.7331457829646435`*^9}, {3.7331459968966503`*^9, 3.73314605177772*^9}, 3.7331460828003397`*^9, {3.7331462354955673`*^9, 3.73314626601443*^9}, { 3.733146510540284*^9, 3.7331466409600363`*^9}, {3.7331468427313757`*^9, 3.7331469163828735`*^9}, {3.7331849739785075`*^9, 3.7331850052315197`*^9}, {3.7331850363288555`*^9, 3.7331853715674276`*^9}, {3.733185406352072*^9, 3.7331854066023936`*^9}, { 3.733185495986588*^9, 3.73318565162829*^9}, {3.733185705946556*^9, 3.7331857186038513`*^9}, {3.733185748881719*^9, 3.733185933619708*^9}, { 3.733185974452237*^9, 3.7331860514605026`*^9}, {3.7331860823072395`*^9, 3.7331860888238688`*^9}, {3.7331861485905466`*^9, 3.7331861806528893`*^9}, {3.73318632946542*^9, 3.7331866054945617`*^9}, { 3.7331866521243863`*^9, 3.733186850583209*^9}, {3.733186882211415*^9, 3.733186936510432*^9}, {3.7331870413499165`*^9, 3.7331870415840445`*^9}, { 3.7331879674988947`*^9, 3.7331880319744196`*^9}, {3.7331881651918564`*^9, 3.7331881933196564`*^9}, 3.733191086909934*^9, {3.7331911351838408`*^9, 3.733191147736865*^9}, 3.7331912484934406`*^9, {3.733365174148862*^9, 3.7333652053719177`*^9}, {3.7333652474550424`*^9, 3.73336530225986*^9}, { 3.733365345435026*^9, 3.7333654072122216`*^9}, {3.7333654661756344`*^9, 3.7333654809508104`*^9}, {3.7333655754319305`*^9, 3.7333655883196373`*^9}, {3.7333656336593266`*^9, 3.733365826529348*^9}, { 3.7333660007878046`*^9, 3.7333661259945803`*^9}, {3.733366213942363*^9, 3.7333663820292597`*^9}, {3.7333664469439106`*^9, 3.7333666851693993`*^9}, {3.7333667258927765`*^9, 3.733366848124815*^9}, { 3.733367113180627*^9, 3.733367164114697*^9}, {3.733370116949722*^9, 3.733370123356784*^9}, {3.7333701567521553`*^9, 3.73337016871292*^9}, 3.733375220779642*^9, {3.733375289256725*^9, 3.733375290146722*^9}, { 3.733375322401083*^9, 3.7333753433967476`*^9}, 3.733375419830647*^9, { 3.733375489324972*^9, 3.733375497369104*^9}, {3.7333783197434835`*^9, 3.7333785027712955`*^9}, {3.733378959210429*^9, 3.7333789691613045`*^9}, { 3.733379027665225*^9, 3.73337905657366*^9}, {3.7333791111712112`*^9, 3.7333791147258387`*^9}, {3.733379242587391*^9, 3.733379246558384*^9}, { 3.733460158370412*^9, 3.733460246098426*^9}, {3.733462208056137*^9, 3.7334622450756254`*^9}, {3.733462341023322*^9, 3.7334623997638617`*^9}, { 3.7334624555041842`*^9, 3.733462528715052*^9}, {3.733462570641363*^9, 3.733462694798615*^9}, {3.7334627467572346`*^9, 3.7334628248123674`*^9}, { 3.7334628550187387`*^9, 3.733462904055173*^9}, {3.7334629671556005`*^9, 3.733462978797456*^9}, {3.7334630620562468`*^9, 3.733463098169458*^9}, { 3.7334631405173225`*^9, 3.733463149436847*^9}, 3.7334632089587193`*^9, { 3.73346327557519*^9, 3.733463332049864*^9}, {3.733463446186983*^9, 3.733463809555442*^9}, {3.7334638492159376`*^9, 3.733463855185268*^9}, { 3.7334767716251354`*^9, 3.733476834063261*^9}, {3.7334769972290936`*^9, 3.7334770088437557`*^9}, 3.7334770567957296`*^9, {3.733477092315215*^9, 3.733477138194766*^9}, {3.7334772404366536`*^9, 3.7334772576345153`*^9}, { 3.73347729577876*^9, 3.7334773633213425`*^9}, 3.7334773954102736`*^9, { 3.733477440028474*^9, 3.733477481853801*^9}, {3.7334775213064594`*^9, 3.7334775410801506`*^9}, {3.733477571612934*^9, 3.7334775976086907`*^9}, { 3.733479205171806*^9, 3.733479270774158*^9}, {3.7334793090712047`*^9, 3.733479323235183*^9}, {3.7334793580248003`*^9, 3.7334793622794266`*^9}, { 3.7334794152394114`*^9, 3.7334794170047197`*^9}, {3.733491484942209*^9, 3.733491537425557*^9}, {3.733491634824994*^9, 3.7334916965170374`*^9}, { 3.7334918139743648`*^9, 3.733491963722246*^9}, {3.733492053507163*^9, 3.733492095873432*^9}, {3.7334922010444903`*^9, 3.73349223247291*^9}, { 3.7334922701027603`*^9, 3.733492286758114*^9}, {3.7334924280790243`*^9, 3.7334924285773735`*^9}, {3.733492494149005*^9, 3.73349267849009*^9}, { 3.733492725915759*^9, 3.733492758210832*^9}, {3.733492801429496*^9, 3.7334928541451373`*^9}, {3.7334930390778527`*^9, 3.73349307234543*^9}, { 3.733493877339528*^9, 3.7334938858486423`*^9}, {3.7334939772887754`*^9, 3.733493984944316*^9}, {3.7334941166790867`*^9, 3.7334941201545987`*^9}, { 3.733494188720145*^9, 3.733494205916135*^9}, 3.7334945908458557`*^9, { 3.7334946408391013`*^9, 3.7334946554737606`*^9}, {3.733494712228484*^9, 3.7334947173491*^9}, {3.7334947502054243`*^9, 3.7334947550749197`*^9}, { 3.733494895653963*^9, 3.7334949139510436`*^9}, {3.7334949643229437`*^9, 3.7334950046689377`*^9}, {3.7334950836861067`*^9, 3.733495090358919*^9}, { 3.733495726850687*^9, 3.7334957676115923`*^9}, {3.733495823595611*^9, 3.7334958507473063`*^9}, {3.733531269271142*^9, 3.7335313776530557`*^9}, { 3.733541219703043*^9, 3.7335412446744366`*^9}, {3.733541302852465*^9, 3.7335413136816845`*^9}, {3.7335413697032337`*^9, 3.7335413877364445`*^9}, 3.733541439632558*^9, {3.7335415319860735`*^9, 3.733541575990713*^9}, { 3.733541611244411*^9, 3.7335416687505403`*^9}, {3.7335417010195293`*^9, 3.7335417209747667`*^9}, {3.733541759775745*^9, 3.733541837315197*^9}, { 3.7335419016188717`*^9, 3.7335423069717045`*^9}, 3.7335423585396986`*^9, { 3.733542402700633*^9, 3.733542430312929*^9}, {3.7335425030862513`*^9, 3.7335425425435495`*^9}, {3.733542588923504*^9, 3.733542610081944*^9}, { 3.733542647038979*^9, 3.7335426658065877`*^9}, {3.733542717796409*^9, 3.7335427242502184`*^9}, {3.733542770348896*^9, 3.733542841892899*^9}, { 3.7335428906636853`*^9, 3.733542891351257*^9}, {3.733542934840231*^9, 3.7335430029724383`*^9}, {3.733543038038699*^9, 3.733543067229287*^9}, { 3.7335431297203255`*^9, 3.733543161520577*^9}, {3.733543194461548*^9, 3.7335432540929084`*^9}, {3.7335432896279144`*^9, 3.733543324741006*^9}, { 3.7335433678705177`*^9, 3.7335433712146716`*^9}, {3.733543416547597*^9, 3.7335434591927276`*^9}, {3.733543665339501*^9, 3.7335436937799883`*^9}, { 3.7335437704131546`*^9, 3.733543829388089*^9}, {3.7335439324459085`*^9, 3.733544022080389*^9}, {3.733544078711331*^9, 3.733544088399853*^9}, { 3.733544128982297*^9, 3.7335441600325413`*^9}, {3.7335442489012585`*^9, 3.733544604345105*^9}, {3.7335446389424615`*^9, 3.7335448189303026`*^9}, { 3.7335448726234818`*^9, 3.7335449297076445`*^9}, {3.733544973899822*^9, 3.733545007012683*^9}, {3.733545064393718*^9, 3.7335451486035585`*^9}, { 3.73354520379685*^9, 3.7335453868318377`*^9}, {3.73354545865193*^9, 3.733545492691042*^9}, {3.7335455524942303`*^9, 3.733545607453182*^9}, { 3.733545697728303*^9, 3.7335457377950926`*^9}, {3.733545797004427*^9, 3.7335458963371177`*^9}, {3.7335600445739202`*^9, 3.733560088062917*^9}, { 3.733560408903097*^9, 3.733560452829359*^9}, {3.7335605451368465`*^9, 3.7335605556220007`*^9}, {3.733560693089568*^9, 3.7335607035594864`*^9}, { 3.733561239190014*^9, 3.7335612427058396`*^9}, {3.733561312635296*^9, 3.7335613287931833`*^9}, {3.733561472343387*^9, 3.7335614887829037`*^9}, { 3.7335615554091043`*^9, 3.7335615603161535`*^9}, {3.7335616875495467`*^9, 3.733561696722621*^9}, {3.733561742118102*^9, 3.733561759948123*^9}, 3.7336328623083553`*^9, {3.733646962487833*^9, 3.733647111081254*^9}, 3.733647151088426*^9, {3.733647324093519*^9, 3.733647378394207*^9}, { 3.733647412605115*^9, 3.7336475196609955`*^9}, {3.733647565706006*^9, 3.7336476022754855`*^9}, {3.733647636405274*^9, 3.733647778494203*^9}, { 3.733647819222044*^9, 3.7336479836130247`*^9}, {3.7336482021874657`*^9, 3.733648306425503*^9}, {3.7336484232471466`*^9, 3.733648477193297*^9}, { 3.73364853750661*^9, 3.7336485385391874`*^9}, {3.733648657113475*^9, 3.7336486903701544`*^9}, {3.7336487208134737`*^9, 3.7336487763770323`*^9}, {3.7336488266999683`*^9, 3.733648877737054*^9}, { 3.7336498837046123`*^9, 3.733649897725542*^9}, 3.7340715959339457`*^9, 3.7340717631159296`*^9, {3.7449685386051035`*^9, 3.7449685889586525`*^9}, { 3.744968770326353*^9, 3.744968774937871*^9}, 3.76570692642441*^9, { 3.765706983442025*^9, 3.7657069940478077`*^9}, {3.765707081603978*^9, 3.765707218576766*^9}, {3.7657073432402773`*^9, 3.7657073596828737`*^9}, { 3.765707390879232*^9, 3.7657074162891026`*^9}, {3.7657074723330274`*^9, 3.765707487356175*^9}, {3.7657075650928235`*^9, 3.765707578757638*^9}, 3.7657674072044277`*^9, {3.765767449966214*^9, 3.7657674633232136`*^9}, { 3.7657675043697915`*^9, 3.765767864340949*^9}, {3.7657678966433263`*^9, 3.7657679003966312`*^9}, {3.765767932129229*^9, 3.7657679379148583`*^9}, { 3.7657681084580746`*^9, 3.765768178628733*^9}, {3.7657682707919188`*^9, 3.7657683129619007`*^9}, {3.765768418973206*^9, 3.765768429106756*^9}, { 3.7657684622674413`*^9, 3.765768479154067*^9}, {3.765768518072398*^9, 3.765768650333042*^9}, {3.7657687377638254`*^9, 3.7657687588782873`*^9}, { 3.765769039563476*^9, 3.765769141752368*^9}, {3.76576919660922*^9, 3.7657692312645564`*^9}, {3.7657692753250647`*^9, 3.765769286859925*^9}, { 3.765769332635785*^9, 3.7657693810321846`*^9}, {3.765769721690398*^9, 3.765769850892215*^9}, {3.7657698954904613`*^9, 3.7657699078542676`*^9}, { 3.7657699543505883`*^9, 3.7657699799114*^9}, 3.7657700377036657`*^9, 3.765770083018873*^9, {3.7657703862072783`*^9, 3.765770445975108*^9}, { 3.7657712977102222`*^9, 3.765771543996472*^9}, {3.7657716470817723`*^9, 3.765771655985817*^9}, {3.765771710816535*^9, 3.765771723516962*^9}, { 3.765771812167878*^9, 3.7657718577668653`*^9}, {3.765787548203395*^9, 3.765787563871632*^9}, {3.7657875982836933`*^9, 3.765787656301631*^9}, { 3.7657879764376545`*^9, 3.765788072300957*^9}, {3.765788167914768*^9, 3.765788174147703*^9}, {3.7657882269599333`*^9, 3.7657882422376156`*^9}, { 3.765788487323238*^9, 3.765788490461094*^9}, {3.7657885592421846`*^9, 3.7657886255167627`*^9}, {3.7657886684913006`*^9, 3.765788699772582*^9}, { 3.7658535454339027`*^9, 3.765853547121047*^9}, {3.765853585583187*^9, 3.7658535876696625`*^9}, {3.7658536294696665`*^9, 3.765853634654695*^9}, { 3.765853681762427*^9, 3.7658536912055206`*^9}, {3.7658538243303814`*^9, 3.7658538454131355`*^9}, {3.7658539157461643`*^9, 3.765854051366618*^9}, 3.7658549146636453`*^9, {3.7658549454327097`*^9, 3.7658549762144003`*^9}, { 3.7658554333652973`*^9, 3.7658554999790025`*^9}, {3.7658555611344366`*^9, 3.7658555729631147`*^9}, {3.7658572968663087`*^9, 3.7658573145137095`*^9}, {3.7658850384108715`*^9, 3.7658850474801846`*^9}, {3.7658850891956606`*^9, 3.7658851178663177`*^9}, 3.7659430922088523`*^9, {3.766116011153117*^9, 3.766116022737113*^9}, { 3.7664753933295326`*^9, 3.7664757716641407`*^9}, {3.7664758424631853`*^9, 3.766475936038104*^9}, 3.7664769809094667`*^9, {3.7664828985714397`*^9, 3.766482923363868*^9}, {3.766554437924354*^9, 3.7665544388624673`*^9}, { 3.7665544970769825`*^9, 3.7665545448261566`*^9}, 3.7764900881502085`*^9, { 3.786678838899349*^9, 3.7866788627471056`*^9}, {3.786678918408305*^9, 3.7866789780469837`*^9}, {3.786679561857725*^9, 3.78667957904008*^9}, { 3.786692829386594*^9, 3.7866928381726027`*^9}, {3.787302020810314*^9, 3.787302137038045*^9}, {3.7873021783189025`*^9, 3.787302294930934*^9}, { 3.7873023274507723`*^9, 3.7873024194617324`*^9}, {3.7873024565329976`*^9, 3.78730246140971*^9}, {3.7873073737926154`*^9, 3.7873074000334363`*^9}, { 3.787307431072998*^9, 3.78730767724796*^9}, {3.7873081674407406`*^9, 3.787308239827574*^9}, {3.7873082717971187`*^9, 3.787308363337903*^9}, { 3.7873084872547255`*^9, 3.7873084885200553`*^9}, {3.7873086075244837`*^9, 3.787308639861372*^9}, 3.787308693940789*^9, {3.787309716537686*^9, 3.787309733290118*^9}, 3.7873097952786875`*^9, {3.7873098732293625`*^9, 3.787309877103456*^9}, {3.787309927645409*^9, 3.7873099284733377`*^9}, { 3.7873099750034046`*^9, 3.787309977884631*^9}, 3.7873101648413973`*^9, { 3.7875377551161613`*^9, 3.787537804362151*^9}, {3.8169343341375113`*^9, 3.8169343461294255`*^9}, {3.8169344631005883`*^9, 3.8169344695509443`*^9}, {3.8169347819529843`*^9, 3.816934825608487*^9}, { 3.8169354178746405`*^9, 3.816935450162275*^9}, {3.8169355139518814`*^9, 3.816935515512082*^9}, {3.8169356003301907`*^9, 3.8169356182809305`*^9}, { 3.818587195418782*^9, 3.818587221075357*^9}, {3.818587280973971*^9, 3.818587334849313*^9}, {3.818587380595599*^9, 3.8185874553524084`*^9}, { 3.8185876970092134`*^9, 3.818587714808615*^9}, {3.8185885077434196`*^9, 3.8185885190382767`*^9}, {3.81960089725202*^9, 3.8196009064923067`*^9}, { 3.8506159402379785`*^9, 3.8506159497990627`*^9}, {3.850615986087698*^9, 3.850616056955044*^9}, {3.850616140431628*^9, 3.8506161901543684`*^9}, { 3.850616225372081*^9, 3.8506162327326393`*^9}, {3.850616273899242*^9, 3.8506162749031043`*^9}, {3.8506163391747694`*^9, 3.8506164301420918`*^9}, {3.851043500105685*^9, 3.851043599892077*^9}, { 3.8510436300421915`*^9, 3.85104377759713*^9}}, CellLabel-> "In[364]:=",ExpressionUUID->"fcc4cb24-7d33-41af-97c4-4c089213800f"] }, Closed]], Cell[CellGroupData[{ Cell["Modelling assignment (FEM with triangles)", "Subsubsection", CellChangeTimes->{{3.473055512584*^9, 3.4730555529630003`*^9}, { 3.4730575328269997`*^9, 3.473057539222*^9}, {3.4734691424642*^9, 3.4734691605758*^9}, {3.4736023142902*^9, 3.4736023273162003`*^9}, { 3.568715518105007*^9, 3.568715523097016*^9}, 3.5994750893663483`*^9, 3.6297916561604834`*^9, {3.63073778491436*^9, 3.630737793931176*^9}, { 3.6624537703648133`*^9, 3.6624537732749796`*^9}, 3.685248933840145*^9, { 3.685267058363743*^9, 3.6852671273738394`*^9}, {3.685323461463516*^9, 3.6853234663335233`*^9}, {3.6858764211836576`*^9, 3.6858764235236607`*^9}, 3.6859482147140565`*^9, {3.686226212775403*^9, 3.6862262151354065`*^9}, { 3.686466369367293*^9, 3.686466390117322*^9}, {3.732333324403823*^9, 3.7323333512571926`*^9}, {3.7330531980857735`*^9, 3.733053222557193*^9}, { 3.7330643803419495`*^9, 3.733064384574917*^9}, {3.7331064314352827`*^9, 3.733106433686386*^9}, {3.7331849245982533`*^9, 3.7331849405062175`*^9}, { 3.733186311322669*^9, 3.7331863141198373`*^9}, {3.764818735955555*^9, 3.764818757330291*^9}, {3.7657068324597855`*^9, 3.7657068329763837`*^9}, { 3.766476969087038*^9, 3.7664769771360793`*^9}, {3.766477197694624*^9, 3.7664771995413065`*^9}, {3.766555582509639*^9, 3.7665555906854963`*^9}, { 3.786678204834051*^9, 3.786678208360791*^9}, {3.786679720427352*^9, 3.786679727097021*^9}, {3.816934890146792*^9, 3.8169348911973934`*^9}, { 3.8185891808580103`*^9, 3.8185891894990625`*^9}, {3.8187685645906105`*^9, 3.8187685770115395`*^9}},ExpressionUUID->"f35287b9-a03a-4574-97fa-\ 237b12c801a3"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"(*", RowBox[{"BOUNDARIES", " ", "OF", " ", "THE", " ", "REGIONS"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "inner", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"n1", "=", "20"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"bnd1", "=", RowBox[{"Table", "[", RowBox[{"i", ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "n1"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"nod1", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Line", "[", "#", "]"}], "&"}], ",", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{"bnd1", ",", RowBox[{"RotateLeft", "[", "bnd1", "]"}]}], "}"}], "]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"crd1", "=", RowBox[{ RowBox[{"CirclePoints", "[", RowBox[{ RowBox[{"{", RowBox[{"Ri", ",", "0"}], "}"}], ",", "n1"}], "]"}], " ", "/.", "val"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "rim", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"n2", "=", "40"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"bnd2", "=", RowBox[{ RowBox[{"Table", "[", RowBox[{"i", ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "n2"}], "}"}]}], "]"}], "+", "n1"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"nod2", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Line", "[", "#", "]"}], "&"}], ",", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{"bnd2", ",", RowBox[{"RotateLeft", "[", "bnd2", "]"}]}], "}"}], "]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"crd2", "=", RowBox[{ RowBox[{"CirclePoints", "[", RowBox[{ RowBox[{"{", RowBox[{"R", ",", "0"}], "}"}], ",", "n2"}], "]"}], " ", "/.", "val"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "outer", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"n3", "=", "40"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"bnd3", "=", RowBox[{ RowBox[{"Table", "[", RowBox[{"i", ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "n3"}], "}"}]}], "]"}], "+", "n1", "+", "n2"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"nod3", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Line", "[", "#", "]"}], "&"}], ",", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{"bnd3", ",", RowBox[{"RotateLeft", "[", "bnd3", "]"}]}], "}"}], "]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"crd3", "=", RowBox[{ RowBox[{"CirclePoints", "[", RowBox[{ RowBox[{"{", RowBox[{"Ro", ",", "0"}], "}"}], ",", "n3"}], "]"}], " ", "/.", "val"}]}], ";"}], "\n", "\[IndentingNewLine]", RowBox[{ RowBox[{"nod4", "=", RowBox[{"Join", "[", RowBox[{"nod1", ",", "nod2", ",", "nod3"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"crd4", "=", RowBox[{"Join", "[", RowBox[{"crd1", ",", "crd2", ",", "crd3"}], "]"}]}], ";"}], " ", "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{ RowBox[{"MeshRegion", "[", RowBox[{"crd4", ",", "nod4"}], "]"}], ",", " ", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.7331065052935543`*^9, 3.7331065455132427`*^9}, { 3.7331065985294237`*^9, 3.7331066038054595`*^9}, {3.7331169427386923`*^9, 3.7331170722995424`*^9}, {3.733117684451476*^9, 3.7331177032503495`*^9}, { 3.7331179347590604`*^9, 3.733118054709407*^9}, {3.7331180944008336`*^9, 3.7331183637373*^9}, {3.7331184294476814`*^9, 3.7331184669670315`*^9}, { 3.7331186831457067`*^9, 3.7331186835208015`*^9}, {3.7331187877505193`*^9, 3.7331188031112776`*^9}, {3.7331189820573163`*^9, 3.7331190570183573`*^9}, {3.7331204383732452`*^9, 3.7331204673922415`*^9}, {3.733120613813942*^9, 3.73312069735923*^9}, { 3.7331207697421885`*^9, 3.733120840437128*^9}, {3.733120897536913*^9, 3.7331208981617327`*^9}, {3.733120950307825*^9, 3.7331209687472754`*^9}, { 3.7331210145021257`*^9, 3.733121019643283*^9}, {3.73312105866333*^9, 3.7331211164194407`*^9}, 3.7331212169925804`*^9, 3.733121511882849*^9, { 3.73313538916969*^9, 3.7331354368934317`*^9}, {3.7331354941964245`*^9, 3.7331354971967516`*^9}, 3.7331356721337495`*^9, {3.73313598594795*^9, 3.733136045626433*^9}, {3.7331360791609364`*^9, 3.733136094912895*^9}, { 3.73313612515032*^9, 3.733136255523641*^9}, {3.733136286980091*^9, 3.733136311373001*^9}, {3.733136365910065*^9, 3.7331363787864265`*^9}, { 3.733136415180851*^9, 3.7331365557116456`*^9}, {3.733136629641155*^9, 3.7331366368608675`*^9}, {3.7331367168846874`*^9, 3.7331367300426655`*^9}, {3.733136761545972*^9, 3.7331367995341597`*^9}, { 3.7331368320220904`*^9, 3.7331368692916746`*^9}, {3.73313695903555*^9, 3.73313701765102*^9}, {3.7331372189690466`*^9, 3.7331372671775126`*^9}, { 3.733137326902588*^9, 3.7331373941594505`*^9}, {3.7331375441517935`*^9, 3.733137628457588*^9}, {3.7331376840728426`*^9, 3.7331377015749903`*^9}, { 3.7331385020500193`*^9, 3.7331385039879985`*^9}, {3.733138561525031*^9, 3.7331385634005165`*^9}, {3.7331457065506525`*^9, 3.733145714629631*^9}, { 3.7331457481800256`*^9, 3.7331457494145594`*^9}, {3.7331457820429187`*^9, 3.7331457829646435`*^9}, {3.7331459968966503`*^9, 3.73314605177772*^9}, 3.7331460828003397`*^9, {3.7331462354955673`*^9, 3.73314626601443*^9}, { 3.733146510540284*^9, 3.7331466409600363`*^9}, {3.7331468427313757`*^9, 3.7331469163828735`*^9}, {3.7331849739785075`*^9, 3.7331850052315197`*^9}, {3.7331850363288555`*^9, 3.7331853715674276`*^9}, {3.733185406352072*^9, 3.7331854066023936`*^9}, { 3.733185495986588*^9, 3.73318565162829*^9}, {3.733185705946556*^9, 3.7331857186038513`*^9}, {3.733185748881719*^9, 3.733185933619708*^9}, { 3.733185974452237*^9, 3.7331860514605026`*^9}, {3.7331860823072395`*^9, 3.7331860888238688`*^9}, {3.7331861485905466`*^9, 3.7331861806528893`*^9}, {3.73318632946542*^9, 3.7331866054945617`*^9}, { 3.7331866521243863`*^9, 3.733186850583209*^9}, {3.733186882211415*^9, 3.733186936510432*^9}, {3.7331870413499165`*^9, 3.7331870415840445`*^9}, { 3.7331879674988947`*^9, 3.7331880319744196`*^9}, {3.7331881651918564`*^9, 3.7331881933196564`*^9}, 3.733191086909934*^9, {3.7331911351838408`*^9, 3.733191147736865*^9}, 3.7331912484934406`*^9, {3.733365174148862*^9, 3.7333652053719177`*^9}, {3.7333652474550424`*^9, 3.73336530225986*^9}, { 3.733365345435026*^9, 3.7333654072122216`*^9}, {3.7333654661756344`*^9, 3.7333654809508104`*^9}, {3.7333655754319305`*^9, 3.7333655883196373`*^9}, {3.7333656336593266`*^9, 3.733365826529348*^9}, { 3.7333660007878046`*^9, 3.7333661259945803`*^9}, {3.733366213942363*^9, 3.7333663820292597`*^9}, {3.7333664469439106`*^9, 3.7333666851693993`*^9}, {3.7333667258927765`*^9, 3.733366848124815*^9}, { 3.733367113180627*^9, 3.733367164114697*^9}, {3.733370116949722*^9, 3.733370123356784*^9}, {3.7333701567521553`*^9, 3.73337016871292*^9}, 3.733375220779642*^9, {3.733375289256725*^9, 3.733375290146722*^9}, { 3.733375322401083*^9, 3.7333753433967476`*^9}, 3.733375419830647*^9, { 3.733375489324972*^9, 3.733375497369104*^9}, {3.7333783197434835`*^9, 3.7333785027712955`*^9}, {3.733378959210429*^9, 3.7333789691613045`*^9}, { 3.733379027665225*^9, 3.73337905657366*^9}, {3.7333791111712112`*^9, 3.7333791147258387`*^9}, {3.733379242587391*^9, 3.733379246558384*^9}, { 3.733460158370412*^9, 3.733460246098426*^9}, {3.733462208056137*^9, 3.7334622450756254`*^9}, {3.733462341023322*^9, 3.7334623997638617`*^9}, { 3.7334624555041842`*^9, 3.733462528715052*^9}, {3.733462570641363*^9, 3.733462694798615*^9}, {3.7334627467572346`*^9, 3.7334628248123674`*^9}, { 3.7334628550187387`*^9, 3.733462904055173*^9}, {3.7334629671556005`*^9, 3.733462978797456*^9}, {3.7334630620562468`*^9, 3.733463098169458*^9}, { 3.7334631405173225`*^9, 3.733463149436847*^9}, 3.7334632089587193`*^9, { 3.73346327557519*^9, 3.733463332049864*^9}, {3.733463446186983*^9, 3.733463809555442*^9}, {3.7334638492159376`*^9, 3.733463855185268*^9}, { 3.7334767716251354`*^9, 3.733476834063261*^9}, {3.7334769972290936`*^9, 3.7334770088437557`*^9}, 3.7334770567957296`*^9, {3.733477092315215*^9, 3.733477138194766*^9}, {3.7334772404366536`*^9, 3.7334772576345153`*^9}, { 3.73347729577876*^9, 3.7334773633213425`*^9}, 3.7334773954102736`*^9, { 3.733477440028474*^9, 3.733477481853801*^9}, {3.7334775213064594`*^9, 3.7334775410801506`*^9}, {3.733477571612934*^9, 3.7334775976086907`*^9}, { 3.733479205171806*^9, 3.733479270774158*^9}, {3.7334793090712047`*^9, 3.733479323235183*^9}, {3.7334793580248003`*^9, 3.7334793622794266`*^9}, { 3.7334794152394114`*^9, 3.7334794170047197`*^9}, {3.733491484942209*^9, 3.733491537425557*^9}, {3.733491634824994*^9, 3.7334916965170374`*^9}, { 3.7334918139743648`*^9, 3.733491963722246*^9}, {3.733492053507163*^9, 3.733492095873432*^9}, {3.7334922010444903`*^9, 3.73349223247291*^9}, { 3.7334922701027603`*^9, 3.733492286758114*^9}, {3.7334924280790243`*^9, 3.7334924285773735`*^9}, {3.733492494149005*^9, 3.73349267849009*^9}, { 3.733492725915759*^9, 3.733492758210832*^9}, {3.733492801429496*^9, 3.7334928541451373`*^9}, {3.7334930390778527`*^9, 3.73349307234543*^9}, { 3.733493877339528*^9, 3.7334938858486423`*^9}, {3.7334939772887754`*^9, 3.733493984944316*^9}, {3.7334941166790867`*^9, 3.7334941201545987`*^9}, { 3.733494188720145*^9, 3.733494205916135*^9}, 3.7334945908458557`*^9, { 3.7334946408391013`*^9, 3.7334946554737606`*^9}, {3.733494712228484*^9, 3.7334947173491*^9}, {3.7334947502054243`*^9, 3.7334947550749197`*^9}, { 3.733494895653963*^9, 3.7334949139510436`*^9}, {3.7334949643229437`*^9, 3.7334950046689377`*^9}, {3.7334950836861067`*^9, 3.733495090358919*^9}, { 3.733495726850687*^9, 3.7334957676115923`*^9}, {3.733495823595611*^9, 3.7334958507473063`*^9}, {3.733531269271142*^9, 3.7335313776530557`*^9}, { 3.733541219703043*^9, 3.7335412446744366`*^9}, {3.733541302852465*^9, 3.7335413136816845`*^9}, {3.7335413697032337`*^9, 3.7335413877364445`*^9}, 3.733541439632558*^9, {3.7335415319860735`*^9, 3.733541575990713*^9}, { 3.733541611244411*^9, 3.7335416687505403`*^9}, {3.7335417010195293`*^9, 3.7335417209747667`*^9}, {3.733541759775745*^9, 3.733541837315197*^9}, { 3.7335419016188717`*^9, 3.7335423069717045`*^9}, 3.7335423585396986`*^9, { 3.733542402700633*^9, 3.733542430312929*^9}, {3.7335425030862513`*^9, 3.7335425425435495`*^9}, {3.733542588923504*^9, 3.733542610081944*^9}, { 3.733542647038979*^9, 3.7335426658065877`*^9}, {3.733542717796409*^9, 3.7335427242502184`*^9}, {3.733542770348896*^9, 3.733542841892899*^9}, { 3.7335428906636853`*^9, 3.733542891351257*^9}, {3.733542934840231*^9, 3.7335430029724383`*^9}, {3.733543038038699*^9, 3.733543067229287*^9}, { 3.7335431297203255`*^9, 3.733543161520577*^9}, {3.733543194461548*^9, 3.7335432540929084`*^9}, {3.7335432896279144`*^9, 3.733543324741006*^9}, { 3.7335433678705177`*^9, 3.7335433712146716`*^9}, {3.733543416547597*^9, 3.7335434591927276`*^9}, {3.733543665339501*^9, 3.7335436937799883`*^9}, { 3.7335437704131546`*^9, 3.733543829388089*^9}, {3.7335439324459085`*^9, 3.733544022080389*^9}, {3.733544078711331*^9, 3.733544088399853*^9}, { 3.733544128982297*^9, 3.7335441600325413`*^9}, {3.7335442489012585`*^9, 3.733544604345105*^9}, {3.7335446389424615`*^9, 3.7335448189303026`*^9}, { 3.7335448726234818`*^9, 3.7335449297076445`*^9}, {3.733544973899822*^9, 3.733545007012683*^9}, {3.733545064393718*^9, 3.7335451486035585`*^9}, { 3.73354520379685*^9, 3.7335453868318377`*^9}, {3.73354545865193*^9, 3.733545492691042*^9}, {3.7335455524942303`*^9, 3.733545607453182*^9}, { 3.733545697728303*^9, 3.7335457377950926`*^9}, {3.733545797004427*^9, 3.7335458963371177`*^9}, {3.7335600445739202`*^9, 3.733560088062917*^9}, { 3.733560408903097*^9, 3.733560452829359*^9}, {3.7335605451368465`*^9, 3.7335605556220007`*^9}, {3.733560693089568*^9, 3.7335607035594864`*^9}, { 3.733561239190014*^9, 3.7335612427058396`*^9}, {3.733561312635296*^9, 3.7335613287931833`*^9}, {3.733561472343387*^9, 3.7335614887829037`*^9}, { 3.7335615554091043`*^9, 3.7335615603161535`*^9}, {3.7335616875495467`*^9, 3.733561696722621*^9}, {3.733561742118102*^9, 3.733561759948123*^9}, 3.7336328623083553`*^9, {3.733646962487833*^9, 3.733647111081254*^9}, 3.733647151088426*^9, {3.733647324093519*^9, 3.733647378394207*^9}, { 3.733647412605115*^9, 3.7336475196609955`*^9}, {3.733647565706006*^9, 3.7336476022754855`*^9}, {3.733647636405274*^9, 3.733647778494203*^9}, { 3.733647819222044*^9, 3.7336479836130247`*^9}, {3.7336482021874657`*^9, 3.733648306425503*^9}, {3.7336484232471466`*^9, 3.733648477193297*^9}, { 3.73364853750661*^9, 3.7336485385391874`*^9}, {3.733648657113475*^9, 3.7336486903701544`*^9}, {3.7336487208134737`*^9, 3.7336487763770323`*^9}, {3.7336488266999683`*^9, 3.733648877737054*^9}, { 3.7336498837046123`*^9, 3.733649897725542*^9}, 3.7340715959339457`*^9, 3.7340717631159296`*^9, {3.7449685386051035`*^9, 3.7449685889586525`*^9}, { 3.744968770326353*^9, 3.744968774937871*^9}, 3.76570692642441*^9, { 3.765706983442025*^9, 3.7657069940478077`*^9}, {3.765707081603978*^9, 3.765707218576766*^9}, {3.7657073432402773`*^9, 3.7657073596828737`*^9}, { 3.765707390879232*^9, 3.7657074162891026`*^9}, {3.7657074723330274`*^9, 3.765707487356175*^9}, {3.7657075650928235`*^9, 3.765707578757638*^9}, 3.7657674072044277`*^9, {3.765767449966214*^9, 3.7657674633232136`*^9}, { 3.7657675043697915`*^9, 3.765767864340949*^9}, {3.7657678966433263`*^9, 3.7657679003966312`*^9}, {3.765767932129229*^9, 3.7657679379148583`*^9}, { 3.7657681084580746`*^9, 3.765768178628733*^9}, {3.7657682707919188`*^9, 3.7657683129619007`*^9}, {3.765768418973206*^9, 3.765768429106756*^9}, { 3.7657684622674413`*^9, 3.765768479154067*^9}, {3.765768518072398*^9, 3.765768650333042*^9}, {3.7657687377638254`*^9, 3.7657687588782873`*^9}, { 3.765769039563476*^9, 3.765769141752368*^9}, {3.76576919660922*^9, 3.7657692312645564`*^9}, {3.7657692753250647`*^9, 3.765769286859925*^9}, { 3.765769332635785*^9, 3.7657693810321846`*^9}, {3.765769721690398*^9, 3.765769850892215*^9}, {3.7657698954904613`*^9, 3.7657699078542676`*^9}, { 3.7657699543505883`*^9, 3.7657699799114*^9}, 3.7657700377036657`*^9, 3.765770083018873*^9, {3.7657703862072783`*^9, 3.765770445975108*^9}, { 3.7657712977102222`*^9, 3.765771543996472*^9}, {3.7657716470817723`*^9, 3.765771655985817*^9}, {3.765771710816535*^9, 3.765771723516962*^9}, { 3.765771812167878*^9, 3.7657718577668653`*^9}, {3.765787548203395*^9, 3.765787563871632*^9}, {3.7657875982836933`*^9, 3.765787656301631*^9}, { 3.7657879764376545`*^9, 3.765788072300957*^9}, {3.765788167914768*^9, 3.765788174147703*^9}, {3.7657882269599333`*^9, 3.7657882422376156`*^9}, { 3.765788487323238*^9, 3.765788490461094*^9}, {3.7657885592421846`*^9, 3.7657886255167627`*^9}, {3.7657886684913006`*^9, 3.765788699772582*^9}, { 3.7658535454339027`*^9, 3.765853547121047*^9}, {3.765853585583187*^9, 3.7658535876696625`*^9}, {3.7658536294696665`*^9, 3.765853634654695*^9}, { 3.765853681762427*^9, 3.7658536912055206`*^9}, {3.7658538243303814`*^9, 3.7658538454131355`*^9}, {3.7658539157461643`*^9, 3.765854051366618*^9}, 3.7658549146636453`*^9, {3.7658549454327097`*^9, 3.7658549762144003`*^9}, { 3.7658554333652973`*^9, 3.7658554999790025`*^9}, {3.7658555611344366`*^9, 3.7658555729631147`*^9}, {3.7658572968663087`*^9, 3.7658573145137095`*^9}, {3.7658850384108715`*^9, 3.7658850474801846`*^9}, {3.7658850891956606`*^9, 3.7658851178663177`*^9}, 3.7659430922088523`*^9, {3.766116011153117*^9, 3.766116022737113*^9}, { 3.7664753933295326`*^9, 3.7664757716641407`*^9}, {3.7664758424631853`*^9, 3.766475936038104*^9}, 3.7664769809094667`*^9, {3.7664828985714397`*^9, 3.766482923363868*^9}, {3.766554437924354*^9, 3.7665544388624673`*^9}, { 3.7665544970769825`*^9, 3.7665545448261566`*^9}, 3.7764900881502085`*^9, { 3.786678838899349*^9, 3.7866788627471056`*^9}, {3.786678918408305*^9, 3.7866789780469837`*^9}, {3.786679561857725*^9, 3.78667957904008*^9}, { 3.786692829386594*^9, 3.7866928381726027`*^9}, {3.787302020810314*^9, 3.787302137038045*^9}, {3.7873021783189025`*^9, 3.787302294930934*^9}, { 3.7873023274507723`*^9, 3.7873024194617324`*^9}, {3.7873024565329976`*^9, 3.78730246140971*^9}, {3.7873073737926154`*^9, 3.7873074000334363`*^9}, { 3.787307431072998*^9, 3.78730767724796*^9}, {3.7873081674407406`*^9, 3.787308239827574*^9}, {3.7873082717971187`*^9, 3.787308363337903*^9}, { 3.7873084872547255`*^9, 3.7873084885200553`*^9}, {3.7873086075244837`*^9, 3.787308639861372*^9}, 3.787308693940789*^9, {3.787309716537686*^9, 3.787309733290118*^9}, 3.7873097952786875`*^9, {3.7873098732293625`*^9, 3.787309877103456*^9}, {3.787309927645409*^9, 3.7873099284733377`*^9}, { 3.7873099750034046`*^9, 3.787309977884631*^9}, 3.7873101648413973`*^9, { 3.7875377551161613`*^9, 3.787537804362151*^9}, {3.8169343341375113`*^9, 3.8169343461294255`*^9}, {3.8169344631005883`*^9, 3.8169344695509443`*^9}, {3.8169347819529843`*^9, 3.816934825608487*^9}, 3.8171888544277773`*^9, {3.8171940311209283`*^9, 3.8171940335911407`*^9}, { 3.818589209756519*^9, 3.818589227241995*^9}, {3.818590047138863*^9, 3.8185900481560698`*^9}, {3.8196009545349965`*^9, 3.8196009565286636`*^9}}, CellLabel-> "In[365]:=",ExpressionUUID->"32388698-befc-4ac2-8cc5-f4b6ea17cab8"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"(*", RowBox[{"TRIANGLE", " ", "REPRESENTATION"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"region", " ", "definitions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"reg", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Ri", "/", "2"}], ",", "0."}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"Ri", "+", "R"}], ")"}], "/", "2"}], ",", "0."}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"R", "+", "Ro"}], ")"}], "/", "2"}], ",", "0."}], "}"}]}], "}"}], "/.", "val"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"atr", "=", RowBox[{"{", RowBox[{"1.", ",", "2.", ",", "3."}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"cns", "=", RowBox[{"{", RowBox[{"1.", ",", "0.1", ",", "1"}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"triangulate", " ", "the", " ", "regions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"crd", ",", "nod", ",", "typ"}], "}"}], "=", RowBox[{"TRIANGULATE", "[", RowBox[{ RowBox[{"{", RowBox[{"crd4", ",", "nod4"}], "}"}], ",", RowBox[{"{", RowBox[{"reg", ",", "atr", ",", "cns"}], "}"}], ",", "10"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{ RowBox[{"MeshRegion", "[", RowBox[{"crd", ",", "nod"}], "]"}], ",", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.816934495506795*^9, 3.816934505535719*^9}, 3.817188849033676*^9, {3.8171925081883955`*^9, 3.8171925302631493`*^9}, { 3.8171932665893154`*^9, 3.817193280749033*^9}, {3.8171933527160435`*^9, 3.8171933700095854`*^9}, {3.817193405387725*^9, 3.817193432269047*^9}, { 3.8185892539136467`*^9, 3.818589298531926*^9}, {3.818590638852883*^9, 3.8185906594634857`*^9}, {3.851044922493782*^9, 3.851044925071*^9}},ExpressionUUID->"3c78de41-cf9b-45a3-8fb6-74fb133600ce"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"(*", RowBox[{"PROBLEM", " ", "DESCRIPTIONS"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "material", " ", "properties", " ", "for", " ", "the", " ", "regions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"mat", "[", "1", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "p"}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"mat", "[", RowBox[{"2", "|", "3"}], "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"condition", " ", "at", " ", "the", " ", "rim"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"cnd", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"uZ", "[", "#", "]"}], "\[Rule]", "0"}], "&"}], ",", "bnd2"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"problem", " ", "decription"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ii", "=", "1"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ele", "=", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"mat", "[", RowBox[{"typ", "[", RowBox[{"[", RowBox[{"First", "[", "#2", "]"}], "]"}], "]"}], "]"}], ",", "#1"}], "}"}], " ", "&"}], ",", "nod"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", "=", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Append", "[", RowBox[{"#", ",", "0"}], "]"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "ii", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", "ii", "]"}], ",", RowBox[{"\[Theta]Y", "[", RowBox[{"ii", "++"}], "]"}], ",", "0"}], "}"}]}], "}"}], " ", "&"}], ",", "crd"}], "]"}], " ", "/.", "cnd"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"MESH", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.7331065052935543`*^9, 3.7331065455132427`*^9}, { 3.7331065985294237`*^9, 3.7331066038054595`*^9}, {3.7331169427386923`*^9, 3.7331170722995424`*^9}, {3.733117684451476*^9, 3.7331177032503495`*^9}, { 3.7331179347590604`*^9, 3.733118054709407*^9}, {3.7331180944008336`*^9, 3.7331183637373*^9}, {3.7331184294476814`*^9, 3.7331184669670315`*^9}, { 3.7331186831457067`*^9, 3.7331186835208015`*^9}, {3.7331187877505193`*^9, 3.7331188031112776`*^9}, {3.7331189820573163`*^9, 3.7331190570183573`*^9}, {3.7331204383732452`*^9, 3.7331204673922415`*^9}, {3.733120613813942*^9, 3.73312069735923*^9}, { 3.7331207697421885`*^9, 3.733120840437128*^9}, {3.733120897536913*^9, 3.7331208981617327`*^9}, {3.733120950307825*^9, 3.7331209687472754`*^9}, { 3.7331210145021257`*^9, 3.733121019643283*^9}, {3.73312105866333*^9, 3.7331211164194407`*^9}, 3.7331212169925804`*^9, 3.733121511882849*^9, { 3.73313538916969*^9, 3.7331354368934317`*^9}, {3.7331354941964245`*^9, 3.7331354971967516`*^9}, 3.7331356721337495`*^9, {3.73313598594795*^9, 3.733136045626433*^9}, {3.7331360791609364`*^9, 3.733136094912895*^9}, { 3.73313612515032*^9, 3.733136255523641*^9}, {3.733136286980091*^9, 3.733136311373001*^9}, {3.733136365910065*^9, 3.7331363787864265`*^9}, { 3.733136415180851*^9, 3.7331365557116456`*^9}, {3.733136629641155*^9, 3.7331366368608675`*^9}, {3.7331367168846874`*^9, 3.7331367300426655`*^9}, {3.733136761545972*^9, 3.7331367995341597`*^9}, { 3.7331368320220904`*^9, 3.7331368692916746`*^9}, {3.73313695903555*^9, 3.73313701765102*^9}, {3.7331372189690466`*^9, 3.7331372671775126`*^9}, { 3.733137326902588*^9, 3.7331373941594505`*^9}, {3.7331375441517935`*^9, 3.733137628457588*^9}, {3.7331376840728426`*^9, 3.7331377015749903`*^9}, { 3.7331385020500193`*^9, 3.7331385039879985`*^9}, {3.733138561525031*^9, 3.7331385634005165`*^9}, {3.7331457065506525`*^9, 3.733145714629631*^9}, { 3.7331457481800256`*^9, 3.7331457494145594`*^9}, {3.7331457820429187`*^9, 3.7331457829646435`*^9}, {3.7331459968966503`*^9, 3.73314605177772*^9}, 3.7331460828003397`*^9, {3.7331462354955673`*^9, 3.73314626601443*^9}, { 3.733146510540284*^9, 3.7331466409600363`*^9}, {3.7331468427313757`*^9, 3.7331469163828735`*^9}, {3.7331849739785075`*^9, 3.7331850052315197`*^9}, {3.7331850363288555`*^9, 3.7331853715674276`*^9}, {3.733185406352072*^9, 3.7331854066023936`*^9}, { 3.733185495986588*^9, 3.73318565162829*^9}, {3.733185705946556*^9, 3.7331857186038513`*^9}, {3.733185748881719*^9, 3.733185933619708*^9}, { 3.733185974452237*^9, 3.7331860514605026`*^9}, {3.7331860823072395`*^9, 3.7331860888238688`*^9}, {3.7331861485905466`*^9, 3.7331861806528893`*^9}, {3.73318632946542*^9, 3.7331866054945617`*^9}, { 3.7331866521243863`*^9, 3.733186850583209*^9}, {3.733186882211415*^9, 3.733186936510432*^9}, {3.7331870413499165`*^9, 3.7331870415840445`*^9}, { 3.7331879674988947`*^9, 3.7331880319744196`*^9}, {3.7331881651918564`*^9, 3.7331881933196564`*^9}, 3.733191086909934*^9, {3.7331911351838408`*^9, 3.733191147736865*^9}, 3.7331912484934406`*^9, {3.733365174148862*^9, 3.7333652053719177`*^9}, {3.7333652474550424`*^9, 3.73336530225986*^9}, { 3.733365345435026*^9, 3.7333654072122216`*^9}, {3.7333654661756344`*^9, 3.7333654809508104`*^9}, {3.7333655754319305`*^9, 3.7333655883196373`*^9}, {3.7333656336593266`*^9, 3.733365826529348*^9}, { 3.7333660007878046`*^9, 3.7333661259945803`*^9}, {3.733366213942363*^9, 3.7333663820292597`*^9}, {3.7333664469439106`*^9, 3.7333666851693993`*^9}, {3.7333667258927765`*^9, 3.733366848124815*^9}, { 3.733367113180627*^9, 3.733367164114697*^9}, {3.733370116949722*^9, 3.733370123356784*^9}, {3.7333701567521553`*^9, 3.73337016871292*^9}, 3.733375220779642*^9, {3.733375289256725*^9, 3.733375290146722*^9}, { 3.733375322401083*^9, 3.7333753433967476`*^9}, 3.733375419830647*^9, { 3.733375489324972*^9, 3.733375497369104*^9}, {3.7333783197434835`*^9, 3.7333785027712955`*^9}, {3.733378959210429*^9, 3.7333789691613045`*^9}, { 3.733379027665225*^9, 3.73337905657366*^9}, {3.7333791111712112`*^9, 3.7333791147258387`*^9}, {3.733379242587391*^9, 3.733379246558384*^9}, { 3.733460158370412*^9, 3.733460246098426*^9}, {3.733462208056137*^9, 3.7334622450756254`*^9}, {3.733462341023322*^9, 3.7334623997638617`*^9}, { 3.7334624555041842`*^9, 3.733462528715052*^9}, {3.733462570641363*^9, 3.733462694798615*^9}, {3.7334627467572346`*^9, 3.7334628248123674`*^9}, { 3.7334628550187387`*^9, 3.733462904055173*^9}, {3.7334629671556005`*^9, 3.733462978797456*^9}, {3.7334630620562468`*^9, 3.733463098169458*^9}, { 3.7334631405173225`*^9, 3.733463149436847*^9}, 3.7334632089587193`*^9, { 3.73346327557519*^9, 3.733463332049864*^9}, {3.733463446186983*^9, 3.733463809555442*^9}, {3.7334638492159376`*^9, 3.733463855185268*^9}, { 3.7334767716251354`*^9, 3.733476834063261*^9}, {3.7334769972290936`*^9, 3.7334770088437557`*^9}, 3.7334770567957296`*^9, {3.733477092315215*^9, 3.733477138194766*^9}, {3.7334772404366536`*^9, 3.7334772576345153`*^9}, { 3.73347729577876*^9, 3.7334773633213425`*^9}, 3.7334773954102736`*^9, { 3.733477440028474*^9, 3.733477481853801*^9}, {3.7334775213064594`*^9, 3.7334775410801506`*^9}, {3.733477571612934*^9, 3.7334775976086907`*^9}, { 3.733479205171806*^9, 3.733479270774158*^9}, {3.7334793090712047`*^9, 3.733479323235183*^9}, {3.7334793580248003`*^9, 3.7334793622794266`*^9}, { 3.7334794152394114`*^9, 3.7334794170047197`*^9}, {3.733491484942209*^9, 3.733491537425557*^9}, {3.733491634824994*^9, 3.7334916965170374`*^9}, { 3.7334918139743648`*^9, 3.733491963722246*^9}, {3.733492053507163*^9, 3.733492095873432*^9}, {3.7334922010444903`*^9, 3.73349223247291*^9}, { 3.7334922701027603`*^9, 3.733492286758114*^9}, {3.7334924280790243`*^9, 3.7334924285773735`*^9}, {3.733492494149005*^9, 3.73349267849009*^9}, { 3.733492725915759*^9, 3.733492758210832*^9}, {3.733492801429496*^9, 3.7334928541451373`*^9}, {3.7334930390778527`*^9, 3.73349307234543*^9}, { 3.733493877339528*^9, 3.7334938858486423`*^9}, {3.7334939772887754`*^9, 3.733493984944316*^9}, {3.7334941166790867`*^9, 3.7334941201545987`*^9}, { 3.733494188720145*^9, 3.733494205916135*^9}, 3.7334945908458557`*^9, { 3.7334946408391013`*^9, 3.7334946554737606`*^9}, {3.733494712228484*^9, 3.7334947173491*^9}, {3.7334947502054243`*^9, 3.7334947550749197`*^9}, { 3.733494895653963*^9, 3.7334949139510436`*^9}, {3.7334949643229437`*^9, 3.7334950046689377`*^9}, {3.7334950836861067`*^9, 3.733495090358919*^9}, { 3.733495726850687*^9, 3.7334957676115923`*^9}, {3.733495823595611*^9, 3.7334958507473063`*^9}, {3.733531269271142*^9, 3.7335313776530557`*^9}, { 3.733541219703043*^9, 3.7335412446744366`*^9}, {3.733541302852465*^9, 3.7335413136816845`*^9}, {3.7335413697032337`*^9, 3.7335413877364445`*^9}, 3.733541439632558*^9, {3.7335415319860735`*^9, 3.733541575990713*^9}, { 3.733541611244411*^9, 3.7335416687505403`*^9}, {3.7335417010195293`*^9, 3.7335417209747667`*^9}, {3.733541759775745*^9, 3.733541837315197*^9}, { 3.7335419016188717`*^9, 3.7335423069717045`*^9}, 3.7335423585396986`*^9, { 3.733542402700633*^9, 3.733542430312929*^9}, {3.7335425030862513`*^9, 3.7335425425435495`*^9}, {3.733542588923504*^9, 3.733542610081944*^9}, { 3.733542647038979*^9, 3.7335426658065877`*^9}, {3.733542717796409*^9, 3.7335427242502184`*^9}, {3.733542770348896*^9, 3.733542841892899*^9}, { 3.7335428906636853`*^9, 3.733542891351257*^9}, {3.733542934840231*^9, 3.7335430029724383`*^9}, {3.733543038038699*^9, 3.733543067229287*^9}, { 3.7335431297203255`*^9, 3.733543161520577*^9}, {3.733543194461548*^9, 3.7335432540929084`*^9}, {3.7335432896279144`*^9, 3.733543324741006*^9}, { 3.7335433678705177`*^9, 3.7335433712146716`*^9}, {3.733543416547597*^9, 3.7335434591927276`*^9}, {3.733543665339501*^9, 3.7335436937799883`*^9}, { 3.7335437704131546`*^9, 3.733543829388089*^9}, {3.7335439324459085`*^9, 3.733544022080389*^9}, {3.733544078711331*^9, 3.733544088399853*^9}, { 3.733544128982297*^9, 3.7335441600325413`*^9}, {3.7335442489012585`*^9, 3.733544604345105*^9}, {3.7335446389424615`*^9, 3.7335448189303026`*^9}, { 3.7335448726234818`*^9, 3.7335449297076445`*^9}, {3.733544973899822*^9, 3.733545007012683*^9}, {3.733545064393718*^9, 3.7335451486035585`*^9}, { 3.73354520379685*^9, 3.7335453868318377`*^9}, {3.73354545865193*^9, 3.733545492691042*^9}, {3.7335455524942303`*^9, 3.733545607453182*^9}, { 3.733545697728303*^9, 3.7335457377950926`*^9}, {3.733545797004427*^9, 3.7335458963371177`*^9}, {3.7335600445739202`*^9, 3.733560088062917*^9}, { 3.733560408903097*^9, 3.733560452829359*^9}, {3.7335605451368465`*^9, 3.7335605556220007`*^9}, {3.733560693089568*^9, 3.7335607035594864`*^9}, { 3.733561239190014*^9, 3.7335612427058396`*^9}, {3.733561312635296*^9, 3.7335613287931833`*^9}, {3.733561472343387*^9, 3.7335614887829037`*^9}, { 3.7335615554091043`*^9, 3.7335615603161535`*^9}, {3.7335616875495467`*^9, 3.733561696722621*^9}, {3.733561742118102*^9, 3.733561759948123*^9}, 3.7336328623083553`*^9, {3.733646962487833*^9, 3.733647111081254*^9}, 3.733647151088426*^9, {3.733647324093519*^9, 3.733647378394207*^9}, { 3.733647412605115*^9, 3.7336475196609955`*^9}, {3.733647565706006*^9, 3.7336476022754855`*^9}, {3.733647636405274*^9, 3.733647778494203*^9}, { 3.733647819222044*^9, 3.7336479836130247`*^9}, {3.7336482021874657`*^9, 3.733648306425503*^9}, {3.7336484232471466`*^9, 3.733648477193297*^9}, { 3.73364853750661*^9, 3.7336485385391874`*^9}, {3.733648657113475*^9, 3.7336486903701544`*^9}, {3.7336487208134737`*^9, 3.7336487763770323`*^9}, {3.7336488266999683`*^9, 3.733648877737054*^9}, { 3.7336498837046123`*^9, 3.733649897725542*^9}, 3.7340715959339457`*^9, 3.7340717631159296`*^9, {3.7449685386051035`*^9, 3.7449685889586525`*^9}, { 3.744968770326353*^9, 3.744968774937871*^9}, 3.76570692642441*^9, { 3.765706983442025*^9, 3.7657069940478077`*^9}, {3.765707081603978*^9, 3.765707218576766*^9}, {3.7657073432402773`*^9, 3.7657073596828737`*^9}, { 3.765707390879232*^9, 3.7657074162891026`*^9}, {3.7657074723330274`*^9, 3.765707487356175*^9}, {3.7657075650928235`*^9, 3.765707578757638*^9}, 3.7657674072044277`*^9, {3.765767449966214*^9, 3.7657674633232136`*^9}, { 3.7657675043697915`*^9, 3.765767864340949*^9}, {3.7657678966433263`*^9, 3.7657679003966312`*^9}, {3.765767932129229*^9, 3.7657679379148583`*^9}, { 3.7657681084580746`*^9, 3.765768178628733*^9}, {3.7657682707919188`*^9, 3.7657683129619007`*^9}, {3.765768418973206*^9, 3.765768429106756*^9}, { 3.7657684622674413`*^9, 3.765768479154067*^9}, {3.765768518072398*^9, 3.765768650333042*^9}, {3.7657687377638254`*^9, 3.7657687588782873`*^9}, { 3.765769039563476*^9, 3.765769141752368*^9}, {3.76576919660922*^9, 3.7657692312645564`*^9}, {3.7657692753250647`*^9, 3.765769286859925*^9}, { 3.765769332635785*^9, 3.7657693810321846`*^9}, {3.765769721690398*^9, 3.765769850892215*^9}, {3.7657698954904613`*^9, 3.7657699078542676`*^9}, { 3.7657699543505883`*^9, 3.7657699799114*^9}, 3.7657700377036657`*^9, 3.765770083018873*^9, {3.7657703862072783`*^9, 3.765770445975108*^9}, { 3.7657712977102222`*^9, 3.765771543996472*^9}, {3.7657716470817723`*^9, 3.765771655985817*^9}, {3.765771710816535*^9, 3.765771723516962*^9}, { 3.765771812167878*^9, 3.7657718577668653`*^9}, {3.765787548203395*^9, 3.765787563871632*^9}, {3.7657875982836933`*^9, 3.765787656301631*^9}, { 3.7657879764376545`*^9, 3.765788072300957*^9}, {3.765788167914768*^9, 3.765788174147703*^9}, {3.7657882269599333`*^9, 3.7657882422376156`*^9}, { 3.765788487323238*^9, 3.765788490461094*^9}, {3.7657885592421846`*^9, 3.7657886255167627`*^9}, {3.7657886684913006`*^9, 3.765788699772582*^9}, { 3.7658535454339027`*^9, 3.765853547121047*^9}, {3.765853585583187*^9, 3.7658535876696625`*^9}, {3.7658536294696665`*^9, 3.765853634654695*^9}, { 3.765853681762427*^9, 3.7658536912055206`*^9}, {3.7658538243303814`*^9, 3.7658538454131355`*^9}, {3.7658539157461643`*^9, 3.765854051366618*^9}, 3.7658549146636453`*^9, {3.7658549454327097`*^9, 3.7658549762144003`*^9}, { 3.7658554333652973`*^9, 3.7658554999790025`*^9}, {3.7658555611344366`*^9, 3.7658555729631147`*^9}, {3.7658572968663087`*^9, 3.7658573145137095`*^9}, {3.7658850384108715`*^9, 3.7658850474801846`*^9}, {3.7658850891956606`*^9, 3.7658851178663177`*^9}, 3.7659430922088523`*^9, {3.766116011153117*^9, 3.766116022737113*^9}, { 3.7664753933295326`*^9, 3.7664757716641407`*^9}, {3.7664759605654993`*^9, 3.7664759688028593`*^9}, {3.7664760085309386`*^9, 3.766476010038458*^9}, { 3.766476138743503*^9, 3.766476143574604*^9}, 3.7664764030747433`*^9, 3.766476448999195*^9, {3.7664795633889008`*^9, 3.7664795678199263`*^9}, { 3.7664798747776756`*^9, 3.766479878585684*^9}, {3.7664799975477943`*^9, 3.766480007574602*^9}, {3.7664820589039545`*^9, 3.766482062864457*^9}, 3.7665403455127153`*^9, {3.766541028143508*^9, 3.766541033095478*^9}, { 3.7665416737998805`*^9, 3.7665418728472652`*^9}, {3.766541933535928*^9, 3.7665419443617644`*^9}, {3.7667415255470357`*^9, 3.76674154015712*^9}, { 3.7668889973044024`*^9, 3.7668890069739532`*^9}, 3.7866789982853584`*^9, { 3.786679036453455*^9, 3.7866790523570843`*^9}, {3.7866790953318987`*^9, 3.786679099544505*^9}, {3.7866791488372993`*^9, 3.7866791497233343`*^9}, { 3.7866791849490194`*^9, 3.7866791862255898`*^9}, {3.786679494212338*^9, 3.786679550404069*^9}, {3.7873084130307207`*^9, 3.787308461871894*^9}, { 3.787308532613593*^9, 3.787308535659466*^9}, {3.7873094152542315`*^9, 3.787309503626961*^9}, {3.787309542481*^9, 3.787309574889223*^9}, { 3.816934561209655*^9, 3.8169345722579055`*^9}, {3.816934674669306*^9, 3.816934676899186*^9}, 3.816934766676038*^9, {3.8171925549372654`*^9, 3.8171925604585485`*^9}, {3.8171926292039795`*^9, 3.8171926580316625`*^9}, {3.817192894555258*^9, 3.817192895360199*^9}, { 3.8171929556676474`*^9, 3.8171929673054504`*^9}, {3.8171930689715395`*^9, 3.8171930895778117`*^9}, {3.8185894534978056`*^9, 3.8185894674326057`*^9}, {3.81858952107568*^9, 3.8185895502488403`*^9}, { 3.8185896190358257`*^9, 3.8185896196263103`*^9}, {3.8185901408166056`*^9, 3.8185901409801383`*^9}, {3.8185903986528263`*^9, 3.8185903990318165`*^9}, {3.818590582541429*^9, 3.8185905834011307`*^9}, { 3.8506164845135922`*^9, 3.850616507912134*^9}, {3.851044745362073*^9, 3.851044783024127*^9}}, CellLabel-> "In[400]:=",ExpressionUUID->"f34cfcc1-81a3-410c-876c-d2e0cf682381"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"DISPLACEMENT", " ", "ANALYSIS"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"sol", "=", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "//.", "val"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SHOW3D", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "100"}], "}"}], ",", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "//.", "val"}], " ", "/.", "sol"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.7331065052935543`*^9, 3.7331065455132427`*^9}, { 3.7331065985294237`*^9, 3.7331066038054595`*^9}, {3.7331169427386923`*^9, 3.7331170722995424`*^9}, {3.733117684451476*^9, 3.7331177032503495`*^9}, { 3.7331179347590604`*^9, 3.733118054709407*^9}, {3.7331180944008336`*^9, 3.7331183637373*^9}, {3.7331184294476814`*^9, 3.7331184669670315`*^9}, { 3.7331186831457067`*^9, 3.7331186835208015`*^9}, {3.7331187877505193`*^9, 3.7331188031112776`*^9}, {3.7331189820573163`*^9, 3.7331190570183573`*^9}, {3.7331204383732452`*^9, 3.7331204673922415`*^9}, {3.733120613813942*^9, 3.73312069735923*^9}, { 3.7331207697421885`*^9, 3.733120840437128*^9}, {3.733120897536913*^9, 3.7331208981617327`*^9}, {3.733120950307825*^9, 3.7331209687472754`*^9}, { 3.7331210145021257`*^9, 3.733121019643283*^9}, {3.73312105866333*^9, 3.7331211164194407`*^9}, 3.7331212169925804`*^9, 3.733121511882849*^9, { 3.73313538916969*^9, 3.7331354368934317`*^9}, {3.7331354941964245`*^9, 3.7331354971967516`*^9}, 3.7331356721337495`*^9, {3.73313598594795*^9, 3.733136045626433*^9}, {3.7331360791609364`*^9, 3.733136094912895*^9}, { 3.73313612515032*^9, 3.733136255523641*^9}, {3.733136286980091*^9, 3.733136311373001*^9}, {3.733136365910065*^9, 3.7331363787864265`*^9}, { 3.733136415180851*^9, 3.7331365557116456`*^9}, {3.733136629641155*^9, 3.7331366368608675`*^9}, {3.7331367168846874`*^9, 3.7331367300426655`*^9}, {3.733136761545972*^9, 3.7331367995341597`*^9}, { 3.7331368320220904`*^9, 3.7331368692916746`*^9}, {3.73313695903555*^9, 3.73313701765102*^9}, {3.7331372189690466`*^9, 3.7331372671775126`*^9}, { 3.733137326902588*^9, 3.7331373941594505`*^9}, {3.7331375441517935`*^9, 3.733137628457588*^9}, {3.7331376840728426`*^9, 3.7331377015749903`*^9}, { 3.7331385020500193`*^9, 3.7331385039879985`*^9}, {3.733138561525031*^9, 3.7331385634005165`*^9}, {3.7331457065506525`*^9, 3.733145714629631*^9}, { 3.7331457481800256`*^9, 3.7331457494145594`*^9}, {3.7331457820429187`*^9, 3.7331457829646435`*^9}, {3.7331459968966503`*^9, 3.73314605177772*^9}, 3.7331460828003397`*^9, {3.7331462354955673`*^9, 3.73314626601443*^9}, { 3.733146510540284*^9, 3.7331466409600363`*^9}, {3.7331468427313757`*^9, 3.7331469163828735`*^9}, {3.7331849739785075`*^9, 3.7331850052315197`*^9}, {3.7331850363288555`*^9, 3.7331853715674276`*^9}, {3.733185406352072*^9, 3.7331854066023936`*^9}, { 3.733185495986588*^9, 3.73318565162829*^9}, {3.733185705946556*^9, 3.7331857186038513`*^9}, {3.733185748881719*^9, 3.733185933619708*^9}, { 3.733185974452237*^9, 3.7331860514605026`*^9}, {3.7331860823072395`*^9, 3.7331860888238688`*^9}, {3.7331861485905466`*^9, 3.7331861806528893`*^9}, {3.73318632946542*^9, 3.7331866054945617`*^9}, { 3.7331866521243863`*^9, 3.733186850583209*^9}, {3.733186882211415*^9, 3.733186936510432*^9}, {3.7331870413499165`*^9, 3.7331870415840445`*^9}, { 3.7331879674988947`*^9, 3.7331880319744196`*^9}, {3.7331881651918564`*^9, 3.7331881933196564`*^9}, 3.733191086909934*^9, {3.7331911351838408`*^9, 3.733191147736865*^9}, 3.7331912484934406`*^9, {3.733365174148862*^9, 3.7333652053719177`*^9}, {3.7333652474550424`*^9, 3.73336530225986*^9}, { 3.733365345435026*^9, 3.7333654072122216`*^9}, {3.7333654661756344`*^9, 3.7333654809508104`*^9}, {3.7333655754319305`*^9, 3.7333655883196373`*^9}, {3.7333656336593266`*^9, 3.733365826529348*^9}, { 3.7333660007878046`*^9, 3.7333661259945803`*^9}, {3.733366213942363*^9, 3.7333663820292597`*^9}, {3.7333664469439106`*^9, 3.7333666851693993`*^9}, {3.7333667258927765`*^9, 3.733366848124815*^9}, { 3.733367113180627*^9, 3.733367164114697*^9}, {3.733370116949722*^9, 3.733370123356784*^9}, {3.7333701567521553`*^9, 3.73337016871292*^9}, 3.733375220779642*^9, {3.733375289256725*^9, 3.733375290146722*^9}, { 3.733375322401083*^9, 3.7333753433967476`*^9}, 3.733375419830647*^9, { 3.733375489324972*^9, 3.733375497369104*^9}, {3.7333783197434835`*^9, 3.7333785027712955`*^9}, {3.733378959210429*^9, 3.7333789691613045`*^9}, { 3.733379027665225*^9, 3.73337905657366*^9}, {3.7333791111712112`*^9, 3.7333791147258387`*^9}, {3.733379242587391*^9, 3.733379246558384*^9}, { 3.733460158370412*^9, 3.733460246098426*^9}, {3.733462208056137*^9, 3.7334622450756254`*^9}, {3.733462341023322*^9, 3.7334623997638617`*^9}, { 3.7334624555041842`*^9, 3.733462528715052*^9}, {3.733462570641363*^9, 3.733462694798615*^9}, {3.7334627467572346`*^9, 3.7334628248123674`*^9}, { 3.7334628550187387`*^9, 3.733462904055173*^9}, {3.7334629671556005`*^9, 3.733462978797456*^9}, {3.7334630620562468`*^9, 3.733463098169458*^9}, { 3.7334631405173225`*^9, 3.733463149436847*^9}, 3.7334632089587193`*^9, { 3.73346327557519*^9, 3.733463332049864*^9}, {3.733463446186983*^9, 3.733463809555442*^9}, {3.7334638492159376`*^9, 3.733463855185268*^9}, { 3.7334767716251354`*^9, 3.733476834063261*^9}, {3.7334769972290936`*^9, 3.7334770088437557`*^9}, 3.7334770567957296`*^9, {3.733477092315215*^9, 3.733477138194766*^9}, {3.7334772404366536`*^9, 3.7334772576345153`*^9}, { 3.73347729577876*^9, 3.7334773633213425`*^9}, 3.7334773954102736`*^9, { 3.733477440028474*^9, 3.733477481853801*^9}, {3.7334775213064594`*^9, 3.7334775410801506`*^9}, {3.733477571612934*^9, 3.7334775976086907`*^9}, { 3.733479205171806*^9, 3.733479270774158*^9}, {3.7334793090712047`*^9, 3.733479323235183*^9}, {3.7334793580248003`*^9, 3.7334793622794266`*^9}, { 3.7334794152394114`*^9, 3.7334794170047197`*^9}, {3.733491484942209*^9, 3.733491537425557*^9}, {3.733491634824994*^9, 3.7334916965170374`*^9}, { 3.7334918139743648`*^9, 3.733491963722246*^9}, {3.733492053507163*^9, 3.733492095873432*^9}, {3.7334922010444903`*^9, 3.73349223247291*^9}, { 3.7334922701027603`*^9, 3.733492286758114*^9}, {3.7334924280790243`*^9, 3.7334924285773735`*^9}, {3.733492494149005*^9, 3.73349267849009*^9}, { 3.733492725915759*^9, 3.733492758210832*^9}, {3.733492801429496*^9, 3.7334928541451373`*^9}, {3.7334930390778527`*^9, 3.73349307234543*^9}, { 3.733493877339528*^9, 3.7334938858486423`*^9}, {3.7334939772887754`*^9, 3.733493984944316*^9}, {3.7334941166790867`*^9, 3.7334941201545987`*^9}, { 3.733494188720145*^9, 3.733494205916135*^9}, 3.7334945908458557`*^9, { 3.7334946408391013`*^9, 3.7334946554737606`*^9}, {3.733494712228484*^9, 3.7334947173491*^9}, {3.7334947502054243`*^9, 3.7334947550749197`*^9}, { 3.733494895653963*^9, 3.7334949139510436`*^9}, {3.7334949643229437`*^9, 3.7334950046689377`*^9}, {3.7334950836861067`*^9, 3.733495090358919*^9}, { 3.733495726850687*^9, 3.7334957676115923`*^9}, {3.733495823595611*^9, 3.7334958507473063`*^9}, {3.733531269271142*^9, 3.7335313776530557`*^9}, { 3.733541219703043*^9, 3.7335412446744366`*^9}, {3.733541302852465*^9, 3.7335413136816845`*^9}, {3.7335413697032337`*^9, 3.7335413877364445`*^9}, 3.733541439632558*^9, {3.7335415319860735`*^9, 3.733541575990713*^9}, { 3.733541611244411*^9, 3.7335416687505403`*^9}, {3.7335417010195293`*^9, 3.7335417209747667`*^9}, {3.733541759775745*^9, 3.733541837315197*^9}, { 3.7335419016188717`*^9, 3.7335423069717045`*^9}, 3.7335423585396986`*^9, { 3.733542402700633*^9, 3.733542430312929*^9}, {3.7335425030862513`*^9, 3.7335425425435495`*^9}, {3.733542588923504*^9, 3.733542610081944*^9}, { 3.733542647038979*^9, 3.7335426658065877`*^9}, {3.733542717796409*^9, 3.7335427242502184`*^9}, {3.733542770348896*^9, 3.733542841892899*^9}, { 3.7335428906636853`*^9, 3.733542891351257*^9}, {3.733542934840231*^9, 3.7335430029724383`*^9}, {3.733543038038699*^9, 3.733543067229287*^9}, { 3.7335431297203255`*^9, 3.733543161520577*^9}, {3.733543194461548*^9, 3.7335432540929084`*^9}, {3.7335432896279144`*^9, 3.733543324741006*^9}, { 3.7335433678705177`*^9, 3.7335433712146716`*^9}, {3.733543416547597*^9, 3.7335434591927276`*^9}, {3.733543665339501*^9, 3.7335436937799883`*^9}, { 3.7335437704131546`*^9, 3.733543829388089*^9}, {3.7335439324459085`*^9, 3.733544022080389*^9}, {3.733544078711331*^9, 3.733544088399853*^9}, { 3.733544128982297*^9, 3.7335441600325413`*^9}, {3.7335442489012585`*^9, 3.733544604345105*^9}, {3.7335446389424615`*^9, 3.7335448189303026`*^9}, { 3.7335448726234818`*^9, 3.7335449297076445`*^9}, {3.733544973899822*^9, 3.733545007012683*^9}, {3.733545064393718*^9, 3.7335451486035585`*^9}, { 3.73354520379685*^9, 3.7335453868318377`*^9}, {3.73354545865193*^9, 3.733545492691042*^9}, {3.7335455524942303`*^9, 3.733545607453182*^9}, { 3.733545697728303*^9, 3.7335457377950926`*^9}, {3.733545797004427*^9, 3.7335458963371177`*^9}, {3.7335600445739202`*^9, 3.733560088062917*^9}, { 3.733560408903097*^9, 3.733560452829359*^9}, {3.7335605451368465`*^9, 3.7335605556220007`*^9}, {3.733560693089568*^9, 3.7335607035594864`*^9}, { 3.733561239190014*^9, 3.7335612427058396`*^9}, {3.733561312635296*^9, 3.7335613287931833`*^9}, {3.733561472343387*^9, 3.7335614887829037`*^9}, { 3.7335615554091043`*^9, 3.7335615603161535`*^9}, {3.7335616875495467`*^9, 3.733561696722621*^9}, {3.733561742118102*^9, 3.733561759948123*^9}, 3.7336328623083553`*^9, {3.733646962487833*^9, 3.733647111081254*^9}, 3.733647151088426*^9, {3.733647324093519*^9, 3.733647378394207*^9}, { 3.733647412605115*^9, 3.7336475196609955`*^9}, {3.733647565706006*^9, 3.7336476022754855`*^9}, {3.733647636405274*^9, 3.733647778494203*^9}, { 3.733647819222044*^9, 3.7336479836130247`*^9}, {3.7336482021874657`*^9, 3.733648306425503*^9}, {3.7336484232471466`*^9, 3.733648477193297*^9}, { 3.73364853750661*^9, 3.7336485385391874`*^9}, {3.733648657113475*^9, 3.7336486903701544`*^9}, {3.7336487208134737`*^9, 3.7336487763770323`*^9}, {3.7336488266999683`*^9, 3.733648877737054*^9}, { 3.7336498837046123`*^9, 3.733649897725542*^9}, 3.7340715959339457`*^9, 3.7340717631159296`*^9, {3.7449685386051035`*^9, 3.7449685889586525`*^9}, { 3.744968770326353*^9, 3.744968774937871*^9}, 3.76570692642441*^9, { 3.765706983442025*^9, 3.7657069940478077`*^9}, {3.765707081603978*^9, 3.765707218576766*^9}, {3.7657073432402773`*^9, 3.7657073596828737`*^9}, { 3.765707390879232*^9, 3.7657074162891026`*^9}, {3.7657074723330274`*^9, 3.765707487356175*^9}, {3.7657075650928235`*^9, 3.765707578757638*^9}, 3.7657674072044277`*^9, {3.765767449966214*^9, 3.7657674633232136`*^9}, { 3.7657675043697915`*^9, 3.765767864340949*^9}, {3.7657678966433263`*^9, 3.7657679003966312`*^9}, {3.765767932129229*^9, 3.7657679379148583`*^9}, { 3.7657681084580746`*^9, 3.765768178628733*^9}, {3.7657682707919188`*^9, 3.7657683129619007`*^9}, {3.765768418973206*^9, 3.765768429106756*^9}, { 3.7657684622674413`*^9, 3.765768479154067*^9}, {3.765768518072398*^9, 3.765768650333042*^9}, {3.7657687377638254`*^9, 3.7657687588782873`*^9}, { 3.765769039563476*^9, 3.765769141752368*^9}, {3.76576919660922*^9, 3.7657692312645564`*^9}, {3.7657692753250647`*^9, 3.765769286859925*^9}, { 3.765769332635785*^9, 3.7657693810321846`*^9}, {3.765769721690398*^9, 3.765769850892215*^9}, {3.7657698954904613`*^9, 3.7657699078542676`*^9}, { 3.7657699543505883`*^9, 3.7657699799114*^9}, 3.7657700377036657`*^9, 3.765770083018873*^9, {3.7657703862072783`*^9, 3.765770445975108*^9}, { 3.7657712977102222`*^9, 3.765771543996472*^9}, {3.7657716470817723`*^9, 3.765771655985817*^9}, {3.765771710816535*^9, 3.765771723516962*^9}, { 3.765771812167878*^9, 3.7657718577668653`*^9}, {3.765787548203395*^9, 3.765787563871632*^9}, {3.7657875982836933`*^9, 3.765787656301631*^9}, { 3.7657879764376545`*^9, 3.765788072300957*^9}, {3.765788167914768*^9, 3.765788174147703*^9}, {3.7657882269599333`*^9, 3.7657882422376156`*^9}, { 3.765788487323238*^9, 3.765788490461094*^9}, {3.7657885592421846`*^9, 3.7657886255167627`*^9}, {3.7657886684913006`*^9, 3.765788699772582*^9}, { 3.7658535454339027`*^9, 3.765853547121047*^9}, {3.765853585583187*^9, 3.7658535876696625`*^9}, {3.7658536294696665`*^9, 3.765853634654695*^9}, { 3.765853681762427*^9, 3.7658536912055206`*^9}, {3.7658538243303814`*^9, 3.7658538454131355`*^9}, {3.7658539157461643`*^9, 3.765854051366618*^9}, 3.7658549146636453`*^9, {3.7658549454327097`*^9, 3.7658549762144003`*^9}, { 3.7658554333652973`*^9, 3.7658554999790025`*^9}, {3.7658555611344366`*^9, 3.7658555729631147`*^9}, {3.7658572968663087`*^9, 3.7658573145137095`*^9}, {3.7658850384108715`*^9, 3.7658850474801846`*^9}, {3.7658850891956606`*^9, 3.7658851178663177`*^9}, 3.7659430922088523`*^9, {3.766116011153117*^9, 3.766116022737113*^9}, { 3.7664753933295326`*^9, 3.7664757716641407`*^9}, {3.7664759605654993`*^9, 3.7664759688028593`*^9}, {3.7664760085309386`*^9, 3.766476010038458*^9}, { 3.766476138743503*^9, 3.766476143574604*^9}, 3.7664764030747433`*^9, 3.766476448999195*^9, {3.7664795633889008`*^9, 3.7664795678199263`*^9}, { 3.7664798747776756`*^9, 3.766479878585684*^9}, {3.7664799975477943`*^9, 3.766480007574602*^9}, {3.7664820589039545`*^9, 3.766482062864457*^9}, 3.7665403455127153`*^9, {3.766541028143508*^9, 3.766541033095478*^9}, { 3.7665416737998805`*^9, 3.7665418728472652`*^9}, {3.766541933535928*^9, 3.7665419443617644`*^9}, {3.7667415255470357`*^9, 3.76674154015712*^9}, { 3.7668889973044024`*^9, 3.7668890069739532`*^9}, 3.7866789982853584`*^9, { 3.786679036453455*^9, 3.7866790523570843`*^9}, {3.7866790953318987`*^9, 3.786679099544505*^9}, {3.7866791488372993`*^9, 3.7866791497233343`*^9}, { 3.7866791849490194`*^9, 3.7866791862255898`*^9}, {3.786679494212338*^9, 3.786679550404069*^9}, {3.7873084130307207`*^9, 3.787308461871894*^9}, { 3.787308532613593*^9, 3.787308535659466*^9}, {3.7873094152542315`*^9, 3.787309503626961*^9}, {3.787309542481*^9, 3.787309574889223*^9}, { 3.816934561209655*^9, 3.8169345722579055`*^9}, {3.816934674669306*^9, 3.816934676899186*^9}, 3.816934766676038*^9, {3.8171925549372654`*^9, 3.8171925832847276`*^9}, 3.817217114381849*^9, 3.8185893395921226`*^9, { 3.818589478095451*^9, 3.8185894784412193`*^9}, {3.818590084919468*^9, 3.8185900891400423`*^9}, {3.8196010320388565`*^9, 3.8196010412961025`*^9}}, CellLabel-> "In[407]:=",ExpressionUUID->"d472a1b3-51e1-4374-b2af-827682c399ad"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"(*", RowBox[{"RIGIDITY", " ", "CALCULATION"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"k", "=", RowBox[{ RowBox[{"(", RowBox[{"F", "/", RowBox[{"(", RowBox[{ RowBox[{"Mean", "[", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"uZ", "[", "#", "]"}], "&"}], ",", "bnd1"}], "]"}], "/.", "sol"}], "]"}], "*", "1000"}], ")"}]}], ")"}], "//.", "val"}]}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.7331065052935543`*^9, 3.7331065455132427`*^9}, { 3.7331065985294237`*^9, 3.7331066038054595`*^9}, {3.7331169427386923`*^9, 3.7331170722995424`*^9}, {3.733117684451476*^9, 3.7331177032503495`*^9}, { 3.7331179347590604`*^9, 3.733118054709407*^9}, {3.7331180944008336`*^9, 3.7331183637373*^9}, {3.7331184294476814`*^9, 3.7331184669670315`*^9}, { 3.7331186831457067`*^9, 3.7331186835208015`*^9}, {3.7331187877505193`*^9, 3.7331188031112776`*^9}, {3.7331189820573163`*^9, 3.7331190570183573`*^9}, {3.7331204383732452`*^9, 3.7331204673922415`*^9}, {3.733120613813942*^9, 3.73312069735923*^9}, { 3.7331207697421885`*^9, 3.733120840437128*^9}, {3.733120897536913*^9, 3.7331208981617327`*^9}, {3.733120950307825*^9, 3.7331209687472754`*^9}, { 3.7331210145021257`*^9, 3.733121019643283*^9}, {3.73312105866333*^9, 3.7331211164194407`*^9}, 3.7331212169925804`*^9, 3.733121511882849*^9, { 3.73313538916969*^9, 3.7331354368934317`*^9}, {3.7331354941964245`*^9, 3.7331354971967516`*^9}, 3.7331356721337495`*^9, {3.73313598594795*^9, 3.733136045626433*^9}, {3.7331360791609364`*^9, 3.733136094912895*^9}, { 3.73313612515032*^9, 3.733136255523641*^9}, {3.733136286980091*^9, 3.733136311373001*^9}, {3.733136365910065*^9, 3.7331363787864265`*^9}, { 3.733136415180851*^9, 3.7331365557116456`*^9}, {3.733136629641155*^9, 3.7331366368608675`*^9}, {3.7331367168846874`*^9, 3.7331367300426655`*^9}, {3.733136761545972*^9, 3.7331367995341597`*^9}, { 3.7331368320220904`*^9, 3.7331368692916746`*^9}, {3.73313695903555*^9, 3.73313701765102*^9}, {3.7331372189690466`*^9, 3.7331372671775126`*^9}, { 3.733137326902588*^9, 3.7331373941594505`*^9}, {3.7331375441517935`*^9, 3.733137628457588*^9}, {3.7331376840728426`*^9, 3.7331377015749903`*^9}, { 3.7331385020500193`*^9, 3.7331385039879985`*^9}, {3.733138561525031*^9, 3.7331385634005165`*^9}, {3.7331457065506525`*^9, 3.733145714629631*^9}, { 3.7331457481800256`*^9, 3.7331457494145594`*^9}, {3.7331457820429187`*^9, 3.7331457829646435`*^9}, {3.7331459968966503`*^9, 3.73314605177772*^9}, 3.7331460828003397`*^9, {3.7331462354955673`*^9, 3.73314626601443*^9}, { 3.733146510540284*^9, 3.7331466409600363`*^9}, {3.7331468427313757`*^9, 3.7331469163828735`*^9}, {3.7331849739785075`*^9, 3.7331850052315197`*^9}, {3.7331850363288555`*^9, 3.7331853715674276`*^9}, {3.733185406352072*^9, 3.7331854066023936`*^9}, { 3.733185495986588*^9, 3.73318565162829*^9}, {3.733185705946556*^9, 3.7331857186038513`*^9}, {3.733185748881719*^9, 3.733185933619708*^9}, { 3.733185974452237*^9, 3.7331860514605026`*^9}, {3.7331860823072395`*^9, 3.7331860888238688`*^9}, {3.7331861485905466`*^9, 3.7331861806528893`*^9}, {3.73318632946542*^9, 3.7331866054945617`*^9}, { 3.7331866521243863`*^9, 3.733186850583209*^9}, {3.733186882211415*^9, 3.733186936510432*^9}, {3.7331870413499165`*^9, 3.7331870415840445`*^9}, { 3.7331879674988947`*^9, 3.7331880319744196`*^9}, {3.7331881651918564`*^9, 3.7331881933196564`*^9}, 3.733191086909934*^9, {3.7331911351838408`*^9, 3.733191147736865*^9}, 3.7331912484934406`*^9, {3.733365174148862*^9, 3.7333652053719177`*^9}, {3.7333652474550424`*^9, 3.73336530225986*^9}, { 3.733365345435026*^9, 3.7333654072122216`*^9}, {3.7333654661756344`*^9, 3.7333654809508104`*^9}, {3.7333655754319305`*^9, 3.7333655883196373`*^9}, {3.7333656336593266`*^9, 3.733365826529348*^9}, { 3.7333660007878046`*^9, 3.7333661259945803`*^9}, {3.733366213942363*^9, 3.7333663820292597`*^9}, {3.7333664469439106`*^9, 3.7333666851693993`*^9}, {3.7333667258927765`*^9, 3.733366848124815*^9}, { 3.733367113180627*^9, 3.733367164114697*^9}, {3.733370116949722*^9, 3.733370123356784*^9}, {3.7333701567521553`*^9, 3.73337016871292*^9}, 3.733375220779642*^9, {3.733375289256725*^9, 3.733375290146722*^9}, { 3.733375322401083*^9, 3.7333753433967476`*^9}, 3.733375419830647*^9, { 3.733375489324972*^9, 3.733375497369104*^9}, {3.7333783197434835`*^9, 3.7333785027712955`*^9}, {3.733378959210429*^9, 3.7333789691613045`*^9}, { 3.733379027665225*^9, 3.73337905657366*^9}, {3.7333791111712112`*^9, 3.7333791147258387`*^9}, {3.733379242587391*^9, 3.733379246558384*^9}, { 3.733460158370412*^9, 3.733460246098426*^9}, {3.733462208056137*^9, 3.7334622450756254`*^9}, {3.733462341023322*^9, 3.7334623997638617`*^9}, { 3.7334624555041842`*^9, 3.733462528715052*^9}, {3.733462570641363*^9, 3.733462694798615*^9}, {3.7334627467572346`*^9, 3.7334628248123674`*^9}, { 3.7334628550187387`*^9, 3.733462904055173*^9}, {3.7334629671556005`*^9, 3.733462978797456*^9}, {3.7334630620562468`*^9, 3.733463098169458*^9}, { 3.7334631405173225`*^9, 3.733463149436847*^9}, 3.7334632089587193`*^9, { 3.73346327557519*^9, 3.733463332049864*^9}, {3.733463446186983*^9, 3.733463809555442*^9}, {3.7334638492159376`*^9, 3.733463855185268*^9}, { 3.7334767716251354`*^9, 3.733476834063261*^9}, {3.7334769972290936`*^9, 3.7334770088437557`*^9}, 3.7334770567957296`*^9, {3.733477092315215*^9, 3.733477138194766*^9}, {3.7334772404366536`*^9, 3.7334772576345153`*^9}, { 3.73347729577876*^9, 3.7334773633213425`*^9}, 3.7334773954102736`*^9, { 3.733477440028474*^9, 3.733477481853801*^9}, {3.7334775213064594`*^9, 3.7334775410801506`*^9}, {3.733477571612934*^9, 3.7334775976086907`*^9}, { 3.733479205171806*^9, 3.733479270774158*^9}, {3.7334793090712047`*^9, 3.733479323235183*^9}, {3.7334793580248003`*^9, 3.7334793622794266`*^9}, { 3.7334794152394114`*^9, 3.7334794170047197`*^9}, {3.733491484942209*^9, 3.733491537425557*^9}, {3.733491634824994*^9, 3.7334916965170374`*^9}, { 3.7334918139743648`*^9, 3.733491963722246*^9}, {3.733492053507163*^9, 3.733492095873432*^9}, {3.7334922010444903`*^9, 3.73349223247291*^9}, { 3.7334922701027603`*^9, 3.733492286758114*^9}, {3.7334924280790243`*^9, 3.7334924285773735`*^9}, {3.733492494149005*^9, 3.73349267849009*^9}, { 3.733492725915759*^9, 3.733492758210832*^9}, {3.733492801429496*^9, 3.7334928541451373`*^9}, {3.7334930390778527`*^9, 3.73349307234543*^9}, { 3.733493877339528*^9, 3.7334938858486423`*^9}, {3.7334939772887754`*^9, 3.733493984944316*^9}, {3.7334941166790867`*^9, 3.7334941201545987`*^9}, { 3.733494188720145*^9, 3.733494205916135*^9}, 3.7334945908458557`*^9, { 3.7334946408391013`*^9, 3.7334946554737606`*^9}, {3.733494712228484*^9, 3.7334947173491*^9}, {3.7334947502054243`*^9, 3.7334947550749197`*^9}, { 3.733494895653963*^9, 3.7334949139510436`*^9}, {3.7334949643229437`*^9, 3.7334950046689377`*^9}, {3.7334950836861067`*^9, 3.733495090358919*^9}, { 3.733495726850687*^9, 3.7334957676115923`*^9}, {3.733495823595611*^9, 3.7334958507473063`*^9}, {3.733531269271142*^9, 3.7335313776530557`*^9}, { 3.733541219703043*^9, 3.7335412446744366`*^9}, {3.733541302852465*^9, 3.7335413136816845`*^9}, {3.7335413697032337`*^9, 3.7335413877364445`*^9}, 3.733541439632558*^9, {3.7335415319860735`*^9, 3.733541575990713*^9}, { 3.733541611244411*^9, 3.7335416687505403`*^9}, {3.7335417010195293`*^9, 3.7335417209747667`*^9}, {3.733541759775745*^9, 3.733541837315197*^9}, { 3.7335419016188717`*^9, 3.7335423069717045`*^9}, 3.7335423585396986`*^9, { 3.733542402700633*^9, 3.733542430312929*^9}, {3.7335425030862513`*^9, 3.7335425425435495`*^9}, {3.733542588923504*^9, 3.733542610081944*^9}, { 3.733542647038979*^9, 3.7335426658065877`*^9}, {3.733542717796409*^9, 3.7335427242502184`*^9}, {3.733542770348896*^9, 3.733542841892899*^9}, { 3.7335428906636853`*^9, 3.733542891351257*^9}, {3.733542934840231*^9, 3.7335430029724383`*^9}, {3.733543038038699*^9, 3.733543067229287*^9}, { 3.7335431297203255`*^9, 3.733543161520577*^9}, {3.733543194461548*^9, 3.7335432540929084`*^9}, {3.7335432896279144`*^9, 3.733543324741006*^9}, { 3.7335433678705177`*^9, 3.7335433712146716`*^9}, {3.733543416547597*^9, 3.7335434591927276`*^9}, {3.733543665339501*^9, 3.7335436937799883`*^9}, { 3.7335437704131546`*^9, 3.733543829388089*^9}, {3.7335439324459085`*^9, 3.733544022080389*^9}, {3.733544078711331*^9, 3.733544088399853*^9}, { 3.733544128982297*^9, 3.7335441600325413`*^9}, {3.7335442489012585`*^9, 3.733544604345105*^9}, {3.7335446389424615`*^9, 3.7335448189303026`*^9}, { 3.7335448726234818`*^9, 3.7335449297076445`*^9}, {3.733544973899822*^9, 3.733545007012683*^9}, {3.733545064393718*^9, 3.7335451486035585`*^9}, { 3.73354520379685*^9, 3.7335453868318377`*^9}, {3.73354545865193*^9, 3.733545492691042*^9}, {3.7335455524942303`*^9, 3.733545607453182*^9}, { 3.733545697728303*^9, 3.7335457377950926`*^9}, {3.733545797004427*^9, 3.7335458963371177`*^9}, {3.7335600445739202`*^9, 3.733560088062917*^9}, { 3.733560408903097*^9, 3.733560452829359*^9}, {3.7335605451368465`*^9, 3.7335605556220007`*^9}, {3.733560693089568*^9, 3.7335607035594864`*^9}, { 3.733561239190014*^9, 3.7335612427058396`*^9}, {3.733561312635296*^9, 3.7335613287931833`*^9}, {3.733561472343387*^9, 3.7335614887829037`*^9}, { 3.7335615554091043`*^9, 3.7335615603161535`*^9}, {3.7335616875495467`*^9, 3.733561696722621*^9}, {3.733561742118102*^9, 3.733561759948123*^9}, 3.7336328623083553`*^9, {3.733646962487833*^9, 3.733647111081254*^9}, 3.733647151088426*^9, {3.733647324093519*^9, 3.733647378394207*^9}, { 3.733647412605115*^9, 3.7336475196609955`*^9}, {3.733647565706006*^9, 3.7336476022754855`*^9}, {3.733647636405274*^9, 3.733647778494203*^9}, { 3.733647819222044*^9, 3.7336479836130247`*^9}, {3.7336482021874657`*^9, 3.733648306425503*^9}, {3.7336484232471466`*^9, 3.733648477193297*^9}, { 3.73364853750661*^9, 3.7336485385391874`*^9}, {3.733648657113475*^9, 3.7336486903701544`*^9}, {3.7336487208134737`*^9, 3.7336487763770323`*^9}, {3.7336488266999683`*^9, 3.733648877737054*^9}, { 3.7336498837046123`*^9, 3.733649897725542*^9}, 3.7340715959339457`*^9, 3.7340717631159296`*^9, {3.7449685386051035`*^9, 3.7449685889586525`*^9}, { 3.744968770326353*^9, 3.744968774937871*^9}, 3.76570692642441*^9, { 3.765706983442025*^9, 3.7657069940478077`*^9}, {3.765707081603978*^9, 3.765707218576766*^9}, {3.7657073432402773`*^9, 3.7657073596828737`*^9}, { 3.765707390879232*^9, 3.7657074162891026`*^9}, {3.7657074723330274`*^9, 3.765707487356175*^9}, {3.7657075650928235`*^9, 3.765707578757638*^9}, 3.7657674072044277`*^9, {3.765767449966214*^9, 3.7657674633232136`*^9}, { 3.7657675043697915`*^9, 3.765767864340949*^9}, {3.7657678966433263`*^9, 3.7657679003966312`*^9}, {3.765767932129229*^9, 3.7657679379148583`*^9}, { 3.7657681084580746`*^9, 3.765768178628733*^9}, {3.7657682707919188`*^9, 3.7657683129619007`*^9}, {3.765768418973206*^9, 3.765768429106756*^9}, { 3.7657684622674413`*^9, 3.765768479154067*^9}, {3.765768518072398*^9, 3.765768650333042*^9}, {3.7657687377638254`*^9, 3.7657687588782873`*^9}, { 3.765769039563476*^9, 3.765769141752368*^9}, {3.76576919660922*^9, 3.7657692312645564`*^9}, {3.7657692753250647`*^9, 3.765769286859925*^9}, { 3.765769332635785*^9, 3.7657693810321846`*^9}, {3.765769721690398*^9, 3.765769850892215*^9}, {3.7657698954904613`*^9, 3.7657699078542676`*^9}, { 3.7657699543505883`*^9, 3.7657699799114*^9}, 3.7657700377036657`*^9, 3.765770083018873*^9, {3.7657703862072783`*^9, 3.765770445975108*^9}, { 3.7657712977102222`*^9, 3.765771543996472*^9}, {3.7657716470817723`*^9, 3.765771655985817*^9}, {3.765771710816535*^9, 3.765771723516962*^9}, { 3.765771812167878*^9, 3.7657718577668653`*^9}, {3.765787548203395*^9, 3.765787563871632*^9}, {3.7657875982836933`*^9, 3.765787656301631*^9}, { 3.7657879764376545`*^9, 3.765788072300957*^9}, {3.765788167914768*^9, 3.765788174147703*^9}, {3.7657882269599333`*^9, 3.7657882422376156`*^9}, { 3.765788487323238*^9, 3.765788490461094*^9}, {3.7657885592421846`*^9, 3.7657886255167627`*^9}, {3.7657886684913006`*^9, 3.765788699772582*^9}, { 3.7658535454339027`*^9, 3.765853547121047*^9}, {3.765853585583187*^9, 3.7658535876696625`*^9}, {3.7658536294696665`*^9, 3.765853634654695*^9}, { 3.765853681762427*^9, 3.7658536912055206`*^9}, {3.7658538243303814`*^9, 3.7658538454131355`*^9}, {3.7658539157461643`*^9, 3.765854051366618*^9}, 3.7658549146636453`*^9, {3.7658549454327097`*^9, 3.7658549762144003`*^9}, { 3.7658554333652973`*^9, 3.7658554999790025`*^9}, {3.7658555611344366`*^9, 3.7658555729631147`*^9}, {3.7658572968663087`*^9, 3.7658573145137095`*^9}, {3.7658850384108715`*^9, 3.7658850474801846`*^9}, {3.7658850891956606`*^9, 3.7658851178663177`*^9}, 3.7659430922088523`*^9, {3.766116011153117*^9, 3.766116022737113*^9}, { 3.7664753933295326`*^9, 3.7664757716641407`*^9}, {3.7664759605654993`*^9, 3.7664759688028593`*^9}, {3.7664760085309386`*^9, 3.766476010038458*^9}, { 3.766476138743503*^9, 3.766476143574604*^9}, 3.7664764030747433`*^9, 3.766476448999195*^9, {3.7664795633889008`*^9, 3.7664795678199263`*^9}, { 3.7664798747776756`*^9, 3.766479878585684*^9}, {3.7664799975477943`*^9, 3.766480007574602*^9}, {3.7664820589039545`*^9, 3.766482062864457*^9}, 3.7665403455127153`*^9, {3.766541028143508*^9, 3.766541033095478*^9}, { 3.7665416737998805`*^9, 3.7665418728472652`*^9}, {3.766541933535928*^9, 3.7665419443617644`*^9}, {3.7667415255470357`*^9, 3.76674154015712*^9}, { 3.7668889973044024`*^9, 3.7668890069739532`*^9}, 3.7866789982853584`*^9, { 3.786679036453455*^9, 3.7866790523570843`*^9}, {3.7866790953318987`*^9, 3.786679099544505*^9}, {3.7866791488372993`*^9, 3.7866791497233343`*^9}, { 3.7866791849490194`*^9, 3.7866791862255898`*^9}, {3.786679494212338*^9, 3.786679550404069*^9}, {3.7873084130307207`*^9, 3.787308461871894*^9}, { 3.787308532613593*^9, 3.787308535659466*^9}, {3.7873094152542315`*^9, 3.787309503626961*^9}, {3.787309542481*^9, 3.787309574889223*^9}, { 3.816934561209655*^9, 3.8169345722579055`*^9}, {3.816934674669306*^9, 3.816934676899186*^9}, {3.816934766676038*^9, 3.8169347688509417`*^9}, { 3.8171930585654454`*^9, 3.8171930599117575`*^9}, {3.817193180994313*^9, 3.817193200756859*^9}, {3.8171932313219566`*^9, 3.8171932318501453`*^9}, 3.817193335688717*^9, {3.818589402384385*^9, 3.8185894162187977`*^9}, { 3.818589484756053*^9, 3.818589497123905*^9}, {3.851044863005064*^9, 3.8510448663897667`*^9}},ExpressionUUID->"b87fa9bb-8fce-48e1-8dcc-\ ff4f6fac18b2"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["DISPLACEMENT ANALYSIS (week 3)", "Subsection", CellChangeTimes->{{3.473055512584*^9, 3.4730555529630003`*^9}, { 3.4730575328269997`*^9, 3.473057539222*^9}, {3.4734691424642*^9, 3.4734691605758*^9}, {3.5681161575453596`*^9, 3.568116161819767*^9}, { 3.59922265025865*^9, 3.599222653363055*^9}, 3.629777520582675*^9, 3.629791653258878*^9, {3.630370559869874*^9, 3.6303705662970853`*^9}, { 3.6618219022583027`*^9, 3.6618219059243093`*^9}, 3.6852488995100965`*^9, 3.685281849223243*^9, {3.6853234590535126`*^9, 3.685323459673514*^9}, { 3.68587640866364*^9, 3.6858764117036448`*^9}, {3.6862101948897667`*^9, 3.6862101984397717`*^9}, {3.686235632357339*^9, 3.6862356325473394`*^9}, { 3.686290377128008*^9, 3.686290380228012*^9}, {3.6863951313545313`*^9, 3.6863951457345514`*^9}, {3.6883646955890894`*^9, 3.6883646971490917`*^9}, 3.69079328920778*^9, 3.7530712354565744`*^9, 3.7866746400333786`*^9},ExpressionUUID->"0ad916ed-a088-4ed6-8e58-\ 9b8987f41ea9"], Cell[CellGroupData[{ Cell["Lecture example 2.1 (bar)", "Subsubsection", CellChangeTimes->{{3.4734694905626*^9, 3.4734694918886003`*^9}, { 3.5992247695247765`*^9, 3.599224771911581*^9}, 3.6862337070346437`*^9, 3.686290215967782*^9, {3.6863951815146017`*^9, 3.6863951817946024`*^9}, { 3.686463495303398*^9, 3.6864634969434004`*^9}, {3.7876248316360073`*^9, 3.787624839161375*^9}, 3.8195159060846395`*^9},ExpressionUUID->"9ce51a4d-240c-4a8f-8db9-\ b1eed2117469"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{ SqrtBox["8"], "A"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "F"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4426465840284452`*^9, 3.4426465892856455`*^9}, { 3.442646804859646*^9, 3.442646838774046*^9}, {3.473469518159*^9, 3.473469542105*^9}, {3.567488659560421*^9, 3.567488679996457*^9}, { 3.6293857978759165`*^9, 3.6293858030083256`*^9}, {3.6293859164049253`*^9, 3.629386031689128*^9}, {3.6297796999883165`*^9, 3.629779712249938*^9}, { 3.6297797534184103`*^9, 3.629779757864418*^9}, {3.6297799558131657`*^9, 3.629779994220433*^9}, {3.6297821687834535`*^9, 3.629782179984273*^9}, { 3.6297822711976333`*^9, 3.6297823082320986`*^9}, {3.6297916313252397`*^9, 3.6297916340240445`*^9}, {3.62987105119119*^9, 3.629871103544882*^9}, { 3.630231689415316*^9, 3.6302317303497877`*^9}, {3.6305529893093967`*^9, 3.63055299723485*^9}, {3.6306697846790886`*^9, 3.630669836330779*^9}, { 3.6306698912116756`*^9, 3.6306699292913427`*^9}, 3.6611752627847633`*^9, { 3.68519377703102*^9, 3.6851937863110332`*^9}, 3.685193829331094*^9, { 3.685233503917756*^9, 3.685233516277773*^9}, {3.685233597647887*^9, 3.685233615337912*^9}, {3.6852337344080787`*^9, 3.685233778910141*^9}, { 3.685233822710202*^9, 3.685233869000267*^9}, {3.685234136752804*^9, 3.685234139506961*^9}, 3.685234415812765*^9, {3.685234451830825*^9, 3.6852344677197337`*^9}, 3.6852619909866486`*^9, {3.6852629455979853`*^9, 3.6852629685880175`*^9}, 3.6852672555340195`*^9, {3.685270602011979*^9, 3.685270662762064*^9}, 3.685270775492222*^9, {3.685271434203144*^9, 3.685271439133151*^9}, {3.6853411055772305`*^9, 3.685341119183009*^9}, { 3.6853412984732637`*^9, 3.6853413099869223`*^9}, {3.6853417310800076`*^9, 3.685341741111581*^9}, {3.6853446026382513`*^9, 3.685344638248288*^9}, { 3.685875619502535*^9, 3.685875662152595*^9}, 3.6858757765527554`*^9, { 3.6863576684041834`*^9, 3.6863576792341986`*^9}, {3.69079336330791*^9, 3.690793478888513*^9}, {3.690793512022971*^9, 3.6907935419126234`*^9}, { 3.690793581973494*^9, 3.6907936094451427`*^9}, {3.690795505722073*^9, 3.690795509076079*^9}, {3.7537624520547013`*^9, 3.75376245992811*^9}, { 3.754127553263769*^9, 3.754127567681919*^9}, {3.754127654073234*^9, 3.7541276553706284`*^9}, 3.7553517003717556`*^9, {3.81951574949915*^9, 3.819515754203024*^9}}, CellLabel-> "In[364]:=",ExpressionUUID->"07ee9c44-080b-4601-8a59-3f0b3e1722ee"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 2.2 (beam truss)", "Subsubsection", CellChangeTimes->{ 3.4734694944314003`*^9, 3.599224766420371*^9, 3.6862337099646473`*^9, 3.686290219307787*^9, {3.6862903012279015`*^9, 3.686290301967902*^9}, { 3.6863951855946074`*^9, 3.686395186494609*^9}, {3.6864635001634054`*^9, 3.6864635018334074`*^9}, {3.6920214694650416`*^9, 3.692021471095044*^9}, 3.787624846976976*^9, 3.819515911959202*^9},ExpressionUUID->"23c8fb87-2b93-4eb1-b055-\ 915248fcc228"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "4"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "f"}], ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"4", ",", "3"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "4", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{ 3.442646896400446*^9, {3.629783307211053*^9, 3.629783319737875*^9}, { 3.6297833622479496`*^9, 3.6297833821535845`*^9}, {3.6297834663625326`*^9, 3.6297834719785423`*^9}, {3.629783540353462*^9, 3.629783541960265*^9}, { 3.629783803978326*^9, 3.629783888920475*^9}, {3.6297840054526796`*^9, 3.6297840056398797`*^9}, {3.6297840416291428`*^9, 3.629784042237544*^9}, { 3.629784285878772*^9, 3.629784299357196*^9}, {3.629784645038203*^9, 3.6297846906682825`*^9}, {3.6297850092208424`*^9, 3.629785101651005*^9}, { 3.629785975190139*^9, 3.629786017294613*^9}, {3.6297860683067026`*^9, 3.6297860840939302`*^9}, {3.629786362148819*^9, 3.6297864363425493`*^9}, { 3.629786900072529*^9, 3.629786945484209*^9}, 3.629786990225087*^9, { 3.629787120366516*^9, 3.6297871260449266`*^9}, {3.629787266780774*^9, 3.629787391144192*^9}, {3.6297874597063127`*^9, 3.629787510344002*^9}, 3.629788110882656*^9, {3.629788171800763*^9, 3.6297881758411703`*^9}, { 3.6297885659354553`*^9, 3.6297885755294724`*^9}, {3.6297892278758183`*^9, 3.629789232243826*^9}, {3.629789276625904*^9, 3.6297893332852035`*^9}, { 3.6297914556533313`*^9, 3.6297914630945444`*^9}, {3.629869949096054*^9, 3.629870013430567*^9}, {3.629870255714593*^9, 3.6298702559641933`*^9}, { 3.630553045404605*^9, 3.6305530553091717`*^9}, {3.6305893694622536`*^9, 3.630589404874316*^9}, {3.6306585642124243`*^9, 3.6306586027288923`*^9}, { 3.630658768962784*^9, 3.6306589911851745`*^9}, 3.630659024070032*^9, { 3.630673454818836*^9, 3.6306734854495883`*^9}, {3.630675026717631*^9, 3.6306750934294467`*^9}, {3.63067528213724*^9, 3.6306752822962494`*^9}, { 3.630675363622901*^9, 3.630675390674448*^9}, {3.630675423882347*^9, 3.6306754692369413`*^9}, 3.6306755736573396`*^9, {3.6306756175005193`*^9, 3.6306756249209433`*^9}, {3.630675655290681*^9, 3.6306756841903334`*^9}, { 3.630675727032784*^9, 3.6306757374963827`*^9}, {3.6306758978040085`*^9, 3.630675909644429*^9}, 3.630739547935058*^9, {3.6852523453938932`*^9, 3.68525240748398*^9}, {3.6852525490681486`*^9, 3.6852525670281763`*^9}, { 3.6852540883581915`*^9, 3.6852541237762175`*^9}, 3.6852541568981113`*^9, { 3.685261324675716*^9, 3.6852613495857506`*^9}, 3.685261974676626*^9, 3.685267244644004*^9, {3.6852714610531816`*^9, 3.6852714662331886`*^9}, { 3.685340224314878*^9, 3.6853402425549035`*^9}, {3.6858757975527844`*^9, 3.685875800692789*^9}, 3.685875976643035*^9, 3.6863952420746865`*^9, { 3.6866590821902657`*^9, 3.6866591337503376`*^9}, {3.686659210920446*^9, 3.6866592825905457`*^9}, 3.686659319650598*^9, 3.692021466075037*^9, { 3.6920215028250885`*^9, 3.6920215243751183`*^9}, {3.6920215584451666`*^9, 3.6920216476452913`*^9}, 3.692021691165352*^9, {3.7529756562277727`*^9, 3.7529756737168665`*^9}, {3.819523472816743*^9, 3.8195234759131594`*^9}, { 3.8197802724004292`*^9, 3.8197802763499517`*^9}}, CellLabel->"In[5]:=",ExpressionUUID->"c8894e60-9066-4599-bec8-91e05a499a8e"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 2.3 (solid)", "Subsubsection", CellChangeTimes->{ 3.4734695002813997`*^9, {3.599225569652184*^9, 3.599225577904598*^9}, 3.5992258478994727`*^9, 3.6862336460745583`*^9, 3.6862909162387624`*^9, { 3.6863755415162687`*^9, 3.686375541876269*^9}, {3.686463504573411*^9, 3.686463506573414*^9}, {3.6920258070089493`*^9, 3.692025809498953*^9}, { 3.692025870269038*^9, 3.692025872639041*^9}, 3.7876248508872952`*^9, 3.8195159139209347`*^9},ExpressionUUID->"6a4aea0d-99ba-4702-8deb-\ 458ed4f15f86"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"-", "\[Rho]"}], " ", "g"}]}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "3", "]"}], ",", RowBox[{"uY", "[", "3", "]"}], ",", RowBox[{"uZ", "[", "3", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "\[IndentingNewLine]", "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4426469450734453`*^9, 3.4426469473978453`*^9}, { 3.630367590488758*^9, 3.6303676088811903`*^9}, {3.630367651765666*^9, 3.630367669549697*^9}, 3.630368414310605*^9, {3.6307482430426474`*^9, 3.6307482456946526`*^9}, 3.685262022046692*^9, {3.6852621067368107`*^9, 3.6852621933569317`*^9}, {3.685262233936989*^9, 3.685262252827015*^9}, 3.685267210253956*^9, {3.6852715412232933`*^9, 3.685271546353301*^9}, { 3.6853429895189857`*^9, 3.6853430232739167`*^9}, 3.6858761692133045`*^9, { 3.68821224839828*^9, 3.6882123179983773`*^9}, {3.68821235531843*^9, 3.6882123899484777`*^9}, 3.6920258039789453`*^9, {3.692025876949047*^9, 3.692025881559054*^9}, {3.6920259277091184`*^9, 3.6920259839391975`*^9}, { 3.692026020869249*^9, 3.6920260636193085`*^9}, {3.6920264969699154`*^9, 3.6920264987399178`*^9}, {3.7530062221144147`*^9, 3.753006264963928*^9}, { 3.787625003286798*^9, 3.78762500483702*^9}, 3.8197804389387846`*^9}, CellLabel->"In[15]:=",ExpressionUUID->"91c78a48-fca8-4c15-ba55-8ebe9b885fd4"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 2.4 (beam)", "Subsubsection", CellChangeTimes->{ 3.4734694944314003`*^9, 3.599224766420371*^9, 3.6862337099646473`*^9, 3.686290219307787*^9, {3.6862903012279015`*^9, 3.686290301967902*^9}, { 3.686377587511134*^9, 3.686377589931137*^9}, 3.6864635125734224`*^9, { 3.6920273329210854`*^9, 3.692027334031087*^9}, {3.787624857073228*^9, 3.787624858265213*^9}, 3.819515917947086*^9},ExpressionUUID->"72c71bae-49b0-42c4-ab87-\ cbe04c178bcc"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{ "A", ",", "\[CapitalIota]yy", ",", "\[CapitalIota]zz", ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "f"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "F"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{ 3.442646896400446*^9, {3.629783307211053*^9, 3.629783319737875*^9}, { 3.6297833622479496`*^9, 3.6297833821535845`*^9}, {3.6297834663625326`*^9, 3.6297834719785423`*^9}, {3.629783540353462*^9, 3.629783541960265*^9}, { 3.629783803978326*^9, 3.629783888920475*^9}, {3.6297840054526796`*^9, 3.6297840056398797`*^9}, {3.6297840416291428`*^9, 3.629784042237544*^9}, { 3.629784285878772*^9, 3.629784299357196*^9}, {3.629784645038203*^9, 3.6297846906682825`*^9}, {3.6297850092208424`*^9, 3.629785101651005*^9}, { 3.629785975190139*^9, 3.629786017294613*^9}, {3.6297860683067026`*^9, 3.6297860840939302`*^9}, {3.629786362148819*^9, 3.6297864363425493`*^9}, { 3.629786900072529*^9, 3.629786945484209*^9}, 3.629786990225087*^9, { 3.629787120366516*^9, 3.6297871260449266`*^9}, {3.629787266780774*^9, 3.629787391144192*^9}, {3.6297874597063127`*^9, 3.629787510344002*^9}, 3.629788110882656*^9, {3.629788171800763*^9, 3.6297881758411703`*^9}, { 3.6297885659354553`*^9, 3.6297885755294724`*^9}, {3.6297892278758183`*^9, 3.629789232243826*^9}, {3.629789276625904*^9, 3.6297893332852035`*^9}, { 3.6297914556533313`*^9, 3.6297914630945444`*^9}, {3.629869949096054*^9, 3.629870013430567*^9}, {3.629870255714593*^9, 3.6298702559641933`*^9}, { 3.630553045404605*^9, 3.6305530553091717`*^9}, {3.6305893694622536`*^9, 3.630589404874316*^9}, {3.6306585642124243`*^9, 3.6306586027288923`*^9}, { 3.630658768962784*^9, 3.6306589911851745`*^9}, 3.630659024070032*^9, { 3.630673454818836*^9, 3.6306734854495883`*^9}, {3.630675026717631*^9, 3.6306750934294467`*^9}, {3.63067528213724*^9, 3.6306752822962494`*^9}, { 3.630675363622901*^9, 3.630675390674448*^9}, {3.630675423882347*^9, 3.6306754692369413`*^9}, 3.6306755736573396`*^9, {3.6306756175005193`*^9, 3.6306756249209433`*^9}, {3.630675655290681*^9, 3.6306756841903334`*^9}, { 3.630675727032784*^9, 3.6306757374963827`*^9}, {3.6306758978040085`*^9, 3.630675909644429*^9}, 3.630739547935058*^9, {3.6852523453938932`*^9, 3.68525240748398*^9}, {3.6852525490681486`*^9, 3.6852525670281763`*^9}, { 3.6852540883581915`*^9, 3.6852541237762175`*^9}, 3.6852541568981113`*^9, { 3.685261324675716*^9, 3.6852613495857506`*^9}, 3.685261974676626*^9, 3.685267244644004*^9, {3.6852714610531816`*^9, 3.6852714662331886`*^9}, { 3.685340224314878*^9, 3.6853402425549035`*^9}, {3.6858757975527844`*^9, 3.685875800692789*^9}, 3.685875976643035*^9, {3.686377605391159*^9, 3.6863776382012053`*^9}, {3.6863791342332993`*^9, 3.6863791914533796`*^9}, {3.692059670428982*^9, 3.6920597048990297`*^9}, { 3.723798411849661*^9, 3.723798434904174*^9}, {3.7237987918993216`*^9, 3.7237987936592455`*^9}, {3.723799349340538*^9, 3.723799350506401*^9}, 3.7530064855925837`*^9, {3.7530074090324397`*^9, 3.7530074156090126`*^9}, { 3.8197805328576946`*^9, 3.8197805360133047`*^9}}, CellLabel->"In[20]:=",ExpressionUUID->"f2fb962d-1b1e-4402-97b7-e538a571f5ee"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 2.5 (thin slab)", "Subsubsection", CellChangeTimes->{ 3.473469503105*^9, {3.599225885667139*^9, 3.5992258876171427`*^9}, { 3.686233649684563*^9, 3.686233650204564*^9}, 3.686290918768766*^9, 3.686291030808923*^9, {3.6863793069335413`*^9, 3.6863793075335417`*^9}, 3.6864635148234253`*^9, {3.6920597199190507`*^9, 3.692059720879052*^9}, { 3.692059925419338*^9, 3.6920599277293415`*^9}, {3.787624862002798*^9, 3.7876248627952986`*^9}, 3.8195159211419706`*^9},ExpressionUUID->"59ab6ed7-ca2a-4964-9858-\ e809d14b67e0"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "F"}], ",", RowBox[{"-", "F"}], ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "1", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "1", "]"}], ",", RowBox[{"uY", "[", "1", "]"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}]}]], "Input", CellChangeTimes->{{3.4426469547766457`*^9, 3.4426469592694454`*^9}, { 3.630368423748622*^9, 3.6303685192207894`*^9}, {3.6303685521992474`*^9, 3.6303685620584645`*^9}, 3.6303705303858223`*^9, {3.685262281457055*^9, 3.685262388467205*^9}, {3.6852624670373154`*^9, 3.685262481977336*^9}, { 3.68526278509776*^9, 3.685262791257769*^9}, 3.685267202483945*^9, { 3.6852715539533114`*^9, 3.685271559193319*^9}, {3.6853430782990637`*^9, 3.6853430894086995`*^9}, 3.686379355343609*^9, {3.6863831012088532`*^9, 3.6863831063588605`*^9}, {3.6863942094232407`*^9, 3.6863942663533206`*^9}, 3.6876000488420086`*^9, {3.692059987549425*^9, 3.6920600009994445`*^9}, 3.692060112739601*^9, {3.692060203029727*^9, 3.692060219839751*^9}, { 3.723943463177676*^9, 3.723943469317417*^9}, {3.723943597251667*^9, 3.7239436127040477`*^9}, {3.7240547317555065`*^9, 3.724054735286746*^9}, { 3.753007457114498*^9, 3.7530075727121468`*^9}, {3.8197805851870413`*^9, 3.8197806010912604`*^9}, {3.8197811716809254`*^9, 3.8197811892458363`*^9}, {3.8197812993773036`*^9, 3.8197813449589143`*^9}, {3.849338627434058*^9, 3.849338634162207*^9}}, CellLabel->"In[10]:=",ExpressionUUID->"dd417420-f0a3-4621-8632-7fa9d67ad09f"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 2.6a (Plate bending mode)", "Subsubsection", CellChangeTimes->{{3.4467272483794003`*^9, 3.446727266257*^9}, { 3.4467288934652*^9, 3.446728896788*^9}, 3.4467805306712*^9, { 3.4801237484706*^9, 3.4801237489386*^9}, {3.5744708417194977`*^9, 3.5744708449019036`*^9}, {3.6042991711100636`*^9, 3.604299196992544*^9}, 3.60430729253247*^9, {3.604310202140381*^9, 3.6043102048235855`*^9}, { 3.6889933424974422`*^9, 3.688993352477456*^9}, 3.6889988585223417`*^9, { 3.689480870769858*^9, 3.6894808898298845`*^9}, {3.7518654678504887`*^9, 3.751865474661203*^9}, {3.7519386265381956`*^9, 3.7519386622978053`*^9}, { 3.75376294503279*^9, 3.7537629487977667`*^9}, 3.755435763828392*^9, { 3.7876248662926145`*^9, 3.7876248671217136`*^9}, 3.8195159229298143`*^9},ExpressionUUID->"d9c59a92-1228-49f5-983a-\ e40a66f27466"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ "block", " ", "to", " ", "localize", " ", "some", " ", "variables"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Block", "[", RowBox[{ RowBox[{"{", RowBox[{ "val", ",", "w", ",", "E\[Sigma]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[CapitalOmega]", ",", "\[Delta]W", ",", "sol", ",", "w0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"val", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"L", "\[Rule]", "1."}], ",", RowBox[{"H", "\[Rule]", RowBox[{"3", "/", "10"}]}], ",", RowBox[{"t", "\[Rule]", RowBox[{"1", "/", "100"}]}], ",", RowBox[{"\[CapitalEpsilon]", "\[Rule]", "100000"}], ",", RowBox[{"\[Nu]", "\[Rule]", "0.33"}], ",", RowBox[{"p", "\[Rule]", RowBox[{"10", "*", "\[CapitalEpsilon]", RowBox[{ RowBox[{"(", RowBox[{"t", "/", "L"}], ")"}], "^", "3"}]}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", FractionBox["x", "L"]}], ")"}], "2"], SuperscriptBox[ RowBox[{"(", FractionBox["x", "L"], " ", ")"}], "2"], RowBox[{"a", "[", "0", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"E\[Sigma]", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "\[Nu]", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Nu]", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Nu]"}], ")"}], "/", "2"}]}], "}"}]}], "}"}], "*", RowBox[{"\[CapitalEpsilon]", "/", RowBox[{"(", RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}], ")"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wint", "[", "w_", "]"}], ":=", RowBox[{"-", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}], ",", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}], ",", RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]}], "}"}], "]"}], ".", RowBox[{"(", RowBox[{ FractionBox[ SuperscriptBox["t", "3"], "12"], "E\[Sigma]"}], ")"}], ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}], ",", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}], ",", RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]}], "}"}]}]}]}], ";", RowBox[{ RowBox[{"\[Delta]wext", "[", "w_", "]"}], ":=", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", "w", "]"}]}], " ", "p"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", "=", RowBox[{"Rectangle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"L", ",", "H"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]W", " ", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]wint", "[", "w", "]"}], "+", RowBox[{"\[Delta]wext", "[", "w", "]"}]}], ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], StyleBox["\[Element]", "OperatorCharacter"], StyleBox["\[CapitalOmega]", "OperatorCharacter"]}]}], StyleBox["]", "OperatorCharacter"]}], StyleBox[",", "OperatorCharacter"], RowBox[{ StyleBox["{", "OperatorCharacter"], RowBox[{ StyleBox[ RowBox[{"L", ">", "0"}], "OperatorCharacter"], ",", RowBox[{"H", ">", "0"}]}], "}"}]}], StyleBox["]", "OperatorCharacter"]}]}], StyleBox[";", "OperatorCharacter"], "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", "\[Delta]W", "]"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"sol", " ", "=", RowBox[{"SOLVE", "[", "\[Delta]W", "]"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"w0", "=", RowBox[{ RowBox[{"w", " ", "/.", "sol"}], " ", "/.", RowBox[{"x", "\[Rule]", RowBox[{"L", "/", "2"}]}]}]}], " ", "]"}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"w0", " ", "//.", "val"}], " ", "]"}]}]}], "]"}]}]], "Input", CellChangeTimes->{{3.4467277951594*^9, 3.4467279649186*^9}, 3.446728037053*^9, {3.4467281489206*^9, 3.4467281816806*^9}, { 3.4467282630708*^9, 3.4467282697788*^9}, 3.4467284401292*^9, { 3.5744707871506023`*^9, 3.5744707892254057`*^9}, {3.5744708230306654`*^9, 3.5744708311270795`*^9}, {3.5744708665859413`*^9, 3.5744709163032293`*^9}, {3.5744709579553022`*^9, 3.5744709639145126`*^9}, {3.5744710148018017`*^9, 3.5744710339742355`*^9}, 3.6042992082891903`*^9, {3.6042992538197947`*^9, 3.6042992780501804`*^9}, { 3.6042993188655148`*^9, 3.6042993269519777`*^9}, {3.604305825073493*^9, 3.604305908252839*^9}, {3.6043059427600994`*^9, 3.6043059892481813`*^9}, { 3.604306056094299*^9, 3.604306314961153*^9}, {3.604308274382595*^9, 3.604308484499364*^9}, {3.604308525933037*^9, 3.604308791414303*^9}, { 3.6043089926234565`*^9, 3.604309008441884*^9}, {3.6043109233452473`*^9, 3.604311002296986*^9}, {3.6043110410942545`*^9, 3.604311044713461*^9}, { 3.604311077301918*^9, 3.6043113010219107`*^9}, 3.604311474057415*^9, { 3.6043115724311876`*^9, 3.6043115749739923`*^9}, {3.6043116205416718`*^9, 3.6043116224136753`*^9}, {3.6043116548617325`*^9, 3.604311738571479*^9}, { 3.6043119619326715`*^9, 3.6043119879847174`*^9}, {3.604312252108781*^9, 3.6043122715620155`*^9}, {3.604312318159297*^9, 3.604312461367549*^9}, { 3.6043125259828625`*^9, 3.6043125318016725`*^9}, {3.6043125750605483`*^9, 3.6043125754037495`*^9}, {3.6043127726660957`*^9, 3.604312785458118*^9}, { 3.636082009030026*^9, 3.6360821021793537`*^9}, {3.6360821353592515`*^9, 3.6360821994179153`*^9}, {3.6360822411353016`*^9, 3.636082308140134*^9}, { 3.636082428925042*^9, 3.6360824672832365`*^9}, 3.636082772513695*^9, { 3.6364550263262777`*^9, 3.636455043447257*^9}, 3.63645529332755*^9, 3.6364553732171187`*^9, {3.636455466633462*^9, 3.6364555214936*^9}, 3.6673026911198535`*^9, {3.688993360197467*^9, 3.6889934094075356`*^9}, { 3.6889934413475804`*^9, 3.6889934979176598`*^9}, {3.6889986435220413`*^9, 3.6889988109722757`*^9}, {3.689070158580252*^9, 3.6890701724702716`*^9}, { 3.75186550410758*^9, 3.7518656604145575`*^9}, {3.751865728032886*^9, 3.751865773303449*^9}, {3.7518658124036255`*^9, 3.7518658214955225`*^9}, { 3.7518658552375374`*^9, 3.7518658598771863`*^9}, {3.7518659717099*^9, 3.751866085179107*^9}, 3.7519702560712104`*^9, {3.7537629790875463`*^9, 3.7537629902408724`*^9}, {3.753764460655489*^9, 3.753764491257679*^9}, { 3.7553522538315935`*^9, 3.755352276164716*^9}, {3.7874855436907077`*^9, 3.7874855491613884`*^9}, 3.787485623549152*^9, {3.787486067951891*^9, 3.787486076053173*^9}, {3.7874946027778063`*^9, 3.7874946422828536`*^9}, { 3.78749467607176*^9, 3.7874946864647493`*^9}, {3.787535715793891*^9, 3.787535739520609*^9}, {3.787583561143423*^9, 3.78758356240777*^9}, { 3.8195157237635217`*^9, 3.819515731584694*^9}, {3.8506382610411806`*^9, 3.8506382622126656`*^9}, {3.85069882110884*^9, 3.8506990207088575`*^9}, { 3.8507907120205226`*^9, 3.850790722706362*^9}, {3.850790761779279*^9, 3.8507907986164536`*^9}, {3.8507908639904423`*^9, 3.8507908871774497`*^9}, {3.8511327011029663`*^9, 3.851132856682681*^9}}, CellLabel-> "In[369]:=",ExpressionUUID->"15570612-d966-4497-9516-a561480ae6e0"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 2.6b (Plate bending mode)", "Subsubsection", CellChangeTimes->{{3.4467272483794003`*^9, 3.446727266257*^9}, { 3.4467288934652*^9, 3.446728896788*^9}, 3.4467805306712*^9, { 3.4801237484706*^9, 3.4801237489386*^9}, {3.5744708417194977`*^9, 3.5744708449019036`*^9}, {3.6042991711100636`*^9, 3.604299196992544*^9}, 3.60430729253247*^9, {3.604310202140381*^9, 3.6043102048235855`*^9}, { 3.6889933424974422`*^9, 3.688993352477456*^9}, 3.6889988585223417`*^9, { 3.689480870769858*^9, 3.6894808898298845`*^9}, {3.7518654678504887`*^9, 3.751865474661203*^9}, {3.7519386265381956`*^9, 3.7519386622978053`*^9}, { 3.75376294503279*^9, 3.7537629487977667`*^9}, 3.7554357667498393`*^9, 3.755523363145975*^9, 3.7866920350953083`*^9, 3.7874847705403285`*^9, { 3.787583534492174*^9, 3.787583543755392*^9}, {3.787624886997221*^9, 3.7876249024322443`*^9}, 3.8195159245188613`*^9},ExpressionUUID->"a0a099cf-522b-401b-93cb-\ fe9cd38c1bd4"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ "one", " ", "may", " ", "use", " ", "the", " ", "triangle", " ", "plate", " ", "bending", " ", "element", " ", "with", " ", "structured", " ", "or", " ", "nonstructured", " ", "element", " ", "divisions", " ", "to", " ", "find", " ", "the", " ", "solution", " ", "by", " ", "FEM"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"val", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"L", "\[Rule]", "1."}], ",", RowBox[{"H", "\[Rule]", RowBox[{"3", "/", "10"}]}], ",", RowBox[{"t", "\[Rule]", RowBox[{"1", "/", "100"}]}], ",", RowBox[{"\[CapitalEpsilon]", "\[Rule]", "100000"}], ",", RowBox[{"\[Nu]", "\[Rule]", "0.33"}], ",", RowBox[{"p", "\[Rule]", RowBox[{"10", "*", "\[CapitalEpsilon]", RowBox[{ RowBox[{"(", RowBox[{"t", "/", "L"}], ")"}], "^", "3"}]}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"-", "p"}]}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "7"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"-", "p"}]}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"2", ",", "3", ",", "7"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"-", "p"}]}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "7", ",", "4"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"-", "p"}]}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"7", ",", "3", ",", "6"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"-", "p"}]}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"4", ",", "7", ",", "5"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"-", "p"}]}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"7", ",", "6", ",", "5"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"L", "/", "2"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", "2", "]"}], ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "H", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"L", "/", "2"}], ",", "H", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "5", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", "5", "]"}], ",", RowBox[{"\[Theta]Y", "[", "5", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "H", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"L", "/", "2"}], ",", RowBox[{"H", "/", "2"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "7", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", "7", "]"}], ",", RowBox[{"\[Theta]Y", "[", "7", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "=", RowBox[{"REFINE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "=", RowBox[{"REFINE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "=", RowBox[{"REFINE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"MESH", "[", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "//.", "val"}], "]"}], ";"}], "\n", RowBox[{ RowBox[{"sol", "=", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "//.", " ", "val"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"uZ", "[", "7", "]"}], "/.", "sol"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SHOW3D", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "1"}], "}"}], ",", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "//.", "val"}], " ", "/.", "sol"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.6888689611245327`*^9, 3.6888691441747894`*^9}, { 3.688869175904834*^9, 3.6888691949848604`*^9}, {3.688869303295012*^9, 3.6888694251851826`*^9}, {3.688869534825336*^9, 3.6888695373653393`*^9}, { 3.6888695909654145`*^9, 3.688869620615456*^9}, {3.6888696695055246`*^9, 3.688869671645528*^9}, {3.688869703665572*^9, 3.688869771185667*^9}, { 3.6888698131457253`*^9, 3.688869843195768*^9}, 3.688869999545987*^9, 3.6888701516861997`*^9, {3.688870779087078*^9, 3.6888708600371914`*^9}, { 3.6888713003778076`*^9, 3.688871303197812*^9}, {3.6888713416978655`*^9, 3.688871422407979*^9}, {3.6888714741080513`*^9, 3.688871476638055*^9}, 3.6888751073437386`*^9, {3.6888752493389473`*^9, 3.6888752569189587`*^9}, { 3.688875289049003*^9, 3.688875320839048*^9}, {3.6888754299492006`*^9, 3.688875430949202*^9}, {3.6888786937177925`*^9, 3.688878750267872*^9}, { 3.6888787903179283`*^9, 3.6888788206179705`*^9}, {3.6888790860283422`*^9, 3.68887909127835*^9}, {3.6890585394429307`*^9, 3.6890585586029577`*^9}, { 3.689058611933032*^9, 3.689058636633067*^9}, 3.6890586753831205`*^9, 3.6890587218131857`*^9, {3.6890588371733475`*^9, 3.6890588479333625`*^9}, 3.6890593143580313`*^9, {3.68939651006566*^9, 3.689396570005744*^9}, 3.7519567199003897`*^9, {3.7519567531116476`*^9, 3.7519568500887613`*^9}, { 3.7519568810345116`*^9, 3.7519569775584803`*^9}, {3.751957015846347*^9, 3.7519570979991937`*^9}, {3.751957130663088*^9, 3.7519571335374126`*^9}, 3.753763435083539*^9, {3.7537636176034584`*^9, 3.753763788907042*^9}, { 3.753763831693569*^9, 3.7537638728401537`*^9}, {3.75376391019105*^9, 3.7537639597106857`*^9}, {3.7537640140260305`*^9, 3.7537640276633615`*^9}, {3.753764070700218*^9, 3.7537641560081577`*^9}, { 3.7537641950926304`*^9, 3.7537643084881086`*^9}, 3.753764389828247*^9, { 3.753764533778655*^9, 3.753764547869378*^9}, {3.7553527505176506`*^9, 3.7553528603017626`*^9}, {3.75538351472929*^9, 3.7553835693549905`*^9}, { 3.755383607438428*^9, 3.7553838360146847`*^9}, {3.7553838766263666`*^9, 3.755383951476962*^9}, {3.755383992736063*^9, 3.7553840478403873`*^9}, { 3.755384124898378*^9, 3.7553842646406417`*^9}, {3.755389313373938*^9, 3.7553893195755854`*^9}, {3.755389381201706*^9, 3.7553894668944387`*^9}, { 3.7553895199108267`*^9, 3.755389537914214*^9}, {3.755389582951442*^9, 3.755389708990402*^9}, 3.7554339398817015`*^9, 3.755434068869628*^9, { 3.7554341297848616`*^9, 3.755434216890894*^9}, {3.7554343528417006`*^9, 3.7554343704056864`*^9}, {3.755434459874297*^9, 3.755434538395585*^9}, 3.755434569759145*^9, {3.7554346233872647`*^9, 3.7554347263294*^9}, { 3.7554347853286095`*^9, 3.7554348093580456`*^9}, {3.755434907172281*^9, 3.755434918847997*^9}, {3.7554349600500207`*^9, 3.7554349983466597`*^9}, { 3.755435110803147*^9, 3.7554351426284623`*^9}, {3.755435324398292*^9, 3.7554353302892075`*^9}, {3.755435441524338*^9, 3.755435445101488*^9}, 3.7554355170109453`*^9, {3.7554358134766097`*^9, 3.755435918833391*^9}, { 3.7554359598830943`*^9, 3.75543598832941*^9}, {3.755436164699664*^9, 3.7554361666501207`*^9}, {3.755436277778627*^9, 3.755436282441655*^9}, { 3.755436433004975*^9, 3.7554365810900373`*^9}, {3.755436713592167*^9, 3.7554367150263915`*^9}, {3.755436752569789*^9, 3.755436782945344*^9}, { 3.75543855564263*^9, 3.755438573014342*^9}, {3.7554386030808535`*^9, 3.75543862876925*^9}, {3.755438665543474*^9, 3.755438666460845*^9}, { 3.755438707655904*^9, 3.7554387115945473`*^9}, {3.7554387585075216`*^9, 3.7554388500917773`*^9}, {3.755523374186784*^9, 3.755523407200748*^9}, { 3.755523628104781*^9, 3.755523629369397*^9}, {3.755523692162763*^9, 3.755523702854873*^9}, 3.7555237667615433`*^9, 3.7555238472382975`*^9, 3.7555241586552105`*^9, 3.755524213729106*^9, 3.755524399719488*^9, 3.75552571772406*^9, {3.7555258075426073`*^9, 3.755525820259694*^9}, 3.755526094753117*^9, 3.7555261757546644`*^9, {3.7555262318295097`*^9, 3.7555262499726152`*^9}, {3.7555370249561615`*^9, 3.755537051432358*^9}, 3.7555372853307257`*^9, {3.755537468732602*^9, 3.755537521108555*^9}, 3.7555375621618104`*^9, {3.7555379391125593`*^9, 3.755537970148187*^9}, { 3.7555674525545197`*^9, 3.755567456059157*^9}, {3.7555675848877916`*^9, 3.7555675985147886`*^9}, {3.7555676718904886`*^9, 3.7555677115434046`*^9}, {3.755567758583485*^9, 3.7555677797901087`*^9}, { 3.755567822059022*^9, 3.755567822195668*^9}, {3.7555678597444773`*^9, 3.7555678604365673`*^9}, 3.7556071757478895`*^9, {3.7556072159647107`*^9, 3.755607332812396*^9}, {3.7556074217009745`*^9, 3.755607426579308*^9}, 3.755607632666421*^9, {3.755607684025096*^9, 3.755607693062358*^9}, { 3.7556077296748147`*^9, 3.755607849742259*^9}, {3.755608033616538*^9, 3.7556080922325497`*^9}, 3.755608142419341*^9, {3.755608958207328*^9, 3.755608980843011*^9}, {3.7559615593543744`*^9, 3.7559615796720657`*^9}, { 3.755961636991267*^9, 3.755961639837885*^9}, {3.755961688066485*^9, 3.7559617050406666`*^9}, {3.75596184181551*^9, 3.755961843331066*^9}, { 3.7560033780948515`*^9, 3.756003424416658*^9}, {3.756003637744131*^9, 3.7560039024762926`*^9}, {3.7560039413994226`*^9, 3.756004010187872*^9}, { 3.75600408826851*^9, 3.7560041132438145`*^9}, {3.7560042095185223`*^9, 3.756004261292776*^9}, {3.7560043015589314`*^9, 3.7560044114376893`*^9}, { 3.7560045878703117`*^9, 3.756004610316883*^9}, {3.756090875492567*^9, 3.756090970250229*^9}, {3.7560910153257923`*^9, 3.756091253656394*^9}, { 3.7560913065394864`*^9, 3.7560913073489447`*^9}, {3.7560913497661376`*^9, 3.7560913829572887`*^9}, {3.7560914229250793`*^9, 3.756091477168485*^9}, { 3.756091512338003*^9, 3.7560916181734085`*^9}, {3.756091734456238*^9, 3.7560917345758953`*^9}, 3.7560919538299203`*^9, {3.756092472598545*^9, 3.7560924728155417`*^9}, {3.756092529494649*^9, 3.7560925295886126`*^9}, { 3.7564428371402044`*^9, 3.7564428827548018`*^9}, {3.756443118409811*^9, 3.7564432825122414`*^9}, {3.7564433139577427`*^9, 3.7564434048585415`*^9}, {3.75644377756419*^9, 3.756443799699541*^9}, { 3.756444020280332*^9, 3.756444052335291*^9}, 3.7564441526092615`*^9, 3.7866921123667355`*^9, {3.786692169420147*^9, 3.786692647713867*^9}, { 3.7866926921591225`*^9, 3.78669273302064*^9}, {3.786692862316063*^9, 3.7866928658349466`*^9}, {3.7866931119911423`*^9, 3.786693309398429*^9}, { 3.7866933409841013`*^9, 3.7866934610423436`*^9}, {3.786693498963604*^9, 3.7866936745285892`*^9}, {3.7866937881495705`*^9, 3.7866937950939436`*^9}, 3.7873246428692293`*^9, {3.787485049135359*^9, 3.787485051961443*^9}, { 3.787485091258519*^9, 3.787485424116222*^9}, {3.7874854543849907`*^9, 3.787485502716935*^9}, {3.7874856358164625`*^9, 3.7874856505267844`*^9}, 3.787494663934597*^9, {3.7874947579329753`*^9, 3.7874947673643074`*^9}, 3.787494920667267*^9, {3.7874950655196714`*^9, 3.7874951753595195`*^9}, { 3.787495215708169*^9, 3.7874952321914797`*^9}, {3.7874953099595947`*^9, 3.7874953434716663`*^9}, {3.7874953776322303`*^9, 3.7874953779837875`*^9}, {3.7875363421179075`*^9, 3.787536342508462*^9}, { 3.7875368085158997`*^9, 3.787536878302806*^9}, {3.7875369599529157`*^9, 3.7875370055885963`*^9}, {3.7875835060582986`*^9, 3.787583520821555*^9}, { 3.787583689937277*^9, 3.787583802553567*^9}, 3.7876259263443413`*^9, { 3.7876552122737617`*^9, 3.787655270155204*^9}, {3.7877076273240643`*^9, 3.7877076330663157`*^9}, {3.8493387287106876`*^9, 3.8493387484197454`*^9}, {3.8493388690505223`*^9, 3.8493389607525234`*^9}, {3.8506381987001867`*^9, 3.850638199323704*^9}, { 3.8506382518387237`*^9, 3.8506382521507797`*^9}, 3.8507909361264725`*^9, { 3.850790968622494*^9, 3.8507909814813538`*^9}, {3.8507910227542276`*^9, 3.850791053573805*^9}, {3.850791116545538*^9, 3.8507911402245955`*^9}, { 3.851132967713168*^9, 3.851132969332811*^9}}, CellLabel-> "In[380]:=",ExpressionUUID->"5b63b3a2-4880-4107-81b0-63d9e1e27f04"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 2.6c (Plate bending mode)", "Subsubsection", CellChangeTimes->{{3.4467272483794003`*^9, 3.446727266257*^9}, { 3.4467288934652*^9, 3.446728896788*^9}, 3.4467805306712*^9, { 3.4801237484706*^9, 3.4801237489386*^9}, {3.5744708417194977`*^9, 3.5744708449019036`*^9}, {3.6042991711100636`*^9, 3.604299196992544*^9}, 3.60430729253247*^9, {3.604310202140381*^9, 3.6043102048235855`*^9}, { 3.6889933424974422`*^9, 3.688993352477456*^9}, 3.6889988585223417`*^9, { 3.689480870769858*^9, 3.6894808898298845`*^9}, {3.7518654678504887`*^9, 3.751865474661203*^9}, {3.7519386265381956`*^9, 3.7519386622978053`*^9}, { 3.75376294503279*^9, 3.7537629487977667`*^9}, 3.7554357667498393`*^9, 3.755523363145975*^9, 3.7866920350953083`*^9, 3.7874847705403285`*^9, { 3.787583534492174*^9, 3.787583543755392*^9}, {3.7875838427605453`*^9, 3.787583846863057*^9}, {3.787624871323914*^9, 3.7876248923342185`*^9}, 3.8195159262390037`*^9},ExpressionUUID->"26efc207-037d-4d05-a43c-\ 306f064bc5f7"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ "one", " ", "may", " ", "use", " ", "the", " ", "triangle", " ", "plate", " ", "bending", " ", "element", " ", "with", " ", "structured", " ", "or", " ", "nonstructured", " ", "element", " ", "divisions", " ", "to", " ", "find", " ", "the", " ", "solution", " ", "by", " ", "FEM"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"val", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"L", "\[Rule]", "1."}], ",", RowBox[{"H", "\[Rule]", RowBox[{"3", "/", "10"}]}], ",", RowBox[{"t", "\[Rule]", RowBox[{"1", "/", "100"}]}], ",", RowBox[{"\[CapitalEpsilon]", "\[Rule]", "100000"}], ",", RowBox[{"\[Nu]", "\[Rule]", "0.33"}], ",", RowBox[{"p", "\[Rule]", RowBox[{"10", "*", "\[CapitalEpsilon]", RowBox[{ RowBox[{"(", RowBox[{"t", "/", "L"}], ")"}], "^", "3"}]}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"crd", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"L", ",", "H"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "H"}], "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "H"}], "}"}], "/", "2"}]}], "}"}], " ", "/.", "val"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"seg", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "5"}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"mrk", "=", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4", ",", "0"}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"crd", ",", "nod", ",", "seg", ",", "mrk"}], "}"}], "=", RowBox[{"TRIANGULATE", "[", RowBox[{ RowBox[{"{", RowBox[{"seg", ",", "mrk"}], "}"}], ",", "crd", ",", "0.008"}], "]"}]}], ";"}], "\n", "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{ RowBox[{"MeshRegion", "[", RowBox[{"crd", ",", "nod"}], "]"}], ",", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"X", ",", "Y"}], "}"}]}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.6888689611245327`*^9, 3.6888691441747894`*^9}, { 3.688869175904834*^9, 3.6888691949848604`*^9}, {3.688869303295012*^9, 3.6888694251851826`*^9}, {3.688869534825336*^9, 3.6888695373653393`*^9}, { 3.6888695909654145`*^9, 3.688869620615456*^9}, {3.6888696695055246`*^9, 3.688869671645528*^9}, {3.688869703665572*^9, 3.688869771185667*^9}, { 3.6888698131457253`*^9, 3.688869843195768*^9}, 3.688869999545987*^9, 3.6888701516861997`*^9, {3.688870779087078*^9, 3.6888708600371914`*^9}, { 3.6888713003778076`*^9, 3.688871303197812*^9}, {3.6888713416978655`*^9, 3.688871422407979*^9}, {3.6888714741080513`*^9, 3.688871476638055*^9}, 3.6888751073437386`*^9, {3.6888752493389473`*^9, 3.6888752569189587`*^9}, { 3.688875289049003*^9, 3.688875320839048*^9}, {3.6888754299492006`*^9, 3.688875430949202*^9}, {3.6888786937177925`*^9, 3.688878750267872*^9}, { 3.6888787903179283`*^9, 3.6888788206179705`*^9}, {3.6888790860283422`*^9, 3.68887909127835*^9}, {3.6890585394429307`*^9, 3.6890585586029577`*^9}, { 3.689058611933032*^9, 3.689058636633067*^9}, 3.6890586753831205`*^9, 3.6890587218131857`*^9, {3.6890588371733475`*^9, 3.6890588479333625`*^9}, 3.6890593143580313`*^9, {3.68939651006566*^9, 3.689396570005744*^9}, 3.7519567199003897`*^9, {3.7519567531116476`*^9, 3.7519568500887613`*^9}, { 3.7519568810345116`*^9, 3.7519569775584803`*^9}, {3.751957015846347*^9, 3.7519570979991937`*^9}, {3.751957130663088*^9, 3.7519571335374126`*^9}, 3.753763435083539*^9, {3.7537636176034584`*^9, 3.753763788907042*^9}, { 3.753763831693569*^9, 3.7537638728401537`*^9}, {3.75376391019105*^9, 3.7537639597106857`*^9}, {3.7537640140260305`*^9, 3.7537640276633615`*^9}, {3.753764070700218*^9, 3.7537641560081577`*^9}, { 3.7537641950926304`*^9, 3.7537643084881086`*^9}, 3.753764389828247*^9, { 3.753764533778655*^9, 3.753764547869378*^9}, {3.7553527505176506`*^9, 3.7553528603017626`*^9}, {3.75538351472929*^9, 3.7553835693549905`*^9}, { 3.755383607438428*^9, 3.7553838360146847`*^9}, {3.7553838766263666`*^9, 3.755383951476962*^9}, {3.755383992736063*^9, 3.7553840478403873`*^9}, { 3.755384124898378*^9, 3.7553842646406417`*^9}, {3.755389313373938*^9, 3.7553893195755854`*^9}, {3.755389381201706*^9, 3.7553894668944387`*^9}, { 3.7553895199108267`*^9, 3.755389537914214*^9}, {3.755389582951442*^9, 3.755389708990402*^9}, 3.7554339398817015`*^9, 3.755434068869628*^9, { 3.7554341297848616`*^9, 3.755434216890894*^9}, {3.7554343528417006`*^9, 3.7554343704056864`*^9}, {3.755434459874297*^9, 3.755434538395585*^9}, 3.755434569759145*^9, {3.7554346233872647`*^9, 3.7554347263294*^9}, { 3.7554347853286095`*^9, 3.7554348093580456`*^9}, {3.755434907172281*^9, 3.755434918847997*^9}, {3.7554349600500207`*^9, 3.7554349983466597`*^9}, { 3.755435110803147*^9, 3.7554351426284623`*^9}, {3.755435324398292*^9, 3.7554353302892075`*^9}, {3.755435441524338*^9, 3.755435445101488*^9}, 3.7554355170109453`*^9, {3.7554358134766097`*^9, 3.755435918833391*^9}, { 3.7554359598830943`*^9, 3.75543598832941*^9}, {3.755436164699664*^9, 3.7554361666501207`*^9}, {3.755436277778627*^9, 3.755436282441655*^9}, { 3.755436433004975*^9, 3.7554365810900373`*^9}, {3.755436713592167*^9, 3.7554367150263915`*^9}, {3.755436752569789*^9, 3.755436782945344*^9}, { 3.75543855564263*^9, 3.755438573014342*^9}, {3.7554386030808535`*^9, 3.75543862876925*^9}, {3.755438665543474*^9, 3.755438666460845*^9}, { 3.755438707655904*^9, 3.7554387115945473`*^9}, {3.7554387585075216`*^9, 3.7554388500917773`*^9}, {3.755523374186784*^9, 3.755523407200748*^9}, { 3.755523628104781*^9, 3.755523629369397*^9}, {3.755523692162763*^9, 3.755523702854873*^9}, 3.7555237667615433`*^9, 3.7555238472382975`*^9, 3.7555241586552105`*^9, 3.755524213729106*^9, 3.755524399719488*^9, 3.75552571772406*^9, {3.7555258075426073`*^9, 3.755525820259694*^9}, 3.755526094753117*^9, 3.7555261757546644`*^9, {3.7555262318295097`*^9, 3.7555262499726152`*^9}, {3.7555370249561615`*^9, 3.755537051432358*^9}, 3.7555372853307257`*^9, {3.755537468732602*^9, 3.755537521108555*^9}, 3.7555375621618104`*^9, {3.7555379391125593`*^9, 3.755537970148187*^9}, { 3.7555674525545197`*^9, 3.755567456059157*^9}, {3.7555675848877916`*^9, 3.7555675985147886`*^9}, {3.7555676718904886`*^9, 3.7555677115434046`*^9}, {3.755567758583485*^9, 3.7555677797901087`*^9}, { 3.755567822059022*^9, 3.755567822195668*^9}, {3.7555678597444773`*^9, 3.7555678604365673`*^9}, 3.7556071757478895`*^9, {3.7556072159647107`*^9, 3.755607332812396*^9}, {3.7556074217009745`*^9, 3.755607426579308*^9}, 3.755607632666421*^9, {3.755607684025096*^9, 3.755607693062358*^9}, { 3.7556077296748147`*^9, 3.755607849742259*^9}, {3.755608033616538*^9, 3.7556080922325497`*^9}, 3.755608142419341*^9, {3.755608958207328*^9, 3.755608980843011*^9}, {3.7559615593543744`*^9, 3.7559615796720657`*^9}, { 3.755961636991267*^9, 3.755961639837885*^9}, {3.755961688066485*^9, 3.7559617050406666`*^9}, {3.75596184181551*^9, 3.755961843331066*^9}, { 3.7560033780948515`*^9, 3.756003424416658*^9}, {3.756003637744131*^9, 3.7560039024762926`*^9}, {3.7560039413994226`*^9, 3.756004010187872*^9}, { 3.75600408826851*^9, 3.7560041132438145`*^9}, {3.7560042095185223`*^9, 3.756004261292776*^9}, {3.7560043015589314`*^9, 3.7560044114376893`*^9}, { 3.7560045878703117`*^9, 3.756004610316883*^9}, {3.756090875492567*^9, 3.756090970250229*^9}, {3.7560910153257923`*^9, 3.756091253656394*^9}, { 3.7560913065394864`*^9, 3.7560913073489447`*^9}, {3.7560913497661376`*^9, 3.7560913829572887`*^9}, {3.7560914229250793`*^9, 3.756091477168485*^9}, { 3.756091512338003*^9, 3.7560916181734085`*^9}, {3.756091734456238*^9, 3.7560917345758953`*^9}, 3.7560919538299203`*^9, {3.756092472598545*^9, 3.7560924728155417`*^9}, {3.756092529494649*^9, 3.7560925295886126`*^9}, { 3.7564428371402044`*^9, 3.7564428827548018`*^9}, {3.756443118409811*^9, 3.7564432825122414`*^9}, {3.7564433139577427`*^9, 3.7564434048585415`*^9}, {3.75644377756419*^9, 3.756443799699541*^9}, { 3.756444020280332*^9, 3.756444052335291*^9}, 3.7564441526092615`*^9, 3.7866921123667355`*^9, {3.786692169420147*^9, 3.786692647713867*^9}, { 3.7866926921591225`*^9, 3.78669273302064*^9}, {3.786692862316063*^9, 3.7866928658349466`*^9}, {3.7866931119911423`*^9, 3.786693309398429*^9}, { 3.7866933409841013`*^9, 3.7866934610423436`*^9}, {3.786693498963604*^9, 3.7866936745285892`*^9}, {3.7866937881495705`*^9, 3.7866937950939436`*^9}, 3.7873246428692293`*^9, {3.787485049135359*^9, 3.787485051961443*^9}, { 3.787485091258519*^9, 3.787485424116222*^9}, {3.7874854543849907`*^9, 3.787485502716935*^9}, {3.7874856358164625`*^9, 3.7874856505267844`*^9}, 3.787494663934597*^9, {3.7874947579329753`*^9, 3.7874947673643074`*^9}, 3.787494920667267*^9, {3.7874950655196714`*^9, 3.7874951753595195`*^9}, { 3.787495215708169*^9, 3.7874952321914797`*^9}, {3.7874953099595947`*^9, 3.7874953434716663`*^9}, {3.7874953776322303`*^9, 3.7874953779837875`*^9}, {3.7875363421179075`*^9, 3.787536342508462*^9}, { 3.7875368085158997`*^9, 3.787536878302806*^9}, {3.7875369599529157`*^9, 3.7875370055885963`*^9}, {3.7875835060582986`*^9, 3.787583520821555*^9}, { 3.787583689937277*^9, 3.787583802553567*^9}, 3.7875838594185114`*^9, { 3.7875847456381392`*^9, 3.787584763036994*^9}, {3.787626017181223*^9, 3.787626056127921*^9}, {3.787626222566106*^9, 3.7876263421533365`*^9}, { 3.787626618958929*^9, 3.787626769278859*^9}, {3.7876268408301697`*^9, 3.7876269773439765`*^9}, {3.787627036414548*^9, 3.7876270708938274`*^9}, { 3.7876271161212626`*^9, 3.787627166521246*^9}, {3.787627218096628*^9, 3.787627360333486*^9}, {3.7876274396002846`*^9, 3.7876275494095793`*^9}, { 3.7876275828585815`*^9, 3.7876276051078897`*^9}, {3.787627643428895*^9, 3.7876279457383013`*^9}, {3.7876279985548644`*^9, 3.7876280606848803`*^9}, {3.7876281009928503`*^9, 3.787628119386298*^9}, { 3.7876283050026827`*^9, 3.7876283207471905`*^9}, {3.787628360297442*^9, 3.7876283695328703`*^9}, {3.7876284743277445`*^9, 3.7876285379433393`*^9}, {3.7876285852938123`*^9, 3.787628625163664*^9}, { 3.7876286848615*^9, 3.7876286910090876`*^9}, 3.7876295116028004`*^9, { 3.7876297046473703`*^9, 3.7876297056283264`*^9}, {3.7876297387312613`*^9, 3.787629757779501*^9}, 3.7876298106703863`*^9, {3.787629859960314*^9, 3.787629902017136*^9}, 3.7876299928494673`*^9, {3.7876506647613673`*^9, 3.7876506804881225`*^9}, {3.7876533444303474`*^9, 3.787653351724442*^9}, { 3.787653758995246*^9, 3.787653955639387*^9}, 3.78765405058292*^9, { 3.7876541175564795`*^9, 3.7876541249132113`*^9}, {3.787654198335023*^9, 3.787654200402335*^9}, {3.7876542598584185`*^9, 3.787654273263777*^9}, { 3.787654576327304*^9, 3.787654600865675*^9}, {3.787654632137179*^9, 3.7876546607774854`*^9}, {3.849339047133091*^9, 3.84933905664736*^9}, { 3.850637993079445*^9, 3.8506380126114783`*^9}, {3.8506380462940454`*^9, 3.8506380669349008`*^9}, {3.850638100377042*^9, 3.8506381057776403`*^9}, { 3.8506382329360204`*^9, 3.8506382380730076`*^9}, 3.8507911757405424`*^9, { 3.8507913292877855`*^9, 3.8507913294289546`*^9}, {3.850791394259633*^9, 3.8507913944337826`*^9}, {3.850791437007037*^9, 3.8507914371461887`*^9}, { 3.8507916615414457`*^9, 3.8507916616667194`*^9}, {3.8507919475410585`*^9, 3.850791948524747*^9}}, CellLabel-> "In[401]:=",ExpressionUUID->"294c0193-e7d5-4b80-8e52-08165ec414d6"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "condition", " ", "at", " ", "the", " ", "clamped", " ", "boundaries"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"bnd2", "=", RowBox[{"Union", "[", RowBox[{"Flatten", "[", RowBox[{"Pick", "[", RowBox[{"seg", ",", RowBox[{"Thread", "[", RowBox[{"mrk", "\[Equal]", "2"}], "]"}]}], "]"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"bnd4", "=", RowBox[{"Union", "[", RowBox[{"Flatten", "[", RowBox[{"Pick", "[", RowBox[{"seg", ",", RowBox[{"Thread", "[", RowBox[{"mrk", "\[Equal]", "4"}], "]"}]}], "]"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"cnd", "=", RowBox[{"Flatten", "[", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"uZ", "[", "#", "]"}], "\[Rule]", "0"}], ",", RowBox[{ RowBox[{"\[Theta]X", "[", "#", "]"}], "\[Rule]", "0"}], ",", RowBox[{ RowBox[{"\[Theta]Y", "[", "#", "]"}], "\[Rule]", "0"}]}], "}"}], "&"}], ",", RowBox[{"Join", "[", RowBox[{"bnd2", ",", "bnd4"}], "]"}]}], "]"}], "]"}]}], ";"}], "\n", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"problem", " ", "decription"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ii", "=", "1"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ele", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"-", "p"}]}], "}"}]}], "}"}], ",", "#"}], "}"}], " ", "&"}], ",", "nod"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", "=", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Append", "[", RowBox[{"#", ",", "0"}], "]"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "ii", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", "ii", "]"}], ",", RowBox[{"\[Theta]Y", "[", RowBox[{"ii", "++"}], "]"}], ",", "0"}], "}"}]}], "}"}], " ", "&"}], ",", "crd"}], "]"}], " ", "/.", "cnd"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"MESH", "[", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "//.", "val"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"displacement", " ", "solution"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"sol", "=", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "//.", "val"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SHOW3D", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "1"}], "}"}], ",", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "//.", "val"}], " ", "/.", "sol"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"uZ", "[", "5", "]"}], " ", "/.", "sol"}], "\[IndentingNewLine]", RowBox[{"Length", "[", "sol", "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.6888689611245327`*^9, 3.6888691441747894`*^9}, { 3.688869175904834*^9, 3.6888691949848604`*^9}, {3.688869303295012*^9, 3.6888694251851826`*^9}, {3.688869534825336*^9, 3.6888695373653393`*^9}, { 3.6888695909654145`*^9, 3.688869620615456*^9}, {3.6888696695055246`*^9, 3.688869671645528*^9}, {3.688869703665572*^9, 3.688869771185667*^9}, { 3.6888698131457253`*^9, 3.688869843195768*^9}, 3.688869999545987*^9, 3.6888701516861997`*^9, {3.688870779087078*^9, 3.6888708600371914`*^9}, { 3.6888713003778076`*^9, 3.688871303197812*^9}, {3.6888713416978655`*^9, 3.688871422407979*^9}, {3.6888714741080513`*^9, 3.688871476638055*^9}, 3.6888751073437386`*^9, {3.6888752493389473`*^9, 3.6888752569189587`*^9}, { 3.688875289049003*^9, 3.688875320839048*^9}, {3.6888754299492006`*^9, 3.688875430949202*^9}, {3.6888786937177925`*^9, 3.688878750267872*^9}, { 3.6888787903179283`*^9, 3.6888788206179705`*^9}, {3.6888790860283422`*^9, 3.68887909127835*^9}, {3.6890585394429307`*^9, 3.6890585586029577`*^9}, { 3.689058611933032*^9, 3.689058636633067*^9}, 3.6890586753831205`*^9, 3.6890587218131857`*^9, {3.6890588371733475`*^9, 3.6890588479333625`*^9}, 3.6890593143580313`*^9, {3.68939651006566*^9, 3.689396570005744*^9}, 3.7519567199003897`*^9, {3.7519567531116476`*^9, 3.7519568500887613`*^9}, { 3.7519568810345116`*^9, 3.7519569775584803`*^9}, {3.751957015846347*^9, 3.7519570979991937`*^9}, {3.751957130663088*^9, 3.7519571335374126`*^9}, 3.753763435083539*^9, {3.7537636176034584`*^9, 3.753763788907042*^9}, { 3.753763831693569*^9, 3.7537638728401537`*^9}, {3.75376391019105*^9, 3.7537639597106857`*^9}, {3.7537640140260305`*^9, 3.7537640276633615`*^9}, {3.753764070700218*^9, 3.7537641560081577`*^9}, { 3.7537641950926304`*^9, 3.7537643084881086`*^9}, 3.753764389828247*^9, { 3.753764533778655*^9, 3.753764547869378*^9}, {3.7553527505176506`*^9, 3.7553528603017626`*^9}, {3.75538351472929*^9, 3.7553835693549905`*^9}, { 3.755383607438428*^9, 3.7553838360146847`*^9}, {3.7553838766263666`*^9, 3.755383951476962*^9}, {3.755383992736063*^9, 3.7553840478403873`*^9}, { 3.755384124898378*^9, 3.7553842646406417`*^9}, {3.755389313373938*^9, 3.7553893195755854`*^9}, {3.755389381201706*^9, 3.7553894668944387`*^9}, { 3.7553895199108267`*^9, 3.755389537914214*^9}, {3.755389582951442*^9, 3.755389708990402*^9}, 3.7554339398817015`*^9, 3.755434068869628*^9, { 3.7554341297848616`*^9, 3.755434216890894*^9}, {3.7554343528417006`*^9, 3.7554343704056864`*^9}, {3.755434459874297*^9, 3.755434538395585*^9}, 3.755434569759145*^9, {3.7554346233872647`*^9, 3.7554347263294*^9}, { 3.7554347853286095`*^9, 3.7554348093580456`*^9}, {3.755434907172281*^9, 3.755434918847997*^9}, {3.7554349600500207`*^9, 3.7554349983466597`*^9}, { 3.755435110803147*^9, 3.7554351426284623`*^9}, {3.755435324398292*^9, 3.7554353302892075`*^9}, {3.755435441524338*^9, 3.755435445101488*^9}, 3.7554355170109453`*^9, {3.7554358134766097`*^9, 3.755435918833391*^9}, { 3.7554359598830943`*^9, 3.75543598832941*^9}, {3.755436164699664*^9, 3.7554361666501207`*^9}, {3.755436277778627*^9, 3.755436282441655*^9}, { 3.755436433004975*^9, 3.7554365810900373`*^9}, {3.755436713592167*^9, 3.7554367150263915`*^9}, {3.755436752569789*^9, 3.755436782945344*^9}, { 3.75543855564263*^9, 3.755438573014342*^9}, {3.7554386030808535`*^9, 3.75543862876925*^9}, {3.755438665543474*^9, 3.755438666460845*^9}, { 3.755438707655904*^9, 3.7554387115945473`*^9}, {3.7554387585075216`*^9, 3.7554388500917773`*^9}, {3.755523374186784*^9, 3.755523407200748*^9}, { 3.755523628104781*^9, 3.755523629369397*^9}, {3.755523692162763*^9, 3.755523702854873*^9}, 3.7555237667615433`*^9, 3.7555238472382975`*^9, 3.7555241586552105`*^9, 3.755524213729106*^9, 3.755524399719488*^9, 3.75552571772406*^9, {3.7555258075426073`*^9, 3.755525820259694*^9}, 3.755526094753117*^9, 3.7555261757546644`*^9, {3.7555262318295097`*^9, 3.7555262499726152`*^9}, {3.7555370249561615`*^9, 3.755537051432358*^9}, 3.7555372853307257`*^9, {3.755537468732602*^9, 3.755537521108555*^9}, 3.7555375621618104`*^9, {3.7555379391125593`*^9, 3.755537970148187*^9}, { 3.7555674525545197`*^9, 3.755567456059157*^9}, {3.7555675848877916`*^9, 3.7555675985147886`*^9}, {3.7555676718904886`*^9, 3.7555677115434046`*^9}, {3.755567758583485*^9, 3.7555677797901087`*^9}, { 3.755567822059022*^9, 3.755567822195668*^9}, {3.7555678597444773`*^9, 3.7555678604365673`*^9}, 3.7556071757478895`*^9, {3.7556072159647107`*^9, 3.755607332812396*^9}, {3.7556074217009745`*^9, 3.755607426579308*^9}, 3.755607632666421*^9, {3.755607684025096*^9, 3.755607693062358*^9}, { 3.7556077296748147`*^9, 3.755607849742259*^9}, {3.755608033616538*^9, 3.7556080922325497`*^9}, 3.755608142419341*^9, {3.755608958207328*^9, 3.755608980843011*^9}, {3.7559615593543744`*^9, 3.7559615796720657`*^9}, { 3.755961636991267*^9, 3.755961639837885*^9}, {3.755961688066485*^9, 3.7559617050406666`*^9}, {3.75596184181551*^9, 3.755961843331066*^9}, { 3.7560033780948515`*^9, 3.756003424416658*^9}, {3.756003637744131*^9, 3.7560039024762926`*^9}, {3.7560039413994226`*^9, 3.756004010187872*^9}, { 3.75600408826851*^9, 3.7560041132438145`*^9}, {3.7560042095185223`*^9, 3.756004261292776*^9}, {3.7560043015589314`*^9, 3.7560044114376893`*^9}, { 3.7560045878703117`*^9, 3.756004610316883*^9}, {3.756090875492567*^9, 3.756090970250229*^9}, {3.7560910153257923`*^9, 3.756091253656394*^9}, { 3.7560913065394864`*^9, 3.7560913073489447`*^9}, {3.7560913497661376`*^9, 3.7560913829572887`*^9}, {3.7560914229250793`*^9, 3.756091477168485*^9}, { 3.756091512338003*^9, 3.7560916181734085`*^9}, {3.756091734456238*^9, 3.7560917345758953`*^9}, 3.7560919538299203`*^9, {3.756092472598545*^9, 3.7560924728155417`*^9}, {3.756092529494649*^9, 3.7560925295886126`*^9}, { 3.7564428371402044`*^9, 3.7564428827548018`*^9}, {3.756443118409811*^9, 3.7564432825122414`*^9}, {3.7564433139577427`*^9, 3.7564434048585415`*^9}, {3.75644377756419*^9, 3.756443799699541*^9}, { 3.756444020280332*^9, 3.756444052335291*^9}, 3.7564441526092615`*^9, 3.7866921123667355`*^9, {3.786692169420147*^9, 3.786692647713867*^9}, { 3.7866926921591225`*^9, 3.78669273302064*^9}, {3.786692862316063*^9, 3.7866928658349466`*^9}, {3.7866931119911423`*^9, 3.786693309398429*^9}, { 3.7866933409841013`*^9, 3.7866934610423436`*^9}, {3.786693498963604*^9, 3.7866936745285892`*^9}, {3.7866937881495705`*^9, 3.7866937950939436`*^9}, 3.7873246428692293`*^9, {3.787485049135359*^9, 3.787485051961443*^9}, { 3.787485091258519*^9, 3.787485424116222*^9}, {3.7874854543849907`*^9, 3.787485502716935*^9}, {3.7874856358164625`*^9, 3.7874856505267844`*^9}, 3.787494663934597*^9, {3.7874947579329753`*^9, 3.7874947673643074`*^9}, 3.787494920667267*^9, {3.7874950655196714`*^9, 3.7874951753595195`*^9}, { 3.787495215708169*^9, 3.7874952321914797`*^9}, {3.7874953099595947`*^9, 3.7874953434716663`*^9}, {3.7874953776322303`*^9, 3.7874953779837875`*^9}, {3.7875363421179075`*^9, 3.787536342508462*^9}, { 3.7875368085158997`*^9, 3.787536878302806*^9}, {3.7875369599529157`*^9, 3.7875370055885963`*^9}, {3.7875835060582986`*^9, 3.787583520821555*^9}, { 3.787583689937277*^9, 3.787583802553567*^9}, 3.7875838594185114`*^9, { 3.7875847456381392`*^9, 3.787584763036994*^9}, {3.787626017181223*^9, 3.787626056127921*^9}, {3.787626222566106*^9, 3.7876263421533365`*^9}, { 3.787626618958929*^9, 3.787626769278859*^9}, {3.7876268408301697`*^9, 3.7876269773439765`*^9}, {3.787627036414548*^9, 3.7876270708938274`*^9}, { 3.7876271161212626`*^9, 3.787627166521246*^9}, {3.787627218096628*^9, 3.787627360333486*^9}, {3.7876274396002846`*^9, 3.7876275494095793`*^9}, { 3.7876275828585815`*^9, 3.7876276051078897`*^9}, {3.787627643428895*^9, 3.7876279457383013`*^9}, {3.7876279985548644`*^9, 3.7876280606848803`*^9}, {3.7876281009928503`*^9, 3.787628119386298*^9}, { 3.7876283050026827`*^9, 3.7876283207471905`*^9}, {3.787628360297442*^9, 3.7876283695328703`*^9}, {3.7876284743277445`*^9, 3.7876285379433393`*^9}, {3.7876285852938123`*^9, 3.787628625163664*^9}, { 3.7876286848615*^9, 3.7876286910090876`*^9}, 3.7876295116028004`*^9, { 3.7876297046473703`*^9, 3.7876297056283264`*^9}, {3.7876297387312613`*^9, 3.787629757779501*^9}, 3.7876298106703863`*^9, {3.787629859960314*^9, 3.787629902017136*^9}, 3.7876299928494673`*^9, {3.7876506647613673`*^9, 3.7876506804881225`*^9}, {3.7876533444303474`*^9, 3.787653351724442*^9}, { 3.787653758995246*^9, 3.787653955639387*^9}, {3.78765405058292*^9, 3.787654070902216*^9}, 3.787654213377517*^9, {3.7876542858754635`*^9, 3.787654287552429*^9}, {3.787654363512497*^9, 3.7876543828791847`*^9}, 3.7877108517929688`*^9, {3.84933901209382*^9, 3.8493390188417115`*^9}, { 3.850638127788494*^9, 3.8506381297019253`*^9}, {3.850638173389373*^9, 3.8506381744526567`*^9}, {3.8507910864194975`*^9, 3.8507911001190476`*^9}, {3.850791460607442*^9, 3.8507914660338907`*^9}}, CellLabel-> "In[407]:=",ExpressionUUID->"7ce693b9-92f9-4095-b3f3-ba8b9c1c44ba"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 1 (bar truss)", "Subsubsection", CellChangeTimes->{{3.473061354483*^9, 3.473061370995*^9}, { 3.4730615048269997`*^9, 3.473061506814*^9}, 3.4730617526730003`*^9, 3.5674300455873146`*^9, 3.5674301547407064`*^9, {3.599224775421587*^9, 3.599224775795988*^9}, {3.686233712964652*^9, 3.686233737814687*^9}, { 3.686462478831975*^9, 3.6864624804619775`*^9}, {3.692004483813607*^9, 3.692004508753642*^9}, 3.7876249165908413`*^9},ExpressionUUID->"f305e74a-235e-4baa-b83e-\ 086cde406e13"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"4", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "4"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{ SqrtBox["8"], "A"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{ SqrtBox["8"], "A"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"4", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"-", "F"}]}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", " ", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", " ", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}], "Input", CellChangeTimes->{{3.4426465840284452`*^9, 3.4426465892856455`*^9}, { 3.442646804859646*^9, 3.442646838774046*^9}, {3.473061388457*^9, 3.473061428737*^9}, 3.4734695779694*^9, {3.56748861907835*^9, 3.567488647267599*^9}, {3.5674887133961153`*^9, 3.567488713786116*^9}, { 3.629779795335684*^9, 3.629779927389916*^9}, {3.6297874043730154`*^9, 3.6297874265094547`*^9}, {3.6305530716721077`*^9, 3.630553079300544*^9}, { 3.630675957233904*^9, 3.630675996863765*^9}, {3.6306760991857443`*^9, 3.6306761426832323`*^9}, {3.6307395810851164`*^9, 3.63073959471954*^9}, { 3.6852608074149914`*^9, 3.6852608342450294`*^9}, 3.685261964306611*^9, 3.685267237733994*^9, {3.6852714775732045`*^9, 3.6852714824832115`*^9}, { 3.68534178007981*^9, 3.6853418242453365`*^9}, {3.6853423481463013`*^9, 3.68534237731597*^9}, {3.685344715012679*^9, 3.685344741643202*^9}, { 3.6864624845319834`*^9, 3.686462628752185*^9}, {3.6864627547623615`*^9, 3.686462780662398*^9}, 3.6876000630120287`*^9, {3.692004516933654*^9, 3.69200472173394*^9}, {3.7238001148135943`*^9, 3.7238001159435806`*^9}, { 3.7552812833582325`*^9, 3.755281465277815*^9}, {3.755281499276145*^9, 3.7552815743148856`*^9}, {3.819777247860895*^9, 3.8197772637280893`*^9}}, CellLabel->"In[75]:=",ExpressionUUID->"1b42415b-f374-4028-bc46-9a8e3c4ff053"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 2 (beam structure)", "Subsubsection", CellChangeTimes->{{3.473061354483*^9, 3.473061370995*^9}, { 3.4730615048269997`*^9, 3.473061506814*^9}, 3.4730617526730003`*^9, 3.5674300455873146`*^9, 3.5674301547407064`*^9, {3.599224775421587*^9, 3.599224775795988*^9}, {3.686233712964652*^9, 3.686233737814687*^9}, 3.686463173752948*^9, 3.692004488803614*^9, {3.692004765984002*^9, 3.6920047817840242`*^9}, 3.7876249198908176`*^9},ExpressionUUID->"40e8ce7f-ca56-4fba-abdb-\ 7521c01c000c"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "4"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "F"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "3", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"3", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}], "Input", CellChangeTimes->{{3.4426465840284452`*^9, 3.4426465892856455`*^9}, { 3.442646804859646*^9, 3.442646838774046*^9}, {3.473061388457*^9, 3.473061428737*^9}, 3.4734695779694*^9, {3.56748861907835*^9, 3.567488647267599*^9}, {3.5674887133961153`*^9, 3.567488713786116*^9}, { 3.629779795335684*^9, 3.629779927389916*^9}, {3.6297874043730154`*^9, 3.6297874265094547`*^9}, {3.6305530716721077`*^9, 3.630553079300544*^9}, { 3.630675957233904*^9, 3.630675996863765*^9}, {3.6306760991857443`*^9, 3.6306761426832323`*^9}, {3.6307395810851164`*^9, 3.63073959471954*^9}, { 3.6852608074149914`*^9, 3.6852608342450294`*^9}, 3.685261964306611*^9, 3.685267237733994*^9, {3.6852714775732045`*^9, 3.6852714824832115`*^9}, { 3.68534178007981*^9, 3.6853418242453365`*^9}, {3.6853423481463013`*^9, 3.68534237731597*^9}, {3.685344715012679*^9, 3.685344741643202*^9}, 3.6876000739430437`*^9, {3.69200479275404*^9, 3.6920050211343594`*^9}, { 3.723800088983532*^9, 3.723800090369502*^9}, {3.755281662771347*^9, 3.755281668907722*^9}, {3.819777312265813*^9, 3.8197773157181125`*^9}, { 3.819781904225833*^9, 3.819781980419295*^9}, {3.8197820206687484`*^9, 3.819782026383217*^9}}, CellLabel->"In[86]:=",ExpressionUUID->"43012530-aa11-497f-87ee-9dffa423d82b"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 3 (beam truss)", "Subsubsection", CellChangeTimes->{{3.473055608665*^9, 3.4730556508570004`*^9}, { 3.473057986849*^9, 3.473057995505*^9}, {3.473061553363*^9, 3.4730615754709997`*^9}, {3.4730617586879997`*^9, 3.4730617595109997`*^9}, 3.567430048036519*^9, {3.5674301970479803`*^9, 3.567430205846396*^9}, { 3.5992247831280007`*^9, 3.599224789570812*^9}, {3.6862337168646574`*^9, 3.6862337397746897`*^9}, {3.68629059311831*^9, 3.6862906012683215`*^9}, 3.6920044912936172`*^9, {3.692005080664443*^9, 3.6920050874244523`*^9}, 3.7876249275793595`*^9},ExpressionUUID->"d1bd5a48-c362-412a-8d6d-\ ba7e898516b3"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0", ",", RowBox[{"-", "M"}], ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}], "Input", CellChangeTimes->{ 3.442646896400446*^9, {3.473058050178*^9, 3.473058242583*^9}, { 3.473058273832*^9, 3.473058275781*^9}, {3.4730583246470003`*^9, 3.473058418342*^9}, {3.473058484495*^9, 3.47305848615*^9}, { 3.473061601906*^9, 3.473061685848*^9}, {3.5674302269220333`*^9, 3.5674302407904577`*^9}, {3.567488739432561*^9, 3.567488848804353*^9}, { 3.5674892287386227`*^9, 3.5674892390034404`*^9}, {3.62978936549926*^9, 3.6297895519507875`*^9}, {3.6297901935019145`*^9, 3.6297902812676687`*^9}, {3.6297915128898315`*^9, 3.62979152889546*^9}, 3.629791607815998*^9, {3.629870491103406*^9, 3.629870525875867*^9}, { 3.630569827149594*^9, 3.6305698469927287`*^9}, {3.6305700587188387`*^9, 3.6305700685033984`*^9}, 3.6305701178622217`*^9, {3.6305702743651733`*^9, 3.630570286132846*^9}, {3.6305884293266025`*^9, 3.6305884379378176`*^9}, { 3.630588892460216*^9, 3.6305889218974676`*^9}, {3.6305890060752153`*^9, 3.630589009351221*^9}, {3.6305890670869226`*^9, 3.6305890695517273`*^9}, { 3.6852609345251694`*^9, 3.6852609544951973`*^9}, {3.685260985325241*^9, 3.6852610561353397`*^9}, {3.6852611137454205`*^9, 3.685261294805674*^9}, 3.6852619439765825`*^9, 3.685267231203985*^9, {3.6852714918932247`*^9, 3.6852714982332335`*^9}, {3.685341844218479*^9, 3.6853419077321115`*^9}, { 3.685876041473126*^9, 3.6858760505831385`*^9}, 3.6862906560183983`*^9, { 3.686290701298462*^9, 3.6862907191684866`*^9}, 3.6876000892040653`*^9, { 3.692005099424469*^9, 3.692005126334507*^9}, {3.6920052956347437`*^9, 3.6920053647348404`*^9}, {3.6920073658081074`*^9, 3.692007368868112*^9}, { 3.755281747342649*^9, 3.7552817544032793`*^9}, {3.8197773382954226`*^9, 3.8197773422706566`*^9}, 3.8197821573500376`*^9}, CellLabel-> "In[339]:=",ExpressionUUID->"6be92904-f706-4f83-b1ba-ec89ab7c83af"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 4 (beam truss)", "Subsubsection", CellChangeTimes->{{3.473061354483*^9, 3.473061370995*^9}, { 3.4730615048269997`*^9, 3.473061506814*^9}, {3.473061742094*^9, 3.473061762285*^9}, 3.567430050922524*^9, {3.567431829809649*^9, 3.5674318300904493`*^9}, {3.567431908886188*^9, 3.567431917965404*^9}, { 3.599224811863251*^9, 3.599224812268852*^9}, 3.686290397238036*^9, { 3.68646345367334*^9, 3.6864634569533443`*^9}, 3.6864663436772566`*^9, { 3.686650112822079*^9, 3.6866501251020966`*^9}, {3.6920072657679677`*^9, 3.692007266607969*^9}, {3.723800212618948*^9, 3.7238002218043814`*^9}, 3.7876249306286964`*^9},ExpressionUUID->"0d12dbb4-74f7-43be-a632-\ eed8f4f70f54"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "f"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"4", ",", "3"}], "}"}], "]"}]}], "}"}]}], "\[IndentingNewLine]", "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}], "Input", CellChangeTimes->{{3.4426465840284452`*^9, 3.4426465892856455`*^9}, { 3.442646804859646*^9, 3.442646838774046*^9}, {3.473061388457*^9, 3.473061428737*^9}, 3.4730617731*^9, 3.567431929993025*^9, { 3.567431974016302*^9, 3.5674320810480905`*^9}, {3.5674890909903803`*^9, 3.5674891595525007`*^9}, {3.6297906188366613`*^9, 3.6297907609373107`*^9}, 3.6297908204358153`*^9, 3.6297911125307283`*^9, {3.629791153356*^9, 3.629791155321604*^9}, {3.629791373097986*^9, 3.6297913814596004`*^9}, { 3.6305532313682413`*^9, 3.6305532595738544`*^9}, {3.685261672976204*^9, 3.685261743386302*^9}, {3.68526183461643*^9, 3.6852619078265324`*^9}, 3.6852620332367077`*^9, {3.68526207754677*^9, 3.685262079426772*^9}, 3.6852672173839655`*^9, {3.6852715282732754`*^9, 3.6852715335432825`*^9}, { 3.685346747734944*^9, 3.685346764006874*^9}, 3.6876002294042616`*^9, 3.6920072921580048`*^9, {3.6920172043090706`*^9, 3.692017263929154*^9}, { 3.6920174300493865`*^9, 3.6920174602394285`*^9}, {3.692017504419491*^9, 3.692017581889599*^9}, {3.7238003598908434`*^9, 3.72380039128267*^9}, { 3.7552818429234576`*^9, 3.755281878876894*^9}, 3.7552820401590757`*^9, { 3.7552820887897696`*^9, 3.7552820920530305`*^9}, {3.819782282769621*^9, 3.819782296979185*^9}}, CellLabel->"In[7]:=",ExpressionUUID->"1918b464-9c6a-4c4b-8265-7ccf8f2a25c3"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 5 (bar)", "Subsubsection", CellChangeTimes->{{3.473055608665*^9, 3.4730556508570004`*^9}, { 3.473057986849*^9, 3.473057995505*^9}, {3.473061553363*^9, 3.4730615754709997`*^9}, {3.4730617586879997`*^9, 3.4730617595109997`*^9}, {3.473061806072*^9, 3.4730618092860003`*^9}, 3.567430053590129*^9, 3.5674302916621466`*^9, {3.59922479409482*^9, 3.5992247947344213`*^9}, 3.686233727874673*^9, 3.6862907545885363`*^9, 3.6920044935936213`*^9, {3.6920055576551104`*^9, 3.692005561315116*^9}, 3.7238002254871435`*^9, 3.7876249331468368`*^9},ExpressionUUID->"af4e2120-5c8e-4192-b992-\ dac529915bad"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Rho]", " ", "A", " ", "g"}], ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}], "Input", CellChangeTimes->{ 3.442646896400446*^9, {3.473058050178*^9, 3.473058242583*^9}, { 3.473058273832*^9, 3.473058275781*^9}, {3.4730583246470003`*^9, 3.473058418342*^9}, {3.473058484495*^9, 3.47305848615*^9}, { 3.473061601906*^9, 3.473061685848*^9}, {3.4730618307860003`*^9, 3.473062130566*^9}, {3.5674305015137157`*^9, 3.567430508034527*^9}, 3.5674306789176273`*^9, {3.5674889411989174`*^9, 3.567489021180258*^9}, { 3.6297903068985133`*^9, 3.629790413571501*^9}, {3.629790456471576*^9, 3.629790478888816*^9}, {3.6297905091060686`*^9, 3.6297905324281096`*^9}, 3.6297915982999816`*^9, {3.629870281797838*^9, 3.629870287819449*^9}, { 3.629870322950711*^9, 3.629870429155697*^9}, {3.6307481815629396`*^9, 3.6307482184414043`*^9}, {3.6852614772659297`*^9, 3.685261629646143*^9}, { 3.6852619208965507`*^9, 3.685261929826563*^9}, 3.6852672248539762`*^9, { 3.6852715094232492`*^9, 3.6852715139832554`*^9}, 3.685330160876338*^9, 3.685330191642098*^9, {3.6853398909644113`*^9, 3.685339924654458*^9}, { 3.6858760739831715`*^9, 3.685876077853177*^9}, {3.686290816478623*^9, 3.6862908363386507`*^9}, {3.6868258114230947`*^9, 3.6868258331431255`*^9}, 3.6868273566352577`*^9, 3.687600102954085*^9, {3.6920055669051237`*^9, 3.6920056989553084`*^9}, {3.7552821496563406`*^9, 3.7552821715493975`*^9}, {3.819782394768776*^9, 3.819782395299322*^9}, { 3.850699113589163*^9, 3.850699114830697*^9}}, CellLabel->"In[10]:=",ExpressionUUID->"50852c4a-36d3-48eb-a933-a250e705b392"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 6 (beam)", "Subsubsection", CellChangeTimes->{{3.473061354483*^9, 3.473061370995*^9}, { 3.4730615048269997`*^9, 3.473061506814*^9}, 3.4730617526730003`*^9, 3.5674300455873146`*^9, 3.5674301547407064`*^9, {3.599224775421587*^9, 3.599224775795988*^9}, {3.686233712964652*^9, 3.686233737814687*^9}, 3.6862904664481325`*^9, 3.686458624014577*^9, 3.6864631774529533`*^9, { 3.686463277853094*^9, 3.6864632843931026`*^9}, 3.692004496313625*^9, { 3.6920057803254223`*^9, 3.692005780945423*^9}, 3.723800228134458*^9, 3.7876249354672213`*^9},ExpressionUUID->"4b1a7d5f-3a18-47d6-b7b5-\ 01339f45040e"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"m", " ", "g"}]}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}], "Input", CellChangeTimes->{{3.4426465840284452`*^9, 3.4426465892856455`*^9}, { 3.442646804859646*^9, 3.442646838774046*^9}, {3.473061388457*^9, 3.473061428737*^9}, 3.4734695779694*^9, {3.56748861907835*^9, 3.567488647267599*^9}, {3.5674887133961153`*^9, 3.567488713786116*^9}, { 3.629779795335684*^9, 3.629779927389916*^9}, {3.6297874043730154`*^9, 3.6297874265094547`*^9}, {3.6305530716721077`*^9, 3.630553079300544*^9}, { 3.630675957233904*^9, 3.630675996863765*^9}, {3.6306760991857443`*^9, 3.6306761426832323`*^9}, {3.6307395810851164`*^9, 3.63073959471954*^9}, { 3.6852608074149914`*^9, 3.6852608342450294`*^9}, 3.685261964306611*^9, 3.685267237733994*^9, {3.6852714775732045`*^9, 3.6852714824832115`*^9}, { 3.68534178007981*^9, 3.6853418242453365`*^9}, {3.6853423481463013`*^9, 3.68534237731597*^9}, {3.685344715012679*^9, 3.685344741643202*^9}, { 3.6862904953181734`*^9, 3.6862905374482317`*^9}, 3.6876001584241624`*^9, { 3.692005777055418*^9, 3.6920058190554767`*^9}, {3.6920073312080593`*^9, 3.6920073392880707`*^9}, {3.723800525178776*^9, 3.7238005261261005`*^9}, { 3.755282243395219*^9, 3.755282245406639*^9}, {3.7552823157132893`*^9, 3.7552823330704985`*^9}, {3.8197774253106804`*^9, 3.8197774297587595`*^9}, {3.8197824801555943`*^9, 3.819782595987687*^9}}, CellLabel-> "In[124]:=",ExpressionUUID->"3e9347cc-0751-43c8-9780-92f344db507a"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 7 (thin slab)", "Subsubsection", CellChangeTimes->{{3.4430685047746*^9, 3.4430685067558002`*^9}, { 3.4430866035033803`*^9, 3.4430866067013803`*^9}, 3.4742603622347393`*^9, { 3.47426082029274*^9, 3.4742608300977397`*^9}, {3.4742616255317397`*^9, 3.4742616631637397`*^9}, 3.47426171431174*^9, {3.569295755520348*^9, 3.569295758265953*^9}, {3.5999975352114353`*^9, 3.5999975364126377`*^9}, { 3.6862916156897416`*^9, 3.6862916164197426`*^9}, {3.6862917162198825`*^9, 3.6862917246998944`*^9}, 3.686463531723449*^9, 3.6920044987836285`*^9, { 3.692006070175828*^9, 3.692006073605833*^9}, 3.72380023043182*^9, 3.7876249380420866`*^9},ExpressionUUID->"f5ab83c3-8bf5-4d11-a646-\ 3233038fcb5c"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", " ", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"p", " ", "t"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "1", "]"}], ",", RowBox[{"uY", "[", "1", "]"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", " ", "\[IndentingNewLine]", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "\[IndentingNewLine]", "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}]}]], "Input", CellChangeTimes->{ 3.4426469719054456`*^9, {3.4430685207022*^9, 3.4430685918694*^9}, { 3.4430686602608*^9, 3.44306866271*^9}, {3.4430687542864*^9, 3.4430688359955997`*^9}, {3.4430866305537806`*^9, 3.44308673150138*^9}, { 3.4742604996717396`*^9, 3.47426061596974*^9}, 3.4742609854677396`*^9, 3.569295818310458*^9, 3.569295934780263*^9, {3.631161797385408*^9, 3.63116192958797*^9}, 3.6311621282873344`*^9, {3.6314096475812645`*^9, 3.6314096645540943`*^9}, 3.63140970193176*^9, {3.6314296672834578`*^9, 3.6314296732582684`*^9}, {3.6314297131943383`*^9, 3.631429723193956*^9}, { 3.6320283190146666`*^9, 3.6320283335070925`*^9}, {3.632028523936627*^9, 3.632028541689458*^9}, {3.6630475834142756`*^9, 3.6630475933982935`*^9}, { 3.685322391232018*^9, 3.685322396442025*^9}, {3.685322434252078*^9, 3.68532247101213*^9}, {3.6853440662625723`*^9, 3.685344095349236*^9}, { 3.6853489765747485`*^9, 3.6853489802747536`*^9}, {3.6862916241397533`*^9, 3.6862916684598155`*^9}, {3.687415123418954*^9, 3.6874151238689547`*^9}, 3.687415669729719*^9, {3.6920060638458195`*^9, 3.6920062159860325`*^9}, { 3.692006278026119*^9, 3.692006360616235*^9}, {3.7238005610940094`*^9, 3.7238005623974686`*^9}, {3.755282537168726*^9, 3.755282773413573*^9}, { 3.7552830525825834`*^9, 3.755283052984254*^9}, {3.819778134314925*^9, 3.819778134798916*^9}, {3.819778172830922*^9, 3.819778178063283*^9}, { 3.819778263451173*^9, 3.8197782788524485`*^9}, {3.8197827016773767`*^9, 3.8197828017916217`*^9}, {3.8506991448914785`*^9, 3.8506991524538593`*^9}}, CellLabel->"In[13]:=",ExpressionUUID->"f7ff71bb-1411-4cf6-8d1b-f3631e9936e7"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 8 (thin slab)", "Subsubsection", CellChangeTimes->{{3.4730556702200003`*^9, 3.473055683948*^9}, { 3.473056486087*^9, 3.4730564925030003`*^9}, 3.473057491051*^9, { 3.473057733758*^9, 3.473057755476*^9}, {3.568116356788909*^9, 3.5681163731689377`*^9}, {3.5992231160658693`*^9, 3.59922314473872*^9}, { 3.5992232122508388`*^9, 3.5992232356352797`*^9}, {3.686463442653324*^9, 3.686463466683358*^9}, {3.686650104192067*^9, 3.686650133092108*^9}, { 3.692017996330179*^9, 3.692017999280184*^9}, {3.723800751264373*^9, 3.723800756977186*^9}, 3.7876249404872465`*^9},ExpressionUUID->"3bd95836-af1e-4f36-af7b-\ fbf998125626"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "4", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"F", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "4", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", " ", "\[IndentingNewLine]", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "4", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}], "Input", CellChangeTimes->{{3.599224897569802*^9, 3.599224926773053*^9}, { 3.630748433394182*^9, 3.630748504265106*^9}, {3.6308320967004905`*^9, 3.6308321133874445`*^9}, {3.685263514118781*^9, 3.6852635972488976`*^9}, 3.685267287144063*^9, {3.6853444422720785`*^9, 3.685344490915861*^9}, { 3.6858763098135014`*^9, 3.6858763218235188`*^9}, {3.686226407525676*^9, 3.6862264116856813`*^9}, 3.686445942025214*^9, {3.6866501652021523`*^9, 3.6866502922323303`*^9}, 3.687600260794306*^9, {3.692020854784181*^9, 3.6920209683943405`*^9}, 3.723800734382908*^9, {3.723801165592532*^9, 3.7238011670178595`*^9}, {3.7553462764320617`*^9, 3.755346282581628*^9}, { 3.8197828870206394`*^9, 3.8197829001345263`*^9}, {3.850699178533646*^9, 3.850699180254986*^9}}, CellLabel->"In[16]:=",ExpressionUUID->"95991a94-3d4e-4970-88c8-f8463df0d556"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 9 (structure)", "Subsubsection", CellChangeTimes->{{3.4430685047746*^9, 3.4430685067558002`*^9}, { 3.4430866035033803`*^9, 3.4430866067013803`*^9}, 3.4742603622347393`*^9, { 3.47426082029274*^9, 3.4742608300977397`*^9}, {3.4742616255317397`*^9, 3.4742616631637397`*^9}, 3.47426171431174*^9, {3.569295755520348*^9, 3.569295758265953*^9}, {3.5999975352114353`*^9, 3.5999975364126377`*^9}, { 3.6862916156897416`*^9, 3.6862916164197426`*^9}, 3.6862917141498795`*^9, 3.686463534413453*^9, 3.6920045014936323`*^9, {3.723800620598589*^9, 3.723800620691759*^9}, {3.723801233232855*^9, 3.7238012573010817`*^9}, 3.7876249436429157`*^9},ExpressionUUID->"fe95b371-272c-4bce-a8ec-\ a165464ba891"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "4"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "F"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "1", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "1", "]"}], ",", RowBox[{"uY", "[", "1", "]"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}], "Input", CellChangeTimes->{ 3.4426469719054456`*^9, {3.4430685207022*^9, 3.4430685918694*^9}, { 3.4430686602608*^9, 3.44306866271*^9}, {3.4430687542864*^9, 3.4430688359955997`*^9}, {3.4430866305537806`*^9, 3.44308673150138*^9}, { 3.4742604996717396`*^9, 3.47426061596974*^9}, 3.4742609854677396`*^9, 3.569295818310458*^9, 3.569295934780263*^9, {3.631161797385408*^9, 3.63116192958797*^9}, 3.6311621282873344`*^9, {3.6314096475812645`*^9, 3.6314096645540943`*^9}, 3.63140970193176*^9, {3.6314296672834578`*^9, 3.6314296732582684`*^9}, {3.6314297131943383`*^9, 3.631429723193956*^9}, { 3.6320283190146666`*^9, 3.6320283335070925`*^9}, {3.632028523936627*^9, 3.632028541689458*^9}, {3.6630475834142756`*^9, 3.6630475933982935`*^9}, { 3.685322391232018*^9, 3.685322396442025*^9}, {3.685322434252078*^9, 3.68532247101213*^9}, {3.6853440662625723`*^9, 3.685344095349236*^9}, { 3.6853489765747485`*^9, 3.6853489802747536`*^9}, {3.6862916241397533`*^9, 3.6862916684598155`*^9}, {3.686291740699917*^9, 3.686291791099987*^9}, { 3.6920064252563252`*^9, 3.692006513386449*^9}, {3.692007015637617*^9, 3.69200708896772*^9}, {3.755346344589837*^9, 3.7553463636390886`*^9}, { 3.8197829739657583`*^9, 3.8197829746637754`*^9}, {3.850699199483954*^9, 3.8506992102188063`*^9}}, CellLabel->"In[19]:=",ExpressionUUID->"6caa92a8-46f0-430d-b301-545e39b91a52"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 10 (plate bending mode)", "Subsubsection", CellChangeTimes->{{3.4430685047746*^9, 3.4430685067558002`*^9}, { 3.4430866035033803`*^9, 3.4430866067013803`*^9}, 3.4742603622347393`*^9, { 3.47426082029274*^9, 3.4742608300977397`*^9}, {3.4742616255317397`*^9, 3.4742616631637397`*^9}, 3.47426171431174*^9, {3.569295755520348*^9, 3.569295758265953*^9}, {3.5999975352114353`*^9, 3.5999975364126377`*^9}, { 3.6862916156897416`*^9, 3.6862916164197426`*^9}, 3.6862917141498795`*^9, 3.686291825440035*^9, 3.686463538583459*^9, 3.6920045036236353`*^9, { 3.692007141747794*^9, 3.6920071424377947`*^9}, {3.7238012915092707`*^9, 3.723801291633401*^9}, {3.7238014377077494`*^9, 3.723801461461709*^9}, { 3.7553516202841806`*^9, 3.755351621212493*^9}, 3.7554388732154655`*^9, { 3.7554389252814445`*^9, 3.75543892920196*^9}, 3.755438960659221*^9, 3.7876249485186167`*^9, 3.7877081438848276`*^9, 3.7877106066678762`*^9},ExpressionUUID->"9422d9bf-aa09-44f3-8a07-\ 039d87d59379"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"Block", "[", RowBox[{ RowBox[{"{", RowBox[{ "w", ",", "\[Delta]wint", ",", "\[Delta]W", ",", "\[CapitalOmega]", ",", "sol"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"w", "=", RowBox[{ RowBox[{"a", "[", "0", "]"}], " ", FractionBox["x", "L"], " ", FractionBox["y", "L"]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wint", "[", "w_", "]"}], ":=", RowBox[{"-", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}], "]"}], "\[Transpose]"}], ".", RowBox[{"(", " ", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["t", "3"], " ", "\[CapitalEpsilon]"}], RowBox[{"12", RowBox[{"(", RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}], ")"}]}]], RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "\[Nu]", "0"}, {"\[Nu]", "1", "0"}, {"0", "0", FractionBox[ RowBox[{"1", "-", "\[Nu]"}], "2"]} }], "\[NoBreak]", ")"}]}], ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", "=", RowBox[{"Rectangle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"L", ",", "L"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]W", " ", "=", RowBox[{ RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Integrate", "[", RowBox[{ RowBox[{"\[Delta]wint", "[", "w", "]"}], ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], StyleBox["\[Element]", "OperatorCharacter"], StyleBox["\[CapitalOmega]", "OperatorCharacter"]}]}], StyleBox["]", "OperatorCharacter"]}], StyleBox[",", "OperatorCharacter"], StyleBox[ RowBox[{"L", ">", "0"}], "OperatorCharacter"]}], StyleBox["]", "OperatorCharacter"]}], StyleBox["+", "OperatorCharacter"], RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"w", " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "L"}], ",", RowBox[{"y", "\[Rule]", "L"}]}], "}"}]}], "]"}], " ", "F"}]}]}], StyleBox[";", "OperatorCharacter"], "\[IndentingNewLine]", RowBox[{"sol", " ", "=", RowBox[{"SOLVE", "[", "\[Delta]W", " ", "]"}]}], ";", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"w", " ", "/.", "sol"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", RowBox[{"L", "/", "2"}]}], ",", RowBox[{"y", "\[Rule]", RowBox[{"L", "/", "2"}]}]}], "}"}]}], "]"}]}]}], "]"}]}]], "Input", CellChangeTimes->{ 3.4426469719054456`*^9, {3.4430685207022*^9, 3.4430685918694*^9}, { 3.4430686602608*^9, 3.44306866271*^9}, {3.4430687542864*^9, 3.4430688359955997`*^9}, {3.4430866305537806`*^9, 3.44308673150138*^9}, { 3.4742604996717396`*^9, 3.47426061596974*^9}, 3.4742609854677396`*^9, 3.569295818310458*^9, 3.569295934780263*^9, {3.631161797385408*^9, 3.63116192958797*^9}, 3.6311621282873344`*^9, {3.6314096475812645`*^9, 3.6314096645540943`*^9}, 3.63140970193176*^9, {3.6314296672834578`*^9, 3.6314296732582684`*^9}, {3.6314297131943383`*^9, 3.631429723193956*^9}, { 3.6320283190146666`*^9, 3.6320283335070925`*^9}, {3.632028523936627*^9, 3.632028541689458*^9}, {3.6630475834142756`*^9, 3.6630475933982935`*^9}, { 3.685322391232018*^9, 3.685322396442025*^9}, {3.685322434252078*^9, 3.68532247101213*^9}, {3.6853440662625723`*^9, 3.685344095349236*^9}, { 3.6853489765747485`*^9, 3.6853489802747536`*^9}, {3.6862916241397533`*^9, 3.6862916684598155`*^9}, {3.686291740699917*^9, 3.686291791099987*^9}, { 3.6862918385400534`*^9, 3.68629185767008*^9}, 3.6920072022978787`*^9, 3.755346424741544*^9, {3.7553464606567307`*^9, 3.755346499889244*^9}, { 3.7553465641565332`*^9, 3.7553465866992493`*^9}, 3.755352181219705*^9, { 3.8197830540070057`*^9, 3.8197831146556287`*^9}, {3.8197831473868027`*^9, 3.8197831720630856`*^9}, {3.8197928508538337`*^9, 3.819792907159875*^9}, { 3.850699232073991*^9, 3.850699376103595*^9}, {3.8511331557648935`*^9, 3.851133177216421*^9}}, CellLabel-> "In[418]:=",ExpressionUUID->"50edbbb6-5a30-4c82-ac9c-d209e5d79db0"] }, Closed]], Cell[CellGroupData[{ Cell["Home assignment 1 (bar truss)", "Subsubsection", CellChangeTimes->{{3.473055608665*^9, 3.4730556508570004`*^9}, { 3.473057986849*^9, 3.473057995505*^9}, {3.473061553363*^9, 3.4730615754709997`*^9}, {3.4730617586879997`*^9, 3.4730617595109997`*^9}, 3.567430048036519*^9, {3.5674301970479803`*^9, 3.567430205846396*^9}, { 3.5992247831280007`*^9, 3.599224789570812*^9}, {3.6862337168646574`*^9, 3.6862337397746897`*^9}, {3.68629059311831*^9, 3.6862906012683215`*^9}, 3.6920044912936172`*^9, {3.692005080664443*^9, 3.6920050874244523`*^9}, { 3.7238016457050695`*^9, 3.7238016485700293`*^9}, {3.7553466534521055`*^9, 3.755346654634207*^9}},ExpressionUUID->"badb3562-d10c-4069-b6f4-\ fb91f1719da7"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "F"}], ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"-", "L"}], " ", RowBox[{"Cos", "[", "\[Alpha]", "]"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"L", " ", RowBox[{"Sin", "[", "\[Alpha]", "]"}]}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"uY", "[", "2", "]"}], ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"L", " ", RowBox[{"Cos", "[", "\[Alpha]", "]"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}], "Input", CellChangeTimes->{ 3.442646896400446*^9, {3.473058050178*^9, 3.473058242583*^9}, { 3.473058273832*^9, 3.473058275781*^9}, {3.4730583246470003`*^9, 3.473058418342*^9}, {3.473058484495*^9, 3.47305848615*^9}, { 3.473061601906*^9, 3.473061685848*^9}, {3.5674302269220333`*^9, 3.5674302407904577`*^9}, {3.567488739432561*^9, 3.567488848804353*^9}, { 3.5674892287386227`*^9, 3.5674892390034404`*^9}, {3.62978936549926*^9, 3.6297895519507875`*^9}, {3.6297901935019145`*^9, 3.6297902812676687`*^9}, {3.6297915128898315`*^9, 3.62979152889546*^9}, 3.629791607815998*^9, {3.629870491103406*^9, 3.629870525875867*^9}, { 3.630569827149594*^9, 3.6305698469927287`*^9}, {3.6305700587188387`*^9, 3.6305700685033984`*^9}, 3.6305701178622217`*^9, {3.6305702743651733`*^9, 3.630570286132846*^9}, {3.6305884293266025`*^9, 3.6305884379378176`*^9}, { 3.630588892460216*^9, 3.6305889218974676`*^9}, {3.6305890060752153`*^9, 3.630589009351221*^9}, {3.6305890670869226`*^9, 3.6305890695517273`*^9}, { 3.6852609345251694`*^9, 3.6852609544951973`*^9}, {3.685260985325241*^9, 3.6852610561353397`*^9}, {3.6852611137454205`*^9, 3.685261294805674*^9}, 3.6852619439765825`*^9, 3.685267231203985*^9, {3.6852714918932247`*^9, 3.6852714982332335`*^9}, {3.685341844218479*^9, 3.6853419077321115`*^9}, { 3.685876041473126*^9, 3.6858760505831385`*^9}, 3.6862906560183983`*^9, { 3.686290701298462*^9, 3.6862907191684866`*^9}, 3.6876000892040653`*^9, { 3.692005099424469*^9, 3.692005126334507*^9}, {3.6920052956347437`*^9, 3.6920053647348404`*^9}, {3.6920073658081074`*^9, 3.692007368868112*^9}, { 3.7238016961299133`*^9, 3.7238018051367826`*^9}, {3.755346661138646*^9, 3.7553468118982153`*^9}, {3.7553471085713587`*^9, 3.755347166185311*^9}, { 3.7876370907454753`*^9, 3.7876372165495167`*^9}, {3.819783343573612*^9, 3.8197834245995045`*^9}}, CellLabel-> "In[419]:=",ExpressionUUID->"49fc406e-9e45-4708-9b42-788abf74c945"] }, Closed]], Cell[CellGroupData[{ Cell["Home assignment 2 (beam structure)", "Subsubsection", CellChangeTimes->{{3.4730556702200003`*^9, 3.473055683948*^9}, { 3.473056486087*^9, 3.4730564925030003`*^9}, 3.473057491051*^9, { 3.473057733758*^9, 3.473057755476*^9}, {3.568116356788909*^9, 3.5681163731689377`*^9}, {3.5992231160658693`*^9, 3.59922314473872*^9}, { 3.5992232122508388`*^9, 3.5992232356352797`*^9}, {3.686463442653324*^9, 3.686463466683358*^9}, {3.686650104192067*^9, 3.686650133092108*^9}, { 3.692017996330179*^9, 3.692017999280184*^9}, {3.7238019986456337`*^9, 3.723802005404753*^9}, {3.755347238509882*^9, 3.7553472460008483`*^9}},ExpressionUUID->"38918417-54be-4911-bf1a-\ 9b931a068ad5"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0", ",", "M", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "3", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "3", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}], "Input", CellChangeTimes->{{3.599224897569802*^9, 3.599224926773053*^9}, { 3.630748433394182*^9, 3.630748504265106*^9}, {3.6308320967004905`*^9, 3.6308321133874445`*^9}, {3.685263514118781*^9, 3.6852635972488976`*^9}, 3.685267287144063*^9, {3.6853444422720785`*^9, 3.685344490915861*^9}, { 3.6858763098135014`*^9, 3.6858763218235188`*^9}, {3.686226407525676*^9, 3.6862264116856813`*^9}, 3.686445942025214*^9, {3.6866501652021523`*^9, 3.6866502922323303`*^9}, 3.687600260794306*^9, {3.692020854784181*^9, 3.6920209683943405`*^9}, {3.7238020220566053`*^9, 3.723802033852277*^9}, { 3.7238020769072275`*^9, 3.723802128986509*^9}, {3.7238021621517096`*^9, 3.723802245010724*^9}, {3.7238022832650642`*^9, 3.7238023365951767`*^9}, 3.7238024021360083`*^9, 3.7238024323330545`*^9, {3.755347265559884*^9, 3.7553473060631647`*^9}, {3.755347343708659*^9, 3.755347428680601*^9}, { 3.787638865656962*^9, 3.787638869316835*^9}, {3.8197887821479673`*^9, 3.8197887827386026`*^9}, {3.850699406492807*^9, 3.850699411807452*^9}}, CellLabel-> "In[422]:=",ExpressionUUID->"0ac17d52-41a6-410f-a836-e5927c8ffc7d"] }, Closed]], Cell[CellGroupData[{ Cell["Home assignment 3 (plate bending)", "Subsubsection", CellChangeTimes->{{3.4730556702200003`*^9, 3.473055683948*^9}, { 3.473056486087*^9, 3.4730564925030003`*^9}, 3.473057491051*^9, { 3.473057733758*^9, 3.473057755476*^9}, {3.568116356788909*^9, 3.5681163731689377`*^9}, {3.5992231160658693`*^9, 3.59922314473872*^9}, { 3.5992232122508388`*^9, 3.5992232356352797`*^9}, {3.686463442653324*^9, 3.686463466683358*^9}, {3.686650104192067*^9, 3.686650133092108*^9}, { 3.692017996330179*^9, 3.692017999280184*^9}, {3.723802446254207*^9, 3.723802463707958*^9}, {3.7553474763676414`*^9, 3.7553474837939305`*^9}, { 3.787633609669371*^9, 3.7876336147400403`*^9}},ExpressionUUID->"d73ae558-5d7b-4068-9a8d-\ 5124feae9e58"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"Block", "[", RowBox[{ RowBox[{"{", RowBox[{ "w", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[CapitalOmega]", ",", "\[Delta]W", ",", "sol"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"w", "=", RowBox[{ RowBox[{"a", "[", "0", "]"}], " ", FractionBox["x", "L"], " ", RowBox[{"(", RowBox[{"1", "-", FractionBox["x", "L"]}], ")"}]}]}], ";", RowBox[{ RowBox[{"\[Delta]wint", "[", "w_", "]"}], ":=", RowBox[{"-", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}], "]"}], "\[Transpose]"}], ".", RowBox[{"(", " ", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["t", "3"], " ", "\[CapitalEpsilon]"}], RowBox[{"12", RowBox[{"(", RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}], ")"}]}]], RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "\[Nu]", "0"}, {"\[Nu]", "1", "0"}, {"0", "0", FractionBox[ RowBox[{"1", "-", "\[Nu]"}], "2"]} }], "\[NoBreak]", ")"}]}], ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wext", "[", "w_", "]"}], ":=", RowBox[{ RowBox[{"\[Delta]", "[", "w", "]"}], " ", "p"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", "=", RowBox[{"Rectangle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"L", ",", "H"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]wint", "[", "w", "]"}], "+", RowBox[{"\[Delta]wext", "[", "w", "]"}]}], ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], StyleBox["\[Element]", "OperatorCharacter"], StyleBox["\[CapitalOmega]", "OperatorCharacter"]}]}], StyleBox["]", "OperatorCharacter"]}], StyleBox[",", "OperatorCharacter"], StyleBox[ RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"H", ">", "0"}]}], "OperatorCharacter"]}], StyleBox["]", "OperatorCharacter"]}]}], StyleBox[";", "OperatorCharacter"], StyleBox["\[IndentingNewLine]", "OperatorCharacter"], RowBox[{"sol", " ", "=", RowBox[{"SOLVE", "[", "\[Delta]W", " ", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"w", " ", "/.", "sol"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", RowBox[{"L", "/", "2"}]}], ",", RowBox[{"y", "\[Rule]", RowBox[{"H", "/", "2"}]}]}], "}"}]}]}]}], "]"}]}]], "Input", CellChangeTimes->{{3.599224897569802*^9, 3.599224926773053*^9}, { 3.630748433394182*^9, 3.630748504265106*^9}, {3.6308320967004905`*^9, 3.6308321133874445`*^9}, {3.685263514118781*^9, 3.6852635972488976`*^9}, 3.685267287144063*^9, {3.6853444422720785`*^9, 3.685344490915861*^9}, { 3.6858763098135014`*^9, 3.6858763218235188`*^9}, {3.686226407525676*^9, 3.6862264116856813`*^9}, 3.686445942025214*^9, {3.6866501652021523`*^9, 3.6866502922323303`*^9}, 3.687600260794306*^9, {3.692020854784181*^9, 3.6920209683943405`*^9}, {3.723802484790901*^9, 3.723802499197665*^9}, { 3.7238025319830265`*^9, 3.7238025647169547`*^9}, {3.7238026083860784`*^9, 3.7238026749923143`*^9}, {3.723802720756008*^9, 3.723802818918144*^9}, { 3.723802858515747*^9, 3.7238028612596664`*^9}, {3.755347519931821*^9, 3.755347550666892*^9}, {3.755347600502432*^9, 3.7553476976960354`*^9}, { 3.7876336452513857`*^9, 3.7876337824990273`*^9}, {3.819788880883937*^9, 3.819788998621375*^9}, {3.8197891540362253`*^9, 3.819789200160994*^9}, { 3.819789231642615*^9, 3.8197892760232506`*^9}, {3.819789326683582*^9, 3.8197893816473036`*^9}, {3.8197894412961254`*^9, 3.819789469001286*^9}, { 3.8197895293743763`*^9, 3.8197896174515867`*^9}, {3.8506994291692486`*^9, 3.8506995018837795`*^9}, {3.8511333048798075`*^9, 3.8511333288027077`*^9}}, CellLabel-> "In[425]:=",ExpressionUUID->"9f0898d0-e20d-4e6a-ba92-2d7e1f3441ce"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture assignment 1 (bar structure)", "Subsubsection", CellChangeTimes->{{3.473055608665*^9, 3.4730556508570004`*^9}, { 3.473057986849*^9, 3.473057995505*^9}, {3.473061553363*^9, 3.4730615754709997`*^9}, {3.4730617586879997`*^9, 3.4730617595109997`*^9}, {3.473061806072*^9, 3.4730618092860003`*^9}, 3.567430053590129*^9, 3.5674302916621466`*^9, {3.59922479409482*^9, 3.5992247947344213`*^9}, 3.686233727874673*^9, 3.6862907545885363`*^9, 3.6920044935936213`*^9, {3.6920055576551104`*^9, 3.692005561315116*^9}, 3.7238002254871435`*^9, {3.7553481278960447`*^9, 3.75534813971142*^9}, { 3.7553514327426157`*^9, 3.7553514385741806`*^9}},ExpressionUUID->"2d9d9826-43d6-4000-b0d1-\ 359613cdb707"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"3", " ", RowBox[{"P", "/", "L"}]}], ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "P"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}], "Input", CellChangeTimes->{ 3.442646896400446*^9, {3.473058050178*^9, 3.473058242583*^9}, { 3.473058273832*^9, 3.473058275781*^9}, {3.4730583246470003`*^9, 3.473058418342*^9}, {3.473058484495*^9, 3.47305848615*^9}, { 3.473061601906*^9, 3.473061685848*^9}, {3.4730618307860003`*^9, 3.473062130566*^9}, {3.5674305015137157`*^9, 3.567430508034527*^9}, 3.5674306789176273`*^9, {3.5674889411989174`*^9, 3.567489021180258*^9}, { 3.6297903068985133`*^9, 3.629790413571501*^9}, {3.629790456471576*^9, 3.629790478888816*^9}, {3.6297905091060686`*^9, 3.6297905324281096`*^9}, 3.6297915982999816`*^9, {3.629870281797838*^9, 3.629870287819449*^9}, { 3.629870322950711*^9, 3.629870429155697*^9}, {3.6307481815629396`*^9, 3.6307482184414043`*^9}, {3.6852614772659297`*^9, 3.685261629646143*^9}, { 3.6852619208965507`*^9, 3.685261929826563*^9}, 3.6852672248539762`*^9, { 3.6852715094232492`*^9, 3.6852715139832554`*^9}, 3.685330160876338*^9, 3.685330191642098*^9, {3.6853398909644113`*^9, 3.685339924654458*^9}, { 3.6858760739831715`*^9, 3.685876077853177*^9}, {3.686290816478623*^9, 3.6862908363386507`*^9}, {3.6868258114230947`*^9, 3.6868258331431255`*^9}, 3.6868273566352577`*^9, 3.687600102954085*^9, {3.6920055669051237`*^9, 3.6920056989553084`*^9}, {3.7552821496563406`*^9, 3.7552821715493975`*^9}, {3.755348147988492*^9, 3.755348203975028*^9}, { 3.7553514516115675`*^9, 3.755351510181407*^9}, {3.755351564011986*^9, 3.7553515656706686`*^9}, {3.787709262831045*^9, 3.7877092674786477`*^9}, { 3.8197897248576317`*^9, 3.8197897252537403`*^9}, {3.81979129812329*^9, 3.819791303703355*^9}, 3.819791338734643*^9, {3.850699536859164*^9, 3.85069953805099*^9}}, CellLabel-> "In[426]:=",ExpressionUUID->"40385832-0d75-4772-9321-889bc452b7e4"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture assignment 2 (bar element)", "Subsubsection", CellChangeTimes->{{3.473055608665*^9, 3.4730556508570004`*^9}, { 3.473057986849*^9, 3.473057995505*^9}, {3.473061553363*^9, 3.4730615754709997`*^9}, {3.4730617586879997`*^9, 3.4730617595109997`*^9}, {3.473061806072*^9, 3.4730618092860003`*^9}, 3.567430053590129*^9, 3.5674302916621466`*^9, {3.59922479409482*^9, 3.5992247947344213`*^9}, 3.686233727874673*^9, 3.6862907545885363`*^9, 3.6920044935936213`*^9, {3.6920055576551104`*^9, 3.692005561315116*^9}, 3.7238002254871435`*^9, {3.7553481278960447`*^9, 3.75534813971142*^9}},ExpressionUUID->"2fcc114f-bd32-467e-83d7-\ 1580c4553c73"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", "1", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"h", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{ 3.442646896400446*^9, {3.473058050178*^9, 3.473058242583*^9}, { 3.473058273832*^9, 3.473058275781*^9}, {3.4730583246470003`*^9, 3.473058418342*^9}, {3.473058484495*^9, 3.47305848615*^9}, { 3.473061601906*^9, 3.473061685848*^9}, {3.4730618307860003`*^9, 3.473062130566*^9}, {3.5674305015137157`*^9, 3.567430508034527*^9}, 3.5674306789176273`*^9, {3.5674889411989174`*^9, 3.567489021180258*^9}, { 3.6297903068985133`*^9, 3.629790413571501*^9}, {3.629790456471576*^9, 3.629790478888816*^9}, {3.6297905091060686`*^9, 3.6297905324281096`*^9}, 3.6297915982999816`*^9, {3.629870281797838*^9, 3.629870287819449*^9}, { 3.629870322950711*^9, 3.629870429155697*^9}, {3.6307481815629396`*^9, 3.6307482184414043`*^9}, {3.6852614772659297`*^9, 3.685261629646143*^9}, { 3.6852619208965507`*^9, 3.685261929826563*^9}, 3.6852672248539762`*^9, { 3.6852715094232492`*^9, 3.6852715139832554`*^9}, 3.685330160876338*^9, 3.685330191642098*^9, {3.6853398909644113`*^9, 3.685339924654458*^9}, { 3.6858760739831715`*^9, 3.685876077853177*^9}, {3.686290816478623*^9, 3.6862908363386507`*^9}, {3.6868258114230947`*^9, 3.6868258331431255`*^9}, 3.6868273566352577`*^9, 3.687600102954085*^9, {3.6920055669051237`*^9, 3.6920056989553084`*^9}, {3.7552821496563406`*^9, 3.7552821715493975`*^9}, {3.755348147988492*^9, 3.755348203975028*^9}, { 3.8198556058358617`*^9, 3.8198556071591415`*^9}, 3.819855639149332*^9, { 3.8506995593066325`*^9, 3.850699559924745*^9}}, CellLabel-> "In[429]:=",ExpressionUUID->"ab57f91a-ea51-45df-8186-1b657517b9c0"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["VIBRATION ANALYSIS (week 4)", "Subsection", CellChangeTimes->{{3.473055512584*^9, 3.4730555529630003`*^9}, { 3.4730575328269997`*^9, 3.473057539222*^9}, {3.4734691424642*^9, 3.4734691605758*^9}, {3.4736023142902*^9, 3.4736023273162003`*^9}, { 3.4932789338394003`*^9, 3.493278944697*^9}, 3.4933062370676003`*^9, { 3.4938708332125845`*^9, 3.493870838516244*^9}, {3.5566240340051107`*^9, 3.556624040463522*^9}, 3.619407916962384*^9, {3.6924123022392583`*^9, 3.692412310189269*^9}, 3.7530712431763153`*^9, 3.7866746422204695`*^9},ExpressionUUID->"8dda4d3a-cb31-4c59-95bf-\ aef4d1a4b2b8"], Cell[CellGroupData[{ Cell["Lecture example 3.1 (decomposition)", "Subsubsection", CellChangeTimes->{ 3.5577964337884617`*^9, 3.6926013396721983`*^9, {3.6926179280029135`*^9, 3.6926179367329254`*^9}, {3.6926179987430124`*^9, 3.692618012853032*^9}, 3.6926777991781263`*^9, {3.6927703328584137`*^9, 3.692770359158451*^9}, { 3.6928550971942673`*^9, 3.6928551052242785`*^9}, {3.787803673092881*^9, 3.787803679378704*^9}, 3.82002459370605*^9},ExpressionUUID->"ec502578-4394-49de-a13b-\ c03363345d3a"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"\[CapitalOmega]2", "=", RowBox[{"(", GridBox[{ {"3", RowBox[{ RowBox[{"-", "1"}], "/", "3"}]}, { RowBox[{"-", "3"}], "3"} }], ")"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"val", ",", "vec"}], "}"}], "=", RowBox[{"Eigensystem", "[", "\[CapitalOmega]2", "]"}]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", "=", RowBox[{"Sqrt", "[", "val", "]"}]}]}], "Input", CellChangeTimes->{ 3.4939782696174*^9, {3.4939783427346*^9, 3.4939784038866*^9}, { 3.557796517623009*^9, 3.5577966195847883`*^9}, {3.557796666556471*^9, 3.5577966698948765`*^9}, 3.692617920032902*^9, {3.6926180027030177`*^9, 3.6926183433034945`*^9}, {3.69261837586354*^9, 3.692618421083604*^9}, 3.6926184702836723`*^9, 3.692770250478299*^9, {3.6927703723784695`*^9, 3.692770588688772*^9}, {3.6927706245488224`*^9, 3.692770674378892*^9}, { 3.6927707053189354`*^9, 3.692770706798938*^9}, {3.692770840599125*^9, 3.6927708450491314`*^9}, {3.69285512772431*^9, 3.692855188474395*^9}, { 3.7244868220050793`*^9, 3.7244868651346254`*^9}, {3.724486900982155*^9, 3.7244869496591587`*^9}, {3.7244869892727127`*^9, 3.7244870143222284`*^9}, {3.724490936279661*^9, 3.724491010626911*^9}, { 3.7244910471773667`*^9, 3.7244911069483156`*^9}, {3.7244950339345055`*^9, 3.7244950625113525`*^9}, {3.85139370048866*^9, 3.8513937647740607`*^9}}, CellLabel->"In[17]:=",ExpressionUUID->"46cd8715-7ef2-4f8a-aad3-7b59833611ee"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 3.2 (ode)", "Subsubsection", CellChangeTimes->{ 3.5577964337884617`*^9, 3.6926013396721983`*^9, {3.6926179280029135`*^9, 3.6926179367329254`*^9}, {3.6926179987430124`*^9, 3.692618012853032*^9}, 3.6926777991781263`*^9, {3.6927703328584137`*^9, 3.692770359158451*^9}, { 3.6928550971942673`*^9, 3.6928551052242785`*^9}, {3.692855267934506*^9, 3.692855272014512*^9}, 3.7878036866544547`*^9, 3.820024595889677*^9},ExpressionUUID->"29a94e8a-b96c-46c5-a83c-\ e292d5f6d8ae"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"MM", "=", RowBox[{"m", RowBox[{"(", GridBox[{ {"0", "1"}, {"1", "0"} }], ")"}]}]}], ";", " ", RowBox[{"KK", "=", RowBox[{"k", RowBox[{"(", GridBox[{ { RowBox[{"-", "1"}], "1"}, {"1", RowBox[{"-", "1"}]} }], ")"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"val", ",", "vec"}], "}"}], "=", RowBox[{"Eigensystem", "[", RowBox[{ RowBox[{"Inverse", "[", "MM", "]"}], ".", "KK"}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"val", ",", "vec"}], "}"}], "=", RowBox[{"Eigensystem", "[", RowBox[{"{", RowBox[{"KK", ",", "MM"}], "}"}], "]"}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Sqrt", "[", "val", "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{ 3.4939782696174*^9, {3.4939783427346*^9, 3.4939784038866*^9}, { 3.557796517623009*^9, 3.5577966195847883`*^9}, {3.557796666556471*^9, 3.5577966698948765`*^9}, 3.692617920032902*^9, {3.6926180027030177`*^9, 3.6926183433034945`*^9}, {3.69261837586354*^9, 3.692618421083604*^9}, 3.6926184702836723`*^9, 3.692770250478299*^9, {3.6927703723784695`*^9, 3.692770588688772*^9}, {3.6927706245488224`*^9, 3.692770674378892*^9}, { 3.6927707053189354`*^9, 3.692770706798938*^9}, {3.692770840599125*^9, 3.6927708450491314`*^9}, {3.69285512772431*^9, 3.692855188474395*^9}, { 3.6928553102645655`*^9, 3.692855394424683*^9}, {3.851393780093685*^9, 3.851393872788854*^9}, {3.8513939134173965`*^9, 3.8513939427413964`*^9}}, CellLabel->"In[38]:=",ExpressionUUID->"895e2fc8-07be-4151-8042-ad18987a74df"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 3.3 (bar structure)", "Subsubsection", CellChangeTimes->{{3.4938724364934034`*^9, 3.493872440377554*^9}, 3.55772174224413*^9, {3.5577222701826577`*^9, 3.557722281898278*^9}, { 3.6925364040653286`*^9, 3.692536414765343*^9}, {3.6926051339045105`*^9, 3.692605137804516*^9}, 3.692616505550922*^9, {3.6926165560409927`*^9, 3.6926165581809955`*^9}, 3.787803700161643*^9, 3.820024597714839*^9},ExpressionUUID->"2ca404f1-d2d9-4496-8cf6-\ 914a4d52b0db"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "4"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"4", ",", "5"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "1", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"3", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "3", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"4", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.4938808707521195`*^9, 3.493880886414419*^9}, { 3.4938809823296185`*^9, 3.4938810743976574`*^9}, {3.493881115862191*^9, 3.49388112389614*^9}, {3.5007185681328*^9, 3.5007185858543997`*^9}, 3.557721807701845*^9, 3.557722301679113*^9, {3.557722338229977*^9, 3.557722345218789*^9}, {3.5577223956380777`*^9, 3.557722557550762*^9}, { 3.5577227444350924`*^9, 3.5577227701751375`*^9}, {3.557722914366191*^9, 3.5577231321893735`*^9}, {3.5577234762323775`*^9, 3.557723673042323*^9}, { 3.557723707440384*^9, 3.557723724257213*^9}, {3.557723808200961*^9, 3.5577238249085903`*^9}, {3.557724032045754*^9, 3.5577240381453648`*^9}, { 3.5577240859750485`*^9, 3.5577241533827667`*^9}, {3.5577255542808275`*^9, 3.557725556340031*^9}, {3.692416572627716*^9, 3.692416634337803*^9}, { 3.6924166962978897`*^9, 3.6924166970178905`*^9}, {3.692416728407934*^9, 3.692416742377954*^9}, 3.692416785478014*^9, {3.692416815828057*^9, 3.692416854678111*^9}, {3.6924172169506187`*^9, 3.6924175298010564`*^9}, { 3.692418050131785*^9, 3.692418107561865*^9}, {3.6924216949310565`*^9, 3.6924216977710605`*^9}, {3.6925022762935333`*^9, 3.6925022791146946`*^9}, {3.6926050714634233`*^9, 3.6926053101657577`*^9}, {3.692605350685814*^9, 3.6926053528358173`*^9}, { 3.692605582596139*^9, 3.692605583946141*^9}, {3.6926777445380497`*^9, 3.69267776592808*^9}, {3.6926948008051434`*^9, 3.69269481310516*^9}, { 3.6926949183153076`*^9, 3.6926949195553093`*^9}, {3.6928546233136034`*^9, 3.6928546243636055`*^9}, {3.6928546875636935`*^9, 3.6928548011538525`*^9}, {3.6928548476139174`*^9, 3.6928548503039217`*^9}, {3.6928549222540216`*^9, 3.6928549237840242`*^9}, {3.692855453534766*^9, 3.692855477104799*^9}, { 3.756618747609501*^9, 3.7566188279765987`*^9}, {3.7566188619999294`*^9, 3.756618981627329*^9}, {3.7566195742452745`*^9, 3.7566195805721426`*^9}, { 3.756619612517589*^9, 3.756619616079483*^9}, {3.7566197161185665`*^9, 3.7566197339734716`*^9}, {3.7882441687016416`*^9, 3.7882442117547374`*^9}, {3.788244272436096*^9, 3.78824427308834*^9}, 3.7882444034202657`*^9, {3.820025067066265*^9, 3.820025096859448*^9}, { 3.820025153417162*^9, 3.820025155783327*^9}, {3.850794221377445*^9, 3.8507942337721004`*^9}}, CellLabel->"In[42]:=",ExpressionUUID->"8cf4aa7c-293f-4c36-8880-388f56950d45"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 3.4 (bar truss)", "Subsubsection", CellChangeTimes->{{3.4938724364934034`*^9, 3.493872440377554*^9}, 3.55772174224413*^9, {3.5577222701826577`*^9, 3.557722281898278*^9}, { 3.6925364040653286`*^9, 3.692536414765343*^9}, {3.6926051339045105`*^9, 3.692605137804516*^9}, 3.692616505550922*^9, {3.6926165560409927`*^9, 3.692616575321019*^9}, 3.7557191504411116`*^9, 3.7878037030530243`*^9, 3.7882445751277723`*^9, 3.8200245994156294`*^9},ExpressionUUID->"2f4572cf-f61a-41de-b682-\ 1e03ef2419f7"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "0"}], "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{ SqrtBox["8"], "A"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "0"}], "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"4", ",", "2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"uZ", "[", RowBox[{"_", ",", "0"}], "]"}], "\[Rule]", "0"}], ",", RowBox[{ RowBox[{"uZ", "[", RowBox[{"_", ",", "1"}], "]"}], "\[Rule]", OverscriptBox["U", "."]}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}], "Input", CellChangeTimes->{{3.4938808707521195`*^9, 3.493880886414419*^9}, { 3.4938809823296185`*^9, 3.4938810743976574`*^9}, {3.493881115862191*^9, 3.49388112389614*^9}, {3.5007185681328*^9, 3.5007185858543997`*^9}, 3.557721807701845*^9, 3.557722301679113*^9, {3.557722338229977*^9, 3.557722345218789*^9}, {3.5577223956380777`*^9, 3.557722557550762*^9}, { 3.5577227444350924`*^9, 3.5577227701751375`*^9}, {3.557722914366191*^9, 3.5577231321893735`*^9}, {3.5577234762323775`*^9, 3.557723673042323*^9}, { 3.557723707440384*^9, 3.557723724257213*^9}, {3.557723808200961*^9, 3.5577238249085903`*^9}, {3.557724032045754*^9, 3.5577240381453648`*^9}, { 3.5577240859750485`*^9, 3.5577241533827667`*^9}, {3.5577255542808275`*^9, 3.557725556340031*^9}, {3.692416572627716*^9, 3.692416634337803*^9}, { 3.6924166962978897`*^9, 3.6924166970178905`*^9}, {3.692416728407934*^9, 3.692416742377954*^9}, 3.692416785478014*^9, {3.692416815828057*^9, 3.692416854678111*^9}, {3.6924172169506187`*^9, 3.6924175298010564`*^9}, { 3.692418050131785*^9, 3.692418107561865*^9}, {3.6924216949310565`*^9, 3.6924216977710605`*^9}, {3.6925022762935333`*^9, 3.6925022791146946`*^9}, {3.6926050714634233`*^9, 3.6926053101657577`*^9}, {3.692605350685814*^9, 3.6926053528358173`*^9}, { 3.692605582596139*^9, 3.692605583946141*^9}, 3.692623496410709*^9, { 3.692623535710764*^9, 3.692623557910795*^9}, {3.6926952837958193`*^9, 3.6926952890058265`*^9}, {3.6928555108448462`*^9, 3.692855525144866*^9}, { 3.6928555801949434`*^9, 3.6928556725450726`*^9}, {3.6928557055151186`*^9, 3.6928557885252347`*^9}, {3.692855881295365*^9, 3.6928558933153815`*^9}, { 3.692855952785465*^9, 3.6928559781655006`*^9}, {3.6928560758856373`*^9, 3.692856170005769*^9}, {3.6928562238658447`*^9, 3.6928562580458927`*^9}, { 3.6928562961859455`*^9, 3.69285631358597*^9}, {3.692856357426031*^9, 3.6928563681360464`*^9}, {3.6928563999060907`*^9, 3.6928564001160913`*^9}, {3.692857702937915*^9, 3.6928577502779813`*^9}, { 3.72429732021502*^9, 3.7242973244091988`*^9}, {3.7242973875274353`*^9, 3.724297390176303*^9}, {3.724297489356834*^9, 3.7242974986059*^9}, { 3.7242975364637938`*^9, 3.724297599229539*^9}, {3.7242977243318577`*^9, 3.7242977252218814`*^9}, {3.7530715281010895`*^9, 3.7530715577593546`*^9}, {3.753071592776411*^9, 3.7530716192701263`*^9}, { 3.753079890337639*^9, 3.753079910015238*^9}, {3.788077556292513*^9, 3.7880775604619904`*^9}, 3.788077612775126*^9, {3.82002517421471*^9, 3.8200252008854923`*^9}, 3.8204702417446294`*^9, {3.820470330146205*^9, 3.8204703911667013`*^9}, {3.820470434077013*^9, 3.820470435462103*^9}, { 3.8204704747341957`*^9, 3.820470531412328*^9}, {3.850796354640504*^9, 3.850796364032633*^9}}, CellLabel->"In[46]:=",ExpressionUUID->"76618255-84a1-4d51-8284-35b792c1ce71"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Lecture example", StyleBox[" ", FontColor->GrayLevel[0]], "3.5 (solid)" }], "Subsubsection", CellChangeTimes->{ 3.4734695002813997`*^9, {3.599225569652184*^9, 3.599225577904598*^9}, 3.5992258478994727`*^9, 3.6862336460745583`*^9, 3.6862909162387624`*^9, { 3.6863755415162687`*^9, 3.686375541876269*^9}, {3.686463504573411*^9, 3.686463506573414*^9}, {3.6920258070089493`*^9, 3.692025809498953*^9}, { 3.692025870269038*^9, 3.692025872639041*^9}, 3.692502004255974*^9, 3.6926165081909256`*^9, 3.6926165783510237`*^9, {3.7878037128961277`*^9, 3.7878037213866677`*^9}, 3.8200246011726475`*^9},ExpressionUUID->"596b8bf2-51e2-4e9a-909f-\ 691760d62b19"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "0", ",", "\[Rho]"}], "}"}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "3", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "\[IndentingNewLine]", "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"uZ", "[", RowBox[{"3", ",", "0"}], "]"}], "\[Rule]", "U"}], ",", RowBox[{ RowBox[{"uZ", "[", RowBox[{"3", ",", "1"}], "]"}], "\[Rule]", "0"}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4426469450734453`*^9, 3.4426469473978453`*^9}, { 3.630367590488758*^9, 3.6303676088811903`*^9}, {3.630367651765666*^9, 3.630367669549697*^9}, 3.630368414310605*^9, {3.6307482430426474`*^9, 3.6307482456946526`*^9}, 3.685262022046692*^9, {3.6852621067368107`*^9, 3.6852621933569317`*^9}, {3.685262233936989*^9, 3.685262252827015*^9}, 3.685267210253956*^9, {3.6852715412232933`*^9, 3.685271546353301*^9}, { 3.6853429895189857`*^9, 3.6853430232739167`*^9}, 3.6858761692133045`*^9, { 3.68821224839828*^9, 3.6882123179983773`*^9}, {3.68821235531843*^9, 3.6882123899484777`*^9}, 3.6920258039789453`*^9, {3.692025876949047*^9, 3.692025881559054*^9}, {3.6920259277091184`*^9, 3.6920259839391975`*^9}, { 3.692026020869249*^9, 3.6920260636193085`*^9}, {3.6920264969699154`*^9, 3.6920264987399178`*^9}, 3.692502011618395*^9, {3.6925022474708843`*^9, 3.6925022520801487`*^9}, {3.692502302176014*^9, 3.6925023736471014`*^9}, { 3.6925025169803*^9, 3.6925025655720787`*^9}, {3.6925026661128297`*^9, 3.6925026706260877`*^9}, {3.6926054666559763`*^9, 3.692605488996008*^9}, { 3.6926055235860567`*^9, 3.6926055236960564`*^9}, 3.69262347584068*^9, { 3.6926953173258657`*^9, 3.6926953218058724`*^9}, {3.6927029458677883`*^9, 3.692702987017846*^9}, {3.692767974815113*^9, 3.6927680130851665`*^9}, { 3.6927681266753254`*^9, 3.6927681303353305`*^9}, {3.692768161725374*^9, 3.6927681639953775`*^9}, {3.6927685368559*^9, 3.692768539955904*^9}, { 3.6927698573477488`*^9, 3.6927699280078473`*^9}, 3.6927700238579817`*^9, { 3.692770056788028*^9, 3.6927701046680946`*^9}, {3.6928578154980726`*^9, 3.692857837888104*^9}, 3.692858122048502*^9, {3.724303840459796*^9, 3.7243038415618286`*^9}, {3.724303879564316*^9, 3.724303894223379*^9}, 3.7243039281242995`*^9, 3.7243040890622582`*^9, {3.724423222711531*^9, 3.7244232431101933`*^9}, 3.7244235987235465`*^9, {3.7244630416618423`*^9, 3.7244630496473045`*^9}, {3.7244630934956675`*^9, 3.7244632541685715`*^9}, {3.72446356412341*^9, 3.724463638943798*^9}, { 3.72446370987291*^9, 3.724463778130144*^9}, {3.724463812618352*^9, 3.724463883547698*^9}, {3.724463917785564*^9, 3.7244640373763733`*^9}, { 3.724464085350275*^9, 3.724464220520729*^9}, {3.7244643161400948`*^9, 3.7244643244220333`*^9}, {3.7244643814283237`*^9, 3.724464454982666*^9}, { 3.7244713771886415`*^9, 3.7244713848341866`*^9}, {3.724471420086172*^9, 3.724471422815348*^9}, {3.724486692210102*^9, 3.7244866984451756`*^9}, { 3.7245557366954913`*^9, 3.724555737789098*^9}, 3.724555838936*^9, 3.7530722584303675`*^9, {3.7557211475246754`*^9, 3.7557211723132725`*^9}, 3.7878941312660275`*^9, 3.788077650022805*^9, {3.820025985576888*^9, 3.820025987333465*^9}, {3.8200260200845194`*^9, 3.8200260249775887`*^9}, { 3.8200261168126965`*^9, 3.8200261306343355`*^9}}, CellLabel->"In[51]:=",ExpressionUUID->"b2dde7b3-4e38-4f81-a1a7-04071abfd87b"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 3.6 (beam)", "Subsubsection", CellChangeTimes->{ 3.4938982987960324`*^9, 3.5577217480785403`*^9, {3.692536423145355*^9, 3.6925364506253934`*^9}, {3.6926054332359295`*^9, 3.6926054525459566`*^9}, 3.69261651130093*^9, 3.6926165853310337`*^9, {3.755721309140517*^9, 3.7557213161329103`*^9}, {3.755722559939822*^9, 3.755722564665438*^9}, 3.7878037265605774`*^9, 3.8200246031738443`*^9, {3.8200298837550116`*^9, 3.8200299159157624`*^9}},ExpressionUUID->"db936206-88e3-4975-8b27-\ 457dda1af8d7"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "1", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], " ", "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4938984436576324`*^9, 3.4938984505060325`*^9}, { 3.4939508930964003`*^9, 3.4939508993052*^9}, 3.5007186129983997`*^9, { 3.692536436605374*^9, 3.692536507425473*^9}, {3.6925365733255653`*^9, 3.69253658391558*^9}, {3.6925366551056795`*^9, 3.6925366962757373`*^9}, 3.692536781945857*^9, 3.692536825315918*^9, {3.6925369042360287`*^9, 3.6925369603361073`*^9}, {3.692537436846774*^9, 3.6925374748468275`*^9}, { 3.6925375064468718`*^9, 3.692537543896924*^9}, {3.6925384725244083`*^9, 3.692538507064457*^9}, {3.692538541444505*^9, 3.6925385532045217`*^9}, { 3.692538591154575*^9, 3.6925388837549844`*^9}, {3.6925391133453054`*^9, 3.6925391566234407`*^9}, {3.6925393311497364`*^9, 3.6925394393698883`*^9}, {3.692539579530084*^9, 3.6925395927701025`*^9}, { 3.692539800900394*^9, 3.692539874350497*^9}, {3.6925400840707903`*^9, 3.6925400981808105`*^9}, {3.6925402819810677`*^9, 3.6925402985610905`*^9}, 3.692540330111135*^9, {3.6925406256615486`*^9, 3.6925406596015964`*^9}, { 3.6925407139216723`*^9, 3.692540842291852*^9}, {3.692540939781988*^9, 3.692540965192024*^9}, {3.692541020762102*^9, 3.692541021512103*^9}, { 3.6925410776721816`*^9, 3.692541095012206*^9}, {3.692542771504553*^9, 3.6925428208046217`*^9}, {3.69259963100324*^9, 3.6925996373546033`*^9}, { 3.692600739241358*^9, 3.69260087649155*^9}, 3.6926012425220623`*^9, 3.692601292102132*^9, {3.6926014023522863`*^9, 3.692601430842326*^9}, { 3.6926021565553417`*^9, 3.692602173695366*^9}, {3.6926028188362694`*^9, 3.69260281947627*^9}, {3.6926035232892556`*^9, 3.6926035238692565`*^9}, 3.692603706969513*^9, {3.692604877223151*^9, 3.692604895363177*^9}, { 3.6926050090333357`*^9, 3.692605020963352*^9}, 3.6926233239704676`*^9, { 3.692623397890571*^9, 3.692623415880596*^9}, {3.6926953498559113`*^9, 3.692695352475915*^9}, {3.6927027061974525`*^9, 3.692702716667467*^9}, { 3.692702815217605*^9, 3.6927028284476237`*^9}, {3.6927713388298225`*^9, 3.6927713433298283`*^9}, {3.692858789939437*^9, 3.692858819149478*^9}, { 3.7245498462061405`*^9, 3.7245499439830046`*^9}, {3.724550010823572*^9, 3.7245500675446234`*^9}, {3.724557628664399*^9, 3.724557643852253*^9}, { 3.7245576929500136`*^9, 3.724557709686152*^9}, {3.724557743595968*^9, 3.724557747868984*^9}, {3.7245577860139046`*^9, 3.7245577926112986`*^9}, { 3.7245578833218794`*^9, 3.7245578838691053`*^9}, {3.7245588273362737`*^9, 3.724558898176444*^9}, {3.724558935228176*^9, 3.7245589885529246`*^9}, { 3.724559339693288*^9, 3.724559376000408*^9}, {3.7557220266671104`*^9, 3.755722040084095*^9}, {3.7567985372844973`*^9, 3.756798578243656*^9}, { 3.756798669627799*^9, 3.7567986729551954`*^9}, {3.7567987534051056`*^9, 3.7567987570136375`*^9}, 3.8200270638226805`*^9, {3.8200278006986237`*^9, 3.820027802357981*^9}, {3.850796567070136*^9, 3.8507965763999834`*^9}}, CellLabel->"In[54]:=",ExpressionUUID->"656a907d-12c1-43a5-b686-c6dee6b593f0"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 3.7 (thin slab)", "Subsubsection", CellChangeTimes->{{3.5577964555661*^9, 3.557796469528125*^9}, 3.6926057358063536`*^9, {3.6926778041981335`*^9, 3.6926778043681335`*^9}, { 3.6926787551494646`*^9, 3.692678770969487*^9}, 3.69267930176023*^9, 3.6927716593602715`*^9, 3.692773807173278*^9, {3.6928590333097773`*^9, 3.6928590340097785`*^9}, {3.755722529254018*^9, 3.7557225536775293`*^9}, 3.7878037498023167`*^9, 3.8200246120636396`*^9, {3.8200298743691416`*^9, 3.820029874901998*^9}},ExpressionUUID->"4aa1cdd1-d1e8-40ec-9779-\ 084830f2ac99"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "h", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "1", "]"}], ",", RowBox[{"uY", "[", "1", "]"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4939930717488003`*^9, 3.4939930974108*^9}, { 3.4939934523719997`*^9, 3.4939934579568*^9}, {3.4940328656694*^9, 3.4940328661686*^9}, {3.4940336074547997`*^9, 3.494033663178*^9}, 3.4940340531*^9, {3.4940343243684*^9, 3.4940343274104*^9}, { 3.500718840384*^9, 3.5007188689944*^9}, {3.557797943855514*^9, 3.5577979639795494`*^9}, 3.6926792938302193`*^9, 3.692771703570333*^9, { 3.6927734376627607`*^9, 3.692773462532796*^9}, {3.6927734931228385`*^9, 3.692773588602972*^9}, 3.692773619943016*^9, {3.692773683713105*^9, 3.692773731253172*^9}, {3.6927737733532305`*^9, 3.6927737739032316`*^9}, { 3.6927738245433025`*^9, 3.692773876463375*^9}, {3.692773939413463*^9, 3.692773995603542*^9}, {3.6927740539236236`*^9, 3.6927740867636695`*^9}, { 3.692859047249797*^9, 3.6928591207299*^9}, {3.724558341263359*^9, 3.7245583544585257`*^9}, {3.7245593962612076`*^9, 3.724559397823843*^9}, 3.7878942085888877`*^9, {3.8200286793925047`*^9, 3.8200286799010334`*^9}, { 3.8200287132036333`*^9, 3.820028715346983*^9}, {3.8518338780309815`*^9, 3.8518339106132174`*^9}}, CellLabel->"In[63]:=",ExpressionUUID->"eb488d1b-53b4-455b-be11-b209b65a0b3d"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 3.8 (beam and rigid body)", "Subsubsection", CellChangeTimes->{ 3.4938723928941984`*^9, 3.557721739014924*^9, {3.692605416175906*^9, 3.692605416405906*^9}, {3.69261644725084*^9, 3.6926164489508424`*^9}, { 3.6926165956910477`*^9, 3.6926166046310606`*^9}, 3.692859036409782*^9, 3.7878037546813784`*^9, 3.8200246140907764`*^9},ExpressionUUID->"d2e920b7-e97a-4989-90a1-\ 9a3faacb4b9a"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"{", RowBox[{"m", ",", RowBox[{"m", " ", RowBox[{ RowBox[{"L", "^", "2"}], "/", "5"}], " ", RowBox[{"IdentityMatrix", "[", "3", "]"}]}]}], "}"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", RowBox[{"uY", "[", "2", "]"}], ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", "2", "]"}], ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", RowBox[{"\[Theta]Z", "[", "2", "]"}]}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.493870948270808*^9, 3.493870974695514*^9}, { 3.4938710837637224`*^9, 3.493871234574854*^9}, {3.5007185298036003`*^9, 3.5007185364804*^9}, 3.6924165503676853`*^9, {3.692605662406251*^9, 3.6926056638062525`*^9}, {3.6926163346506824`*^9, 3.6926163355806837`*^9}, {3.6926166166210775`*^9, 3.692616866261427*^9}, 3.6926169155314956`*^9, 3.692617091411742*^9, 3.692617244301956*^9, { 3.692623259860378*^9, 3.6926232673403883`*^9}, {3.692699048081089*^9, 3.6926990489010906`*^9}, {3.6926995790618324`*^9, 3.692699589401847*^9}, { 3.6926996396619177`*^9, 3.69269965575194*^9}, {3.6926997301520443`*^9, 3.692699736682053*^9}, {3.6928589787397013`*^9, 3.6928589854697104`*^9}, { 3.692859254510087*^9, 3.6928592940201426`*^9}, {3.755722787395869*^9, 3.7557228081237707`*^9}, 3.7557231852619715`*^9, {3.755723220656005*^9, 3.755723263671439*^9}, {3.755723435970131*^9, 3.755723458365805*^9}, 3.756001870205928*^9, {3.7882453811064157`*^9, 3.7882453893709884`*^9}, { 3.788245616548293*^9, 3.788245627763839*^9}, {3.820029466509404*^9, 3.8200294969772806`*^9}, {3.8204708439732113`*^9, 3.820470844932032*^9}}, CellLabel->"In[61]:=",ExpressionUUID->"b26e9b07-1af4-4b94-b89b-e621305f1456"], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{ 3.8514028963261724`*^9},ExpressionUUID->"b336c1d1-1088-4fd2-a00a-\ c759558e461b"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 3.9a (plate bending)", "Subsubsection", CellChangeTimes->{ 3.4938723928941984`*^9, 3.557721739014924*^9, {3.692605416175906*^9, 3.692605416405906*^9}, {3.69261644725084*^9, 3.6926164489508424`*^9}, { 3.6926165956910477`*^9, 3.6926166046310606`*^9}, {3.6926896111178775`*^9, 3.692689619257889*^9}, {3.7241476447423286`*^9, 3.7241476607760677`*^9}, { 3.724318554593711*^9, 3.7243185670306544`*^9}, {3.724318639035441*^9, 3.7243186477809887`*^9}, {3.756083392953127*^9, 3.756083398473401*^9}, 3.7561676827881355`*^9, {3.7561688892534256`*^9, 3.7561688903110223`*^9}, 3.7878038031871395`*^9, {3.8514029661882243`*^9, 3.851402967215026*^9}, { 3.851404172035494*^9, 3.8514041768278866`*^9}},ExpressionUUID->"98f7c702-73de-4696-9946-\ f357e79a0cca"], Cell[BoxData[ RowBox[{"Clear", "[", "\[Delta]W", "]"}]], "Input", CellChangeTimes->{{3.851404791778432*^9, 3.851404795976716*^9}}, CellLabel->"In[51]:=",ExpressionUUID->"2f221a1e-fc52-4058-af51-1e5ba90ff91a"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"val", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"L", "\[Rule]", "1."}], ",", RowBox[{"H", "\[Rule]", RowBox[{"3", "/", "10"}]}], ",", RowBox[{"h", "\[Rule]", RowBox[{"1", "/", "100"}]}], ",", RowBox[{"\[CapitalEpsilon]", "\[Rule]", "100000"}], ",", RowBox[{"\[Nu]", "\[Rule]", "0.33"}], ",", RowBox[{"\[Rho]", "\[Rule]", "100"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Block", "[", RowBox[{ RowBox[{"{", RowBox[{ "w", ",", "\[Delta]wint", ",", "\[Delta]wine", ",", "\[CapitalOmega]", ",", "rule", ",", "\[Delta]W", ",", "equ", ",", "f"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"w", "=", RowBox[{ RowBox[{"a", "[", "t", "]"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", FractionBox[ RowBox[{"x", " "}], "L"]}], ")"}], "2"], SuperscriptBox[ RowBox[{"(", FractionBox[ RowBox[{"x", " "}], "L"], ")"}], "2"]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{"Tr", "[", RowBox[{"-", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}], "]"}], "\[Transpose]"}], ".", RowBox[{"(", " ", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["h", "3"], " ", "\[CapitalEpsilon]"}], RowBox[{"12", RowBox[{"(", RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}], ")"}]}]], RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "\[Nu]", "0"}, {"\[Nu]", "1", "0"}, {"0", "0", FractionBox[ RowBox[{"1", "-", "\[Nu]"}], "2"]} }], "\[NoBreak]", ")"}]}], ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}]}]}], "]"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wine", "=", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", "w", "]"}]}], "h", " ", "\[Rho]", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"t", ",", "t"}]], "w"}]}]}], " ", ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", "=", RowBox[{"Rectangle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"L", ",", "H"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]W", " ", "=", RowBox[{"Integrate", "[", RowBox[{ RowBox[{"\[Delta]wint", "+", "\[Delta]wine"}], ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], StyleBox["\[Element]", "OperatorCharacter"], StyleBox["\[CapitalOmega]", "OperatorCharacter"]}], StyleBox[",", "OperatorCharacter"], RowBox[{ StyleBox["Assumptions", "OperatorCharacter"], StyleBox["\[Rule]", "OperatorCharacter"], RowBox[{"{", StyleBox[ RowBox[{ RowBox[{"L", ">", "0"}], ",", RowBox[{"H", ">", "0"}]}], "OperatorCharacter"], StyleBox["}", "OperatorCharacter"]}]}]}], StyleBox["]", "OperatorCharacter"]}]}], StyleBox[";", "OperatorCharacter"], StyleBox["\[IndentingNewLine]", "OperatorCharacter"], RowBox[{"equ", " ", "=", RowBox[{"Simplify", "[", RowBox[{"D", "[", RowBox[{"\[Delta]W", ",", RowBox[{"\[Delta]a", "[", "t", "]"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"f", "=", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{ RowBox[{"D", "[", RowBox[{"equ", ",", " ", RowBox[{"a", "[", "t", "]"}]}], "]"}], "/", RowBox[{"D", "[", RowBox[{"equ", ",", " ", RowBox[{ SuperscriptBox["a", "\[Prime]\[Prime]", MultilineFunction->None], "[", "t", "]"}]}], "]"}]}], "]"}], "/", RowBox[{"(", RowBox[{"2", " ", "Pi"}], ")"}]}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"f", "/.", "val"}]}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.493870948270808*^9, 3.493870974695514*^9}, { 3.4938710837637224`*^9, 3.493871234574854*^9}, {3.5007185298036003`*^9, 3.5007185364804*^9}, 3.6924165503676853`*^9, {3.692605662406251*^9, 3.6926056638062525`*^9}, {3.6926163346506824`*^9, 3.6926163355806837`*^9}, {3.6926166166210775`*^9, 3.692616866261427*^9}, 3.6926169155314956`*^9, 3.692617091411742*^9, 3.692617244301956*^9, { 3.692623259860378*^9, 3.6926232673403883`*^9}, {3.6926896317579064`*^9, 3.692689711518018*^9}, {3.692689820758171*^9, 3.6926898578282228`*^9}, { 3.692689896468277*^9, 3.692689897088278*^9}, {3.692690014838443*^9, 3.6926900476684885`*^9}, {3.6926900934285526`*^9, 3.692690117348586*^9}, { 3.6926902055287094`*^9, 3.69269020587871*^9}, 3.6928609619624777`*^9, { 3.692861016462554*^9, 3.6928610911626587`*^9}, 3.72431862763145*^9, { 3.724318668395855*^9, 3.724318825041748*^9}, {3.724318858739579*^9, 3.7243189338658123`*^9}, {3.7243189720383387`*^9, 3.724319145407913*^9}, 3.724319208486961*^9, {3.7243192540420113`*^9, 3.724319356123252*^9}, { 3.7243193912820797`*^9, 3.7243195405119486`*^9}, {3.756167692670187*^9, 3.756167728563061*^9}, {3.756167762169789*^9, 3.756167773023137*^9}, { 3.7561684121514606`*^9, 3.7561684532242527`*^9}, 3.756168493394074*^9, { 3.756168523659057*^9, 3.756168541518296*^9}, 3.756168708578459*^9, { 3.756168892902129*^9, 3.7561688954336596`*^9}, {3.75616897494083*^9, 3.7561690482816935`*^9}, {3.7561691813922987`*^9, 3.7561692339973936`*^9}, {3.7561693580796013`*^9, 3.75616936042686*^9}, { 3.7561693934476376`*^9, 3.756169399702859*^9}, {3.8204717185326157`*^9, 3.820471721437819*^9}, {3.8204718972479753`*^9, 3.820472076545085*^9}, { 3.8204721293908577`*^9, 3.8204722964801106`*^9}, {3.820472329751877*^9, 3.8204728148865786`*^9}, {3.82047285590029*^9, 3.820472858982582*^9}, { 3.8204729167180543`*^9, 3.820472939308642*^9}, {3.8204729848855286`*^9, 3.8204730343634877`*^9}, {3.8204730817979555`*^9, 3.8204731144511437`*^9}, {3.851395698951174*^9, 3.8513958353723865`*^9}, { 3.8514029742058396`*^9, 3.8514030930267406`*^9}, {3.8514031380801764`*^9, 3.8514031729914455`*^9}, {3.851403240832218*^9, 3.851403242746932*^9}, { 3.85140337932438*^9, 3.851403410529518*^9}, {3.85140347082749*^9, 3.85140347792332*^9}, {3.851403692532213*^9, 3.8514037349381704`*^9}, { 3.8514037950845313`*^9, 3.851403811863141*^9}, {3.851403847434928*^9, 3.8514039179686556`*^9}, {3.851403953359006*^9, 3.851404046096203*^9}, { 3.8514040929851227`*^9, 3.8514041042122087`*^9}, {3.851404207642264*^9, 3.8514042103962193`*^9}, {3.851404251408242*^9, 3.8514043054509754`*^9}, { 3.852171342323964*^9, 3.8521713625378327`*^9}, {3.8521722168961735`*^9, 3.852172217231166*^9}}, CellLabel-> "In[391]:=",ExpressionUUID->"3ff52ac8-d40b-4b95-9228-69666621ac82"] }, Closed]], Cell[CellGroupData[{ Cell["Example example 3.9b (plate bending)", "Subsubsection", CellChangeTimes->{{3.4467272483794003`*^9, 3.446727266257*^9}, { 3.4467288934652*^9, 3.446728896788*^9}, 3.4467805306712*^9, { 3.4801237484706*^9, 3.4801237489386*^9}, {3.5744708417194977`*^9, 3.5744708449019036`*^9}, {3.6042991711100636`*^9, 3.604299196992544*^9}, 3.60430729253247*^9, {3.604310202140381*^9, 3.6043102048235855`*^9}, { 3.6889933424974422`*^9, 3.688993352477456*^9}, 3.6889988585223417`*^9, { 3.689480870769858*^9, 3.6894808898298845`*^9}, {3.7518654678504887`*^9, 3.751865474661203*^9}, {3.7519386265381956`*^9, 3.7519386622978053`*^9}, { 3.75376294503279*^9, 3.7537629487977667`*^9}, 3.7554357667498393`*^9, 3.755523363145975*^9, 3.7866920350953083`*^9, 3.7874847705403285`*^9, { 3.787583534492174*^9, 3.787583543755392*^9}, {3.787624886997221*^9, 3.7876249024322443`*^9}, 3.8195159245188613`*^9, {3.8514041606047773`*^9, 3.8514041866311812`*^9}, {3.8514144420507417`*^9, 3.8514144462454934`*^9}},ExpressionUUID->"6ab56740-4e14-46f1-a00a-\ a093fdf3db1e"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ "one", " ", "may", " ", "use", " ", "the", " ", "triangle", " ", "plate", " ", "bending", " ", "element", " ", "with", " ", "structured", " ", "or", " ", "nonstructured", " ", "element", " ", "divisions", " ", "to", " ", "find", " ", "the", " ", "solution", " ", "by", " ", "FEM"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"val", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"L", "\[Rule]", "1."}], ",", RowBox[{"H", "\[Rule]", RowBox[{"3", "/", "10"}]}], ",", RowBox[{"t", "\[Rule]", RowBox[{"1", "/", "100"}]}], ",", RowBox[{"\[CapitalEpsilon]", "\[Rule]", "100000"}], ",", RowBox[{"\[Nu]", "\[Rule]", "0.33"}], ",", RowBox[{"\[Rho]", "\[Rule]", "100"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "7"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"2", ",", "3", ",", "7"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "7", ",", "4"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"7", ",", "3", ",", "6"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"4", ",", "7", ",", "5"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"7", ",", "6", ",", "5"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"L", "/", "2"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", "2", "]"}], ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "H", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"L", "/", "2"}], ",", "H", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "5", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", "5", "]"}], ",", RowBox[{"\[Theta]Y", "[", "5", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "H", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"L", "/", "2"}], ",", RowBox[{"H", "/", "2"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "7", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", "7", "]"}], ",", RowBox[{"\[Theta]Y", "[", "7", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "=", RowBox[{"REFINE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"MESH", "[", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "/.", "val"}], " ", "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"sol", "=", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "//.", " ", "val"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Last", "[", "sol", "]"}], "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "/", RowBox[{"(", RowBox[{"2", " ", "Pi"}], ")"}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SHOW3D", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "5"}], "}"}], ",", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "//.", "val"}], " ", "/.", RowBox[{ RowBox[{"Last", "[", "sol", "]"}], "[", RowBox[{"[", "2", "]"}], "]"}]}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.6888689611245327`*^9, 3.6888691441747894`*^9}, { 3.688869175904834*^9, 3.6888691949848604`*^9}, {3.688869303295012*^9, 3.6888694251851826`*^9}, {3.688869534825336*^9, 3.6888695373653393`*^9}, { 3.6888695909654145`*^9, 3.688869620615456*^9}, {3.6888696695055246`*^9, 3.688869671645528*^9}, {3.688869703665572*^9, 3.688869771185667*^9}, { 3.6888698131457253`*^9, 3.688869843195768*^9}, 3.688869999545987*^9, 3.6888701516861997`*^9, {3.688870779087078*^9, 3.6888708600371914`*^9}, { 3.6888713003778076`*^9, 3.688871303197812*^9}, {3.6888713416978655`*^9, 3.688871422407979*^9}, {3.6888714741080513`*^9, 3.688871476638055*^9}, 3.6888751073437386`*^9, {3.6888752493389473`*^9, 3.6888752569189587`*^9}, { 3.688875289049003*^9, 3.688875320839048*^9}, {3.6888754299492006`*^9, 3.688875430949202*^9}, {3.6888786937177925`*^9, 3.688878750267872*^9}, { 3.6888787903179283`*^9, 3.6888788206179705`*^9}, {3.6888790860283422`*^9, 3.68887909127835*^9}, {3.6890585394429307`*^9, 3.6890585586029577`*^9}, { 3.689058611933032*^9, 3.689058636633067*^9}, 3.6890586753831205`*^9, 3.6890587218131857`*^9, {3.6890588371733475`*^9, 3.6890588479333625`*^9}, 3.6890593143580313`*^9, {3.68939651006566*^9, 3.689396570005744*^9}, 3.7519567199003897`*^9, {3.7519567531116476`*^9, 3.7519568500887613`*^9}, { 3.7519568810345116`*^9, 3.7519569775584803`*^9}, {3.751957015846347*^9, 3.7519570979991937`*^9}, {3.751957130663088*^9, 3.7519571335374126`*^9}, 3.753763435083539*^9, {3.7537636176034584`*^9, 3.753763788907042*^9}, { 3.753763831693569*^9, 3.7537638728401537`*^9}, {3.75376391019105*^9, 3.7537639597106857`*^9}, {3.7537640140260305`*^9, 3.7537640276633615`*^9}, {3.753764070700218*^9, 3.7537641560081577`*^9}, { 3.7537641950926304`*^9, 3.7537643084881086`*^9}, 3.753764389828247*^9, { 3.753764533778655*^9, 3.753764547869378*^9}, {3.7553527505176506`*^9, 3.7553528603017626`*^9}, {3.75538351472929*^9, 3.7553835693549905`*^9}, { 3.755383607438428*^9, 3.7553838360146847`*^9}, {3.7553838766263666`*^9, 3.755383951476962*^9}, {3.755383992736063*^9, 3.7553840478403873`*^9}, { 3.755384124898378*^9, 3.7553842646406417`*^9}, {3.755389313373938*^9, 3.7553893195755854`*^9}, {3.755389381201706*^9, 3.7553894668944387`*^9}, { 3.7553895199108267`*^9, 3.755389537914214*^9}, {3.755389582951442*^9, 3.755389708990402*^9}, 3.7554339398817015`*^9, 3.755434068869628*^9, { 3.7554341297848616`*^9, 3.755434216890894*^9}, {3.7554343528417006`*^9, 3.7554343704056864`*^9}, {3.755434459874297*^9, 3.755434538395585*^9}, 3.755434569759145*^9, {3.7554346233872647`*^9, 3.7554347263294*^9}, { 3.7554347853286095`*^9, 3.7554348093580456`*^9}, {3.755434907172281*^9, 3.755434918847997*^9}, {3.7554349600500207`*^9, 3.7554349983466597`*^9}, { 3.755435110803147*^9, 3.7554351426284623`*^9}, {3.755435324398292*^9, 3.7554353302892075`*^9}, {3.755435441524338*^9, 3.755435445101488*^9}, 3.7554355170109453`*^9, {3.7554358134766097`*^9, 3.755435918833391*^9}, { 3.7554359598830943`*^9, 3.75543598832941*^9}, {3.755436164699664*^9, 3.7554361666501207`*^9}, {3.755436277778627*^9, 3.755436282441655*^9}, { 3.755436433004975*^9, 3.7554365810900373`*^9}, {3.755436713592167*^9, 3.7554367150263915`*^9}, {3.755436752569789*^9, 3.755436782945344*^9}, { 3.75543855564263*^9, 3.755438573014342*^9}, {3.7554386030808535`*^9, 3.75543862876925*^9}, {3.755438665543474*^9, 3.755438666460845*^9}, { 3.755438707655904*^9, 3.7554387115945473`*^9}, {3.7554387585075216`*^9, 3.7554388500917773`*^9}, {3.755523374186784*^9, 3.755523407200748*^9}, { 3.755523628104781*^9, 3.755523629369397*^9}, {3.755523692162763*^9, 3.755523702854873*^9}, 3.7555237667615433`*^9, 3.7555238472382975`*^9, 3.7555241586552105`*^9, 3.755524213729106*^9, 3.755524399719488*^9, 3.75552571772406*^9, {3.7555258075426073`*^9, 3.755525820259694*^9}, 3.755526094753117*^9, 3.7555261757546644`*^9, {3.7555262318295097`*^9, 3.7555262499726152`*^9}, {3.7555370249561615`*^9, 3.755537051432358*^9}, 3.7555372853307257`*^9, {3.755537468732602*^9, 3.755537521108555*^9}, 3.7555375621618104`*^9, {3.7555379391125593`*^9, 3.755537970148187*^9}, { 3.7555674525545197`*^9, 3.755567456059157*^9}, {3.7555675848877916`*^9, 3.7555675985147886`*^9}, {3.7555676718904886`*^9, 3.7555677115434046`*^9}, {3.755567758583485*^9, 3.7555677797901087`*^9}, { 3.755567822059022*^9, 3.755567822195668*^9}, {3.7555678597444773`*^9, 3.7555678604365673`*^9}, 3.7556071757478895`*^9, {3.7556072159647107`*^9, 3.755607332812396*^9}, {3.7556074217009745`*^9, 3.755607426579308*^9}, 3.755607632666421*^9, {3.755607684025096*^9, 3.755607693062358*^9}, { 3.7556077296748147`*^9, 3.755607849742259*^9}, {3.755608033616538*^9, 3.7556080922325497`*^9}, 3.755608142419341*^9, {3.755608958207328*^9, 3.755608980843011*^9}, {3.7559615593543744`*^9, 3.7559615796720657`*^9}, { 3.755961636991267*^9, 3.755961639837885*^9}, {3.755961688066485*^9, 3.7559617050406666`*^9}, {3.75596184181551*^9, 3.755961843331066*^9}, { 3.7560033780948515`*^9, 3.756003424416658*^9}, {3.756003637744131*^9, 3.7560039024762926`*^9}, {3.7560039413994226`*^9, 3.756004010187872*^9}, { 3.75600408826851*^9, 3.7560041132438145`*^9}, {3.7560042095185223`*^9, 3.756004261292776*^9}, {3.7560043015589314`*^9, 3.7560044114376893`*^9}, { 3.7560045878703117`*^9, 3.756004610316883*^9}, {3.756090875492567*^9, 3.756090970250229*^9}, {3.7560910153257923`*^9, 3.756091253656394*^9}, { 3.7560913065394864`*^9, 3.7560913073489447`*^9}, {3.7560913497661376`*^9, 3.7560913829572887`*^9}, {3.7560914229250793`*^9, 3.756091477168485*^9}, { 3.756091512338003*^9, 3.7560916181734085`*^9}, {3.756091734456238*^9, 3.7560917345758953`*^9}, 3.7560919538299203`*^9, {3.756092472598545*^9, 3.7560924728155417`*^9}, {3.756092529494649*^9, 3.7560925295886126`*^9}, { 3.7564428371402044`*^9, 3.7564428827548018`*^9}, {3.756443118409811*^9, 3.7564432825122414`*^9}, {3.7564433139577427`*^9, 3.7564434048585415`*^9}, {3.75644377756419*^9, 3.756443799699541*^9}, { 3.756444020280332*^9, 3.756444052335291*^9}, 3.7564441526092615`*^9, 3.7866921123667355`*^9, {3.786692169420147*^9, 3.786692647713867*^9}, { 3.7866926921591225`*^9, 3.78669273302064*^9}, {3.786692862316063*^9, 3.7866928658349466`*^9}, {3.7866931119911423`*^9, 3.786693309398429*^9}, { 3.7866933409841013`*^9, 3.7866934610423436`*^9}, {3.786693498963604*^9, 3.7866936745285892`*^9}, {3.7866937881495705`*^9, 3.7866937950939436`*^9}, 3.7873246428692293`*^9, {3.787485049135359*^9, 3.787485051961443*^9}, { 3.787485091258519*^9, 3.787485424116222*^9}, {3.7874854543849907`*^9, 3.787485502716935*^9}, {3.7874856358164625`*^9, 3.7874856505267844`*^9}, 3.787494663934597*^9, {3.7874947579329753`*^9, 3.7874947673643074`*^9}, 3.787494920667267*^9, {3.7874950655196714`*^9, 3.7874951753595195`*^9}, { 3.787495215708169*^9, 3.7874952321914797`*^9}, {3.7874953099595947`*^9, 3.7874953434716663`*^9}, {3.7874953776322303`*^9, 3.7874953779837875`*^9}, {3.7875363421179075`*^9, 3.787536342508462*^9}, { 3.7875368085158997`*^9, 3.787536878302806*^9}, {3.7875369599529157`*^9, 3.7875370055885963`*^9}, {3.7875835060582986`*^9, 3.787583520821555*^9}, { 3.787583689937277*^9, 3.787583802553567*^9}, 3.7876259263443413`*^9, { 3.7876552122737617`*^9, 3.787655270155204*^9}, {3.7877076273240643`*^9, 3.7877076330663157`*^9}, {3.8493387287106876`*^9, 3.8493387484197454`*^9}, {3.8493388690505223`*^9, 3.8493389607525234`*^9}, {3.8506381987001867`*^9, 3.850638199323704*^9}, { 3.8506382518387237`*^9, 3.8506382521507797`*^9}, 3.8507909361264725`*^9, { 3.850790968622494*^9, 3.8507909814813538`*^9}, {3.8507910227542276`*^9, 3.850791053573805*^9}, {3.850791116545538*^9, 3.8507911402245955`*^9}, { 3.8514043340993366`*^9, 3.8514044427104735`*^9}, {3.8514044803348703`*^9, 3.8514045282808294`*^9}, {3.8514046757991276`*^9, 3.8514047382171335`*^9}, {3.8514048639344797`*^9, 3.851405048797428*^9}, { 3.8514073608057184`*^9, 3.851407372693451*^9}, {3.8514076870255766`*^9, 3.8514076887032995`*^9}, {3.851407773017706*^9, 3.8514077811951346`*^9}, { 3.851407884878668*^9, 3.851407886958976*^9}, {3.8514079306283693`*^9, 3.8514079496190023`*^9}, {3.8514087740430136`*^9, 3.85140879767111*^9}, { 3.8514143934466867`*^9, 3.851414425703439*^9}, {3.851414497406939*^9, 3.851414571302442*^9}, {3.8514146041353254`*^9, 3.8514146600460863`*^9}, { 3.8514147004976883`*^9, 3.851414702555371*^9}, {3.851826345022826*^9, 3.851826362735227*^9}, {3.851835458306039*^9, 3.851835462056913*^9}, { 3.8518357385467224`*^9, 3.851835743411894*^9}, {3.852173361088862*^9, 3.852173361466459*^9}, {3.852174390177535*^9, 3.852174390585162*^9}},ExpressionUUID->"1fed5131-c575-4c94-8f68-\ 9296ca309f23"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 1 (decomposition)", "Subsubsection", CellChangeTimes->{ 3.5577964337884617`*^9, 3.6926013396721983`*^9, {3.6926179280029135`*^9, 3.6926179367329254`*^9}, {3.6926179987430124`*^9, 3.692618012853032*^9}, 3.6926777991781263`*^9, {3.6927703328584137`*^9, 3.692770359158451*^9}, { 3.7238984640156884`*^9, 3.7238984642268667`*^9}, {3.78780376721542*^9, 3.7878037739599547`*^9}},ExpressionUUID->"9fefd3ad-065d-49ce-b10f-\ a13da6966524"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", " ", RowBox[{ RowBox[{ RowBox[{"AA", "=", RowBox[{"(", GridBox[{ {"4", "0"}, { RowBox[{"-", "1"}], "1"} }], ")"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"MatrixForm", "[", "AA", "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"val", ",", "vec"}], "}"}], "=", RowBox[{"Eigensystem", "[", "AA", "]"}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"original", " ", "matrix"}], "*)"}], "\[IndentingNewLine]", RowBox[{"MatrixForm", "[", RowBox[{ RowBox[{"Transpose", "[", "vec", "]"}], ".", RowBox[{"DiagonalMatrix", "[", "val", "]"}], ".", RowBox[{"Inverse", "[", RowBox[{"Transpose", "[", "vec", "]"}], "]"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"square", " ", "root", " ", "of", " ", "the", " ", "matrix"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"SQRTA", "=", RowBox[{ RowBox[{"Transpose", "[", "vec", "]"}], ".", RowBox[{"DiagonalMatrix", "[", RowBox[{"Sqrt", "[", "val", "]"}], "]"}], ".", RowBox[{"Inverse", "[", RowBox[{"Transpose", "[", "vec", "]"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{"MatrixForm", "[", "SQRTA", "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"original", " ", "matrix", " ", "again"}], "*)"}], "\[IndentingNewLine]", RowBox[{"MatrixForm", "[", RowBox[{"SQRTA", ".", "SQRTA"}], "]"}]}]}]], "Input", CellChangeTimes->{ 3.4939782696174*^9, {3.4939783427346*^9, 3.4939784038866*^9}, { 3.557796517623009*^9, 3.5577966195847883`*^9}, {3.557796666556471*^9, 3.5577966698948765`*^9}, 3.692617920032902*^9, {3.6926180027030177`*^9, 3.6926183433034945`*^9}, {3.69261837586354*^9, 3.692618421083604*^9}, 3.6926184702836723`*^9, 3.692770250478299*^9, {3.6927703723784695`*^9, 3.692770588688772*^9}, {3.6927706245488224`*^9, 3.692770674378892*^9}, { 3.6927707053189354`*^9, 3.692770706798938*^9}, {3.692770840599125*^9, 3.6927708450491314`*^9}, {3.7879894502526913`*^9, 3.787989564120285*^9}, 3.787989599184903*^9, {3.8513953218783903`*^9, 3.851395338086149*^9}}, CellLabel->"In[66]:=",ExpressionUUID->"66c512a2-56e2-44ce-b978-5d562066707e"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 2 (mass matrix)", "Subsubsection", CellChangeTimes->{ 3.5577964337884617`*^9, 3.6926013396721983`*^9, {3.6926179280029135`*^9, 3.6926179367329254`*^9}, {3.6926179987430124`*^9, 3.692618012853032*^9}, 3.6926777991781263`*^9, {3.6927703328584137`*^9, 3.692770332958414*^9}, { 3.723898467783272*^9, 3.7238984690825796`*^9}, 3.788323982435176*^9},ExpressionUUID->"da6103d4-5508-40a8-adf5-\ 7c59179977a4"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", " ", RowBox[{ RowBox[{ RowBox[{"NN", "=", RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", FractionBox["x", "h"]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", " ", FractionBox["x", "h"]}]}], ")"}]}], ",", RowBox[{ RowBox[{"-", "h"}], SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", FractionBox["x", "h"]}], ")"}], "2"], " ", FractionBox["x", "h"]}], ",", RowBox[{ RowBox[{"(", RowBox[{"3", "-", RowBox[{"2", " ", FractionBox["x", "h"]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", FractionBox["x", "h"], ")"}], "2"]}], ",", " ", RowBox[{ RowBox[{"-", "h"}], SuperscriptBox[ RowBox[{"(", FractionBox["x", "h"], ")"}], "2"], " ", RowBox[{"(", " ", RowBox[{ FractionBox["x", "h"], "-", "1"}], ")"}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ FractionBox[ RowBox[{"A", " ", "\[Rho]", " ", "h"}], "420"], RowBox[{"MatrixForm", "[", RowBox[{ RowBox[{"420", " ", "/", RowBox[{"(", RowBox[{"A", " ", "\[Rho]", " ", "h"}], ")"}]}], " ", RowBox[{"Integrate", "[", RowBox[{ RowBox[{"A", " ", "\[Rho]", " ", RowBox[{"Outer", "[", RowBox[{"Times", ",", "NN", ",", "NN"}], "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "h"}], "}"}]}], "]"}]}], "]"}]}]}]}]], "Input", CellChangeTimes->{ 3.4939782696174*^9, {3.4939783427346*^9, 3.4939784038866*^9}, { 3.557796517623009*^9, 3.5577966195847883`*^9}, {3.557796666556471*^9, 3.5577966698948765`*^9}, 3.692617920032902*^9, {3.6926180027030177`*^9, 3.6926183433034945`*^9}, {3.69261837586354*^9, 3.692618421083604*^9}, 3.6926184702836723`*^9, 3.692770250478299*^9}, CellLabel->"In[73]:=",ExpressionUUID->"f255a474-dbc1-4258-b91f-850f262ba426"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 3 (beam)", "Subsubsection", CellChangeTimes->{ 3.4938723928941984`*^9, 3.557721739014924*^9, {3.5584046929813704`*^9, 3.5584047005778046`*^9}, {3.692770773469031*^9, 3.6927707787390385`*^9}, { 3.7238984714976816`*^9, 3.723898472723172*^9}, 3.787803783214076*^9, { 3.8200299016182303`*^9, 3.820029908762121*^9}},ExpressionUUID->"c134b95d-7c64-4d77-b441-\ a275ce11739e"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"{", RowBox[{"m", ",", RowBox[{"J", " ", RowBox[{"IdentityMatrix", "[", "3", "]"}]}]}], "}"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", " ", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.493870948270808*^9, 3.493870974695514*^9}, { 3.4938710837637224`*^9, 3.493871234574854*^9}, {3.5007185298036003`*^9, 3.5007185364804*^9}, {3.5584046678649335`*^9, 3.5584046710121136`*^9}, { 3.5584047189538555`*^9, 3.558404752896797*^9}, 3.692770788659052*^9, { 3.6927709300492496`*^9, 3.6927709553892856`*^9}, {3.692770994979341*^9, 3.692771057999429*^9}, {3.692771113499507*^9, 3.6927712426596875`*^9}, 3.692771357129848*^9, {3.694688152497208*^9, 3.694688172367236*^9}, { 3.6946882062172832`*^9, 3.69468822500731*^9}, {3.787990670100729*^9, 3.787990730568595*^9}, {3.7882474943557243`*^9, 3.78824751934991*^9}, { 3.788323884969909*^9, 3.7883238993101425`*^9}, {3.820029639027835*^9, 3.820029643030367*^9}, {3.8204711842343283`*^9, 3.82047118526092*^9}}, CellLabel->"In[75]:=",ExpressionUUID->"6125d2ae-1ba2-454b-8b3d-4d17292ff27d"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 4 (beam)", "Subsubsection", CellChangeTimes->{ 3.4938723928941984`*^9, 3.557721739014924*^9, {3.5584046929813704`*^9, 3.5584047005778046`*^9}, {3.692770773469031*^9, 3.6927707787390385`*^9}, 3.692771448509976*^9, {3.723898475265663*^9, 3.7238984765616097`*^9}, 3.7878037851088552`*^9},ExpressionUUID->"3aaa1ef3-e79e-478b-81c1-\ 07c5c6f5711e"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"{", RowBox[{"m", ",", RowBox[{"J", " ", RowBox[{"IdentityMatrix", "[", "3", "]"}]}]}], "}"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "1", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", " ", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", RowBox[{"\[Theta]Y", "[", "1", "]"}]}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "Notice", " ", "that", " ", "the", " ", "outcome", " ", "is", " ", "a", " ", "DAE"}], "*)"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.493870948270808*^9, 3.493870974695514*^9}, { 3.4938710837637224`*^9, 3.493871234574854*^9}, {3.5007185298036003`*^9, 3.5007185364804*^9}, {3.5584046678649335`*^9, 3.5584046710121136`*^9}, { 3.5584047189538555`*^9, 3.558404752896797*^9}, 3.692770788659052*^9, { 3.6927709300492496`*^9, 3.6927709553892856`*^9}, {3.692770994979341*^9, 3.692771057999429*^9}, {3.692771113499507*^9, 3.6927712426596875`*^9}, 3.692771357129848*^9, {3.692771480630021*^9, 3.692771506500057*^9}, { 3.692771639520243*^9, 3.692771640700245*^9}, {3.6927831457021666`*^9, 3.6927831608780346`*^9}, {3.692784340726518*^9, 3.692784341439559*^9}, { 3.6928536110215693`*^9, 3.6928536155915756`*^9}, {3.6928537322117386`*^9, 3.692853733971741*^9}, {3.6928550433641915`*^9, 3.692855061004216*^9}, { 3.7241471535011015`*^9, 3.72414718348577*^9}, {3.7561285637728353`*^9, 3.7561285705443535`*^9}, {3.7561286039354935`*^9, 3.7561286436098185`*^9}, {3.788247754027643*^9, 3.7882477631278453`*^9}, 3.788323871033355*^9, {3.8200296822958837`*^9, 3.8200296874979696`*^9}, { 3.8204712303223195`*^9, 3.8204712313140793`*^9}}, CellLabel->"In[79]:=",ExpressionUUID->"d2ee6931-eb4e-4961-b767-10d73a7c748b"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 5 (beam)", "Subsubsection", CellChangeTimes->{ 3.4938723928941984`*^9, 3.557721739014924*^9, {3.692605416175906*^9, 3.692605416405906*^9}, {3.69261644725084*^9, 3.6926164489508424`*^9}, { 3.6926165956910477`*^9, 3.6926166046310606`*^9}, {3.6926896111178775`*^9, 3.692689619257889*^9}, 3.6926912170301256`*^9, {3.724147332033448*^9, 3.7241473416172805`*^9}, 3.7878037895910273`*^9},ExpressionUUID->"dda18dd1-bbcd-4707-b150-\ cbd4aaba729b"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"{", RowBox[{"m", ",", RowBox[{ RowBox[{"1", "/", "5"}], " ", "m", " ", SuperscriptBox["L", "2"], " ", RowBox[{"IdentityMatrix", "[", "3", "]"}]}]}], "}"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.493870948270808*^9, 3.493870974695514*^9}, { 3.4938710837637224`*^9, 3.493871234574854*^9}, {3.5007185298036003`*^9, 3.5007185364804*^9}, 3.6924165503676853`*^9, {3.692605662406251*^9, 3.6926056638062525`*^9}, {3.6926163346506824`*^9, 3.6926163355806837`*^9}, {3.6926166166210775`*^9, 3.692616866261427*^9}, 3.6926169155314956`*^9, 3.692617091411742*^9, 3.692617244301956*^9, { 3.692623259860378*^9, 3.6926232673403883`*^9}, {3.6926896317579064`*^9, 3.692689711518018*^9}, {3.692689820758171*^9, 3.6926898578282228`*^9}, { 3.692689896468277*^9, 3.692689897088278*^9}, {3.692690014838443*^9, 3.6926900476684885`*^9}, {3.6926900934285526`*^9, 3.692690117348586*^9}, { 3.6926902055287094`*^9, 3.69269020587871*^9}, {3.6926912368001537`*^9, 3.692691265400193*^9}, 3.692691388690366*^9, {3.6928606784320807`*^9, 3.692860680972084*^9}, {3.6928607128321285`*^9, 3.6928607136321297`*^9}, { 3.692860762222198*^9, 3.692860774902216*^9}, {3.788247837339185*^9, 3.788247879734177*^9}, 3.788323863754079*^9, {3.8200297469603596`*^9, 3.820029763651271*^9}, {3.820471421059429*^9, 3.8204714221072345`*^9}}, CellLabel->"In[84]:=",ExpressionUUID->"cf41cb56-5935-45b4-81c6-58eccff89957"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 6 (thin slab)", "Subsubsection", CellChangeTimes->{{3.5577964555661*^9, 3.557796469528125*^9}, 3.6926057358063536`*^9, {3.6926778041981335`*^9, 3.6926778043681335`*^9}, { 3.6926787551494646`*^9, 3.692678770969487*^9}, 3.69267930176023*^9, 3.6927716593602715`*^9, {3.7238984792910604`*^9, 3.723898480878615*^9}, 3.724147396313452*^9, 3.7878037915008307`*^9, {3.8200298618306556`*^9, 3.8200298644538116`*^9}, {3.820029930033001*^9, 3.820029930658329*^9}},ExpressionUUID->"4fd0149b-cb09-457e-894c-\ d1215af53706"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "0", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "h", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "4", ",", "3"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "4", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4939930717488003`*^9, 3.4939930974108*^9}, { 3.4939934523719997`*^9, 3.4939934579568*^9}, {3.4940328656694*^9, 3.4940328661686*^9}, {3.4940336074547997`*^9, 3.494033663178*^9}, 3.4940340531*^9, {3.4940343243684*^9, 3.4940343274104*^9}, { 3.500718840384*^9, 3.5007188689944*^9}, {3.557797943855514*^9, 3.5577979639795494`*^9}, 3.6926792938302193`*^9, 3.692771703570333*^9, { 3.6927734376627607`*^9, 3.692773462532796*^9}, {3.6927734931228385`*^9, 3.692773588602972*^9}, 3.692773619943016*^9, {3.692773683713105*^9, 3.692773731253172*^9}, {3.6927737733532305`*^9, 3.6927737739032316`*^9}, { 3.7246437503335924`*^9, 3.7246437671242456`*^9}, {3.7246438175496655`*^9, 3.7246438334559956`*^9}, {3.7247565282659345`*^9, 3.724756535705496*^9}, 3.7883238553004894`*^9, {3.820029801163093*^9, 3.8200298556551743`*^9}}, CellLabel->"In[89]:=",ExpressionUUID->"8f714d42-58ff-4328-af20-9d80e9083ba8"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 7 (beam)", "Subsubsection", CellChangeTimes->{ 3.4938723928941984`*^9, 3.557721739014924*^9, {3.692605416175906*^9, 3.692605416405906*^9}, {3.69261644725084*^9, 3.6926164489508424`*^9}, { 3.6926165956910477`*^9, 3.6926166046310606`*^9}, {3.6926896111178775`*^9, 3.692689619257889*^9}, {3.724147617138194*^9, 3.724147631820558*^9}, 3.7561657335722027`*^9, 3.7878037936611233`*^9},ExpressionUUID->"137610b8-126f-4d7c-a09b-\ 6b62aef6c587"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"STEP", " ", "1"}], ":", " ", RowBox[{"t", " ", "<", " ", "0"}]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0", ",", "M", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Theta]Y2", " ", "=", " ", RowBox[{ RowBox[{"\[Theta]Y", "[", "2", "]"}], "/.", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.493870948270808*^9, 3.493870974695514*^9}, { 3.4938710837637224`*^9, 3.493871234574854*^9}, {3.5007185298036003`*^9, 3.5007185364804*^9}, 3.6924165503676853`*^9, {3.692605662406251*^9, 3.6926056638062525`*^9}, {3.6926163346506824`*^9, 3.6926163355806837`*^9}, {3.6926166166210775`*^9, 3.692616866261427*^9}, 3.6926169155314956`*^9, 3.692617091411742*^9, 3.692617244301956*^9, { 3.692623259860378*^9, 3.6926232673403883`*^9}, {3.6926896317579064`*^9, 3.692689711518018*^9}, {3.692689820758171*^9, 3.6926898578282228`*^9}, { 3.692689896468277*^9, 3.692689897088278*^9}, {3.692690014838443*^9, 3.6926900476684885`*^9}, {3.6926900934285526`*^9, 3.692690117348586*^9}, { 3.6926902055287094`*^9, 3.69269020587871*^9}, 3.6928609619624777`*^9, { 3.692861016462554*^9, 3.6928610911626587`*^9}, {3.788248230022855*^9, 3.7882482592696548`*^9}, {3.78824833634833*^9, 3.788248343272706*^9}, { 3.8200299414032726`*^9, 3.8200299433364167`*^9}, {3.820029996475786*^9, 3.820030000803342*^9}, 3.820471517540506*^9}, CellLabel->"In[93]:=",ExpressionUUID->"b9974d30-220b-42ba-924c-5edb8fc02603"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"STEP", " ", "2"}], ":", " ", RowBox[{"t", " ", ">", " ", "0"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.493870948270808*^9, 3.493870974695514*^9}, { 3.4938710837637224`*^9, 3.493871234574854*^9}, {3.5007185298036003`*^9, 3.5007185364804*^9}, 3.6924165503676853`*^9, {3.692605662406251*^9, 3.6926056638062525`*^9}, {3.6926163346506824`*^9, 3.6926163355806837`*^9}, {3.6926166166210775`*^9, 3.692616866261427*^9}, 3.6926169155314956`*^9, 3.692617091411742*^9, 3.692617244301956*^9, { 3.692623259860378*^9, 3.6926232673403883`*^9}, {3.6926896317579064`*^9, 3.692689711518018*^9}, {3.692689820758171*^9, 3.6926898578282228`*^9}, { 3.692689896468277*^9, 3.692689897088278*^9}, {3.692690014838443*^9, 3.6926900476684885`*^9}, {3.6926900934285526`*^9, 3.692690117348586*^9}, { 3.6926902055287094`*^9, 3.69269020587871*^9}, {3.6928609619624777`*^9, 3.692861003972536*^9}, {3.6928611195326986`*^9, 3.6928611624827585`*^9}, 3.6928612124628286`*^9, {3.788248269799512*^9, 3.78824829352197*^9}, { 3.7882483493246202`*^9, 3.788248352056753*^9}, {3.8200299552126503`*^9, 3.820030007977022*^9}, 3.8204715426955304`*^9}, CellLabel->"In[97]:=",ExpressionUUID->"988fab71-8d6f-463a-9c6f-30208dd7aa41"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 8 (thin slab)", "Subsubsection", CellChangeTimes->{{3.5577964555661*^9, 3.557796469528125*^9}, 3.6926057358063536`*^9, {3.6926778041981335`*^9, 3.6926778043681335`*^9}, { 3.6926787551494646`*^9, 3.692678770969487*^9}, 3.69267930176023*^9, 3.6927716593602715`*^9, 3.692773807173278*^9, {3.723898484965362*^9, 3.723898488502695*^9}, 3.724147399565941*^9, 3.724147635566226*^9, { 3.7245527509658732`*^9, 3.724552771340017*^9}, 3.7561657371136637`*^9, 3.7878037964843206`*^9, {3.8200300362663517`*^9, 3.820030041779605*^9}},ExpressionUUID->"1d113d45-b64b-4176-916f-\ 61fe0321cd08"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "h", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "4", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "h", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "4"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "1", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"uX", "[", RowBox[{"1", ",", "0"}], "]"}], "\[Rule]", "U"}], ",", RowBox[{ RowBox[{"uX", "[", RowBox[{"_", ",", "1"}], "]"}], "\[Rule]", "0"}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.4939930717488003`*^9, 3.4939930974108*^9}, { 3.4939934523719997`*^9, 3.4939934579568*^9}, {3.4940328656694*^9, 3.4940328661686*^9}, {3.4940336074547997`*^9, 3.494033663178*^9}, 3.4940340531*^9, {3.4940343243684*^9, 3.4940343274104*^9}, { 3.500718840384*^9, 3.5007188689944*^9}, {3.557797943855514*^9, 3.5577979639795494`*^9}, 3.6926792938302193`*^9, 3.692771703570333*^9, { 3.6927734376627607`*^9, 3.692773462532796*^9}, {3.6927734931228385`*^9, 3.692773588602972*^9}, 3.692773619943016*^9, {3.692773683713105*^9, 3.692773731253172*^9}, {3.6927737733532305`*^9, 3.6927737739032316`*^9}, { 3.6927738245433025`*^9, 3.692773876463375*^9}, {3.692773939413463*^9, 3.692773995603542*^9}, {3.6927740539236236`*^9, 3.6927740867636695`*^9}, { 3.6928600883112545`*^9, 3.6928600952012644`*^9}, {3.724510813340685*^9, 3.7245108439239902`*^9}, {3.7245110894899054`*^9, 3.7245111362366643`*^9}, {3.7245111759684496`*^9, 3.7245111800040627`*^9}, {3.7245112142827435`*^9, 3.724511357099068*^9}, { 3.72451139044884*^9, 3.7245113908943324`*^9}, {3.7245114354388523`*^9, 3.724511619873787*^9}, {3.724511680905528*^9, 3.724511684090825*^9}, { 3.724511739941152*^9, 3.7245117444832473`*^9}, {3.7245117919587584`*^9, 3.724511792442217*^9}, {3.7245119452797728`*^9, 3.7245119591135845`*^9}, { 3.7245121768708963`*^9, 3.7245121842326193`*^9}, {3.724512227324604*^9, 3.7245122284688077`*^9}, {3.7245122615399647`*^9, 3.724512272739452*^9}, { 3.7245123874801135`*^9, 3.724512394482444*^9}, {3.7245124864476037`*^9, 3.724512492861*^9}, {3.724512563393937*^9, 3.7245125642590384`*^9}, { 3.724512686336095*^9, 3.724512686647025*^9}, {3.7245523986395607`*^9, 3.724552428037301*^9}, {3.7245524590510445`*^9, 3.7245524906776133`*^9}, { 3.7245525335305943`*^9, 3.7245525493372817`*^9}, {3.7245525915792074`*^9, 3.724552624903928*^9}, {3.724552700655877*^9, 3.7245527010974026`*^9}, { 3.7245527827516294`*^9, 3.724552841959256*^9}, {3.756129737744466*^9, 3.7561297576506205`*^9}, {3.756166282287259*^9, 3.7561662832618446`*^9}, { 3.8200300491040134`*^9, 3.8200300539125266`*^9}}, CellLabel-> "In[101]:=",ExpressionUUID->"71b41a9d-992c-4d5f-b1fb-52dcc213da63"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 9 (bar truss)", "Subsubsection", CellChangeTimes->{{3.4938724364934034`*^9, 3.493872440377554*^9}, 3.55772174224413*^9, {3.5577222701826577`*^9, 3.557722281898278*^9}, { 3.6925364040653286`*^9, 3.692536414765343*^9}, {3.6926051339045105`*^9, 3.692605137804516*^9}, 3.692616505550922*^9, {3.6926165560409927`*^9, 3.692616575321019*^9}, {3.692860264491501*^9, 3.6928602694915085`*^9}, { 3.723898500282627*^9, 3.7238985038248096`*^9}, 3.724147406515576*^9, { 3.724147638325242*^9, 3.7241476397263546`*^9}, 3.7561673435357966`*^9, 3.7878037990280237`*^9},ExpressionUUID->"ca0bed05-480f-4077-9f56-\ d2f6a343f7fe"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"STEP", " ", "1"}], ":", " ", RowBox[{"t", " ", "<", " ", "0"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"4", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "F"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"sol", "=", " ", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"U", " ", "=", " ", RowBox[{ RowBox[{"uZ", "[", "2", "]"}], " ", "/.", " ", "sol"}]}], ";"}]}]}]], "Input", CellChangeTimes->{{3.4938808707521195`*^9, 3.493880886414419*^9}, { 3.4938809823296185`*^9, 3.4938810743976574`*^9}, {3.493881115862191*^9, 3.49388112389614*^9}, {3.5007185681328*^9, 3.5007185858543997`*^9}, 3.557721807701845*^9, 3.557722301679113*^9, {3.557722338229977*^9, 3.557722345218789*^9}, {3.5577223956380777`*^9, 3.557722557550762*^9}, { 3.5577227444350924`*^9, 3.5577227701751375`*^9}, {3.557722914366191*^9, 3.5577231321893735`*^9}, {3.5577234762323775`*^9, 3.557723673042323*^9}, { 3.557723707440384*^9, 3.557723724257213*^9}, {3.557723808200961*^9, 3.5577238249085903`*^9}, {3.557724032045754*^9, 3.5577240381453648`*^9}, { 3.5577240859750485`*^9, 3.5577241533827667`*^9}, {3.5577255542808275`*^9, 3.557725556340031*^9}, {3.692416572627716*^9, 3.692416634337803*^9}, { 3.6924166962978897`*^9, 3.6924166970178905`*^9}, {3.692416728407934*^9, 3.692416742377954*^9}, 3.692416785478014*^9, {3.692416815828057*^9, 3.692416854678111*^9}, {3.6924172169506187`*^9, 3.6924175298010564`*^9}, { 3.692418050131785*^9, 3.692418107561865*^9}, {3.6924216949310565`*^9, 3.6924216977710605`*^9}, {3.6925022762935333`*^9, 3.6925022791146946`*^9}, {3.6926050714634233`*^9, 3.6926053101657577`*^9}, {3.692605350685814*^9, 3.6926053528358173`*^9}, { 3.692605582596139*^9, 3.692605583946141*^9}, 3.692623496410709*^9, { 3.692623535710764*^9, 3.692623557910795*^9}, {3.6926952837958193`*^9, 3.6926952890058265`*^9}, {3.6928555108448462`*^9, 3.692855525144866*^9}, { 3.6928555801949434`*^9, 3.6928556725450726`*^9}, {3.6928557055151186`*^9, 3.6928557885252347`*^9}, {3.692855881295365*^9, 3.6928558933153815`*^9}, { 3.692855952785465*^9, 3.6928559781655006`*^9}, {3.6928560758856373`*^9, 3.692856170005769*^9}, {3.6928562238658447`*^9, 3.6928562580458927`*^9}, { 3.6928562961859455`*^9, 3.69285631358597*^9}, {3.692856357426031*^9, 3.6928563681360464`*^9}, {3.6928563999060907`*^9, 3.6928564001160913`*^9}, {3.692857702937915*^9, 3.6928577502779813`*^9}, { 3.6928602931015415`*^9, 3.6928603882816744`*^9}, {3.6928604508717623`*^9, 3.6928604766617985`*^9}, {3.7561674019881897`*^9, 3.756167413743063*^9}, { 3.7561674582881846`*^9, 3.7561674667464952`*^9}, {3.756167612300265*^9, 3.756167626175462*^9}, {3.7882485578101134`*^9, 3.788248586015726*^9}, { 3.8200300876828213`*^9, 3.820030094371929*^9}}, CellLabel-> "In[106]:=",ExpressionUUID->"710a6b9f-deb0-4750-847e-de05528a3dd1"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"STEP2", ":", " ", RowBox[{"t", " ", ">", " ", "0"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "0"}], "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "0"}], "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"4", ",", "2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"uZ", "[", RowBox[{"_", ",", "0"}], "]"}], "\[Rule]", "U"}], ",", RowBox[{ RowBox[{"uZ", "[", RowBox[{"_", ",", "1"}], "]"}], "\[Rule]", "0"}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.4938808707521195`*^9, 3.493880886414419*^9}, { 3.4938809823296185`*^9, 3.4938810743976574`*^9}, {3.493881115862191*^9, 3.49388112389614*^9}, {3.5007185681328*^9, 3.5007185858543997`*^9}, 3.557721807701845*^9, 3.557722301679113*^9, {3.557722338229977*^9, 3.557722345218789*^9}, {3.5577223956380777`*^9, 3.557722557550762*^9}, { 3.5577227444350924`*^9, 3.5577227701751375`*^9}, {3.557722914366191*^9, 3.5577231321893735`*^9}, {3.5577234762323775`*^9, 3.557723673042323*^9}, { 3.557723707440384*^9, 3.557723724257213*^9}, {3.557723808200961*^9, 3.5577238249085903`*^9}, {3.557724032045754*^9, 3.5577240381453648`*^9}, { 3.5577240859750485`*^9, 3.5577241533827667`*^9}, {3.5577255542808275`*^9, 3.557725556340031*^9}, {3.692416572627716*^9, 3.692416634337803*^9}, { 3.6924166962978897`*^9, 3.6924166970178905`*^9}, {3.692416728407934*^9, 3.692416742377954*^9}, 3.692416785478014*^9, {3.692416815828057*^9, 3.692416854678111*^9}, {3.6924172169506187`*^9, 3.6924175298010564`*^9}, { 3.692418050131785*^9, 3.692418107561865*^9}, {3.6924216949310565`*^9, 3.6924216977710605`*^9}, {3.6925022762935333`*^9, 3.6925022791146946`*^9}, {3.6926050714634233`*^9, 3.6926053101657577`*^9}, {3.692605350685814*^9, 3.6926053528358173`*^9}, { 3.692605582596139*^9, 3.692605583946141*^9}, 3.692623496410709*^9, { 3.692623535710764*^9, 3.692623557910795*^9}, {3.6926952837958193`*^9, 3.6926952890058265`*^9}, {3.6928555108448462`*^9, 3.692855525144866*^9}, { 3.6928555801949434`*^9, 3.6928556725450726`*^9}, {3.6928557055151186`*^9, 3.6928557885252347`*^9}, {3.692855881295365*^9, 3.6928558933153815`*^9}, { 3.692855952785465*^9, 3.6928559781655006`*^9}, {3.6928560758856373`*^9, 3.692856170005769*^9}, {3.6928562238658447`*^9, 3.6928562580458927`*^9}, { 3.6928562961859455`*^9, 3.69285631358597*^9}, {3.692856357426031*^9, 3.6928563681360464`*^9}, {3.6928563999060907`*^9, 3.6928564001160913`*^9}, {3.692857702937915*^9, 3.6928577502779813`*^9}, { 3.6928602931015415`*^9, 3.692860442871751*^9}, {3.692860490661818*^9, 3.6928605008218317`*^9}, 3.724148526274141*^9, {3.7561674288237047`*^9, 3.7561674323586836`*^9}, {3.7561674878338723`*^9, 3.756167499857013*^9}, { 3.7882485720615144`*^9, 3.7882485780249004`*^9}, {3.8200301062970314`*^9, 3.820030112781686*^9}}, CellLabel-> "In[112]:=",ExpressionUUID->"e2130f23-bca8-410e-b353-51210869b0ce"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 10 (plate)", "Subsubsection", CellChangeTimes->{ 3.4938723928941984`*^9, 3.557721739014924*^9, {3.692605416175906*^9, 3.692605416405906*^9}, {3.69261644725084*^9, 3.6926164489508424`*^9}, { 3.6926165956910477`*^9, 3.6926166046310606`*^9}, {3.6926896111178775`*^9, 3.692689619257889*^9}, {3.7241476447423286`*^9, 3.7241476607760677`*^9}, { 3.724318554593711*^9, 3.7243185670306544`*^9}, {3.724318639035441*^9, 3.7243186477809887`*^9}, {3.756083392953127*^9, 3.756083398473401*^9}, 3.7561676827881355`*^9, {3.7561688892534256`*^9, 3.7561688903110223`*^9}, 3.7878038031871395`*^9},ExpressionUUID->"b5e860d5-d0f2-46a5-b239-\ 8fbbfe5c8a57"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{"Block", "[", RowBox[{ RowBox[{"{", RowBox[{ "wm", ",", "\[Delta]wint", ",", "\[Delta]wine", ",", "\[CapitalOmega]", ",", "rule", ",", "\[Delta]W"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"w", "=", RowBox[{ RowBox[{ RowBox[{"a", "[", "0", "]"}], "[", "t", "]"}], " ", "x", " ", RowBox[{"y", "/", SuperscriptBox["L", "2"]}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{"Tr", "[", RowBox[{"-", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}], "]"}], "\[Transpose]"}], ".", RowBox[{"(", " ", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["h", "3"], " ", "\[CapitalEpsilon]"}], RowBox[{"12", RowBox[{"(", RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}], ")"}]}]], RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "\[Nu]", "0"}, {"\[Nu]", "1", "0"}, {"0", "0", FractionBox[ RowBox[{"1", "-", "\[Nu]"}], "2"]} }], "\[NoBreak]", ")"}]}], ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}]}]}], "]"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wine", "=", RowBox[{ RowBox[{"-", RowBox[{"\[Delta]", "[", "w", "]"}]}], "h", " ", "\[Rho]", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"t", ",", "t"}]], "w"}]}]}], " ", ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", "=", RowBox[{"Rectangle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"L", ",", "L"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"rule", ":=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"a", "[", "any_", "]"}], "[", "t", "]"}], "->", RowBox[{"a", "[", RowBox[{"any", ",", "0"}], "]"}]}], ",", RowBox[{ RowBox[{ RowBox[{"\[Delta]a", "[", "any_", "]"}], "[", "t", "]"}], "\[Rule]", RowBox[{"\[Delta]a", "[", RowBox[{"any", ",", "0"}], "]"}]}], ",", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"a", "[", "any_", "]"}], "\[Prime]\[Prime]", MultilineFunction->None], "[", "t", "]"}], "->", RowBox[{"a", "[", RowBox[{"any", ",", "2"}], "]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]W", " ", "=", RowBox[{ RowBox[{"Integrate", "[", RowBox[{ RowBox[{"\[Delta]wint", "+", "\[Delta]wine"}], ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], StyleBox["\[Element]", "OperatorCharacter"], StyleBox["\[CapitalOmega]", "OperatorCharacter"]}], StyleBox[",", "OperatorCharacter"], RowBox[{ StyleBox["Assumptions", "OperatorCharacter"], StyleBox["\[Rule]", "OperatorCharacter"], RowBox[{"{", StyleBox[ RowBox[{"L", ">", "0"}], "OperatorCharacter"], StyleBox["}", "OperatorCharacter"]}]}]}], StyleBox["]", "OperatorCharacter"]}], StyleBox[" ", "OperatorCharacter"], StyleBox["/.", "OperatorCharacter"], StyleBox["rule", "OperatorCharacter"]}]}], StyleBox[";", "OperatorCharacter"], StyleBox["\[IndentingNewLine]", "OperatorCharacter"], StyleBox["\[IndentingNewLine]", "OperatorCharacter"], RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"a", "[", RowBox[{"0", ",", "0"}], "]"}], "\[Rule]", "U"}], ",", RowBox[{ RowBox[{"a", "[", RowBox[{"0", ",", "1"}], "]"}], "\[Rule]", "0"}]}], "}"}]}], "}"}], ",", "\[Delta]W"}], "]"}]}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.493870948270808*^9, 3.493870974695514*^9}, { 3.4938710837637224`*^9, 3.493871234574854*^9}, {3.5007185298036003`*^9, 3.5007185364804*^9}, 3.6924165503676853`*^9, {3.692605662406251*^9, 3.6926056638062525`*^9}, {3.6926163346506824`*^9, 3.6926163355806837`*^9}, {3.6926166166210775`*^9, 3.692616866261427*^9}, 3.6926169155314956`*^9, 3.692617091411742*^9, 3.692617244301956*^9, { 3.692623259860378*^9, 3.6926232673403883`*^9}, {3.6926896317579064`*^9, 3.692689711518018*^9}, {3.692689820758171*^9, 3.6926898578282228`*^9}, { 3.692689896468277*^9, 3.692689897088278*^9}, {3.692690014838443*^9, 3.6926900476684885`*^9}, {3.6926900934285526`*^9, 3.692690117348586*^9}, { 3.6926902055287094`*^9, 3.69269020587871*^9}, 3.6928609619624777`*^9, { 3.692861016462554*^9, 3.6928610911626587`*^9}, 3.72431862763145*^9, { 3.724318668395855*^9, 3.724318825041748*^9}, {3.724318858739579*^9, 3.7243189338658123`*^9}, {3.7243189720383387`*^9, 3.724319145407913*^9}, 3.724319208486961*^9, {3.7243192540420113`*^9, 3.724319356123252*^9}, { 3.7243193912820797`*^9, 3.7243195405119486`*^9}, {3.756167692670187*^9, 3.756167728563061*^9}, {3.756167762169789*^9, 3.756167773023137*^9}, { 3.7561684121514606`*^9, 3.7561684532242527`*^9}, 3.756168493394074*^9, { 3.756168523659057*^9, 3.756168541518296*^9}, 3.756168708578459*^9, { 3.756168892902129*^9, 3.7561688954336596`*^9}, {3.75616897494083*^9, 3.7561690482816935`*^9}, {3.7561691813922987`*^9, 3.7561692339973936`*^9}, {3.7561693580796013`*^9, 3.75616936042686*^9}, { 3.7561693934476376`*^9, 3.756169399702859*^9}, {3.8204717185326157`*^9, 3.820471721437819*^9}, {3.8204718972479753`*^9, 3.820472076545085*^9}, { 3.8204721293908577`*^9, 3.8204722964801106`*^9}, {3.820472329751877*^9, 3.8204728148865786`*^9}, {3.82047285590029*^9, 3.820472858982582*^9}, { 3.8204729167180543`*^9, 3.820472939308642*^9}, {3.8204729848855286`*^9, 3.8204730343634877`*^9}, {3.8204730817979555`*^9, 3.8204731144511437`*^9}, {3.851395698951174*^9, 3.8513958353723865`*^9}}, CellLabel-> "In[369]:=",ExpressionUUID->"58704f56-5287-48d7-a4d7-dceebca4f2e7"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"a", "[", "0", "]"}], "\[Rule]", RowBox[{"U", " ", RowBox[{"Cos", "[", RowBox[{ SqrtBox[ FractionBox["3", "2"]], " ", "t", " ", SqrtBox[ FractionBox[ RowBox[{ SuperscriptBox["h", "2"], " ", "\[CapitalEpsilon]"}], RowBox[{ SuperscriptBox["L", "4"], " ", RowBox[{"(", RowBox[{"1", "+", "\[Nu]"}], ")"}], " ", "\[Rho]"}]]]}], "]"}]}]}], "}"}]], "Output", CellChangeTimes->{3.8518477598331366`*^9}, CellLabel-> "Out[369]=",ExpressionUUID->"d5ba9069-f53b-4c6c-928e-c2704925ff5f"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Home assignment 1 (torsion)", "Subsubsection", CellChangeTimes->{ 3.4938723928941984`*^9, 3.557721739014924*^9, {3.692605416175906*^9, 3.692605416405906*^9}, {3.69261644725084*^9, 3.6926164489508424`*^9}, { 3.6926165956910477`*^9, 3.6926166046310606`*^9}, {3.6926896111178775`*^9, 3.692689619257889*^9}, 3.6926912170301256`*^9, 3.7241476428310165`*^9, { 3.7561696233666773`*^9, 3.7561696272662334`*^9}},ExpressionUUID->"7dfc468d-8647-4341-b9fa-\ 3647224b7b57"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", " ", RowBox[{"G", ",", "0"}], "}"}], ",", RowBox[{"{", "J", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", " ", RowBox[{"G", ",", "0"}], "}"}], ",", RowBox[{"{", "J", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"TORSION", ",", RowBox[{"{", RowBox[{ RowBox[{"{", " ", RowBox[{"G", ",", "0"}], "}"}], ",", RowBox[{"{", "J", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "4"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"{", RowBox[{"m", ",", " ", RowBox[{"J", " ", "\[Rho]", " ", RowBox[{"IdentityMatrix", "[", "3", "]"}]}]}], "}"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"{", RowBox[{"m", ",", RowBox[{"J", " ", "\[Rho]", " ", RowBox[{"IdentityMatrix", "[", "3", "]"}]}]}], "}"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "3", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", " ", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", "3", "]"}], ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"3", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\n", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.493870948270808*^9, 3.493870974695514*^9}, { 3.4938710837637224`*^9, 3.493871234574854*^9}, {3.5007185298036003`*^9, 3.5007185364804*^9}, 3.6924165503676853`*^9, {3.692605662406251*^9, 3.6926056638062525`*^9}, {3.6926163346506824`*^9, 3.6926163355806837`*^9}, {3.6926166166210775`*^9, 3.692616866261427*^9}, 3.6926169155314956`*^9, 3.692617091411742*^9, 3.692617244301956*^9, { 3.692623259860378*^9, 3.6926232673403883`*^9}, {3.6926896317579064`*^9, 3.692689711518018*^9}, {3.692689820758171*^9, 3.6926898578282228`*^9}, { 3.692689896468277*^9, 3.692689897088278*^9}, {3.692690014838443*^9, 3.6926900476684885`*^9}, {3.6926900934285526`*^9, 3.692690117348586*^9}, { 3.6926902055287094`*^9, 3.69269020587871*^9}, {3.6926912368001537`*^9, 3.692691265400193*^9}, 3.692691388690366*^9, {3.6928606784320807`*^9, 3.692860680972084*^9}, {3.6928607128321285`*^9, 3.6928607136321297`*^9}, { 3.692860762222198*^9, 3.692860774902216*^9}, {3.7244128700993214`*^9, 3.7244129701227965`*^9}, {3.7244130670991325`*^9, 3.7244130717781334`*^9}, 3.7244131625258923`*^9, 3.7244132119761505`*^9, {3.756009769254346*^9, 3.7560097984891305`*^9}, {3.7560098572479444`*^9, 3.756009862164278*^9}, { 3.756009902579606*^9, 3.7560099327082233`*^9}, {3.78815401519639*^9, 3.7881540650661397`*^9}, {3.7881574724992065`*^9, 3.788157475676734*^9}, { 3.7881575243056536`*^9, 3.788157681083987*^9}, {3.788157722103042*^9, 3.7881577241628485`*^9}, {3.788167388102944*^9, 3.7881674312767434`*^9}, { 3.7881674649924335`*^9, 3.7881674661429844`*^9}, {3.788167519535819*^9, 3.7881675664713097`*^9}, {3.788167604092924*^9, 3.7881676089149256`*^9}, { 3.788167661942783*^9, 3.7881676953934765`*^9}, {3.788167773185461*^9, 3.7881677855166874`*^9}, {3.7881678334032145`*^9, 3.7881678586136866`*^9}, {3.788167891417267*^9, 3.7881678967624526`*^9}, 3.788167932902671*^9, {3.7881679839981923`*^9, 3.7881680183386154`*^9}, { 3.788168061655179*^9, 3.7881680619558244`*^9}, {3.7881681892901645`*^9, 3.788168248400946*^9}, {3.7881682999284353`*^9, 3.7881683333488336`*^9}, { 3.788168367778096*^9, 3.7881683915103207`*^9}, {3.788168427513071*^9, 3.78816847687361*^9}, {3.788168526669993*^9, 3.788168542590762*^9}, { 3.7882487122059045`*^9, 3.7882487460135994`*^9}, {3.8209918195508137`*^9, 3.820991829836608*^9}, {3.820993961804452*^9, 3.8209939790613947`*^9}, { 3.8209940160718555`*^9, 3.8209940462085943`*^9}, {3.851395882047143*^9, 3.85139588849801*^9}, {3.851396260037772*^9, 3.851396299542898*^9}, { 3.851826584458306*^9, 3.8518266442053823`*^9}}, CellLabel->"In[10]:=",ExpressionUUID->"bbf5dce5-5554-4fb3-997d-2445c818bfe9"] }, Closed]], Cell[CellGroupData[{ Cell["Home assignment 2 (beam truss)", "Subsubsection", CellChangeTimes->{ 3.4938723928941984`*^9, 3.557721739014924*^9, {3.692605416175906*^9, 3.692605416405906*^9}, {3.69261644725084*^9, 3.6926164489508424`*^9}, { 3.6926165956910477`*^9, 3.6926166046310606`*^9}, {3.6926896111178775`*^9, 3.692689619257889*^9}, 3.7241476447423286`*^9, {3.756169630729544*^9, 3.756169634741873*^9}},ExpressionUUID->"f6e54321-d312-49ea-b1a3-\ 57a3b1e06f2a"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ "beam", " ", "element", " ", "takes", " ", "into", " ", "account", " ", "also", " ", "the", " ", "rotation", " ", "part", " ", "of", " ", "inertia", " ", "forces"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "4"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", " ", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", " ", RowBox[{"L", ",", "0", ",", RowBox[{"-", "L"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.493870948270808*^9, 3.493870974695514*^9}, { 3.4938710837637224`*^9, 3.493871234574854*^9}, {3.5007185298036003`*^9, 3.5007185364804*^9}, 3.6924165503676853`*^9, {3.692605662406251*^9, 3.6926056638062525`*^9}, {3.6926163346506824`*^9, 3.6926163355806837`*^9}, {3.6926166166210775`*^9, 3.692616866261427*^9}, 3.6926169155314956`*^9, 3.692617091411742*^9, 3.692617244301956*^9, { 3.692623259860378*^9, 3.6926232673403883`*^9}, {3.6926896317579064`*^9, 3.692689711518018*^9}, {3.692689820758171*^9, 3.6926898578282228`*^9}, { 3.692689896468277*^9, 3.692689897088278*^9}, {3.692690014838443*^9, 3.6926900476684885`*^9}, {3.6926900934285526`*^9, 3.692690117348586*^9}, { 3.6926902055287094`*^9, 3.69269020587871*^9}, 3.6928609619624777`*^9, { 3.692861016462554*^9, 3.6928610911626587`*^9}, {3.7244132320712056`*^9, 3.7244133401327267`*^9}, {3.7244133787614565`*^9, 3.72441343334622*^9}, 3.7244134790769606`*^9, {3.7560831913266315`*^9, 3.756083210075788*^9}, { 3.788239176072998*^9, 3.7882391831676254`*^9}, {3.7882392218547583`*^9, 3.7882392518713074`*^9}, {3.788239300862713*^9, 3.7882393040966797`*^9}, { 3.7882393550286527`*^9, 3.7882393912127934`*^9}, {3.851396395663067*^9, 3.8513964045571775`*^9}}, CellLabel-> "In[147]:=",ExpressionUUID->"8acc7bac-0bc3-4c44-9772-c796a1417d68"] }, Closed]], Cell[CellGroupData[{ Cell["Home assignment 3 (thin slab)", "Subsubsection", CellChangeTimes->{{3.5577964555661*^9, 3.557796469528125*^9}, 3.6926057358063536`*^9, {3.6926778041981335`*^9, 3.6926778043681335`*^9}, { 3.6926787551494646`*^9, 3.692678770969487*^9}, 3.69267930176023*^9, 3.6927716593602715`*^9, 3.692773807173278*^9, {3.723898484965362*^9, 3.723898488502695*^9}, 3.724147399565941*^9, 3.724147635566226*^9, { 3.7245527509658732`*^9, 3.724552771340017*^9}, {3.756082802720545*^9, 3.756082814674419*^9}, {3.756169638505012*^9, 3.756169642626027*^9}},ExpressionUUID->"e5f61de8-1182-47cf-8a7b-\ 2337b20298c7"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "h", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"uY", "[", "1", "]"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.4939930717488003`*^9, 3.4939930974108*^9}, { 3.4939934523719997`*^9, 3.4939934579568*^9}, {3.4940328656694*^9, 3.4940328661686*^9}, {3.4940336074547997`*^9, 3.494033663178*^9}, 3.4940340531*^9, {3.4940343243684*^9, 3.4940343274104*^9}, { 3.500718840384*^9, 3.5007188689944*^9}, {3.557797943855514*^9, 3.5577979639795494`*^9}, 3.6926792938302193`*^9, 3.692771703570333*^9, { 3.6927734376627607`*^9, 3.692773462532796*^9}, {3.6927734931228385`*^9, 3.692773588602972*^9}, 3.692773619943016*^9, {3.692773683713105*^9, 3.692773731253172*^9}, {3.6927737733532305`*^9, 3.6927737739032316`*^9}, { 3.6927738245433025`*^9, 3.692773876463375*^9}, {3.692773939413463*^9, 3.692773995603542*^9}, {3.6927740539236236`*^9, 3.6927740867636695`*^9}, { 3.6928600883112545`*^9, 3.6928600952012644`*^9}, {3.724510813340685*^9, 3.7245108439239902`*^9}, {3.7245110894899054`*^9, 3.7245111362366643`*^9}, {3.7245111759684496`*^9, 3.7245111800040627`*^9}, {3.7245112142827435`*^9, 3.724511357099068*^9}, { 3.72451139044884*^9, 3.7245113908943324`*^9}, {3.7245114354388523`*^9, 3.724511619873787*^9}, {3.724511680905528*^9, 3.724511684090825*^9}, { 3.724511739941152*^9, 3.7245117444832473`*^9}, {3.7245117919587584`*^9, 3.724511792442217*^9}, {3.7245119452797728`*^9, 3.7245119591135845`*^9}, { 3.7245121768708963`*^9, 3.7245121842326193`*^9}, {3.724512227324604*^9, 3.7245122284688077`*^9}, {3.7245122615399647`*^9, 3.724512272739452*^9}, { 3.7245123874801135`*^9, 3.724512394482444*^9}, {3.7245124864476037`*^9, 3.724512492861*^9}, {3.724512563393937*^9, 3.7245125642590384`*^9}, { 3.724512686336095*^9, 3.724512686647025*^9}, {3.7245523986395607`*^9, 3.724552428037301*^9}, {3.7245524590510445`*^9, 3.7245524906776133`*^9}, { 3.7245525335305943`*^9, 3.7245525493372817`*^9}, {3.7245525915792074`*^9, 3.724552624903928*^9}, {3.724552700655877*^9, 3.7245527010974026`*^9}, { 3.7245527827516294`*^9, 3.724552841959256*^9}, 3.756082823673523*^9, { 3.756082858149851*^9, 3.75608296491168*^9}, {3.78823639018388*^9, 3.788236434946477*^9}, 3.7882487921577525`*^9, {3.851396431326043*^9, 3.851396432629086*^9}}, CellLabel-> "In[152]:=",ExpressionUUID->"79b8f2d9-ca4c-4293-ab3b-748aa33c9007"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture assignment 1 (decomposition)", "Subsubsection", CellChangeTimes->{ 3.5577964337884617`*^9, 3.6926013396721983`*^9, {3.6926179280029135`*^9, 3.6926179367329254`*^9}, {3.6926179987430124`*^9, 3.692618012853032*^9}, 3.6926777991781263`*^9, {3.6927703328584137`*^9, 3.692770359158451*^9}, { 3.6928550971942673`*^9, 3.6928551052242785`*^9}, {3.7561697245665956`*^9, 3.7561697310039177`*^9}},ExpressionUUID->"561787f6-0dc9-4a69-b6c6-\ f45656ca6c4e"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{"AA", "=", RowBox[{"(", GridBox[{ {"1", "0"}, { RowBox[{"-", "3"}], "2"} }], ")"}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"val", ",", "vec"}], "}"}], "=", RowBox[{"Eigensystem", "[", "AA", "]"}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"Transpose", "[", "vec", "]"}], ".", RowBox[{"DiagonalMatrix", "[", "val", "]"}], ".", RowBox[{"Inverse", "[", RowBox[{"Transpose", "[", "vec", "]"}], "]"}]}]}]}]], "Input", CellChangeTimes->{ 3.4939782696174*^9, {3.4939783427346*^9, 3.4939784038866*^9}, { 3.557796517623009*^9, 3.5577966195847883`*^9}, {3.557796666556471*^9, 3.5577966698948765`*^9}, 3.692617920032902*^9, {3.6926180027030177`*^9, 3.6926183433034945`*^9}, {3.69261837586354*^9, 3.692618421083604*^9}, 3.6926184702836723`*^9, 3.692770250478299*^9, {3.6927703723784695`*^9, 3.692770588688772*^9}, {3.6927706245488224`*^9, 3.692770674378892*^9}, { 3.6927707053189354`*^9, 3.692770706798938*^9}, {3.692770840599125*^9, 3.6927708450491314`*^9}, {3.69285512772431*^9, 3.692855188474395*^9}, { 3.7244868220050793`*^9, 3.7244868651346254`*^9}, {3.724486900982155*^9, 3.7244869496591587`*^9}, {3.7244869892727127`*^9, 3.7244870143222284`*^9}, {3.724490936279661*^9, 3.724491010626911*^9}, { 3.7244910471773667`*^9, 3.7244911069483156`*^9}, {3.7244950339345055`*^9, 3.7244950625113525`*^9}, {3.7561697403667555`*^9, 3.7561698534389057`*^9}, {3.756170216621559*^9, 3.756170222933326*^9}, { 3.7881539279744625`*^9, 3.7881539332430315`*^9}, {3.851396491623579*^9, 3.8513965092572613`*^9}}, CellLabel-> "In[157]:=",ExpressionUUID->"59b2c91f-58a8-4f60-8830-95d335dd8371"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture assignment 2 (bar)", "Subsubsection", CellChangeTimes->{ 3.5577964337884617`*^9, 3.6926013396721983`*^9, {3.6926179280029135`*^9, 3.6926179367329254`*^9}, {3.6926179987430124`*^9, 3.692618012853032*^9}, 3.6926777991781263`*^9, {3.6927703328584137`*^9, 3.692770359158451*^9}, { 3.6928550971942673`*^9, 3.6928551052242785`*^9}, {3.7561697245665956`*^9, 3.7561697310039177`*^9}, {3.7561699168665485`*^9, 3.756169926040078*^9}, { 3.851396588241513*^9, 3.851396588803507*^9}},ExpressionUUID->"dd8b7af0-2026-4bd6-b747-\ c7bfa820e746"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "VIBR", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"VIBR", ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"uX", "[", RowBox[{"2", ",", "0"}], "]"}], "\[Rule]", "0"}], ",", RowBox[{ RowBox[{"uX", "[", RowBox[{"2", ",", "1"}], "]"}], "\[Rule]", "V"}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.756170020583084*^9, 3.756170122811846*^9}, { 3.756170186032323*^9, 3.756170193896617*^9}, {3.7561702297956877`*^9, 3.7561702556648417`*^9}, 3.7561702928875675`*^9, {3.7881517536935062`*^9, 3.7881517566616244`*^9}, {3.7881517969523706`*^9, 3.7881519195047984`*^9}, {3.78815195737908*^9, 3.788151961328389*^9}, { 3.788152060927085*^9, 3.7881520655631504`*^9}, {3.788152223800831*^9, 3.7881522879125333`*^9}, {3.7881523590964017`*^9, 3.7881523643461895`*^9}, {3.8513902921173325`*^9, 3.8513902927554083`*^9}}, CellLabel-> "In[160]:=",ExpressionUUID->"6531450a-9d39-4046-adec-55848e374ce2"], Cell[BoxData[ TagBox[GridBox[{ { TagBox[ TagBox[GridBox[{ { StyleBox["\[Null]", ShowStringCharacters->False], TagBox["\<\"model\"\>", HoldForm], TagBox["\<\"properties\"\>", HoldForm], TagBox["\<\"geometry\"\>", HoldForm]}, { TagBox["1", HoldForm], "BAR", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]} }, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{ "Columns" -> {False, True, {False}, False}, "Rows" -> {False, True, {False}, False}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[2.0999999999999996`]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], {OutputFormsDump`HeadedRows, OutputFormsDump`HeadedColumns}], Function[BoxForm`e$, TableForm[ BoxForm`e$, TableDepth -> 2, TableHeadings -> {{1}, {"model", "properties", "geometry"}}]]]}, {""}, { TagBox[ TagBox[GridBox[{ { StyleBox["\[Null]", ShowStringCharacters->False], TagBox["\<\"{X,Y,Z}\"\>", HoldForm], TagBox["\<\"{\\!\\(\\*SubscriptBox[\\(u\\), \ \\(X\\)]\\),\\!\\(\\*SubscriptBox[\\(u\\), \\(Y\\)]\\),\\!\\(\\*SubscriptBox[\ \\(u\\), \\(Z\\)]\\)}\"\>", HoldForm], TagBox["\<\"{\\!\\(\\*SubscriptBox[\\(\[Theta]\\), \ \\(X\\)]\\),\\!\\(\\*SubscriptBox[\\(\[Theta]\\), \ \\(Y\\)]\\),\\!\\(\\*SubscriptBox[\\(\[Theta]\\), \\(Z\\)]\\)}\"\>", HoldForm]}, { TagBox["1", HoldForm], RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}, { TagBox["2", HoldForm], RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]} }, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{ "Columns" -> {False, True, {False}, False}, "Rows" -> {False, True, {False}, False}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[2.0999999999999996`]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], {OutputFormsDump`HeadedRows, OutputFormsDump`HeadedColumns}], Function[BoxForm`e$, TableForm[ BoxForm`e$, TableDepth -> 2, TableHeadings -> {{1, 2}, { "{X,Y,Z}", "{\!\(\*SubscriptBox[\(u\), \(X\)]\),\!\(\*SubscriptBox[\(u\), \(Y\ \)]\),\!\(\*SubscriptBox[\(u\), \(Z\)]\)}", "{\!\(\*SubscriptBox[\(\[Theta]\), \(X\)]\),\!\(\*SubscriptBox[\(\ \[Theta]\), \(Y\)]\),\!\(\*SubscriptBox[\(\[Theta]\), \(Z\)]\)}", "\[CurlyTheta]"}}]]]} }, AutoDelete->False, GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{3.851393593085744*^9, 3.8513965359639378`*^9}, CellLabel-> "Out[162]=",ExpressionUUID->"9feb3fa3-2916-4b23-8a13-f4125e05b85a"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["STABILITY ANALYSIS (week 5)", "Subsection", CellChangeTimes->{{3.473055512584*^9, 3.4730555529630003`*^9}, { 3.4730575328269997`*^9, 3.473057539222*^9}, {3.4734691424642*^9, 3.4734691605758*^9}, {3.4736023142902*^9, 3.4736023273162003`*^9}, { 3.4742602258717394`*^9, 3.4742602349087396`*^9}, {3.4751533480335493`*^9, 3.4751533839809494`*^9}, {3.47515343117095*^9, 3.47515343786335*^9}, { 3.4932790718213997`*^9, 3.4932790791534*^9}, 3.4933062444776*^9, { 3.4950884313529997`*^9, 3.49508843741*^9}, {3.5566240770574865`*^9, 3.5566240810666933`*^9}, 3.55662411296815*^9, 3.6194079237937746`*^9, { 3.6929652502711906`*^9, 3.692965262811208*^9}, 3.7530712459656515`*^9, 3.7866746442735834`*^9, {3.788503131545534*^9, 3.7885031338061256`*^9}, { 3.788595834713565*^9, 3.7885958369488535`*^9}},ExpressionUUID->"8b8ebf36-44ef-455a-b584-\ 4760b97dc02a"], Cell[CellGroupData[{ Cell["Lecture example 4.1 (beam)", "Subsubsection", CellChangeTimes->{ 3.495088447506*^9, {3.495153177701*^9, 3.4951531894166*^9}, 3.558946122925826*^9, {3.692965302131263*^9, 3.692965317401284*^9}, { 3.693118843765126*^9, 3.693118845845129*^9}, {3.6932188494010425`*^9, 3.693218859311056*^9}, {3.7887479930494013`*^9, 3.7887479955453067`*^9}, 3.788748026336192*^9, 3.8209949267048826`*^9, 3.82161384593501*^9},ExpressionUUID->"0b58f323-8e74-4bb4-a7dd-\ 0e1f19a67740"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "p"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "1", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "p"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}]}], "Input", CellChangeTimes->{{3.495088465875*^9, 3.495088486899*^9}, { 3.4950995009309998`*^9, 3.4950995016879997`*^9}, {3.495099819053*^9, 3.4950998310769997`*^9}, {3.4951004772609997`*^9, 3.495100482592*^9}, 3.4951534205774*^9, {3.4951664440478*^9, 3.4951664463722*^9}, { 3.6930154709945107`*^9, 3.693015620124719*^9}, {3.6930158215750012`*^9, 3.693015826975009*^9}, {3.6930158923661003`*^9, 3.693015945397175*^9}, { 3.693016038087304*^9, 3.6930160810173645`*^9}, {3.693016118977418*^9, 3.6930161267674284`*^9}, {3.6930164434978724`*^9, 3.6930164831779275`*^9}, {3.6930168959426355`*^9, 3.693016943842702*^9}, { 3.6930170211728106`*^9, 3.6930170221728115`*^9}, {3.6930176493256903`*^9, 3.693017670245719*^9}, {3.693017801865904*^9, 3.6930178264559383`*^9}, { 3.693018008816193*^9, 3.6930180566662602`*^9}, {3.693018115636343*^9, 3.693018129476362*^9}, {3.69301832058663*^9, 3.693018424926776*^9}, { 3.693018546686946*^9, 3.6930185536569557`*^9}, {3.6930185926270103`*^9, 3.6930186247670555`*^9}, {3.6930188500773706`*^9, 3.693018865057392*^9}, { 3.6930189745895452`*^9, 3.6930189769895487`*^9}, {3.6930192574799414`*^9, 3.6930192579099417`*^9}, {3.693019392680131*^9, 3.693019394440133*^9}, { 3.6930578337843657`*^9, 3.693057906174467*^9}, {3.6930579909745865`*^9, 3.6930579918445873`*^9}, {3.6930580481846666`*^9, 3.693058052384672*^9}, { 3.693058089464724*^9, 3.6930580925547285`*^9}, {3.693058215804901*^9, 3.6930582164549017`*^9}, {3.693212952706787*^9, 3.6932129823968287`*^9}, 3.693213467247507*^9, {3.6932135374976053`*^9, 3.6932135509376245`*^9}, { 3.693381863369029*^9, 3.693381881739055*^9}, {3.6933819124090977`*^9, 3.6933820064392295`*^9}, {3.6933820370092726`*^9, 3.6933820461892853`*^9}, {3.6933821009293623`*^9, 3.6933821288894014`*^9}, {3.6933824368598323`*^9, 3.693382462739868*^9}, { 3.6933825457799845`*^9, 3.693382576760028*^9}, {3.6933826141100807`*^9, 3.6933826142500806`*^9}, {3.6933826572201405`*^9, 3.6933826812701745`*^9}, {3.693459467865974*^9, 3.693459506396028*^9}, { 3.724756588022208*^9, 3.7247565916191807`*^9}, {3.756264691579814*^9, 3.756264745142851*^9}, {3.7562973521187143`*^9, 3.756297363296737*^9}, { 3.7563543673779197`*^9, 3.7563544020228167`*^9}, {3.756354503721473*^9, 3.756354518145298*^9}, {3.756354577259649*^9, 3.75635458078909*^9}, 3.788518279999304*^9, {3.7885740257291007`*^9, 3.788574029610507*^9}, { 3.7885743271776943`*^9, 3.7885743373156376`*^9}, {3.788574370184829*^9, 3.7885743901774464`*^9}, {3.788574558310573*^9, 3.788574561866705*^9}, { 3.7885749091230097`*^9, 3.7885749094690733`*^9}, {3.7888328012255797`*^9, 3.7888328014755106`*^9}, {3.850964677630747*^9, 3.850964681411261*^9}, { 3.8519921582317715`*^9, 3.8519921709661217`*^9}}, CellLabel-> "In[378]:=",ExpressionUUID->"88404147-fc06-4614-945f-dbfbabb7f718"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 4.2 (truss)", "Subsubsection", CellChangeTimes->{{3.4938724364934034`*^9, 3.493872440377554*^9}, 3.55772174224413*^9, {3.5577222701826577`*^9, 3.557722281898278*^9}, { 3.6925364040653286`*^9, 3.692536414765343*^9}, {3.6926051339045105`*^9, 3.692605137804516*^9}, 3.692616505550922*^9, {3.6926165560409927`*^9, 3.692616575321019*^9}, 3.693218780550946*^9, {3.693222197869731*^9, 3.6932222001297336`*^9}, {3.788748002129151*^9, 3.788748030379919*^9}, 3.820994928778037*^9, 3.8216138491335354`*^9},ExpressionUUID->"60e84868-8762-419a-995b-\ 4bca4326c86c"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{ SqrtBox["8"], "A"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{ SqrtBox["8"], "A"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"4", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "F"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "3", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", RowBox[{"\[Theta]Y", "[", "2", "]"}]}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "F"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4938808707521195`*^9, 3.493880886414419*^9}, { 3.4938809823296185`*^9, 3.4938810743976574`*^9}, {3.493881115862191*^9, 3.49388112389614*^9}, {3.5007185681328*^9, 3.5007185858543997`*^9}, 3.557721807701845*^9, 3.557722301679113*^9, {3.557722338229977*^9, 3.557722345218789*^9}, {3.5577223956380777`*^9, 3.557722557550762*^9}, { 3.5577227444350924`*^9, 3.5577227701751375`*^9}, {3.557722914366191*^9, 3.5577231321893735`*^9}, {3.5577234762323775`*^9, 3.557723673042323*^9}, { 3.557723707440384*^9, 3.557723724257213*^9}, {3.557723808200961*^9, 3.5577238249085903`*^9}, {3.557724032045754*^9, 3.5577240381453648`*^9}, { 3.5577240859750485`*^9, 3.5577241533827667`*^9}, {3.5577255542808275`*^9, 3.557725556340031*^9}, {3.692416572627716*^9, 3.692416634337803*^9}, { 3.6924166962978897`*^9, 3.6924166970178905`*^9}, {3.692416728407934*^9, 3.692416742377954*^9}, 3.692416785478014*^9, {3.692416815828057*^9, 3.692416854678111*^9}, {3.6924172169506187`*^9, 3.6924175298010564`*^9}, { 3.692418050131785*^9, 3.692418107561865*^9}, {3.6924216949310565`*^9, 3.6924216977710605`*^9}, {3.6925022762935333`*^9, 3.6925022791146946`*^9}, {3.6926050714634233`*^9, 3.6926053101657577`*^9}, {3.692605350685814*^9, 3.6926053528358173`*^9}, { 3.692605582596139*^9, 3.692605583946141*^9}, 3.692623496410709*^9, { 3.692623535710764*^9, 3.692623557910795*^9}, {3.6926952837958193`*^9, 3.6926952890058265`*^9}, {3.6928555108448462`*^9, 3.692855525144866*^9}, { 3.6928555801949434`*^9, 3.6928556725450726`*^9}, {3.6928557055151186`*^9, 3.6928557885252347`*^9}, {3.692855881295365*^9, 3.6928558933153815`*^9}, { 3.692855952785465*^9, 3.6928559781655006`*^9}, {3.6928560758856373`*^9, 3.692856170005769*^9}, {3.6928562238658447`*^9, 3.6928562580458927`*^9}, { 3.6928562961859455`*^9, 3.69285631358597*^9}, {3.692856357426031*^9, 3.6928563681360464`*^9}, {3.6928563999060907`*^9, 3.6928564001160913`*^9}, {3.692857702937915*^9, 3.6928577502779813`*^9}, { 3.6932187731509356`*^9, 3.693218803870979*^9}, {3.6932188341410213`*^9, 3.6932190222012844`*^9}, {3.693219079141364*^9, 3.6932191418014517`*^9}, { 3.693219256141612*^9, 3.6932192620916204`*^9}, 3.6932196368521447`*^9, { 3.693220450485284*^9, 3.6932204509352846`*^9}, {3.6932220864395747`*^9, 3.6932220972695894`*^9}, {3.6933108503929434`*^9, 3.6933108669129667`*^9}, {3.7247570961974792`*^9, 3.7247571143473463`*^9}, {3.724757453331685*^9, 3.7247574543256564`*^9}, { 3.756265531029621*^9, 3.756265550206148*^9}, {3.756265772588833*^9, 3.7562658449593987`*^9}, {3.7562661007343545`*^9, 3.7562661052102594`*^9}, {3.756267778188237*^9, 3.756267782135869*^9}, { 3.756297557622207*^9, 3.7562975640313606`*^9}, {3.788575454272171*^9, 3.788575455203708*^9}, 3.7888342686666775`*^9, {3.788834320638523*^9, 3.7888343488289104`*^9}, {3.850965304883685*^9, 3.850965317023302*^9}, { 3.850965467547227*^9, 3.850965521691221*^9}, {3.850965677474887*^9, 3.850965680130317*^9}}, CellLabel-> "In[383]:=",ExpressionUUID->"47296f0a-5f24-4548-954b-7fd453b1bd76"], Cell[BoxData[ TagBox[GridBox[{ { TagBox[ TagBox[GridBox[{ { StyleBox["\[Null]", ShowStringCharacters->False], TagBox["\<\"model\"\>", HoldForm], TagBox["\<\"properties\"\>", HoldForm], TagBox["\<\"geometry\"\>", HoldForm]}, { TagBox["1", HoldForm], "BAR", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"2", " ", SqrtBox["2"], " ", "A"}], "}"}]}], "}"}], RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "3"}], "}"}], "]"}]}, { TagBox["2", HoldForm], "BEAM", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}, { TagBox["3", HoldForm], "BAR", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"2", " ", SqrtBox["2"], " ", "A"}], "}"}]}], "}"}], RowBox[{"Line", "[", RowBox[{"{", RowBox[{"4", ",", "2"}], "}"}], "]"}]}, { TagBox["4", HoldForm], "FORCE", RowBox[{"{", RowBox[{"0", ",", "0", ",", "F"}], "}"}], RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]} }, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{ "Columns" -> {False, True, {False}, False}, "Rows" -> {False, True, {False}, False}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[2.0999999999999996`]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], {OutputFormsDump`HeadedRows, OutputFormsDump`HeadedColumns}], Function[BoxForm`e$, TableForm[ BoxForm`e$, TableDepth -> 2, TableHeadings -> {{1, 2, 3, 4}, { "model", "properties", "geometry"}}]]]}, {""}, { TagBox[ TagBox[GridBox[{ { StyleBox["\[Null]", ShowStringCharacters->False], TagBox["\<\"{X,Y,Z}\"\>", HoldForm], TagBox["\<\"{\\!\\(\\*SubscriptBox[\\(u\\), \ \\(X\\)]\\),\\!\\(\\*SubscriptBox[\\(u\\), \\(Y\\)]\\),\\!\\(\\*SubscriptBox[\ \\(u\\), \\(Z\\)]\\)}\"\>", HoldForm], TagBox["\<\"{\\!\\(\\*SubscriptBox[\\(\[Theta]\\), \ \\(X\\)]\\),\\!\\(\\*SubscriptBox[\\(\[Theta]\\), \ \\(Y\\)]\\),\\!\\(\\*SubscriptBox[\\(\[Theta]\\), \\(Z\\)]\\)}\"\>", HoldForm]}, { TagBox["1", HoldForm], RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}, { TagBox["2", HoldForm], RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}, { TagBox["3", HoldForm], RowBox[{"{", RowBox[{"L", ",", "0", ",", "L"}], "}"}], RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "3", "]"}]}], "}"}], RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", RowBox[{"\[Theta]Y", "[", "2", "]"}]}], ",", "0"}], "}"}]}, { TagBox["4", HoldForm], RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]} }, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{ "Columns" -> {False, True, {False}, False}, "Rows" -> {False, True, {False}, False}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[2.0999999999999996`]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], {OutputFormsDump`HeadedRows, OutputFormsDump`HeadedColumns}], Function[BoxForm`e$, TableForm[ BoxForm`e$, TableDepth -> 2, TableHeadings -> {{1, 2, 3, 4}, { "{X,Y,Z}", "{\!\(\*SubscriptBox[\(u\), \(X\)]\),\!\(\*SubscriptBox[\(u\), \(Y\ \)]\),\!\(\*SubscriptBox[\(u\), \(Z\)]\)}", "{\!\(\*SubscriptBox[\(\[Theta]\), \(X\)]\),\!\(\*SubscriptBox[\(\ \[Theta]\), \(Y\)]\),\!\(\*SubscriptBox[\(\[Theta]\), \(Z\)]\)}", "\[CurlyTheta]"}}]]]} }, AutoDelete->False, GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{3.852358063773245*^9}, CellLabel-> "Out[385]=",ExpressionUUID->"158ee92a-de6e-4da4-bc94-70b2513dcc70"], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"\[Delta]W = -\"\>", "\[InvisibleSpace]", SuperscriptBox[ TagBox[ RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ { RowBox[{"\[Delta]uZ", "[", "2", "]"}]}, { RowBox[{"\[Delta]uZ", "[", "3", "]"}]}, { RowBox[{"\[Delta]\[Theta]Y", "[", "2", "]"}]} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], Column], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]], "T"], "\[InvisibleSpace]", TagBox[ RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ { RowBox[{"F", "+", FractionBox[ RowBox[{"A", " ", "\[CapitalEpsilon]", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", RowBox[{"uZ", "[", "2", "]"}]}], "+", RowBox[{"uZ", "[", "3", "]"}]}], ")"}]}], "L"]}]}, { FractionBox[ RowBox[{"A", " ", "\[CapitalEpsilon]", " ", RowBox[{"(", RowBox[{ RowBox[{"uZ", "[", "2", "]"}], "-", RowBox[{"2", " ", RowBox[{"uZ", "[", "3", "]"}]}]}], ")"}]}], "L"]}, { FractionBox[ RowBox[{"\[CapitalEpsilon]", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "12"}], " ", "\[CapitalIota]"}], "+", RowBox[{"A", " ", "L", " ", RowBox[{"(", RowBox[{ RowBox[{"uZ", "[", "2", "]"}], "-", RowBox[{"uZ", "[", "3", "]"}]}], ")"}]}]}], ")"}], " ", RowBox[{"\[Theta]Y", "[", "2", "]"}]}], RowBox[{"3", " ", "L"}]]} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], Column], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]}], SequenceForm["\[Delta]W = -", MatrixForm[{ $CellContext`\[Delta]uZ[2], $CellContext`\[Delta]uZ[3], $CellContext`\[Delta]\[Theta]Y[2]}]^$CellContext`T, MatrixForm[{$CellContext`F + $CellContext`A $CellContext`L^(-1) \ $CellContext`\[CapitalEpsilon] ((-2) $CellContext`uZ[2] + $CellContext`uZ[ 3]), $CellContext`A $CellContext`L^(-1) \ $CellContext`\[CapitalEpsilon] ($CellContext`uZ[2] - 2 $CellContext`uZ[3]), Rational[1, 3] $CellContext`L^(-1) $CellContext`\[CapitalEpsilon] ((-12) \ $CellContext`\[CapitalIota] + $CellContext`A $CellContext`L ($CellContext`uZ[ 2] - $CellContext`uZ[3])) $CellContext`\[Theta]Y[2]}]], Editable->False]], "Print", CellChangeTimes->{3.8523580638221216`*^9}, CellLabel-> "During evaluation of \ In[383]:=",ExpressionUUID->"6f5e4a15-536b-488f-847a-21baefd76655"], Cell[BoxData[ TemplateBox[{ "Eigensystem", "geinsl1", "\"Warning: a solution for the generalized eigenproblem may be \ incorrect.\"", 2, 387, 1, 16188703561132297582, "Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{3.8523580642190914`*^9}, CellLabel-> "During evaluation of \ In[383]:=",ExpressionUUID->"d1ab0d5d-6efd-45ea-8420-27c9214520a3"], Cell[BoxData[ TagBox[GridBox[{ { RowBox[{ RowBox[{"F", "[", "1", "]"}], "\[Rule]", FractionBox[ RowBox[{"36", " ", "\[CapitalEpsilon]", " ", "\[CapitalIota]"}], SuperscriptBox["L", "2"]]}], RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"uZ", "[", "2", "]"}], "\[Rule]", "0"}], ",", RowBox[{ RowBox[{"uZ", "[", "3", "]"}], "\[Rule]", "0"}], ",", RowBox[{ RowBox[{"\[Theta]Y", "[", "2", "]"}], "\[Rule]", "1"}]}], "}"}]} }, AutoDelete->False, GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{3.8523580642470136`*^9}, CellLabel-> "Out[387]=",ExpressionUUID->"d2522899-c372-4aa8-a5c2-50a35ad46f27"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 4.3a (plate )", "Subsubsection", CellChangeTimes->{{3.4430685047746*^9, 3.4430685067558002`*^9}, { 3.4430866035033803`*^9, 3.4430866067013803`*^9}, 3.4742603622347393`*^9, { 3.47426082029274*^9, 3.4742608300977397`*^9}, {3.4742616255317397`*^9, 3.4742616631637397`*^9}, 3.47426171431174*^9, {3.569295755520348*^9, 3.569295758265953*^9}, {3.5999975352114353`*^9, 3.5999975364126377`*^9}, { 3.6862916156897416`*^9, 3.6862916164197426`*^9}, 3.6862917141498795`*^9, 3.686291825440035*^9, 3.686463538583459*^9, 3.6920045036236353`*^9, { 3.692007141747794*^9, 3.6920071424377947`*^9}, {3.7238012915092707`*^9, 3.723801291633401*^9}, {3.7238014377077494`*^9, 3.723801461461709*^9}, { 3.7249853977242336`*^9, 3.7249854098192596`*^9}, {3.725025728192973*^9, 3.7250257332263174`*^9}, 3.7563606916546392`*^9, {3.7887480056212215`*^9, 3.788748032773177*^9}, 3.820994931205215*^9, 3.8216138511743236`*^9, 3.8523380510477495`*^9},ExpressionUUID->"eb086934-c2a7-4973-9560-\ 059df91090fe"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"start", " ", "with", " ", "the", " ", "building", " ", "blocks"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"val", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"L", "\[Rule]", "1"}], ",", RowBox[{"t", "\[Rule]", RowBox[{"1", "/", "1000"}]}], ",", RowBox[{"\[CapitalEpsilon]", "\[Rule]", RowBox[{"210", "*", RowBox[{"10", "^", "6"}]}]}], ",", RowBox[{"\[Nu]", "\[Rule]", "0.33"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Block", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"w", "=", RowBox[{ RowBox[{"a", "[", "0", "]"}], " ", FractionBox["x", "L"], " ", RowBox[{"(", RowBox[{"1", "-", FractionBox["x", "L"]}], ")"}], FractionBox["y", "L"], RowBox[{"(", RowBox[{"1", "-", FractionBox["y", "L"]}], ")"}]}]}], ",", "\[CapitalOmega]", ",", "\[Delta]W", ",", "\[Delta]wint", ",", "\[Delta]wsta"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wint", ":=", RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", " ", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["t", "3"], " ", "\[CapitalEpsilon]"}], RowBox[{"12", RowBox[{"(", RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}], ")"}]}]], RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "\[Nu]", "0"}, {"\[Nu]", "1", "0"}, {"0", "0", FractionBox[ RowBox[{"1", "-", "\[Nu]"}], "2"]} }], "\[NoBreak]", ")"}]}], ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wsta", ":=", RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"-", "p"}], "0"}, {"0", "0"} }], "\[NoBreak]", ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}]} }], "\[NoBreak]", ")"}]}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", "=", RowBox[{"Rectangle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"L", ",", "L"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Integrate", "[", RowBox[{ RowBox[{"\[Delta]wint", "+", "\[Delta]wsta"}], ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], StyleBox["\[Element]", "OperatorCharacter"], StyleBox["\[CapitalOmega]", "OperatorCharacter"]}]}], StyleBox["]", "OperatorCharacter"]}], StyleBox[",", "OperatorCharacter"], StyleBox[ RowBox[{"L", ">", "0"}], "OperatorCharacter"]}], StyleBox["]", "OperatorCharacter"]}]}], StyleBox[";", "OperatorCharacter"], StyleBox["\[IndentingNewLine]", "OperatorCharacter"], StyleBox["\[IndentingNewLine]", "OperatorCharacter"], RowBox[{"STANDARDFORM", "[", "\[Delta]W", "]"}], ";", "\[IndentingNewLine]", StyleBox["\[IndentingNewLine]", "OperatorCharacter"], RowBox[{ StyleBox["Print", "OperatorCharacter"], StyleBox["[", "OperatorCharacter"], RowBox[{ StyleBox["sol", "OperatorCharacter"], StyleBox["=", "OperatorCharacter"], RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "p"}], "}"}], ",", "\[Delta]W"}], "]"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"sol", " ", "//.", "val"}]}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{ 3.4426469719054456`*^9, {3.4430685207022*^9, 3.4430685918694*^9}, { 3.4430686602608*^9, 3.44306866271*^9}, {3.4430687542864*^9, 3.4430688359955997`*^9}, {3.4430866305537806`*^9, 3.44308673150138*^9}, { 3.4742604996717396`*^9, 3.47426061596974*^9}, 3.4742609854677396`*^9, 3.569295818310458*^9, 3.569295934780263*^9, {3.631161797385408*^9, 3.63116192958797*^9}, 3.6311621282873344`*^9, {3.6314096475812645`*^9, 3.6314096645540943`*^9}, 3.63140970193176*^9, {3.6314296672834578`*^9, 3.6314296732582684`*^9}, {3.6314297131943383`*^9, 3.631429723193956*^9}, { 3.6320283190146666`*^9, 3.6320283335070925`*^9}, {3.632028523936627*^9, 3.632028541689458*^9}, {3.6630475834142756`*^9, 3.6630475933982935`*^9}, { 3.685322391232018*^9, 3.685322396442025*^9}, {3.685322434252078*^9, 3.68532247101213*^9}, {3.6853440662625723`*^9, 3.685344095349236*^9}, { 3.6853489765747485`*^9, 3.6853489802747536`*^9}, {3.6862916241397533`*^9, 3.6862916684598155`*^9}, {3.686291740699917*^9, 3.686291791099987*^9}, { 3.6862918385400534`*^9, 3.68629185767008*^9}, 3.6920072022978787`*^9, { 3.724985419429654*^9, 3.7249854733258133`*^9}, {3.7249855047198954`*^9, 3.724985672643574*^9}, {3.724985823331335*^9, 3.72498583108245*^9}, { 3.7249859256363735`*^9, 3.724985954061252*^9}, {3.7249860773711185`*^9, 3.7249860873564367`*^9}, {3.72498667993143*^9, 3.7249867213577213`*^9}, { 3.724986817961895*^9, 3.7249868212275767`*^9}, {3.725021200723025*^9, 3.725021205166871*^9}, {3.7250283445255947`*^9, 3.725028396615054*^9}, { 3.756356116074851*^9, 3.756356120183282*^9}, {3.7563566489829216`*^9, 3.7563566578401747`*^9}, {3.788834572625896*^9, 3.788834618899085*^9}, 3.7889369904230375`*^9, {3.8209956217654243`*^9, 3.8209956870168357`*^9}, { 3.8209957300921974`*^9, 3.820995747209697*^9}, 3.8209957933597546`*^9, { 3.850965869737995*^9, 3.850965953030941*^9}, {3.8509660365154552`*^9, 3.850966037463144*^9}, {3.8523386081362963`*^9, 3.8523386861808577`*^9}, { 3.8523387379162607`*^9, 3.852338855522773*^9}, {3.8523388859408307`*^9, 3.852338902296262*^9}, {3.8523399842130704`*^9, 3.852339992832653*^9}, { 3.8523404097131805`*^9, 3.852340458988041*^9}, {3.8523420674574647`*^9, 3.8523421185256324`*^9}, {3.852345892964356*^9, 3.852345908082739*^9}, { 3.852358319661192*^9, 3.8523583389907236`*^9}}, CellLabel-> "In[390]:=",ExpressionUUID->"7ec895fb-cd7a-44c0-939e-1e973b73d711"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 4.3b (plate )", "Subsubsection", CellChangeTimes->{{3.4467272483794003`*^9, 3.446727266257*^9}, { 3.4467288934652*^9, 3.446728896788*^9}, 3.4467805306712*^9, { 3.4801237484706*^9, 3.4801237489386*^9}, {3.5744708417194977`*^9, 3.5744708449019036`*^9}, {3.6042991711100636`*^9, 3.604299196992544*^9}, 3.60430729253247*^9, {3.604310202140381*^9, 3.6043102048235855`*^9}, { 3.6889933424974422`*^9, 3.688993352477456*^9}, 3.6889988585223417`*^9, { 3.689480870769858*^9, 3.6894808898298845`*^9}, {3.7518654678504887`*^9, 3.751865474661203*^9}, {3.7519386265381956`*^9, 3.7519386622978053`*^9}, { 3.75376294503279*^9, 3.7537629487977667`*^9}, 3.7554357667498393`*^9, 3.755523363145975*^9, 3.7866920350953083`*^9, 3.7874847705403285`*^9, { 3.787583534492174*^9, 3.787583543755392*^9}, {3.787624886997221*^9, 3.7876249024322443`*^9}, 3.8195159245188613`*^9, {3.8514041606047773`*^9, 3.8514041866311812`*^9}, {3.8514144420507417`*^9, 3.8514144462454934`*^9}, 3.8518339806890965`*^9, {3.8523380602723303`*^9, 3.8523380646606827`*^9}},ExpressionUUID->"4285d1e0-c7c1-460d-9721-\ ee694f21d713"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"val", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"L", "\[Rule]", "1"}], ",", RowBox[{"t", "\[Rule]", RowBox[{"1", "/", "1000"}]}], ",", RowBox[{"\[CapitalEpsilon]", "\[Rule]", RowBox[{"210", "*", RowBox[{"10", "^", "6"}]}]}], ",", RowBox[{"\[Nu]", "\[Rule]", "0.33"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"3", ",", "1", ",", "5"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "5"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"2", ",", "4", ",", "5"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SHELL", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"4", ",", "3", ",", "5"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "p"}], ",", RowBox[{"-", "p"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "4"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", "1", "]"}], ",", RowBox[{"\[Theta]Y", "[", "1", "]"}], ",", RowBox[{"\[Theta]Z", "[", "1", "]"}]}], "}"}]}], "}"}], ",", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", RowBox[{"uY", "[", "2", "]"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", "2", "]"}], ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", RowBox[{"\[Theta]Z", "[", "2", "]"}]}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", "3", "]"}], ",", RowBox[{"\[Theta]Y", "[", "3", "]"}], ",", RowBox[{"\[Theta]Z", "[", "3", "]"}]}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "4", "]"}], ",", RowBox[{"uY", "[", "4", "]"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", "4", "]"}], ",", RowBox[{"\[Theta]Y", "[", "4", "]"}], ",", RowBox[{"\[Theta]Z", "[", "4", "]"}]}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"L", "/", "2"}], ",", RowBox[{"L", "/", "2"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "5", "]"}], ",", RowBox[{"uY", "[", "5", "]"}], ",", RowBox[{"uZ", "[", "5", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\[Theta]X", "[", "5", "]"}], ",", RowBox[{"\[Theta]Y", "[", "5", "]"}], ",", RowBox[{"\[Theta]Z", "[", "5", "]"}]}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "=", RowBox[{"REFINE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"MESH", "[", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "/.", "val"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"sol", "=", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "p"}], "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "//.", " ", "val"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"Last", "[", "sol", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SHOW3D", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "//.", "val"}], " ", "/.", RowBox[{ RowBox[{"Last", "[", "sol", "]"}], "[", RowBox[{"[", "2", "]"}], "]"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.6888689611245327`*^9, 3.6888691441747894`*^9}, { 3.688869175904834*^9, 3.6888691949848604`*^9}, {3.688869303295012*^9, 3.6888694251851826`*^9}, {3.688869534825336*^9, 3.6888695373653393`*^9}, { 3.6888695909654145`*^9, 3.688869620615456*^9}, {3.6888696695055246`*^9, 3.688869671645528*^9}, {3.688869703665572*^9, 3.688869771185667*^9}, { 3.6888698131457253`*^9, 3.688869843195768*^9}, 3.688869999545987*^9, 3.6888701516861997`*^9, {3.688870779087078*^9, 3.6888708600371914`*^9}, { 3.6888713003778076`*^9, 3.688871303197812*^9}, {3.6888713416978655`*^9, 3.688871422407979*^9}, {3.6888714741080513`*^9, 3.688871476638055*^9}, 3.6888751073437386`*^9, {3.6888752493389473`*^9, 3.6888752569189587`*^9}, { 3.688875289049003*^9, 3.688875320839048*^9}, {3.6888754299492006`*^9, 3.688875430949202*^9}, {3.6888786937177925`*^9, 3.688878750267872*^9}, { 3.6888787903179283`*^9, 3.6888788206179705`*^9}, {3.6888790860283422`*^9, 3.68887909127835*^9}, {3.6890585394429307`*^9, 3.6890585586029577`*^9}, { 3.689058611933032*^9, 3.689058636633067*^9}, 3.6890586753831205`*^9, 3.6890587218131857`*^9, {3.6890588371733475`*^9, 3.6890588479333625`*^9}, 3.6890593143580313`*^9, {3.68939651006566*^9, 3.689396570005744*^9}, 3.7519567199003897`*^9, {3.7519567531116476`*^9, 3.7519568500887613`*^9}, { 3.7519568810345116`*^9, 3.7519569775584803`*^9}, {3.751957015846347*^9, 3.7519570979991937`*^9}, {3.751957130663088*^9, 3.7519571335374126`*^9}, 3.753763435083539*^9, {3.7537636176034584`*^9, 3.753763788907042*^9}, { 3.753763831693569*^9, 3.7537638728401537`*^9}, {3.75376391019105*^9, 3.7537639597106857`*^9}, {3.7537640140260305`*^9, 3.7537640276633615`*^9}, {3.753764070700218*^9, 3.7537641560081577`*^9}, { 3.7537641950926304`*^9, 3.7537643084881086`*^9}, 3.753764389828247*^9, { 3.753764533778655*^9, 3.753764547869378*^9}, {3.7553527505176506`*^9, 3.7553528603017626`*^9}, {3.75538351472929*^9, 3.7553835693549905`*^9}, { 3.755383607438428*^9, 3.7553838360146847`*^9}, {3.7553838766263666`*^9, 3.755383951476962*^9}, {3.755383992736063*^9, 3.7553840478403873`*^9}, { 3.755384124898378*^9, 3.7553842646406417`*^9}, {3.755389313373938*^9, 3.7553893195755854`*^9}, {3.755389381201706*^9, 3.7553894668944387`*^9}, { 3.7553895199108267`*^9, 3.755389537914214*^9}, {3.755389582951442*^9, 3.755389708990402*^9}, 3.7554339398817015`*^9, 3.755434068869628*^9, { 3.7554341297848616`*^9, 3.755434216890894*^9}, {3.7554343528417006`*^9, 3.7554343704056864`*^9}, {3.755434459874297*^9, 3.755434538395585*^9}, 3.755434569759145*^9, {3.7554346233872647`*^9, 3.7554347263294*^9}, { 3.7554347853286095`*^9, 3.7554348093580456`*^9}, {3.755434907172281*^9, 3.755434918847997*^9}, {3.7554349600500207`*^9, 3.7554349983466597`*^9}, { 3.755435110803147*^9, 3.7554351426284623`*^9}, {3.755435324398292*^9, 3.7554353302892075`*^9}, {3.755435441524338*^9, 3.755435445101488*^9}, 3.7554355170109453`*^9, {3.7554358134766097`*^9, 3.755435918833391*^9}, { 3.7554359598830943`*^9, 3.75543598832941*^9}, {3.755436164699664*^9, 3.7554361666501207`*^9}, {3.755436277778627*^9, 3.755436282441655*^9}, { 3.755436433004975*^9, 3.7554365810900373`*^9}, {3.755436713592167*^9, 3.7554367150263915`*^9}, {3.755436752569789*^9, 3.755436782945344*^9}, { 3.75543855564263*^9, 3.755438573014342*^9}, {3.7554386030808535`*^9, 3.75543862876925*^9}, {3.755438665543474*^9, 3.755438666460845*^9}, { 3.755438707655904*^9, 3.7554387115945473`*^9}, {3.7554387585075216`*^9, 3.7554388500917773`*^9}, {3.755523374186784*^9, 3.755523407200748*^9}, { 3.755523628104781*^9, 3.755523629369397*^9}, {3.755523692162763*^9, 3.755523702854873*^9}, 3.7555237667615433`*^9, 3.7555238472382975`*^9, 3.7555241586552105`*^9, 3.755524213729106*^9, 3.755524399719488*^9, 3.75552571772406*^9, {3.7555258075426073`*^9, 3.755525820259694*^9}, 3.755526094753117*^9, 3.7555261757546644`*^9, {3.7555262318295097`*^9, 3.7555262499726152`*^9}, {3.7555370249561615`*^9, 3.755537051432358*^9}, 3.7555372853307257`*^9, {3.755537468732602*^9, 3.755537521108555*^9}, 3.7555375621618104`*^9, {3.7555379391125593`*^9, 3.755537970148187*^9}, { 3.7555674525545197`*^9, 3.755567456059157*^9}, {3.7555675848877916`*^9, 3.7555675985147886`*^9}, {3.7555676718904886`*^9, 3.7555677115434046`*^9}, {3.755567758583485*^9, 3.7555677797901087`*^9}, { 3.755567822059022*^9, 3.755567822195668*^9}, {3.7555678597444773`*^9, 3.7555678604365673`*^9}, 3.7556071757478895`*^9, {3.7556072159647107`*^9, 3.755607332812396*^9}, {3.7556074217009745`*^9, 3.755607426579308*^9}, 3.755607632666421*^9, {3.755607684025096*^9, 3.755607693062358*^9}, { 3.7556077296748147`*^9, 3.755607849742259*^9}, {3.755608033616538*^9, 3.7556080922325497`*^9}, 3.755608142419341*^9, {3.755608958207328*^9, 3.755608980843011*^9}, {3.7559615593543744`*^9, 3.7559615796720657`*^9}, { 3.755961636991267*^9, 3.755961639837885*^9}, {3.755961688066485*^9, 3.7559617050406666`*^9}, {3.75596184181551*^9, 3.755961843331066*^9}, { 3.7560033780948515`*^9, 3.756003424416658*^9}, {3.756003637744131*^9, 3.7560039024762926`*^9}, {3.7560039413994226`*^9, 3.756004010187872*^9}, { 3.75600408826851*^9, 3.7560041132438145`*^9}, {3.7560042095185223`*^9, 3.756004261292776*^9}, {3.7560043015589314`*^9, 3.7560044114376893`*^9}, { 3.7560045878703117`*^9, 3.756004610316883*^9}, {3.756090875492567*^9, 3.756090970250229*^9}, {3.7560910153257923`*^9, 3.756091253656394*^9}, { 3.7560913065394864`*^9, 3.7560913073489447`*^9}, {3.7560913497661376`*^9, 3.7560913829572887`*^9}, {3.7560914229250793`*^9, 3.756091477168485*^9}, { 3.756091512338003*^9, 3.7560916181734085`*^9}, {3.756091734456238*^9, 3.7560917345758953`*^9}, 3.7560919538299203`*^9, {3.756092472598545*^9, 3.7560924728155417`*^9}, {3.756092529494649*^9, 3.7560925295886126`*^9}, { 3.7564428371402044`*^9, 3.7564428827548018`*^9}, {3.756443118409811*^9, 3.7564432825122414`*^9}, {3.7564433139577427`*^9, 3.7564434048585415`*^9}, {3.75644377756419*^9, 3.756443799699541*^9}, { 3.756444020280332*^9, 3.756444052335291*^9}, 3.7564441526092615`*^9, 3.7866921123667355`*^9, {3.786692169420147*^9, 3.786692647713867*^9}, { 3.7866926921591225`*^9, 3.78669273302064*^9}, {3.786692862316063*^9, 3.7866928658349466`*^9}, {3.7866931119911423`*^9, 3.786693309398429*^9}, { 3.7866933409841013`*^9, 3.7866934610423436`*^9}, {3.786693498963604*^9, 3.7866936745285892`*^9}, {3.7866937881495705`*^9, 3.7866937950939436`*^9}, 3.7873246428692293`*^9, {3.787485049135359*^9, 3.787485051961443*^9}, { 3.787485091258519*^9, 3.787485424116222*^9}, {3.7874854543849907`*^9, 3.787485502716935*^9}, {3.7874856358164625`*^9, 3.7874856505267844`*^9}, 3.787494663934597*^9, {3.7874947579329753`*^9, 3.7874947673643074`*^9}, 3.787494920667267*^9, {3.7874950655196714`*^9, 3.7874951753595195`*^9}, { 3.787495215708169*^9, 3.7874952321914797`*^9}, {3.7874953099595947`*^9, 3.7874953434716663`*^9}, {3.7874953776322303`*^9, 3.7874953779837875`*^9}, {3.7875363421179075`*^9, 3.787536342508462*^9}, { 3.7875368085158997`*^9, 3.787536878302806*^9}, {3.7875369599529157`*^9, 3.7875370055885963`*^9}, {3.7875835060582986`*^9, 3.787583520821555*^9}, { 3.787583689937277*^9, 3.787583802553567*^9}, 3.7876259263443413`*^9, { 3.7876552122737617`*^9, 3.787655270155204*^9}, {3.7877076273240643`*^9, 3.7877076330663157`*^9}, {3.8493387287106876`*^9, 3.8493387484197454`*^9}, {3.8493388690505223`*^9, 3.8493389607525234`*^9}, {3.8506381987001867`*^9, 3.850638199323704*^9}, { 3.8506382518387237`*^9, 3.8506382521507797`*^9}, 3.8507909361264725`*^9, { 3.850790968622494*^9, 3.8507909814813538`*^9}, {3.8507910227542276`*^9, 3.850791053573805*^9}, {3.850791116545538*^9, 3.8507911402245955`*^9}, { 3.8514043340993366`*^9, 3.8514044427104735`*^9}, {3.8514044803348703`*^9, 3.8514045282808294`*^9}, {3.8514046757991276`*^9, 3.8514047382171335`*^9}, {3.8514048639344797`*^9, 3.851405048797428*^9}, { 3.8514073608057184`*^9, 3.851407372693451*^9}, {3.8514076870255766`*^9, 3.8514076887032995`*^9}, {3.851407773017706*^9, 3.8514077811951346`*^9}, { 3.851407884878668*^9, 3.851407886958976*^9}, {3.8514079306283693`*^9, 3.8514079496190023`*^9}, {3.8514087740430136`*^9, 3.85140879767111*^9}, { 3.8514143934466867`*^9, 3.851414425703439*^9}, {3.851414497406939*^9, 3.851414571302442*^9}, {3.8514146041353254`*^9, 3.8514146600460863`*^9}, { 3.8514147004976883`*^9, 3.851414702555371*^9}, {3.851826345022826*^9, 3.851826362735227*^9}, {3.8518339902024612`*^9, 3.8518340324887753`*^9}, { 3.851834067359583*^9, 3.8518340887776065`*^9}, {3.85183413027966*^9, 3.8518341363630505`*^9}, {3.8518342009484644`*^9, 3.851834369129287*^9}, { 3.8518344143060737`*^9, 3.851834414983051*^9}, {3.8518344553869543`*^9, 3.851834543885075*^9}, {3.8518347971351566`*^9, 3.8518348017593184`*^9}, { 3.851835132695306*^9, 3.8518352479240956`*^9}, {3.851835295849347*^9, 3.851835329468197*^9}, 3.851835409451404*^9, {3.851835498320532*^9, 3.8518355048099184`*^9}, {3.8523380748030825`*^9, 3.852338264306811*^9}, { 3.8523383137720175`*^9, 3.852338478052122*^9}, {3.852338528637382*^9, 3.8523385640260878`*^9}, {3.8523389175888343`*^9, 3.8523389328262997`*^9}, {3.8523389629519563`*^9, 3.8523389753518944`*^9}, {3.852339008354312*^9, 3.852339059295692*^9}, { 3.8523390994118304`*^9, 3.852339099778098*^9}, {3.8523392626639595`*^9, 3.8523392811947136`*^9}, {3.8523393634846168`*^9, 3.8523394295923953`*^9}, {3.8523394782379665`*^9, 3.852339478823139*^9}, { 3.852339593926757*^9, 3.852339671084174*^9}, {3.852339711931484*^9, 3.852339784041746*^9}, {3.852339827771785*^9, 3.8523398280877805`*^9}, { 3.852339885054994*^9, 3.852339906414003*^9}, {3.852340395971958*^9, 3.8523403966426587`*^9}, {3.8523404751881404`*^9, 3.852340475781088*^9}, { 3.8523405200732336`*^9, 3.852340532179105*^9}, {3.8523406121578665`*^9, 3.852340785094775*^9}, {3.852340819276718*^9, 3.85234085816973*^9}, { 3.852340942090009*^9, 3.852340966879814*^9}, {3.852341026617176*^9, 3.8523411396731977`*^9}, {3.8523412660930223`*^9, 3.852341295802722*^9}, { 3.8523414435025682`*^9, 3.852341499929787*^9}, {3.8523415713395557`*^9, 3.8523415826878004`*^9}, {3.852341616970917*^9, 3.8523416180391808`*^9}, { 3.8523417316215086`*^9, 3.8523418610746107`*^9}, {3.852341941277248*^9, 3.8523419730084944`*^9}, {3.852342006990124*^9, 3.852342007408225*^9}, 3.852345951600083*^9, {3.8523585532830524`*^9, 3.852358553659275*^9}, { 3.8523585917608223`*^9, 3.8523586243402653`*^9}}, CellLabel-> "In[408]:=",ExpressionUUID->"411b1990-dd2c-48c4-9406-26f1d718f7d7"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 4.4 (truss)", "Subsubsection", CellChangeTimes->{{3.4938724364934034`*^9, 3.493872440377554*^9}, 3.55772174224413*^9, {3.5577222701826577`*^9, 3.557722281898278*^9}, { 3.6925364040653286`*^9, 3.692536414765343*^9}, {3.6926051339045105`*^9, 3.692605137804516*^9}, 3.692616505550922*^9, {3.6926165560409927`*^9, 3.692616575321019*^9}, 3.693218780550946*^9, {3.693222197869731*^9, 3.6932222001297336`*^9}, 3.6933062830792246`*^9, {3.725021164213514*^9, 3.725021164371165*^9}, {3.7887480090753746`*^9, 3.788748035234958*^9}, 3.8209949332267866`*^9, 3.821613854016477*^9},ExpressionUUID->"a4627f7d-a9f6-48ee-93cb-\ 5eed0b94f0d8"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ SqrtBox["8"], "A"}], ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "4"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "F"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "1", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "3", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "4", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"Simplify", "[", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "F"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4938808707521195`*^9, 3.493880886414419*^9}, { 3.4938809823296185`*^9, 3.4938810743976574`*^9}, {3.493881115862191*^9, 3.49388112389614*^9}, {3.5007185681328*^9, 3.5007185858543997`*^9}, 3.557721807701845*^9, 3.557722301679113*^9, {3.557722338229977*^9, 3.557722345218789*^9}, {3.5577223956380777`*^9, 3.557722557550762*^9}, { 3.5577227444350924`*^9, 3.5577227701751375`*^9}, {3.557722914366191*^9, 3.5577231321893735`*^9}, {3.5577234762323775`*^9, 3.557723673042323*^9}, { 3.557723707440384*^9, 3.557723724257213*^9}, {3.557723808200961*^9, 3.5577238249085903`*^9}, {3.557724032045754*^9, 3.5577240381453648`*^9}, { 3.5577240859750485`*^9, 3.5577241533827667`*^9}, {3.5577255542808275`*^9, 3.557725556340031*^9}, {3.692416572627716*^9, 3.692416634337803*^9}, { 3.6924166962978897`*^9, 3.6924166970178905`*^9}, {3.692416728407934*^9, 3.692416742377954*^9}, 3.692416785478014*^9, {3.692416815828057*^9, 3.692416854678111*^9}, {3.6924172169506187`*^9, 3.6924175298010564`*^9}, { 3.692418050131785*^9, 3.692418107561865*^9}, {3.6924216949310565`*^9, 3.6924216977710605`*^9}, {3.6925022762935333`*^9, 3.6925022791146946`*^9}, {3.6926050714634233`*^9, 3.6926053101657577`*^9}, {3.692605350685814*^9, 3.6926053528358173`*^9}, { 3.692605582596139*^9, 3.692605583946141*^9}, 3.692623496410709*^9, { 3.692623535710764*^9, 3.692623557910795*^9}, {3.6926952837958193`*^9, 3.6926952890058265`*^9}, {3.6928555108448462`*^9, 3.692855525144866*^9}, { 3.6928555801949434`*^9, 3.6928556725450726`*^9}, {3.6928557055151186`*^9, 3.6928557885252347`*^9}, {3.692855881295365*^9, 3.6928558933153815`*^9}, { 3.692855952785465*^9, 3.6928559781655006`*^9}, {3.6928560758856373`*^9, 3.692856170005769*^9}, {3.6928562238658447`*^9, 3.6928562580458927`*^9}, { 3.6928562961859455`*^9, 3.69285631358597*^9}, {3.692856357426031*^9, 3.6928563681360464`*^9}, {3.6928563999060907`*^9, 3.6928564001160913`*^9}, {3.692857702937915*^9, 3.6928577502779813`*^9}, { 3.6932187731509356`*^9, 3.693218803870979*^9}, {3.6932188341410213`*^9, 3.6932190222012844`*^9}, {3.693219079141364*^9, 3.6932191418014517`*^9}, { 3.693219256141612*^9, 3.6932192620916204`*^9}, 3.6932196368521447`*^9, { 3.693220450485284*^9, 3.6932204509352846`*^9}, {3.6932220864395747`*^9, 3.6932220972695894`*^9}, {3.6933062924792376`*^9, 3.6933064184694138`*^9}, 3.693306456369467*^9, {3.6933065958296623`*^9, 3.6933066138196874`*^9}, { 3.693306650569739*^9, 3.693306653189742*^9}, {3.693309085270472*^9, 3.693309087550475*^9}, {3.6933103271322107`*^9, 3.6933103356922226`*^9}, 3.6933103698722706`*^9, {3.693310470252411*^9, 3.6933104893324375`*^9}, 3.6933808415755987`*^9, {3.7247583889821615`*^9, 3.724758390348864*^9}, { 3.725021816037766*^9, 3.725021819733665*^9}, {3.7250219746947784`*^9, 3.72502200025261*^9}, {3.725022093649005*^9, 3.725022237603272*^9}, { 3.7250224542170396`*^9, 3.7250225220350323`*^9}, {3.725022679332588*^9, 3.7250227046999483`*^9}, {3.7250227409406877`*^9, 3.725022817280752*^9}, 3.725022850568372*^9, {3.7563597514070015`*^9, 3.7563598068261595`*^9}, { 3.7563598644359274`*^9, 3.756359867482433*^9}, {3.756451754376941*^9, 3.7564517906965075`*^9}, {3.788835297331105*^9, 3.788835324873559*^9}, { 3.7888353621680546`*^9, 3.788835402651895*^9}, 3.788836723146744*^9, 3.7888369215645175`*^9, {3.788837233063264*^9, 3.788837239768136*^9}, { 3.7888374428535147`*^9, 3.788837474666474*^9}, {3.7888375252778425`*^9, 3.788837553081115*^9}, {3.788937058688222*^9, 3.788937067270863*^9}, { 3.8210034460614004`*^9, 3.8210034551945815`*^9}, 3.8211530771253767`*^9, { 3.8519924934642563`*^9, 3.851992500294387*^9}}, CellLabel-> "In[416]:=",ExpressionUUID->"32895d8f-67a9-4b1f-91dd-f7a587c1acd4"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 1 (beam)", "Subsubsection", CellChangeTimes->{ 3.495088447506*^9, {3.495153177701*^9, 3.4951531894166*^9}, 3.558946122925826*^9, {3.692965302131263*^9, 3.692965317401284*^9}, { 3.6931188811951785`*^9, 3.6931188813051786`*^9}, 3.6931363637484083`*^9, 3.693190210631563*^9, {3.7250240785764503`*^9, 3.725024106360828*^9}, { 3.7250241751824183`*^9, 3.725024175334324*^9}, {3.788748048003364*^9, 3.788748054932249*^9}},ExpressionUUID->"d17c8db5-4e2b-4129-986d-\ 47c9263640c4"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "p"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "p"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}]}], "Input", CellChangeTimes->{{3.495088465875*^9, 3.495088486899*^9}, { 3.4950995009309998`*^9, 3.4950995016879997`*^9}, {3.495099819053*^9, 3.4950998310769997`*^9}, {3.4951004772609997`*^9, 3.495100482592*^9}, 3.4951534205774*^9, {3.4951664440478*^9, 3.4951664463722*^9}, { 3.6930154709945107`*^9, 3.693015620124719*^9}, {3.6930158215750012`*^9, 3.693015826975009*^9}, {3.6930158923661003`*^9, 3.693015945397175*^9}, { 3.693016038087304*^9, 3.6930160810173645`*^9}, {3.693016118977418*^9, 3.6930161267674284`*^9}, {3.6930164434978724`*^9, 3.6930164831779275`*^9}, {3.6930168959426355`*^9, 3.693016943842702*^9}, { 3.6930170211728106`*^9, 3.6930170221728115`*^9}, {3.6930176493256903`*^9, 3.693017670245719*^9}, {3.693017801865904*^9, 3.6930178264559383`*^9}, { 3.693018008816193*^9, 3.6930180566662602`*^9}, {3.693018115636343*^9, 3.693018129476362*^9}, {3.69301832058663*^9, 3.693018424926776*^9}, { 3.693018546686946*^9, 3.6930185536569557`*^9}, {3.6930185926270103`*^9, 3.6930186247670555`*^9}, {3.6930188500773706`*^9, 3.693018865057392*^9}, { 3.6930189745895452`*^9, 3.6930189769895487`*^9}, {3.6930192574799414`*^9, 3.6930192579099417`*^9}, {3.693019392680131*^9, 3.693019394440133*^9}, { 3.6930578337843657`*^9, 3.693057906174467*^9}, {3.6930579909745865`*^9, 3.6930579918445873`*^9}, {3.6930580481846666`*^9, 3.693058052384672*^9}, { 3.693058089464724*^9, 3.6930580925547285`*^9}, {3.693058215804901*^9, 3.6930582164549017`*^9}, 3.693136371008418*^9, {3.693190222241579*^9, 3.693190243191609*^9}, {3.6931902881216717`*^9, 3.693190295981683*^9}, 3.693190659322191*^9, {3.6931907050422554`*^9, 3.6931907075822587`*^9}, { 3.693190781282362*^9, 3.69319078689237*^9}, {3.693191377313196*^9, 3.693191381893203*^9}, {3.693191416663252*^9, 3.693191421643258*^9}, { 3.693191600493509*^9, 3.693191606243517*^9}, {3.6931920988862066`*^9, 3.6931921222862396`*^9}, {3.6933810050758276`*^9, 3.6933810224858522`*^9}, {3.6953566059258137`*^9, 3.6953566365958567`*^9}, 3.6953567310559893`*^9, {3.725024159454912*^9, 3.7250241609315004`*^9}, { 3.8509671092125254`*^9, 3.850967111163235*^9}}, CellLabel->"In[31]:=",ExpressionUUID->"676fec74-2d22-477e-9ac2-45c0bb92dc7a"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 2 (beam)", "Subsubsection", CellChangeTimes->{ 3.495088447506*^9, {3.495153177701*^9, 3.4951531894166*^9}, 3.558946122925826*^9, {3.692965302131263*^9, 3.692965317401284*^9}, { 3.6931188811951785`*^9, 3.6931188813051786`*^9}, 3.6931363637484083`*^9, 3.725024083228655*^9, 3.7887480631275167`*^9},ExpressionUUID->"285c06a9-aee3-4c8a-bac6-\ 5756bba88a2f"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "p"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "p"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}]}], "Input", CellChangeTimes->{{3.495088465875*^9, 3.495088486899*^9}, { 3.4950995009309998`*^9, 3.4950995016879997`*^9}, {3.495099819053*^9, 3.4950998310769997`*^9}, {3.4951004772609997`*^9, 3.495100482592*^9}, 3.4951534205774*^9, {3.4951664440478*^9, 3.4951664463722*^9}, { 3.6930154709945107`*^9, 3.693015620124719*^9}, {3.6930158215750012`*^9, 3.693015826975009*^9}, {3.6930158923661003`*^9, 3.693015945397175*^9}, { 3.693016038087304*^9, 3.6930160810173645`*^9}, {3.693016118977418*^9, 3.6930161267674284`*^9}, {3.6930164434978724`*^9, 3.6930164831779275`*^9}, {3.6930168959426355`*^9, 3.693016943842702*^9}, { 3.6930170211728106`*^9, 3.6930170221728115`*^9}, {3.6930176493256903`*^9, 3.693017670245719*^9}, {3.693017801865904*^9, 3.6930178264559383`*^9}, { 3.693018008816193*^9, 3.6930180566662602`*^9}, {3.693018115636343*^9, 3.693018129476362*^9}, {3.69301832058663*^9, 3.693018424926776*^9}, { 3.693018546686946*^9, 3.6930185536569557`*^9}, {3.6930185926270103`*^9, 3.6930186247670555`*^9}, {3.6930188500773706`*^9, 3.693018865057392*^9}, { 3.6930189745895452`*^9, 3.6930189769895487`*^9}, {3.6930192574799414`*^9, 3.6930192579099417`*^9}, {3.693019392680131*^9, 3.693019394440133*^9}, { 3.6930578337843657`*^9, 3.693057906174467*^9}, {3.6930579909745865`*^9, 3.6930579918445873`*^9}, {3.6930580481846666`*^9, 3.693058052384672*^9}, { 3.693058089464724*^9, 3.6930580925547285`*^9}, {3.693058215804901*^9, 3.6930582164549017`*^9}, 3.693136371008418*^9, {3.6933811029259644`*^9, 3.69338111405598*^9}, {3.7250242362488475`*^9, 3.7250242375071917`*^9}, { 3.756794146965371*^9, 3.7567941814263396`*^9}, {3.850967135594717*^9, 3.850967137461238*^9}}, CellLabel->"In[36]:=",ExpressionUUID->"acb1daa5-9316-43f7-aef0-eb3308efac2b"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 3 (beam)", "Subsubsection", CellChangeTimes->{ 3.495088447506*^9, {3.495153177701*^9, 3.4951531894166*^9}, 3.558946122925826*^9, {3.692965302131263*^9, 3.692965317401284*^9}, { 3.6931188811951785`*^9, 3.6931188813051786`*^9}, 3.6931363637484083`*^9, 3.725024083228655*^9, 3.725024360634966*^9, 3.788748067180313*^9},ExpressionUUID->"d32409d0-2e1a-49b3-9453-\ 0f0c7b2c83c5"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "p"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"Simplify", "[", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "p"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}]}], "Input", CellChangeTimes->{{3.495088465875*^9, 3.495088486899*^9}, { 3.4950995009309998`*^9, 3.4950995016879997`*^9}, {3.495099819053*^9, 3.4950998310769997`*^9}, {3.4951004772609997`*^9, 3.495100482592*^9}, 3.4951534205774*^9, {3.4951664440478*^9, 3.4951664463722*^9}, { 3.6930154709945107`*^9, 3.693015620124719*^9}, {3.6930158215750012`*^9, 3.693015826975009*^9}, {3.6930158923661003`*^9, 3.693015945397175*^9}, { 3.693016038087304*^9, 3.6930160810173645`*^9}, {3.693016118977418*^9, 3.6930161267674284`*^9}, {3.6930164434978724`*^9, 3.6930164831779275`*^9}, {3.6930168959426355`*^9, 3.693016943842702*^9}, { 3.6930170211728106`*^9, 3.6930170221728115`*^9}, {3.6930176493256903`*^9, 3.693017670245719*^9}, {3.693017801865904*^9, 3.6930178264559383`*^9}, { 3.693018008816193*^9, 3.6930180566662602`*^9}, {3.693018115636343*^9, 3.693018129476362*^9}, {3.69301832058663*^9, 3.693018424926776*^9}, { 3.693018546686946*^9, 3.6930185536569557`*^9}, {3.6930185926270103`*^9, 3.6930186247670555`*^9}, {3.6930188500773706`*^9, 3.693018865057392*^9}, { 3.6930189745895452`*^9, 3.6930189769895487`*^9}, {3.6930192574799414`*^9, 3.6930192579099417`*^9}, {3.693019392680131*^9, 3.693019394440133*^9}, { 3.6930578337843657`*^9, 3.693057906174467*^9}, {3.6930579909745865`*^9, 3.6930579918445873`*^9}, {3.6930580481846666`*^9, 3.693058052384672*^9}, { 3.693058089464724*^9, 3.6930580925547285`*^9}, {3.693058215804901*^9, 3.6930582164549017`*^9}, 3.693136371008418*^9, {3.6933811029259644`*^9, 3.69338111405598*^9}, {3.7250242362488475`*^9, 3.7250242375071917`*^9}, { 3.725024378941745*^9, 3.725024406343743*^9}, {3.7567942416934767`*^9, 3.7567942432555633`*^9}, {3.8210036683680515`*^9, 3.821003675582391*^9}, { 3.850967165278871*^9, 3.850967167210659*^9}}, CellLabel->"In[41]:=",ExpressionUUID->"a39b6254-aa20-4e85-8d2f-c95a993bd33b"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 4 (beam)", "Subsubsection", CellChangeTimes->{ 3.495088447506*^9, {3.495153177701*^9, 3.4951531894166*^9}, 3.558946122925826*^9, {3.692965302131263*^9, 3.692965317401284*^9}, { 3.6931188811951785`*^9, 3.6931188813051786`*^9}, 3.725024466017606*^9, 3.788748070204897*^9},ExpressionUUID->"246bee83-9644-4128-bc0f-\ 80aeefa97a01"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "p"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "1", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "p"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}]}], "Input", CellChangeTimes->{{3.495088465875*^9, 3.495088486899*^9}, { 3.4950995009309998`*^9, 3.4950995016879997`*^9}, {3.495099819053*^9, 3.4950998310769997`*^9}, {3.4951004772609997`*^9, 3.495100482592*^9}, 3.4951534205774*^9, {3.4951664440478*^9, 3.4951664463722*^9}, { 3.6930154709945107`*^9, 3.693015620124719*^9}, {3.6930158215750012`*^9, 3.693015826975009*^9}, {3.6930158923661003`*^9, 3.693015945397175*^9}, { 3.693016038087304*^9, 3.6930160810173645`*^9}, {3.693016118977418*^9, 3.6930161267674284`*^9}, {3.6930164434978724`*^9, 3.6930164831779275`*^9}, {3.6930168959426355`*^9, 3.693016943842702*^9}, { 3.6930170211728106`*^9, 3.6930170221728115`*^9}, {3.6930176493256903`*^9, 3.693017670245719*^9}, {3.693017801865904*^9, 3.6930178264559383`*^9}, { 3.693018008816193*^9, 3.6930180566662602`*^9}, {3.693018115636343*^9, 3.693018129476362*^9}, {3.69301832058663*^9, 3.693018424926776*^9}, { 3.693018546686946*^9, 3.6930185536569557`*^9}, {3.6930185926270103`*^9, 3.6930186247670555`*^9}, {3.6930188500773706`*^9, 3.693018865057392*^9}, { 3.6930189745895452`*^9, 3.6930189769895487`*^9}, {3.6930192574799414`*^9, 3.6930192579099417`*^9}, {3.693019392680131*^9, 3.693019394440133*^9}, { 3.6930578337843657`*^9, 3.693057906174467*^9}, {3.6930579909745865`*^9, 3.6930579918445873`*^9}, {3.6930580481846666`*^9, 3.693058052384672*^9}, { 3.693058089464724*^9, 3.6930580925547285`*^9}, {3.693058215804901*^9, 3.6930582164549017`*^9}, {3.69338113518601*^9, 3.6933811496960297`*^9}, { 3.725024496244114*^9, 3.7250245030147038`*^9}, {3.7567945162383647`*^9, 3.7567945170664864`*^9}, {3.756800697920469*^9, 3.7568007144705143`*^9}, { 3.7568007575697813`*^9, 3.7568007580853047`*^9}, {3.8509671904069457`*^9, 3.85096719249596*^9}}, CellLabel->"In[70]:=",ExpressionUUID->"8bbdf06b-fa2b-4713-88c0-236df0d265db"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 5 (beam)", "Subsubsection", CellChangeTimes->{ 3.495088447506*^9, {3.495153177701*^9, 3.4951531894166*^9}, 3.558946122925826*^9, {3.692965302131263*^9, 3.692965317401284*^9}, { 3.6931188811951785`*^9, 3.6931188813051786`*^9}, {3.6931379329206047`*^9, 3.693137933030605*^9}, 3.7250245231314993`*^9, 3.7250245562248693`*^9, 3.7567964396238427`*^9, 3.7887480754354105`*^9},ExpressionUUID->"16f9256e-d318-4635-8b17-\ fad8ca43fede"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "p"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "3", "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"p", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "3", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "3", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "p"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}]}], "Input", CellChangeTimes->{{3.495088465875*^9, 3.495088486899*^9}, { 3.4950995009309998`*^9, 3.4950995016879997`*^9}, {3.495099819053*^9, 3.4950998310769997`*^9}, {3.4951004772609997`*^9, 3.495100482592*^9}, 3.4951534205774*^9, {3.4951664440478*^9, 3.4951664463722*^9}, { 3.6930154709945107`*^9, 3.693015620124719*^9}, {3.6930158215750012`*^9, 3.693015826975009*^9}, {3.6930158923661003`*^9, 3.693015945397175*^9}, { 3.693016038087304*^9, 3.6930160810173645`*^9}, {3.693016118977418*^9, 3.6930161267674284`*^9}, {3.6930164434978724`*^9, 3.6930164831779275`*^9}, {3.6930168959426355`*^9, 3.693016943842702*^9}, { 3.6930170211728106`*^9, 3.6930170221728115`*^9}, {3.6930176493256903`*^9, 3.693017670245719*^9}, {3.693017801865904*^9, 3.6930178264559383`*^9}, { 3.693018008816193*^9, 3.6930180566662602`*^9}, {3.693018115636343*^9, 3.693018129476362*^9}, {3.69301832058663*^9, 3.693018424926776*^9}, { 3.693018546686946*^9, 3.6930185536569557`*^9}, {3.6930185926270103`*^9, 3.6930186247670555`*^9}, {3.6930188500773706`*^9, 3.693018865057392*^9}, { 3.6930189745895452`*^9, 3.6930189769895487`*^9}, {3.6930192574799414`*^9, 3.6930192579099417`*^9}, {3.693019392680131*^9, 3.693019394440133*^9}, { 3.6930578337843657`*^9, 3.693057906174467*^9}, {3.6930579909745865`*^9, 3.6930579918445873`*^9}, {3.6930580481846666`*^9, 3.693058052384672*^9}, { 3.693058089464724*^9, 3.6930580925547285`*^9}, {3.693058215804901*^9, 3.6930582164549017`*^9}, {3.6931379460006227`*^9, 3.6931380135417175`*^9}, 3.693138069661796*^9, {3.693138284313097*^9, 3.69313831553314*^9}, { 3.6932961835350847`*^9, 3.6932962439151697`*^9}, {3.6932962790552187`*^9, 3.6932962897252336`*^9}, {3.6933811840760784`*^9, 3.6933811866760817`*^9}, {3.7250246542359395`*^9, 3.725024658292693*^9}, { 3.756796446919061*^9, 3.7567964727723756`*^9}, {3.8509672172375956`*^9, 3.850967223320303*^9}}, CellLabel->"In[46]:=",ExpressionUUID->"74ce939a-3fad-4aee-80e5-c2f520f22dc4"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 6 (beam)", "Subsubsection", CellChangeTimes->{ 3.495088447506*^9, {3.495153177701*^9, 3.4951531894166*^9}, 3.558946122925826*^9, {3.692965302131263*^9, 3.692965317401284*^9}, { 3.6931188811951785`*^9, 3.6931188813051786`*^9}, {3.6931379329206047`*^9, 3.693137933030605*^9}, 3.6932973174666724`*^9, {3.7250246897196236`*^9, 3.7250246902801123`*^9}, {3.7567965014531136`*^9, 3.7567965016718607`*^9}, 3.788748083302801*^9},ExpressionUUID->"20cd57fc-3258-46df-8e82-\ c358ddd91eac"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "p"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "3", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "1", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"L", "/", "2"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "3", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", RowBox[{"\[Theta]Y", "[", "1", "]"}]}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "p"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}]}], "Input", CellChangeTimes->{{3.495088465875*^9, 3.495088486899*^9}, { 3.4950995009309998`*^9, 3.4950995016879997`*^9}, {3.495099819053*^9, 3.4950998310769997`*^9}, {3.4951004772609997`*^9, 3.495100482592*^9}, 3.4951534205774*^9, {3.4951664440478*^9, 3.4951664463722*^9}, { 3.6930154709945107`*^9, 3.693015620124719*^9}, {3.6930158215750012`*^9, 3.693015826975009*^9}, {3.6930158923661003`*^9, 3.693015945397175*^9}, { 3.693016038087304*^9, 3.6930160810173645`*^9}, {3.693016118977418*^9, 3.6930161267674284`*^9}, {3.6930164434978724`*^9, 3.6930164831779275`*^9}, {3.6930168959426355`*^9, 3.693016943842702*^9}, { 3.6930170211728106`*^9, 3.6930170221728115`*^9}, {3.6930176493256903`*^9, 3.693017670245719*^9}, {3.693017801865904*^9, 3.6930178264559383`*^9}, { 3.693018008816193*^9, 3.6930180566662602`*^9}, {3.693018115636343*^9, 3.693018129476362*^9}, {3.69301832058663*^9, 3.693018424926776*^9}, { 3.693018546686946*^9, 3.6930185536569557`*^9}, {3.6930185926270103`*^9, 3.6930186247670555`*^9}, {3.6930188500773706`*^9, 3.693018865057392*^9}, { 3.6930189745895452`*^9, 3.6930189769895487`*^9}, {3.6930192574799414`*^9, 3.6930192579099417`*^9}, {3.693019392680131*^9, 3.693019394440133*^9}, { 3.6930578337843657`*^9, 3.693057906174467*^9}, {3.6930579909745865`*^9, 3.6930579918445873`*^9}, {3.6930580481846666`*^9, 3.693058052384672*^9}, { 3.693058089464724*^9, 3.6930580925547285`*^9}, {3.693058215804901*^9, 3.6930582164549017`*^9}, {3.6931379460006227`*^9, 3.6931380135417175`*^9}, 3.693138069661796*^9, {3.693138284313097*^9, 3.69313831553314*^9}, { 3.6932961835350847`*^9, 3.6932962439151697`*^9}, {3.6932962790552187`*^9, 3.6932962897252336`*^9}, {3.69329733021669*^9, 3.693297434086836*^9}, { 3.693381220626129*^9, 3.6933812440971622`*^9}, 3.7250247134269934`*^9, { 3.7567967044368567`*^9, 3.7567967060458655`*^9}, {3.850967268464264*^9, 3.850967274798299*^9}}, CellLabel->"In[80]:=",ExpressionUUID->"714fefbe-7f3d-439f-b790-a8c2661043f9"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 7 (beam)", "Subsubsection", CellChangeTimes->{ 3.495088447506*^9, {3.495153177701*^9, 3.4951531894166*^9}, 3.558946122925826*^9, {3.692965302131263*^9, 3.692965317401284*^9}, { 3.6931188811951785`*^9, 3.6931188813051786`*^9}, {3.6931379329206047`*^9, 3.693137933030605*^9}, 3.6931420947472496`*^9, 3.693298925868924*^9, { 3.7250253226298213`*^9, 3.725025323475069*^9}, 3.7567967669378643`*^9, 3.7887480861452737`*^9},ExpressionUUID->"ef4376c4-f29f-43f9-a625-\ b0f3824d3448"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Rho]"}], " ", "A", " ", "g"}], ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}]}], "Input", CellChangeTimes->{{3.495088465875*^9, 3.495088486899*^9}, { 3.4950995009309998`*^9, 3.4950995016879997`*^9}, {3.495099819053*^9, 3.4950998310769997`*^9}, {3.4951004772609997`*^9, 3.495100482592*^9}, 3.4951534205774*^9, {3.4951664440478*^9, 3.4951664463722*^9}, { 3.6930154709945107`*^9, 3.693015620124719*^9}, {3.6930158215750012`*^9, 3.693015826975009*^9}, {3.6930158923661003`*^9, 3.693015945397175*^9}, { 3.693016038087304*^9, 3.6930160810173645`*^9}, {3.693016118977418*^9, 3.6930161267674284`*^9}, {3.6930164434978724`*^9, 3.6930164831779275`*^9}, {3.6930168959426355`*^9, 3.693016943842702*^9}, { 3.6930170211728106`*^9, 3.6930170221728115`*^9}, {3.6930176493256903`*^9, 3.693017670245719*^9}, {3.693017801865904*^9, 3.6930178264559383`*^9}, { 3.693018008816193*^9, 3.6930180566662602`*^9}, {3.693018115636343*^9, 3.693018129476362*^9}, {3.69301832058663*^9, 3.693018424926776*^9}, { 3.693018546686946*^9, 3.6930185536569557`*^9}, {3.6930185926270103`*^9, 3.6930186247670555`*^9}, {3.6930188500773706`*^9, 3.693018865057392*^9}, { 3.6930189745895452`*^9, 3.6930189769895487`*^9}, {3.6930192574799414`*^9, 3.6930192579099417`*^9}, {3.693019392680131*^9, 3.693019394440133*^9}, { 3.6930578337843657`*^9, 3.693057906174467*^9}, {3.6930579909745865`*^9, 3.6930579918445873`*^9}, {3.6930580481846666`*^9, 3.693058052384672*^9}, { 3.693058089464724*^9, 3.6930580925547285`*^9}, {3.693058215804901*^9, 3.6930582164549017`*^9}, {3.6931379460006227`*^9, 3.6931380135417175`*^9}, 3.693138069661796*^9, {3.693138284313097*^9, 3.69313831553314*^9}, { 3.6931421018572598`*^9, 3.693142185437377*^9}, {3.693381313068259*^9, 3.6933813189282675`*^9}, {3.756796779122508*^9, 3.756796780606487*^9}}, CellLabel->"In[85]:=",ExpressionUUID->"fa7ec5d1-d4ff-463f-99b3-065309989c90"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 8 (truss)", "Subsubsection", CellChangeTimes->{ 3.495088447506*^9, {3.495153177701*^9, 3.4951531894166*^9}, 3.558946122925826*^9, {3.692965302131263*^9, 3.692965317401284*^9}, { 3.6931188811951785`*^9, 3.6931188813051786`*^9}, {3.6931379329206047`*^9, 3.693137933030605*^9}, {3.693138364413209*^9, 3.693138367713214*^9}, 3.6931934898815126`*^9, 3.693370799325358*^9, 3.72502550453412*^9, 3.756796830657314*^9, 3.7887480892105436`*^9},ExpressionUUID->"feed8171-7f0c-4097-bf86-\ 16df543c265b"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"7", ",", "6"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"RIGID", ",", RowBox[{"{", "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "4"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"RIGID", ",", RowBox[{"{", "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"4", ",", "5"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "F"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "4", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "L"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "3", "]"}], ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "4", "]"}], ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "3", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "4", "]"}], ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "6", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "F"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], " ", ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}]}], "Input", CellChangeTimes->{{3.495088465875*^9, 3.495088486899*^9}, { 3.4950995009309998`*^9, 3.4950995016879997`*^9}, {3.495099819053*^9, 3.4950998310769997`*^9}, {3.4951004772609997`*^9, 3.495100482592*^9}, 3.4951534205774*^9, {3.4951664440478*^9, 3.4951664463722*^9}, { 3.6930154709945107`*^9, 3.693015620124719*^9}, {3.6930158215750012`*^9, 3.693015826975009*^9}, {3.6930158923661003`*^9, 3.693015945397175*^9}, { 3.693016038087304*^9, 3.6930160810173645`*^9}, {3.693016118977418*^9, 3.6930161267674284`*^9}, {3.6930164434978724`*^9, 3.6930164831779275`*^9}, {3.6930168959426355`*^9, 3.693016943842702*^9}, { 3.6930170211728106`*^9, 3.6930170221728115`*^9}, {3.6930176493256903`*^9, 3.693017670245719*^9}, {3.693017801865904*^9, 3.6930178264559383`*^9}, { 3.693018008816193*^9, 3.6930180566662602`*^9}, {3.693018115636343*^9, 3.693018129476362*^9}, {3.69301832058663*^9, 3.693018424926776*^9}, { 3.693018546686946*^9, 3.6930185536569557`*^9}, {3.6930185926270103`*^9, 3.6930186247670555`*^9}, {3.6930188500773706`*^9, 3.693018865057392*^9}, { 3.6930189745895452`*^9, 3.6930189769895487`*^9}, {3.6930192574799414`*^9, 3.6930192579099417`*^9}, {3.693019392680131*^9, 3.693019394440133*^9}, { 3.6930578337843657`*^9, 3.693057906174467*^9}, {3.6930579909745865`*^9, 3.6930579918445873`*^9}, {3.6930580481846666`*^9, 3.693058052384672*^9}, { 3.693058089464724*^9, 3.6930580925547285`*^9}, {3.693058215804901*^9, 3.6930582164549017`*^9}, {3.6931379460006227`*^9, 3.6931380135417175`*^9}, 3.693138069661796*^9, {3.693138284313097*^9, 3.69313831553314*^9}, { 3.6931384072632685`*^9, 3.693138464483349*^9}, 3.6931385504534693`*^9, { 3.693139539130171*^9, 3.6931395422501755`*^9}, {3.6931407590133796`*^9, 3.6931407900734234`*^9}, {3.69314082374347*^9, 3.6931408243334713`*^9}, { 3.693141231804042*^9, 3.693141239914053*^9}, 3.6931418049058437`*^9, { 3.693381352298314*^9, 3.6933813606583257`*^9}, {3.69346018351458*^9, 3.6934601845445805`*^9}, {3.693460277494711*^9, 3.6934602906747293`*^9}, { 3.693460328224782*^9, 3.693460473154985*^9}, {3.6934605861451435`*^9, 3.693460590465149*^9}, {3.6934606275952015`*^9, 3.6934608558655205`*^9}, { 3.6934609279556217`*^9, 3.69346093378563*^9}, {3.693461071075822*^9, 3.6934610732858253`*^9}, {3.6934617808668156`*^9, 3.693461781226816*^9}, { 3.693461815406864*^9, 3.6934618242468767`*^9}, {3.6934618548969193`*^9, 3.6934618984369802`*^9}, {3.6934619751070876`*^9, 3.693461978447092*^9}, { 3.6934621984574003`*^9, 3.69346223375745*^9}, {3.693462346117607*^9, 3.6934624185677085`*^9}, {3.72502542640604*^9, 3.725025427855894*^9}, { 3.7567969527224703`*^9, 3.756796954268941*^9}, {3.821066361356242*^9, 3.821066365768322*^9}, {3.82106642496561*^9, 3.8210664371231837`*^9}, { 3.8210667024813805`*^9, 3.821066774667529*^9}, {3.8210668836756763`*^9, 3.8210668862200065`*^9}, {3.8211526289041243`*^9, 3.8211526336727953`*^9}, {3.821152687932913*^9, 3.821152705567244*^9}}, CellLabel-> "In[421]:=",ExpressionUUID->"0263de8a-ea22-41b1-921d-8145303e70f3"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 9 (truss)", "Subsubsection", CellChangeTimes->{ 3.495088447506*^9, {3.495153177701*^9, 3.4951531894166*^9}, 3.558946122925826*^9, {3.692965302131263*^9, 3.692965317401284*^9}, { 3.6931188811951785`*^9, 3.6931188813051786`*^9}, {3.6931379329206047`*^9, 3.693137933030605*^9}, {3.693138364413209*^9, 3.693138367713214*^9}, 3.6931934898815126`*^9, {3.6933707838353357`*^9, 3.6933707954953527`*^9}, { 3.725025573634933*^9, 3.725025582913336*^9}, 3.756797263336627*^9, 3.788748091540877*^9},ExpressionUUID->"336900a9-ba1b-41d3-a7b4-\ 04e9c282b157"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"NOTICE", ":", " ", RowBox[{ "the", " ", "outcome", " ", "of", " ", "the", " ", "hand", " ", "calculation", " ", RowBox[{"(", RowBox[{"analytical", " ", "solution"}], ")"}], " ", "and", " ", "the", " ", "one", " ", "by", " ", "the", " ", "code", " ", RowBox[{"(", RowBox[{"numerical", " ", "solution"}], ")"}], " ", "differ", " ", "due", " ", "to", " ", "discretization", " ", RowBox[{"error", ".", "\[IndentingNewLine]", "The"}], " ", "solution", " ", "by", " ", "FEM", " ", "converges", " ", "to", " ", "the", " ", "analytical", " ", "solution", " ", "when", " ", "the", " ", "mesh", " ", "is", " ", "refined"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"2", "A"}], ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "6"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ SqrtBox["8"], " ", "A"}], ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ SqrtBox["8"], "A"}], ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"4", ",", "5"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"-", "F"}]}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "3", "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "F"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "5", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "1", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "3", "]"}], ",", "0", ",", RowBox[{"uZ", "[", "3", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "3", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "3", "]"}], ",", "0", ",", RowBox[{"uZ", "[", "3", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "4", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "5", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "5", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "5", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "6", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"Simplify", "[", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "F"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "]"}], "[", RowBox[{"[", RowBox[{";;", ",", "1"}], "]"}], "]"}]}]}]], "Input", CellChangeTimes->{{3.495088465875*^9, 3.495088486899*^9}, { 3.4950995009309998`*^9, 3.4950995016879997`*^9}, {3.495099819053*^9, 3.4950998310769997`*^9}, {3.4951004772609997`*^9, 3.495100482592*^9}, 3.4951534205774*^9, {3.4951664440478*^9, 3.4951664463722*^9}, { 3.6930154709945107`*^9, 3.693015620124719*^9}, {3.6930158215750012`*^9, 3.693015826975009*^9}, {3.6930158923661003`*^9, 3.693015945397175*^9}, { 3.693016038087304*^9, 3.6930160810173645`*^9}, {3.693016118977418*^9, 3.6930161267674284`*^9}, {3.6930164434978724`*^9, 3.6930164831779275`*^9}, {3.6930168959426355`*^9, 3.693016943842702*^9}, { 3.6930170211728106`*^9, 3.6930170221728115`*^9}, {3.6930176493256903`*^9, 3.693017670245719*^9}, {3.693017801865904*^9, 3.6930178264559383`*^9}, { 3.693018008816193*^9, 3.6930180566662602`*^9}, {3.693018115636343*^9, 3.693018129476362*^9}, {3.69301832058663*^9, 3.693018424926776*^9}, { 3.693018546686946*^9, 3.6930185536569557`*^9}, {3.6930185926270103`*^9, 3.6930186247670555`*^9}, {3.6930188500773706`*^9, 3.693018865057392*^9}, { 3.6930189745895452`*^9, 3.6930189769895487`*^9}, {3.6930192574799414`*^9, 3.6930192579099417`*^9}, {3.693019392680131*^9, 3.693019394440133*^9}, { 3.6930578337843657`*^9, 3.693057906174467*^9}, {3.6930579909745865`*^9, 3.6930579918445873`*^9}, {3.6930580481846666`*^9, 3.693058052384672*^9}, { 3.693058089464724*^9, 3.6930580925547285`*^9}, {3.693058215804901*^9, 3.6930582164549017`*^9}, {3.6931379460006227`*^9, 3.6931380135417175`*^9}, 3.693138069661796*^9, {3.693138284313097*^9, 3.69313831553314*^9}, { 3.6931384072632685`*^9, 3.693138464483349*^9}, 3.6931385504534693`*^9, { 3.693139539130171*^9, 3.6931395422501755`*^9}, {3.6931407590133796`*^9, 3.6931407900734234`*^9}, {3.69314082374347*^9, 3.6931408243334713`*^9}, { 3.693141231804042*^9, 3.693141239914053*^9}, 3.6931418049058437`*^9, { 3.693370814495379*^9, 3.6933710347856874`*^9}, {3.6933710912757664`*^9, 3.6933712196459465`*^9}, {3.693371517086363*^9, 3.6933715226363707`*^9}, { 3.6933746737607822`*^9, 3.693374840391015*^9}, {3.6933750748613434`*^9, 3.693375094561371*^9}, {3.6933751349114275`*^9, 3.6933751375414314`*^9}, { 3.693375277291627*^9, 3.6933752833316355`*^9}, {3.6933816414087186`*^9, 3.693381657478741*^9}, {3.756797338506524*^9, 3.756797339818715*^9}, { 3.7568008125108557`*^9, 3.7568008148696814`*^9}, {3.8210040138880997`*^9, 3.8210040319696836`*^9}, {3.8210040880487194`*^9, 3.8210040958925037`*^9}, {3.8519936603511744`*^9, 3.8519936750219097`*^9}, {3.8519937307384048`*^9, 3.851993734346714*^9}, { 3.851993768822936*^9, 3.8519937697449074`*^9}}, CellLabel->"In[71]:=",ExpressionUUID->"751083b7-d8e4-4c5c-84a2-683db8b25f99"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 10 (plate)", "Subsubsection", CellChangeTimes->{ 3.495088447506*^9, {3.495153177701*^9, 3.4951531894166*^9}, 3.558946122925826*^9, {3.692965302131263*^9, 3.692965317401284*^9}, { 3.6931188811951785`*^9, 3.6931188813051786`*^9}, {3.6931379329206047`*^9, 3.693137933030605*^9}, {3.693138364413209*^9, 3.693138367713214*^9}, 3.6931934898815126`*^9, {3.6933707838353357`*^9, 3.6933707954953527`*^9}, { 3.69362388551801*^9, 3.693623887178013*^9}, {3.7250256670291777`*^9, 3.7250257058821273`*^9}, {3.756361573013221*^9, 3.756361580747472*^9}, 3.7567975459735603`*^9, {3.7567975787939963`*^9, 3.7567975796219316`*^9}, 3.788748094743372*^9},ExpressionUUID->"3cdc9a17-cca7-4803-a78a-\ 2f661e2f52a9"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"use", " ", "the", " ", "building", " ", "blocks"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Block", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"w", "=", RowBox[{ RowBox[{"a", "[", "0", "]"}], RowBox[{"Sin", "[", RowBox[{"Pi", " ", FractionBox["x", "L"]}], " ", "]"}], RowBox[{"Sin", "[", RowBox[{"Pi", " ", FractionBox["y", "L"]}], " ", "]"}]}]}], ",", "\[Delta]wint", ",", "\[Delta]wsta", ",", "\[CapitalOmega]", ",", "\[Delta]W"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wint", ":=", RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", " ", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["t", "3"], " ", "\[CapitalEpsilon]"}], RowBox[{"12", RowBox[{"(", RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}], ")"}]}]], RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "\[Nu]", "0"}, {"\[Nu]", "1", "0"}, {"0", "0", FractionBox[ RowBox[{"1", "-", "\[Nu]"}], "2"]} }], "\[NoBreak]", ")"}]}], ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wsta", ":=", RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"-", "p"}], "0"}, {"0", "0"} }], "\[NoBreak]", ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}]} }], "\[NoBreak]", ")"}]}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", "=", RowBox[{"Rectangle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"L", ",", "L"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Integrate", "[", RowBox[{ RowBox[{"\[Delta]wint", "+", "\[Delta]wsta"}], ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], StyleBox["\[Element]", "OperatorCharacter"], StyleBox["\[CapitalOmega]", "OperatorCharacter"]}]}], StyleBox["]", "OperatorCharacter"]}], StyleBox[",", "OperatorCharacter"], StyleBox[ RowBox[{"L", ">", "0"}], "OperatorCharacter"]}], StyleBox["]", "OperatorCharacter"]}]}], StyleBox[";", "OperatorCharacter"], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", "\[Delta]W", "]"}], ";", "\[IndentingNewLine]", RowBox[{ StyleBox["Grid", "OperatorCharacter"], StyleBox["[", "OperatorCharacter"], RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "p"}], "}"}], ",", "\[Delta]W"}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}]}]}], "]"}]}]], "Input", CellChangeTimes->{{3.495088465875*^9, 3.495088486899*^9}, { 3.4950995009309998`*^9, 3.4950995016879997`*^9}, {3.495099819053*^9, 3.4950998310769997`*^9}, {3.4951004772609997`*^9, 3.495100482592*^9}, 3.4951534205774*^9, {3.4951664440478*^9, 3.4951664463722*^9}, { 3.6930154709945107`*^9, 3.693015620124719*^9}, {3.6930158215750012`*^9, 3.693015826975009*^9}, {3.6930158923661003`*^9, 3.693015945397175*^9}, { 3.693016038087304*^9, 3.6930160810173645`*^9}, {3.693016118977418*^9, 3.6930161267674284`*^9}, {3.6930164434978724`*^9, 3.6930164831779275`*^9}, {3.6930168959426355`*^9, 3.693016943842702*^9}, { 3.6930170211728106`*^9, 3.6930170221728115`*^9}, {3.6930176493256903`*^9, 3.693017670245719*^9}, {3.693017801865904*^9, 3.6930178264559383`*^9}, { 3.693018008816193*^9, 3.6930180566662602`*^9}, {3.693018115636343*^9, 3.693018129476362*^9}, {3.69301832058663*^9, 3.693018424926776*^9}, { 3.693018546686946*^9, 3.6930185536569557`*^9}, {3.6930185926270103`*^9, 3.6930186247670555`*^9}, {3.6930188500773706`*^9, 3.693018865057392*^9}, { 3.6930189745895452`*^9, 3.6930189769895487`*^9}, {3.6930192574799414`*^9, 3.6930192579099417`*^9}, {3.693019392680131*^9, 3.693019394440133*^9}, { 3.6930578337843657`*^9, 3.693057906174467*^9}, {3.6930579909745865`*^9, 3.6930579918445873`*^9}, {3.6930580481846666`*^9, 3.693058052384672*^9}, { 3.693058089464724*^9, 3.6930580925547285`*^9}, {3.693058215804901*^9, 3.6930582164549017`*^9}, {3.6931379460006227`*^9, 3.6931380135417175`*^9}, 3.693138069661796*^9, {3.693138284313097*^9, 3.69313831553314*^9}, { 3.6931384072632685`*^9, 3.693138464483349*^9}, 3.6931385504534693`*^9, { 3.693139539130171*^9, 3.6931395422501755`*^9}, {3.6931407590133796`*^9, 3.6931407900734234`*^9}, {3.69314082374347*^9, 3.6931408243334713`*^9}, { 3.693141231804042*^9, 3.693141239914053*^9}, 3.6931418049058437`*^9, { 3.693370814495379*^9, 3.6933710347856874`*^9}, {3.6933710912757664`*^9, 3.6933712196459465`*^9}, {3.693371517086363*^9, 3.6933715226363707`*^9}, { 3.6933746737607822`*^9, 3.693374840391015*^9}, {3.6933750748613434`*^9, 3.693375094561371*^9}, {3.6933751349114275`*^9, 3.6933751375414314`*^9}, { 3.693375277291627*^9, 3.6933752833316355`*^9}, {3.6933816414087186`*^9, 3.693381657478741*^9}, {3.693623898148028*^9, 3.6936240857282906`*^9}, { 3.6936241755384164`*^9, 3.693624186658432*^9}, {3.6936242236884837`*^9, 3.6936242455985146`*^9}, {3.693624308838603*^9, 3.6936243276586294`*^9}, { 3.6936243601386747`*^9, 3.693624369098687*^9}, {3.6936244076487412`*^9, 3.6936244551088076`*^9}, {3.693624537678923*^9, 3.6936245600289545`*^9}, 3.6936246237090435`*^9, {3.6936248231593227`*^9, 3.6936248490093594`*^9}, { 3.6936249813995447`*^9, 3.6936249911795583`*^9}, {3.693625250289921*^9, 3.693625251009922*^9}, 3.7250279951942205`*^9, {3.7250284810413065`*^9, 3.725028490580618*^9}, {3.7567975871357956`*^9, 3.756797612661065*^9}, { 3.7567976536670847`*^9, 3.7567976726626425`*^9}, {3.756797924163059*^9, 3.7567979425331545`*^9}, {3.756798013969554*^9, 3.7567980154535646`*^9}, { 3.7567983041359205`*^9, 3.756798330801605*^9}, {3.788937859790479*^9, 3.7889378647702503`*^9}, {3.8210042148062916`*^9, 3.8210042284122076`*^9}, {3.8509674829508924`*^9, 3.8509675434163094`*^9}, {3.8509675794392633`*^9, 3.8509675852019043`*^9}}, CellLabel->"In[76]:=",ExpressionUUID->"52b73e57-81c5-4125-a12c-504081a9b651"] }, Closed]], Cell[CellGroupData[{ Cell["Home assignment 1 (beam)", "Subsubsection", CellChangeTimes->{ 3.495088447506*^9, {3.495153177701*^9, 3.4951531894166*^9}, 3.558946122925826*^9, {3.692965302131263*^9, 3.692965317401284*^9}, { 3.6931188811951785`*^9, 3.6931188813051786`*^9}, 3.6931363637484083`*^9, 3.725024083228655*^9, {3.7567988696810017`*^9, 3.756798876476287*^9}},ExpressionUUID->"d94bf0e7-3dfd-4ffc-8ca8-\ 2dc5f1e81ec0"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "p"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "4"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "1", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "4", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "p"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}]}], "Input", CellChangeTimes->{{3.495088465875*^9, 3.495088486899*^9}, { 3.4950995009309998`*^9, 3.4950995016879997`*^9}, {3.495099819053*^9, 3.4950998310769997`*^9}, {3.4951004772609997`*^9, 3.495100482592*^9}, 3.4951534205774*^9, {3.4951664440478*^9, 3.4951664463722*^9}, { 3.6930154709945107`*^9, 3.693015620124719*^9}, {3.6930158215750012`*^9, 3.693015826975009*^9}, {3.6930158923661003`*^9, 3.693015945397175*^9}, { 3.693016038087304*^9, 3.6930160810173645`*^9}, {3.693016118977418*^9, 3.6930161267674284`*^9}, {3.6930164434978724`*^9, 3.6930164831779275`*^9}, {3.6930168959426355`*^9, 3.693016943842702*^9}, { 3.6930170211728106`*^9, 3.6930170221728115`*^9}, {3.6930176493256903`*^9, 3.693017670245719*^9}, {3.693017801865904*^9, 3.6930178264559383`*^9}, { 3.693018008816193*^9, 3.6930180566662602`*^9}, {3.693018115636343*^9, 3.693018129476362*^9}, {3.69301832058663*^9, 3.693018424926776*^9}, { 3.693018546686946*^9, 3.6930185536569557`*^9}, {3.6930185926270103`*^9, 3.6930186247670555`*^9}, {3.6930188500773706`*^9, 3.693018865057392*^9}, { 3.6930189745895452`*^9, 3.6930189769895487`*^9}, {3.6930192574799414`*^9, 3.6930192579099417`*^9}, {3.693019392680131*^9, 3.693019394440133*^9}, { 3.6930578337843657`*^9, 3.693057906174467*^9}, {3.6930579909745865`*^9, 3.6930579918445873`*^9}, {3.6930580481846666`*^9, 3.693058052384672*^9}, { 3.693058089464724*^9, 3.6930580925547285`*^9}, {3.693058215804901*^9, 3.6930582164549017`*^9}, 3.693136371008418*^9, {3.6933811029259644`*^9, 3.69338111405598*^9}, {3.7250242362488475`*^9, 3.7250242375071917`*^9}, { 3.756794146965371*^9, 3.7567941814263396`*^9}, {3.756799517431947*^9, 3.756799522727543*^9}, {3.788843854837902*^9, 3.788843875913063*^9}, { 3.788843907038912*^9, 3.7888439554722376`*^9}, {3.788843993884048*^9, 3.788844021087784*^9}, {3.788844053360984*^9, 3.788844071769227*^9}, { 3.8509675986277914`*^9, 3.850967600568553*^9}}, CellLabel-> "In[426]:=",ExpressionUUID->"d9790db1-861d-4fdc-8ede-6b8a7af687df"] }, Closed]], Cell[CellGroupData[{ Cell["Home assignment 2 (beam)", "Subsubsection", CellChangeTimes->{ 3.495088447506*^9, {3.495153177701*^9, 3.4951531894166*^9}, 3.558946122925826*^9, {3.692965302131263*^9, 3.692965317401284*^9}, { 3.6931188811951785`*^9, 3.6931188813051786`*^9}, {3.6931379329206047`*^9, 3.693137933030605*^9}, 3.7250245231314993`*^9, {3.7567995655612087`*^9, 3.756799571966011*^9}, {3.788840101401081*^9, 3.788840103479334*^9}},ExpressionUUID->"9ce68ed8-8d13-4807-83a1-\ b744bea5dd4a"], Cell[BoxData[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Rho]"}], " ", "A", " ", "g"}], ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], "}"}]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "\[Rho]"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}]}], "Input", CellChangeTimes->{{3.495088465875*^9, 3.495088486899*^9}, { 3.4950995009309998`*^9, 3.4950995016879997`*^9}, {3.495099819053*^9, 3.4950998310769997`*^9}, {3.4951004772609997`*^9, 3.495100482592*^9}, 3.4951534205774*^9, {3.4951664440478*^9, 3.4951664463722*^9}, { 3.6930154709945107`*^9, 3.693015620124719*^9}, {3.6930158215750012`*^9, 3.693015826975009*^9}, {3.6930158923661003`*^9, 3.693015945397175*^9}, { 3.693016038087304*^9, 3.6930160810173645`*^9}, {3.693016118977418*^9, 3.6930161267674284`*^9}, {3.6930164434978724`*^9, 3.6930164831779275`*^9}, {3.6930168959426355`*^9, 3.693016943842702*^9}, { 3.6930170211728106`*^9, 3.6930170221728115`*^9}, {3.6930176493256903`*^9, 3.693017670245719*^9}, {3.693017801865904*^9, 3.6930178264559383`*^9}, { 3.693018008816193*^9, 3.6930180566662602`*^9}, {3.693018115636343*^9, 3.693018129476362*^9}, {3.69301832058663*^9, 3.693018424926776*^9}, { 3.693018546686946*^9, 3.6930185536569557`*^9}, {3.6930185926270103`*^9, 3.6930186247670555`*^9}, {3.6930188500773706`*^9, 3.693018865057392*^9}, { 3.6930189745895452`*^9, 3.6930189769895487`*^9}, {3.6930192574799414`*^9, 3.6930192579099417`*^9}, {3.693019392680131*^9, 3.693019394440133*^9}, { 3.6930578337843657`*^9, 3.693057906174467*^9}, {3.6930579909745865`*^9, 3.6930579918445873`*^9}, {3.6930580481846666`*^9, 3.693058052384672*^9}, { 3.693058089464724*^9, 3.6930580925547285`*^9}, {3.693058215804901*^9, 3.6930582164549017`*^9}, {3.6931379460006227`*^9, 3.6931380135417175`*^9}, 3.693138069661796*^9, {3.693138284313097*^9, 3.69313831553314*^9}, { 3.6932961835350847`*^9, 3.6932962439151697`*^9}, {3.6932962790552187`*^9, 3.6932962897252336`*^9}, {3.6933811840760784`*^9, 3.6933811866760817`*^9}, {3.725024574725236*^9, 3.725024588839964*^9}, { 3.756795212116538*^9, 3.7567952132725544`*^9}, {3.7888401120623245`*^9, 3.788840168934473*^9}}, CellLabel-> "In[431]:=",ExpressionUUID->"9f943fd8-f8df-47b5-b5e3-8580e365d2fc"] }, Closed]], Cell[CellGroupData[{ Cell["Home assignment 3a (plate)", "Subsubsection", CellChangeTimes->{ 3.495088447506*^9, {3.495153177701*^9, 3.4951531894166*^9}, 3.558946122925826*^9, {3.692965302131263*^9, 3.692965317401284*^9}, { 3.6931188811951785`*^9, 3.6931188813051786`*^9}, {3.6931379329206047`*^9, 3.693137933030605*^9}, {3.693138364413209*^9, 3.693138367713214*^9}, 3.6931934898815126`*^9, {3.6933707838353357`*^9, 3.6933707954953527`*^9}, { 3.69362388551801*^9, 3.693623887178013*^9}, {3.7250256670291777`*^9, 3.7250257058821273`*^9}, {3.7567983913186817`*^9, 3.7567983923028216`*^9}, {3.7567988730240245`*^9, 3.7567988734926634`*^9}, {3.788748105249518*^9, 3.7887481164935627`*^9}, 3.7891831869749146`*^9},ExpressionUUID->"5a922c3d-9c7f-490c-b437-\ 35b4af900a7e"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"use", " ", "the", " ", "building", " ", "blocks"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Block", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"w", "=", RowBox[{ RowBox[{"a", "[", "0", "]"}], SuperscriptBox[ RowBox[{"(", " ", RowBox[{"x", "/", "L"}], " ", ")"}], "2"]}]}], " ", ",", "\[Delta]wint", ",", "\[Delta]wsta", ",", "\[CapitalOmega]", ",", "\[Delta]W"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wint", ":=", RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", " ", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["t", "3"], " ", "\[CapitalEpsilon]"}], RowBox[{"12", RowBox[{"(", RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}], ")"}]}]], RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "\[Nu]", "0"}, {"\[Nu]", "1", "0"}, {"0", "0", FractionBox[ RowBox[{"1", "-", "\[Nu]"}], "2"]} }], "\[NoBreak]", ")"}]}], ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wsta", ":=", RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"-", "p"}], "0"}, {"0", "0"} }], "\[NoBreak]", ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}]} }], "\[NoBreak]", ")"}]}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", "=", RowBox[{"Rectangle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"L", ",", "H"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "=", RowBox[{"Integrate", "[", RowBox[{ RowBox[{"\[Delta]wint", "+", "\[Delta]wsta"}], ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], StyleBox["\[Element]", "OperatorCharacter"], StyleBox["\[CapitalOmega]", "OperatorCharacter"]}], StyleBox[",", "OperatorCharacter"], StyleBox[ RowBox[{"Assumptions", "->", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"H", ">", "0"}]}]}], "OperatorCharacter"]}], StyleBox["]", "OperatorCharacter"]}]}], StyleBox[";", "OperatorCharacter"], StyleBox["\[IndentingNewLine]", "OperatorCharacter"], StyleBox["\[IndentingNewLine]", "OperatorCharacter"], RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", "\[Delta]W"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "p"}], "}"}], ",", "\[Delta]W"}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}]}]}], "]"}]}]], "Input", CellChangeTimes->{{3.495088465875*^9, 3.495088486899*^9}, { 3.4950995009309998`*^9, 3.4950995016879997`*^9}, {3.495099819053*^9, 3.4950998310769997`*^9}, {3.4951004772609997`*^9, 3.495100482592*^9}, 3.4951534205774*^9, {3.4951664440478*^9, 3.4951664463722*^9}, { 3.6930154709945107`*^9, 3.693015620124719*^9}, {3.6930158215750012`*^9, 3.693015826975009*^9}, {3.6930158923661003`*^9, 3.693015945397175*^9}, { 3.693016038087304*^9, 3.6930160810173645`*^9}, {3.693016118977418*^9, 3.6930161267674284`*^9}, {3.6930164434978724`*^9, 3.6930164831779275`*^9}, {3.6930168959426355`*^9, 3.693016943842702*^9}, { 3.6930170211728106`*^9, 3.6930170221728115`*^9}, {3.6930176493256903`*^9, 3.693017670245719*^9}, {3.693017801865904*^9, 3.6930178264559383`*^9}, { 3.693018008816193*^9, 3.6930180566662602`*^9}, {3.693018115636343*^9, 3.693018129476362*^9}, {3.69301832058663*^9, 3.693018424926776*^9}, { 3.693018546686946*^9, 3.6930185536569557`*^9}, {3.6930185926270103`*^9, 3.6930186247670555`*^9}, {3.6930188500773706`*^9, 3.693018865057392*^9}, { 3.6930189745895452`*^9, 3.6930189769895487`*^9}, {3.6930192574799414`*^9, 3.6930192579099417`*^9}, {3.693019392680131*^9, 3.693019394440133*^9}, { 3.6930578337843657`*^9, 3.693057906174467*^9}, {3.6930579909745865`*^9, 3.6930579918445873`*^9}, {3.6930580481846666`*^9, 3.693058052384672*^9}, { 3.693058089464724*^9, 3.6930580925547285`*^9}, {3.693058215804901*^9, 3.6930582164549017`*^9}, {3.6931379460006227`*^9, 3.6931380135417175`*^9}, 3.693138069661796*^9, {3.693138284313097*^9, 3.69313831553314*^9}, { 3.6931384072632685`*^9, 3.693138464483349*^9}, 3.6931385504534693`*^9, { 3.693139539130171*^9, 3.6931395422501755`*^9}, {3.6931407590133796`*^9, 3.6931407900734234`*^9}, {3.69314082374347*^9, 3.6931408243334713`*^9}, { 3.693141231804042*^9, 3.693141239914053*^9}, 3.6931418049058437`*^9, { 3.693370814495379*^9, 3.6933710347856874`*^9}, {3.6933710912757664`*^9, 3.6933712196459465`*^9}, {3.693371517086363*^9, 3.6933715226363707`*^9}, { 3.6933746737607822`*^9, 3.693374840391015*^9}, {3.6933750748613434`*^9, 3.693375094561371*^9}, {3.6933751349114275`*^9, 3.6933751375414314`*^9}, { 3.693375277291627*^9, 3.6933752833316355`*^9}, {3.6933816414087186`*^9, 3.693381657478741*^9}, {3.693623898148028*^9, 3.6936240857282906`*^9}, { 3.6936241755384164`*^9, 3.693624186658432*^9}, {3.6936242236884837`*^9, 3.6936242455985146`*^9}, {3.693624308838603*^9, 3.6936243276586294`*^9}, { 3.6936243601386747`*^9, 3.693624369098687*^9}, {3.6936244076487412`*^9, 3.6936244551088076`*^9}, {3.693624537678923*^9, 3.6936245600289545`*^9}, 3.6936246237090435`*^9, {3.6936248231593227`*^9, 3.6936248490093594`*^9}, { 3.6936249813995447`*^9, 3.6936249911795583`*^9}, {3.693625250289921*^9, 3.693625251009922*^9}, 3.7250279951942205`*^9, {3.7250284810413065`*^9, 3.725028490580618*^9}, {3.7567983982076926`*^9, 3.7567984239828525`*^9}, { 3.7887481273800044`*^9, 3.788748215523306*^9}, {3.788748413175475*^9, 3.7887484423859124`*^9}, {3.7887485191144743`*^9, 3.7887486497810545`*^9}, {3.788748687254717*^9, 3.7887489614574223`*^9}, { 3.788748991789321*^9, 3.78874899810791*^9}, {3.7887490376198225`*^9, 3.7887491341764884`*^9}, {3.78874917431256*^9, 3.7887491787653856`*^9}, { 3.788749332203596*^9, 3.788749333422468*^9}, {3.7887495187401657`*^9, 3.788749518947988*^9}, {3.7887496202302227`*^9, 3.788749714698633*^9}, { 3.7887497461152906`*^9, 3.7887498407885494`*^9}, {3.788749893111492*^9, 3.7887500238561907`*^9}, {3.788750111184518*^9, 3.7887502130101995`*^9}, { 3.788750264719532*^9, 3.788750294322283*^9}, {3.788750325600979*^9, 3.788750332029645*^9}, {3.7887508516476316`*^9, 3.788750859206896*^9}, 3.7887509041484995`*^9, {3.7887509404866304`*^9, 3.7887509949082747`*^9}, { 3.788751123863784*^9, 3.7887511282999883`*^9}, 3.788751244897051*^9, { 3.788752133868101*^9, 3.7887522058274875`*^9}, {3.788752250488551*^9, 3.788752263391296*^9}, {3.788783436306548*^9, 3.7887834370208373`*^9}, { 3.7887835317770376`*^9, 3.788783536185897*^9}, 3.7888304361161485`*^9, { 3.7888305028927526`*^9, 3.788830652045955*^9}, {3.7888307180920086`*^9, 3.7888307825148835`*^9}, {3.788830877589118*^9, 3.7888310509498787`*^9}, { 3.7888310857014413`*^9, 3.788831095283891*^9}, {3.788831424648365*^9, 3.7888314269779997`*^9}, {3.7888316708814416`*^9, 3.7888317083030467`*^9}, {3.788831746673021*^9, 3.788831782064163*^9}, 3.7888319386906347`*^9, {3.788831982079364*^9, 3.7888320273484716`*^9}, { 3.788832096707038*^9, 3.788832115036332*^9}, {3.7888321459251814`*^9, 3.788832223572315*^9}, {3.7888323588598866`*^9, 3.788832383013463*^9}, { 3.788832456010735*^9, 3.7888324760643673`*^9}, {3.7888325387804146`*^9, 3.7888325873274*^9}, {3.788838267786459*^9, 3.788838268161379*^9}, { 3.788838459288808*^9, 3.78883856690706*^9}, {3.7888386181373606`*^9, 3.788838618418537*^9}, {3.789183340270694*^9, 3.7891833597626085`*^9}, { 3.78918339686213*^9, 3.789183397965809*^9}, {3.789292599980801*^9, 3.789292603534729*^9}, {3.8210045932980566`*^9, 3.8210045972144156`*^9}, { 3.821004634135273*^9, 3.8210046864976444`*^9}, {3.8210047390708046`*^9, 3.8210047400171223`*^9}, {3.8509676731783075`*^9, 3.850967750562674*^9}}, CellLabel-> "In[436]:=",ExpressionUUID->"b19c9cce-e3bc-4ab3-b065-c0d2719404be"] }, Closed]], Cell[CellGroupData[{ Cell["Home assignment 3b (plate)", "Subsubsection", CellChangeTimes->{ 3.495088447506*^9, {3.495153177701*^9, 3.4951531894166*^9}, 3.558946122925826*^9, {3.692965302131263*^9, 3.692965317401284*^9}, { 3.6931188811951785`*^9, 3.6931188813051786`*^9}, {3.6931379329206047`*^9, 3.693137933030605*^9}, {3.693138364413209*^9, 3.693138367713214*^9}, 3.6931934898815126`*^9, {3.6933707838353357`*^9, 3.6933707954953527`*^9}, { 3.69362388551801*^9, 3.693623887178013*^9}, {3.7250256670291777`*^9, 3.7250257058821273`*^9}, {3.7567983913186817`*^9, 3.7567983923028216`*^9}, {3.7567988730240245`*^9, 3.7567988734926634`*^9}, {3.788748105249518*^9, 3.7887481164935627`*^9}, 3.7891831869749146`*^9, 3.8210045757349916`*^9},ExpressionUUID->"b27c0df3-7c21-4260-8763-\ 72ad9a48c96c"], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{"use", " ", "the", " ", "building", " ", "blocks"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Block", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"u", "=", RowBox[{ RowBox[{"a", "[", "1", "]"}], RowBox[{"(", RowBox[{"x", "/", "L"}], " ", ")"}]}]}], ",", " ", RowBox[{"v", "=", "0"}], ",", RowBox[{"w", "=", RowBox[{ RowBox[{"a", "[", "0", "]"}], SuperscriptBox[ RowBox[{"(", " ", RowBox[{"x", "/", "L"}], " ", ")"}], "2"]}]}], " ", ",", "Nxx", ",", "Nyy", ",", "Nxy", ",", "Mxx", ",", "Myy", ",", "Mxy", ",", "\[Delta]wint", ",", "\[Delta]wsta", ",", "\[Delta]wext", ",", "\[CapitalOmega]", ",", "\[CapitalGamma]", ",", "\[Delta]W"}], "}"}], ",", "\n", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"Nxx", ",", "Nyy", ",", "Nxy"}], "}"}], "=", RowBox[{"Flatten", "[", RowBox[{ FractionBox[ RowBox[{"t", " ", "\[CapitalEpsilon]"}], RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}]], RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "\[Nu]", "0"}, {"\[Nu]", "1", "0"}, {"0", "0", FractionBox[ RowBox[{"1", "-", "\[Nu]"}], "2"]} }], "\[NoBreak]", ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}]}, { RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], "+", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}]}]} }], "\[NoBreak]", ")"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"Mxx", ",", "Myy", ",", "Mxy"}], "}"}], "=", RowBox[{"Flatten", "[", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["t", "3"], " ", "\[CapitalEpsilon]"}], RowBox[{"12", RowBox[{"(", RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}], ")"}]}]], RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "\[Nu]", "0"}, {"\[Nu]", "1", "0"}, {"0", "0", FractionBox[ RowBox[{"1", "-", "\[Nu]"}], "2"]} }], "\[NoBreak]", ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", ":=", RowBox[{ RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"Mxx"}, {"Myy"}, {"Mxy"} }], "\[NoBreak]", ")"}]}], "]"}]}], "-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "u"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "v"}]}, { RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "v"}], "+", RowBox[{ SubscriptBox["\[PartialD]", "y"], "u"}]}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"Nxx"}, {"Nyy"}, {"Nxy"} }], "\[NoBreak]", ")"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wsta", ":=", RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"Nxx", "Nxy"}, {"Nxy", "Nyy"} }], "\[NoBreak]", ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", "x"], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", "y"], "w"}]} }], "\[NoBreak]", ")"}]}], "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", ":=", RowBox[{"Tr", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"(", "\[NoBreak]", GridBox[{ {"u"}, {"v"} }], "\[NoBreak]", ")"}], "]"}], "\[Transpose]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"-", "p"}]}, {"0"} }], "\[NoBreak]", ")"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", "=", RowBox[{"Rectangle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"L", ",", "H"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalGamma]", "=", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"L", ",", "H"}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "=", RowBox[{ RowBox[{"Integrate", "[", RowBox[{ RowBox[{"\[Delta]wint", "+", "\[Delta]wsta"}], ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], StyleBox["\[Element]", "OperatorCharacter"], StyleBox["\[CapitalOmega]", "OperatorCharacter"]}], StyleBox[",", "OperatorCharacter"], StyleBox[ RowBox[{"Assumptions", "->", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"H", ">", "0"}]}]}], "OperatorCharacter"]}], StyleBox["]", "OperatorCharacter"]}], StyleBox["+", "OperatorCharacter"], StyleBox[ RowBox[{"Integrate", "[", RowBox[{"\[Delta]wext", " ", ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], "\[Element]", "\[CapitalGamma]"}], ",", RowBox[{"Assumptions", "->", RowBox[{"H", ">", "0"}]}]}], "]"}], "OperatorCharacter"]}]}], StyleBox[";", "OperatorCharacter"], StyleBox["\[IndentingNewLine]", "OperatorCharacter"], StyleBox["\[IndentingNewLine]", "OperatorCharacter"], RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", "\[Delta]W"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "p"}], "}"}], ",", "\[Delta]W"}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}]}]}], "]"}]}]], "Input", CellChangeTimes->{{3.495088465875*^9, 3.495088486899*^9}, { 3.4950995009309998`*^9, 3.4950995016879997`*^9}, {3.495099819053*^9, 3.4950998310769997`*^9}, {3.4951004772609997`*^9, 3.495100482592*^9}, 3.4951534205774*^9, {3.4951664440478*^9, 3.4951664463722*^9}, { 3.6930154709945107`*^9, 3.693015620124719*^9}, {3.6930158215750012`*^9, 3.693015826975009*^9}, {3.6930158923661003`*^9, 3.693015945397175*^9}, { 3.693016038087304*^9, 3.6930160810173645`*^9}, {3.693016118977418*^9, 3.6930161267674284`*^9}, {3.6930164434978724`*^9, 3.6930164831779275`*^9}, {3.6930168959426355`*^9, 3.693016943842702*^9}, { 3.6930170211728106`*^9, 3.6930170221728115`*^9}, {3.6930176493256903`*^9, 3.693017670245719*^9}, {3.693017801865904*^9, 3.6930178264559383`*^9}, { 3.693018008816193*^9, 3.6930180566662602`*^9}, {3.693018115636343*^9, 3.693018129476362*^9}, {3.69301832058663*^9, 3.693018424926776*^9}, { 3.693018546686946*^9, 3.6930185536569557`*^9}, {3.6930185926270103`*^9, 3.6930186247670555`*^9}, {3.6930188500773706`*^9, 3.693018865057392*^9}, { 3.6930189745895452`*^9, 3.6930189769895487`*^9}, {3.6930192574799414`*^9, 3.6930192579099417`*^9}, {3.693019392680131*^9, 3.693019394440133*^9}, { 3.6930578337843657`*^9, 3.693057906174467*^9}, {3.6930579909745865`*^9, 3.6930579918445873`*^9}, {3.6930580481846666`*^9, 3.693058052384672*^9}, { 3.693058089464724*^9, 3.6930580925547285`*^9}, {3.693058215804901*^9, 3.6930582164549017`*^9}, {3.6931379460006227`*^9, 3.6931380135417175`*^9}, 3.693138069661796*^9, {3.693138284313097*^9, 3.69313831553314*^9}, { 3.6931384072632685`*^9, 3.693138464483349*^9}, 3.6931385504534693`*^9, { 3.693139539130171*^9, 3.6931395422501755`*^9}, {3.6931407590133796`*^9, 3.6931407900734234`*^9}, {3.69314082374347*^9, 3.6931408243334713`*^9}, { 3.693141231804042*^9, 3.693141239914053*^9}, 3.6931418049058437`*^9, { 3.693370814495379*^9, 3.6933710347856874`*^9}, {3.6933710912757664`*^9, 3.6933712196459465`*^9}, {3.693371517086363*^9, 3.6933715226363707`*^9}, { 3.6933746737607822`*^9, 3.693374840391015*^9}, {3.6933750748613434`*^9, 3.693375094561371*^9}, {3.6933751349114275`*^9, 3.6933751375414314`*^9}, { 3.693375277291627*^9, 3.6933752833316355`*^9}, {3.6933816414087186`*^9, 3.693381657478741*^9}, {3.693623898148028*^9, 3.6936240857282906`*^9}, { 3.6936241755384164`*^9, 3.693624186658432*^9}, {3.6936242236884837`*^9, 3.6936242455985146`*^9}, {3.693624308838603*^9, 3.6936243276586294`*^9}, { 3.6936243601386747`*^9, 3.693624369098687*^9}, {3.6936244076487412`*^9, 3.6936244551088076`*^9}, {3.693624537678923*^9, 3.6936245600289545`*^9}, 3.6936246237090435`*^9, {3.6936248231593227`*^9, 3.6936248490093594`*^9}, { 3.6936249813995447`*^9, 3.6936249911795583`*^9}, {3.693625250289921*^9, 3.693625251009922*^9}, 3.7250279951942205`*^9, {3.7250284810413065`*^9, 3.725028490580618*^9}, {3.7567983982076926`*^9, 3.7567984239828525`*^9}, { 3.7887481273800044`*^9, 3.788748215523306*^9}, {3.788748413175475*^9, 3.7887484423859124`*^9}, {3.7887485191144743`*^9, 3.7887486497810545`*^9}, {3.788748687254717*^9, 3.7887489614574223`*^9}, { 3.788748991789321*^9, 3.78874899810791*^9}, {3.7887490376198225`*^9, 3.7887491341764884`*^9}, {3.78874917431256*^9, 3.7887491787653856`*^9}, { 3.788749332203596*^9, 3.788749333422468*^9}, {3.7887495187401657`*^9, 3.788749518947988*^9}, {3.7887496202302227`*^9, 3.788749714698633*^9}, { 3.7887497461152906`*^9, 3.7887498407885494`*^9}, {3.788749893111492*^9, 3.7887500238561907`*^9}, {3.788750111184518*^9, 3.7887502130101995`*^9}, { 3.788750264719532*^9, 3.788750294322283*^9}, {3.788750325600979*^9, 3.788750332029645*^9}, {3.7887508516476316`*^9, 3.788750859206896*^9}, 3.7887509041484995`*^9, {3.7887509404866304`*^9, 3.7887509949082747`*^9}, { 3.788751123863784*^9, 3.7887511282999883`*^9}, 3.788751244897051*^9, { 3.788752133868101*^9, 3.7887522058274875`*^9}, {3.788752250488551*^9, 3.788752263391296*^9}, {3.788783436306548*^9, 3.7887834370208373`*^9}, { 3.7887835317770376`*^9, 3.788783536185897*^9}, 3.7888304361161485`*^9, { 3.7888305028927526`*^9, 3.788830652045955*^9}, {3.7888307180920086`*^9, 3.7888307825148835`*^9}, {3.788830877589118*^9, 3.7888310509498787`*^9}, { 3.7888310857014413`*^9, 3.788831095283891*^9}, {3.788831424648365*^9, 3.7888314269779997`*^9}, {3.7888316708814416`*^9, 3.7888317083030467`*^9}, {3.788831746673021*^9, 3.788831782064163*^9}, 3.7888319386906347`*^9, {3.788831982079364*^9, 3.7888320273484716`*^9}, { 3.788832096707038*^9, 3.788832115036332*^9}, {3.7888321459251814`*^9, 3.788832223572315*^9}, {3.7888323588598866`*^9, 3.788832383013463*^9}, { 3.788832456010735*^9, 3.7888324760643673`*^9}, {3.7888325387804146`*^9, 3.7888325873274*^9}, {3.788838267786459*^9, 3.788838268161379*^9}, { 3.788838459288808*^9, 3.78883856690706*^9}, {3.7888386181373606`*^9, 3.788838618418537*^9}, {3.789183340270694*^9, 3.7891833597626085`*^9}, { 3.78918339686213*^9, 3.789183397965809*^9}, {3.789292599980801*^9, 3.789292603534729*^9}, {3.8210048275148125`*^9, 3.8210048289863663`*^9}, { 3.821004880937112*^9, 3.821004916999135*^9}, {3.821004956835596*^9, 3.821004958617885*^9}, {3.8210050188944173`*^9, 3.821005022253108*^9}, { 3.8210050574197173`*^9, 3.8210051554046335`*^9}, {3.821005192513445*^9, 3.821005212994562*^9}, {3.821005250295355*^9, 3.821005276846246*^9}, { 3.821005307393458*^9, 3.8210054940520124`*^9}, {3.8210055542551365`*^9, 3.821005578232196*^9}, {3.8210056288097687`*^9, 3.821005687149138*^9}, { 3.821005752261304*^9, 3.8210057747204976`*^9}, {3.821005808015217*^9, 3.8210058204076123`*^9}, 3.8210058571785417`*^9, {3.8210059347144084`*^9, 3.8210060005564404`*^9}, {3.8210061543710423`*^9, 3.821006264566473*^9}, { 3.8210062987426324`*^9, 3.821006329464186*^9}, {3.8509677989255586`*^9, 3.850967922006175*^9}}, CellLabel->"In[88]:=",ExpressionUUID->"856964ac-d9a6-46d7-8f04-3b3c029c3b53"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture assignment 1 (beam)", "Subsubsection", CellChangeTimes->{ 3.495088447506*^9, {3.495153177701*^9, 3.4951531894166*^9}, 3.558946122925826*^9, {3.692965302131263*^9, 3.692965317401284*^9}, { 3.6931188811951785`*^9, 3.6931188813051786`*^9}, 3.6931363637484083`*^9, 3.693190210631563*^9, {3.7250240785764503`*^9, 3.725024106360828*^9}, { 3.7250241751824183`*^9, 3.725024175334324*^9}, {3.7567997363805785`*^9, 3.7567997408170395`*^9}},ExpressionUUID->"aaf3364e-7f43-4c24-a587-\ cd8a3f671168"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "F"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "F"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}]}], "Input", CellChangeTimes->{{3.495088465875*^9, 3.495088486899*^9}, { 3.4950995009309998`*^9, 3.4950995016879997`*^9}, {3.495099819053*^9, 3.4950998310769997`*^9}, {3.4951004772609997`*^9, 3.495100482592*^9}, 3.4951534205774*^9, {3.4951664440478*^9, 3.4951664463722*^9}, { 3.6930154709945107`*^9, 3.693015620124719*^9}, {3.6930158215750012`*^9, 3.693015826975009*^9}, {3.6930158923661003`*^9, 3.693015945397175*^9}, { 3.693016038087304*^9, 3.6930160810173645`*^9}, {3.693016118977418*^9, 3.6930161267674284`*^9}, {3.6930164434978724`*^9, 3.6930164831779275`*^9}, {3.6930168959426355`*^9, 3.693016943842702*^9}, { 3.6930170211728106`*^9, 3.6930170221728115`*^9}, {3.6930176493256903`*^9, 3.693017670245719*^9}, {3.693017801865904*^9, 3.6930178264559383`*^9}, { 3.693018008816193*^9, 3.6930180566662602`*^9}, {3.693018115636343*^9, 3.693018129476362*^9}, {3.69301832058663*^9, 3.693018424926776*^9}, { 3.693018546686946*^9, 3.6930185536569557`*^9}, {3.6930185926270103`*^9, 3.6930186247670555`*^9}, {3.6930188500773706`*^9, 3.693018865057392*^9}, { 3.6930189745895452`*^9, 3.6930189769895487`*^9}, {3.6930192574799414`*^9, 3.6930192579099417`*^9}, {3.693019392680131*^9, 3.693019394440133*^9}, { 3.6930578337843657`*^9, 3.693057906174467*^9}, {3.6930579909745865`*^9, 3.6930579918445873`*^9}, {3.6930580481846666`*^9, 3.693058052384672*^9}, { 3.693058089464724*^9, 3.6930580925547285`*^9}, {3.693058215804901*^9, 3.6930582164549017`*^9}, 3.693136371008418*^9, {3.693190222241579*^9, 3.693190243191609*^9}, {3.6931902881216717`*^9, 3.693190295981683*^9}, 3.693190659322191*^9, {3.6931907050422554`*^9, 3.6931907075822587`*^9}, { 3.693190781282362*^9, 3.69319078689237*^9}, {3.693191377313196*^9, 3.693191381893203*^9}, {3.693191416663252*^9, 3.693191421643258*^9}, { 3.693191600493509*^9, 3.693191606243517*^9}, {3.6931920988862066`*^9, 3.6931921222862396`*^9}, {3.6933810050758276`*^9, 3.6933810224858522`*^9}, {3.6953566059258137`*^9, 3.6953566365958567`*^9}, 3.6953567310559893`*^9, {3.725024159454912*^9, 3.7250241609315004`*^9}, { 3.756799750939721*^9, 3.7567997691073275`*^9}, {3.788849300089596*^9, 3.7888493641716824`*^9}, {3.7888494139346*^9, 3.7888494286062584`*^9}, { 3.8509679745270205`*^9, 3.850967976044734*^9}}, CellLabel->"In[89]:=",ExpressionUUID->"0cb582ab-e411-412c-a48d-f3f4c00e2d23"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture assignment 2 (beam)", "Subsubsection", CellChangeTimes->{ 3.495088447506*^9, {3.495153177701*^9, 3.4951531894166*^9}, 3.558946122925826*^9, {3.692965302131263*^9, 3.692965317401284*^9}, { 3.6931188811951785`*^9, 3.6931188813051786`*^9}, 3.6931363637484083`*^9, 3.693190210631563*^9, {3.7250240785764503`*^9, 3.725024106360828*^9}, { 3.7250241751824183`*^9, 3.725024175334324*^9}, {3.7567997363805785`*^9, 3.7567997408170395`*^9}, 3.7567998127065244`*^9},ExpressionUUID->"661e0cab-663c-44e0-b4e6-\ e0cfee622745"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"(*", RowBox[{"NOTICE", ":", " ", RowBox[{ "the", " ", "outcome", " ", "of", " ", "the", " ", "hand", " ", "calculation", " ", RowBox[{"(", RowBox[{"analytical", " ", "solution"}], ")"}], " ", "and", " ", "the", " ", "one", " ", "by", " ", "the", " ", "code", " ", RowBox[{"(", RowBox[{"numerical", " ", "solution"}], ")"}], " ", "differ", " ", "due", " ", "to", " ", "discretization", " ", RowBox[{"error", ".", "\[IndentingNewLine]", "The"}], " ", "solution", " ", "by", " ", "FEM", " ", "converges", " ", "to", " ", "the", " ", "analytical", " ", "solution", " ", "when", " ", "the", " ", "mesh", " ", "is", " ", "refined"}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "G"}], "}"}], ",", RowBox[{"{", RowBox[{"A", ",", "\[CapitalIota]", ",", "\[CapitalIota]"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "4"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "p"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "1", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "2", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "3", "]"}], ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Theta]Y", "[", "4", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "STAB", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "p"}], "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], ",", RowBox[{"Alignment", "\[Rule]", "Left"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.495088465875*^9, 3.495088486899*^9}, { 3.4950995009309998`*^9, 3.4950995016879997`*^9}, {3.495099819053*^9, 3.4950998310769997`*^9}, {3.4951004772609997`*^9, 3.495100482592*^9}, 3.4951534205774*^9, {3.4951664440478*^9, 3.4951664463722*^9}, { 3.6930154709945107`*^9, 3.693015620124719*^9}, {3.6930158215750012`*^9, 3.693015826975009*^9}, {3.6930158923661003`*^9, 3.693015945397175*^9}, { 3.693016038087304*^9, 3.6930160810173645`*^9}, {3.693016118977418*^9, 3.6930161267674284`*^9}, {3.6930164434978724`*^9, 3.6930164831779275`*^9}, {3.6930168959426355`*^9, 3.693016943842702*^9}, { 3.6930170211728106`*^9, 3.6930170221728115`*^9}, {3.6930176493256903`*^9, 3.693017670245719*^9}, {3.693017801865904*^9, 3.6930178264559383`*^9}, { 3.693018008816193*^9, 3.6930180566662602`*^9}, {3.693018115636343*^9, 3.693018129476362*^9}, {3.69301832058663*^9, 3.693018424926776*^9}, { 3.693018546686946*^9, 3.6930185536569557`*^9}, {3.6930185926270103`*^9, 3.6930186247670555`*^9}, {3.6930188500773706`*^9, 3.693018865057392*^9}, { 3.6930189745895452`*^9, 3.6930189769895487`*^9}, {3.6930192574799414`*^9, 3.6930192579099417`*^9}, {3.693019392680131*^9, 3.693019394440133*^9}, { 3.6930578337843657`*^9, 3.693057906174467*^9}, {3.6930579909745865`*^9, 3.6930579918445873`*^9}, {3.6930580481846666`*^9, 3.693058052384672*^9}, { 3.693058089464724*^9, 3.6930580925547285`*^9}, {3.693058215804901*^9, 3.6930582164549017`*^9}, 3.693136371008418*^9, {3.693190222241579*^9, 3.693190243191609*^9}, {3.6931902881216717`*^9, 3.693190295981683*^9}, 3.693190659322191*^9, {3.6931907050422554`*^9, 3.6931907075822587`*^9}, { 3.693190781282362*^9, 3.69319078689237*^9}, {3.693191377313196*^9, 3.693191381893203*^9}, {3.693191416663252*^9, 3.693191421643258*^9}, { 3.693191600493509*^9, 3.693191606243517*^9}, {3.6931920988862066`*^9, 3.6931921222862396`*^9}, {3.6933810050758276`*^9, 3.6933810224858522`*^9}, {3.6953566059258137`*^9, 3.6953566365958567`*^9}, 3.6953567310559893`*^9, {3.725024159454912*^9, 3.7250241609315004`*^9}, { 3.756799750939721*^9, 3.7567997691073275`*^9}, {3.7567998612882752`*^9, 3.756799866162119*^9}, {3.756799899607374*^9, 3.756799904293829*^9}, { 3.7567999450186663`*^9, 3.756799956968975*^9}, 3.756800144331313*^9, { 3.756800239090415*^9, 3.7568002683648157`*^9}, {3.756800429170906*^9, 3.7568006426365423`*^9}, {3.85096799619191*^9, 3.85096800193428*^9}}, CellLabel->"In[94]:=",ExpressionUUID->"31e5238a-de2e-4251-a8cc-960a94ed5b84"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["NONLINEAR ANALYSIS (week 6)", "Subsection", CellChangeTimes->{{3.473055512584*^9, 3.4730555529630003`*^9}, { 3.4730575328269997`*^9, 3.473057539222*^9}, {3.4734691424642*^9, 3.4734691605758*^9}, {3.4736023142902*^9, 3.4736023273162003`*^9}, { 3.4742602258717394`*^9, 3.4742602349087396`*^9}, {3.4751533480335493`*^9, 3.4751533839809494`*^9}, {3.47515343117095*^9, 3.47515343786335*^9}, { 3.4758461893361397`*^9, 3.4758462006617393`*^9}, {3.4932790852218*^9, 3.493279095939*^9}, 3.4933062471764*^9, {3.4957658835755997`*^9, 3.4957658864927998`*^9}, {3.5566241871999807`*^9, 3.556624190959587*^9}, { 3.6228061501747093`*^9, 3.622806154790973*^9}, 3.693717161087909*^9, 3.753071247963187*^9, 3.7866746464915423`*^9, {3.789440471859059*^9, 3.7894404765124073`*^9}, {3.8530301289001417`*^9, 3.853030131242997*^9}},ExpressionUUID->"e6002408-5188-4cef-9615-\ f76049bb97ab"], Cell[CellGroupData[{ Cell["Lecture example 5.1 (truss)", "Subsubsection", CellChangeTimes->{ 3.560218382980301*^9, 3.62311554059295*^9, {3.6937172119879804`*^9, 3.6937172178979883`*^9}, {3.6937211383542433`*^9, 3.6937211426242495`*^9}, 3.693721197964327*^9, 3.6938966537217274`*^9, {3.694084104105713*^9, 3.694084119395734*^9}, 3.725367865956423*^9, 3.7254169957392054`*^9, 3.725619293450783*^9, 3.7894404895193176`*^9, 3.789440520087886*^9, { 3.8216137883682137`*^9, 3.8216138191786532`*^9}},ExpressionUUID->"f09943b2-64a5-4a87-9f1a-\ 40f684f91dbe"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"val", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"A", "->", "0.01"}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"F", "\[Rule]", "0.2"}], ",", RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"Pi", "/", "3"}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "F"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "L"}], " ", RowBox[{"Cos", "[", "\[Alpha]", "]"}]}], " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"L", " ", RowBox[{"Sin", "[", "\[Alpha]", "]"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"L", " ", RowBox[{"Cos", "[", "\[Alpha]", "]"}]}], " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", " ", "val"}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.4957897010062*^9, 3.4957898096446*^9}, { 3.4957898416870003`*^9, 3.4957898986426*^9}, {3.4957899396882*^9, 3.495789941841*^9}, {3.4957901948417997`*^9, 3.4957902000053997`*^9}, { 3.4957902785358*^9, 3.4957903351542*^9}, {3.4957903960098*^9, 3.4957904880708*^9}, {3.4957905206904*^9, 3.4957906521984*^9}, { 3.495791040888*^9, 3.4957911068136*^9}, {3.5007281090162*^9, 3.500728132467*^9}, {3.500728173828*^9, 3.5007282325972*^9}, { 3.56021839402512*^9, 3.560218396209124*^9}, {3.5602185052533154`*^9, 3.5602185542686014`*^9}, {3.5602185915994673`*^9, 3.5602185949222727`*^9}, {3.560218692750045*^9, 3.5602187145276833`*^9}, { 3.5602187506417465`*^9, 3.5602187818886013`*^9}, {3.5602188606999397`*^9, 3.560218873320362*^9}, {3.6937172406680202`*^9, 3.693717252648037*^9}, { 3.6937173212881336`*^9, 3.6937174206482725`*^9}, {3.693717572178485*^9, 3.6937175810284967`*^9}, {3.6937178570408835`*^9, 3.693717891700932*^9}, { 3.6937181376412764`*^9, 3.693718153091298*^9}, {3.693721075124155*^9, 3.6937210792641606`*^9}, {3.693721145474253*^9, 3.693721304004475*^9}, { 3.693721744775092*^9, 3.69372176445512*^9}, {3.6937217962751646`*^9, 3.693721800965171*^9}, 3.6937218775552783`*^9, {3.6937219143353295`*^9, 3.693721933395356*^9}, {3.693896663161741*^9, 3.6938966894117775`*^9}, 3.6938967300618343`*^9, {3.693896766931886*^9, 3.693896793821924*^9}, { 3.693896839311988*^9, 3.693896850372003*^9}, 3.7253679391831865`*^9, { 3.725416801610667*^9, 3.7254168037393713`*^9}, {3.725417020175501*^9, 3.725417208382349*^9}, {3.7254172395621457`*^9, 3.725417331171501*^9}, { 3.72541736659235*^9, 3.7254174053459697`*^9}, {3.7254175339924426`*^9, 3.7254175638615866`*^9}, {3.7254176054682207`*^9, 3.7254177051164927`*^9}, {3.7254177546826105`*^9, 3.72541776095835*^9}, { 3.7254178550580482`*^9, 3.725417924563362*^9}, {3.7254179949719176`*^9, 3.725418003642275*^9}, {3.725419046991951*^9, 3.7254190552133617`*^9}, { 3.7254194172303123`*^9, 3.72541944937505*^9}, {3.7254194818473325`*^9, 3.725419485387669*^9}, {3.7254195657537193`*^9, 3.725419650915449*^9}, { 3.725419711549879*^9, 3.7254197315678883`*^9}, {3.7254197742112017`*^9, 3.7254197805431004`*^9}, {3.725419829789277*^9, 3.725419874631874*^9}, 3.7254199087655344`*^9, {3.7255375940526752`*^9, 3.7255377029827466`*^9}, 3.7256193854673696`*^9, 3.725702820357547*^9, {3.7257028545765643`*^9, 3.7257028650282364`*^9}, {3.756832416999443*^9, 3.756832462271259*^9}, { 3.789440802913806*^9, 3.789440809277025*^9}, 3.7894411773565855`*^9, { 3.821615147466235*^9, 3.821615153888829*^9}, {3.821620611340539*^9, 3.821620645941663*^9}, {3.852693575912036*^9, 3.8526935802020254`*^9}, { 3.852693867597412*^9, 3.852693881304184*^9}, {3.8530309367110014`*^9, 3.8530310058199167`*^9}, 3.853031080312402*^9, {3.853031119109433*^9, 3.853031143011203*^9}, {3.853031199178816*^9, 3.85303120695147*^9}}, CellLabel-> "In[408]:=",ExpressionUUID->"9d5ce7fe-55d7-4e9c-8b53-0557bb9655e6"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 5.2 (truss)", "Subsubsection", CellChangeTimes->{ 3.560218382980301*^9, 3.62311554059295*^9, {3.6937172119879804`*^9, 3.6937172178979883`*^9}, {3.6937211383542433`*^9, 3.6937211426242495`*^9}, 3.693721197964327*^9, 3.693722041065507*^9, 3.6938968649020233`*^9, 3.6940841249057417`*^9, 3.725368143386225*^9, 3.7254227249314785`*^9, { 3.725619397031089*^9, 3.725619400828313*^9}, 3.78944049266901*^9, 3.789440522746374*^9, {3.821613791241439*^9, 3.82161379143657*^9}, 3.8216138269048543`*^9},ExpressionUUID->"1181fa58-bb92-4bed-b6d2-\ 6046802d2e9f"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"val", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"A", "->", "0.01"}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"F", "->", "0.05"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", " "}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "1"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"4", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "F"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", " ", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "3", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"sol", "=", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "/.", "val"}]}], "]"}]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"DISP", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "/.", "val"}], " ", "/.", "sol"}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4957897010062*^9, 3.4957898096446*^9}, { 3.4957898416870003`*^9, 3.4957898986426*^9}, {3.4957899396882*^9, 3.495789941841*^9}, {3.4957901948417997`*^9, 3.4957902000053997`*^9}, { 3.4957902785358*^9, 3.4957903351542*^9}, {3.4957903960098*^9, 3.4957904880708*^9}, {3.4957905206904*^9, 3.4957906521984*^9}, { 3.495791040888*^9, 3.4957911068136*^9}, {3.5007281090162*^9, 3.500728132467*^9}, {3.500728173828*^9, 3.5007282325972*^9}, { 3.56021839402512*^9, 3.560218396209124*^9}, {3.5602185052533154`*^9, 3.5602185542686014`*^9}, {3.5602185915994673`*^9, 3.5602185949222727`*^9}, {3.560218692750045*^9, 3.5602187145276833`*^9}, { 3.5602187506417465`*^9, 3.5602187818886013`*^9}, {3.5602188606999397`*^9, 3.560218873320362*^9}, {3.6937172406680202`*^9, 3.693717252648037*^9}, { 3.6937173212881336`*^9, 3.6937174206482725`*^9}, {3.693717572178485*^9, 3.6937175810284967`*^9}, {3.6937178570408835`*^9, 3.693717891700932*^9}, { 3.6937181376412764`*^9, 3.693718153091298*^9}, {3.693721075124155*^9, 3.6937210792641606`*^9}, {3.693721145474253*^9, 3.693721304004475*^9}, { 3.693721744775092*^9, 3.69372176445512*^9}, {3.6937217962751646`*^9, 3.693721800965171*^9}, 3.6937218775552783`*^9, {3.6937219143353295`*^9, 3.693721933395356*^9}, {3.693722084405568*^9, 3.6937222760578365`*^9}, 3.6937223222279005`*^9, 3.693722372317971*^9, {3.693722442468069*^9, 3.693722451698082*^9}, {3.693723787907967*^9, 3.6937237904979706`*^9}, { 3.6937241372284565`*^9, 3.693724139258459*^9}, {3.693724172548506*^9, 3.6937241752985096`*^9}, {3.693724292058673*^9, 3.6937242951286774`*^9}, 3.6937375511385093`*^9, {3.693896878692043*^9, 3.693896901652075*^9}, { 3.7253681563091784`*^9, 3.725368157559586*^9}, {3.72542273277819*^9, 3.725422854026498*^9}, {3.725422885282486*^9, 3.7254228865161843`*^9}, { 3.725422942650051*^9, 3.725423062788546*^9}, 3.725423150321371*^9, { 3.7254316686112423`*^9, 3.7254316747812223`*^9}, {3.725538838588361*^9, 3.725538851246591*^9}, 3.72561943608208*^9, {3.7257026059808226`*^9, 3.72570261040317*^9}, {3.725702644912425*^9, 3.7257026487253065`*^9}, { 3.7257027965211077`*^9, 3.725702797865259*^9}, {3.72575626980612*^9, 3.725756351318025*^9}, {3.725756456625953*^9, 3.725756477189308*^9}, { 3.7257565440976725`*^9, 3.725756583186432*^9}, {3.7257566457338176`*^9, 3.7257567431369677`*^9}, {3.725756778112492*^9, 3.725756778494486*^9}, { 3.725761648915716*^9, 3.7257617139225607`*^9}, {3.725765194189823*^9, 3.7257652065034933`*^9}, {3.7257652623736453`*^9, 3.7257652896111813`*^9}, {3.725765341710131*^9, 3.725765462395775*^9}, { 3.7257698694622154`*^9, 3.7257699169022665`*^9}, {3.7894412582865925`*^9, 3.7894412708273354`*^9}, {3.7894413278185287`*^9, 3.789441329143035*^9}, 3.789441601886338*^9, {3.789441642006256*^9, 3.7894416431309566`*^9}, { 3.789441907932015*^9, 3.789441908494623*^9}, {3.789442049256173*^9, 3.7894420727362723`*^9}, {3.8216212981760674`*^9, 3.8216213084817343`*^9}, {3.8526939057531404`*^9, 3.8526939163136587`*^9}}, CellLabel->"In[23]:=",ExpressionUUID->"4121510e-13df-43ca-b53d-39b4b2880586"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 5.3 (solid)", "Subsubsection", CellChangeTimes->{ 3.4734695002813997`*^9, {3.599225569652184*^9, 3.599225577904598*^9}, 3.5992258478994727`*^9, 3.6862336460745583`*^9, 3.6862909162387624`*^9, { 3.6863755415162687`*^9, 3.686375541876269*^9}, {3.686463504573411*^9, 3.686463506573414*^9}, {3.6920258070089493`*^9, 3.692025809498953*^9}, { 3.692025870269038*^9, 3.692025872639041*^9}, 3.692502004255974*^9, 3.6926165081909256`*^9, 3.6926165783510237`*^9, {3.694086478127248*^9, 3.6940864796572495`*^9}, 3.7256194498022785`*^9, 3.789440495427185*^9, 3.789440526797804*^9, {3.821613793957991*^9, 3.8216137941890326`*^9}, 3.821613829297106*^9},ExpressionUUID->"ef9301ad-ffc5-4d0c-88eb-\ 96c861350e40"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"-", "\[Rho]"}], " ", "g"}]}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "3", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4426469450734453`*^9, 3.4426469473978453`*^9}, { 3.630367590488758*^9, 3.6303676088811903`*^9}, {3.630367651765666*^9, 3.630367669549697*^9}, 3.630368414310605*^9, {3.6307482430426474`*^9, 3.6307482456946526`*^9}, 3.685262022046692*^9, {3.6852621067368107`*^9, 3.6852621933569317`*^9}, {3.685262233936989*^9, 3.685262252827015*^9}, 3.685267210253956*^9, {3.6852715412232933`*^9, 3.685271546353301*^9}, { 3.6853429895189857`*^9, 3.6853430232739167`*^9}, 3.6858761692133045`*^9, { 3.68821224839828*^9, 3.6882123179983773`*^9}, {3.68821235531843*^9, 3.6882123899484777`*^9}, 3.6920258039789453`*^9, {3.692025876949047*^9, 3.692025881559054*^9}, {3.6920259277091184`*^9, 3.6920259839391975`*^9}, { 3.692026020869249*^9, 3.6920260636193085`*^9}, {3.6920264969699154`*^9, 3.6920264987399178`*^9}, 3.692502011618395*^9, {3.6925022474708843`*^9, 3.6925022520801487`*^9}, {3.692502302176014*^9, 3.6925023736471014`*^9}, { 3.6925025169803*^9, 3.6925025655720787`*^9}, {3.6925026661128297`*^9, 3.6925026706260877`*^9}, {3.6926054666559763`*^9, 3.692605488996008*^9}, { 3.6926055235860567`*^9, 3.6926055236960564`*^9}, 3.69262347584068*^9, { 3.6926953173258657`*^9, 3.6926953218058724`*^9}, {3.6927029458677883`*^9, 3.692702987017846*^9}, {3.692767974815113*^9, 3.6927680130851665`*^9}, { 3.6927681266753254`*^9, 3.6927681303353305`*^9}, {3.692768161725374*^9, 3.6927681639953775`*^9}, {3.6927685368559*^9, 3.692768539955904*^9}, { 3.6927698573477488`*^9, 3.6927699280078473`*^9}, 3.6927700238579817`*^9, { 3.692770056788028*^9, 3.6927701046680946`*^9}, {3.6928578154980726`*^9, 3.692857837888104*^9}, 3.692858122048502*^9, {3.694086496987274*^9, 3.6940865394073334`*^9}, {3.6940865889274025`*^9, 3.694086607197428*^9}, { 3.694086727667597*^9, 3.6940867569976377`*^9}, {3.6940869078278494`*^9, 3.6940869938779697`*^9}, {3.694087033478025*^9, 3.694087055018055*^9}, { 3.7894421264127007`*^9, 3.78944213687227*^9}, {3.789443395559586*^9, 3.7894434045015726`*^9}, {3.7894434621551476`*^9, 3.7894434648330545`*^9}, {3.8530312712190065`*^9, 3.853031299008956*^9}}, CellLabel-> "In[423]:=",ExpressionUUID->"1fdd7032-7349-4aa0-8da9-8423330696a0"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 5.4 (thin slab)", "Subsubsection", CellChangeTimes->{ 3.5602188818535767`*^9, {3.560232633043067*^9, 3.5602326460718117`*^9}, { 3.6231155453472214`*^9, 3.6231155575109177`*^9}, {3.6939914338993196`*^9, 3.6939914462693367`*^9}, 3.7256061978333664`*^9, {3.7256068862806683`*^9, 3.725606887702759*^9}, {3.725621905609552*^9, 3.725621910203785*^9}, 3.789440497743353*^9, 3.7894405294401426`*^9, {3.789616129613903*^9, 3.7896161325182133`*^9}, {3.821613801831195*^9, 3.8216138319367895`*^9}},ExpressionUUID->"f0f841e7-5a88-416e-899f-\ 33d21c65fabd"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "F"}], ",", RowBox[{"-", "F"}], ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "1", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"a", "[", "1", "]"}], " ", "L"}], ",", RowBox[{ RowBox[{"a", "[", "1", "]"}], " ", "L"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.5602189175776396`*^9, 3.5602191908121195`*^9}, { 3.560220898687519*^9, 3.560220996499691*^9}, {3.5602210407725687`*^9, 3.5602210595082016`*^9}, {3.560232658016495*^9, 3.560232736925009*^9}, { 3.69399146250936*^9, 3.6939915637295017`*^9}, {3.693991594919545*^9, 3.69399161264957*^9}, {3.693991672259653*^9, 3.6939916977196894`*^9}, { 3.6939917326897383`*^9, 3.6939917519997654`*^9}, {3.6939922575704727`*^9, 3.6939922802405043`*^9}, {3.693992547910879*^9, 3.6939925531808867`*^9}, { 3.6939928093312454`*^9, 3.693992934961421*^9}, {3.693992986601494*^9, 3.693992999141511*^9}, {3.6940007615401044`*^9, 3.6940008877102814`*^9}, { 3.6940647063690863`*^9, 3.6940647123490944`*^9}, 3.694064814159237*^9, { 3.7256219225800886`*^9, 3.7256219748824816`*^9}, {3.8217726494619627`*^9, 3.8217726509231224`*^9}}, CellLabel-> "In[427]:=",ExpressionUUID->"ce62ebec-db36-4ce8-92da-2451a1edc970"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture problem 5.5 (truss)", "Subsubsection", CellChangeTimes->{ 3.560218382980301*^9, 3.62311554059295*^9, {3.6937172119879804`*^9, 3.6937172178979883`*^9}, {3.6937211383542433`*^9, 3.6937211426242495`*^9}, 3.693721197964327*^9, 3.6938966537217274`*^9, {3.6939014955025063`*^9, 3.6939015033425174`*^9}, 3.694084133545754*^9, 3.725622374631402*^9, 3.789440502156151*^9, 3.7894405325936704`*^9, 3.8217726748188086`*^9},ExpressionUUID->"9be380f3-8a6c-4840-bbc1-\ 427b3277e6a4"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"val", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"A", "->", "0.01"}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"F", "->", "0.05"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", " "}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "1"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"4", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "F"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", " ", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "3", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "/.", "val"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4957897010062*^9, 3.4957898096446*^9}, { 3.4957898416870003`*^9, 3.4957898986426*^9}, {3.4957899396882*^9, 3.495789941841*^9}, {3.4957901948417997`*^9, 3.4957902000053997`*^9}, { 3.4957902785358*^9, 3.4957903351542*^9}, {3.4957903960098*^9, 3.4957904880708*^9}, {3.4957905206904*^9, 3.4957906521984*^9}, { 3.495791040888*^9, 3.4957911068136*^9}, {3.5007281090162*^9, 3.500728132467*^9}, {3.500728173828*^9, 3.5007282325972*^9}, { 3.56021839402512*^9, 3.560218396209124*^9}, {3.5602185052533154`*^9, 3.5602185542686014`*^9}, {3.5602185915994673`*^9, 3.5602185949222727`*^9}, {3.560218692750045*^9, 3.5602187145276833`*^9}, { 3.5602187506417465`*^9, 3.5602187818886013`*^9}, {3.5602188606999397`*^9, 3.560218873320362*^9}, {3.6937172406680202`*^9, 3.693717252648037*^9}, { 3.6937173212881336`*^9, 3.6937174206482725`*^9}, {3.693717572178485*^9, 3.6937175810284967`*^9}, {3.6937178570408835`*^9, 3.693717891700932*^9}, { 3.6937181376412764`*^9, 3.693718153091298*^9}, {3.693721075124155*^9, 3.6937210792641606`*^9}, {3.693721145474253*^9, 3.693721304004475*^9}, { 3.693721744775092*^9, 3.69372176445512*^9}, {3.6937217962751646`*^9, 3.693721800965171*^9}, 3.6937218775552783`*^9, {3.6937219143353295`*^9, 3.693721933395356*^9}, {3.693896663161741*^9, 3.6938966894117775`*^9}, 3.6938967300618343`*^9, {3.693896766931886*^9, 3.693896793821924*^9}, { 3.693896839311988*^9, 3.693896850372003*^9}, {3.6939015427525725`*^9, 3.6939015577525935`*^9}, {3.693901595302646*^9, 3.693901710112807*^9}, 3.693901779572904*^9, {3.693901827053971*^9, 3.693901833313979*^9}, { 3.6939028718864336`*^9, 3.6939028933264637`*^9}, {3.6939031776668615`*^9, 3.6939031787968636`*^9}, 3.6939032303569355`*^9, {3.725622627200715*^9, 3.725622636357994*^9}, {3.725622670908451*^9, 3.725622676455966*^9}, { 3.725622713881729*^9, 3.7256227145067945`*^9}, {3.7256228147673635`*^9, 3.7256228380354414`*^9}, {3.7894448956833925`*^9, 3.789444900781643*^9}, { 3.821772681889474*^9, 3.821772691294238*^9}, {3.8217729059137716`*^9, 3.8217729142460537`*^9}, {3.852696295749216*^9, 3.852696315470949*^9}, { 3.853031378522255*^9, 3.8530313975919647`*^9}, 3.8530314366225433`*^9},ExpressionUUID->"3fcfcedf-1b9f-4f00-9321-\ 6c9ffeca868a"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture problem 5.6 (truss)", "Subsubsection", CellChangeTimes->{ 3.560218382980301*^9, 3.62311554059295*^9, {3.6937172119879804`*^9, 3.6937172178979883`*^9}, {3.6937211383542433`*^9, 3.6937211426242495`*^9}, 3.693721197964327*^9, 3.6938966537217274`*^9, {3.6939014955025063`*^9, 3.6939015033425174`*^9}, 3.694084133545754*^9, 3.725622374631402*^9, 3.725622469610036*^9, 3.789440504983571*^9, 3.789440536851226*^9, { 3.821613806131517*^9, 3.821613806325562*^9}},ExpressionUUID->"5c0dcdbc-0d73-47d2-a90e-\ 4fa2202c567a"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"val", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"A", "->", "0.01"}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"F", "->", "0.05"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", " "}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", " ", RowBox[{"A", "/", RowBox[{"Sqrt", "[", "2", "]"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "F"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "L"}], " ", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "val"}]}], "]"}], " "}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4957897010062*^9, 3.4957898096446*^9}, { 3.4957898416870003`*^9, 3.4957898986426*^9}, {3.4957899396882*^9, 3.495789941841*^9}, {3.4957901948417997`*^9, 3.4957902000053997`*^9}, { 3.4957902785358*^9, 3.4957903351542*^9}, {3.4957903960098*^9, 3.4957904880708*^9}, {3.4957905206904*^9, 3.4957906521984*^9}, { 3.495791040888*^9, 3.4957911068136*^9}, {3.5007281090162*^9, 3.500728132467*^9}, {3.500728173828*^9, 3.5007282325972*^9}, { 3.56021839402512*^9, 3.560218396209124*^9}, {3.5602185052533154`*^9, 3.5602185542686014`*^9}, {3.5602185915994673`*^9, 3.5602185949222727`*^9}, {3.560218692750045*^9, 3.5602187145276833`*^9}, { 3.5602187506417465`*^9, 3.5602187818886013`*^9}, {3.5602188606999397`*^9, 3.560218873320362*^9}, {3.6937172406680202`*^9, 3.693717252648037*^9}, { 3.6937173212881336`*^9, 3.6937174206482725`*^9}, {3.693717572178485*^9, 3.6937175810284967`*^9}, {3.6937178570408835`*^9, 3.693717891700932*^9}, { 3.6937181376412764`*^9, 3.693718153091298*^9}, {3.693721075124155*^9, 3.6937210792641606`*^9}, {3.693721145474253*^9, 3.693721304004475*^9}, { 3.693721744775092*^9, 3.69372176445512*^9}, {3.6937217962751646`*^9, 3.693721800965171*^9}, 3.6937218775552783`*^9, {3.6937219143353295`*^9, 3.693721933395356*^9}, {3.693896663161741*^9, 3.6938966894117775`*^9}, 3.6938967300618343`*^9, {3.693896766931886*^9, 3.693896793821924*^9}, { 3.693896839311988*^9, 3.693896850372003*^9}, {3.6939015427525725`*^9, 3.6939015577525935`*^9}, {3.693901595302646*^9, 3.693901710112807*^9}, 3.693901779572904*^9, {3.693901827053971*^9, 3.693901833313979*^9}, { 3.6939028718864336`*^9, 3.6939028933264637`*^9}, {3.6939031776668615`*^9, 3.6939031787968636`*^9}, 3.6939032303569355`*^9, {3.7256231338316407`*^9, 3.725623166444374*^9}, {3.7256232233409953`*^9, 3.7256232237316127`*^9}, { 3.78944492033692*^9, 3.7894449444018607`*^9}, {3.821772950085473*^9, 3.821772963956665*^9}}, CellLabel->"In[55]:=",ExpressionUUID->"25f5f230-28cd-4656-ad1c-ea840b845079"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 1 (spring)", "Subsubsection", CellChangeTimes->{{3.623115527697212*^9, 3.6231155371217513`*^9}, { 3.693839654576663*^9, 3.6938396779966955`*^9}, 3.7255115587029552`*^9, { 3.725621898421294*^9, 3.7256218998589478`*^9}, {3.789956416920804*^9, 3.789956421197747*^9}},ExpressionUUID->"a5a98b11-9f02-45a2-a503-\ e46ac73368f1"], Cell[BoxData[ RowBox[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"1", "/", "4"}], "-", RowBox[{"(", RowBox[{"a", "-", RowBox[{"a", "^", "2"}], "+", RowBox[{ RowBox[{"a", "^", "3"}], "/", "3"}]}], ")"}]}], "\[Equal]", "0"}], ",", "a", ",", "Reals"}], "]"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.693839700606727*^9, 3.693839706596736*^9}, { 3.7258583766945887`*^9, 3.725858514740307*^9}, {3.7258589890580573`*^9, 3.7258590052316246`*^9}, {3.7894450781230726`*^9, 3.789445086798571*^9}, { 3.7894451238521996`*^9, 3.7894451303609877`*^9}, {3.789445227887929*^9, 3.7894452869782376`*^9}, {3.853031487036024*^9, 3.853031516290058*^9}}, CellLabel-> "In[447]:=",ExpressionUUID->"44bba056-9048-4dde-a062-28fc438f843d"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 2 (bar)", "Subsubsection", CellChangeTimes->{ 3.560218382980301*^9, 3.62311554059295*^9, {3.693819973244685*^9, 3.6938199838982944`*^9}, 3.6938411704287853`*^9, 3.725511566328563*^9, { 3.725592082848161*^9, 3.7255920894741154`*^9}, {3.7574772683958*^9, 3.7574772707544985`*^9}, 3.7894405584275*^9},ExpressionUUID->"76970886-d128-421f-bdc8-d800eeffc9a3"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "F"}], ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"uY", "[", "2", "]"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", "L"}], ",", "0", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}], "Input", CellChangeTimes->{{3.4957897010062*^9, 3.4957898096446*^9}, { 3.4957898416870003`*^9, 3.4957898986426*^9}, {3.4957899396882*^9, 3.495789941841*^9}, {3.4957901948417997`*^9, 3.4957902000053997`*^9}, { 3.4957902785358*^9, 3.4957903351542*^9}, {3.4957903960098*^9, 3.4957904880708*^9}, {3.4957905206904*^9, 3.4957906521984*^9}, { 3.495791040888*^9, 3.4957911068136*^9}, {3.5007281090162*^9, 3.500728132467*^9}, {3.500728173828*^9, 3.5007282325972*^9}, { 3.56021839402512*^9, 3.560218396209124*^9}, {3.5602185052533154`*^9, 3.5602185542686014`*^9}, {3.5602185915994673`*^9, 3.5602185949222727`*^9}, {3.560218692750045*^9, 3.5602187145276833`*^9}, { 3.5602187506417465`*^9, 3.5602187818886013`*^9}, {3.5602188606999397`*^9, 3.560218873320362*^9}, {3.693819990129651*^9, 3.6938200061045647`*^9}, { 3.6938200670680513`*^9, 3.6938201641626053`*^9}, {3.693820198061544*^9, 3.6938201991256046`*^9}, 3.693820230839419*^9, {3.693820383431128*^9, 3.6938204160959964`*^9}, {3.693820485276953*^9, 3.6938204875870857`*^9}, { 3.6938207040664673`*^9, 3.693820736507323*^9}, {3.693821098334018*^9, 3.693821155875309*^9}, 3.693821299836543*^9, {3.6938409020884094`*^9, 3.693840936258457*^9}, {3.69384100242855*^9, 3.6938410079285574`*^9}, 3.694069910702713*^9, {3.694079748974413*^9, 3.694079837934538*^9}, { 3.725593395599037*^9, 3.7255934828895507`*^9}, 3.725593520033848*^9, { 3.757477295865029*^9, 3.7574773017672763`*^9}, {3.757477333536891*^9, 3.757477336868082*^9}, {3.7894453325389366`*^9, 3.7894453581147127`*^9}, { 3.8217731177026515`*^9, 3.8217731352407045`*^9}}, CellLabel->"In[29]:=",ExpressionUUID->"01c83bb6-b98c-47e9-a8cf-8b7753bc36d4"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 3 (bar)", "Subsubsection", CellChangeTimes->{ 3.560218382980301*^9, 3.62311554059295*^9, {3.693819973244685*^9, 3.6938199838982944`*^9}, 3.725511564062546*^9, 3.7256253111624565`*^9, 3.7894405617112646`*^9},ExpressionUUID->"ed69b494-2d0e-4d53-b0b4-\ ce52ffbdb7e8"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"F", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"a", "[", "1", "]"}], " ", "L"}], ",", RowBox[{ RowBox[{"a", "[", "2", "]"}], "L"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"val", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"A", "\[Rule]", RowBox[{"1", "/", "100"}]}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"F", "\[Rule]", RowBox[{"1", "/", "2."}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "val"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4957897010062*^9, 3.4957898096446*^9}, { 3.4957898416870003`*^9, 3.4957898986426*^9}, {3.4957899396882*^9, 3.495789941841*^9}, {3.4957901948417997`*^9, 3.4957902000053997`*^9}, { 3.4957902785358*^9, 3.4957903351542*^9}, {3.4957903960098*^9, 3.4957904880708*^9}, {3.4957905206904*^9, 3.4957906521984*^9}, { 3.495791040888*^9, 3.4957911068136*^9}, {3.5007281090162*^9, 3.500728132467*^9}, {3.500728173828*^9, 3.5007282325972*^9}, { 3.56021839402512*^9, 3.560218396209124*^9}, {3.5602185052533154`*^9, 3.5602185542686014`*^9}, {3.5602185915994673`*^9, 3.5602185949222727`*^9}, {3.560218692750045*^9, 3.5602187145276833`*^9}, { 3.5602187506417465`*^9, 3.5602187818886013`*^9}, {3.5602188606999397`*^9, 3.560218873320362*^9}, {3.693819990129651*^9, 3.6938200061045647`*^9}, { 3.6938200670680513`*^9, 3.6938201641626053`*^9}, {3.693820198061544*^9, 3.6938201991256046`*^9}, 3.693820230839419*^9, {3.693820383431128*^9, 3.6938204160959964`*^9}, {3.693820485276953*^9, 3.6938204875870857`*^9}, { 3.6938207040664673`*^9, 3.693820736507323*^9}, {3.693821098334018*^9, 3.693821155875309*^9}, 3.693821299836543*^9, {3.6938409020884094`*^9, 3.693840936258457*^9}, {3.69384100242855*^9, 3.6938410079285574`*^9}, { 3.6940795899041905`*^9, 3.694079609914219*^9}, {3.725604753175531*^9, 3.7256047697710576`*^9}, {3.725605100772751*^9, 3.725605136125828*^9}, { 3.7574774861000786`*^9, 3.757477494918944*^9}, {3.757477531238297*^9, 3.7574775404777417`*^9}, 3.757477907422058*^9, {3.7894453915348864`*^9, 3.7894453952536936`*^9}, {3.821773174203444*^9, 3.8217731831461883`*^9}}, CellLabel->"In[33]:=",ExpressionUUID->"387150a2-1f6c-43ee-8df8-ff57a74b5691"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 4 (bar)", "Subsubsection", CellChangeTimes->{ 3.560218382980301*^9, 3.62311554059295*^9, {3.693819973244685*^9, 3.6938199838982944`*^9}, 3.6938411704287853`*^9, 3.725511566328563*^9, 3.725625314225254*^9, 3.7894405642067876`*^9},ExpressionUUID->"ae2b9564-f9f2-4a4e-bc50-\ ff27a0c53146"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"val", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"A", "\[Rule]", RowBox[{"1", "/", "100"}]}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"F", "\[Rule]", RowBox[{"1", "/", "2."}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"F", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"L", "/", "2"}], ",", "0", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"a", "[", "0", "]"}], "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "val"}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.4957897010062*^9, 3.4957898096446*^9}, { 3.4957898416870003`*^9, 3.4957898986426*^9}, {3.4957899396882*^9, 3.495789941841*^9}, {3.4957901948417997`*^9, 3.4957902000053997`*^9}, { 3.4957902785358*^9, 3.4957903351542*^9}, {3.4957903960098*^9, 3.4957904880708*^9}, {3.4957905206904*^9, 3.4957906521984*^9}, { 3.495791040888*^9, 3.4957911068136*^9}, {3.5007281090162*^9, 3.500728132467*^9}, {3.500728173828*^9, 3.5007282325972*^9}, { 3.56021839402512*^9, 3.560218396209124*^9}, {3.5602185052533154`*^9, 3.5602185542686014`*^9}, {3.5602185915994673`*^9, 3.5602185949222727`*^9}, {3.560218692750045*^9, 3.5602187145276833`*^9}, { 3.5602187506417465`*^9, 3.5602187818886013`*^9}, {3.5602188606999397`*^9, 3.560218873320362*^9}, {3.693819990129651*^9, 3.6938200061045647`*^9}, { 3.6938200670680513`*^9, 3.6938201641626053`*^9}, {3.693820198061544*^9, 3.6938201991256046`*^9}, 3.693820230839419*^9, {3.693820383431128*^9, 3.6938204160959964`*^9}, {3.693820485276953*^9, 3.6938204875870857`*^9}, { 3.6938207040664673`*^9, 3.693820736507323*^9}, {3.693821098334018*^9, 3.693821155875309*^9}, 3.693821299836543*^9, {3.6938409020884094`*^9, 3.693840936258457*^9}, {3.69384100242855*^9, 3.6938410079285574`*^9}, 3.694069910702713*^9, {3.694079748974413*^9, 3.694079837934538*^9}, { 3.725605220875243*^9, 3.7256052567071037`*^9}, {3.7574779149067807`*^9, 3.757477933470075*^9}, {3.7894454202635717`*^9, 3.789445453371543*^9}, { 3.8217732116204844`*^9, 3.821773228375927*^9}, {3.853031583718212*^9, 3.853031642120866*^9}}, CellLabel-> "In[378]:=",ExpressionUUID->"67ed0c58-9ecf-4810-ab6d-d5cf7153a5a7"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 5 (bar)", "Subsubsection", CellChangeTimes->{ 3.560218382980301*^9, 3.62311554059295*^9, {3.693819973244685*^9, 3.6938199838982944`*^9}, 3.6938411704287853`*^9, 3.694067326282754*^9, 3.725511573876234*^9, 3.7256253185069685`*^9, 3.789440568716662*^9},ExpressionUUID->"26291586-55e4-4878-ba3f-\ 4844b4d7fe4e"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"val", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"A", "\[Rule]", RowBox[{"1", "/", "100"}]}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"g", "\[Rule]", "10."}], ",", RowBox[{"\[Rho]", "->", "1"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Rho]"}], " ", "g", " ", "A"}], ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"a", "[", "0", "]"}], " ", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "val"}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.4957897010062*^9, 3.4957898096446*^9}, { 3.4957898416870003`*^9, 3.4957898986426*^9}, {3.4957899396882*^9, 3.495789941841*^9}, {3.4957901948417997`*^9, 3.4957902000053997`*^9}, { 3.4957902785358*^9, 3.4957903351542*^9}, {3.4957903960098*^9, 3.4957904880708*^9}, {3.4957905206904*^9, 3.4957906521984*^9}, { 3.495791040888*^9, 3.4957911068136*^9}, {3.5007281090162*^9, 3.500728132467*^9}, {3.500728173828*^9, 3.5007282325972*^9}, { 3.56021839402512*^9, 3.560218396209124*^9}, {3.5602185052533154`*^9, 3.5602185542686014`*^9}, {3.5602185915994673`*^9, 3.5602185949222727`*^9}, {3.560218692750045*^9, 3.5602187145276833`*^9}, { 3.5602187506417465`*^9, 3.5602187818886013`*^9}, {3.5602188606999397`*^9, 3.560218873320362*^9}, {3.693819990129651*^9, 3.6938200061045647`*^9}, { 3.6938200670680513`*^9, 3.6938201641626053`*^9}, {3.693820198061544*^9, 3.6938201991256046`*^9}, 3.693820230839419*^9, {3.693820383431128*^9, 3.6938204160959964`*^9}, {3.693820485276953*^9, 3.6938204875870857`*^9}, { 3.6938207040664673`*^9, 3.693820736507323*^9}, {3.693821098334018*^9, 3.693821155875309*^9}, 3.693821299836543*^9, {3.6938409020884094`*^9, 3.693840936258457*^9}, {3.69384100242855*^9, 3.6938410079285574`*^9}, { 3.6940673358027673`*^9, 3.694067439482912*^9}, 3.725605406295211*^9, { 3.725605452096917*^9, 3.725605453284552*^9}, {3.7574780822686853`*^9, 3.75747813974619*^9}, {3.7574782361050873`*^9, 3.7574782462962294`*^9}, 3.757478313116293*^9, 3.7574784080512347`*^9, {3.757478440370651*^9, 3.757478441201786*^9}, {3.7894455024136286`*^9, 3.789445505678503*^9}, { 3.8217732619969983`*^9, 3.821773264921981*^9}, {3.821773373722191*^9, 3.821773400868431*^9}, {3.853031781624614*^9, 3.853031811473053*^9}, { 3.8530318813596945`*^9, 3.853031945476489*^9}, 3.853031978817148*^9}, CellLabel-> "In[409]:=",ExpressionUUID->"5e03bc45-29d4-4cf7-b210-ba804be3b291"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 6 (truss)", "Subsubsection", CellChangeTimes->{ 3.5602188818535767`*^9, 3.560232633043067*^9, 3.623115542820077*^9, { 3.693826261353222*^9, 3.6938262737929335`*^9}, 3.7256055657495413`*^9, 3.7256253208821793`*^9, 3.7894405715213823`*^9},ExpressionUUID->"2b586baa-41d8-4a81-98dd-\ 33c4919146de"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"val", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"A", "\[Rule]", RowBox[{"1", "/", "100"}]}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"F", "\[Rule]", RowBox[{"1", "/", "2."}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "1"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "1"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "F"}], ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "1", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"a", "[", "1", "]"}], " ", "L"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "val"}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.5602189175776396`*^9, 3.5602191908121195`*^9}, { 3.560220898687519*^9, 3.560220996499691*^9}, {3.5602210407725687`*^9, 3.5602210595082016`*^9}, {3.623115276991873*^9, 3.623115290541648*^9}, { 3.693826310417028*^9, 3.6938265443454075`*^9}, {3.693826600766635*^9, 3.693826603632799*^9}, {3.693826784929142*^9, 3.6938267876833*^9}, { 3.6938268227563057`*^9, 3.6938268239953766`*^9}, {3.6940648454692802`*^9, 3.6940648624993043`*^9}, {3.694065539960253*^9, 3.694065548660265*^9}, 3.694067257222657*^9, {3.7256055732346945`*^9, 3.725605582626178*^9}, { 3.7256056129888973`*^9, 3.7256057518003635`*^9}, 3.725605788178935*^9, { 3.75747883408612*^9, 3.7574788831159344`*^9}, {3.7894455582931757`*^9, 3.7894455611163583`*^9}, {3.8217734334717894`*^9, 3.821773440018031*^9}, { 3.853032006421949*^9, 3.853032013225816*^9}, {3.853032099465707*^9, 3.8530321012045107`*^9}}, CellLabel-> "In[421]:=",ExpressionUUID->"b0dbb4df-4690-429a-b696-6e24889a7695"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 7 (thin slab)", "Subsubsection", CellChangeTimes->{ 3.5602188818535767`*^9, {3.560232633043067*^9, 3.5602326460718117`*^9}, { 3.6231155453472214`*^9, 3.6231155575109177`*^9}, {3.6939914338993196`*^9, 3.6939914462693367`*^9}, 3.7256061978333664`*^9, {3.7256068862806683`*^9, 3.725606887702759*^9}, 3.725625327336037*^9, 3.757429808988515*^9, { 3.75747944029515*^9, 3.757479442795718*^9}, 3.789440574620819*^9},ExpressionUUID->"df62930c-91c9-42db-aa05-\ fd2381197ded"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"val", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"\[Nu]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"t", "\[Rule]", RowBox[{"1", "/", "10"}]}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"F", "\[Rule]", RowBox[{"1", "/", "2."}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"F", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "1", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"a", "[", "0", "]"}], " ", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "L", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "val"}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.5602189175776396`*^9, 3.5602191908121195`*^9}, { 3.560220898687519*^9, 3.560220996499691*^9}, {3.5602210407725687`*^9, 3.5602210595082016`*^9}, {3.560232658016495*^9, 3.560232736925009*^9}, { 3.69399146250936*^9, 3.6939915637295017`*^9}, {3.693991594919545*^9, 3.69399161264957*^9}, {3.693991672259653*^9, 3.6939916977196894`*^9}, { 3.6939917326897383`*^9, 3.6939917519997654`*^9}, {3.6939922575704727`*^9, 3.6939922802405043`*^9}, {3.693992547910879*^9, 3.6939925531808867`*^9}, { 3.6939928093312454`*^9, 3.693992934961421*^9}, {3.693992986601494*^9, 3.693992999141511*^9}, {3.6940007615401044`*^9, 3.6940008877102814`*^9}, { 3.6940647063690863`*^9, 3.6940647123490944`*^9}, 3.694064814159237*^9, { 3.757479006718543*^9, 3.7574790329387393`*^9}, {3.757479092367199*^9, 3.7574791238375545`*^9}, {3.7894455966038275`*^9, 3.7894455998939514`*^9}, {3.8217734770561576`*^9, 3.821773478385603*^9}, { 3.8530321321431284`*^9, 3.8530321395013227`*^9}}, CellLabel-> "In[427]:=",ExpressionUUID->"6420ca88-ba6e-4516-b442-bdf14253658a"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 8 (bar-slab structure)", "Subsubsection", CellChangeTimes->{ 3.5602188818535767`*^9, {3.560232633043067*^9, 3.5602326460718117`*^9}, { 3.6231155453472214`*^9, 3.6231155575109177`*^9}, {3.6939914338993196`*^9, 3.6939914462693367`*^9}, 3.694000913010317*^9, 3.7256065797642317`*^9, { 3.7256068906873064`*^9, 3.7256068999228387`*^9}, {3.7256070257017245`*^9, 3.725607038640582*^9}, 3.757429551201259*^9, 3.789440578103948*^9},ExpressionUUID->"8d5f287e-3483-43be-9a3b-\ 1e8e6d818387"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"val", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"\[Nu]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"t", "\[Rule]", RowBox[{"1", "/", "10"}]}], ",", RowBox[{"A", "\[Rule]", RowBox[{"1", "/", "10"}]}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"F", "\[Rule]", RowBox[{"1", "/", "2."}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "4"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "F"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "1", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", " ", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"a", "[", "0", "]"}], " ", "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "L", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "val"}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.5602189175776396`*^9, 3.5602191908121195`*^9}, { 3.560220898687519*^9, 3.560220996499691*^9}, {3.5602210407725687`*^9, 3.5602210595082016`*^9}, {3.560232658016495*^9, 3.560232736925009*^9}, { 3.69399146250936*^9, 3.6939915637295017`*^9}, {3.693991594919545*^9, 3.69399161264957*^9}, {3.693991672259653*^9, 3.6939916977196894`*^9}, { 3.6939917326897383`*^9, 3.6939917519997654`*^9}, {3.6939922575704727`*^9, 3.6939922802405043`*^9}, {3.693992547910879*^9, 3.6939925531808867`*^9}, { 3.6939928093312454`*^9, 3.693992934961421*^9}, {3.693992986601494*^9, 3.693992999141511*^9}, {3.6940007615401044`*^9, 3.6940008877102814`*^9}, { 3.6940009203803267`*^9, 3.694000948260366*^9}, {3.6940010109604535`*^9, 3.6940011008205795`*^9}, {3.694064269308474*^9, 3.694064314118537*^9}, 3.6940644008986583`*^9, {3.694064645619001*^9, 3.6940646749190416`*^9}, { 3.7256066079390864`*^9, 3.725606648115192*^9}, {3.75747929130151*^9, 3.757479338941169*^9}, {3.7894456232434034`*^9, 3.7894456264651394`*^9}, { 3.821773508757564*^9, 3.8217735199487343`*^9}, {3.853032185344742*^9, 3.8530321964386606`*^9}}, CellLabel-> "In[433]:=",ExpressionUUID->"e76d2789-e421-4b03-b286-aba9c5d861dc"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 9 (thin slab)", "Subsubsection", CellChangeTimes->{ 3.5602188818535767`*^9, 3.560232633043067*^9, 3.623115542820077*^9, { 3.693826261353222*^9, 3.6938262737929335`*^9}, {3.6940649374494095`*^9, 3.6940649713794565`*^9}, {3.725607064440168*^9, 3.725607133619341*^9}, 3.725625333930484*^9, {3.757428024654767*^9, 3.7574280306883173`*^9}, { 3.757479448872733*^9, 3.7574794509871073`*^9}, 3.7894405822954435`*^9},ExpressionUUID->"e3d0e78f-43f0-432c-8e55-\ 77ac019d8949"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"val", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"t", "->", "0.01"}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100."}], ",", " ", RowBox[{"\[Nu]", "\[Rule]", RowBox[{"1", "/", "3"}]}], ",", RowBox[{"g", "\[Rule]", "10"}], ",", RowBox[{"\[Rho]", " ", "\[Rule]", "1"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"-", "\[Rho]"}], " ", "g", " ", "t"}], ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "L"}], "/", "2"}], " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"L", "/", "2"}], ",", "0", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"a", "[", "0", "]"}], "L"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "val"}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.5602189175776396`*^9, 3.5602191908121195`*^9}, { 3.560220898687519*^9, 3.560220996499691*^9}, {3.5602210407725687`*^9, 3.5602210595082016`*^9}, {3.623115276991873*^9, 3.623115290541648*^9}, { 3.693826310417028*^9, 3.6938265443454075`*^9}, {3.693826600766635*^9, 3.693826603632799*^9}, {3.693826784929142*^9, 3.6938267876833*^9}, { 3.6938268227563057`*^9, 3.6938268239953766`*^9}, {3.6940648454692802`*^9, 3.6940648624993043`*^9}, 3.6940649754294624`*^9, {3.6940653595200005`*^9, 3.6940654171000805`*^9}, {3.694065467160151*^9, 3.6940654682101526`*^9}, { 3.694066944192219*^9, 3.69406694514222*^9}, {3.694066982352272*^9, 3.6940669912222843`*^9}, 3.6940670456323605`*^9, {3.6940672305226192`*^9, 3.69406723070262*^9}, 3.72560709045855*^9, 3.7256071789678783`*^9, { 3.7256072733243494`*^9, 3.7256072756058626`*^9}, {3.725608309756126*^9, 3.7256083116471977`*^9}, {3.725771734466016*^9, 3.7257721969195395`*^9}, { 3.7257722328380303`*^9, 3.7257722332153444`*^9}, {3.725772288027615*^9, 3.725772479650519*^9}, {3.725772530529035*^9, 3.72577257412286*^9}, { 3.7257914159401326`*^9, 3.725791520523611*^9}, 3.7257916969801884`*^9, { 3.725791734069311*^9, 3.7257917344076314`*^9}, {3.7257923081234202`*^9, 3.7257923707246*^9}, {3.7258595954969983`*^9, 3.7258596647855377`*^9}, { 3.7258915046964464`*^9, 3.725891709651156*^9}, {3.725892062990927*^9, 3.7258920633470783`*^9}, {3.725892218379181*^9, 3.7258922203544364`*^9}, { 3.7258922592064257`*^9, 3.7258922593340416`*^9}, 3.725892329129791*^9, { 3.7258924167535458`*^9, 3.7258924714289207`*^9}, {3.7258925212512045`*^9, 3.725892591360572*^9}, {3.725941541310729*^9, 3.7259415780623465`*^9}, { 3.757428049418125*^9, 3.757428054913843*^9}, {3.757428087909403*^9, 3.7574280934841433`*^9}, {3.7574284280978804`*^9, 3.7574284568388243`*^9}, {3.757479457969281*^9, 3.757479477327525*^9}, { 3.789445656969535*^9, 3.7894456641009045`*^9}, {3.789527751387431*^9, 3.7895277970802803`*^9}, {3.8217735920327053`*^9, 3.8217736608186865`*^9}, {3.8530322302223673`*^9, 3.8530322367987704`*^9}}, CellLabel-> "In[439]:=",ExpressionUUID->"e688d383-03e4-46b4-9200-ba0802aea915"] }, Closed]], Cell[CellGroupData[{ Cell["Example problem 10 (thin slab)", "Subsubsection", CellChangeTimes->{ 3.5602188818535767`*^9, 3.560232633043067*^9, 3.623115542820077*^9, { 3.693826261353222*^9, 3.6938262737929335`*^9}, {3.6940649374494095`*^9, 3.6940649713794565`*^9}, {3.6940809835093436`*^9, 3.6940809892393517`*^9}, {3.694083731665191*^9, 3.6940837325151925`*^9}, { 3.725591075758112*^9, 3.7255910824931173`*^9}, 3.7574177204968224`*^9, { 3.7574795432836018`*^9, 3.7574795459317837`*^9}, 3.789440584620143*^9},ExpressionUUID->"a9acad1d-fe57-43ef-a833-\ 738de675aa5c"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"val", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"t", "\[Rule]", RowBox[{"1", "/", "10"}]}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"F", "\[Rule]", RowBox[{"1", "/", "2."}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "0"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "4", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"F", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "4", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "L", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"a", "[", "0", "]"}], "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "\[IndentingNewLine]", "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "val"}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.5602189175776396`*^9, 3.5602191908121195`*^9}, { 3.560220898687519*^9, 3.560220996499691*^9}, {3.5602210407725687`*^9, 3.5602210595082016`*^9}, {3.623115276991873*^9, 3.623115290541648*^9}, { 3.693826310417028*^9, 3.6938265443454075`*^9}, {3.693826600766635*^9, 3.693826603632799*^9}, {3.693826784929142*^9, 3.6938267876833*^9}, { 3.6938268227563057`*^9, 3.6938268239953766`*^9}, {3.6940648454692802`*^9, 3.6940648624993043`*^9}, 3.6940649754294624`*^9, {3.6940653595200005`*^9, 3.6940654171000805`*^9}, {3.694065467160151*^9, 3.6940654682101526`*^9}, { 3.694066944192219*^9, 3.69406694514222*^9}, {3.694066982352272*^9, 3.6940669912222843`*^9}, 3.6940670456323605`*^9, {3.6940672305226192`*^9, 3.69406723070262*^9}, {3.6940810147793875`*^9, 3.6940810826494827`*^9}, { 3.6940811130095253`*^9, 3.694081168489603*^9}, 3.6940827811428604`*^9, { 3.6940828325929327`*^9, 3.6940828345429354`*^9}, {3.7255910853840923`*^9, 3.7255911544538746`*^9}, {3.7255918177576747`*^9, 3.725591901469971*^9}, { 3.725591981775208*^9, 3.725592015903798*^9}, {3.757416801791027*^9, 3.757416821306521*^9}, 3.7574795541241035`*^9, {3.757479595088483*^9, 3.757479596023892*^9}, {3.757479635696697*^9, 3.757479653341745*^9}, { 3.7894456941573915`*^9, 3.789445701224625*^9}, {3.8217736706623697`*^9, 3.8217736940708227`*^9}, {3.8217737317524047`*^9, 3.821773734571*^9}, { 3.821780323407436*^9, 3.8217803662117853`*^9}, {3.853032278923683*^9, 3.853032287932805*^9}}, CellLabel-> "In[445]:=",ExpressionUUID->"ece3ce0e-bd5a-42e9-95a0-a66340c940c5"] }, Closed]], Cell[CellGroupData[{ Cell["Home assignment 1 (bar)", "Subsubsection", CellChangeTimes->{ 3.560218382980301*^9, 3.62311554059295*^9, {3.693819973244685*^9, 3.6938199838982944`*^9}, 3.6938411704287853`*^9, 3.725511566328563*^9, { 3.725592082848161*^9, 3.7255920894741154`*^9}},ExpressionUUID->"f621edbf-3a25-4533-8014-\ 085169a4974e"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"-", "\[Rho]"}], " ", "g", " ", "A"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", " ", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4957897010062*^9, 3.4957898096446*^9}, { 3.4957898416870003`*^9, 3.4957898986426*^9}, {3.4957899396882*^9, 3.495789941841*^9}, {3.4957901948417997`*^9, 3.4957902000053997`*^9}, { 3.4957902785358*^9, 3.4957903351542*^9}, {3.4957903960098*^9, 3.4957904880708*^9}, {3.4957905206904*^9, 3.4957906521984*^9}, { 3.495791040888*^9, 3.4957911068136*^9}, {3.5007281090162*^9, 3.500728132467*^9}, {3.500728173828*^9, 3.5007282325972*^9}, { 3.56021839402512*^9, 3.560218396209124*^9}, {3.5602185052533154`*^9, 3.5602185542686014`*^9}, {3.5602185915994673`*^9, 3.5602185949222727`*^9}, {3.560218692750045*^9, 3.5602187145276833`*^9}, { 3.5602187506417465`*^9, 3.5602187818886013`*^9}, {3.5602188606999397`*^9, 3.560218873320362*^9}, {3.693819990129651*^9, 3.6938200061045647`*^9}, { 3.6938200670680513`*^9, 3.6938201641626053`*^9}, {3.693820198061544*^9, 3.6938201991256046`*^9}, 3.693820230839419*^9, {3.693820383431128*^9, 3.6938204160959964`*^9}, {3.693820485276953*^9, 3.6938204875870857`*^9}, { 3.6938207040664673`*^9, 3.693820736507323*^9}, {3.693821098334018*^9, 3.693821155875309*^9}, 3.693821299836543*^9, {3.6938409020884094`*^9, 3.693840936258457*^9}, {3.69384100242855*^9, 3.6938410079285574`*^9}, 3.694069910702713*^9, {3.694079748974413*^9, 3.694079837934538*^9}, { 3.725593395599037*^9, 3.7255934828895507`*^9}, 3.725593520033848*^9, { 3.7574798317865477`*^9, 3.757479924484078*^9}, {3.7574799757703543`*^9, 3.7574799982811112`*^9}, {3.757480089314517*^9, 3.7574801025691175`*^9}, { 3.7574806066027913`*^9, 3.757480607392909*^9}, {3.7574808967018805`*^9, 3.757480897227325*^9}, {3.7894568754764276`*^9, 3.7894569725694103`*^9}, { 3.7895279423749056`*^9, 3.789527942729209*^9}, {3.821774005946034*^9, 3.8217740074829407`*^9}, {3.8217740392795753`*^9, 3.8217740417489767`*^9}, {3.821774080885614*^9, 3.821774082008611*^9}, { 3.8217743771908073`*^9, 3.82177441796832*^9}, {3.821775449472017*^9, 3.821775450119286*^9}, 3.8530323229130535`*^9, {3.8530324590255346`*^9, 3.853032460771165*^9}}, CellLabel-> "In[385]:=",ExpressionUUID->"f35377ef-1dec-482b-9405-9e5036852707"] }, Closed]], Cell[CellGroupData[{ Cell["Home assignment 2 (bar structure)", "Subsubsection", CellChangeTimes->{ 3.560218382980301*^9, 3.62311554059295*^9, {3.693819973244685*^9, 3.6938199838982944`*^9}, 3.6938398962370014`*^9, 3.7255115616720257`*^9, 3.725625308724648*^9, 3.757477396494967*^9, {3.757481085296235*^9, 3.7574810942571373`*^9}},ExpressionUUID->"e1f660bf-95df-433b-8788-\ 6b7701c7e3e7"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"val", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"A", "\[Rule]", RowBox[{"1", "/", "100"}]}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"F", "\[Rule]", RowBox[{"1", "/", "100."}]}], ",", RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"Pi", "/", "4"}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{ RowBox[{"Sin", "[", "\[Alpha]", "]"}], ",", RowBox[{"Cos", "[", "\[Alpha]", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{"Sin", "[", "\[Alpha]", "]"}]}], ",", RowBox[{"Cos", "[", "\[Alpha]", "]"}], ",", "0"}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "F"}], ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "L"}], " ", RowBox[{"Cos", "[", "\[Alpha]", "]"}]}], " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"L", " ", RowBox[{"Sin", "[", "\[Alpha]", "]"}]}], " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"a", "[", "0", "]"}], " ", "L"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"L", " ", RowBox[{"Cos", "[", "\[Alpha]", "]"}]}], " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "val"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "val"}], "]"}]}]}]], "Input", CellChangeTimes->{{3.4957897010062*^9, 3.4957898096446*^9}, { 3.4957898416870003`*^9, 3.4957898986426*^9}, {3.4957899396882*^9, 3.495789941841*^9}, {3.4957901948417997`*^9, 3.4957902000053997`*^9}, { 3.4957902785358*^9, 3.4957903351542*^9}, {3.4957903960098*^9, 3.4957904880708*^9}, {3.4957905206904*^9, 3.4957906521984*^9}, { 3.495791040888*^9, 3.4957911068136*^9}, {3.5007281090162*^9, 3.500728132467*^9}, {3.500728173828*^9, 3.5007282325972*^9}, { 3.56021839402512*^9, 3.560218396209124*^9}, {3.5602185052533154`*^9, 3.5602185542686014`*^9}, {3.5602185915994673`*^9, 3.5602185949222727`*^9}, {3.560218692750045*^9, 3.5602187145276833`*^9}, { 3.5602187506417465`*^9, 3.5602187818886013`*^9}, {3.5602188606999397`*^9, 3.560218873320362*^9}, {3.693819990129651*^9, 3.6938200061045647`*^9}, { 3.6938200670680513`*^9, 3.6938201641626053`*^9}, {3.693820198061544*^9, 3.6938201991256046`*^9}, 3.693820230839419*^9, {3.693820383431128*^9, 3.6938204160959964`*^9}, {3.693820485276953*^9, 3.6938204875870857`*^9}, { 3.6938207040664673`*^9, 3.693820736507323*^9}, {3.693821098334018*^9, 3.693821155875309*^9}, 3.693821299836543*^9, {3.6938399692971034`*^9, 3.6938400282071857`*^9}, {3.6938400695572433`*^9, 3.693840082837262*^9}, { 3.693840140197343*^9, 3.6938401716273866`*^9}, {3.6938402404574833`*^9, 3.693840254527503*^9}, {3.6940795213440943`*^9, 3.6940795257441006`*^9}, { 3.7256045368402443`*^9, 3.725604579344708*^9}, {3.757481102253356*^9, 3.7574811642823534`*^9}, {3.757481194330432*^9, 3.75748129838559*^9}, { 3.757481353914442*^9, 3.7574814199329386`*^9}, {3.7574819467375937`*^9, 3.7574819907312126`*^9}, 3.7574820869091225`*^9, {3.7574821221663103`*^9, 3.7574821223027587`*^9}, {3.8217745890548897`*^9, 3.821774665005913*^9}, { 3.821775402089509*^9, 3.821775422114235*^9}, {3.853033107381581*^9, 3.853033141062274*^9}}, CellLabel-> "In[397]:=",ExpressionUUID->"4ba14765-9ebd-4832-b5eb-6cd58ea378e4"] }, Closed]], Cell[CellGroupData[{ Cell["Home assignment 3 (thin slab)", "Subsubsection", CellChangeTimes->{ 3.5602188818535767`*^9, 3.560232633043067*^9, 3.623115542820077*^9, { 3.693826261353222*^9, 3.6938262737929335`*^9}, {3.6940649374494095`*^9, 3.6940649713794565`*^9}, {3.6940809835093436`*^9, 3.6940809892393517`*^9}, {3.694083731665191*^9, 3.6940837325151925`*^9}, { 3.725591075758112*^9, 3.7255910824931173`*^9}, 3.725595925542554*^9, { 3.757482185630768*^9, 3.7574821879362445`*^9}},ExpressionUUID->"0dd6c074-3fcc-448f-a945-\ 58ab6f49a459"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "F"}], ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "3", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", " ", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"a", "[", "0", "]"}], " ", "L"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}], "Input", CellChangeTimes->{{3.5602189175776396`*^9, 3.5602191908121195`*^9}, { 3.560220898687519*^9, 3.560220996499691*^9}, {3.5602210407725687`*^9, 3.5602210595082016`*^9}, {3.623115276991873*^9, 3.623115290541648*^9}, { 3.693826310417028*^9, 3.6938265443454075`*^9}, {3.693826600766635*^9, 3.693826603632799*^9}, {3.693826784929142*^9, 3.6938267876833*^9}, { 3.6938268227563057`*^9, 3.6938268239953766`*^9}, {3.6940648454692802`*^9, 3.6940648624993043`*^9}, 3.6940649754294624`*^9, {3.6940653595200005`*^9, 3.6940654171000805`*^9}, {3.694065467160151*^9, 3.6940654682101526`*^9}, { 3.694066944192219*^9, 3.69406694514222*^9}, {3.694066982352272*^9, 3.6940669912222843`*^9}, 3.6940670456323605`*^9, {3.6940672305226192`*^9, 3.69406723070262*^9}, {3.6940810147793875`*^9, 3.6940810826494827`*^9}, { 3.6940811130095253`*^9, 3.694081168489603*^9}, 3.6940827811428604`*^9, { 3.6940828325929327`*^9, 3.6940828345429354`*^9}, {3.7255910853840923`*^9, 3.7255911544538746`*^9}, {3.7255918177576747`*^9, 3.725591901469971*^9}, { 3.725591981775208*^9, 3.725592015903798*^9}, {3.7255959457945385`*^9, 3.725596052648704*^9}, 3.7255963100979967`*^9, 3.7255977652254705`*^9, { 3.7256002235096517`*^9, 3.725600225384837*^9}, 3.725601577369067*^9, { 3.7256024833399587`*^9, 3.725602485246642*^9}, {3.72560256753648*^9, 3.7256025692711873`*^9}, {3.7259408859758453`*^9, 3.725940887709132*^9}, { 3.7259487058805704`*^9, 3.7259487077258434`*^9}, {3.725949106810832*^9, 3.725949108652855*^9}, {3.75748219356618*^9, 3.75748221683813*^9}, { 3.7574822889872437`*^9, 3.757482355027481*^9}, 3.7574823860843687`*^9, { 3.7574829602375355`*^9, 3.7574829610241528`*^9}, 3.7574830010830545`*^9, { 3.789528195024557*^9, 3.7895281981964283`*^9}, {3.8217755133852262`*^9, 3.821775546830598*^9}, {3.8217756136000214`*^9, 3.821775685087927*^9}}, CellLabel-> "In[404]:=",ExpressionUUID->"0f68b044-b524-4fb2-b39b-bfc9783bfe85"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture assignment 1 (bar)", "Subsubsection", CellChangeTimes->{ 3.560218382980301*^9, 3.62311554059295*^9, {3.693819973244685*^9, 3.6938199838982944`*^9}, 3.6938411704287853`*^9, 3.725511566328563*^9, { 3.725592082848161*^9, 3.7255920894741154`*^9}, {3.821775715744479*^9, 3.8217757190247297`*^9}},ExpressionUUID->"cbffb78f-f288-4b9d-9208-\ 23c0cdec7cf8"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{ RowBox[{"-", "\[Rho]"}], " ", "g", " ", "A"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "1"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", " ", ",", "h", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "1", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4957897010062*^9, 3.4957898096446*^9}, { 3.4957898416870003`*^9, 3.4957898986426*^9}, {3.4957899396882*^9, 3.495789941841*^9}, {3.4957901948417997`*^9, 3.4957902000053997`*^9}, { 3.4957902785358*^9, 3.4957903351542*^9}, {3.4957903960098*^9, 3.4957904880708*^9}, {3.4957905206904*^9, 3.4957906521984*^9}, { 3.495791040888*^9, 3.4957911068136*^9}, {3.5007281090162*^9, 3.500728132467*^9}, {3.500728173828*^9, 3.5007282325972*^9}, { 3.56021839402512*^9, 3.560218396209124*^9}, {3.5602185052533154`*^9, 3.5602185542686014`*^9}, {3.5602185915994673`*^9, 3.5602185949222727`*^9}, {3.560218692750045*^9, 3.5602187145276833`*^9}, { 3.5602187506417465`*^9, 3.5602187818886013`*^9}, {3.5602188606999397`*^9, 3.560218873320362*^9}, {3.693819990129651*^9, 3.6938200061045647`*^9}, { 3.6938200670680513`*^9, 3.6938201641626053`*^9}, {3.693820198061544*^9, 3.6938201991256046`*^9}, 3.693820230839419*^9, {3.693820383431128*^9, 3.6938204160959964`*^9}, {3.693820485276953*^9, 3.6938204875870857`*^9}, { 3.6938207040664673`*^9, 3.693820736507323*^9}, {3.693821098334018*^9, 3.693821155875309*^9}, 3.693821299836543*^9, {3.6938409020884094`*^9, 3.693840936258457*^9}, {3.69384100242855*^9, 3.6938410079285574`*^9}, 3.694069910702713*^9, {3.694079748974413*^9, 3.694079837934538*^9}, { 3.725593395599037*^9, 3.7255934828895507`*^9}, 3.725593520033848*^9, { 3.7574798317865477`*^9, 3.757479924484078*^9}, {3.7574799757703543`*^9, 3.7574799982811112`*^9}, {3.757480089314517*^9, 3.7574801025691175`*^9}, { 3.7574806066027913`*^9, 3.757480607392909*^9}, {3.7574808967018805`*^9, 3.757480897227325*^9}, {3.7894568754764276`*^9, 3.7894569725694103`*^9}, { 3.7895279423749056`*^9, 3.789527942729209*^9}, {3.789536132513161*^9, 3.7895361346615615`*^9}, {3.7895363990824757`*^9, 3.789536421795721*^9}, { 3.7895364549154024`*^9, 3.789536455571832*^9}, {3.8217758025127687`*^9, 3.8217758072277403`*^9}, 3.8217759265158787`*^9}, CellLabel-> "In[210]:=",ExpressionUUID->"cbf4c2b4-279c-414b-8c49-798882e74397"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture assignment 2 (bar)", "Subsubsection", CellChangeTimes->{ 3.560218382980301*^9, 3.62311554059295*^9, {3.693819973244685*^9, 3.6938199838982944`*^9}, 3.725511564062546*^9, 3.7256253111624565`*^9, { 3.757484623695022*^9, 3.757484629267005*^9}},ExpressionUUID->"34f37bc1-0a2d-47c2-8192-\ b56237ad70ef"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"-", "\[Rho]"}], " ", "g", " ", "A"}], ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", " ", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"uY", "[", "2", "]"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}], "Input", CellChangeTimes->{{3.4957897010062*^9, 3.4957898096446*^9}, { 3.4957898416870003`*^9, 3.4957898986426*^9}, {3.4957899396882*^9, 3.495789941841*^9}, {3.4957901948417997`*^9, 3.4957902000053997`*^9}, { 3.4957902785358*^9, 3.4957903351542*^9}, {3.4957903960098*^9, 3.4957904880708*^9}, {3.4957905206904*^9, 3.4957906521984*^9}, { 3.495791040888*^9, 3.4957911068136*^9}, {3.5007281090162*^9, 3.500728132467*^9}, {3.500728173828*^9, 3.5007282325972*^9}, { 3.56021839402512*^9, 3.560218396209124*^9}, {3.5602185052533154`*^9, 3.5602185542686014`*^9}, {3.5602185915994673`*^9, 3.5602185949222727`*^9}, {3.560218692750045*^9, 3.5602187145276833`*^9}, { 3.5602187506417465`*^9, 3.5602187818886013`*^9}, {3.5602188606999397`*^9, 3.560218873320362*^9}, {3.693819990129651*^9, 3.6938200061045647`*^9}, { 3.6938200670680513`*^9, 3.6938201641626053`*^9}, {3.693820198061544*^9, 3.6938201991256046`*^9}, 3.693820230839419*^9, {3.693820383431128*^9, 3.6938204160959964`*^9}, {3.693820485276953*^9, 3.6938204875870857`*^9}, { 3.6938207040664673`*^9, 3.693820736507323*^9}, {3.693821098334018*^9, 3.693821155875309*^9}, 3.693821299836543*^9, {3.6938409020884094`*^9, 3.693840936258457*^9}, {3.69384100242855*^9, 3.6938410079285574`*^9}, { 3.6940795899041905`*^9, 3.694079609914219*^9}, {3.725604753175531*^9, 3.7256047697710576`*^9}, {3.725605100772751*^9, 3.725605136125828*^9}, { 3.7574774861000786`*^9, 3.757477494918944*^9}, {3.757477531238297*^9, 3.7574775404777417`*^9}, 3.757477907422058*^9, {3.7574846406363564`*^9, 3.7574846661830144`*^9}, 3.7574847007165318`*^9, {3.757484732772525*^9, 3.757484789221012*^9}, 3.7574848314657393`*^9, {3.789537267060418*^9, 3.7895372785150332`*^9}, {3.853033225058108*^9, 3.8530332270173187`*^9}}, CellLabel-> "In[409]:=",ExpressionUUID->"04736e3e-ef1a-4cbd-b5f3-fc5fd2f6c040"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["THERMO-MECHANICAL ANALYSIS (week 7)", "Subsection", CellChangeTimes->{{3.473055512584*^9, 3.4730555529630003`*^9}, { 3.4730575328269997`*^9, 3.473057539222*^9}, {3.4734691424642*^9, 3.4734691605758*^9}, {3.4736023142902*^9, 3.4736023273162003`*^9}, { 3.4742602258717394`*^9, 3.4742602349087396`*^9}, {3.4751533480335493`*^9, 3.4751533839809494`*^9}, {3.47515343117095*^9, 3.47515343786335*^9}, { 3.4758461893361397`*^9, 3.4758462006617393`*^9}, {3.4782569733691998`*^9, 3.4782570107312*^9}, {3.4801235510838003`*^9, 3.480123567495*^9}, { 3.480123621705*^9, 3.480123624903*^9}, {3.4806711082098*^9, 3.4806711221874*^9}, 3.4932793244166*^9, {3.4932794430078*^9, 3.4932794467362003`*^9}, 3.4933062560684*^9, 3.4933063832108*^9, { 3.4993508417324*^9, 3.4993508506556*^9}, {3.556624315771208*^9, 3.556624319733615*^9}, {3.6258072267653327`*^9, 3.625807232594666*^9}, { 3.6941709370629888`*^9, 3.694170967183031*^9}, 3.7530712518136296`*^9, 3.7866746488145547`*^9},ExpressionUUID->"a14c39cc-f745-491a-b289-\ 0eeae4dca678"], Cell[CellGroupData[{ Cell["Lecture example 6.1 (bar)", "Subsubsection", CellChangeTimes->{{3.694171020333105*^9, 3.6941710492031455`*^9}, 3.7262286037412453`*^9, 3.7901332035999823`*^9, 3.790133334060174*^9, 3.8222827885111046`*^9},ExpressionUUID->"812f0502-f78f-4580-b738-\ fc035a5be776"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"s", " ", "A"}], ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"s", " ", "A"}], ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"s", " ", "A"}], ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "4"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"L", "/", "3"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]", "[", "2", "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", RowBox[{"L", "/", "3"}]}], " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]", "[", "3", "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Simplify", "[", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "]"}], " "}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4994814977164*^9, 3.4994815003996*^9}, { 3.5009579937654*^9, 3.5009579961366*^9}, {3.562572124071875*^9, 3.5625721267862797`*^9}, {3.694260485600563*^9, 3.6942606645008135`*^9}, { 3.6942650080031333`*^9, 3.6942650178531475`*^9}, 3.694265087583245*^9, { 3.694265149373331*^9, 3.6942651519033346`*^9}, {3.694265222753434*^9, 3.694265249783472*^9}, 3.6942654753437877`*^9, {3.694265521843853*^9, 3.6942655286938624`*^9}, 3.6943211611572475`*^9, {3.726228620805838*^9, 3.7262287578043633`*^9}, {3.7262287989808445`*^9, 3.7262288053721733`*^9}, {3.726307977457318*^9, 3.726308020131757*^9}, { 3.7264017436165338`*^9, 3.72640178352305*^9}, {3.7264019537489176`*^9, 3.726401957040406*^9}, {3.7264022142676086`*^9, 3.726402218486952*^9}, 3.7264023700160475`*^9, 3.7264024806731453`*^9, 3.726402544409398*^9, { 3.7576854743135223`*^9, 3.757685482154978*^9}, 3.757685551287126*^9, { 3.8223700571434655`*^9, 3.822370084352723*^9}, 3.8223704271627655`*^9, { 3.822370686877767*^9, 3.822370688321907*^9}, {3.853210161799122*^9, 3.8532101666054835`*^9}, {3.8532101973125954`*^9, 3.8532102139581337`*^9}, {3.8532102444456997`*^9, 3.853210267026037*^9}, { 3.8532103315393543`*^9, 3.85321047360437*^9}}, CellLabel-> "In[388]:=",ExpressionUUID->"125f1d62-9708-4583-bffd-932cad43bcb5"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 6.2 (bar)", "Subsubsection", CellChangeTimes->{{3.694171020333105*^9, 3.6941710492031455`*^9}, { 3.726228956887848*^9, 3.7262289611229362`*^9}, 3.7901332092818146`*^9, 3.79013333701427*^9, 3.822282790665161*^9},ExpressionUUID->"d6dee3c3-ac4c-4f03-96d2-\ 62857d2ae5ad"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"L", "/", "2"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]", "[", "2", "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], " ", "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.4994814977164*^9, 3.4994815003996*^9}, { 3.5009579937654*^9, 3.5009579961366*^9}, {3.562572124071875*^9, 3.5625721267862797`*^9}, {3.694260485600563*^9, 3.6942606645008135`*^9}, { 3.6942650080031333`*^9, 3.6942650178531475`*^9}, 3.694265087583245*^9, { 3.694265149373331*^9, 3.6942651519033346`*^9}, {3.694265222753434*^9, 3.694265249783472*^9}, 3.6942654753437877`*^9, {3.694265521843853*^9, 3.6942655286938624`*^9}, 3.6943211611572475`*^9, {3.757685613033372*^9, 3.7576856239578505`*^9}, {3.8223707404873247`*^9, 3.8223707450521207`*^9}, {3.8532105085811586`*^9, 3.853210517669177*^9}}, CellLabel-> "In[393]:=",ExpressionUUID->"f76634f5-7aa9-4b4b-b89c-568032c4fe4b"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 6.3 (solid)", "Subsubsection", CellChangeTimes->{ 3.4734695002813997`*^9, {3.599225569652184*^9, 3.599225577904598*^9}, 3.5992258478994727`*^9, 3.6862336460745583`*^9, 3.6862909162387624`*^9, { 3.6863755415162687`*^9, 3.686375541876269*^9}, {3.686463504573411*^9, 3.686463506573414*^9}, {3.6920258070089493`*^9, 3.692025809498953*^9}, { 3.692025870269038*^9, 3.692025872639041*^9}, 3.692502004255974*^9, 3.6926165081909256`*^9, 3.6926165783510237`*^9, {3.694086478127248*^9, 3.6940864796572495`*^9}, {3.694527958552099*^9, 3.6945279596421003`*^9}, 3.726229008596427*^9, 3.7901333397983*^9, 3.8222827963204393`*^9},ExpressionUUID->"0c92047e-91c6-445f-9cae-\ d916b5244a5c"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]0", "+", "\[CapitalDelta]\[CurlyTheta]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]0", "+", "\[CapitalDelta]\[CurlyTheta]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "3", "]"}], ",", RowBox[{"uY", "[", "3", "]"}], ",", RowBox[{"uZ", "[", "3", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]0", "+", "\[CapitalDelta]\[CurlyTheta]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]0", "+", "\[CapitalDelta]\[CurlyTheta]"}]}], "}"}]}], "\[IndentingNewLine]", "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.4426469450734453`*^9, 3.4426469473978453`*^9}, { 3.630367590488758*^9, 3.6303676088811903`*^9}, {3.630367651765666*^9, 3.630367669549697*^9}, 3.630368414310605*^9, {3.6307482430426474`*^9, 3.6307482456946526`*^9}, 3.685262022046692*^9, {3.6852621067368107`*^9, 3.6852621933569317`*^9}, {3.685262233936989*^9, 3.685262252827015*^9}, 3.685267210253956*^9, {3.6852715412232933`*^9, 3.685271546353301*^9}, { 3.6853429895189857`*^9, 3.6853430232739167`*^9}, 3.6858761692133045`*^9, { 3.68821224839828*^9, 3.6882123179983773`*^9}, {3.68821235531843*^9, 3.6882123899484777`*^9}, 3.6920258039789453`*^9, {3.692025876949047*^9, 3.692025881559054*^9}, {3.6920259277091184`*^9, 3.6920259839391975`*^9}, { 3.692026020869249*^9, 3.6920260636193085`*^9}, {3.6920264969699154`*^9, 3.6920264987399178`*^9}, 3.692502011618395*^9, {3.6925022474708843`*^9, 3.6925022520801487`*^9}, {3.692502302176014*^9, 3.6925023736471014`*^9}, { 3.6925025169803*^9, 3.6925025655720787`*^9}, {3.6925026661128297`*^9, 3.6925026706260877`*^9}, {3.6926054666559763`*^9, 3.692605488996008*^9}, { 3.6926055235860567`*^9, 3.6926055236960564`*^9}, 3.69262347584068*^9, { 3.6926953173258657`*^9, 3.6926953218058724`*^9}, {3.6927029458677883`*^9, 3.692702987017846*^9}, {3.692767974815113*^9, 3.6927680130851665`*^9}, { 3.6927681266753254`*^9, 3.6927681303353305`*^9}, {3.692768161725374*^9, 3.6927681639953775`*^9}, {3.6927685368559*^9, 3.692768539955904*^9}, { 3.6927698573477488`*^9, 3.6927699280078473`*^9}, 3.6927700238579817`*^9, { 3.692770056788028*^9, 3.6927701046680946`*^9}, {3.6928578154980726`*^9, 3.692857837888104*^9}, 3.692858122048502*^9, {3.694086496987274*^9, 3.6940865394073334`*^9}, {3.6940865889274025`*^9, 3.694086607197428*^9}, { 3.694086727667597*^9, 3.6940867569976377`*^9}, {3.6940869078278494`*^9, 3.6940869938779697`*^9}, {3.694087033478025*^9, 3.694087055018055*^9}, { 3.6945279734021196`*^9, 3.6945280260321937`*^9}, {3.6945785500664263`*^9, 3.6945785683464518`*^9}, {3.694578605956504*^9, 3.6945786374265485`*^9}, 3.694578861606862*^9, {3.726229172285854*^9, 3.7262291729421663`*^9}, { 3.726370894343026*^9, 3.7263709151890526`*^9}, 3.726370949425577*^9, { 3.757746365026296*^9, 3.757746365750707*^9}, {3.822370788479022*^9, 3.8223707909713583`*^9}, {3.853211959109535*^9, 3.8532119769237614`*^9}}, CellLabel-> "In[398]:=",ExpressionUUID->"64c8dd03-37ec-4eb7-a9d6-02d5732b4c67"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 6.4 (thin slab)", "Subsubsection", CellChangeTimes->{{3.499487466582*^9, 3.4994874779544*^9}, 3.5625704065950556`*^9, 3.562572422219599*^9, {3.694171035043126*^9, 3.6941710410831347`*^9}, 3.69435160335544*^9, {3.6943533950379486`*^9, 3.6943533990579543`*^9}, 3.6945278571619573`*^9, 3.7262292354172134`*^9, 3.7901333429549046`*^9, 3.8222827981893544`*^9},ExpressionUUID->"41ecc0d8-4571-4703-991c-\ 38a3b24be17b"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "1", "]"}], ",", RowBox[{"uY", "[", "1", "]"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]0", "+", "\[CapitalDelta]\[CurlyTheta]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]0", "+", "\[CapitalDelta]\[CurlyTheta]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]0", "+", "\[CapitalDelta]\[CurlyTheta]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4994814977164*^9, 3.4994815003996*^9}, { 3.4994876433445997`*^9, 3.4994877082562*^9}, {3.4994877391286*^9, 3.4994877845558*^9}, {3.499488182645*^9, 3.4994881831442003`*^9}, { 3.4994883706562*^9, 3.4994884042586*^9}, {3.4994887442918*^9, 3.499488748301*^9}, {3.4994889348146*^9, 3.4994889623018*^9}, { 3.6943516119654527`*^9, 3.694351647105502*^9}, {3.694351682395551*^9, 3.69435172440561*^9}, {3.6943519533159304`*^9, 3.6943519616459417`*^9}, { 3.69435227463638*^9, 3.6943522845163937`*^9}, {3.694527885081996*^9, 3.6945278869719987`*^9}, {3.7263672378971424`*^9, 3.726367307373107*^9}, { 3.757746592466322*^9, 3.7577465938551464`*^9}, {3.822370824852784*^9, 3.8223708528069525`*^9}, {3.8532122889340525`*^9, 3.853212298143783*^9}}, CellLabel-> "In[403]:=",ExpressionUUID->"1e6d3493-8def-480f-b41a-c95e4cbde4b3"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture example 6.5 (plate)", "Subsubsection", CellChangeTimes->{{3.4430685047746*^9, 3.4430685067558002`*^9}, { 3.4430866035033803`*^9, 3.4430866067013803`*^9}, 3.4742603622347393`*^9, { 3.47426082029274*^9, 3.4742608300977397`*^9}, {3.4742616255317397`*^9, 3.4742616631637397`*^9}, 3.47426171431174*^9, {3.569295755520348*^9, 3.569295758265953*^9}, {3.5999975352114353`*^9, 3.5999975364126377`*^9}, { 3.6862916156897416`*^9, 3.6862916164197426`*^9}, 3.6862917141498795`*^9, 3.686291825440035*^9, 3.686463538583459*^9, 3.6920045036236353`*^9, { 3.692007141747794*^9, 3.6920071424377947`*^9}, {3.7238012915092707`*^9, 3.723801291633401*^9}, {3.7238014377077494`*^9, 3.723801461461709*^9}, { 3.7249853977242336`*^9, 3.7249854098192596`*^9}, {3.725025728192973*^9, 3.7250257332263174`*^9}, {3.7262058835652957`*^9, 3.7262058850498314`*^9}, 3.7262293274428325`*^9, {3.7577467035580034`*^9, 3.7577467044452553`*^9}, 3.790133345955064*^9, 3.822282801134905*^9},ExpressionUUID->"5155c48d-5507-4db8-8087-\ b1317c7bf071"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{"Block", "[", RowBox[{ RowBox[{"{", RowBox[{ "w", ",", "\[CapitalDelta]\[CurlyTheta]", ",", "\[Delta]wint", ",", "\[Delta]wcpl", ",", "\[CapitalOmega]", ",", "\[Delta]W"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"w", "=", RowBox[{ RowBox[{"a", "[", "0", "]"}], " ", FractionBox["x", "L"], " ", RowBox[{"(", RowBox[{"1", "-", FractionBox["x", "L"]}], ")"}], FractionBox["y", "L"], RowBox[{"(", RowBox[{"1", "-", FractionBox["y", "L"]}], ")"}]}]}], ";", " ", RowBox[{"\[CapitalDelta]\[CurlyTheta]", "=", RowBox[{ RowBox[{"-", FractionBox["z", "t"]}], "2", "\[CurlyTheta]0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", " ", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["t", "3"], " ", "\[CapitalEpsilon]"}], RowBox[{"12", RowBox[{"(", RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}], ")"}]}]], RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "\[Nu]", "0"}, {"\[Nu]", "1", "0"}, {"0", "0", FractionBox[ RowBox[{"1", "-", "\[Nu]"}], "2"]} }], "\[NoBreak]", ")"}]}], ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wcpl", "=", RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1"}, {"1"} }], "\[NoBreak]", ")"}]}], FractionBox[ RowBox[{" ", RowBox[{"\[Alpha]", " ", "\[CapitalEpsilon]"}]}], RowBox[{"1", "-", "\[Nu]"}]], RowBox[{ SubsuperscriptBox["\[Integral]", RowBox[{ RowBox[{"-", "t"}], "/", "2"}], RowBox[{"t", "/", "2"}]], RowBox[{"z", " ", "\[CapitalDelta]\[CurlyTheta]", RowBox[{"\[DifferentialD]", "z"}]}]}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", "=", RowBox[{"Rectangle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"L", ",", "L"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "=", RowBox[{"Integrate", "[", RowBox[{ RowBox[{"\[Delta]wint", "+", "\[Delta]wcpl"}], ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], StyleBox["\[Element]", "OperatorCharacter"], StyleBox["\[CapitalOmega]", "OperatorCharacter"]}], StyleBox[",", "OperatorCharacter"], StyleBox[ RowBox[{"Assumptions", "->", RowBox[{"L", ">", "0"}]}], "OperatorCharacter"]}], StyleBox["]", "OperatorCharacter"]}]}], StyleBox[";", "OperatorCharacter"], StyleBox["\[IndentingNewLine]", "OperatorCharacter"], RowBox[{"SOLVE", "[", "\[Delta]W", "]"}]}]}], "]"}], StyleBox["\[IndentingNewLine]", "OperatorCharacter"]}]}]], "Input", CellChangeTimes->{ 3.4426469719054456`*^9, {3.4430685207022*^9, 3.4430685918694*^9}, { 3.4430686602608*^9, 3.44306866271*^9}, {3.4430687542864*^9, 3.4430688359955997`*^9}, {3.4430866305537806`*^9, 3.44308673150138*^9}, { 3.4742604996717396`*^9, 3.47426061596974*^9}, 3.4742609854677396`*^9, 3.569295818310458*^9, 3.569295934780263*^9, {3.631161797385408*^9, 3.63116192958797*^9}, 3.6311621282873344`*^9, {3.6314096475812645`*^9, 3.6314096645540943`*^9}, 3.63140970193176*^9, {3.6314296672834578`*^9, 3.6314296732582684`*^9}, {3.6314297131943383`*^9, 3.631429723193956*^9}, { 3.6320283190146666`*^9, 3.6320283335070925`*^9}, {3.632028523936627*^9, 3.632028541689458*^9}, {3.6630475834142756`*^9, 3.6630475933982935`*^9}, { 3.685322391232018*^9, 3.685322396442025*^9}, {3.685322434252078*^9, 3.68532247101213*^9}, {3.6853440662625723`*^9, 3.685344095349236*^9}, { 3.6853489765747485`*^9, 3.6853489802747536`*^9}, {3.6862916241397533`*^9, 3.6862916684598155`*^9}, {3.686291740699917*^9, 3.686291791099987*^9}, { 3.6862918385400534`*^9, 3.68629185767008*^9}, 3.6920072022978787`*^9, { 3.724985419429654*^9, 3.7249854733258133`*^9}, {3.7249855047198954`*^9, 3.724985672643574*^9}, {3.724985823331335*^9, 3.72498583108245*^9}, { 3.7249859256363735`*^9, 3.724985954061252*^9}, {3.7249860773711185`*^9, 3.7249860873564367`*^9}, {3.72498667993143*^9, 3.7249867213577213`*^9}, { 3.724986817961895*^9, 3.7249868212275767`*^9}, {3.725021200723025*^9, 3.725021205166871*^9}, {3.7250283445255947`*^9, 3.725028396615054*^9}, { 3.7262059023641534`*^9, 3.726205930038945*^9}, {3.726205996702224*^9, 3.726206127347*^9}, {3.7262061677575116`*^9, 3.7262063337281322`*^9}, { 3.7262063654658585`*^9, 3.726206365997158*^9}, 3.7262064731803665`*^9, 3.7262065193258057`*^9, {3.7262065827700586`*^9, 3.726206588161188*^9}, { 3.726206639401017*^9, 3.726206685124585*^9}, 3.7577467115613346`*^9, { 3.757746928634151*^9, 3.757746956452608*^9}, {3.790562134068997*^9, 3.790562144580222*^9}, {3.7905628426912985`*^9, 3.790562853795657*^9}, { 3.8222904142238913`*^9, 3.8222904484586935`*^9}, {3.8222905396678267`*^9, 3.822290621977132*^9}, {3.8222908062333317`*^9, 3.8222909103840895`*^9}, { 3.82229104434663*^9, 3.822291057762763*^9}, 3.822291090107176*^9, 3.822291237551684*^9, {3.8222913237630434`*^9, 3.822291351423003*^9}, { 3.8222913877665834`*^9, 3.822291413365552*^9}, {3.85321265478815*^9, 3.8532127425832305`*^9}}, CellLabel-> "In[408]:=",ExpressionUUID->"01a9db10-842c-403f-9829-4ee0908a1731"] }, Closed]], Cell[CellGroupData[{ Cell["Exercise problem 1 (bar)", "Subsubsection", CellChangeTimes->{{3.694171020333105*^9, 3.6941710492031455`*^9}, { 3.694320635316511*^9, 3.694320645406525*^9}, 3.7262215852006197`*^9, 3.7901335709930058`*^9, {3.790133686084855*^9, 3.790133688198171*^9}},ExpressionUUID->"34af25ea-9700-49b0-8288-\ 26e6f8064d79"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"s", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]", "[", "1", "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"h", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]", "[", "2", "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4994814977164*^9, 3.4994815003996*^9}, { 3.5009579937654*^9, 3.5009579961366*^9}, {3.562572124071875*^9, 3.5625721267862797`*^9}, {3.694260485600563*^9, 3.6942606645008135`*^9}, { 3.6942650080031333`*^9, 3.6942650178531475`*^9}, 3.694265087583245*^9, { 3.694265149373331*^9, 3.6942651519033346`*^9}, {3.694265222753434*^9, 3.694265249783472*^9}, 3.6942654753437877`*^9, {3.694265521843853*^9, 3.6942655286938624`*^9}, {3.694320658056543*^9, 3.6943206662965546`*^9}, 3.694321100397162*^9, {3.6943211808672748`*^9, 3.694321198067299*^9}, { 3.6943212603173857`*^9, 3.6943212821274166`*^9}, {3.6945792415273943`*^9, 3.6945793147174964`*^9}, 3.694579360637561*^9, 3.6945797039280415`*^9, { 3.7264646047356343`*^9, 3.726464609439276*^9}, {3.726464678493162*^9, 3.726464682868911*^9}, {3.758007980609372*^9, 3.7580080180068483`*^9}, 3.7580080766027403`*^9, 3.8223709049177957`*^9, {3.8532127808477497`*^9, 3.853212811144683*^9}}, CellLabel-> "In[409]:=",ExpressionUUID->"ea437664-d702-486c-ab1c-df75110d87fc"] }, Closed]], Cell[CellGroupData[{ Cell["Exercise problem 2 (bar)", "Subsubsection", CellChangeTimes->{{3.694171020333105*^9, 3.6941710492031455`*^9}, { 3.694320635316511*^9, 3.694320645406525*^9}, 3.6945793783775854`*^9, 3.7262215921075077`*^9, 3.7901335744252267`*^9, 3.790133710048728*^9},ExpressionUUID->"2a746516-ac0d-4c5a-9471-\ 4c17790fb028"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"L", "/", "2"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]", "[", "2", "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Simplify", "[", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4994814977164*^9, 3.4994815003996*^9}, { 3.5009579937654*^9, 3.5009579961366*^9}, {3.562572124071875*^9, 3.5625721267862797`*^9}, {3.694260485600563*^9, 3.6942606645008135`*^9}, { 3.6942650080031333`*^9, 3.6942650178531475`*^9}, 3.694265087583245*^9, { 3.694265149373331*^9, 3.6942651519033346`*^9}, {3.694265222753434*^9, 3.694265249783472*^9}, 3.6942654753437877`*^9, {3.694265521843853*^9, 3.6942655286938624`*^9}, {3.694320658056543*^9, 3.6943206662965546`*^9}, 3.694321100397162*^9, {3.6943211808672748`*^9, 3.694321198067299*^9}, { 3.6943212603173857`*^9, 3.6943212821274166`*^9}, {3.6945793934976068`*^9, 3.6945793962276106`*^9}, {3.6945794336976633`*^9, 3.694579462597704*^9}, 3.694579720658065*^9, {3.7262244135330825`*^9, 3.7262244245498486`*^9}, { 3.7264645323529987`*^9, 3.726464592984414*^9}, {3.726464693010617*^9, 3.726464717278513*^9}, {3.726464754564005*^9, 3.7264647552046957`*^9}, { 3.758008181593988*^9, 3.7580081866865425`*^9}, {3.758008239533526*^9, 3.7580083000659113`*^9}, {3.822370934113742*^9, 3.8223709384032736`*^9}, { 3.8532140624120817`*^9, 3.8532140706327295`*^9}}, CellLabel-> "In[413]:=",ExpressionUUID->"43c233eb-a8d9-4850-b1ee-2ed9777ecd83"] }, Closed]], Cell[CellGroupData[{ Cell["Exercise problem 3 (truss)", "Subsubsection", CellChangeTimes->{{3.694171020333105*^9, 3.6941710492031455`*^9}, { 3.694320635316511*^9, 3.694320645406525*^9}, {3.6943246286761017`*^9, 3.6943246319861064`*^9}, 3.6944060216654315`*^9, 3.7262215999677*^9, 3.7262246878276234`*^9, 3.758008381328991*^9, {3.758009251812319*^9, 3.7580092645611873`*^9}, 3.7901335767519703`*^9, 3.790133712716427*^9},ExpressionUUID->"ec7cb860-2bf7-41a9-bf96-\ 0c71afc0de81"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", RowBox[{ SqrtBox["2"], "A"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"4", ",", "2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"uZ", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]0", "+", "\[CapitalDelta]\[CurlyTheta]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", " ", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"-", RowBox[{"uZ", "[", "2", "]"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]0", "+", "\[CapitalDelta]\[CurlyTheta]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", " ", ",", "0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], " "}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4994814977164*^9, 3.4994815003996*^9}, { 3.5009579937654*^9, 3.5009579961366*^9}, {3.562572124071875*^9, 3.5625721267862797`*^9}, {3.694260485600563*^9, 3.6942606645008135`*^9}, { 3.6942650080031333`*^9, 3.6942650178531475`*^9}, 3.694265087583245*^9, { 3.694265149373331*^9, 3.6942651519033346`*^9}, {3.694265222753434*^9, 3.694265249783472*^9}, 3.6942654753437877`*^9, {3.694265521843853*^9, 3.6942655286938624`*^9}, {3.694320658056543*^9, 3.6943206662965546`*^9}, 3.694321100397162*^9, {3.6943211808672748`*^9, 3.694321198067299*^9}, { 3.6943212603173857`*^9, 3.6943212821274166`*^9}, {3.6943246384761157`*^9, 3.6943248045763483`*^9}, {3.69432489844648*^9, 3.694324945836546*^9}, { 3.6943251833568783`*^9, 3.694325219286929*^9}, {3.6945795367478075`*^9, 3.694579566187848*^9}, {3.726402666829811*^9, 3.726402670383405*^9}, { 3.726465914917368*^9, 3.7264659162925005`*^9}, {3.7580092113374405`*^9, 3.7580092179296255`*^9}, {3.8223709655616674`*^9, 3.8223709683980846`*^9}, {3.8532141617484627`*^9, 3.853214183919198*^9}}, CellLabel-> "In[418]:=",ExpressionUUID->"62fb041f-0df8-452c-a701-4362943eb87b"] }, Closed]], Cell[CellGroupData[{ Cell["Exercise problem 4 (truss)", "Subsubsection", CellChangeTimes->{{3.694171020333105*^9, 3.6941710492031455`*^9}, { 3.694320635316511*^9, 3.694320645406525*^9}, {3.6943246286761017`*^9, 3.6943246319861064`*^9}, 3.694327323881875*^9, 3.694406024055435*^9, 3.7262216047647996`*^9, 3.7262246917341337`*^9, 3.7580092950074606`*^9, 3.790133580363652*^9, 3.7901337156039553`*^9},ExpressionUUID->"8dca84da-6271-46e4-8a2e-\ 481d1ae1ec49"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "4"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "1", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", " ", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", " ", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], " "}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4994814977164*^9, 3.4994815003996*^9}, { 3.5009579937654*^9, 3.5009579961366*^9}, {3.562572124071875*^9, 3.5625721267862797`*^9}, {3.694260485600563*^9, 3.6942606645008135`*^9}, { 3.6942650080031333`*^9, 3.6942650178531475`*^9}, 3.694265087583245*^9, { 3.694265149373331*^9, 3.6942651519033346`*^9}, {3.694265222753434*^9, 3.694265249783472*^9}, 3.6942654753437877`*^9, {3.694265521843853*^9, 3.6942655286938624`*^9}, {3.694320658056543*^9, 3.6943206662965546`*^9}, 3.694321100397162*^9, {3.6943211808672748`*^9, 3.694321198067299*^9}, { 3.6943212603173857`*^9, 3.6943212821274166`*^9}, {3.6943246384761157`*^9, 3.6943248045763483`*^9}, {3.69432489844648*^9, 3.694324945836546*^9}, { 3.6943251833568783`*^9, 3.694325219286929*^9}, {3.69432737006194*^9, 3.6943274488520503`*^9}, 3.694419382534791*^9, {3.7580103793082*^9, 3.758010389133934*^9}, {3.82237099593052*^9, 3.822370998714036*^9}, { 3.8532142179061117`*^9, 3.8532142241206512`*^9}}, CellLabel-> "In[423]:=",ExpressionUUID->"9f8a5367-5cb2-4d84-a861-d9fd22e8d0a9"] }, Closed]], Cell[CellGroupData[{ Cell["Exercise problem 5 (thin slab)", "Subsubsection", CellChangeTimes->{{3.499487466582*^9, 3.4994874779544*^9}, { 3.4994910657246*^9, 3.4994910793122*^9}, {3.562569560449569*^9, 3.5625695636631746`*^9}, 3.562570402929049*^9, {3.6943375929467063`*^9, 3.6943376002267165`*^9}, 3.694406026805439*^9, {3.6944312298724174`*^9, 3.694431233695636*^9}, {3.7262249061162586`*^9, 3.726224912569766*^9}, 3.7580244401018515`*^9, 3.7901335828870106`*^9, 3.790133718434207*^9},ExpressionUUID->"bd6bde99-16ce-472b-a55e-\ d94c88513402"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "1", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4994814977164*^9, 3.4994815003996*^9}, { 3.4994876433445997`*^9, 3.4994877082562*^9}, {3.4994877391286*^9, 3.4994877845558*^9}, {3.499488182645*^9, 3.4994881831442003`*^9}, { 3.4994883706562*^9, 3.4994884042586*^9}, {3.4994887442918*^9, 3.499488748301*^9}, {3.4994889348146*^9, 3.4994889623018*^9}, { 3.4994910895926*^9, 3.4994911605257998`*^9}, {3.4994912009765997`*^9, 3.4994912105081997`*^9}, {3.499492512803*^9, 3.4994925228494*^9}, 3.499492575359*^9, {3.5625696348461*^9, 3.5625696391049075`*^9}, { 3.6943376083067274`*^9, 3.6943377050568633`*^9}, {3.694337736226907*^9, 3.694337836567047*^9}, {3.69433799542727*^9, 3.69433799558727*^9}, { 3.6943382395276117`*^9, 3.6943382530976305`*^9}, {3.6943386652882075`*^9, 3.694338672808218*^9}, 3.6943400978202133`*^9, {3.694340128930257*^9, 3.6943401346302643`*^9}, {3.694352247876343*^9, 3.69435226019636*^9}, { 3.6944312433631887`*^9, 3.6944312664045067`*^9}, {3.6944314730323253`*^9, 3.694431491689392*^9}, {3.6944317924565706`*^9, 3.6944318024421415`*^9}, 3.694431834732989*^9, {3.7580244524019127`*^9, 3.7580244589711*^9}, { 3.822371024737362*^9, 3.8223710408253517`*^9}, 3.8532142715195665`*^9}, CellLabel-> "In[428]:=",ExpressionUUID->"800820a1-a119-46b2-bafb-a6fe6935c401"] }, Closed]], Cell[CellGroupData[{ Cell["Exercise problem 6 (thin slab)", "Subsubsection", CellChangeTimes->{{3.499487466582*^9, 3.4994874779544*^9}, { 3.4994910657246*^9, 3.4994910793122*^9}, {3.562569560449569*^9, 3.5625695636631746`*^9}, 3.562570402929049*^9, {3.6943375929467063`*^9, 3.6943376002267165`*^9}, 3.694406026805439*^9, 3.726224696312886*^9, 3.7262249172111826`*^9, {3.7580244975473228`*^9, 3.7580245477488456`*^9}, 3.790133585140024*^9, 3.7901337229271965`*^9},ExpressionUUID->"7565dc7e-2ddf-422f-90e5-\ 73be0d409be4"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "1", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "1", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4994814977164*^9, 3.4994815003996*^9}, { 3.4994876433445997`*^9, 3.4994877082562*^9}, {3.4994877391286*^9, 3.4994877845558*^9}, {3.499488182645*^9, 3.4994881831442003`*^9}, { 3.4994883706562*^9, 3.4994884042586*^9}, {3.4994887442918*^9, 3.499488748301*^9}, {3.4994889348146*^9, 3.4994889623018*^9}, { 3.4994910895926*^9, 3.4994911605257998`*^9}, {3.4994912009765997`*^9, 3.4994912105081997`*^9}, {3.499492512803*^9, 3.4994925228494*^9}, 3.499492575359*^9, {3.5625696348461*^9, 3.5625696391049075`*^9}, { 3.6943376083067274`*^9, 3.6943377050568633`*^9}, {3.694337736226907*^9, 3.694337836567047*^9}, {3.69433799542727*^9, 3.69433799558727*^9}, { 3.6943382395276117`*^9, 3.6943382530976305`*^9}, {3.6943386652882075`*^9, 3.694338672808218*^9}, 3.6943400978202133`*^9, {3.694340128930257*^9, 3.6943401346302643`*^9}, {3.694352247876343*^9, 3.69435226019636*^9}, { 3.7262248580015087`*^9, 3.726224868877959*^9}, {3.758024561586712*^9, 3.7580245682001753`*^9}, {3.82237107153525*^9, 3.8223710739547815`*^9}, 3.853214306941168*^9}, CellLabel-> "In[433]:=",ExpressionUUID->"581b87c7-aa08-4cc6-9eed-991ce0728ce4"] }, Closed]], Cell[CellGroupData[{ Cell["Exercise problem 7 (thin slab)", "Subsubsection", CellChangeTimes->{{3.499487466582*^9, 3.4994874779544*^9}, { 3.4994910657246*^9, 3.4994910793122*^9}, {3.562569560449569*^9, 3.5625695636631746`*^9}, 3.562570402929049*^9, {3.6943375929467063`*^9, 3.6943376002267165`*^9}, 3.694406026805439*^9, 3.6944148753044806`*^9, 3.7262247019228444`*^9, {3.7262249870466585`*^9, 3.7262249914062004`*^9}, 3.7580246923686523`*^9, 3.7901335915540752`*^9, 3.7901337251492295`*^9},ExpressionUUID->"fcfc481a-5ce3-4751-a9c3-\ c6f322445fe2"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"s", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "4", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"s", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "4"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]", "[", "3", "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]", "[", "3", "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Simplify", "[", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4994814977164*^9, 3.4994815003996*^9}, { 3.4994876433445997`*^9, 3.4994877082562*^9}, {3.4994877391286*^9, 3.4994877845558*^9}, {3.499488182645*^9, 3.4994881831442003`*^9}, { 3.4994883706562*^9, 3.4994884042586*^9}, {3.4994887442918*^9, 3.499488748301*^9}, {3.4994889348146*^9, 3.4994889623018*^9}, { 3.4994910895926*^9, 3.4994911605257998`*^9}, {3.4994912009765997`*^9, 3.4994912105081997`*^9}, {3.499492512803*^9, 3.4994925228494*^9}, 3.499492575359*^9, {3.5625696348461*^9, 3.5625696391049075`*^9}, { 3.6943376083067274`*^9, 3.6943377050568633`*^9}, {3.694337736226907*^9, 3.694337836567047*^9}, {3.69433799542727*^9, 3.69433799558727*^9}, { 3.6943382395276117`*^9, 3.6943382530976305`*^9}, {3.6943386652882075`*^9, 3.694338672808218*^9}, 3.6943400978202133`*^9, {3.694340128930257*^9, 3.6943401346302643`*^9}, {3.694352247876343*^9, 3.69435226019636*^9}, { 3.69441488183449*^9, 3.6944149755846214`*^9}, 3.6944150060146637`*^9, { 3.6944150741247587`*^9, 3.69441508906478*^9}, {3.6944160613381414`*^9, 3.6944160921781845`*^9}, {3.6944167992291746`*^9, 3.694416815579197*^9}, { 3.6944168620292625`*^9, 3.694416875959282*^9}, {3.6944183207233047`*^9, 3.6944183712233753`*^9}, 3.694579665157987*^9, {3.726214230347681*^9, 3.7262142305040207`*^9}, {3.7262250279256763`*^9, 3.7262250419115257`*^9}, {3.7580246498391137`*^9, 3.758024663579355*^9}, { 3.8223710961344852`*^9, 3.822371115052908*^9}, {3.853214342204943*^9, 3.8532143622068267`*^9}}, CellLabel-> "In[438]:=",ExpressionUUID->"db63d7ff-b48a-4b41-a5d2-a147db0d3b75"] }, Closed]], Cell[CellGroupData[{ Cell["Exercise problem 8 (thin slab)", "Subsubsection", CellChangeTimes->{{3.499487466582*^9, 3.4994874779544*^9}, { 3.4994910657246*^9, 3.4994910793122*^9}, {3.562569560449569*^9, 3.5625695636631746`*^9}, 3.562570402929049*^9, {3.6943375929467063`*^9, 3.6943376002267165`*^9}, 3.694406026805439*^9, {3.726213788988196*^9, 3.726213794488776*^9}, {3.7580247319153395`*^9, 3.758024734229988*^9}, 3.790133593902794*^9, 3.7901337270427856`*^9},ExpressionUUID->"28ae77f4-523a-4be5-a103-\ 2ed3fcd70ef6"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"s", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]", "[", "3", "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]", "[", "4", "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Simplify", "[", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4994814977164*^9, 3.4994815003996*^9}, { 3.4994876433445997`*^9, 3.4994877082562*^9}, {3.4994877391286*^9, 3.4994877845558*^9}, {3.499488182645*^9, 3.4994881831442003`*^9}, { 3.4994883706562*^9, 3.4994884042586*^9}, {3.4994887442918*^9, 3.499488748301*^9}, {3.4994889348146*^9, 3.4994889623018*^9}, { 3.4994910895926*^9, 3.4994911605257998`*^9}, {3.4994912009765997`*^9, 3.4994912105081997`*^9}, {3.499492512803*^9, 3.4994925228494*^9}, 3.499492575359*^9, {3.5625696348461*^9, 3.5625696391049075`*^9}, { 3.6943376083067274`*^9, 3.6943377050568633`*^9}, {3.694337736226907*^9, 3.694337836567047*^9}, {3.69433799542727*^9, 3.69433799558727*^9}, { 3.6943382395276117`*^9, 3.6943382530976305`*^9}, {3.6943386652882075`*^9, 3.694338672808218*^9}, 3.6943400978202133`*^9, {3.694340128930257*^9, 3.6943401346302643`*^9}, {3.694352247876343*^9, 3.69435226019636*^9}, { 3.7262140346078444`*^9, 3.7262140541567793`*^9}, {3.7262141086781483`*^9, 3.726214166277943*^9}, {3.726214525816331*^9, 3.7262145263633146`*^9}, { 3.7262145697272577`*^9, 3.726214575524747*^9}, {3.726226638345352*^9, 3.726226638689148*^9}, {3.758024742273337*^9, 3.7580247486205378`*^9}, { 3.82237114956907*^9, 3.8223711637889395`*^9}, 3.8532143956016684`*^9}, CellLabel-> "In[443]:=",ExpressionUUID->"d34ea64d-54cb-4146-a450-92c300bd1a1f"] }, Closed]], Cell[CellGroupData[{ Cell["Exercise problem 9 (bar)", "Subsubsection", CellChangeTimes->{{3.694171020333105*^9, 3.6941710492031455`*^9}, { 3.694320635316511*^9, 3.694320645406525*^9}, 3.7262215852006197`*^9, { 3.726226718228784*^9, 3.726226721713334*^9}, {3.7580248169988203`*^9, 3.758024819056037*^9}, 3.7901335961384783`*^9, 3.790133729247693*^9},ExpressionUUID->"d9fc8a54-e25e-46f1-9a61-\ aeb047ab4408"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Rho]"}], " ", "A", " ", "g"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", " ", "\[CurlyTheta]0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Simplify", "[", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4994814977164*^9, 3.4994815003996*^9}, { 3.5009579937654*^9, 3.5009579961366*^9}, {3.562572124071875*^9, 3.5625721267862797`*^9}, {3.694260485600563*^9, 3.6942606645008135`*^9}, { 3.6942650080031333`*^9, 3.6942650178531475`*^9}, 3.694265087583245*^9, { 3.694265149373331*^9, 3.6942651519033346`*^9}, {3.694265222753434*^9, 3.694265249783472*^9}, 3.6942654753437877`*^9, {3.694265521843853*^9, 3.6942655286938624`*^9}, {3.694320658056543*^9, 3.6943206662965546`*^9}, 3.694321100397162*^9, {3.6943211808672748`*^9, 3.694321198067299*^9}, { 3.6943212603173857`*^9, 3.6943212821274166`*^9}, {3.6945792415273943`*^9, 3.6945793147174964`*^9}, 3.694579360637561*^9, 3.6945797039280415`*^9, { 3.7262267310582952`*^9, 3.7262268937472987`*^9}, {3.758024835013898*^9, 3.758024846532082*^9}, {3.822371189664237*^9, 3.822371193232697*^9}, { 3.8532144304204135`*^9, 3.853214441853069*^9}}, CellLabel-> "In[448]:=",ExpressionUUID->"1f52f6b5-fe93-47d5-a047-f64d7b9e6458"] }, Closed]], Cell[CellGroupData[{ Cell["Exercise problem 10 (plate)", "Subsubsection", CellChangeTimes->{{3.4430685047746*^9, 3.4430685067558002`*^9}, { 3.4430866035033803`*^9, 3.4430866067013803`*^9}, 3.4742603622347393`*^9, { 3.47426082029274*^9, 3.4742608300977397`*^9}, {3.4742616255317397`*^9, 3.4742616631637397`*^9}, 3.47426171431174*^9, {3.569295755520348*^9, 3.569295758265953*^9}, {3.5999975352114353`*^9, 3.5999975364126377`*^9}, { 3.6862916156897416`*^9, 3.6862916164197426`*^9}, 3.6862917141498795`*^9, 3.686291825440035*^9, 3.686463538583459*^9, 3.6920045036236353`*^9, { 3.692007141747794*^9, 3.6920071424377947`*^9}, {3.7238012915092707`*^9, 3.723801291633401*^9}, {3.7238014377077494`*^9, 3.723801461461709*^9}, { 3.7249853977242336`*^9, 3.7249854098192596`*^9}, {3.725025728192973*^9, 3.7250257332263174`*^9}, {3.7262058835652957`*^9, 3.7262058850498314`*^9}, {3.7262067305356245`*^9, 3.726206738333324*^9}, { 3.7577470295179353`*^9, 3.7577470300668592`*^9}, {3.7580248225537596`*^9, 3.7580248247305193`*^9}, 3.790133598222252*^9, 3.7901337315379934`*^9},ExpressionUUID->"020dfa95-9901-42e0-8cba-\ 7f947e811a92"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{"Block", "[", RowBox[{ RowBox[{"{", RowBox[{ "w", ",", "\[Delta]wint", ",", "\[Delta]wcpl", ",", "\[CapitalOmega]", ",", "\[Delta]W"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"w", "=", RowBox[{ RowBox[{"a", "[", "0", "]"}], " ", RowBox[{"Sin", "[", RowBox[{"Pi", " ", FractionBox["x", "L"]}], " ", "]"}], " ", RowBox[{"Sin", "[", RowBox[{"Pi", " ", FractionBox["y", "L"]}], " ", "]"}]}]}], ";", " ", RowBox[{"\[CapitalDelta]\[CurlyTheta]", "=", RowBox[{ RowBox[{"-", FractionBox["z", "t"]}], "2", "\[CurlyTheta]0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", " ", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["t", "3"], " ", "\[CapitalEpsilon]"}], RowBox[{"12", RowBox[{"(", RowBox[{"1", "-", SuperscriptBox["\[Nu]", "2"]}], ")"}]}]], RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "\[Nu]", "0"}, {"\[Nu]", "1", "0"}, {"0", "0", FractionBox[ RowBox[{"1", "-", "\[Nu]"}], "2"]} }], "\[NoBreak]", ")"}]}], ")"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]}, { RowBox[{"2", " ", RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "y"}]], "w"}]}]} }], "\[NoBreak]", ")"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wcpl", "=", RowBox[{"-", RowBox[{"Tr", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"x", ",", "x"}]], "w"}]}, { RowBox[{ SubscriptBox["\[PartialD]", RowBox[{"y", ",", "y"}]], "w"}]} }], "\[NoBreak]", ")"}], "\[Transpose]"}], "]"}], ".", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1"}, {"1"} }], "\[NoBreak]", ")"}]}], FractionBox[ RowBox[{" ", RowBox[{"\[Alpha]", " ", "\[CapitalEpsilon]"}]}], RowBox[{"1", "-", "\[Nu]"}]], RowBox[{ SubsuperscriptBox["\[Integral]", RowBox[{ RowBox[{"-", "t"}], "/", "2"}], RowBox[{"t", "/", "2"}]], RowBox[{"z", " ", "\[CapitalDelta]\[CurlyTheta]", RowBox[{"\[DifferentialD]", "z"}]}]}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", "=", RowBox[{"Rectangle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"L", ",", "L"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "=", RowBox[{"Integrate", "[", RowBox[{ RowBox[{"\[Delta]wint", "+", "\[Delta]wcpl"}], ",", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], "\[Element]", "\[CapitalOmega]"}], ",", RowBox[{"Assumptions", "->", RowBox[{"L", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"SOLVE", "[", "\[Delta]W", "]"}]}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{ 3.4426469719054456`*^9, {3.4430685207022*^9, 3.4430685918694*^9}, { 3.4430686602608*^9, 3.44306866271*^9}, {3.4430687542864*^9, 3.4430688359955997`*^9}, {3.4430866305537806`*^9, 3.44308673150138*^9}, { 3.4742604996717396`*^9, 3.47426061596974*^9}, 3.4742609854677396`*^9, 3.569295818310458*^9, 3.569295934780263*^9, {3.631161797385408*^9, 3.63116192958797*^9}, 3.6311621282873344`*^9, {3.6314096475812645`*^9, 3.6314096645540943`*^9}, 3.63140970193176*^9, {3.6314296672834578`*^9, 3.6314296732582684`*^9}, {3.6314297131943383`*^9, 3.631429723193956*^9}, { 3.6320283190146666`*^9, 3.6320283335070925`*^9}, {3.632028523936627*^9, 3.632028541689458*^9}, {3.6630475834142756`*^9, 3.6630475933982935`*^9}, { 3.685322391232018*^9, 3.685322396442025*^9}, {3.685322434252078*^9, 3.68532247101213*^9}, {3.6853440662625723`*^9, 3.685344095349236*^9}, { 3.6853489765747485`*^9, 3.6853489802747536`*^9}, {3.6862916241397533`*^9, 3.6862916684598155`*^9}, {3.686291740699917*^9, 3.686291791099987*^9}, { 3.6862918385400534`*^9, 3.68629185767008*^9}, 3.6920072022978787`*^9, { 3.724985419429654*^9, 3.7249854733258133`*^9}, {3.7249855047198954`*^9, 3.724985672643574*^9}, {3.724985823331335*^9, 3.72498583108245*^9}, { 3.7249859256363735`*^9, 3.724985954061252*^9}, {3.7249860773711185`*^9, 3.7249860873564367`*^9}, {3.72498667993143*^9, 3.7249867213577213`*^9}, { 3.724986817961895*^9, 3.7249868212275767`*^9}, {3.725021200723025*^9, 3.725021205166871*^9}, {3.7250283445255947`*^9, 3.725028396615054*^9}, { 3.7262059023641534`*^9, 3.726205930038945*^9}, {3.726205996702224*^9, 3.726206127347*^9}, {3.7262061677575116`*^9, 3.7262063337281322`*^9}, { 3.7262063654658585`*^9, 3.726206365997158*^9}, 3.7262064731803665`*^9, 3.7262065193258057`*^9, {3.7262065827700586`*^9, 3.726206588161188*^9}, { 3.726206639401017*^9, 3.726206685124585*^9}, {3.726206752741091*^9, 3.7262067959487677`*^9}, {3.7580248983260403`*^9, 3.7580249229575377`*^9}, {3.790563741361431*^9, 3.7905637452182727`*^9}, { 3.8222916789160852`*^9, 3.8222917385257483`*^9}, {3.8532160512328773`*^9, 3.853216125366497*^9}}, CellLabel-> "In[453]:=",ExpressionUUID->"0e7e8295-10f7-49a3-8b1b-f3ae4127f07e"] }, Closed]], Cell[CellGroupData[{ Cell["Home assignment 1 (bar)", "Subsubsection", CellChangeTimes->{{3.694171020333105*^9, 3.6941710492031455`*^9}, { 3.694320635316511*^9, 3.694320645406525*^9}, 3.6945793783775854`*^9, 3.7262215921075077`*^9, 3.7579961343745155`*^9},ExpressionUUID->"12644844-84ad-46c3-ac44-\ b43908b5aa02"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"s", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"s", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "2"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", "L"}], " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]", "[", "3", "]"}]}], "}"}]}], "\[IndentingNewLine]", "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], " ", " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Simplify", "[", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4994814977164*^9, 3.4994815003996*^9}, { 3.5009579937654*^9, 3.5009579961366*^9}, {3.562572124071875*^9, 3.5625721267862797`*^9}, {3.694260485600563*^9, 3.6942606645008135`*^9}, { 3.6942650080031333`*^9, 3.6942650178531475`*^9}, 3.694265087583245*^9, { 3.694265149373331*^9, 3.6942651519033346`*^9}, {3.694265222753434*^9, 3.694265249783472*^9}, 3.6942654753437877`*^9, {3.694265521843853*^9, 3.6942655286938624`*^9}, {3.694320658056543*^9, 3.6943206662965546`*^9}, 3.694321100397162*^9, {3.6943211808672748`*^9, 3.694321198067299*^9}, { 3.6943212603173857`*^9, 3.6943212821274166`*^9}, {3.6945793934976068`*^9, 3.6945793962276106`*^9}, {3.6945794336976633`*^9, 3.694579462597704*^9}, 3.694579720658065*^9, {3.7262244135330825`*^9, 3.7262244245498486`*^9}, { 3.7264645323529987`*^9, 3.726464592984414*^9}, {3.726464693010617*^9, 3.726464717278513*^9}, {3.726464754564005*^9, 3.7264647552046957`*^9}, { 3.757996141779167*^9, 3.757996162899214*^9}, {3.7901290539312696`*^9, 3.7901290792093644`*^9}, 3.7901291237424383`*^9, 3.7901341599938126`*^9, { 3.8223713485518274`*^9, 3.8223713514371142`*^9}, {3.8532161596280184`*^9, 3.8532161716866455`*^9}}, CellLabel-> "In[454]:=",ExpressionUUID->"e0a93ec1-fd46-4119-b0df-efdd2d226ed7"] }, Closed]], Cell[CellGroupData[{ Cell["Home assignment 2 (bar)", "Subsubsection", CellChangeTimes->{{3.694171020333105*^9, 3.6941710492031455`*^9}, { 3.694320635316511*^9, 3.694320645406525*^9}, 3.694406019025428*^9, { 3.6944239890468645`*^9, 3.6944239974668765`*^9}, {3.7262246384942493`*^9, 3.726224644510517*^9}, 3.7579982269300756`*^9},ExpressionUUID->"d7c37cef-b389-4fac-bb43-\ 6c1ec837f560"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", RowBox[{"4", "A"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "2", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]", "[", "2", "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", "L"}], " ", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], " "}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4994814977164*^9, 3.4994815003996*^9}, { 3.5009579937654*^9, 3.5009579961366*^9}, {3.562572124071875*^9, 3.5625721267862797`*^9}, {3.694260485600563*^9, 3.6942606645008135`*^9}, { 3.6942650080031333`*^9, 3.6942650178531475`*^9}, 3.694265087583245*^9, { 3.694265149373331*^9, 3.6942651519033346`*^9}, {3.694265222753434*^9, 3.694265249783472*^9}, 3.6942654753437877`*^9, {3.694265521843853*^9, 3.6942655286938624`*^9}, {3.694320658056543*^9, 3.6943206662965546`*^9}, 3.694321100397162*^9, {3.6943211808672748`*^9, 3.694321198067299*^9}, { 3.6943212603173857`*^9, 3.6943212821274166`*^9}, {3.6944240081368914`*^9, 3.6944240281469193`*^9}, 3.6945798778882847`*^9, 3.6953433513909397`*^9, { 3.726402609129484*^9, 3.726402618632744*^9}, {3.726465882296791*^9, 3.726465882687396*^9}, 3.757998251252205*^9, {3.7579982838698497`*^9, 3.7579982907273273`*^9}, {3.790051020706258*^9, 3.790051030075369*^9}, { 3.822371375469983*^9, 3.822371378140842*^9}, {3.853216197933406*^9, 3.853216206620552*^9}}, CellLabel-> "In[459]:=",ExpressionUUID->"c32192a0-b56f-4588-8ff2-68fec2bccdf8"] }, Closed]], Cell[CellGroupData[{ Cell["Home assignment 3a (thin slab)", "Subsubsection", CellChangeTimes->{{3.499487466582*^9, 3.4994874779544*^9}, { 3.4994910657246*^9, 3.4994910793122*^9}, {3.562569560449569*^9, 3.5625695636631746`*^9}, 3.562570402929049*^9, {3.6943375929467063`*^9, 3.6943376002267165`*^9}, 3.694406026805439*^9, 3.6944148753044806`*^9, 3.7262247019228444`*^9, {3.7262249870466585`*^9, 3.7262249914062004`*^9}, { 3.7580045257709618`*^9, 3.75800453036374*^9}, 3.790664201546558*^9},ExpressionUUID->"e03e23ef-6461-4edd-923f-\ 604e264ce75b"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"F", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "1", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "1", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Simplify", "[", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4994814977164*^9, 3.4994815003996*^9}, { 3.4994876433445997`*^9, 3.4994877082562*^9}, {3.4994877391286*^9, 3.4994877845558*^9}, {3.499488182645*^9, 3.4994881831442003`*^9}, { 3.4994883706562*^9, 3.4994884042586*^9}, {3.4994887442918*^9, 3.499488748301*^9}, {3.4994889348146*^9, 3.4994889623018*^9}, { 3.4994910895926*^9, 3.4994911605257998`*^9}, {3.4994912009765997`*^9, 3.4994912105081997`*^9}, {3.499492512803*^9, 3.4994925228494*^9}, 3.499492575359*^9, {3.5625696348461*^9, 3.5625696391049075`*^9}, { 3.6943376083067274`*^9, 3.6943377050568633`*^9}, {3.694337736226907*^9, 3.694337836567047*^9}, {3.69433799542727*^9, 3.69433799558727*^9}, { 3.6943382395276117`*^9, 3.6943382530976305`*^9}, {3.6943386652882075`*^9, 3.694338672808218*^9}, 3.6943400978202133`*^9, {3.694340128930257*^9, 3.6943401346302643`*^9}, {3.694352247876343*^9, 3.69435226019636*^9}, { 3.69441488183449*^9, 3.6944149755846214`*^9}, 3.6944150060146637`*^9, { 3.6944150741247587`*^9, 3.69441508906478*^9}, {3.6944160613381414`*^9, 3.6944160921781845`*^9}, {3.6944167992291746`*^9, 3.694416815579197*^9}, { 3.6944168620292625`*^9, 3.694416875959282*^9}, {3.6944183207233047`*^9, 3.6944183712233753`*^9}, 3.694579665157987*^9, {3.726214230347681*^9, 3.7262142305040207`*^9}, {3.7262250279256763`*^9, 3.7262250419115257`*^9}, {3.7580045551078463`*^9, 3.758004623903921*^9}, { 3.7580073627335653`*^9, 3.7580073655297947`*^9}, {3.758007441011799*^9, 3.758007523008495*^9}, {3.758007652134451*^9, 3.7580076757538967`*^9}, { 3.7580077486896324`*^9, 3.758007769997414*^9}, {3.7901344035944896`*^9, 3.790134445500792*^9}, {3.7901345399910994`*^9, 3.790134540526645*^9}, { 3.7901345933460937`*^9, 3.790134594099427*^9}, {3.790664206724592*^9, 3.7906642332850227`*^9}, {3.822371406006948*^9, 3.8223714241545277`*^9}, { 3.8532163314339643`*^9, 3.8532163356909313`*^9}}, CellLabel-> "In[464]:=",ExpressionUUID->"374590f6-e341-45fa-9b77-4f91c393bed3"] }, Closed]], Cell[CellGroupData[{ Cell["Home assignment 3b (thin slab)", "Subsubsection", CellChangeTimes->{{3.499487466582*^9, 3.4994874779544*^9}, { 3.4994910657246*^9, 3.4994910793122*^9}, {3.562569560449569*^9, 3.5625695636631746`*^9}, 3.562570402929049*^9, {3.6943375929467063`*^9, 3.6943376002267165`*^9}, 3.694406026805439*^9, 3.6944148753044806`*^9, 3.7262247019228444`*^9, {3.7262249870466585`*^9, 3.7262249914062004`*^9}, { 3.7580045257709618`*^9, 3.75800453036374*^9}, 3.8222921071868744`*^9},ExpressionUUID->"8591d200-63b5-4567-a8cf-\ 8ea681f0c9b6"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"JOINT", ",", RowBox[{"{", "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "1", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "1", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Simplify", "[", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4994814977164*^9, 3.4994815003996*^9}, { 3.4994876433445997`*^9, 3.4994877082562*^9}, {3.4994877391286*^9, 3.4994877845558*^9}, {3.499488182645*^9, 3.4994881831442003`*^9}, { 3.4994883706562*^9, 3.4994884042586*^9}, {3.4994887442918*^9, 3.499488748301*^9}, {3.4994889348146*^9, 3.4994889623018*^9}, { 3.4994910895926*^9, 3.4994911605257998`*^9}, {3.4994912009765997`*^9, 3.4994912105081997`*^9}, {3.499492512803*^9, 3.4994925228494*^9}, 3.499492575359*^9, {3.5625696348461*^9, 3.5625696391049075`*^9}, { 3.6943376083067274`*^9, 3.6943377050568633`*^9}, {3.694337736226907*^9, 3.694337836567047*^9}, {3.69433799542727*^9, 3.69433799558727*^9}, { 3.6943382395276117`*^9, 3.6943382530976305`*^9}, {3.6943386652882075`*^9, 3.694338672808218*^9}, 3.6943400978202133`*^9, {3.694340128930257*^9, 3.6943401346302643`*^9}, {3.694352247876343*^9, 3.69435226019636*^9}, { 3.69441488183449*^9, 3.6944149755846214`*^9}, 3.6944150060146637`*^9, { 3.6944150741247587`*^9, 3.69441508906478*^9}, {3.6944160613381414`*^9, 3.6944160921781845`*^9}, {3.6944167992291746`*^9, 3.694416815579197*^9}, { 3.6944168620292625`*^9, 3.694416875959282*^9}, {3.6944183207233047`*^9, 3.6944183712233753`*^9}, 3.694579665157987*^9, {3.726214230347681*^9, 3.7262142305040207`*^9}, {3.7262250279256763`*^9, 3.7262250419115257`*^9}, {3.7580045551078463`*^9, 3.758004623903921*^9}, { 3.7580073627335653`*^9, 3.7580073655297947`*^9}, {3.758007441011799*^9, 3.758007523008495*^9}, {3.758007652134451*^9, 3.7580076757538967`*^9}, { 3.7580077486896324`*^9, 3.758007769997414*^9}, {3.7901344035944896`*^9, 3.790134445500792*^9}, {3.7901345399910994`*^9, 3.790134540526645*^9}, { 3.7901345933460937`*^9, 3.790134594099427*^9}, {3.8223714777672*^9, 3.8223714817615223`*^9}, {3.8223715237911577`*^9, 3.822371525768871*^9}, { 3.8532163712164097`*^9, 3.8532163744231157`*^9}, {3.8532164448448315`*^9, 3.8532164468166456`*^9}, {3.853216554311017*^9, 3.853216575510727*^9}}, CellLabel-> "In[469]:=",ExpressionUUID->"a8427689-b905-4b1e-a282-5012b2abafff"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture assignment 1 (bar)", "Subsubsection", CellChangeTimes->{{3.694171020333105*^9, 3.6941710492031455`*^9}, { 3.694320635316511*^9, 3.694320645406525*^9}, 3.6945793783775854`*^9, 3.7262215921075077`*^9, 3.7579961343745155`*^9, {3.7580340701852493`*^9, 3.758034071905482*^9}},ExpressionUUID->"e51c8a82-3282-4a2b-8270-\ 56c8df2c8a13"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "A", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", RowBox[{"2", "\[CurlyTheta]0"}]}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "1"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"uX", "[", "1", "]"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}]}], "\[IndentingNewLine]", "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4994814977164*^9, 3.4994815003996*^9}, { 3.5009579937654*^9, 3.5009579961366*^9}, {3.562572124071875*^9, 3.5625721267862797`*^9}, {3.694260485600563*^9, 3.6942606645008135`*^9}, { 3.6942650080031333`*^9, 3.6942650178531475`*^9}, 3.694265087583245*^9, { 3.694265149373331*^9, 3.6942651519033346`*^9}, {3.694265222753434*^9, 3.694265249783472*^9}, 3.6942654753437877`*^9, {3.694265521843853*^9, 3.6942655286938624`*^9}, {3.694320658056543*^9, 3.6943206662965546`*^9}, 3.694321100397162*^9, {3.6943211808672748`*^9, 3.694321198067299*^9}, { 3.6943212603173857`*^9, 3.6943212821274166`*^9}, {3.6945793934976068`*^9, 3.6945793962276106`*^9}, {3.6945794336976633`*^9, 3.694579462597704*^9}, 3.694579720658065*^9, {3.7262244135330825`*^9, 3.7262244245498486`*^9}, { 3.7264645323529987`*^9, 3.726464592984414*^9}, {3.726464693010617*^9, 3.726464717278513*^9}, {3.726464754564005*^9, 3.7264647552046957`*^9}, { 3.757996141779167*^9, 3.757996162899214*^9}, {3.758034080038931*^9, 3.758034162389186*^9}, {3.790135407955392*^9, 3.7901354577592163`*^9}, { 3.822371577744916*^9, 3.8223715800846605`*^9}, {3.8532166227812743`*^9, 3.8532166327701883`*^9}}, CellLabel-> "In[474]:=",ExpressionUUID->"c93b8f26-d595-42d5-ba9b-424742e42646"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture assignment 2 (thin slab)", "Subsubsection", CellChangeTimes->{{3.499487466582*^9, 3.4994874779544*^9}, { 3.4994910657246*^9, 3.4994910793122*^9}, {3.562569560449569*^9, 3.5625695636631746`*^9}, 3.562570402929049*^9, {3.6943375929467063`*^9, 3.6943376002267165`*^9}, 3.694406026805439*^9, {3.6944312298724174`*^9, 3.694431233695636*^9}, {3.7262249061162586`*^9, 3.726224912569766*^9}, 3.7580244401018515`*^9, {3.758034254108346*^9, 3.7580342597702637`*^9}},ExpressionUUID->"4bd8e63d-e6fb-4e0b-85b9-\ 3f2b1abf80aa"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "\[CapitalEpsilon]", ",", "\[Nu]", ",", "\[Alpha]", ",", "k"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "\[CurlyTheta]0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fun", " ", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "\[CurlyTheta]0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"\[CurlyTheta]", "[", "3", "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "TMEC", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4994814977164*^9, 3.4994815003996*^9}, { 3.4994876433445997`*^9, 3.4994877082562*^9}, {3.4994877391286*^9, 3.4994877845558*^9}, {3.499488182645*^9, 3.4994881831442003`*^9}, { 3.4994883706562*^9, 3.4994884042586*^9}, {3.4994887442918*^9, 3.499488748301*^9}, {3.4994889348146*^9, 3.4994889623018*^9}, { 3.4994910895926*^9, 3.4994911605257998`*^9}, {3.4994912009765997`*^9, 3.4994912105081997`*^9}, {3.499492512803*^9, 3.4994925228494*^9}, 3.499492575359*^9, {3.5625696348461*^9, 3.5625696391049075`*^9}, { 3.6943376083067274`*^9, 3.6943377050568633`*^9}, {3.694337736226907*^9, 3.694337836567047*^9}, {3.69433799542727*^9, 3.69433799558727*^9}, { 3.6943382395276117`*^9, 3.6943382530976305`*^9}, {3.6943386652882075`*^9, 3.694338672808218*^9}, 3.6943400978202133`*^9, {3.694340128930257*^9, 3.6943401346302643`*^9}, {3.694352247876343*^9, 3.69435226019636*^9}, { 3.6944312433631887`*^9, 3.6944312664045067`*^9}, {3.6944314730323253`*^9, 3.694431491689392*^9}, {3.6944317924565706`*^9, 3.6944318024421415`*^9}, 3.694431834732989*^9, {3.7580244524019127`*^9, 3.7580244589711*^9}, { 3.758034298112458*^9, 3.758034338813531*^9}, 3.758034384209874*^9, { 3.758034554681752*^9, 3.758034556090353*^9}, {3.7901358214025326`*^9, 3.7901358306030035`*^9}, {3.8223716085615296`*^9, 3.8223716161801615`*^9}, {3.8532166774932394`*^9, 3.8532166827890825`*^9}}, CellLabel-> "In[479]:=",ExpressionUUID->"945bf50a-77d3-4b29-9615-136fe696a2c6"] }, Closed]] }, Open ]] }, Open ]] }, AutoGeneratedPackage->Automatic, WindowSize->{776.25, 463.75}, WindowMargins->{{63.5, Automatic}, {Automatic, 0}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, PrivateNotebookOptions->{"VersionedStylesheet"->{"Default.nb"[8.] -> False}}, Magnification:>1.25 Inherited, FrontEndVersion->"12.3 for Microsoft Windows (64-bit) (July 9, 2021)", StyleDefinitions->"Default.nb", ExpressionUUID->"76641b04-0615-4ae6-91c5-3bb72ff35351" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[567, 22, 1597, 23, 199, "Title",ExpressionUUID->"f9c2c148-a01a-4dcf-b5a2-59c8faa291c7"], Cell[CellGroupData[{ Cell[2189, 49, 914, 15, 83, "Section",ExpressionUUID->"7b219000-c4f4-41ef-90a2-e545639024f2"], Cell[CellGroupData[{ Cell[3128, 68, 156, 2, 65, "Subsection",ExpressionUUID->"9f625864-b9bc-40ff-bf39-665b1dfd8d1c"], Cell[3287, 72, 31650, 715, 2124, "Input",ExpressionUUID->"e32c8819-c40a-4fc2-9333-bc065e3c69c0", InitializationCell->True], Cell[34940, 789, 154, 3, 29, "Input",ExpressionUUID->"4874a0c9-8cff-4280-8cb3-1ff5c94a752a"] }, Closed]], Cell[CellGroupData[{ Cell[35131, 797, 88, 0, 43, "Subsection",ExpressionUUID->"eec57070-ff9d-4fae-86ab-c05296189c15"], Cell[35222, 799, 33129, 973, 1118481053, "Input",ExpressionUUID->"0d84d048-10b8-4020-80f1-474bbf6e6928", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[68388, 1777, 87, 0, 43, "Subsection",ExpressionUUID->"bb23d42e-ddee-4fa6-b7ad-482b53d6586c"], Cell[68478, 1779, 38463, 1011, 2741, "Input",ExpressionUUID->"576b99af-d39f-40c6-a17e-774066c43b83", InitializationCell->True], Cell[CellGroupData[{ Cell[106966, 2794, 4483, 127, 412, "Input",ExpressionUUID->"b6207a37-a9af-46be-93c2-e328fab05069"], Cell[111452, 2923, 553, 13, 36, "Output",ExpressionUUID->"70d10832-ca9d-4b10-bbb7-f22345d51098"], Cell[112008, 2938, 368, 7, 53, "Output",ExpressionUUID->"80ac7773-60a7-42e9-878a-b3857f105846"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[112425, 2951, 92, 0, 43, "Subsection",ExpressionUUID->"86802962-6405-448c-bfca-277c3d443e13"], Cell[112520, 2953, 7120, 206, 644, "Input",ExpressionUUID->"07a8cdfb-4723-40a1-a6c6-318acecc057a", InitializationCell->True] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[119689, 3165, 1136, 18, 64, "Section",ExpressionUUID->"11730195-1052-43dc-a707-b2ccaa2937d3"], Cell[CellGroupData[{ Cell[120850, 3187, 273, 4, 66, "Subsection",ExpressionUUID->"10a3b971-55d0-4ff8-9913-748f6b1fc9a3"], Cell[121126, 3193, 844, 21, 101, "Input",ExpressionUUID->"f8ae57a5-1c27-407e-9962-6e5080babd59"] }, Closed]], Cell[CellGroupData[{ Cell[122007, 3219, 379, 6, 45, "Subsection",ExpressionUUID->"b572a4a7-8c0c-4655-8d88-90163b53d75b"], Cell[122389, 3227, 14812, 355, 841, "Input",ExpressionUUID->"4ef1200c-ad4e-4c34-8e06-2931ac75ffb3", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[137238, 3587, 459, 7, 45, "Subsection",ExpressionUUID->"eb02d56d-6103-4cea-b42e-30117bb7222f"], Cell[137700, 3596, 4944, 81, 122, "Input",ExpressionUUID->"5a76afda-3e2b-407f-828d-a064af3284c8", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[142681, 3682, 273, 4, 45, "Subsection",ExpressionUUID->"66e83de4-cdf2-4efb-953b-7b1ca775f27d"], Cell[142957, 3688, 20958, 521, 1173, "Input",ExpressionUUID->"a0f62632-6cb5-4616-a306-7f3d44298dc4", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[163952, 4214, 324, 5, 45, "Subsection",ExpressionUUID->"00760fe3-96a5-4648-a12e-bd9d44d56567"], Cell[164279, 4221, 10145, 222, 553, "Input",ExpressionUUID->"89d5eea9-5a18-4852-9d52-bb525ff9ee28", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[174461, 4448, 375, 6, 45, "Subsection",ExpressionUUID->"05f18933-8805-4dd4-9044-2c67ffb9e9ee"], Cell[174839, 4456, 10558, 222, 555, "Input",ExpressionUUID->"754cb2f7-16f1-484b-b777-131739da99a4", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell[185434, 4683, 425, 6, 66, "Subsection",ExpressionUUID->"4a94c2a2-6f79-4c85-bf73-05c16b93f2ed"], Cell[185862, 4691, 5002, 78, 122, "Input",ExpressionUUID->"01ec5291-3a5a-46f6-af67-96b1daf55db2", InitializationCell->True] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[190913, 4775, 1138, 18, 64, "Section",ExpressionUUID->"cc1def21-86d8-4618-aebf-14e5a843c2c6"], Cell[CellGroupData[{ Cell[192076, 4797, 555, 8, 66, "Subsection",ExpressionUUID->"e06fe3be-e95c-4877-90ee-4a809db41a90"], Cell[192634, 4807, 15310, 346, 699, "Input",ExpressionUUID->"4addbcb1-2ea6-496d-981f-9f7e1be7e07d", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[207981, 5158, 631, 9, 45, "Subsection",ExpressionUUID->"6d6aaea5-f790-4af3-bf7c-3274b903fd14"], Cell[208615, 5169, 16004, 331, 929, "Input",ExpressionUUID->"3b98d934-ed89-4766-ae8f-7f3b11c7602b", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[224656, 5505, 477, 7, 45, "Subsection",ExpressionUUID->"ac4d2151-f977-47ab-89d2-cba20d90a0c1"], Cell[225136, 5514, 16148, 374, 879, "Input",ExpressionUUID->"5ae1b60c-b700-40b1-9a48-e53a1cc07540", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[241321, 5893, 583, 8, 45, "Subsection",ExpressionUUID->"ce934794-0db1-42c7-9127-acf682062b33"], Cell[241907, 5903, 6852, 116, 265, "Input",ExpressionUUID->"c4542834-7089-48fe-bac4-7e114ab3a12b", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[248796, 6024, 637, 9, 45, "Subsection",ExpressionUUID->"707c619e-862d-4a34-9d6f-9ce5b5329e63"], Cell[249436, 6035, 6904, 117, 265, "Input",ExpressionUUID->"36b01e2c-345f-4788-8083-087747d27a4d", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[256377, 6157, 691, 10, 45, "Subsection",ExpressionUUID->"24fcb166-9cd4-4b87-a143-f5a36af4d49f"], Cell[257071, 6169, 6958, 118, 265, "Input",ExpressionUUID->"cb46ea58-8ee7-4f83-8317-3c04612e4669", InitializationCell->True] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[264078, 6293, 1135, 18, 64, "Section",ExpressionUUID->"05a7c66b-fbed-4e48-83b3-e8cfa2f8e9b8"], Cell[CellGroupData[{ Cell[265238, 6315, 279, 5, 66, "Subsection",ExpressionUUID->"6bfc85ed-f105-4a6b-85be-4228df237726", InitializationCell->True], Cell[265520, 6322, 42257, 851, 2513, "Input",ExpressionUUID->"8da43dad-153a-4069-a012-c6a592fa09b0", InitializationCell->True], Cell[307780, 7175, 25668, 501, 1227, "Input",ExpressionUUID->"29a8cc6d-3e9d-4cc8-b075-be9a813667e8"], Cell[333451, 7678, 18117, 303, 513, "Input",ExpressionUUID->"8b48a7c8-e995-4bfa-aa44-595f56c6c1f8"], Cell[351571, 7983, 34788, 755, 2133, "Input",ExpressionUUID->"8eee6ea7-8e3e-4fd6-a599-af158de67901"] }, Closed]], Cell[CellGroupData[{ Cell[386396, 8743, 355, 6, 45, "Subsection",ExpressionUUID->"a33ee5fa-f607-4577-b5e4-49dc900e2e2f", InitializationCell->True], Cell[386754, 8751, 14273, 208, 144, "Input",ExpressionUUID->"406b3cca-7d82-49dd-af4f-2774c3349319", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[401064, 8964, 277, 5, 45, "Subsection",ExpressionUUID->"f36d60ea-4a6a-4c2b-8982-3cd23a80abe5", InitializationCell->True], Cell[401344, 8971, 18524, 345, 674, "Input",ExpressionUUID->"37832c68-eb7f-4a75-935e-0915a7e2a13a", InitializationCell->True], Cell[419871, 9318, 16394, 284, 585, "Input",ExpressionUUID->"91a94a3b-6460-4e61-9415-5af8add0b018"] }, Closed]], Cell[CellGroupData[{ Cell[436302, 9607, 276, 5, 45, "Subsection",ExpressionUUID->"304352cb-c654-483d-b6eb-9e908263043a", InitializationCell->True], Cell[436581, 9614, 13811, 224, 221, "Input",ExpressionUUID->"a70afda4-fad2-4c81-a4da-50f7c3ab46c0", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[450429, 9843, 298, 5, 45, "Subsection",ExpressionUUID->"272f1965-2555-46e0-9de8-e1a410e2024b", InitializationCell->True], Cell[450730, 9850, 21224, 423, 912, "Input",ExpressionUUID->"7df3ec16-4b8b-45cb-8015-ca721564c3d5", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[471991, 10278, 408, 7, 45, "Subsection",ExpressionUUID->"cfec64be-5244-4b11-aa3d-7416a16cdcd9", InitializationCell->True], Cell[472402, 10287, 21088, 408, 963, "Input",ExpressionUUID->"9eb002e1-9863-43c9-96e2-cfe763b385fd", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[493527, 10700, 333, 6, 45, "Subsection",ExpressionUUID->"1d455053-ab43-4028-9372-89426eb6cdbe", InitializationCell->True], Cell[493863, 10708, 20655, 372, 820, "Input",ExpressionUUID->"4d523384-9111-4e5f-bc74-e0e134ba5179", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[514555, 11085, 409, 7, 45, "Subsection",ExpressionUUID->"8bf2b28f-bdbb-4c8e-b241-a461a8c907e5", InitializationCell->True], Cell[514967, 11094, 14234, 208, 144, "Input",ExpressionUUID->"7f1d8f80-4c88-4a1c-9118-d8f7367ce72a", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[529238, 11307, 378, 6, 45, "Subsection",ExpressionUUID->"52d7337e-01ce-475c-9a61-6b4210776b58", InitializationCell->True], Cell[529619, 11315, 21049, 380, 675, "Input",ExpressionUUID->"901b597d-d5c6-4937-9c30-705ce8a39225", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[550705, 11700, 383, 6, 45, "Subsection",ExpressionUUID->"009b90fc-3172-4340-a53d-6b92288a94d3", InitializationCell->True], Cell[551091, 11708, 14511, 218, 122, "Input",ExpressionUUID->"c74c377f-e765-4c55-8c9f-cc4ffa46a71f", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[565639, 11931, 437, 7, 45, "Subsection",ExpressionUUID->"98996e5f-4490-4a7e-bf15-b1b937f97cff", InitializationCell->True], Cell[566079, 11940, 14090, 204, 150, "Input",ExpressionUUID->"7e4a66c0-0db9-40e8-94f5-29ce7f2b7e62", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[580206, 12149, 583, 8, 45, "Subsection",ExpressionUUID->"238c2337-8ec9-471f-befd-2926af1c9d23"], Cell[580792, 12159, 51572, 771, 484, "Input",ExpressionUUID->"90f2e58a-5392-4b26-b45d-dddeafd00cd0", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[632401, 12935, 635, 9, 45, "Subsection",ExpressionUUID->"37b1c143-470c-45fd-bc65-79466d47cc47"], Cell[633039, 12946, 48239, 720, 412, "Input",ExpressionUUID->"b35ad1d3-1e12-4044-a4b6-3a447654c9a1", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[681315, 13671, 633, 9, 45, "Subsection",ExpressionUUID->"bc4db6e1-aed8-42a6-b88c-38ede4d891c1"], Cell[681951, 13682, 47361, 657, 126, "Input",ExpressionUUID->"e31964a9-fd10-447e-9cb9-0775bb52af68", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[729349, 14344, 578, 8, 45, "Subsection",ExpressionUUID->"49cc3388-fa6c-4867-a3aa-e5d8eb58f69b"], Cell[729930, 14354, 77924, 1363, 2157, "Input",ExpressionUUID->"902fe585-897b-4259-aabb-f537011656bc", InitializationCell->True], Cell[807857, 15719, 87022, 1664, 4387, "Input",ExpressionUUID->"f5dc159b-dfac-430e-a432-c1a7b9bafe16"] }, Closed]], Cell[CellGroupData[{ Cell[894916, 17388, 635, 9, 45, "Subsection",ExpressionUUID->"14357180-6a08-4b4a-b9da-b727a3841e7e"], Cell[895554, 17399, 388303, 7476, 22776, "Input",ExpressionUUID->"1ab0d6bb-50b0-4ab4-a9e6-e185dc46e365", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[1283894, 24880, 406, 6, 45, "Subsection",ExpressionUUID->"00c98f89-5b34-4350-9f2a-cbf0b8dc6dc8"], Cell[1284303, 24888, 92608, 1741, 2742, "Input",ExpressionUUID->"952ad393-ea79-4d42-b527-7582ac977961", InitializationCell->True], Cell[1376914, 26631, 84840, 1570, 2143, "Input",ExpressionUUID->"fd362622-c1e3-4356-b6fc-a24956b44459"], Cell[1461757, 28203, 169697, 3471, 8244, "Input",ExpressionUUID->"f502c001-f09d-4c09-854f-2f76074bffa3"] }, Closed]], Cell[CellGroupData[{ Cell[1631491, 31679, 454, 7, 45, "Subsection",ExpressionUUID->"57e3c84a-fd55-4b4e-bae5-1a516add187a", InitializationCell->True], Cell[1631948, 31688, 14279, 208, 144, "Input",ExpressionUUID->"9f4e35d3-8759-444d-af8a-37d96abffa12", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[1646264, 31901, 302, 5, 45, "Subsection",ExpressionUUID->"0dcc77b2-81d9-45bf-913d-861264d462d9"], Cell[1646569, 31908, 68772, 1205, 1753, "Input",ExpressionUUID->"444b167e-bccb-4ea5-b199-ec19bc9c80b5", InitializationCell->True], Cell[1715344, 33115, 58291, 986, 1496, "Input",ExpressionUUID->"54be39e6-3c82-4e0b-b05a-59ff1239990b"] }, Closed]], Cell[CellGroupData[{ Cell[1773672, 34106, 739, 10, 45, "Subsection",ExpressionUUID->"593b153a-85e3-4705-8251-1376e04cb34a"], Cell[1774414, 34118, 56188, 891, 854, "Input",ExpressionUUID->"d9156204-3b55-401d-92de-546075f23b33", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell[1830639, 35014, 328, 5, 66, "Subsection",ExpressionUUID->"22fd3af4-820c-4389-83ac-d39e8e057331"], Cell[1830970, 35021, 420036, 9117, 25233, "Input",ExpressionUUID->"baeab370-f64d-49f1-a4ea-3223fb21e390"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[2251055, 44144, 1060, 17, 64, "Section",ExpressionUUID->"53e88fa2-3263-4b89-af46-d70dc8c83236"], Cell[CellGroupData[{ Cell[2252140, 44165, 224, 4, 66, "Subsection",ExpressionUUID->"1f5e47b0-f670-4db4-ad2c-9e4ef3bda787"], Cell[2252367, 44171, 59434, 1320, 3532, "Input",ExpressionUUID->"2d2dcd52-3c40-4702-a04b-d68350cdb23b", InitializationCell->True], Cell[2311804, 45493, 110372, 2579, 7846, "Input",ExpressionUUID->"011777fb-5213-41bb-a29f-4836f1a5efd3"] }, Closed]], Cell[CellGroupData[{ Cell[2422213, 48077, 505, 8, 45, "Subsection",ExpressionUUID->"ea12c303-fa8b-4684-9abb-f0e78137131f", InitializationCell->True], Cell[2422721, 48087, 14335, 209, 144, "Input",ExpressionUUID->"7bf9157a-5288-4830-ac6a-ed9a8a1f8b82", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[2437093, 48301, 275, 4, 45, "Subsection",ExpressionUUID->"5ae82b95-f0fd-43fb-a5f1-353de1edd4c4"], Cell[2437371, 48307, 41256, 865, 2150, "Input",ExpressionUUID->"f67fddb7-31f7-4f35-a9f0-7e763617fabc", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[2478664, 49177, 227, 4, 45, "Subsection",ExpressionUUID->"27e33fef-e1d9-482f-ae22-13ba3c4b5aa6"], Cell[2478894, 49183, 31368, 632, 1531, "Input",ExpressionUUID->"789ff18c-02c4-4c25-92e6-da4904f027bb", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[2510299, 49820, 274, 4, 45, "Subsection",ExpressionUUID->"40bab93a-cb0f-46ed-887b-7b7a9234f336"], Cell[2510576, 49826, 19880, 324, 436, "Input",ExpressionUUID->"e30b30d1-f4fc-4b90-b189-ecf785028196", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[2530493, 50155, 307, 5, 45, "Subsection",ExpressionUUID->"71983723-34bb-49cc-83f5-d5537d96e557"], Cell[2530803, 50162, 33019, 675, 1579, "Input",ExpressionUUID->"28d2293e-8a04-44d8-a288-643ade99678c", InitializationCell->True], Cell[2563825, 50839, 24098, 452, 888, "Input",ExpressionUUID->"9c3ae2e4-46f0-4717-b32c-5c9d4baaa58c"] }, Closed]], Cell[CellGroupData[{ Cell[2587960, 51296, 226, 4, 45, "Subsection",ExpressionUUID->"12fe72e9-7d6c-409c-888f-fd1cfd4e4141"], Cell[2588189, 51302, 32512, 666, 1560, "Input",ExpressionUUID->"6c5ea344-3532-48e2-8358-f6e53755c076", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell[2620738, 51973, 330, 5, 66, "Subsection",ExpressionUUID->"3eeb74f9-ff05-4e6e-bef9-4948d2376dbf"], Cell[2621071, 51980, 95687, 1815, 4120, "Input",ExpressionUUID->"01613799-7c68-4c0f-8663-961896f0ebdd", InitializationCell->True], Cell[2716761, 53797, 235983, 5434, 17066, "Input",ExpressionUUID->"8c146a0a-8398-489f-8e7b-cf853995ea71"] }, Closed]], Cell[CellGroupData[{ Cell[2952781, 59236, 527, 8, 45, "Subsection",ExpressionUUID->"746ec010-b55b-4f1c-a482-156a399311ff", InitializationCell->True], Cell[2953311, 59246, 14385, 210, 144, "Input",ExpressionUUID->"2eb5706f-5726-4702-b960-6b10b57e5450", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[2967733, 59461, 381, 6, 45, "Subsection",ExpressionUUID->"eb7cfdca-700f-4b39-b577-f326a187aea4"], Cell[2968117, 59469, 69984, 1206, 2128, "Input",ExpressionUUID->"89c0204a-fb4f-4908-9034-80bcab446e30", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[3038138, 60680, 429, 6, 45, "Subsection",ExpressionUUID->"3c79e90f-496d-48fd-9ed6-750c6fa2d168"], Cell[3038570, 60688, 95184, 1816, 3895, "Input",ExpressionUUID->"00aec84a-89ef-40e4-a783-0877f479d20c", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[3133791, 62509, 383, 6, 45, "Subsection",ExpressionUUID->"fc5dac56-bcbb-46bb-a381-801edad5d733"], Cell[3134177, 62517, 69069, 1157, 1727, "Input",ExpressionUUID->"6ff08674-2241-4cd8-8297-12ad7cb39b48"] }, Closed]], Cell[CellGroupData[{ Cell[3203283, 63679, 199, 3, 45, "Subsection",ExpressionUUID->"37cdd6b0-516c-4445-ba8a-c7931007bf1e"], Cell[3203485, 63684, 122705, 2357, 5384, "Input",ExpressionUUID->"38a1d62e-f4fc-40f7-87e9-9b1e5d40372c", InitializationCell->True], Cell[3326193, 66043, 27103, 655, 1947, "Input",ExpressionUUID->"11762837-f9ea-4ad2-bb92-27671ab9b1fb"], Cell[3353299, 66700, 81493, 1394, 2086, "Input",ExpressionUUID->"e3e2b6a6-a76c-4ab4-b328-fc173879191d"], Cell[3434795, 68096, 65431, 1087, 1515, "Input",ExpressionUUID->"5daf46ec-6720-4b2e-babe-01c85a382836"], Cell[3500229, 69185, 88996, 1920, 5621, "Input",ExpressionUUID->"d063c5b7-f601-414e-adaa-f8def9fd5096"] }, Closed]], Cell[CellGroupData[{ Cell[3589262, 71110, 251, 4, 45, "Subsection",ExpressionUUID->"2efb13fd-b3b7-44c9-95ba-e06234fe92ea"], Cell[3589516, 71116, 94062, 1618, 2582, "Input",ExpressionUUID->"a180b637-52a4-4fc9-9aad-d0cc1e6f83a4", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[3683615, 72739, 480, 7, 45, "Subsection",ExpressionUUID->"66dd7a59-1024-4a03-aab8-a2ce73879f4a"], Cell[3684098, 72748, 95184, 1816, 3895, "Input",ExpressionUUID->"8fbb140a-f217-4c97-b25a-f0ab664d5b0f", InitializationCell->True] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[3779331, 74570, 1058, 17, 64, "Section",ExpressionUUID->"63ada71e-dde0-461f-a58e-67224f0ae52e"], Cell[CellGroupData[{ Cell[3780414, 74591, 279, 4, 66, "Subsection",ExpressionUUID->"a049ace8-7330-4df1-8b56-0697f104fbba"], Cell[3780696, 74597, 55595, 1220, 3809, "Input",ExpressionUUID->"2765c3d3-7e63-4a4d-b27a-8d8791bb3da0", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[3836328, 75822, 583, 9, 45, "Subsection",ExpressionUUID->"8e3e71c8-83f5-4e3c-9c4a-4edb840e08a2", InitializationCell->True], Cell[3836914, 75833, 14437, 210, 144, "Input",ExpressionUUID->"4181ac41-3f39-4509-9d69-0ecf763e44c4", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[3851388, 76048, 253, 4, 45, "Subsection",ExpressionUUID->"78fbdbaa-de20-48de-9ab2-0b9c998c4e2c"], Cell[3851644, 76054, 43164, 930, 2649, "Input",ExpressionUUID->"1549c103-2862-4066-aa0b-ab54b37c9133", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[3894845, 76989, 277, 4, 45, "Subsection",ExpressionUUID->"64dc96c6-9d02-4fcd-855a-21396312acb3"], Cell[3895125, 76995, 27972, 547, 1365, "Input",ExpressionUUID->"07155f4e-e4f1-47a1-aae9-b3e711a4a89c", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[3923134, 77547, 303, 5, 45, "Subsection",ExpressionUUID->"a5ff34d6-b1dc-4e8d-8a6c-d1fd929002ae"], Cell[3923440, 77554, 29782, 593, 1393, "Input",ExpressionUUID->"95a35a51-fd58-4aaf-9734-dc4e0b34c7b6", InitializationCell->True], Cell[3953225, 78149, 98753, 2322, 8251, "Input",ExpressionUUID->"ff0f4c3e-24c9-4ccb-bc86-287a006d781e"] }, Closed]], Cell[CellGroupData[{ Cell[4052015, 80476, 269, 4, 45, "Subsection",ExpressionUUID->"fabe559d-d45e-4c99-bb7b-a29e3c28074c"], Cell[4052287, 80482, 114123, 2663, 5834, "Input",ExpressionUUID->"03e80675-88b3-491b-9b61-7f27fb007711"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[4166459, 83151, 1057, 17, 64, "Section",ExpressionUUID->"d8ffbf13-27a0-4328-9a21-be6a7e8473f4"], Cell[CellGroupData[{ Cell[4167541, 83172, 239, 4, 66, "Subsection",ExpressionUUID->"06a9dfe0-2adc-4915-94ed-87c3071c4eb7"], Cell[4167783, 83178, 37963, 796, 2880, "Input",ExpressionUUID->"0c482183-6ef6-4cc4-9461-c4c6b57fa359", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[4205783, 83979, 314, 5, 45, "Subsection",ExpressionUUID->"e15916b1-3f71-49e0-bf31-6ecab0c9b0b3"], Cell[4206100, 83986, 16529, 274, 379, "Input",ExpressionUUID->"bbbfdf88-41d3-44a1-ad5a-9c1bd72c7b1b", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[4222666, 84265, 236, 4, 45, "Subsection",ExpressionUUID->"80029a0f-ea91-4cfe-9c78-1860aa1e6e10"], Cell[4222905, 84271, 29500, 613, 1860, "Input",ExpressionUUID->"1582abbd-5e02-4bfd-8ff3-78c5fc645090", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[4252442, 84889, 210, 4, 45, "Subsection",ExpressionUUID->"a68027a3-726d-49a5-bd4f-a2b1fb59ecfe"], Cell[4252655, 84895, 25305, 478, 1245, "Input",ExpressionUUID->"ba787390-fd49-49b1-a24b-6149cb9b7456", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[4277997, 85378, 308, 5, 45, "Subsection",ExpressionUUID->"98b2b612-b5f8-47eb-afd4-a2bc79752afc"], Cell[4278308, 85385, 28743, 587, 1577, "Input",ExpressionUUID->"93f8f26c-cc52-4815-b9c5-8e8d29ab34ca", InitializationCell->True], Cell[4307054, 85974, 3387, 93, 345, "Input",ExpressionUUID->"8c0972a6-d0bf-4366-bd28-6830262bc5aa"] }, Closed]], Cell[CellGroupData[{ Cell[4310478, 86072, 314, 5, 45, "Subsection",ExpressionUUID->"68b5c243-34c4-4245-a1bc-2f082a71a9f7"], Cell[4310795, 86079, 14252, 221, 216, "Input",ExpressionUUID->"f9ea8ad7-d4e3-4408-a24d-b067e7bee725", InitializationCell->True] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[4325096, 86306, 1007, 16, 64, "Section",ExpressionUUID->"af367fee-9121-44e2-ad23-5df36af01ac8"], Cell[CellGroupData[{ Cell[4326128, 86326, 431, 7, 66, "Subsection",ExpressionUUID->"25e4566d-0b26-45f6-becc-777d07235552"], Cell[4326562, 86335, 19552, 469, 1604, "Input",ExpressionUUID->"c7b010b8-6fe0-4bb5-9e12-73bc81e245cb", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[4346151, 86809, 86, 0, 45, "Subsection",ExpressionUUID->"aed2bdbf-0063-4f44-a187-438df80d0c2c"], Cell[4346240, 86811, 15190, 404, 1118481053, "Input",ExpressionUUID->"9310e4cd-2b6b-41c8-8c04-6144ef4a2da3", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[4361467, 87220, 163, 3, 45, "Subsection",ExpressionUUID->"57ef130e-2ec6-4c2e-82c4-e3084f15fed5"], Cell[4361633, 87225, 151084, 3613, 11424, "Input",ExpressionUUID->"797ad8d2-c1f3-436b-bcf0-ab6a58e6258f", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[4512754, 90843, 214, 4, 45, "Subsection",ExpressionUUID->"24f0f609-0d0a-432d-be7b-5b7e02cf05fb"], Cell[4512971, 90849, 22240, 487, 1622, "Input",ExpressionUUID->"1975a601-4da2-46da-a032-7825d595170e", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[4535248, 91341, 316, 5, 45, "Subsection",ExpressionUUID->"2a69b2ad-4531-4e5a-ae19-d98593b19786"], Cell[4535567, 91348, 16363, 356, 1178, "Input",ExpressionUUID->"0283d983-d817-46a5-b74b-efb5cf0d716b", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[4551967, 91709, 362, 6, 45, "Subsection",ExpressionUUID->"e0a2ce5b-c393-42b9-ad19-4b155e375583"], Cell[4552332, 91717, 11181, 244, 1118481053, "Input",ExpressionUUID->"a5793423-1f61-46c4-b427-822da44b0f71", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[4563550, 91966, 219, 4, 45, "Subsection",ExpressionUUID->"a3eec395-d0e8-4965-9dc2-7cbf7329b094"], Cell[4563772, 91972, 32333, 640, 3116, "Input",ExpressionUUID->"f52ed36f-c8fe-4fa7-9a38-2db375a610e7", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[4596142, 92617, 271, 4, 45, "Subsection",ExpressionUUID->"1a20d09c-0a54-45c1-8947-5b7037e80b9a"], Cell[4596416, 92623, 74157, 1703, 5408, "Input",ExpressionUUID->"890883ed-125f-4947-8651-685e9ea67989", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[4670610, 94331, 86, 0, 45, "Subsection",ExpressionUUID->"86c035c4-399f-40a3-9748-ab2d70534b08"], Cell[4670699, 94333, 49163, 1259, 4301, "Input",ExpressionUUID->"6c784c18-cbe7-41d4-9317-3394ef19b985"] }, Closed]], Cell[CellGroupData[{ Cell[4719899, 95597, 438, 7, 45, "Subsection",ExpressionUUID->"773b4adc-8178-438d-9847-2e15a35aa106"], Cell[4720340, 95606, 73701, 1870, 4999, "Input",ExpressionUUID->"1b3236c8-2377-4f6a-97a6-8ea6af071442", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell[4794078, 97481, 416, 6, 66, "Subsection",ExpressionUUID->"f00aec32-f5de-4e85-88aa-4ceffa8f1e09"], Cell[4794497, 97489, 32742, 760, 2209, "Input",ExpressionUUID->"6da38beb-2bb8-4c31-889a-cf48e67a1a60", InitializationCell->True], Cell[4827242, 98251, 85958, 2143, 6507, "Input",ExpressionUUID->"7653a3c0-7297-41d0-9ec9-41ef62c16876", InitializationCell->True], Cell[4913203, 100396, 35368, 792, 2625, "Input",ExpressionUUID->"9401b9b0-0d65-4f8f-abf7-575cd33ebc44", InitializationCell->True], Cell[4948574, 101190, 14596, 244, 507, "Input",ExpressionUUID->"bdf0fee5-0f58-42a5-8728-bc93f8964f93", InitializationCell->True] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[4963231, 101441, 983, 15, 88, "Title",ExpressionUUID->"6a385782-eb61-456f-9f91-380d4036a0d8"], Cell[CellGroupData[{ Cell[4964239, 101460, 1392, 20, 66, "Subsection",ExpressionUUID->"0d2913ef-0aef-4ae5-ae1f-42a83bd3e7cd"], Cell[CellGroupData[{ Cell[4965656, 101484, 624, 14, 56, "Subsubsection",ExpressionUUID->"162ac754-d74f-4ca6-80c8-d8d961edea19"], Cell[4966283, 101500, 2394, 72, 221, "Input",ExpressionUUID->"667512d3-b54f-4fe9-bb73-3019faaf7bea"] }, Closed]], Cell[CellGroupData[{ Cell[4968714, 101577, 549, 13, 44, "Subsubsection",ExpressionUUID->"8b303821-a3bc-4d02-b626-00ac8af3f93c"], Cell[4969266, 101592, 1253, 33, 77, "Input",ExpressionUUID->"5b39d0a4-4bf4-459f-b04a-9fa6a08b00f4"] }, Closed]], Cell[CellGroupData[{ Cell[4970556, 101630, 459, 11, 44, "Subsubsection",ExpressionUUID->"efb27dda-7a73-487d-b443-3bf17635a222"], Cell[4971018, 101643, 1340, 41, 101, "Input",ExpressionUUID->"ff1ebdca-191a-4f41-8713-99748a72fee9"], Cell[CellGroupData[{ Cell[4972383, 101688, 1992, 56, 201, "Input",ExpressionUUID->"5f613cb9-a9e2-4794-85a6-86c846186544"], Cell[4974378, 101746, 485, 14, 64, "Output",ExpressionUUID->"84d03451-e88f-406c-9148-b5d4913b09f7"], Cell[4974866, 101762, 321, 9, 64, "Output",ExpressionUUID->"d2fcd6f9-9b75-4a34-97bf-6cbadd9df4e4"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[4975248, 101778, 1399, 20, 45, "Subsection",ExpressionUUID->"afb80a20-e5d9-4db8-bc99-2e402a0d6607"], Cell[CellGroupData[{ Cell[4976672, 101802, 312, 5, 56, "Subsubsection",ExpressionUUID->"b1de8e05-e4e5-4906-a827-733bd6c4e2d5"], Cell[4976987, 101809, 6030, 128, 416, "Input",ExpressionUUID->"61f5f099-228b-4fce-ba92-c0ab305b436c"], Cell[4983020, 101939, 3578, 67, 202, "Input",ExpressionUUID->"6f10e45f-13a2-4cd5-b8a1-1c9e3ac2ff00"], Cell[4986601, 102008, 2255, 63, 251, "Input",ExpressionUUID->"c1bf58ef-f98e-4e6a-9256-3c88e0b79a73"], Cell[4988859, 102073, 2303, 63, 251, "Input",ExpressionUUID->"f0631ef9-a9cf-4715-8dd7-c748b9f841b0"], Cell[CellGroupData[{ Cell[4991187, 102140, 2058, 58, 177, "Input",ExpressionUUID->"19bb77ba-380c-49d2-99b3-5d1a77644648"], Cell[4993248, 102200, 632, 18, 64, "Output",ExpressionUUID->"a07f3917-4445-4893-bac5-45a1114501cc"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[4993929, 102224, 346, 5, 44, "Subsubsection",ExpressionUUID->"d7109425-1791-4931-ad0b-bad3a9ba7ad1"], Cell[4994278, 102231, 10368, 278, 652, "Input",ExpressionUUID->"5530c711-9694-4aec-86f0-257c15d0f1e4"], Cell[5004649, 102511, 8902, 229, 503, "Input",ExpressionUUID->"75e89c8c-d624-4c79-98fc-b38ed11332bf"], Cell[5013554, 102742, 6799, 168, 343, "Input",ExpressionUUID->"9b14d110-ca4c-4d7c-9f3f-55060cbac994"] }, Closed]], Cell[CellGroupData[{ Cell[5020390, 102915, 344, 5, 44, "Subsubsection",ExpressionUUID->"fb5115cb-5c46-462d-b545-09d24c3dbd84"], Cell[CellGroupData[{ Cell[5020759, 102924, 10269, 299, 512, "Input",ExpressionUUID->"b7110b20-43d4-4a4c-bc9d-f2e4dc4a8bf3"], Cell[5031031, 103225, 2588, 39, 64, "Message",ExpressionUUID->"c7a71a78-70a8-444d-a8cd-eed5443e5d16"], Cell[5033622, 103266, 1690, 27, 64, "Message",ExpressionUUID->"00d9d89d-2a8c-45ec-9d5d-f4cb2ec9f2a5"], Cell[5035315, 103295, 950, 17, 64, "Message",ExpressionUUID->"20b8ba8d-1bba-4407-9622-8d359f493c3e"] }, Open ]] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[5036338, 103320, 688, 11, 88, "Title",ExpressionUUID->"c094e867-eedb-49ea-81fe-4ac178148a9f"], Cell[CellGroupData[{ Cell[5037051, 103335, 1091, 15, 67, "Subsection",ExpressionUUID->"4b032a41-028b-4092-b65a-9e634ae03405"], Cell[CellGroupData[{ Cell[5038167, 103354, 496, 7, 55, "Subsubsection",ExpressionUUID->"9aac42a8-292f-4229-ba7a-ff683fbe5b47"], Cell[5038666, 103363, 5798, 129, 368, "Input",ExpressionUUID->"791e3657-2892-4e7f-b01c-e4d90582ccdc"] }, Closed]], Cell[CellGroupData[{ Cell[5044501, 103497, 499, 7, 44, "Subsubsection",ExpressionUUID->"61bce4a2-2758-460e-9011-10d261d3455b"], Cell[5045003, 103506, 4556, 96, 249, "Input",ExpressionUUID->"6584dfe0-7603-49d3-94da-5575af117569"] }, Closed]], Cell[CellGroupData[{ Cell[5049596, 103607, 568, 8, 44, "Subsubsection",ExpressionUUID->"5f18722c-d360-4af9-9f52-1aaae1c2afe0"], Cell[5050167, 103617, 5892, 127, 296, "Input",ExpressionUUID->"0e14e494-89ab-4ad0-b8c0-10a6284cae93"] }, Closed]], Cell[CellGroupData[{ Cell[5056096, 103749, 596, 8, 44, "Subsubsection",ExpressionUUID->"d5ab2f1f-fe7d-4b0c-b713-7e504f9c030c"], Cell[5056695, 103759, 5847, 120, 249, "Input",ExpressionUUID->"20359c31-e79a-44dc-9d11-ffe8fcaffa83"] }, Closed]], Cell[CellGroupData[{ Cell[5062579, 103884, 763, 11, 44, "Subsubsection",ExpressionUUID->"3e2f56e3-2eb0-44d4-bbb4-11727f8765cd"], Cell[5063345, 103897, 6475, 132, 296, "Input",ExpressionUUID->"8d781f7e-6bba-4547-a9f9-dfc08320210e"] }, Closed]], Cell[CellGroupData[{ Cell[5069857, 104034, 814, 12, 44, "Subsubsection",ExpressionUUID->"5de18652-2348-4485-9982-16fe2124dc17"], Cell[5070674, 104048, 6396, 128, 273, "Input",ExpressionUUID->"35452574-3b83-4220-8780-2ea80d30e195"] }, Closed]], Cell[CellGroupData[{ Cell[5077107, 104181, 1543, 22, 44, "Subsubsection",ExpressionUUID->"612e6103-9000-4ecc-a3de-0c310ea17db1", InitializationCell->True], Cell[CellGroupData[{ Cell[5078675, 104207, 13118, 200, 412, "Input",ExpressionUUID->"d7c7bfec-f72f-483c-aaac-e4c477a9b7b6", InitializationCell->True], Cell[5091796, 104409, 1400, 38, 70, "Output",ExpressionUUID->"f3230e1b-db94-4add-869d-4daa61d4edd4"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[5093245, 104453, 1386, 19, 44, "Subsubsection",ExpressionUUID->"2a3fdd82-94d7-4d25-86ae-7cd9b8408625"], Cell[5094634, 104474, 5028, 100, 201, "Input",ExpressionUUID->"f0883c56-221e-49b0-8337-be21b0915171"] }, Closed]], Cell[CellGroupData[{ Cell[5099699, 104579, 1502, 20, 44, "Subsubsection",ExpressionUUID->"f8eaea5b-7add-4647-9717-93d42ce100ae"], Cell[5101204, 104601, 3784, 70, 236, "Input",ExpressionUUID->"3b12001d-9df2-4f5a-b356-794dcdd33b58"] }, Closed]], Cell[CellGroupData[{ Cell[5105025, 104676, 1532, 21, 44, "Subsubsection",ExpressionUUID->"b56efb6f-e083-4955-a2a8-0cfd3b4e340c"], Cell[5106560, 104699, 4049, 77, 213, "Input",ExpressionUUID->"1a147b60-e71c-4838-a395-4e9b0c2bdd8d"] }, Closed]], Cell[CellGroupData[{ Cell[5110646, 104781, 1493, 20, 44, "Subsubsection",ExpressionUUID->"d6c09b2d-0060-462f-9e65-edce649c8801"], Cell[5112142, 104803, 4531, 92, 236, "Input",ExpressionUUID->"9418a6e5-055c-43ef-87e1-2c501a162f13"] }, Closed]], Cell[CellGroupData[{ Cell[5116710, 104900, 1701, 23, 44, "Subsubsection",ExpressionUUID->"30c837b8-77d7-4a14-876c-0bddffc8916f"], Cell[5118414, 104925, 20003, 342, 412, "Input",ExpressionUUID->"fcc4cb24-7d33-41af-97c4-4c089213800f"] }, Closed]], Cell[CellGroupData[{ Cell[5138454, 105272, 1646, 22, 44, "Subsubsection",ExpressionUUID->"f35287b9-a03a-4574-97fa-237b12c801a3"], Cell[5140103, 105296, 18356, 309, 582, "Input",ExpressionUUID->"32388698-befc-4ac2-8cc5-f4b6ea17cab8"], Cell[5158462, 105607, 2458, 66, 296, "Input",ExpressionUUID->"3c78de41-cf9b-45a3-8fb6-74fb133600ce"], Cell[5160923, 105675, 17652, 284, 416, "Input",ExpressionUUID->"f34cfcc1-81a3-410c-876c-d2e0cf682381"], Cell[5178578, 105961, 15116, 216, 130, "Input",ExpressionUUID->"d472a1b3-51e1-4374-b2af-827682c399ad"], Cell[5193697, 106179, 15152, 215, 130, "Input",ExpressionUUID->"b87fa9bb-8fce-48e1-8dcc-ff4f6fac18b2"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[5208898, 106400, 998, 14, 46, "Subsection",ExpressionUUID->"0ad916ed-a088-4ed6-8e58-9b8987f41ea9"], Cell[CellGroupData[{ Cell[5209921, 106418, 457, 7, 56, "Subsubsection",ExpressionUUID->"9ce51a4d-240c-4a8f-8db9-b1eed2117469"], Cell[5210381, 106427, 5066, 114, 424, "Input",ExpressionUUID->"07ee9c44-080b-4601-8a59-3f0b3e1722ee"] }, Closed]], Cell[CellGroupData[{ Cell[5215484, 106546, 487, 8, 44, "Subsubsection",ExpressionUUID->"23c8fb87-2b93-4eb1-b055-915248fcc228"], Cell[5215974, 106556, 6635, 146, 416, "Input",ExpressionUUID->"c8894e60-9066-4599-bec8-91e05a499a8e"] }, Closed]], Cell[CellGroupData[{ Cell[5222646, 106707, 530, 8, 44, "Subsubsection",ExpressionUUID->"6a4aea0d-99ba-4702-8deb-458ed4f15f86"], Cell[5223179, 106717, 3652, 90, 392, "Input",ExpressionUUID->"91c78a48-fca8-4c15-ba55-8ebe9b885fd4"] }, Closed]], Cell[CellGroupData[{ Cell[5226868, 106812, 477, 8, 44, "Subsubsection",ExpressionUUID->"72c71bae-49b0-42c4-ab87-cbe04c178bcc"], Cell[5227348, 106822, 5379, 108, 345, "Input",ExpressionUUID->"f2fb962d-1b1e-4402-97b7-e538a571f5ee"] }, Closed]], Cell[CellGroupData[{ Cell[5232764, 106935, 559, 9, 44, "Subsubsection",ExpressionUUID->"59ab6ed7-ca2a-4964-9858-e809d14b67e0"], Cell[5233326, 106946, 3705, 87, 368, "Input",ExpressionUUID->"dd417420-f0a3-4621-8632-7fa9d67ad09f"] }, Closed]], Cell[CellGroupData[{ Cell[5237068, 107038, 859, 12, 44, "Subsubsection",ExpressionUUID->"d9c59a92-1228-49f5-983a-e40a66f27466"], Cell[5237930, 107052, 8523, 188, 516, "Input",ExpressionUUID->"15570612-d966-4497-9516-a561480ae6e0"] }, Closed]], Cell[CellGroupData[{ Cell[5246490, 107245, 983, 14, 44, "Subsubsection",ExpressionUUID->"a0a099cf-522b-401b-93cb-fe9cd38c1bd4"], Cell[5247476, 107261, 16753, 352, 773, "Input",ExpressionUUID->"5b63b3a2-4880-4107-81b0-63d9e1e27f04"] }, Closed]], Cell[CellGroupData[{ Cell[5264266, 107618, 1031, 14, 44, "Subsubsection",ExpressionUUID->"26efc207-037d-4d05-a43c-306f064bc5f7"], Cell[5265300, 107634, 12472, 211, 297, "Input",ExpressionUUID->"294c0193-e7d5-4b80-8e52-08165ec414d6"], Cell[5277775, 107847, 13064, 234, 487, "Input",ExpressionUUID->"7ce693b9-92f9-4095-b3f3-ba8b9c1c44ba"] }, Closed]], Cell[CellGroupData[{ Cell[5290876, 108086, 522, 8, 44, "Subsubsection",ExpressionUUID->"f305e74a-235e-4baa-b83e-086cde406e13"], Cell[5291401, 108096, 5809, 151, 504, "Input",ExpressionUUID->"1b42415b-f374-4028-bc46-9a8e3c4ff053"] }, Closed]], Cell[CellGroupData[{ Cell[5297247, 108252, 525, 8, 44, "Subsubsection",ExpressionUUID->"40e8ce7f-ca56-4fba-abdb-7521c01c000c"], Cell[5297775, 108262, 4270, 105, 297, "Input",ExpressionUUID->"43012530-aa11-497f-87ee-9dffa423d82b"] }, Closed]], Cell[CellGroupData[{ Cell[5302082, 108372, 651, 9, 44, "Subsubsection",ExpressionUUID->"d1bd5a48-c362-412a-8d6d-ba7e898516b3"], Cell[5302736, 108383, 4424, 102, 273, "Input",ExpressionUUID->"6be92904-f706-4f83-b1ba-ec89ab7c83af"] }, Closed]], Cell[CellGroupData[{ Cell[5307197, 108490, 712, 10, 44, "Subsubsection",ExpressionUUID->"0d12dbb4-74f7-43be-a632-eed8f4f70f54"], Cell[5307912, 108502, 4100, 99, 297, "Input",ExpressionUUID->"1918b464-9c6a-4c4b-8265-7ccf8f2a25c3"] }, Closed]], Cell[CellGroupData[{ Cell[5312049, 108606, 641, 10, 44, "Subsubsection",ExpressionUUID->"af4e2120-5c8e-4192-b992-dac529915bad"], Cell[5312693, 108618, 3003, 67, 178, "Input",ExpressionUUID->"50852c4a-36d3-48eb-a933-a250e705b392"] }, Closed]], Cell[CellGroupData[{ Cell[5315733, 108690, 637, 9, 44, "Subsubsection",ExpressionUUID->"4b1a7d5f-3a18-47d6-b7b5-01339f45040e"], Cell[5316373, 108701, 4025, 97, 273, "Input",ExpressionUUID->"3e9347cc-0751-43c8-9780-92f344db507a"] }, Closed]], Cell[CellGroupData[{ Cell[5320435, 108803, 734, 10, 44, "Subsubsection",ExpressionUUID->"f5ab83c3-8bf5-4d11-a646-3233038fcb5c"], Cell[5321172, 108815, 4085, 92, 297, "Input",ExpressionUUID->"f7ff71bb-1411-4cf6-8d1b-f3631e9936e7"] }, Closed]], Cell[CellGroupData[{ Cell[5325294, 108912, 665, 10, 44, "Subsubsection",ExpressionUUID->"3bd95836-af1e-4f36-af7b-fbf998125626"], Cell[5325962, 108924, 3176, 80, 273, "Input",ExpressionUUID->"95991a94-3d4e-4970-88c8-f8463df0d556"] }, Closed]], Cell[CellGroupData[{ Cell[5329175, 109009, 735, 10, 44, "Subsubsection",ExpressionUUID->"fe95b371-272c-4bce-a8ec-a165464ba891"], Cell[5329913, 109021, 4105, 100, 297, "Input",ExpressionUUID->"6caa92a8-46f0-430d-b301-545e39b91a52"] }, Closed]], Cell[CellGroupData[{ Cell[5334055, 109126, 1022, 14, 44, "Subsubsection",ExpressionUUID->"9422d9bf-aa09-44f3-8a07-039d87d59379"], Cell[5335080, 109142, 5612, 135, 326, "Input",ExpressionUUID->"50edbbb6-5a30-4c82-ac9c-d209e5d79db0"] }, Closed]], Cell[CellGroupData[{ Cell[5340729, 109282, 728, 10, 44, "Subsubsection",ExpressionUUID->"badb3562-d10c-4069-b6f4-fb91f1719da7"], Cell[5341460, 109294, 4586, 106, 273, "Input",ExpressionUUID->"49fc406e-9e45-4708-9b42-788abf74c945"] }, Closed]], Cell[CellGroupData[{ Cell[5346083, 109405, 696, 10, 44, "Subsubsection",ExpressionUUID->"38918417-54be-4911-bf1a-9b931a068ad5"], Cell[5346782, 109417, 3766, 93, 273, "Input",ExpressionUUID->"0ac17d52-41a6-410f-a836-e5927c8ffc7d"] }, Closed]], Cell[CellGroupData[{ Cell[5350585, 109515, 747, 11, 44, "Subsubsection",ExpressionUUID->"d73ae558-5d7b-4068-9a8d-5124feae9e58"], Cell[5351335, 109528, 5512, 134, 398, "Input",ExpressionUUID->"9f0898d0-e20d-4e6a-ba92-2d7e1f3441ce"] }, Closed]], Cell[CellGroupData[{ Cell[5356884, 109667, 731, 11, 44, "Subsubsection",ExpressionUUID->"2d9d9826-43d6-4000-b0d1-359613cdb707"], Cell[5357618, 109680, 3623, 82, 225, "Input",ExpressionUUID->"40385832-0d75-4772-9321-889bc452b7e4"] }, Closed]], Cell[CellGroupData[{ Cell[5361278, 109767, 675, 10, 44, "Subsubsection",ExpressionUUID->"2fcc114f-bd32-467e-83d7-1580c4553c73"], Cell[5361956, 109779, 3168, 71, 249, "Input",ExpressionUUID->"ab57f91a-ea51-45df-8186-1b657517b9c0"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[5365173, 109856, 615, 9, 46, "Subsection",ExpressionUUID->"8dda4d3a-cb31-4c59-95bf-aef4d1a4b2b8"], Cell[CellGroupData[{ Cell[5365813, 109869, 495, 8, 56, "Subsubsection",ExpressionUUID->"ec502578-4394-49de-a13b-c03363345d3a"], Cell[5366311, 109879, 1618, 33, 140, "Input",ExpressionUUID->"46cd8715-7ef2-4f8a-aad3-7b59833611ee"] }, Closed]], Cell[CellGroupData[{ Cell[5367966, 109917, 510, 8, 44, "Subsubsection",ExpressionUUID->"29a94e8a-b96c-46c5-a83c-e292d5f6d8ae"], Cell[5368479, 109927, 1820, 44, 207, "Input",ExpressionUUID->"895e2fc8-07be-4151-8042-ad18987a74df"] }, Closed]], Cell[CellGroupData[{ Cell[5370336, 109976, 486, 7, 44, "Subsubsection",ExpressionUUID->"2ca404f1-d2d9-4496-8cf6-914a4d52b0db"], Cell[5370825, 109985, 6377, 148, 385, "Input",ExpressionUUID->"8cf4aa7c-293f-4c36-8880-388f56950d45"] }, Closed]], Cell[CellGroupData[{ Cell[5377239, 110138, 536, 8, 44, "Subsubsection",ExpressionUUID->"2f4572cf-f61a-41de-b682-1e03ef2419f7"], Cell[5377778, 110148, 6482, 150, 396, "Input",ExpressionUUID->"76618255-84a1-4d51-8284-35b792c1ce71"] }, Closed]], Cell[CellGroupData[{ Cell[5384297, 110303, 696, 15, 44, "Subsubsection",ExpressionUUID->"596b8bf2-51e2-4e9a-909f-691760d62b19"], Cell[5384996, 110320, 5373, 113, 274, "Input",ExpressionUUID->"b2dde7b3-4e38-4f81-a1a7-04071abfd87b"] }, Closed]], Cell[CellGroupData[{ Cell[5390406, 110438, 534, 8, 44, "Subsubsection",ExpressionUUID->"db936206-88e3-4975-8b27-457dda1af8d7"], Cell[5390943, 110448, 4780, 93, 253, "Input",ExpressionUUID->"656a907d-12c1-43a5-b686-c6dee6b593f0"] }, Closed]], Cell[CellGroupData[{ Cell[5395760, 110546, 584, 8, 44, "Subsubsection",ExpressionUUID->"4aa1cdd1-d1e8-40ec-9779-084830f2ac99"], Cell[5396347, 110556, 3074, 73, 249, "Input",ExpressionUUID->"eb488d1b-53b4-455b-be11-b209b65a0b3d"] }, Closed]], Cell[CellGroupData[{ Cell[5399458, 110634, 421, 7, 44, "Subsubsection",ExpressionUUID->"d2e920b7-e97a-4989-90a1-9a3faacb4b9a"], Cell[5399882, 110643, 3951, 97, 319, "Input",ExpressionUUID->"b26e9b07-1af4-4b94-b89b-e621305f1456"], Cell[5403836, 110742, 149, 3, 55, "Input",ExpressionUUID->"b336c1d1-1088-4fd2-a00a-c759558e461b"] }, Closed]], Cell[CellGroupData[{ Cell[5404022, 110750, 800, 12, 44, "Subsubsection",ExpressionUUID->"98f7c702-73de-4696-9946-f357e79a0cca"], Cell[5404825, 110764, 211, 3, 35, "Input",ExpressionUUID->"2f221a1e-fc52-4058-af51-1e5ba90ff91a"], Cell[5405039, 110769, 8453, 193, 471, "Input",ExpressionUUID->"3ff52ac8-d40b-4b95-9228-69666621ac82"] }, Closed]], Cell[CellGroupData[{ Cell[5413529, 110967, 1082, 15, 44, "Subsubsection",ExpressionUUID->"6ab56740-4e14-46f1-a00a-a093fdf3db1e"], Cell[5414614, 110984, 16820, 341, 725, "Input",ExpressionUUID->"1fed5131-c575-4c94-8f68-9296ca309f23"] }, Closed]], Cell[CellGroupData[{ Cell[5431471, 111330, 469, 7, 44, "Subsubsection",ExpressionUUID->"9fefd3ad-065d-49ce-b10f-a13da6966524"], Cell[5431943, 111339, 2430, 55, 427, "Input",ExpressionUUID->"66c512a2-56e2-44ce-b978-5d562066707e"] }, Closed]], Cell[CellGroupData[{ Cell[5434410, 111399, 441, 7, 44, "Subsubsection",ExpressionUUID->"da6103d4-5508-40a8-adf5-7c59179977a4"], Cell[5434854, 111408, 2177, 62, 249, "Input",ExpressionUUID->"f255a474-dbc1-4258-b91f-850f262ba426"] }, Closed]], Cell[CellGroupData[{ Cell[5437068, 111475, 407, 7, 44, "Subsubsection",ExpressionUUID->"c134b95d-7c64-4d77-b441-a275ce11739e"], Cell[5437478, 111484, 3916, 97, 319, "Input",ExpressionUUID->"6125d2ae-1ba2-454b-8b3d-4d17292ff27d"] }, Closed]], Cell[CellGroupData[{ Cell[5441431, 111586, 379, 6, 44, "Subsubsection",ExpressionUUID->"3aaa1ef3-e79e-478b-81c1-07c5c6f5711e"], Cell[5441813, 111594, 4624, 117, 385, "Input",ExpressionUUID->"d2ee6931-eb4e-4961-b767-10d73a7c748b"] }, Closed]], Cell[CellGroupData[{ Cell[5446474, 111716, 482, 8, 44, "Subsubsection",ExpressionUUID->"dda18dd1-bbcd-4707-b150-cbd4aaba729b"], Cell[5446959, 111726, 3738, 87, 325, "Input",ExpressionUUID->"cf41cb56-5935-45b4-81c6-58eccff89957"] }, Closed]], Cell[CellGroupData[{ Cell[5450734, 111818, 556, 8, 44, "Subsubsection",ExpressionUUID->"4fd0149b-cb09-457e-894c-d1215af53706"], Cell[5451293, 111828, 3250, 81, 321, "Input",ExpressionUUID->"8f714d42-58ff-4328-af20-9d80e9083ba8"] }, Closed]], Cell[CellGroupData[{ Cell[5454580, 111914, 480, 8, 44, "Subsubsection",ExpressionUUID->"137610b8-126f-4d7c-a09b-6b62aef6c587"], Cell[5455063, 111924, 3528, 84, 319, "Input",ExpressionUUID->"b9974d30-220b-42ba-924c-5edb8fc02603"], Cell[5458594, 112010, 3108, 72, 297, "Input",ExpressionUUID->"988fab71-8d6f-463a-9c6f-30208dd7aa41"] }, Closed]], Cell[CellGroupData[{ Cell[5461739, 112087, 626, 9, 44, "Subsubsection",ExpressionUUID->"1d113d45-b64b-4176-916f-61fe0321cd08"], Cell[5462368, 112098, 5661, 131, 416, "Input",ExpressionUUID->"71b41a9d-992c-4d5f-b1fb-52dcc213da63"] }, Closed]], Cell[CellGroupData[{ Cell[5468066, 112234, 656, 9, 44, "Subsubsection",ExpressionUUID->"ca0bed05-480f-4077-9f56-d2f6a343f7fe"], Cell[5468725, 112245, 6358, 146, 473, "Input",ExpressionUUID->"710a6b9f-deb0-4750-847e-de05528a3dd1"], Cell[5475086, 112393, 6241, 145, 407, "Input",ExpressionUUID->"e2130f23-bca8-410e-b353-51210869b0ce"] }, Closed]], Cell[CellGroupData[{ Cell[5481364, 112543, 686, 10, 44, "Subsubsection",ExpressionUUID->"b5e860d5-d0f2-46a5-b239-8fbbfe5c8a57"], Cell[CellGroupData[{ Cell[5482075, 112557, 7634, 177, 477, "Input",ExpressionUUID->"58704f56-5287-48d7-a4d7-dceebca4f2e7"], Cell[5489712, 112736, 630, 20, 73, "Output",ExpressionUUID->"d5ba9069-f53b-4c6c-928e-c2704925ff5f"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[5490391, 112762, 487, 8, 44, "Subsubsection",ExpressionUUID->"7dfc468d-8647-4341-b9fa-3647224b7b57"], Cell[5490881, 112772, 6888, 154, 451, "Input",ExpressionUUID->"bbf5dce5-5554-4fb3-997d-2445c818bfe9"] }, Closed]], Cell[CellGroupData[{ Cell[5497806, 112931, 458, 7, 44, "Subsubsection",ExpressionUUID->"f6e54321-d312-49ea-b1a3-57a3b1e06f2a"], Cell[5498267, 112940, 5350, 133, 451, "Input",ExpressionUUID->"8acc7bac-0bc3-4c44-9772-c796a1417d68"] }, Closed]], Cell[CellGroupData[{ Cell[5503654, 113078, 622, 9, 44, "Subsubsection",ExpressionUUID->"e5f61de8-1182-47cf-8a7b-2337b20298c7"], Cell[5504279, 113089, 4555, 98, 368, "Input",ExpressionUUID->"79b8f2d9-ca4c-4293-ab3b-748aa33c9007"] }, Closed]], Cell[CellGroupData[{ Cell[5508871, 113192, 475, 7, 44, "Subsubsection",ExpressionUUID->"561787f6-0dc9-4a69-b6c6-f45656ca6c4e"], Cell[5509349, 113201, 1835, 37, 163, "Input",ExpressionUUID->"59b2c91f-58a8-4f60-8830-95d335dd8371"] }, Closed]], Cell[CellGroupData[{ Cell[5511221, 113243, 567, 9, 44, "Subsubsection",ExpressionUUID->"dd8b7af0-2026-4bd6-b747-c7bfa820e746"], Cell[CellGroupData[{ Cell[5511813, 113256, 2814, 75, 297, "Input",ExpressionUUID->"6531450a-9d39-4046-adec-55848e374ce2"], Cell[5514630, 113333, 3952, 110, 139, "Output",ExpressionUUID->"9feb3fa3-2916-4b23-8a13-f4125e05b85a"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[5518643, 113450, 889, 13, 46, "Subsection",ExpressionUUID->"8b8ebf36-44ef-455a-b584-4760b97dc02a"], Cell[CellGroupData[{ Cell[5519557, 113467, 491, 8, 56, "Subsubsection",ExpressionUUID->"0b58f323-8e74-4bb4-a7dd-0e1f19a67740"], Cell[5520051, 113477, 5329, 114, 321, "Input",ExpressionUUID->"88404147-fc06-4614-945f-dbfbabb7f718"] }, Closed]], Cell[CellGroupData[{ Cell[5525417, 113596, 603, 9, 44, "Subsubsection",ExpressionUUID->"60e84868-8762-419a-995b-4bca4326c86c"], Cell[CellGroupData[{ Cell[5526045, 113609, 7031, 162, 457, "Input",ExpressionUUID->"47296f0a-5f24-4548-954b-7fd453b1bd76"], Cell[5533079, 113773, 5774, 166, 273, "Output",ExpressionUUID->"158ee92a-de6e-4da4-bc94-70b2513dcc70"], Cell[5538856, 113941, 3352, 88, 95, "Print",ExpressionUUID->"6f5e4a15-536b-488f-847a-21baefd76655"], Cell[5542211, 114031, 374, 9, 34, "Message",ExpressionUUID->"d1ab0d5d-6efd-45ea-8420-27c9214520a3"], Cell[5542588, 114042, 808, 23, 46, "Output",ExpressionUUID->"d2522899-c372-4aa8-a5c2-50a35ad46f27"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[5543445, 114071, 1040, 14, 44, "Subsubsection",ExpressionUUID->"eb086934-c2a7-4973-9560-059df91090fe"], Cell[5544488, 114087, 8305, 193, 508, "Input",ExpressionUUID->"7ec895fb-cd7a-44c0-939e-1e973b73d711"] }, Closed]], Cell[CellGroupData[{ Cell[5552830, 114285, 1154, 16, 44, "Subsubsection",ExpressionUUID->"4285d1e0-c7c1-460d-9721-ee694f21d713"], Cell[5553987, 114303, 17534, 334, 606, "Input",ExpressionUUID->"411b1990-dd2c-48c4-9406-26f1d718f7d7"] }, Closed]], Cell[CellGroupData[{ Cell[5571558, 114642, 679, 10, 44, "Subsubsection",ExpressionUUID->"a4627f7d-a9f6-48ee-93cb-5eed0b94f0d8"], Cell[5572240, 114654, 7637, 165, 427, "Input",ExpressionUUID->"32895d8f-67a9-4b1f-91dd-f7a587c1acd4"] }, Closed]], Cell[CellGroupData[{ Cell[5579914, 114824, 515, 8, 44, "Subsubsection",ExpressionUUID->"d17c8db5-4e2b-4129-986d-47c9263640c4"], Cell[5580432, 114834, 4619, 103, 321, "Input",ExpressionUUID->"676fec74-2d22-477e-9ac2-45c0bb92dc7a"] }, Closed]], Cell[CellGroupData[{ Cell[5585088, 114942, 393, 7, 44, "Subsubsection",ExpressionUUID->"285c06a9-aee3-4c8a-bac6-5756bba88a2f"], Cell[5585484, 114951, 4177, 97, 321, "Input",ExpressionUUID->"acb1daa5-9316-43f7-aef0-eb3308efac2b"] }, Closed]], Cell[CellGroupData[{ Cell[5589698, 115053, 413, 7, 44, "Subsubsection",ExpressionUUID->"d32409d0-2e1a-49b3-9453-0f0c7b2c83c5"], Cell[5590114, 115062, 4356, 100, 321, "Input",ExpressionUUID->"a39b6254-aa20-4e85-8d2f-c95a993bd33b"] }, Closed]], Cell[CellGroupData[{ Cell[5594507, 115167, 363, 6, 44, "Subsubsection",ExpressionUUID->"246bee83-9644-4128-bc0f-80aeefa97a01"], Cell[5594873, 115175, 4302, 99, 321, "Input",ExpressionUUID->"8bbdf06b-fa2b-4713-88c0-236df0d265db"] }, Closed]], Cell[CellGroupData[{ Cell[5599212, 115279, 471, 8, 44, "Subsubsection",ExpressionUUID->"16f9256e-d318-4635-8b17-fad8ca43fede"], Cell[5599686, 115289, 5500, 131, 392, "Input",ExpressionUUID->"74ce939a-3fad-4aee-80e5-c2f520f22dc4"] }, Closed]], Cell[CellGroupData[{ Cell[5605223, 115425, 521, 8, 44, "Subsubsection",ExpressionUUID->"20cd57fc-3258-46df-8e82-c358ddd91eac"], Cell[5605747, 115435, 5354, 128, 368, "Input",ExpressionUUID->"714fefbe-7f3d-439f-b790-a8c2661043f9"] }, Closed]], Cell[CellGroupData[{ Cell[5611138, 115568, 517, 8, 44, "Subsubsection",ExpressionUUID->"ef4376c4-f29f-43f9-a625-b0f3824d3448"], Cell[5611658, 115578, 4132, 94, 297, "Input",ExpressionUUID->"fa7ec5d1-d4ff-463f-99b3-065309989c90"] }, Closed]], Cell[CellGroupData[{ Cell[5615827, 115677, 539, 9, 44, "Subsubsection",ExpressionUUID->"feed8171-7f0c-4097-bf86-16df543c265b"], Cell[5616369, 115688, 8489, 201, 511, "Input",ExpressionUUID->"0263de8a-ea22-41b1-921d-8145303e70f3"] }, Closed]], Cell[CellGroupData[{ Cell[5624895, 115894, 590, 9, 44, "Subsubsection",ExpressionUUID->"336900a9-ba1b-41d3-a7b4-04e9c282b157"], Cell[5625488, 115905, 9104, 211, 648, "Input",ExpressionUUID->"751083b7-d8e4-4c5c-84a2-683db8b25f99"] }, Closed]], Cell[CellGroupData[{ Cell[5634629, 116121, 746, 11, 44, "Subsubsection",ExpressionUUID->"3cdc9a17-cca7-4803-a78a-2f661e2f52a9"], Cell[5635378, 116134, 8404, 185, 388, "Input",ExpressionUUID->"52b73e57-81c5-4125-a12c-504081a9b651"] }, Closed]], Cell[CellGroupData[{ Cell[5643819, 116324, 417, 7, 44, "Subsubsection",ExpressionUUID->"d94bf0e7-3dfd-4ffc-8ca8-2dc5f1e81ec0"], Cell[5644239, 116333, 5441, 129, 368, "Input",ExpressionUUID->"d9790db1-861d-4fdc-8ede-6b8a7af687df"] }, Closed]], Cell[CellGroupData[{ Cell[5649717, 116467, 493, 8, 44, "Subsubsection",ExpressionUUID->"9ce68ed8-8d13-4807-83a1-b744bea5dd4a"], Cell[5650213, 116477, 4224, 96, 297, "Input",ExpressionUUID->"9f943fd8-f8df-47b5-b5e3-8580e365d2fc"] }, Closed]], Cell[CellGroupData[{ Cell[5654474, 116578, 780, 12, 44, "Subsubsection",ExpressionUUID->"5a922c3d-9c7f-490c-b437-35b4af900a7e"], Cell[5655257, 116592, 10308, 210, 379, "Input",ExpressionUUID->"b19c9cce-e3bc-4ab3-b065-c0d2719404be"] }, Closed]], Cell[CellGroupData[{ Cell[5665602, 116807, 808, 13, 44, "Subsubsection",ExpressionUUID->"b27c0df3-7c21-4260-8763-72ad9a48c96c"], Cell[5666413, 116822, 14588, 324, 689, "Input",ExpressionUUID->"856964ac-d9a6-46d7-8f04-3b3c029c3b53"] }, Closed]], Cell[CellGroupData[{ Cell[5681038, 117151, 522, 8, 44, "Subsubsection",ExpressionUUID->"aaf3364e-7f43-4c24-a587-cd8a3f671168"], Cell[5681563, 117161, 4769, 105, 321, "Input",ExpressionUUID->"0cb582ab-e411-412c-a48d-f3f4c00e2d23"] }, Closed]], Cell[CellGroupData[{ Cell[5686369, 117271, 550, 9, 44, "Subsubsection",ExpressionUUID->"661e0cab-663c-44e0-b4e6-e0cfee622745"], Cell[5686922, 117282, 7114, 157, 559, "Input",ExpressionUUID->"31e5238a-de2e-4251-a8cc-960a94ed5b84"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[5694085, 117445, 913, 13, 46, "Subsection",ExpressionUUID->"e6002408-5188-4cef-9615-f76049bb97ab"], Cell[CellGroupData[{ Cell[5695023, 117462, 556, 9, 56, "Subsubsection",ExpressionUUID->"f09943b2-64a5-4a87-9f1a-40f684f91dbe"], Cell[5695582, 117473, 6657, 145, 463, "Input",ExpressionUUID->"9d5ce7fe-55d7-4e9c-8b53-0557bb9655e6"] }, Closed]], Cell[CellGroupData[{ Cell[5702276, 117623, 596, 9, 44, "Subsubsection",ExpressionUUID->"1181fa58-bb92-4bed-b6d2-6046802d2e9f"], Cell[5702875, 117634, 7248, 166, 535, "Input",ExpressionUUID->"4121510e-13df-43ca-b53d-39b4b2880586"] }, Closed]], Cell[CellGroupData[{ Cell[5710160, 117805, 751, 11, 44, "Subsubsection",ExpressionUUID->"ef9301ad-ffc5-4d0c-88eb-96c861350e40"], Cell[5710914, 117818, 4652, 102, 321, "Input",ExpressionUUID->"1fdd7032-7349-4aa0-8da9-8423330696a0"] }, Closed]], Cell[CellGroupData[{ Cell[5715603, 117925, 593, 9, 44, "Subsubsection",ExpressionUUID->"f0f841e7-5a88-416e-899f-33d21c65fabd"], Cell[5716199, 117936, 3345, 86, 321, "Input",ExpressionUUID->"ce62ebec-db36-4ce8-92da-2451a1edc970"] }, Closed]], Cell[CellGroupData[{ Cell[5719581, 118027, 506, 8, 44, "Subsubsection",ExpressionUUID->"9be380f3-8a6c-4840-bbc1-427b3277e6a4"], Cell[5720090, 118037, 6130, 147, 487, "Input",ExpressionUUID->"3fcfcedf-1b9f-4f00-9321-6c9ffeca868a"] }, Closed]], Cell[CellGroupData[{ Cell[5726257, 118189, 552, 9, 44, "Subsubsection",ExpressionUUID->"5c0dcdbc-0d73-47d2-a90e-4fa2202c567a"], Cell[5726812, 118200, 5115, 120, 392, "Input",ExpressionUUID->"25f5f230-28cd-4656-ad1c-ea840b845079"] }, Closed]], Cell[CellGroupData[{ Cell[5731964, 118325, 354, 5, 44, "Subsubsection",ExpressionUUID->"a5a98b11-9f02-45a2-a503-e46ac73368f1"], Cell[5732321, 118332, 826, 19, 59, "Input",ExpressionUUID->"44bba056-9048-4dde-a062-28fc438f843d"] }, Closed]], Cell[CellGroupData[{ Cell[5733184, 118356, 393, 6, 44, "Subsubsection",ExpressionUUID->"76970886-d128-421f-bdc8-d800eeffc9a3"], Cell[5733580, 118364, 4287, 101, 321, "Input",ExpressionUUID->"01c83bb6-b98c-47e9-a8cf-8b7753bc36d4"] }, Closed]], Cell[CellGroupData[{ Cell[5737904, 118470, 297, 5, 44, "Subsubsection",ExpressionUUID->"ed69b494-2d0e-4d53-b0b4-ce52ffbdb7e8"], Cell[5738204, 118477, 4313, 102, 368, "Input",ExpressionUUID->"387150a2-1f6c-43ee-8df8-ff57a74b5691"] }, Closed]], Cell[CellGroupData[{ Cell[5742554, 118584, 323, 6, 44, "Subsubsection",ExpressionUUID->"ae2b9564-f9f2-4a4e-bc50-ff27a0c53146"], Cell[5742880, 118592, 4974, 119, 463, "Input",ExpressionUUID->"67ed0c58-9ecf-4810-ab6d-d5cf7153a5a7"] }, Closed]], Cell[CellGroupData[{ Cell[5747891, 118716, 345, 6, 44, "Subsubsection",ExpressionUUID->"26291586-55e4-4878-ba3f-4844b4d7fe4e"], Cell[5748239, 118724, 4505, 101, 392, "Input",ExpressionUUID->"5e03bc45-29d4-4cf7-b210-ba804be3b291"] }, Closed]], Cell[CellGroupData[{ Cell[5752781, 118830, 330, 6, 44, "Subsubsection",ExpressionUUID->"2b586baa-41d8-4a81-98dd-33c4919146de"], Cell[5753114, 118838, 4444, 113, 463, "Input",ExpressionUUID->"b0dbb4df-4690-429a-b696-6e24889a7695"] }, Closed]], Cell[CellGroupData[{ Cell[5757595, 118956, 509, 8, 44, "Subsubsection",ExpressionUUID->"df62930c-91c9-42db-aa05-fd2381197ded"], Cell[5758107, 118966, 4178, 104, 439, "Input",ExpressionUUID->"6420ca88-ba6e-4516-b442-bdf14253658a"] }, Closed]], Cell[CellGroupData[{ Cell[5762322, 119075, 523, 8, 44, "Subsubsection",ExpressionUUID->"8d5f287e-3483-43be-9a3b-1e8e6d818387"], Cell[5762848, 119085, 5104, 128, 487, "Input",ExpressionUUID->"e76d2789-e421-4b03-b286-aba9c5d861dc"] }, Closed]], Cell[CellGroupData[{ Cell[5767989, 119218, 508, 8, 44, "Subsubsection",ExpressionUUID->"e3d0e78f-43f0-432c-8e55-77ac019d8949"], Cell[5768500, 119228, 5305, 119, 416, "Input",ExpressionUUID->"e688d383-03e4-46b4-9200-ba0802aea915"] }, Closed]], Cell[CellGroupData[{ Cell[5773842, 119352, 567, 9, 44, "Subsubsection",ExpressionUUID->"a9acad1d-fe57-43ef-a833-738de675aa5c"], Cell[5774412, 119363, 4976, 119, 487, "Input",ExpressionUUID->"ece3ce0e-bd5a-42e9-95a0-a66340c940c5"] }, Closed]], Cell[CellGroupData[{ Cell[5779425, 119487, 325, 6, 44, "Subsubsection",ExpressionUUID->"f621edbf-3a25-4533-8014-085169a4974e"], Cell[5779753, 119495, 4267, 94, 321, "Input",ExpressionUUID->"f35377ef-1dec-482b-9405-9e5036852707"] }, Closed]], Cell[CellGroupData[{ Cell[5784057, 119594, 382, 6, 44, "Subsubsection",ExpressionUUID->"e1f660bf-95df-433b-8788-6b7701c7e3e7"], Cell[5784442, 119602, 6352, 154, 487, "Input",ExpressionUUID->"4ba14765-9ebd-4832-b5eb-6cd58ea378e4"] }, Closed]], Cell[CellGroupData[{ Cell[5790831, 119761, 540, 9, 44, "Subsubsection",ExpressionUUID->"0dd6c074-3fcc-448f-a945-58ab6f49a459"], Cell[5791374, 119772, 4452, 102, 345, "Input",ExpressionUUID->"0f68b044-b524-4fb2-b39b-bfc9783bfe85"] }, Closed]], Cell[CellGroupData[{ Cell[5795863, 119879, 376, 6, 44, "Subsubsection",ExpressionUUID->"cbffb78f-f288-4b9d-9208-23c0cdec7cf8"], Cell[5796242, 119887, 3989, 87, 273, "Input",ExpressionUUID->"cbf4c2b4-279c-414b-8c49-798882e74397"] }, Closed]], Cell[CellGroupData[{ Cell[5800268, 119979, 326, 6, 44, "Subsubsection",ExpressionUUID->"34f37bc1-0a2d-47c2-8192-b56237ad70ef"], Cell[5800597, 119987, 3652, 80, 249, "Input",ExpressionUUID->"04736e3e-ef1a-4cbd-b5f3-fc5fd2f6c040"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[5804298, 120073, 1069, 15, 46, "Subsection",ExpressionUUID->"a14c39cc-f745-491a-b289-0eeae4dca678"], Cell[CellGroupData[{ Cell[5805392, 120092, 277, 4, 56, "Subsubsection",ExpressionUUID->"812f0502-f78f-4580-b738-fc035a5be776"], Cell[5805672, 120098, 5431, 142, 416, "Input",ExpressionUUID->"125f1d62-9708-4583-bffd-932cad43bcb5"] }, Closed]], Cell[CellGroupData[{ Cell[5811140, 120245, 302, 5, 45, "Subsubsection",ExpressionUUID->"d6dee3c3-ac4c-4f03-96d2-62857d2ae5ad"], Cell[5811445, 120252, 3797, 97, 393, "Input",ExpressionUUID->"f76634f5-7aa9-4b4b-b89c-568032c4fe4b"] }, Closed]], Cell[CellGroupData[{ Cell[5815279, 120354, 726, 11, 45, "Subsubsection",ExpressionUUID->"0c92047e-91c6-445f-9cae-d916b5244a5c"], Cell[5816008, 120367, 5634, 118, 416, "Input",ExpressionUUID->"64c8dd03-37ec-4eb7-a9d6-02d5732b4c67"] }, Closed]], Cell[CellGroupData[{ Cell[5821679, 120490, 455, 7, 45, "Subsubsection",ExpressionUUID->"41ecc0d8-4571-4703-991c-38a3b24be17b"], Cell[5822137, 120499, 3482, 89, 345, "Input",ExpressionUUID->"1e6d3493-8def-480f-b41a-c95e4cbde4b3"] }, Closed]], Cell[CellGroupData[{ Cell[5825656, 120593, 1067, 15, 45, "Subsubsection",ExpressionUUID->"5155c48d-5507-4db8-8087-b1317c7bf071"], Cell[5826726, 120610, 7714, 175, 430, "Input",ExpressionUUID->"01a9db10-842c-403f-9829-4ee0908a1731"] }, Closed]], Cell[CellGroupData[{ Cell[5834477, 120790, 326, 5, 45, "Subsubsection",ExpressionUUID->"34af25ea-9700-49b0-8288-26e6f8064d79"], Cell[5834806, 120797, 2931, 71, 274, "Input",ExpressionUUID->"ea437664-d702-486c-ab1c-df75110d87fc"] }, Closed]], Cell[CellGroupData[{ Cell[5837774, 120873, 326, 5, 45, "Subsubsection",ExpressionUUID->"2a746516-ac0d-4c5a-9471-4c17790fb028"], Cell[5838103, 120880, 3771, 92, 345, "Input",ExpressionUUID->"43c233eb-a8d9-4850-b1ee-2ed9777ecd83"] }, Closed]], Cell[CellGroupData[{ Cell[5841911, 120977, 476, 7, 45, "Subsubsection",ExpressionUUID->"ec7cb860-2bf7-41a9-bf96-0c71afc0de81"], Cell[5842390, 120986, 5225, 135, 448, "Input",ExpressionUUID->"62fb041f-0df8-452c-a701-4362943eb87b"] }, Closed]], Cell[CellGroupData[{ Cell[5847652, 121126, 454, 7, 45, "Subsubsection",ExpressionUUID->"8dca84da-6271-46e4-8a2e-481d1ae1ec49"], Cell[5848109, 121135, 4930, 128, 416, "Input",ExpressionUUID->"9f8a5367-5cb2-4d84-a861-d9fd22e8d0a9"] }, Closed]], Cell[CellGroupData[{ Cell[5853076, 121268, 547, 8, 45, "Subsubsection",ExpressionUUID->"bd6bde99-16ce-472b-a55e-d94c88513402"], Cell[5853626, 121278, 3774, 91, 345, "Input",ExpressionUUID->"800820a1-a119-46b2-bafb-a6fe6935c401"] }, Closed]], Cell[CellGroupData[{ Cell[5857437, 121374, 523, 8, 45, "Subsubsection",ExpressionUUID->"7565dc7e-2ddf-422f-90e5-73be0d409be4"], Cell[5857963, 121384, 4048, 100, 369, "Input",ExpressionUUID->"581b87c7-aa08-4cc6-9eed-991ce0728ce4"] }, Closed]], Cell[CellGroupData[{ Cell[5862048, 121489, 551, 8, 45, "Subsubsection",ExpressionUUID->"fcfc481a-5ce3-4751-a9c3-c6f322445fe2"], Cell[5862602, 121499, 5025, 123, 393, "Input",ExpressionUUID->"db63d7ff-b48a-4b41-a5d2-a147db0d3b75"] }, Closed]], Cell[CellGroupData[{ Cell[5867664, 121627, 521, 8, 45, "Subsubsection",ExpressionUUID->"28ae77f4-523a-4be5-a103-2ed3fcd70ef6"], Cell[5868188, 121637, 4208, 102, 369, "Input",ExpressionUUID->"d34ea64d-54cb-4146-a450-92c300bd1a1f"] }, Closed]], Cell[CellGroupData[{ Cell[5872433, 121744, 400, 6, 45, "Subsubsection",ExpressionUUID->"d9fc8a54-e25e-46f1-9a61-aeb047ab4408"], Cell[5872836, 121752, 3345, 86, 321, "Input",ExpressionUUID->"1f52f6b5-fe93-47d5-a047-f64d7b9e6458"] }, Closed]], Cell[CellGroupData[{ Cell[5876218, 121843, 1147, 16, 45, "Subsubsection",ExpressionUUID->"020dfa95-9901-42e0-8cba-7f947e811a92"], Cell[5877368, 121861, 7011, 162, 430, "Input",ExpressionUUID->"0e7e8295-10f7-49a3-8b1b-f3ae4127f07e"] }, Closed]], Cell[CellGroupData[{ Cell[5884416, 122028, 303, 5, 45, "Subsubsection",ExpressionUUID->"12644844-84ad-46c3-ac44-b43908b5aa02"], Cell[5884722, 122035, 4329, 108, 393, "Input",ExpressionUUID->"e0a93ec1-fd46-4119-b0df-efdd2d226ed7"] }, Closed]], Cell[CellGroupData[{ Cell[5889088, 122148, 379, 6, 45, "Subsubsection",ExpressionUUID->"d7c37cef-b389-4fac-bb43-6c1ec837f560"], Cell[5889470, 122156, 4206, 108, 369, "Input",ExpressionUUID->"c32192a0-b56f-4588-8ff2-68fec2bccdf8"] }, Closed]], Cell[CellGroupData[{ Cell[5893713, 122269, 548, 8, 45, "Subsubsection",ExpressionUUID->"e03e23ef-6461-4edd-923f-604e264ce75b"], Cell[5894264, 122279, 5157, 119, 393, "Input",ExpressionUUID->"374590f6-e341-45fa-9b77-4f91c393bed3"] }, Closed]], Cell[CellGroupData[{ Cell[5899458, 122403, 550, 8, 45, "Subsubsection",ExpressionUUID->"8591d200-63b5-4567-a8cf-8ea681f0c9b6"], Cell[5900011, 122413, 4858, 110, 369, "Input",ExpressionUUID->"a8427689-b905-4b1e-a282-5012b2abafff"] }, Closed]], Cell[CellGroupData[{ Cell[5904906, 122528, 354, 5, 45, "Subsubsection",ExpressionUUID->"e51c8a82-3282-4a2b-8270-56c8df2c8a13"], Cell[5905263, 122535, 3396, 82, 345, "Input",ExpressionUUID->"c93b8f26-d595-42d5-ba9b-424742e42646"] }, Closed]], Cell[CellGroupData[{ Cell[5908696, 122622, 551, 8, 45, "Subsubsection",ExpressionUUID->"4bd8e63d-e6fb-4e0b-85b9-3f2b1abf80aa"], Cell[5909250, 122632, 3713, 86, 297, "Input",ExpressionUUID->"945bf50a-77d3-4b29-9615-136fe696a2c6"] }, Closed]] }, Open ]] }, Open ]] } ] *)