(* 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[ 2654524, 60576] NotebookOptionsPosition[ 2639679, 60301] NotebookOutlinePosition[ 2640226, 60321] CellTagsIndexPosition[ 2640183, 60318] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["MEC-E8001 Finite Element Analysis 2019 code", "Chapter", InitializationCell->True, 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, {3.755441061106991*^9, 3.7554410629365644`*^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->"e3a7af86-4b21-4f7c-818a-\ 4f3ab57ac50c"], Cell[CellGroupData[{ Cell["DEFS defs ", "Subsection", CellChangeTimes->{{3.4770537307790003`*^9, 3.4770537313562*^9}},ExpressionUUID->"a4d44395-72a1-4756-8608-684d4c13df83"], 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[{ SubscriptBox["u", "X"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["\[Delta]u", "X"], "[", "any", "]"}]}], ",", RowBox[{ RowBox[{ SubscriptBox["u", "Y"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["\[Delta]u", "Y"], "[", "any", "]"}]}], ",", RowBox[{ RowBox[{ SubscriptBox["u", "Z"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["\[Delta]u", "Z"], "[", "any", "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ SubscriptBox["\[Theta]", "X"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["\[Delta]\[Theta]", "X"], "[", "any", "]"}]}], ",", RowBox[{ RowBox[{ SubscriptBox["\[Theta]", "Y"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["\[Delta]\[Theta]", "Y"], "[", "any", "]"}]}], ",", RowBox[{ RowBox[{ SubscriptBox["\[Theta]", "Z"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["\[Delta]\[Theta]", "Z"], "[", "any", "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ SubscriptBox["u", "x"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["\[Delta]u", "x"], "[", "any", "]"}]}], ",", RowBox[{ RowBox[{ SubscriptBox["u", "y"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["\[Delta]u", "y"], "[", "any", "]"}]}], ",", RowBox[{ RowBox[{ SubscriptBox["u", "z"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["\[Delta]u", "z"], "[", "any", "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ SubscriptBox["\[Theta]", "x"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["\[Delta]\[Theta]", "x"], "[", "any", "]"}]}], ",", RowBox[{ RowBox[{ SubscriptBox["\[Theta]", "y"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["\[Delta]\[Theta]", "y"], "[", "any", "]"}]}], ",", RowBox[{ RowBox[{ SubscriptBox["\[Theta]", "z"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["\[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[{"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[{"\[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[{ SubscriptBox["\[Delta]u", "X"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["u", "X"], "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{ SubscriptBox["\[Delta]u", "Y"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["u", "Y"], "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{ SubscriptBox["\[Delta]u", "Z"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["u", "Z"], "[", "any", "]"}]}], ",", "\[IndentingNewLine]", " ", RowBox[{ RowBox[{ SubscriptBox["\[Delta]\[Theta]", "X"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["\[Theta]", "X"], "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{ SubscriptBox["\[Delta]\[Theta]", "Y"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["\[Theta]", "Y"], "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{ SubscriptBox["\[Delta]\[Theta]", "Z"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["\[Theta]", "Z"], "[", "any", "]"}]}], ",", "\[IndentingNewLine]", " ", RowBox[{ RowBox[{ SubscriptBox["\[Delta]u", "x"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["u", "x"], "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{ SubscriptBox["\[Delta]u", "y"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["u", "y"], "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{ SubscriptBox["\[Delta]u", "z"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["u", "z"], "[", "any", "]"}]}], ",", "\[IndentingNewLine]", " ", RowBox[{ RowBox[{ SubscriptBox["\[Delta]\[Theta]", "x"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["\[Theta]", "x"], "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{ SubscriptBox["\[Delta]\[Theta]", "y"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["\[Theta]", "y"], "[", "any", "]"}]}], ",", " ", RowBox[{ RowBox[{ SubscriptBox["\[Delta]\[Theta]", "z"], "[", "any__", "]"}], "\[Rule]", RowBox[{ SubscriptBox["\[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]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]\[CurlyTheta]", "[", "any__", "]"}], "\[Rule]", RowBox[{"\[CurlyTheta]", "[", "any", "]"}]}]}], "}"}]}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"DOFS", "[", "exp_", "]"}], " ", ":=", RowBox[{"Union", "[", RowBox[{"Cases", "[", RowBox[{"exp", ",", RowBox[{ RowBox[{"a", "[", "__", "]"}], "|", RowBox[{"b", "[", "__", "]"}], "|", RowBox[{"c", "[", "__", "]"}], " ", "|", RowBox[{ SubscriptBox["u", "X"], "[", "__", "]"}], "|", RowBox[{ SubscriptBox["u", "Y"], "[", "__", "]"}], "|", RowBox[{ SubscriptBox["u", "Z"], "[", "__", "]"}], "|", " ", RowBox[{ SubscriptBox["\[Theta]", "X"], "[", "__", "]"}], "|", " ", RowBox[{ SubscriptBox["\[Theta]", "Y"], "[", "__", "]"}], "|", RowBox[{ SubscriptBox["\[Theta]", "Z"], "[", "__", "]"}], "|", RowBox[{ SubscriptBox["u", "x"], "[", "__", "]"}], "|", RowBox[{ SubscriptBox["u", "y"], "[", "__", "]"}], "|", RowBox[{ SubscriptBox["u", "z"], "[", "__", "]"}], "|", " ", RowBox[{ SubscriptBox["\[Theta]", "x"], "[", "__", "]"}], "|", " ", RowBox[{ SubscriptBox["\[Theta]", "y"], "[", "__", "]"}], "|", RowBox[{ SubscriptBox["\[Theta]", "z"], "[", "__", "]"}], "|", 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[{"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[{"exp", ",", RowBox[{ RowBox[{"FX", "[", "__", "]"}], "|", RowBox[{"FY", "[", "__", "]"}], "|", RowBox[{"FZ", "[", "__", "]"}], "|", " ", RowBox[{"MX", "[", "__", "]"}], "|", " ", RowBox[{"MY", "[", "__", "]"}], "|", RowBox[{"MZ", "[", "__", "]"}], "|", 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[{"exp", ",", RowBox[{ RowBox[{"\[Delta]FX", "[", "__", "]"}], "|", RowBox[{"\[Delta]FY", "[", "__", "]"}], "|", RowBox[{"\[Delta]FZ", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]MX", "[", "__", "]"}], "|", " ", RowBox[{"\[Delta]MY", "[", "__", "]"}], "|", RowBox[{"\[Delta]MZ", "[", "__", "]"}], "|", 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[{"exp", ",", RowBox[{ RowBox[{"\[Delta]a", "[", "__", "]"}], "|", RowBox[{"\[Delta]b", "[", "__", "]"}], "|", RowBox[{"\[Delta]c", "[", "__", "]"}], " ", "|", RowBox[{ SubscriptBox["\[Delta]u", "X"], "[", "__", "]"}], "|", RowBox[{ SubscriptBox["\[Delta]u", "Y"], "[", "__", "]"}], "|", RowBox[{ SubscriptBox["\[Delta]u", "Z"], "[", "__", "]"}], "|", " ", RowBox[{ SubscriptBox["\[Delta]\[Theta]", "X"], "[", "__", "]"}], "|", " ", RowBox[{ SubscriptBox["\[Delta]\[Theta]", "Y"], "[", "__", "]"}], "|", RowBox[{ SubscriptBox["\[Delta]\[Theta]", "Z"], "[", "__", "]"}], "|", RowBox[{ SubscriptBox["\[Delta]u", "x"], "[", "__", "]"}], "|", RowBox[{ SubscriptBox["\[Delta]u", "y"], "[", "__", "]"}], "|", RowBox[{ SubscriptBox["\[Delta]u", "z"], "[", "__", "]"}], "|", " ", RowBox[{ SubscriptBox["\[Delta]\[Theta]", "x"], "[", "__", "]"}], "|", " ", RowBox[{ SubscriptBox["\[Delta]\[Theta]", "y"], "[", "__", "]"}], "|", RowBox[{ SubscriptBox["\[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]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]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[{"exp", ",", RowBox[{ RowBox[{"a", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"b", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"c", "[", RowBox[{"__", ",", "n"}], "]"}], " ", "|", RowBox[{ SubscriptBox["u", "X"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{ SubscriptBox["u", "Y"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{ SubscriptBox["u", "Z"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{ SubscriptBox["\[Theta]", "X"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{ SubscriptBox["\[Theta]", "Y"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{ SubscriptBox["\[Theta]", "Z"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{ SubscriptBox["u", "x"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{ SubscriptBox["u", "y"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{ SubscriptBox["u", "z"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{ SubscriptBox["\[Theta]", "x"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{ SubscriptBox["\[Theta]", "y"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{ SubscriptBox["\[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[{"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[{"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[{"exp", ",", RowBox[{ RowBox[{"\[Delta]a", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]b", "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{"\[Delta]c", "[", RowBox[{"__", ",", "n"}], "]"}], " ", "|", RowBox[{ SubscriptBox["\[Delta]u", "X"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{ SubscriptBox["\[Delta]u", "Y"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{ SubscriptBox["\[Delta]u", "Z"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{ SubscriptBox["\[Delta]\[Theta]", "X"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{ SubscriptBox["\[Delta]\[Theta]", "Y"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{ SubscriptBox["\[Delta]\[Theta]", "Z"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{ SubscriptBox["\[Delta]u", "x"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{ SubscriptBox["\[Delta]u", "y"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{ SubscriptBox["\[Delta]u", "z"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{ SubscriptBox["\[Delta]\[Theta]", "x"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", " ", RowBox[{ SubscriptBox["\[Delta]\[Theta]", "y"], "[", RowBox[{"__", ",", "n"}], "]"}], "|", RowBox[{ SubscriptBox["\[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]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]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[{"{", RowBox[{ RowBox[{ RowBox[{"a", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"a", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"b", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"b", "[", RowBox[{"any", ",", "n"}], "]"}]}], ",", RowBox[{ RowBox[{"b", "[", "any__", "]"}], "\[Rule]", " ", RowBox[{"a", "[", 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[{"\[CurlyTheta]", "[", "any__", "]"}], "->", " ", RowBox[{"\[CurlyTheta]", "[", 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]", "\[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[{"{", "}"}]}], " ", ",", "u", ",", RowBox[{ RowBox[{"D", "[", RowBox[{"u", ",", RowBox[{"{", "dof", "}"}]}], "]"}], ".", RowBox[{"\[Delta]", "[", "dof", "]"}]}]}], "]"}]}]}], "]"}]}], ";"}], " "}], "\[IndentingNewLine]"}], "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}}, CellLabel->"In[1]:=",ExpressionUUID->"ed2ed2d9-b99d-448f-86da-4386184d8516"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.686831884411597*^9, 3.6868318902216053`*^9}},ExpressionUUID->"159472bf-417f-4070-aad8-\ 5406fd42698c"] }, Closed]], Cell[CellGroupData[{ Cell["SHAPE defs ", "Subsection",ExpressionUUID->"dbc33de8-90b2-471d-b3b5-959be2de0621"], 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->"b47a83a3-02c6-481a-b0dc-20c1e7dd8763"] }, Closed]], Cell[CellGroupData[{ Cell["QUAD defs ", "Subsection",ExpressionUUID->"8266d6dd-1c96-4d34-8a50-ec145ea0115d"], 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[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "1", "}"}]}], "}"}], "/", "2"}]}], ";", "\[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[{"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[{"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[{"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[{"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]"}]}]], "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}}, CellLabel->"In[37]:=",ExpressionUUID->"af4563ad-fa9d-4f51-a4b2-3a24f6978422"] }, Closed]], Cell[CellGroupData[{ Cell["INTEGRATE defs ", "Subsection",ExpressionUUID->"a127969d-25ad-4bec-83a1-b69315f3f613"], 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[51]:=",ExpressionUUID->"828a39db-754e-4b24-8574-97a4b4b24377"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["ELEMENT", "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}},ExpressionUUID->"5a669127-ee0a-4eb5-ae91-\ 329d0652de0d"], Cell[CellGroupData[{ Cell["FORCE ELEMENT defs ", "Subsection", CellChangeTimes->{{3.6926098999374723`*^9, 3.6926099165674953`*^9}},ExpressionUUID->"e7500266-a0d0-49fb-8baa-\ 660b6426cd64"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", " ", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"FX_", ",", "FY_", ",", "FZ_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "I1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "I1", "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ "FX_", ",", "FY_", ",", "FZ_", ",", "MX_", ",", "MY_", ",", "MZ_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "I1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ"}], "}"}], ".", RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "2"}], "]"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"{", RowBox[{"MX", ",", "MY", ",", "MZ"}], "}"}], ".", RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "3"}], "]"}], "]"}], "]"}]}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "prule_"}], "}"}], " ", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"FX_", ",", "FY_", ",", "FZ_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "I1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "prule"}], "}"}], " ", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "I1", "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "prule_"}], "}"}], ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ "FX_", ",", "FY_", ",", "FZ_", ",", "MX_", ",", "MY_", ",", "MZ_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "I1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ"}], "}"}], ".", RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "2"}], "]"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"{", RowBox[{"MX", ",", "MY", ",", "MZ"}], "}"}], ".", RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "3"}], "]"}], "]"}], "]"}]}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"FX_", ",", "FY_", ",", "FZ_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "I1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "I1", "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"NONL", ",", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ "FX_", ",", "FY_", ",", "FZ_", ",", "MX_", ",", "MY_", ",", "MZ_"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "I1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ"}], "}"}], ".", RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "2"}], "]"}], "]"}], "]"}]}], "+", RowBox[{ RowBox[{"{", RowBox[{"MX", ",", "MY", ",", "MZ"}], "}"}], ".", RowBox[{"\[Delta]", "[", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "3"}], "]"}], "]"}], "]"}]}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX1_", ",", "fX2_"}], "}"}], ",", RowBox[{"{", RowBox[{"fY1_", ",", "fY2_"}], "}"}], ",", RowBox[{"{", RowBox[{"fZ1_", ",", "fZ2_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"I1_", ",", "I2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", "\[IndentingNewLine]", 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[{"I1", ",", "I2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fX1_", ",", "fX2_"}], "}"}], ",", RowBox[{"{", RowBox[{"fY1_", ",", "fY2_"}], "}"}], ",", RowBox[{"{", RowBox[{"fZ1_", ",", "fZ2_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"I1_", ",", "I2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", "\[IndentingNewLine]", 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[{"I1", ",", "I2"}], "}"}], "]"}]}], "}"}], ",", "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[{"I1_", ",", "I2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"nl", ",", "r0", ",", "h0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"r0", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "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[{"I1", ",", "I2"}], "}"}], ",", "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[{"I1", ",", "I2"}], "}"}], ",", "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[{"I1", ",", "I2"}], "}"}], ",", "2", ",", "3"}], "]"}], "]"}], "]"}], ".", 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[{ RowBox[{"{", "m_", "}"}], ",", RowBox[{"{", RowBox[{"FX_", ",", "FY_", ",", "FZ_"}], "}"}]}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ"}], "}"}], "-", RowBox[{"m", " ", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}]}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}], ")"}], ".", " ", 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[{"{", RowBox[{"m_", ",", "J_"}], "}"}], ",", RowBox[{"{", RowBox[{ "FX_", ",", "FY_", ",", "FZ_", ",", "MX_", ",", "MY_", ",", "MZ_"}], "}"}]}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "n1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"FX", ",", "FY", ",", "FZ"}], "}"}], "-", 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[{ RowBox[{"{", RowBox[{"MX", ",", "MY", ",", "MZ"}], "}"}], "-", RowBox[{"J", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}]}], "/.", RowBox[{"DRULE", "[", "2", "]"}]}], ")"}], ".", RowBox[{"(", RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}], ")"}]}]}]}], ";"}]}]}]], "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}}, CellLabel->"In[57]:=",ExpressionUUID->"ec855259-b181-4621-bff6-5b06692ed070"] }, Closed]], Cell[CellGroupData[{ Cell["RIGID ELEMENT 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}},ExpressionUUID->"d7faebba-7395-4e68-ab54-\ f492589db395"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"(*", RowBox[{"force", " ", "2", " ", "to", " ", "be", " ", "1"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"RIGID", ",", "any_", ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], ")"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"FX", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"FY", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"FZ", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}]}], "}"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "2"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "2"}], "]"}], "]"}]}], ")"}], ".", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"FX", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"FY", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"FZ", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}]}], "}"}], "]"}]}], "+", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}], ")"}], "]"}], ".", 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[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}], ")"}], ".", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"MX", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"MY", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"MZ", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}]}], "}"}], "]"}]}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "force", " ", "2", " ", "to", " ", "be", " ", "1", " ", "modulo", " ", "rigid", " ", "body", " ", "motion"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "prule_"}], "}"}], ",", RowBox[{"{", RowBox[{"RIGID", ",", RowBox[{"{", "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"I1_", ",", "I2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"RIGID", ",", RowBox[{"{", "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"I1", ",", "I2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"RIGID", ",", RowBox[{"{", "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", 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[{ 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[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"FX", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"FY", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}], ",", RowBox[{"FZ", "[", RowBox[{"{", RowBox[{"n2", ",", "n1"}], "}"}], "]"}]}], "}"}], "]"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]", "[", 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]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}], ")"}], ".", RowBox[{"\[Delta]", "[", 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[{"VIBR", ",", RowBox[{"{", RowBox[{"RIGID", ",", RowBox[{"{", "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[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[{"DRULE", "[", "0", "]"}]}], "]"}], ".", RowBox[{"(", RowBox[{ 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[{ 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[{"DRULE", "[", "0", "]"}]}], ")"}], ".", RowBox[{"\[Delta]", "[", RowBox[{ 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[{ RowBox[{"\[Delta]", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], "]"}], ".", RowBox[{"(", RowBox[{ 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]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n2", ",", "3"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"n1", ",", "3"}], "]"}], "]"}]}], ")"}], "/.", RowBox[{"DRULE", "[", "0", "]"}]}], ")"}], ".", RowBox[{"\[Delta]", "[", RowBox[{ 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[{"DISP", ",", RowBox[{"{", RowBox[{"CONST", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"uX1_", ",", "uY1_", ",", "uZ1_"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Theta]X1_", ",", "\[Theta]Y1_", ",", "\[Theta]Z1_"}], "}"}]}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "I1_", "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "2"}], "]"}], "]"}], "-", RowBox[{"{", RowBox[{"uX1", ",", "uY1", ",", "uZ1"}], "}"}]}], ")"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"FX", "[", "I1", "]"}], ",", RowBox[{"FY", "[", "I1", "]"}], ",", RowBox[{"FZ", "[", "I1", "]"}]}], "}"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "2"}], "]"}], "]"}], "-", RowBox[{"{", RowBox[{"uX1", ",", "uY1", ",", "uZ1"}], "}"}]}], ")"}], ".", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"FX", "[", "I1", "]"}], ",", RowBox[{"FY", "[", "I1", "]"}], ",", RowBox[{"FZ", "[", "I1", "]"}]}], "}"}], "]"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "3"}], "]"}], "]"}], "-", RowBox[{"{", RowBox[{"\[Theta]X1", ",", "\[Theta]Y1", ",", "\[Theta]Z1"}], "}"}]}], ")"}], "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"MX", "[", "I1", "]"}], ",", RowBox[{"MY", "[", "I1", "]"}], ",", RowBox[{"MZ", "[", "I1", "]"}]}], "}"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "3"}], "]"}], "]"}], "-", RowBox[{"{", RowBox[{"\[Theta]X1", ",", "\[Theta]Y1", ",", "\[Theta]Z1"}], "}"}]}], ")"}], ".", RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{ RowBox[{"MX", "[", "I1", "]"}], ",", RowBox[{"MY", "[", "I1", "]"}], ",", RowBox[{"MZ", "[", "I1", "]"}]}], "}"}], "]"}]}]}]}], " ", ";"}], "\[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}}, CellLabel->"In[68]:=",ExpressionUUID->"c6d3c1cf-f70a-4ff4-a688-e8af531ec381"] }, Closed]], Cell[CellGroupData[{ Cell["BAR ELEMENT (static) defs ", "Subsection", InitializationCell->True, CellChangeTimes->{{3.753018875511382*^9, 3.7530188786265306`*^9}},ExpressionUUID->"b7e0fb49-27d0-4286-aad7-\ 5e4f444291fb"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", 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", "[", "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[{"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[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", "AA_", "}"}], ",", RowBox[{"{", "fx_", "}"}]}], "}"}], ",", 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[{"fx", " ", "/.", "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]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", "AA_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE", "}"}], ",", RowBox[{"{", RowBox[{"AA", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"fX", ",", "fY", ",", "fZ"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "iy0_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "r0", ",", "h0", ",", "ix0", ",", "iz0", ",", "ux", ",", "\[Delta]ux", ",", "uy", ",", "\[Delta]uy", ",", "uz", ",", "\[Delta]uz"}], "}"}], ",", "\[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]", 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[{"\[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]", "\[IndentingNewLine]", RowBox[{ FractionBox["1", RowBox[{"2", " ", "h0"}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "AA", " ", "EE", " ", RowBox[{"(", RowBox[{ RowBox[{"ux", "[", "1", "]"}], "-", RowBox[{"ux", "[", "2", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "-", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"fX", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"fY", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uy", "[", "1", "]"}], "+", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"fZ", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]uz", "[", "1", "]"}], "+", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", 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", 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}}, CellLabel->"In[73]:=",ExpressionUUID->"6c2cad90-e06d-4e59-8532-520f3d2b4ff1"] }, Closed]], Cell[CellGroupData[{ Cell["BAR ELEMENT (dynamic) defs ", "Subsection", InitializationCell->True, CellChangeTimes->{{3.7530188810407906`*^9, 3.753018884630788*^9}},ExpressionUUID->"f2915892-cf02-4b47-a282-\ bce92178c7c9"], Cell[BoxData[{ RowBox[{ 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"}], "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", 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", 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}, CellLabel->"In[78]:=",ExpressionUUID->"d6d4fa4d-302f-4234-b1e0-4992bce4f95c"] }, Closed]], Cell[CellGroupData[{ Cell["BAR ELEMENT (stability) defs ", "Subsection", InitializationCell->True, CellChangeTimes->{{3.753018875511382*^9, 3.7530188786265306`*^9}, { 3.756267607734783*^9, 3.756267609945469*^9}},ExpressionUUID->"dab2a20e-37b0-46fe-a9da-\ bb15afd82a63"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "rule_"}], "}"}], ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE_", "}"}], ",", RowBox[{"{", "AA_", "}"}], ",", RowBox[{"{", "fx_", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "EE", "}"}], ",", RowBox[{"{", "AA", "}"}], ",", RowBox[{"{", "fx", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "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}, { 3.7562676525896635`*^9, 3.756267707097726*^9}}, CellLabel->"In[80]:=",ExpressionUUID->"fc4bc255-0184-4db9-9632-2475e5a9fab7"] }, Closed]], Cell[CellGroupData[{ Cell["BAR ELEMENT (nonlinear) defs ", "Subsection", InitializationCell->True, CellChangeTimes->{{3.7530188810407906`*^9, 3.753018884630788*^9}, { 3.753019375620509*^9, 3.753019378557259*^9}},ExpressionUUID->"06e798ca-1dd4-40a4-a05a-\ ff4b895a2b95"], Cell[BoxData[ 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[{"I1_", ",", "I2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[CapitalDelta]h", ",", "h0", ",", "ix", ",", "iz", ",", "NN", ",", "x", ",", "uu", ",", "vv", ",", "ww", ",", "EE", ",", "\[Delta]EE", ",", "\[Delta]wint", ",", "\[Delta]wext"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[CapitalDelta]h", "=", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I2", ",", "1"}], "]"}], "]"}], "-", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "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[{"uu", "=", " ", RowBox[{"NN", ".", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "2"}], "]"}], "]"}], ".", "ix"}], ",", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I2", ",", "2"}], "]"}], "]"}], ".", "ix"}]}], "}"}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"vv", "=", " ", RowBox[{"NN", ".", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "2"}], "]"}], "]"}], ".", "iy"}], ",", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I2", ",", "2"}], "]"}], "]"}], ".", "iy"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"ww", "=", " ", RowBox[{"NN", ".", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I1", ",", "2"}], "]"}], "]"}], ".", "iz"}], ",", RowBox[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{"I2", ",", "2"}], "]"}], "]"}], ".", "iz"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"EE", "=", " ", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "uu"}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "uu"}], ")"}], "^", "2"}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "vv"}], ")"}], "^", "2"}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "x"], "ww"}], ")"}], "^", "2"}]}], ")"}], "/", "2"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]EE", "=", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], "uu"}], "]"}], "+", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "uu"}], " ", RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], "uu"}], "]"}]}], "+", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "vv"}], " ", RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], "vv"}], "]"}]}], "+", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "ww"}], " ", RowBox[{"\[Delta]", "[", RowBox[{ SubscriptBox["\[PartialD]", "x"], "ww"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", "\[Delta]EE"}], " ", "CC", " ", "AA", " ", "EE"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{ RowBox[{"\[Delta]", "[", "uu", "]"}], " ", "fx"}], "+", RowBox[{ RowBox[{"\[Delta]", "[", "vv", "]"}], " ", "fy"}], "+", RowBox[{ RowBox[{"\[Delta]", "[", "ww", "]"}], " ", "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}}, CellLabel->"In[81]:=",ExpressionUUID->"71233d3c-e96a-40ba-8291-d489cc54cc36"] }, Closed]], Cell[CellGroupData[{ Cell["BAR ELEMENT (thermomechanic) defs ", "Subsection", InitializationCell->True, CellChangeTimes->{{3.7530188810407906`*^9, 3.753018884630788*^9}, { 3.753019375620509*^9, 3.753019378557259*^9}, {3.7530200248509674`*^9, 3.7530200339415607`*^9}},ExpressionUUID->"189929f0-3d23-4124-9e22-\ 07173e3f9540"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Alpha]\[Alpha]_", ",", "kk_"}], "}"}], ",", RowBox[{"{", "AA_", "}"}], ",", RowBox[{"{", RowBox[{"ff_", ",", "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", ",", "fff", ",", "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[{"fff", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "ff", "]"}], "===", "Function"}], ",", RowBox[{"ff", "[", "x", "]"}], ",", "ff"}], "]"}]}], ";", "\[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", "]"}], " ", "fff"}]}]}], ";", "\[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}, CellLabel->"In[82]:=",ExpressionUUID->"1315eef7-3f98-48f3-a5f1-93f83f9a04ff"] }, Closed]], Cell[CellGroupData[{ Cell["BEAM ELEMENT (static) defs ", "Subsection", CellChangeTimes->{{3.7530187996679964`*^9, 3.753018803413909*^9}},ExpressionUUID->"0b4ce7e2-c37d-4aa4-be76-\ 85624d17acf7"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "II_"}], "}"}], ",", 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", ",", "II", ",", "II", ",", 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_", ",", "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_"}], "]"}], ":=", 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]", RowBox[{ RowBox[{"{", RowBox[{"fx1", ",", "fx2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fx"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"fy1", ",", "fy2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fy"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"fz1", ",", "fz2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fz"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"mx1", ",", "mx2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "mx"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"my1", ",", "my2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "my"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"mz1", ",", "mz2"}], "}"}], "=", 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", "]"}]}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[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_"}], "}"}]}], "}"}], ",", 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_"}], "}"}], ",", 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[{ "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"}], "}"}], ",", "\[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]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_", ",", "Ip_"}], "}"}], ",", 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"}], "}"}], ",", "Ip"}], "}"}], ",", RowBox[{"{", RowBox[{ "fx", ",", "fy", ",", "fz", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{ "AA_", ",", "Iyy_", ",", "Izz_", ",", "iy0_", ",", "Ip_"}], "}"}], ",", 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", ",", "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[{"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", "[", "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]", RowBox[{ RowBox[{"{", RowBox[{"fx1", ",", "fx2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fx"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"fy1", ",", "fy2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fy"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"fz1", ",", "fz2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fz"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"mx1", ",", "mx2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "mx"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"my1", ",", "my2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "my"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"mz1", ",", "mz2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "mz"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"GGm", "=", RowBox[{"GGm", "*", RowBox[{"Ip", "/", RowBox[{"(", RowBox[{"Iyym", "+", "Izzm"}], ")"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ FractionBox["1", RowBox[{"60", " ", SuperscriptBox["h", "3"]}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "60"}], " ", "AAm", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"60", " ", "AAm", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"60", " ", "AAm", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "-", RowBox[{"60", " ", "AAm", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"10", " ", "fx1", " ", SuperscriptBox["h", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"10", " ", "fx2", " ", SuperscriptBox["h", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}]}], ")"}]}], "+", RowBox[{"21", " ", "fy1", " ", SuperscriptBox["h", "4"], " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "+", RowBox[{"9", " ", "fy2", " ", SuperscriptBox["h", "4"], " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "-", RowBox[{"30", " ", SuperscriptBox["h", "3"], " ", "mz1", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "-", RowBox[{"30", " ", SuperscriptBox["h", "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["h", "4"], " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"21", " ", "fy2", " ", SuperscriptBox["h", "4"], " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"30", " ", SuperscriptBox["h", "3"], " ", "mz1", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"30", " ", SuperscriptBox["h", "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["h", "4"], " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"9", " ", "fz2", " ", SuperscriptBox["h", "4"], " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"30", " ", SuperscriptBox["h", "3"], " ", "my1", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"30", " ", SuperscriptBox["h", "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["h", "4"], " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "+", RowBox[{"21", " ", "fz2", " ", SuperscriptBox["h", "4"], " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "-", RowBox[{"30", " ", SuperscriptBox["h", "3"], " ", "my1", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "-", RowBox[{"30", " ", SuperscriptBox["h", "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["h", "4"], " ", "mx1", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"10", " ", SuperscriptBox["h", "4"], " ", "mx2", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"10", " ", SuperscriptBox["h", "4"], " ", "mx1", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}]}], "+", RowBox[{"20", " ", SuperscriptBox["h", "4"], " ", "mx2", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}]}], "-", RowBox[{"3", " ", "fz1", " ", SuperscriptBox["h", "5"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"2", " ", "fz2", " ", SuperscriptBox["h", "5"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"5", " ", SuperscriptBox["h", "4"], " ", "my1", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"5", " ", SuperscriptBox["h", "4"], " ", "my2", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h", " ", "Iyym", " ", RowBox[{"uz", "[", "1", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h", " ", "Iyym", " ", RowBox[{"uz", "[", "2", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"2", " ", "fz1", " ", SuperscriptBox["h", "5"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"3", " ", "fz2", " ", SuperscriptBox["h", "5"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "-", RowBox[{"5", " ", SuperscriptBox["h", "4"], " ", "my1", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"5", " ", SuperscriptBox["h", "4"], " ", "my2", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h", " ", "Iyym", " ", RowBox[{"uz", "[", "1", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h", " ", "Iyym", " ", RowBox[{"uz", "[", "2", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"3", " ", "fy1", " ", SuperscriptBox["h", "5"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"2", " ", "fy2", " ", SuperscriptBox["h", "5"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"5", " ", SuperscriptBox["h", "4"], " ", "mz1", " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"5", " ", SuperscriptBox["h", "4"], " ", "mz2", " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h", " ", "Izzm", " ", RowBox[{"uy", "[", "1", "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h", " ", "Izzm", " ", RowBox[{"uy", "[", "2", "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"2", " ", "fy1", " ", SuperscriptBox["h", "5"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"3", " ", "fy2", " ", SuperscriptBox["h", "5"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"5", " ", SuperscriptBox["h", "4"], " ", "mz1", " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "+", RowBox[{"5", " ", SuperscriptBox["h", "4"], " ", "mz2", " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h", " ", "Izzm", " ", RowBox[{"uy", "[", "1", "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h", " ", "Izzm", " ", RowBox[{"uy", "[", "2", "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], " ", RowBox[{"\[Theta]x", "[", "1", "]"}]}], "-", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], " ", RowBox[{"\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], " ", RowBox[{"\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], " ", RowBox[{"\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], " ", RowBox[{"\[Theta]x", "[", "2", "]"}]}], "+", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], " ", RowBox[{"\[Theta]x", "[", "2", "]"}]}], "-", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], " ", RowBox[{"\[Theta]x", "[", "2", "]"}]}], "-", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], " ", RowBox[{"\[Theta]x", "[", "2", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h", " ", "Iyym", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h", " ", "Iyym", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"240", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"120", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h", " ", "Iyym", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h", " ", "Iyym", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "-", RowBox[{"120", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "-", RowBox[{"240", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h", " ", "Izzm", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h", " ", "Izzm", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"240", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"120", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h", " ", "Izzm", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h", " ", "Izzm", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"120", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"240", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "*)"}], "\[IndentingNewLine]", "\[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_"}], "}"}], ",", 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[{"AA", ",", "Iyy", ",", "Izz", ",", 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]\[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\[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]", 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["h0", "4"], " ", SuperscriptBox["\[Kappa]\[Kappa]", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "fx", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"6", " ", "fz", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"6", " ", "fz", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "-", RowBox[{"fz", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"fz", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"fy", " ", SuperscriptBox["h0", "2"], " ", 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[{"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["h0", "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["h0", "2"], " ", "Iyy", " ", "Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"Iyy", " ", "Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"fz", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"6", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "-", RowBox[{"h0", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"h0", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}]}], ")"}]}], "+", RowBox[{"fy", " ", SuperscriptBox["h0", "2"], " ", 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[{"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["h0", "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["h0", "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", " ", "h0", " ", RowBox[{"uz", "[", "1", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"3", " ", "h0", " ", RowBox[{"uz", "[", "2", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"3", " ", "h0", " ", RowBox[{"uz", "[", "1", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"3", " ", "h0", " ", 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[{"h0", " ", 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[{"h0", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"3", " ", "h0", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"3", " ", "h0", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{ SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"3", " ", "h0", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"3", " ", "h0", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{ SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"3", " ", "h0", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"3", " ", "h0", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{ SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"3", " ", "h0", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"3", " ", "h0", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "+", RowBox[{ SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"12", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "\[Kappa]\[Kappa]", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["AA", "2"], " ", "GG", " ", SuperscriptBox["h0", "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["h0", "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["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"6", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "-", RowBox[{"h0", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"h0", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}]}], ")"}]}], "+", RowBox[{"fy", " ", SuperscriptBox["h0", "2"], " ", 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[{"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[{"h0", " ", 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[{"h0", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"h0", " ", 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[{"h0", " ", 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[{"h0", " ", 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[{"h0", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"h0", " ", 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[{"h0", " ", 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", " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", "Iyy"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "\[Kappa]\[Kappa]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", "Izz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "\[Kappa]\[Kappa]"}]}], ")"}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"GENERICBEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[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[{ "\[Alpha]", ",", "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]", ",", "AE", ",", "CE", ",", "BE", ",", "\[Epsilon]", ",", "\[Kappa]", ",", "Irr", ",", "F", ",", "M", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]WW", ",", "equ", ",", "sol", ",", "bl", ",", "EEE", ",", "GGG", ",", "\[Kappa]\[Kappa]\[Kappa]", ",", "AAA", ",", "SSz", ",", "SSy", ",", "IIyy", ",", "IIzz", ",", "IIyz", ",", "ffx", ",", "ffy", ",", "ffz", ",", "mmx", ",", "mmy", ",", "mmz"}], "}"}], ",", "\[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]", RowBox[{"PP", "=", RowBox[{"LeviCivitaTensor", "[", "3", "]"}]}], ";", "\[IndentingNewLine]", "\[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[{"\[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", "[", "Izz", "]"}], "===", "Function"}], ",", RowBox[{"Izz", "[", "x", "]"}], ",", "Izz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIzz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Iyy", "]"}], "===", "Function"}], ",", RowBox[{"Iyy", "[", "x", "]"}], ",", "Iyy"}], "]"}]}], ";", "\[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[{"AE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EEE", " ", "AAA"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Kappa]\[Kappa]\[Kappa]", " ", "GGG", " ", "AAA"}], ",", "0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"\[Kappa]\[Kappa]\[Kappa]", " ", "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", " ", RowBox[{"(", RowBox[{"IIyy", "+", "IIzz"}], ")"}]}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"EEE", " ", "IIyy"}], ",", RowBox[{ RowBox[{"-", "EEE"}], " ", "IIyz"}]}], "}"}], ",", "\[IndentingNewLine]", 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]", "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"LINE7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[Alpha]", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "1", "}"}]}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"\[Delta]WW", "=", RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "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]", RowBox[{"\[Delta]WW", " ", "/.", "sol"}]}]}], "\[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}}, CellLabel->"In[83]:=",ExpressionUUID->"62be5c9d-13e2-4eb6-bfe3-f354e8ffe2e2"] }, Closed]], Cell[CellGroupData[{ Cell["BEAM ELEMENT (dynamic) defs ", "Subsection", CellChangeTimes->{{3.7530187996679964`*^9, 3.753018818586525*^9}},ExpressionUUID->"7b50e1e5-43b3-48dd-ab3c-\ 7f7fab53534c"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "II_"}], "}"}], ",", 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", ",", "II", ",", "II", ",", 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_", ",", "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_"}], "]"}], ":=", 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]", RowBox[{ RowBox[{"{", RowBox[{"fx1", ",", "fx2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fx"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"fy1", ",", "fy2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fy"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"fz1", ",", "fz2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fz"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"mx1", ",", "mx2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "mx"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"my1", ",", "my2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "my"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"mz1", ",", "mz2"}], "}"}], "=", 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", "]"}]}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[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_"}], "}"}]}], "}"}], ",", 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_"}], "}"}], ",", 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[{ "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"}], "}"}], ",", "\[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]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{"AA_", ",", "Iyy_", ",", "Izz_", ",", "Ip_"}], "}"}], ",", 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"}], "}"}], ",", "Ip"}], "}"}], ",", RowBox[{"{", RowBox[{ "fx", ",", "fy", ",", "fz", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_"}], "}"}], ",", RowBox[{"{", RowBox[{ "AA_", ",", "Iyy_", ",", "Izz_", ",", "iy0_", ",", "Ip_"}], "}"}], ",", 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", ",", "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[{"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", "[", "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]", RowBox[{ RowBox[{"{", RowBox[{"fx1", ",", "fx2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fx"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"fy1", ",", "fy2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fy"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"fz1", ",", "fz2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "fz"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"mx1", ",", "mx2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "mx"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"my1", ",", "my2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "my"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"mz1", ",", "mz2"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "*", "mz"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"GGm", "=", RowBox[{"GGm", "*", RowBox[{"Ip", "/", RowBox[{"(", RowBox[{"Iyym", "+", "Izzm"}], ")"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ FractionBox["1", RowBox[{"60", " ", SuperscriptBox["h", "3"]}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "60"}], " ", "AAm", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"60", " ", "AAm", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"60", " ", "AAm", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", RowBox[{"ux", "[", "1", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "-", RowBox[{"60", " ", "AAm", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", RowBox[{"ux", "[", "2", "]"}], " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], "+", RowBox[{"10", " ", "fx1", " ", SuperscriptBox["h", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"\[Delta]ux", "[", "1", "]"}]}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"10", " ", "fx2", " ", SuperscriptBox["h", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "+", RowBox[{"2", " ", RowBox[{"\[Delta]ux", "[", "2", "]"}]}]}], ")"}]}], "+", RowBox[{"21", " ", "fy1", " ", SuperscriptBox["h", "4"], " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "+", RowBox[{"9", " ", "fy2", " ", SuperscriptBox["h", "4"], " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "-", RowBox[{"30", " ", SuperscriptBox["h", "3"], " ", "mz1", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}]}], "-", RowBox[{"30", " ", SuperscriptBox["h", "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["h", "4"], " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"21", " ", "fy2", " ", SuperscriptBox["h", "4"], " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"30", " ", SuperscriptBox["h", "3"], " ", "mz1", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}]}], "+", RowBox[{"30", " ", SuperscriptBox["h", "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["h", "4"], " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"9", " ", "fz2", " ", SuperscriptBox["h", "4"], " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"30", " ", SuperscriptBox["h", "3"], " ", "my1", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"30", " ", SuperscriptBox["h", "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["h", "4"], " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "+", RowBox[{"21", " ", "fz2", " ", SuperscriptBox["h", "4"], " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "-", RowBox[{"30", " ", SuperscriptBox["h", "3"], " ", "my1", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "-", RowBox[{"30", " ", SuperscriptBox["h", "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["h", "4"], " ", "mx1", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"10", " ", SuperscriptBox["h", "4"], " ", "mx2", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"10", " ", SuperscriptBox["h", "4"], " ", "mx1", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}]}], "+", RowBox[{"20", " ", SuperscriptBox["h", "4"], " ", "mx2", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}]}], "-", RowBox[{"3", " ", "fz1", " ", SuperscriptBox["h", "5"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"2", " ", "fz2", " ", SuperscriptBox["h", "5"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"5", " ", SuperscriptBox["h", "4"], " ", "my1", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"5", " ", SuperscriptBox["h", "4"], " ", "my2", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h", " ", "Iyym", " ", RowBox[{"uz", "[", "1", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h", " ", "Iyym", " ", RowBox[{"uz", "[", "2", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"2", " ", "fz1", " ", SuperscriptBox["h", "5"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"3", " ", "fz2", " ", SuperscriptBox["h", "5"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "-", RowBox[{"5", " ", SuperscriptBox["h", "4"], " ", "my1", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"5", " ", SuperscriptBox["h", "4"], " ", "my2", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h", " ", "Iyym", " ", RowBox[{"uz", "[", "1", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h", " ", "Iyym", " ", RowBox[{"uz", "[", "2", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"3", " ", "fy1", " ", SuperscriptBox["h", "5"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"2", " ", "fy2", " ", SuperscriptBox["h", "5"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"5", " ", SuperscriptBox["h", "4"], " ", "mz1", " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"5", " ", SuperscriptBox["h", "4"], " ", "mz2", " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h", " ", "Izzm", " ", RowBox[{"uy", "[", "1", "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h", " ", "Izzm", " ", RowBox[{"uy", "[", "2", "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"2", " ", "fy1", " ", SuperscriptBox["h", "5"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"3", " ", "fy2", " ", SuperscriptBox["h", "5"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"5", " ", SuperscriptBox["h", "4"], " ", "mz1", " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "+", RowBox[{"5", " ", SuperscriptBox["h", "4"], " ", "mz2", " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h", " ", "Izzm", " ", RowBox[{"uy", "[", "1", "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h", " ", "Izzm", " ", RowBox[{"uy", "[", "2", "]"}], " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], " ", RowBox[{"\[Theta]x", "[", "1", "]"}]}], "-", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], " ", RowBox[{"\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], " ", RowBox[{"\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], " ", RowBox[{"\[Theta]x", "[", "1", "]"}]}], "+", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], " ", RowBox[{"\[Theta]x", "[", "2", "]"}]}], "+", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]x", "[", "1", "]"}], " ", RowBox[{"\[Theta]x", "[", "2", "]"}]}], "-", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], " ", RowBox[{"\[Theta]x", "[", "2", "]"}]}], "-", RowBox[{"60", " ", "GGm", " ", SuperscriptBox["h", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]x", "[", "2", "]"}], " ", RowBox[{"\[Theta]x", "[", "2", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h", " ", "Iyym", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h", " ", "Iyym", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"240", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"120", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h", " ", "Iyym", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h", " ", "Iyym", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "-", RowBox[{"120", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "-", RowBox[{"240", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", "Iyym", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h", " ", "Izzm", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h", " ", "Izzm", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"240", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"120", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"360", " ", "EEm", " ", "h", " ", "Izzm", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "+", RowBox[{"360", " ", "EEm", " ", "h", " ", "Izzm", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"120", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"240", " ", "EEm", " ", SuperscriptBox["h", "2"], " ", "Izzm", " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "*)"}], "\[IndentingNewLine]", "\[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_"}], "}"}], ",", 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[{"AA", ",", "Iyy", ",", "Izz", ",", 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]\[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\[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]", 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["h0", "4"], " ", SuperscriptBox["\[Kappa]\[Kappa]", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", "fx", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"6", " ", "fz", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"6", " ", "fz", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "-", RowBox[{"fz", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"fz", " ", SuperscriptBox["h0", "3"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"fy", " ", SuperscriptBox["h0", "2"], " ", 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[{"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["h0", "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["h0", "2"], " ", "Iyy", " ", "Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]ux", "[", "1", "]"}], "+", RowBox[{"\[Delta]ux", "[", "2", "]"}]}], ")"}]}], "+", RowBox[{"Iyy", " ", "Izz", " ", RowBox[{"(", RowBox[{ RowBox[{"fz", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"6", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "-", RowBox[{"h0", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"h0", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}]}], ")"}]}], "+", RowBox[{"fy", " ", SuperscriptBox["h0", "2"], " ", 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[{"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["h0", "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["h0", "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", " ", "h0", " ", RowBox[{"uz", "[", "1", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"3", " ", "h0", " ", RowBox[{"uz", "[", "2", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"3", " ", "h0", " ", RowBox[{"uz", "[", "1", "]"}], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"3", " ", "h0", " ", 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[{"h0", " ", 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[{"h0", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"3", " ", "h0", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"3", " ", "h0", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{ SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "1", "]"}]}], "-", RowBox[{"3", " ", "h0", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"3", " ", "h0", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{ SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}], " ", RowBox[{"\[Theta]y", "[", "2", "]"}]}], "+", RowBox[{"3", " ", "h0", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "-", RowBox[{"3", " ", "h0", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{ SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "1", "]"}]}], "+", RowBox[{"3", " ", "h0", " ", RowBox[{"\[Delta]uy", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "-", RowBox[{"3", " ", "h0", " ", RowBox[{"\[Delta]uy", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "+", RowBox[{ SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["h0", "2"], " ", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}], " ", RowBox[{"\[Theta]z", "[", "2", "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"12", " ", "AA", " ", "EE", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "\[Kappa]\[Kappa]", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["AA", "2"], " ", "GG", " ", SuperscriptBox["h0", "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["h0", "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["h0", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", RowBox[{"\[Delta]uz", "[", "1", "]"}]}], "+", RowBox[{"6", " ", RowBox[{"\[Delta]uz", "[", "2", "]"}]}], "-", RowBox[{"h0", " ", RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}]}], "+", RowBox[{"h0", " ", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}]}], ")"}]}], "+", RowBox[{"fy", " ", SuperscriptBox["h0", "2"], " ", 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[{"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[{"h0", " ", 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[{"h0", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]y", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]y", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"h0", " ", 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[{"h0", " ", 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[{"h0", " ", 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[{"h0", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Delta]\[Theta]z", "[", "1", "]"}], "+", RowBox[{"\[Delta]\[Theta]z", "[", "2", "]"}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"h0", " ", 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[{"h0", " ", 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", " ", "h0", " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", "Iyy"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "\[Kappa]\[Kappa]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"12", " ", "EE", " ", "Izz"}], "+", RowBox[{"AA", " ", "GG", " ", SuperscriptBox["h0", "2"], " ", "\[Kappa]\[Kappa]"}]}], ")"}]}], ")"}]}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"GENERICBEAM", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[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_"}], "]"}], ":=", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Alpha]", ",", "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]", ",", "AE", ",", "CE", ",", "BE", ",", "\[Epsilon]", ",", "\[Kappa]", ",", "Irr", ",", "F", ",", "M", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]WW", ",", "equ", ",", "sol", ",", "bl", ",", "EEE", ",", "GGG", ",", "\[Kappa]\[Kappa]\[Kappa]", ",", "AAA", ",", "SSz", ",", "SSy", ",", "IIyy", ",", "IIzz", ",", "IIyz", ",", "ffx", ",", "ffy", ",", "ffz", ",", "mmx", ",", "mmy", ",", "mmz"}], "}"}], ",", "\[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]", RowBox[{"PP", "=", RowBox[{"LeviCivitaTensor", "[", "3", "]"}]}], ";", "\[IndentingNewLine]", "\[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[{"\[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", "[", "Izz", "]"}], "===", "Function"}], ",", RowBox[{"Izz", "[", "x", "]"}], ",", "Izz"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"IIzz", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Head", "[", "Iyy", "]"}], "===", "Function"}], ",", RowBox[{"Iyy", "[", "x", "]"}], ",", "Iyy"}], "]"}]}], ";", "\[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[{"AE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EEE", " ", "AAA"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"\[Kappa]\[Kappa]\[Kappa]", " ", "GGG", " ", "AAA"}], ",", "0"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"\[Kappa]\[Kappa]\[Kappa]", " ", "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", " ", RowBox[{"(", RowBox[{"IIyy", "+", "IIzz"}], ")"}]}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"EEE", " ", "IIyy"}], ",", RowBox[{ RowBox[{"-", "EEE"}], " ", "IIyz"}]}], "}"}], ",", "\[IndentingNewLine]", 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]", "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"LINE7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[Alpha]", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "1", "}"}]}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"\[Delta]WW", "=", RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "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]", RowBox[{"\[Delta]WW", " ", "/.", "sol"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[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", "[", "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]", "\[IndentingNewLine]", 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]", "\[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_", ",", "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[{"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[{"\[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]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"BEAMB", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{ "AA_", ",", "Irr_", ",", "Iyy_", ",", "Izz_", ",", "iy_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"I1_", ",", "I2_"}], "}"}], "]"}]}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "domx", ",", "NL", ",", "NC", ",", "uu", ",", "uup", ",", "\[Delta]uu", ",", "vv", ",", "\[Delta]vv", ",", "ww", ",", "\[Delta]ww", ",", "\[Phi]\[Phi]", ",", "\[Delta]\[Phi]\[Phi]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wsta"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"rule", " ", "=", RowBox[{"RULE", "[", RowBox[{ RowBox[{"{", "iy", "}"}], ",", RowBox[{"{", RowBox[{"I1", ",", "I2"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"hx", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"x", "[", "2", "]"}], "-", RowBox[{"x", "[", "1", "]"}]}], ")"}], " ", "/.", " ", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "hx", "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[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[{"uu", "=", RowBox[{ RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", "1", "]"}], ",", RowBox[{"ux", "[", "2", "]"}]}], "}"}]}], "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]uu", "=", RowBox[{"uu", "/.", RowBox[{"{", " ", RowBox[{ RowBox[{"a", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]a", "[", "any", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"uup", " ", "=", RowBox[{"(", RowBox[{"uu", " ", "/.", " ", "PRULE"}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"vv", "=", RowBox[{ RowBox[{"NC", ".", RowBox[{"{", RowBox[{ RowBox[{"uy", "[", "1", "]"}], ",", RowBox[{"\[CapitalTheta]z", "[", "1", "]"}], ",", RowBox[{"uy", "[", "2", "]"}], ",", RowBox[{"\[CapitalTheta]z", "[", "2", "]"}]}], "}"}]}], "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]vv", "=", RowBox[{"vv", "/.", RowBox[{"{", " ", RowBox[{ RowBox[{"a", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]a", "[", "any", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"ww", "=", RowBox[{ RowBox[{"NC", ".", RowBox[{"{", RowBox[{ RowBox[{"uz", "[", "1", "]"}], ",", RowBox[{"-", RowBox[{"\[CapitalTheta]y", "[", "1", "]"}]}], ",", RowBox[{"uz", "[", "2", "]"}], ",", RowBox[{"-", RowBox[{"\[CapitalTheta]y", "[", "2", "]"}]}]}], "}"}]}], "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]ww", "=", RowBox[{"ww", "/.", RowBox[{"{", " ", RowBox[{ RowBox[{"a", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]a", "[", "any", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]\[Phi]", "=", RowBox[{ RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"\[CapitalTheta]x", "[", "1", "]"}], ",", RowBox[{"\[CapitalTheta]x", "[", "2", "]"}]}], "}"}]}], "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]\[Phi]\[Phi]", "=", RowBox[{"\[Phi]\[Phi]", "/.", RowBox[{"{", " ", RowBox[{ RowBox[{"a", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]a", "[", "any", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Delta]uu"}], "*", "AA", "*", "EE", "*", RowBox[{ SubscriptBox["\[PartialD]", "x"], "uu"}]}], "+", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Delta]vv"}]}], "*", "Iyy", "*", "EE", "*", RowBox[{ SubscriptBox["\[PartialD]", "x"], RowBox[{ SubscriptBox["\[PartialD]", "x"], "vv"}]}]}], "+", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Delta]ww"}]}], "*", "Izz", "*", "EE", "*", RowBox[{ SubscriptBox["\[PartialD]", "x"], RowBox[{ SubscriptBox["\[PartialD]", "x"], "ww"}]}]}], "+", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Delta]\[Phi]\[Phi]"}], "*", "Irr", "*", "GG", "*", RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Phi]\[Phi]"}]}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]uu", "*", "fx"}], "+", RowBox[{"\[Delta]vv", "*", "fy"}], "+", RowBox[{"\[Delta]ww", "*", "fz"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wsta", "=", RowBox[{ RowBox[{"-", "AA"}], "*", "EE", "*", RowBox[{ SubscriptBox["\[PartialD]", "x"], "uup"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Delta]vv"}], "*", RowBox[{ SubscriptBox["\[PartialD]", "x"], "vv"}]}], "+", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Delta]ww"}], "*", RowBox[{ SubscriptBox["\[PartialD]", "x"], "ww"}]}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"QUAD", "[", RowBox[{"LINEEXACT", ",", RowBox[{"\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wsta"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "x", "}"}], ",", "\[CapitalOmega]"}], "}"}]}], "]"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "prule_"}], "}"}], ",", 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_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "prule"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAMB", ",", 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", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "prule_"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAMB", ",", 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_"}], "]"}], ":=", 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", ",", "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[{"sape", " ", "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]", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", "1", "]"}], ",", RowBox[{"ux", "[", "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[{"CE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"EE", " ", "Sy"}], ",", RowBox[{ RowBox[{"-", "EE"}], " ", "Sz"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "GG"}], " ", "Sy"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"GG", " ", "Sz"}], ",", "0", ",", "0"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"BE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"GG", " ", "Iyy"}], "+", RowBox[{"GG", " ", "Izz"}]}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"EE", " ", "Iyy"}], ",", RowBox[{ RowBox[{"-", "EE"}], " ", "Iyz"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"-", "EE"}], " ", "Iyz"}], ",", 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[{ "axial", " ", "displacement", " ", "of", " ", "linear", " ", "analysis"}], "*)"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{"first", " ", "step", " ", "up"}], " ", "=", " ", "0"}], "*)"}], "\[IndentingNewLine]", RowBox[{"up", " ", "=", RowBox[{"u", "/.", "prule"}]}], ";", "\[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[{"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]", "]"}]}], ";"}], "\[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}}, CellLabel->"In[95]:=",ExpressionUUID->"e31fa415-db4b-408c-bea5-a9ffaf7481fc"] }, Closed]], Cell[CellGroupData[{ Cell["BEAM ELEMENT (stability) defs ", "Subsection", CellChangeTimes->{{3.7530187996679964`*^9, 3.753018818586525*^9}, { 3.7562662293745375`*^9, 3.7562662313353577`*^9}},ExpressionUUID->"3c1cc687-9e5c-4f89-bb45-\ 0c546743d3b9"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STAB", ",", RowBox[{"{", RowBox[{"BEAMB", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "GG_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", RowBox[{ "AA_", ",", "Irr_", ",", "Iyy_", ",", "Izz_", ",", "iy_"}], "}"}], ",", RowBox[{"{", RowBox[{"fx_", ",", "fy_", ",", "fz_"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"I1_", ",", "I2_"}], "}"}], "]"}]}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "domx", ",", "NL", ",", "NC", ",", "uu", ",", "uup", ",", "\[Delta]uu", ",", "vv", ",", "\[Delta]vv", ",", "ww", ",", "\[Delta]ww", ",", "\[Phi]\[Phi]", ",", "\[Delta]\[Phi]\[Phi]", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wsta"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"rule", " ", "=", RowBox[{"RULE", "[", RowBox[{ RowBox[{"{", "iy", "}"}], ",", RowBox[{"{", RowBox[{"I1", ",", "I2"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"hx", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"x", "[", "2", "]"}], "-", RowBox[{"x", "[", "1", "]"}]}], ")"}], " ", "/.", " ", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalOmega]", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "hx", "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[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[{"uu", "=", RowBox[{ RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", "1", "]"}], ",", RowBox[{"ux", "[", "2", "]"}]}], "}"}]}], "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]uu", "=", RowBox[{"uu", "/.", RowBox[{"{", " ", RowBox[{ RowBox[{"a", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]a", "[", "any", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"uup", " ", "=", RowBox[{"(", RowBox[{"uu", " ", "/.", " ", "PRULE"}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"vv", "=", RowBox[{ RowBox[{"NC", ".", RowBox[{"{", RowBox[{ RowBox[{"uy", "[", "1", "]"}], ",", RowBox[{"\[CapitalTheta]z", "[", "1", "]"}], ",", RowBox[{"uy", "[", "2", "]"}], ",", RowBox[{"\[CapitalTheta]z", "[", "2", "]"}]}], "}"}]}], "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]vv", "=", RowBox[{"vv", "/.", RowBox[{"{", " ", RowBox[{ RowBox[{"a", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]a", "[", "any", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"ww", "=", RowBox[{ RowBox[{"NC", ".", RowBox[{"{", RowBox[{ RowBox[{"uz", "[", "1", "]"}], ",", RowBox[{"-", RowBox[{"\[CapitalTheta]y", "[", "1", "]"}]}], ",", RowBox[{"uz", "[", "2", "]"}], ",", RowBox[{"-", RowBox[{"\[CapitalTheta]y", "[", "2", "]"}]}]}], "}"}]}], "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]ww", "=", RowBox[{"ww", "/.", RowBox[{"{", " ", RowBox[{ RowBox[{"a", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]a", "[", "any", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]\[Phi]", "=", RowBox[{ RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"\[CapitalTheta]x", "[", "1", "]"}], ",", RowBox[{"\[CapitalTheta]x", "[", "2", "]"}]}], "}"}]}], "/.", "rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]\[Phi]\[Phi]", "=", RowBox[{"\[Phi]\[Phi]", "/.", RowBox[{"{", " ", RowBox[{ RowBox[{"a", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]a", "[", "any", "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Delta]uu"}], "*", "AA", "*", "EE", "*", RowBox[{ SubscriptBox["\[PartialD]", "x"], "uu"}]}], "+", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Delta]vv"}]}], "*", "Iyy", "*", "EE", "*", RowBox[{ SubscriptBox["\[PartialD]", "x"], RowBox[{ SubscriptBox["\[PartialD]", "x"], "vv"}]}]}], "+", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Delta]ww"}]}], "*", "Izz", "*", "EE", "*", RowBox[{ SubscriptBox["\[PartialD]", "x"], RowBox[{ SubscriptBox["\[PartialD]", "x"], "ww"}]}]}], "+", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Delta]\[Phi]\[Phi]"}], "*", "Irr", "*", "GG", "*", RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Phi]\[Phi]"}]}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]uu", "*", "fx"}], "+", RowBox[{"\[Delta]vv", "*", "fy"}], "+", RowBox[{"\[Delta]ww", "*", "fz"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wsta", "=", RowBox[{ RowBox[{"-", "AA"}], "*", "EE", "*", RowBox[{ SubscriptBox["\[PartialD]", "x"], "uup"}], "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Delta]vv"}], "*", RowBox[{ SubscriptBox["\[PartialD]", "x"], "vv"}]}], "+", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "x"], "\[Delta]ww"}], "*", RowBox[{ SubscriptBox["\[PartialD]", "x"], "ww"}]}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"QUAD", "[", RowBox[{"LINEEXACT", ",", RowBox[{"\[Delta]wint", "+", "\[Delta]wext", "+", "\[Delta]wsta"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "x", "}"}], ",", "\[CapitalOmega]"}], "}"}]}], "]"}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "prule_"}], "}"}], ",", 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_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "prule"}], "}"}], ",", 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", "[", RowBox[{"{", RowBox[{"n1", ",", "n2"}], "}"}], "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "prule_"}], "}"}], ",", 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_"}], "]"}], ":=", 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", ",", "NN", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wstb", ",", "\[Delta]W", ",", "ux", ",", "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]", "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"NL", ".", RowBox[{"{", RowBox[{ RowBox[{"ux", "[", "1", "]"}], ",", RowBox[{"ux", "[", "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[{"CE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"EE", " ", "Sy"}], ",", RowBox[{ RowBox[{"-", "EE"}], " ", "Sz"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "GG"}], " ", "Sy"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"GG", " ", "Sz"}], ",", "0", ",", "0"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"BE", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"GG", " ", "Iyy"}], "+", RowBox[{"GG", " ", "Izz"}]}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"EE", " ", "Iyy"}], ",", RowBox[{ RowBox[{"-", "EE"}], " ", "Iyz"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"-", "EE"}], " ", "Iyz"}], ",", 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[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Length", "[", "prule", "]"}], "==", "0"}], ",", RowBox[{"NN", "=", "0"}]}], "]"}], ";", " ", RowBox[{"(*", RowBox[{"first", " ", "step"}], "*)"}], "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"prule", "\[Equal]", "Null"}], ",", RowBox[{"NN", "=", RowBox[{"AA", " ", "EE", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}]}]}]}], "]"}], ";", " ", RowBox[{"(*", RowBox[{"symbolic", " ", "form"}], "*)"}], "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Length", "[", "prule", "]"}], ">", "0"}], ",", RowBox[{"NN", "=", RowBox[{"AA", " ", "EE", " ", RowBox[{"(", RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], RowBox[{"(", RowBox[{"u", "/.", "prule"}], ")"}]}], ")"}]}]}]}], "]"}], ";", " ", RowBox[{"(*", RowBox[{"second", " ", "step"}], "*)"}], "\[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[{"fx", ",", "fy", ",", "fz"}], "}"}]}], "+", RowBox[{ RowBox[{"\[Delta]", "[", RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "]"}], ".", RowBox[{"{", RowBox[{"mx", ",", "my", ",", "mz"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]wstb", "=", RowBox[{ RowBox[{"-", " ", "NN"}], "*", 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]", "]"}]}], ";"}], "\[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}, {3.7562663077370443`*^9, 3.7562663112925215`*^9}, { 3.75626643466018*^9, 3.756266439170367*^9}, 3.75626659814073*^9, { 3.7562668779774446`*^9, 3.7562668813469515`*^9}, {3.756267102338399*^9, 3.7562671154649625`*^9}, 3.756267840776702*^9, {3.756268206653613*^9, 3.756268317933144*^9}, {3.7562683535967026`*^9, 3.75626839517597*^9}, { 3.756269176072233*^9, 3.756269242752178*^9}, {3.7562692739390063`*^9, 3.756269274663946*^9}, {3.7562693089452143`*^9, 3.756269417281339*^9}, { 3.756269467316238*^9, 3.7562696545713525`*^9}, 3.756291560630211*^9, { 3.756296948925913*^9, 3.7562969609940443`*^9}, 3.756297219002653*^9, { 3.756297719561038*^9, 3.7562977422236896`*^9}}, CellLabel-> "In[116]:=",ExpressionUUID->"10195547-9e08-4de6-b8ba-6f68b277fa39"] }, Closed]], Cell[CellGroupData[{ Cell["BEAM ELEMENT (static curved) defs ", "Subsection", CellChangeTimes->{{3.5579867801590133`*^9, 3.557986782249417*^9}, { 3.7530188279461737`*^9, 3.75301883733206*^9}},ExpressionUUID->"91adccb2-269e-4a19-9a4a-\ 91ccc1e79579"], 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", 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, 3.557986797646644*^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[119]:=",ExpressionUUID->"06e3e177-9d54-4611-b583-2e9378b34b1d"] }, Closed]], Cell[CellGroupData[{ Cell["PLANE ELEMENT defs ", "Subsection",ExpressionUUID->"b0e0c39c-1804-43da-be7d-9b95f8708dba"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"{", RowBox[{"PLANE", ",", 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[{"PLANE", ",", 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[{"{", 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_"}], "}"}]}], "}"}], ",", 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[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"Lx", ">", "0"}], "&&", RowBox[{"Ly", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"e1", ",", " ", "e2", ",", "nn"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFINV", " ", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inverse", "[", "FF", "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"Lx", ">", "0"}], "&&", RowBox[{"Ly", ">", "0"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}], ",", RowBox[{ RowBox[{"L", ">", "0"}], "&&", RowBox[{"Lx", ">", "0"}], "&&", RowBox[{"Ly", ">", "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"}], "]"}], "]"}]}]}], "]"}]}]}], "]"}]}], ";", RowBox[{"EEEE", "=", RowBox[{"tt", "*", 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[{"Flatten", "[", RowBox[{"\[Delta]", "[", "\[Epsilon]", "]"}], "]"}], ".", RowBox[{"Flatten", "[", "\[Sigma]", "]"}]}]}]}], ";", "\[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]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_", ",", "fZ_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}], "]"}], ":=", "\[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", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", 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", ",", "r", ",", "e1", ",", "e2", ",", "e3", ",", "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[{"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[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]"}], ",", RowBox[{"\[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]", "\[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[{"{", 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", ".", "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[{"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[{ RowBox[{"INT", "[", "nl", "]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"Simplify", "[", RowBox[{"\[Sigma]", " ", "/.", " ", RowBox[{"MID", "[", "nl", "]"}]}], "]"}], "]"}]}], "]"}]}]}], "\[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[{"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[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]"}], ",", RowBox[{"\[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[{ 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]", "\[IndentingNewLine]", "\[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[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]"}], ",", RowBox[{"\[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]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE_", ",", "\[Nu]\[Nu]_", ",", "\[Alpha]\[Alpha]_", ",", "kk_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "ss_", ",", "\[CurlyTheta]0_"}], "}"}]}], "}"}], ",", RowBox[{"Triangle", "[", "node_", "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE", ",", "\[Nu]\[Nu]", ",", "\[Alpha]\[Alpha]", ",", "kk"}], "}"}], ",", RowBox[{"{", "tt", "}"}], ",", RowBox[{"{", RowBox[{ "fX", ",", "fY", ",", "fZ", ",", "ss", ",", "\[CurlyTheta]0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node", "]"}]}], "}"}], ",", "fun"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE_", ",", "\[Nu]\[Nu]_", ",", "\[Alpha]\[Alpha]_", ",", "kk_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "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]", "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE_", ",", "\[Nu]\[Nu]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{ "\[Epsilon]xx_", ",", "\[Epsilon]yy_", ",", "\[Epsilon]xx_"}], "}"}], ",", RowBox[{"{", RowBox[{"fX_", ",", "fY_"}], "}"}]}], "}"}], ",", 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[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]"}], ",", RowBox[{"\[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[{"Inverse", "[", "FF", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Abs", "[", RowBox[{"Det", "[", "FF", "]"}], "]"}]}], ";", "\[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]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"non", "-", RowBox[{"symmetric", " ", "stress"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Sigma]", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "i", ",", "j"}], "]"}], "]"}], "*", RowBox[{"(", RowBox[{ RowBox[{"\[Epsilon]0", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}], "+", RowBox[{"\[Epsilon]", "[", RowBox[{"[", RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ")"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[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[{ RowBox[{ 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[{"non", "-", RowBox[{"symmetric", " ", "stress"}]}], "*)"}], "\[IndentingNewLine]", "\[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]", "]"}]}], ";"}]}]}]], "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}}, CellLabel-> "In[121]:=",ExpressionUUID->"6a0e0d0d-c6ce-4720-9792-13f58dcffffc"] }, Closed]], Cell[CellGroupData[{ Cell["PLANE ELEMENT (dynamic) defs ", "Subsection", CellChangeTimes->{{3.7574178626155615`*^9, 3.757417866610338*^9}},ExpressionUUID->"cac1f4d2-6abb-4583-9715-\ def566f4dcfc"], Cell[BoxData[ 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[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]"}], ",", RowBox[{"\[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}, CellLabel-> "In[135]:=",ExpressionUUID->"4ef5f2d0-fa25-49ec-acf2-77ac9741a235"] }, Closed]], Cell[CellGroupData[{ Cell["PLANE ELEMENT (large-displacement) defs ", "Subsection", CellChangeTimes->{{3.7574169773814163`*^9, 3.7574169848245335`*^9}, { 3.7574180750707226`*^9, 3.757418078890803*^9}},ExpressionUUID->"3a7fcb2c-809c-491e-8008-\ ff44eaa4ff92"], Cell[BoxData[{ RowBox[{ 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[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]"}], ",", RowBox[{"\[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]", "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", 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", 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}}, CellLabel-> "In[136]:=",ExpressionUUID->"af7a02fa-7ee0-4fd9-a30b-c90bf1abbac8"] }, Open ]], Cell[CellGroupData[{ Cell["PLATE ELEMENT defs ", "Subsection", CellChangeTimes->{{3.6302475626780834`*^9, 3.6302475636452847`*^9}, { 3.6303896204112215`*^9, 3.630389621175623*^9}},ExpressionUUID->"d80eaf00-72a4-4ce4-bc60-\ d25c0abc146d"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", 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", ",", "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[{ 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[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "\[Beta]"}], ",", RowBox[{"\[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[{"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[{ RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"nl", ",", "2"}], "]"}], "]"}], ".", "en"}], "+", RowBox[{ RowBox[{"NN", "[", RowBox[{"[", "1", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "2", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "3", "]"}], "]"}], "*", RowBox[{"NN", "[", RowBox[{"[", "4", "]"}], "]"}], "*", RowBox[{"a", "[", "nl", "]"}], "*", "0"}]}]}], ";", "\[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[{"y", "\[Rule]", RowBox[{"hy", "/", "2"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Theta]", "=", RowBox[{"\[Theta]", "/.", RowBox[{"x", "\[Rule]", RowBox[{"hx", "/", "2"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Psi]x", "=", RowBox[{"\[Psi]", "/.", RowBox[{"y", "\[Rule]", RowBox[{"hy", "/", "2"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Pi]\[Psi]y", "=", RowBox[{"\[Psi]", "/.", RowBox[{"x", "\[Rule]", RowBox[{"hx", "/", "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[{ 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[{"REC9", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wext", "+", "\[Delta]wint"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[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[{"PLATE", ",", 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]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "\[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", "[", "node_", "]"}]}], "}"}]}], "]"}], ":=", RowBox[{ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "n\[Alpha]", ",", "n\[Beta]", ",", "nne", ",", "enode", ",", "\[Delta]", ",", "\[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", ",", "F", ",", "M", ",", "\[Epsilon]", ",", "\[Kappa]", ",", "II0", ",", "III", ",", "IIII", ",", "IIII1", ",", "IIII2", ",", "EEEE", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]WW"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"(*", "rule", "*)"}], "\[IndentingNewLine]", RowBox[{ 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]", RowBox[{"(*", "nodes", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"n\[Alpha]", ",", "n\[Beta]"}], "}"}], "=", RowBox[{"Dimensions", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"enode", "=", RowBox[{"Flatten", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "mapping", "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"Flatten", "[", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n\[Alpha]", ",", "\[Alpha]"}], "}"}], ",", RowBox[{"{", RowBox[{"n\[Beta]", ",", "\[Beta]"}], "}"}]}], "}"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"generic", " ", "basis", " ", "vectors"}], "*)"}], "\[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[{"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[{"\[Alpha]\[Beta]n", "=", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"r\[Alpha]0", ",", "r\[Beta]0", ",", "in0"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"MatrixForm", "[", "\[Alpha]\[Beta]n", "]"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"ijk", "=", RowBox[{"FFINV", "=", RowBox[{"Inverse", "[", "FF", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"GG", " ", "=", RowBox[{"FF", ".", RowBox[{"Transpose", "[", "FF", "]"}]}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"PP", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"\[Alpha]\[Beta]n", "[", RowBox[{"[", RowBox[{"a", ",", "i"}], "]"}], "]"}], "*", RowBox[{"\[Alpha]\[Beta]n", "[", RowBox[{"[", RowBox[{"b", ",", "j"}], "]"}], "]"}], "*", RowBox[{"ijk", "[", 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]", RowBox[{"(*", RowBox[{ RowBox[{"Print", "[", RowBox[{"Simplify", "[", RowBox[{"PP", ",", RowBox[{"{", RowBox[{ RowBox[{"Lx", ">", "0"}], ",", RowBox[{"Ly", ">", "0"}]}], "}"}]}], "]"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"FF", ".", RowBox[{"(", RowBox[{"FF", ".", RowBox[{"LeviCivitaTensor", "[", "3", "]"}]}], ")"}], ".", "FFINV"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Lx", ">", "0"}], ",", RowBox[{"Ly", ">", "0"}]}], "}"}]}], "]"}], "]"}]}], "*)"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "displacement", " ", "and", " ", "rotation", " ", "test", " ", "case"}], "*)"}], "\[IndentingNewLine]", RowBox[{"u0", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]0", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "3"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "displacement", " ", "and", " ", "rotation", " ", "test", " ", "case"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "\[IndentingNewLine]", RowBox[{ RowBox[{"u0", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"ux", "*", "x"}], "+", RowBox[{"uy", "*", "y"}]}], ",", RowBox[{ RowBox[{"vx", "*", "x"}], "+", RowBox[{"vy", "*", "y"}]}], ",", RowBox[{ RowBox[{"wx", "*", "x"}], "+", RowBox[{"wy", "*", "y"}]}]}], "}"}], "/.", RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}], "\[Rule]", "r0"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Theta]0", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"\[Phi]x", "*", "x"}], "+", RowBox[{"\[Phi]y", "*", "y"}]}], ",", RowBox[{ RowBox[{"\[Theta]x", "*", "x"}], "+", RowBox[{"\[Theta]y", "*", "y"}]}], ",", RowBox[{ RowBox[{"\[Psi]x", "*", "x"}], "+", RowBox[{"\[Psi]y", "*", "y"}]}]}], "}"}], "/.", RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}], "\[Rule]", "r0"}], "]"}]}]}], ";"}], " ", "\[IndentingNewLine]", "*)"}], "\[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[{"(*", "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{ RowBox[{"\[Theta]0", "\[Cross]", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}], ",", RowBox[{"{", RowBox[{ RowBox[{"Lx", ">", "0"}], ",", RowBox[{"Ly", ">", "0"}]}], "}"}]}], "]"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{ RowBox[{"\[Omega]00", ".", "FF"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}], ",", RowBox[{"{", RowBox[{ RowBox[{"Lx", ">", "0"}], ",", RowBox[{"Ly", ">", "0"}]}], "}"}]}], "]"}], "]"}], ";"}], "\[IndentingNewLine]", "*)"}], "\[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", "[", "ijk", "]"}], ".", "ijk"}], "+", RowBox[{"Outer", "[", RowBox[{"Times", ",", "in0", ",", "\[Omega]00"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]", "=", RowBox[{ RowBox[{"D", "[", RowBox[{"\[Omega]00", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "n"}], "}"}], "}"}]}], "]"}], ".", RowBox[{"Transpose", "[", "ijk", "]"}], ".", "ijk"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"Print", "[", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Transpose", "[", "FF", "]"}], ".", "\[Epsilon]", ".", "FF"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}], ",", RowBox[{"{", RowBox[{ RowBox[{"Lx", ">", "0"}], ",", RowBox[{"Ly", ">", "0"}]}], "}"}]}], "]"}], "]"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"\[Epsilon]", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}], ",", RowBox[{"{", RowBox[{ RowBox[{"Lx", ">", "0"}], ",", RowBox[{"Ly", ">", "0"}]}], "}"}]}], "]"}], "]"}], "]"}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"Print", "[", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Transpose", "[", "FF", "]"}], ".", "\[Kappa]", ".", "FF"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}], ",", RowBox[{"{", RowBox[{ RowBox[{"Lx", ">", "0"}], ",", RowBox[{"Ly", ">", "0"}]}], "}"}]}], "]"}], "]"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"\[Kappa]", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}], ",", RowBox[{"{", RowBox[{ RowBox[{"Lx", ">", "0"}], ",", RowBox[{"Ly", ">", "0"}]}], "}"}]}], "]"}], "]"}], "]"}], ";"}], "*)"}], "\[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[{"(*", RowBox[{ RowBox[{"II", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", RowBox[{"FFINV", "[", RowBox[{"[", "i", "]"}], "]"}], ",", RowBox[{"FFINV", "[", RowBox[{"[", "i", "]"}], "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"FF", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"II", ".", "GG", ".", RowBox[{"FF", "[", RowBox[{"[", "1", "]"}], "]"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Lx", ">", "0"}], ",", RowBox[{"Ly", ">", "0"}]}], "}"}]}], "]"}], "]"}], ";"}], "*)"}], "\[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[{"Print", "[", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Transpose", "[", "FF", "]"}], ".", "M", ".", "FF"}], " ", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Beta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}], ",", RowBox[{"{", RowBox[{ RowBox[{"Lx", ">", "0"}], ",", RowBox[{"Ly", ">", "0"}]}], "}"}]}], "]"}], "]"}], "]"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "density"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"GG", ".", "F"}], "]"}], ".", RowBox[{"\[Delta]", "[", RowBox[{"Flatten", "[", RowBox[{"Transpose", "[", RowBox[{"GG", ".", "\[Epsilon]"}], "]"}], "]"}], "]"}]}]}], "*", "0"}], "-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"GG", ".", "M"}], "]"}], ".", RowBox[{"\[Delta]", "[", RowBox[{"Flatten", "[", RowBox[{"Transpose", "[", RowBox[{"GG", ".", "\[Kappa]"}], "]"}], "]"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", "\[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]", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "u00", "]"}], ".", "GG", ".", "f00"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"LINE7", ",", RowBox[{"QUAD", "[", RowBox[{"LINE7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[Alpha]", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "1", "}"}]}], "}"}]}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[Beta]", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "1", "}"}]}], "}"}]}], "}"}]}], "]"}]}]}]}], "\[IndentingNewLine]", "]"}], "/;", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}]}], " ", "||", " ", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", RowBox[{"3", ",", "3"}], "}"}]}], "||", " ", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", RowBox[{"4", ",", "4"}], "}"}]}]}], ")"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE_", ",", "GG_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{ "fx_", ",", "fy_", ",", "fz_", ",", "mx_", ",", "my_", ",", "mz_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}]}], "]"}], ":=", RowBox[{ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]", ",", "nne", ",", "enode", ",", "NN", ",", "jac", ",", "r0", ",", "r\[Alpha]0", ",", "r\[Beta]0", ",", "rn0", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "h\[Beta]0", ",", "i\[Beta]0", ",", "hn0", ",", "in0", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "n\[Alpha]", ",", "n\[Beta]", ",", "HH", ",", "FF", ",", "DD", ",", " ", "Qx", ",", "Qy", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]WW", ",", "u0", ",", "\[CapitalTheta]0", ",", "\[Omega]0", ",", "f\[Alpha]", ",", "f\[Beta]", ",", "fn", ",", "F", ",", "M", ",", "\[Epsilon]", ",", "\[Kappa]", ",", "\[IndentingNewLine]", "II0", ",", "II", ",", "IIII", ",", "IIII1", ",", "IIII2"}], "}"}], ",", "\[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]", RowBox[{"(*", "nodes", "*)"}], "\[IndentingNewLine]", 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", " ", "and", " ", "orientation", " ", "of", " ", "the", " ", "material", " ", "axes"}], "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"Flatten", "[", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n\[Alpha]", ",", "\[Alpha]"}], "}"}], ",", RowBox[{"{", RowBox[{"n\[Beta]", ",", "\[Beta]"}], "}"}]}], "}"}], "]"}], "]"}]}], ";", "\[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[{"r\[Alpha]0", "\[Cross]", "r\[Beta]0"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Alpha]0", "=", RowBox[{"Norm", "[", "r\[Alpha]0", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]0", "=", RowBox[{"Norm", "[", "r\[Beta]0", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"hn0", "=", RowBox[{"Norm", "[", "rn0", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"i\[Alpha]0", "=", RowBox[{"r\[Alpha]0", "/", "h\[Alpha]0"}]}], ";", "\[IndentingNewLine]", RowBox[{"i\[Beta]0", "=", RowBox[{"r\[Beta]0", "/", "h\[Beta]0"}]}], ";", "\[IndentingNewLine]", RowBox[{"in0", "=", RowBox[{"rn0", "/", "hn0"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", " ", "=", "hn0"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"in", " ", "flat", " ", "curvilinear", " ", "geometry"}], "*)"}], "\[IndentingNewLine]", RowBox[{"HH", "=", RowBox[{"{", RowBox[{"r\[Alpha]0", ",", "r\[Beta]0", ",", "in0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"i\[Alpha]0", ",", "i\[Beta]0", ",", "in0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"DD", "=", RowBox[{"Inverse", "[", RowBox[{"HH", ".", RowBox[{"Transpose", "[", "FF", "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "transform", " ", "into", " ", "the", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{"u0", "=", RowBox[{"FF", ".", RowBox[{"(", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "2"}], "]"}], "]"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalTheta]0", "=", 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[{"\[Omega]0", "=", RowBox[{"\[CapitalTheta]0", "\[Cross]", "in0"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"strain", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Epsilon]", "=", RowBox[{ RowBox[{"DD", ".", RowBox[{"Transpose", "[", RowBox[{"D", "[", RowBox[{"u0", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "n"}], "}"}], "}"}]}], "]"}], "]"}]}], "+", RowBox[{"Outer", "[", RowBox[{"Times", ",", "in0", ",", "\[Omega]0"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Kappa]", "=", RowBox[{"DD", ".", RowBox[{"Transpose", "[", RowBox[{"D", "[", RowBox[{"\[Omega]0", ",", RowBox[{"{", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "n"}], "}"}], "}"}]}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"elasticity", " ", "dyad", " ", "of", " ", "plate"}], "*)"}], "\[IndentingNewLine]", RowBox[{"II0", "=", RowBox[{ RowBox[{"Outer", "[", RowBox[{"Times", ",", "i\[Alpha]0", ",", "i\[Alpha]0"}], "]"}], "+", RowBox[{"Outer", "[", RowBox[{"Times", ",", "i\[Beta]0", ",", "i\[Beta]0"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"II", "=", RowBox[{"II0", "+", RowBox[{"Outer", "[", RowBox[{"Times", ",", "in0", ",", "in0"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"IIII1", "=", RowBox[{"Outer", "[", RowBox[{"Times", ",", "II0", ",", "II0"}], "]"}]}], ";", "\[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[{ 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[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "ii", ",", "jj"}], "]"}], "]"}], "*", RowBox[{"\[Epsilon]\[Epsilon]", "[", RowBox[{"[", RowBox[{"jj", ",", "ii"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"jj", ",", "1", ",", "3"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", "3"}], "}"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"M", "=", RowBox[{ RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", RowBox[{"Sum", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"EEEE", "[", RowBox[{"[", RowBox[{";;", ",", ";;", ",", "ii", ",", "jj"}], "]"}], "]"}], "*", RowBox[{"\[Kappa]\[Kappa]", "[", RowBox[{"[", RowBox[{"jj", ",", "ii"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"jj", ",", "1", ",", "3"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"ii", ",", "1", ",", "3"}], "}"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"virtual", " ", "work", " ", "expression"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"\[Delta]", "[", RowBox[{"Transpose", "[", "\[Epsilon]\[Epsilon]", "]"}], "]"}], "]"}], ".", RowBox[{"Flatten", "[", "F", "]"}]}]}], "-", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"Transpose", "[", RowBox[{"\[Delta]", "[", "\[Kappa]\[Kappa]", "]"}], "]"}], "]"}], ".", RowBox[{"Flatten", "[", "M", "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"\[Delta]", "[", "u0", "]"}], ".", RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"LINE7", ",", RowBox[{"QUAD", "[", RowBox[{"LINE7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[Alpha]", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "1", "}"}]}], "}"}]}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[Beta]", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "1", "}"}]}], "}"}]}], "}"}]}], "]"}]}]}]}], "\[IndentingNewLine]", "]"}], "/;", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}]}], " ", "||", " ", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", RowBox[{"3", ",", "3"}], "}"}]}], "||", " ", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", RowBox[{"4", ",", "4"}], "}"}]}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ "(*", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"PLATEC", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE_", ",", "GG_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{ "fx_", ",", "fy_", ",", "fz_", ",", "mx_", ",", "my_", ",", "mz_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}]}], "]"}], ":=", RowBox[{ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]rule", ",", "nne", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "enode", ",", "NL", ",", "NN", ",", "r0", ",", "r\[Alpha]0", ",", "r\[Beta]0", ",", "jac", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "h\[Beta]0", ",", "i\[Beta]0", ",", "in0", ",", "HH", ",", "FF", ",", "DD"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "rule", "*)"}], "\[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", "]"}]}], ",", RowBox[{ RowBox[{"c", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]c", "[", "any", "]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "nodes", "*)"}], "\[IndentingNewLine]", RowBox[{"nne", "=", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"enode", "=", RowBox[{"Flatten", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", " ", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NL", "[", "3", "]"}], "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NL", "[", "6", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}]}], ",", RowBox[{"\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", 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[{"4", " ", "\[Alpha]", " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"-", "4"}], " ", "\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}]}], ",", RowBox[{ RowBox[{"-", "4"}], " ", "\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NL", "[", "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]", RowBox[{"NN", "=", RowBox[{"NL", "[", "nne", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "mapping", "*)"}], "\[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", "/", "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[{"(*", RowBox[{"for", " ", "integration"}], "*)"}], "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Norm", "[", RowBox[{"r\[Alpha]0", "\[Cross]", "r\[Beta]0"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"h\[Alpha]0", "=", RowBox[{"Sqrt", "[", RowBox[{"r\[Alpha]0", ".", "r\[Alpha]0"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"i\[Alpha]0", "=", RowBox[{"r\[Alpha]0", "/", "h\[Alpha]0"}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Beta]0", "=", RowBox[{"(", RowBox[{"r\[Beta]0", "-", RowBox[{ RowBox[{"(", RowBox[{"r\[Beta]0", ".", "i\[Alpha]0"}], ")"}], "*", "i\[Alpha]0"}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]0", "=", RowBox[{"Sqrt", "[", RowBox[{"r\[Beta]0", ".", "r\[Beta]0"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"i\[Beta]0", "=", RowBox[{"r\[Beta]0", "/", "h\[Beta]0"}]}], ";", "\[IndentingNewLine]", RowBox[{"in0", "=", RowBox[{"i\[Alpha]0", "\[Cross]", "i\[Beta]0"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"in", " ", "flat", " ", "curvilinear", " ", "geometry"}], "*)"}], "\[IndentingNewLine]", RowBox[{"HH", "=", RowBox[{"{", RowBox[{"r\[Alpha]0", ",", "r\[Beta]0", ",", "in0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"i\[Alpha]0", ",", "i\[Beta]0", ",", "in0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"MatrixForm", "[", "FF", "]"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"DD", "=", RowBox[{"Inverse", "[", RowBox[{"HH", ".", RowBox[{"Transpose", "[", "FF", "]"}]}], "]"}]}], ";", "\[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]", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Delta]u", ",", "\[Delta]v", ",", "\[Delta]w"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "/.", " ", "\[Delta]rule"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fz"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "gradient", " ", "components", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["u", "\[Alpha]"], ",", SubscriptBox["u", "\[Beta]"], ",", SubscriptBox["u", "n"]}], "}"}], "=", RowBox[{"DD", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "n"], "u"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["v", "\[Alpha]"], ",", SubscriptBox["v", "\[Beta]"], ",", SubscriptBox["v", "n"]}], "}"}], "=", RowBox[{"DD", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "n"], "v"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["w", "\[Alpha]"], ",", SubscriptBox["w", "\[Beta]"], ",", SubscriptBox["w", "n"]}], "}"}], "=", RowBox[{"DD", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "n"], "w"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["\[Phi]", "\[Alpha]"], ",", SubscriptBox["\[Phi]", "\[Beta]"], ",", SubscriptBox["\[Phi]", "n"]}], "}"}], "=", RowBox[{"DD", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "n"], "\[Phi]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["\[CapitalTheta]", "\[Alpha]"], ",", SubscriptBox["\[CapitalTheta]", "\[Beta]"], ",", SubscriptBox["\[CapitalTheta]", "n"]}], "}"}], "=", RowBox[{"DD", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[CapitalTheta]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[CapitalTheta]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "n"], "\[CapitalTheta]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["\[Psi]", "\[Alpha]"], ",", SubscriptBox["\[Psi]", "\[Beta]"], ",", SubscriptBox["\[Psi]", "n"]}], "}"}], "=", RowBox[{"DD", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Psi]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Psi]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "n"], "\[Psi]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"strain", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]"}], "}"}], "=", RowBox[{"{", RowBox[{ SubscriptBox["u", "\[Alpha]"], ",", SubscriptBox["v", "\[Beta]"], ",", RowBox[{ SubscriptBox["v", "\[Alpha]"], "-", "\[Psi]"}], ",", RowBox[{ SubscriptBox["u", "\[Beta]"], "+", "\[Psi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Delta]\[Epsilon]\[Beta]\[Beta]", ",", "\[Delta]\[Epsilon]\[Alpha]\[Beta]", ",", "\[Delta]\[Epsilon]\[Beta]\[Alpha]"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]"}], "}"}], " ", "/.", " ", "\[Delta]rule"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]"}], "}"}], "=", RowBox[{"{", RowBox[{ SubscriptBox["\[CapitalTheta]", "\[Alpha]"], ",", RowBox[{"-", SubscriptBox["\[Phi]", "\[Beta]"]}], ",", RowBox[{ SubscriptBox["\[CapitalTheta]", "\[Beta]"], "-", SubscriptBox["\[Phi]", "\[Alpha]"]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]\[Kappa]\[Alpha]\[Alpha]", ",", "\[Delta]\[Kappa]\[Beta]\[Beta]", ",", "\[Delta]\[Kappa]\[Alpha]\[Beta]"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]"}], "}"}], " ", "/.", " ", "\[Delta]rule"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Epsilon]\[Alpha]n", ",", "\[Epsilon]\[Beta]n"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["w", "\[Alpha]"], "+", "\[CapitalTheta]"}], ",", RowBox[{ SubscriptBox["w", "\[Beta]"], "-", "\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]\[Epsilon]\[Alpha]n", ",", "\[Delta]\[Epsilon]\[Beta]n"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"\[Epsilon]\[Alpha]n", ",", "\[Epsilon]\[Beta]n"}], "}"}], "/.", " ", "\[Delta]rule"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "resultants"}], "*)"}], "\[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", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "*", RowBox[{"\[Epsilon]\[Alpha]\[Beta]", "/", "2"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Beta]\[Alpha]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "*", RowBox[{"\[Epsilon]\[Beta]\[Alpha]", "/", "2"}]}]}], ";", "\[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"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "*", RowBox[{"\[Kappa]\[Alpha]\[Beta]", "/", "2"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{"GG", "*", "tt", "*", "\[Epsilon]\[Alpha]n"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Beta]", "=", RowBox[{"GG", "*", "tt", "*", "\[Epsilon]\[Beta]n"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Delta]\[Epsilon]\[Beta]\[Beta]", ",", "\[Delta]\[Epsilon]\[Alpha]\[Beta]", ",", "\[Delta]\[Epsilon]\[Beta]\[Alpha]"}], "}"}], ".", RowBox[{"{", RowBox[{ "N\[Alpha]\[Alpha]", ",", "N\[Beta]\[Beta]", ",", "N\[Alpha]\[Beta]", ",", "N\[Beta]\[Alpha]"}], "}"}]}]}], "-", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]\[Kappa]\[Alpha]\[Alpha]", ",", "\[Delta]\[Kappa]\[Beta]\[Beta]", ",", "\[Delta]\[Kappa]\[Alpha]\[Beta]"}], "}"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Beta]\[Beta]", ",", "M\[Alpha]\[Beta]"}], "}"}]}], "-", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]\[Epsilon]\[Alpha]n", ",", "\[Delta]\[Epsilon]\[Beta]n"}], "}"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Beta]"}], "}"}]}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"{", RowBox[{"\[Delta]u", ",", "\[Delta]v", ",", "\[Delta]w"}], "}"}], ".", RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"TRI28", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", "\[Delta]WW", "]"}]}]}], "]"}], "/;", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", "3", "}"}]}], " ", "||", " ", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", "6", "}"}]}], "||", " ", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", "10", "}"}]}]}], ")"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE_", ",", "GG_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{ "fx_", ",", "fy_", ",", "fz_", ",", "mx_", ",", "my_", ",", "mz_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}]}], "]"}], ":=", RowBox[{ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]", ",", "n\[Alpha]", ",", "n\[Beta]", ",", "nne", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "enode", ",", "NN", ",", "r0", ",", "r\[Alpha]0", ",", "r\[Beta]0", ",", "rn0", ",", "jac", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "h\[Beta]0", ",", "i\[Beta]0", ",", "hn0", ",", "in0", ",", "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]", ",", "\[Epsilon]\[Alpha]n", ",", "\[Epsilon]\[Beta]n", ",", "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]", 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[{"(*", "nodes", "*)"}], "\[IndentingNewLine]", 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[{"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[{"h\[Alpha]0", "=", RowBox[{"Norm", "[", "r\[Alpha]0", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"i\[Alpha]0", "=", RowBox[{"r\[Alpha]0", "/", "h\[Alpha]0"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]0", "=", RowBox[{"Norm", "[", "r\[Beta]0", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"i\[Beta]0", "=", RowBox[{"r\[Beta]0", "/", "h\[Beta]0"}]}], ";", "\[IndentingNewLine]", RowBox[{"hn0", "=", RowBox[{"Norm", "[", "rn0", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"in0", "=", RowBox[{"rn0", "/", "hn0"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", " ", "=", "hn0"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"in", " ", "flat", " ", "geometry"}], "*)"}], "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"i\[Alpha]0", ",", "i\[Beta]0", ",", "in0"}], "}"}]}], ";", "\[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]0"}], ",", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}], "/", "h\[Beta]0"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], "/", "h\[Alpha]0"}], "-", "\[Psi]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}], "/", "h\[Beta]0"}], "+", "\[Psi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[CapitalTheta]"}], "/", "h\[Alpha]0"}], ",", RowBox[{ RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}]}], "/", "h\[Beta]0"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[CapitalTheta]"}], "/", "h\[Beta]0"}], "-", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], "/", "h\[Alpha]0"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Epsilon]\[Alpha]n", ",", "\[Epsilon]\[Beta]n"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], "/", "h\[Alpha]0"}], "+", "\[CapitalTheta]"}], ",", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}], "/", "h\[Beta]0"}], "-", "\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "stress", " ", "resultants", " ", "with", " ", "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", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "*", RowBox[{"\[Epsilon]\[Alpha]\[Beta]", "/", "2"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Beta]\[Alpha]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "*", RowBox[{"\[Epsilon]\[Beta]\[Alpha]", "/", "2"}]}]}], ";", "\[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"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "*", RowBox[{"\[Kappa]\[Alpha]\[Beta]", "/", "2"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{"GG", "*", "tt", "*", "\[Epsilon]\[Alpha]n"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Beta]", "=", RowBox[{"GG", "*", "tt", "*", "\[Epsilon]\[Beta]n"}]}], ";", "\[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[{"\[Epsilon]\[Alpha]n", ",", "\[Epsilon]\[Beta]n"}], "}"}], "]"}], ".", 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[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"LINE7", ",", RowBox[{"QUAD", "[", RowBox[{"LINE7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[Alpha]", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "1", "}"}]}], "}"}]}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[Beta]", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "1", "}"}]}], "}"}]}], "}"}]}], "]"}]}]}]}], "]"}], "/;", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}]}], " ", "||", " ", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", RowBox[{"3", ",", "3"}], "}"}]}], "||", " ", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", RowBox[{"4", ",", "4"}], "}"}]}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"PLATEC", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE_", ",", "GG_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{ "fx_", ",", "fy_", ",", "fz_", ",", "mx_", ",", "my_", ",", "mz_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}]}], "]"}], ":=", RowBox[{ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]", ",", "nne", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "enode", ",", "NL", ",", "NN", ",", "r0", ",", "r\[Alpha]0", ",", "r\[Beta]0", ",", "jac", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "h\[Beta]0", ",", "i\[Beta]0", ",", "in0", ",", "HH", ",", "FF", ",", "DD"}], "}"}], ",", "\[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[{"(*", "nodes", "*)"}], "\[IndentingNewLine]", RowBox[{"nne", "=", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"enode", "=", RowBox[{"Flatten", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", " ", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NL", "[", "3", "]"}], "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NL", "[", "6", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}]}], ",", RowBox[{"\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", 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[{"4", " ", "\[Alpha]", " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"-", "4"}], " ", "\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}]}], ",", RowBox[{ RowBox[{"-", "4"}], " ", "\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"these", " ", "are", " ", "OK"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NL", "[", "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]", RowBox[{"NN", "=", RowBox[{"NL", "[", "nne", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "mapping", "*)"}], "\[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", "/", "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[{"r\[Alpha]0", "\[Cross]", "r\[Beta]0"}]}], ";", "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Norm", "[", RowBox[{"r\[Alpha]0", "\[Cross]", "r\[Beta]0"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"rn0", "=", RowBox[{"rn0", "/", "jac"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"r\[Alpha]0", ",", "r\[Beta]0", ",", "rn0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"MatrixForm", "[", "FF", "]"}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"DD", "=", RowBox[{"Inverse", "[", RowBox[{"FF", ".", RowBox[{"Transpose", "[", "FF", "]"}]}], "]"}]}], ";", "\[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[{ "gradient", " ", "components", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["u", "\[Alpha]"], ",", SubscriptBox["u", "\[Beta]"], ",", SubscriptBox["u", "n"]}], "}"}], "=", RowBox[{"DD", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "n"], "u"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["v", "\[Alpha]"], ",", SubscriptBox["v", "\[Beta]"], ",", SubscriptBox["v", "n"]}], "}"}], "=", RowBox[{"DD", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "n"], "v"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["w", "\[Alpha]"], ",", SubscriptBox["w", "\[Beta]"], ",", SubscriptBox["w", "n"]}], "}"}], "=", RowBox[{"DD", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "n"], "w"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["\[Phi]", "\[Alpha]"], ",", SubscriptBox["\[Phi]", "\[Beta]"], ",", SubscriptBox["\[Phi]", "n"]}], "}"}], "=", RowBox[{"DD", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "n"], "\[Phi]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["\[CapitalTheta]", "\[Alpha]"], ",", SubscriptBox["\[CapitalTheta]", "\[Beta]"], ",", SubscriptBox["\[CapitalTheta]", "n"]}], "}"}], "=", RowBox[{"DD", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[CapitalTheta]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[CapitalTheta]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "n"], "\[CapitalTheta]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["\[Psi]", "\[Alpha]"], ",", SubscriptBox["\[Psi]", "\[Beta]"], ",", SubscriptBox["\[Psi]", "n"]}], "}"}], "=", RowBox[{"DD", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Psi]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Psi]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "n"], "\[Psi]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"strain", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]"}], "}"}], "=", RowBox[{"{", RowBox[{ SubscriptBox["u", "\[Alpha]"], ",", SubscriptBox["v", "\[Beta]"], ",", RowBox[{ SubscriptBox["v", "\[Alpha]"], "-", "\[Psi]"}], ",", RowBox[{ SubscriptBox["u", "\[Beta]"], "+", "\[Psi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]"}], "}"}], "=", RowBox[{"{", RowBox[{ SubscriptBox["\[CapitalTheta]", "\[Alpha]"], ",", RowBox[{"-", SubscriptBox["\[Phi]", "\[Beta]"]}], ",", RowBox[{ SubscriptBox["\[CapitalTheta]", "\[Beta]"], "-", SubscriptBox["\[Phi]", "\[Alpha]"]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Epsilon]\[Alpha]n", ",", "\[Epsilon]\[Beta]n"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["w", "\[Alpha]"], "+", "\[CapitalTheta]"}], ",", RowBox[{ SubscriptBox["w", "\[Beta]"], "-", "\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "resultants"}], "*)"}], "\[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", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "*", RowBox[{"\[Epsilon]\[Alpha]\[Beta]", "/", "2"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Beta]\[Alpha]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "*", RowBox[{"\[Epsilon]\[Beta]\[Alpha]", "/", "2"}]}]}], ";", "\[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"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "*", RowBox[{"\[Kappa]\[Alpha]\[Beta]", "/", "2"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{"GG", "*", "tt", "*", "\[Epsilon]\[Alpha]n"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Beta]", "=", RowBox[{"GG", "*", "tt", "*", "\[Epsilon]\[Beta]n"}]}], ";", "\[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[{"{", RowBox[{ "\[Delta]\[Epsilon]\[Alpha]n", ",", "\[Delta]\[Epsilon]\[Beta]n"}], "}"}], ".", 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[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"TRI28", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", "\[Delta]WW", "]"}]}]}], "]"}], "/;", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", "3", "}"}]}], " ", "||", " ", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", "6", "}"}]}], "||", " ", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", "10", "}"}]}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE_", ",", "GG_", ",", "\[Nu]\[Nu]_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{ "fx_", ",", "fy_", ",", "fz_", ",", "mx_", ",", "my_", ",", "mz_"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", "node_", "]"}]}], "}"}]}], "]"}], ":=", RowBox[{ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]rule", ",", "nne", ",", "\[Alpha]", ",", "\[Beta]", ",", "n", ",", "enode", ",", "NL", ",", "NN", ",", "r0", ",", "r\[Alpha]0", ",", "r\[Beta]0", ",", "jac", ",", "h\[Alpha]0", ",", "i\[Alpha]0", ",", "h\[Beta]0", ",", "i\[Beta]0", ",", "in0"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "rule", "*)"}], "\[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", "]"}]}], ",", RowBox[{ RowBox[{"c", "[", "any__", "]"}], " ", "\[Rule]", " ", RowBox[{"\[Delta]c", "[", "any", "]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "nodes", "*)"}], "\[IndentingNewLine]", RowBox[{"nne", "=", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"enode", "=", RowBox[{"Flatten", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", " ", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"shape", " ", "functions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NL", "[", "3", "]"}], "=", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", RowBox[{"1", "-", "\[Alpha]", "-", "\[Beta]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NL", "[", "6", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Alpha]"}]}], ")"}]}], ",", RowBox[{"\[Beta]", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "\[Beta]"}]}], ")"}]}], ",", 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[{"4", " ", "\[Alpha]", " ", "\[Beta]"}], ",", RowBox[{ RowBox[{"-", "4"}], " ", "\[Beta]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}]}], ",", RowBox[{ RowBox[{"-", "4"}], " ", "\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]", "+", "\[Beta]"}], ")"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"NL", "[", "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]", RowBox[{"NN", "=", RowBox[{"NL", "[", "nne", "]"}]}], ";", "\[IndentingNewLine]", "\[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", "/", "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[{"(*", RowBox[{"for", " ", "integration"}], "*)"}], "\[IndentingNewLine]", RowBox[{"jac", "=", RowBox[{"Norm", "[", RowBox[{"r\[Alpha]0", "\[Cross]", "r\[Beta]0"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"h\[Alpha]0", "=", RowBox[{"Sqrt", "[", RowBox[{"r\[Alpha]0", ".", "r\[Alpha]0"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"i\[Alpha]0", "=", RowBox[{"r\[Alpha]0", "/", "h\[Alpha]0"}]}], ";", "\[IndentingNewLine]", RowBox[{"r\[Beta]0", "=", RowBox[{"(", RowBox[{"r\[Beta]0", "-", RowBox[{ RowBox[{"(", RowBox[{"r\[Beta]0", ".", "i\[Alpha]0"}], ")"}], "*", "i\[Alpha]0"}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"h\[Beta]0", "=", RowBox[{"Sqrt", "[", RowBox[{"r\[Beta]0", ".", "r\[Beta]0"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"i\[Beta]0", "=", RowBox[{"r\[Beta]0", "/", "h\[Beta]0"}]}], ";", "\[IndentingNewLine]", RowBox[{"in0", "=", RowBox[{"i\[Alpha]0", "\[Cross]", "i\[Beta]0"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"in", " ", "flat", " ", "curvilinear", " ", "geometry"}], "*)"}], "\[IndentingNewLine]", RowBox[{"HH", "=", RowBox[{"{", RowBox[{"r\[Alpha]0", ",", "r\[Beta]0", ",", "in0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"FF", "=", RowBox[{"{", RowBox[{"i\[Alpha]0", ",", "i\[Beta]0", ",", "in0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"DD", "=", RowBox[{"Inverse", "[", RowBox[{"HH", ".", RowBox[{"Transpose", "[", "FF", "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "transform", " ", "into", " ", "the", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"FF", ".", "#"}], "&"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "2"}], "]"}], "]"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[CapitalTheta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"FF", ".", "#"}], "&"}], ",", RowBox[{"fun", "[", RowBox[{"[", RowBox[{"enode", ",", "3"}], "]"}], "]"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Delta]u", ",", "\[Delta]v", ",", "\[Delta]w"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "/.", " ", "\[Delta]rule"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}], "=", RowBox[{"FF", ".", RowBox[{"{", RowBox[{"fx", ",", "fy", ",", "fz"}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "gradient", " ", "components", " ", "in", " ", "the", " ", "material", " ", "system"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["u", "\[Alpha]"], ",", SubscriptBox["u", "\[Beta]"], ",", SubscriptBox["u", "n"]}], "}"}], "=", RowBox[{"DD", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "u"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "u"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "n"], "u"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["v", "\[Alpha]"], ",", SubscriptBox["v", "\[Beta]"], ",", SubscriptBox["v", "n"]}], "}"}], "=", RowBox[{"DD", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "v"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "v"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "n"], "v"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["w", "\[Alpha]"], ",", SubscriptBox["w", "\[Beta]"], ",", SubscriptBox["w", "n"]}], "}"}], "=", RowBox[{"DD", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "w"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "w"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "n"], "w"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["\[Phi]", "\[Alpha]"], ",", SubscriptBox["\[Phi]", "\[Beta]"], ",", SubscriptBox["\[Phi]", "n"]}], "}"}], "=", RowBox[{"DD", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Phi]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Phi]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "n"], "\[Phi]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["\[CapitalTheta]", "\[Alpha]"], ",", SubscriptBox["\[CapitalTheta]", "\[Beta]"], ",", SubscriptBox["\[CapitalTheta]", "n"]}], "}"}], "=", RowBox[{"DD", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[CapitalTheta]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[CapitalTheta]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "n"], "\[CapitalTheta]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["\[Psi]", "\[Alpha]"], ",", SubscriptBox["\[Psi]", "\[Beta]"], ",", SubscriptBox["\[Psi]", "n"]}], "}"}], "=", RowBox[{"DD", ".", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "\[Alpha]"], "\[Psi]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "\[Beta]"], "\[Psi]"}], ",", RowBox[{ SubscriptBox["\[PartialD]", "n"], "\[Psi]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"strain", " ", "measures"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]"}], "}"}], "=", RowBox[{"{", RowBox[{ SubscriptBox["u", "\[Alpha]"], ",", SubscriptBox["v", "\[Beta]"], ",", RowBox[{ SubscriptBox["v", "\[Alpha]"], "-", "\[Psi]"}], ",", RowBox[{ SubscriptBox["u", "\[Beta]"], "+", "\[Psi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Delta]\[Epsilon]\[Beta]\[Beta]", ",", "\[Delta]\[Epsilon]\[Alpha]\[Beta]", ",", "\[Delta]\[Epsilon]\[Beta]\[Alpha]"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{ "\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Epsilon]\[Beta]\[Beta]", ",", "\[Epsilon]\[Alpha]\[Beta]", ",", "\[Epsilon]\[Beta]\[Alpha]"}], "}"}], " ", "/.", " ", "\[Delta]rule"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]"}], "}"}], "=", RowBox[{"{", RowBox[{ SubscriptBox["\[CapitalTheta]", "\[Alpha]"], ",", RowBox[{"-", SubscriptBox["\[Phi]", "\[Beta]"]}], ",", RowBox[{ SubscriptBox["\[CapitalTheta]", "\[Beta]"], "-", SubscriptBox["\[Phi]", "\[Alpha]"]}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]\[Kappa]\[Alpha]\[Alpha]", ",", "\[Delta]\[Kappa]\[Beta]\[Beta]", ",", "\[Delta]\[Kappa]\[Alpha]\[Beta]"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{ "\[Kappa]\[Alpha]\[Alpha]", ",", "\[Kappa]\[Beta]\[Beta]", ",", "\[Kappa]\[Alpha]\[Beta]"}], "}"}], " ", "/.", " ", "\[Delta]rule"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Epsilon]\[Alpha]n", ",", "\[Epsilon]\[Beta]n"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{ SubscriptBox["w", "\[Alpha]"], "+", "\[CapitalTheta]"}], ",", RowBox[{ SubscriptBox["w", "\[Beta]"], "-", "\[Phi]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]\[Epsilon]\[Alpha]n", ",", "\[Delta]\[Epsilon]\[Beta]n"}], "}"}], "=", RowBox[{ RowBox[{"{", RowBox[{"\[Epsilon]\[Alpha]n", ",", "\[Epsilon]\[Beta]n"}], "}"}], "/.", " ", "\[Delta]rule"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"stress", " ", "resultants"}], "*)"}], "\[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", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "*", RowBox[{"\[Epsilon]\[Alpha]\[Beta]", "/", "2"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"N\[Beta]\[Alpha]", "=", RowBox[{"tt", "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "*", RowBox[{"\[Epsilon]\[Beta]\[Alpha]", "/", "2"}]}]}], ";", "\[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"}], ")"}], "*", RowBox[{"EE", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]\[Nu]", "^", "2"}]}], ")"}]}], "*", RowBox[{"(", RowBox[{"1", "-", "\[Nu]\[Nu]"}], ")"}], "*", RowBox[{"\[Kappa]\[Alpha]\[Beta]", "/", "2"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Alpha]", "=", RowBox[{"GG", "*", "tt", "*", "\[Epsilon]\[Alpha]n"}]}], ";", "\[IndentingNewLine]", RowBox[{"Q\[Beta]", "=", RowBox[{"GG", "*", "tt", "*", "\[Epsilon]\[Beta]n"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]wint1", "=", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Delta]\[Epsilon]\[Beta]\[Beta]", ",", "\[Delta]\[Epsilon]\[Alpha]\[Beta]", ",", "\[Delta]\[Epsilon]\[Beta]\[Alpha]"}], "}"}], ".", RowBox[{"{", RowBox[{ "N\[Alpha]\[Alpha]", ",", "N\[Beta]\[Beta]", ",", "N\[Alpha]\[Beta]", ",", "N\[Beta]\[Alpha]"}], "}"}]}]}], "-", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]\[Kappa]\[Alpha]\[Alpha]", ",", "\[Delta]\[Kappa]\[Beta]\[Beta]", ",", "\[Delta]\[Kappa]\[Alpha]\[Beta]"}], "}"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Beta]\[Beta]", ",", "M\[Alpha]\[Beta]"}], "}"}]}], "-", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]\[Epsilon]\[Alpha]n", ",", "\[Delta]\[Epsilon]\[Beta]n"}], "}"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Beta]"}], "}"}]}], " ", "*", "0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint2", "=", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]\[Epsilon]\[Alpha]\[Alpha]", ",", "\[Delta]\[Epsilon]\[Beta]\[Beta]", ",", "\[Delta]\[Epsilon]\[Alpha]\[Beta]", ",", "\[Delta]\[Epsilon]\[Beta]\[Alpha]"}], "}"}], ".", RowBox[{"{", RowBox[{ "N\[Alpha]\[Alpha]", ",", "N\[Beta]\[Beta]", ",", "N\[Alpha]\[Beta]", ",", "N\[Beta]\[Alpha]"}], "}"}]}]}], "*", "0"}], "-", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]\[Kappa]\[Alpha]\[Alpha]", ",", "\[Delta]\[Kappa]\[Beta]\[Beta]", ",", "\[Delta]\[Kappa]\[Alpha]\[Beta]"}], "}"}], ".", RowBox[{"{", RowBox[{ "M\[Alpha]\[Alpha]", ",", "M\[Beta]\[Beta]", ",", "M\[Alpha]\[Beta]"}], "}"}]}], "*", "0"}], "-", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]\[Epsilon]\[Alpha]n", ",", "\[Delta]\[Epsilon]\[Beta]n"}], "}"}], ".", RowBox[{"{", RowBox[{"Q\[Alpha]", ",", "Q\[Beta]"}], "}"}]}]}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"{", RowBox[{"\[Delta]u", ",", "\[Delta]v", ",", "\[Delta]w"}], "}"}], ".", RowBox[{"{", RowBox[{"f\[Alpha]", ",", "f\[Beta]", ",", "fn"}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{ RowBox[{"QUAD", "[", RowBox[{"TRI12", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint1", "+", "\[Delta]wext"}], ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}], "+", RowBox[{"QUAD", "[", RowBox[{"TRI7", ",", RowBox[{ RowBox[{"(", "\[Delta]wint2", ")"}], "*", "jac"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "}"}]}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", "\[Delta]WW", "]"}]}]}], "]"}], "/;", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", "3", "}"}]}], " ", "||", " ", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", "6", "}"}]}], "||", " ", RowBox[{ RowBox[{"Dimensions", "[", "node", "]"}], "\[Equal]", RowBox[{"{", "10", "}"}]}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{ RowBox[{"Orthotropic", " ", "plate", " ", RowBox[{"(", RowBox[{"R", "-", "M"}], ")"}], "\[IndentingNewLine]", RowBox[{"\[Delta]W", "[", RowBox[{"MODE_", ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "E1_", ",", "E2_", ",", "G12_", ",", "G13_", ",", "G23_", ",", "\[Nu]12_", ",", "\[Rho]\[Rho]_"}], "}"}], ",", RowBox[{"{", "tt_", "}"}], ",", RowBox[{"{", RowBox[{ "fx_", ",", "fy_", ",", "fz_", ",", "mx_", ",", "my_", ",", "mz_"}], "}"}]}], "}"}], ",", "node_"}], "}"}]}], "]"}]}], ":=", RowBox[{ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]rule", ",", "rule", ",", "n\[Xi]", ",", "n\[Eta]", ",", "nne", ",", "ver", ",", "NN", ",", "FFT", ",", "dNN", ",", "FFTI", ",", "Nx", ",", "Ny", ",", "d\[CapitalOmega]", ",", "xx", ",", "yy", ",", "uu", ",", "uux", ",", "uuy", ",", "\[Delta]uu", ",", "\[Delta]uux", ",", "\[Delta]uuy", ",", "vv", ",", "vvx", ",", "vvy", ",", "\[Delta]vv", ",", "\[Delta]vvx", ",", "\[Delta]vvy", ",", "ww", ",", "wwx", ",", "wwy", ",", "\[Delta]ww", ",", "\[Delta]wwx", ",", "\[Delta]wwy", ",", "\[Phi]\[Phi]", ",", "\[Phi]\[Phi]x", ",", "\[Phi]\[Phi]y", ",", "\[Delta]\[Phi]\[Phi]", ",", "\[Delta]\[Phi]\[Phi]x", ",", "\[Delta]\[Phi]\[Phi]y", ",", "\[CapitalTheta]\[CapitalTheta]", ",", "\[CapitalTheta]\[CapitalTheta]x", ",", "\[CapitalTheta]\[CapitalTheta]y", ",", "\[Delta]\[CapitalTheta]\[CapitalTheta]", ",", "\[Delta]\[CapitalTheta]\[CapitalTheta]x", ",", "\[Delta]\[CapitalTheta]\[CapitalTheta]y", ",", "\[Psi]\[Psi]", ",", "\[Psi]\[Psi]x", ",", "\[Psi]\[Psi]y", ",", "\[Delta]\[Psi]\[Psi]", ",", "\[Delta]\[Psi]\[Psi]x", ",", "\[Delta]\[Psi]\[Psi]y", ",", "aa", ",", "\[Delta]aa", ",", "\[Nu]21", ",", "DD", ",", "GGG", ",", "Nxx", ",", "Nyy", ",", "Nxy", ",", "Nyx", ",", "Mxx", ",", "Myy", ",", "Mxy", ",", "Qx", ",", "Qy", ",", "\[Delta]wint", ",", "\[Delta]wext", ",", "\[Delta]wext2", ",", "x1", ",", "y1", ",", "x2", ",", "y2", ",", "\[Xi]0", ",", "\[Eta]0", ",", "\[Xi]1", ",", "\[Eta]1", ",", "\[Delta]WW", ",", "AA", ",", "sigxx", ",", "sigyy", ",", "\[IndentingNewLine]", "sigxy", ",", "sigxz", ",", "sigyz"}], "}"}] , ",", "\[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]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "number", " ", "of", " ", "nodes", " ", "in", " ", "element"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"n\[Eta]", ",", "n\[Xi]"}], "}"}], "=", RowBox[{"Dimensions", "[", "node", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"nne", " ", "=", RowBox[{"n\[Xi]", "*", "n\[Eta]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"shape", " ", "functions"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"NN", "=", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n\[Xi]", ",", "\[Xi]"}], "}"}], ",", RowBox[{"{", RowBox[{"n\[Eta]", ",", "\[Eta]"}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"rule", "=", RowBox[{"RULE2", "[", RowBox[{"NN", ",", RowBox[{"Flatten", "[", "node", "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "tranformation", " ", "to", " ", "material", " ", "coordinates"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"FFT", " ", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"i\[Xi]", "*", "h\[Xi]"}], ",", RowBox[{"i\[Eta]", "*", "h\[Eta]"}], ",", RowBox[{"i\[Zeta]", "*", "h\[Zeta]"}]}], "}"}], " ", "/.", "rule"}], ")"}], "[", RowBox[{"[", RowBox[{ RowBox[{"1", ";;", "2"}], ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFT", "=", RowBox[{"FFT", "/.", RowBox[{"{", RowBox[{ RowBox[{"\[Xi]", "\[Rule]", RowBox[{"1", "/", "2"}]}], ",", RowBox[{"\[Eta]", "\[Rule]", RowBox[{"1", "/", "2"}]}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"dNN", "=", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"D", "[", RowBox[{"NN", ",", "\[Xi]"}], "]"}], ",", RowBox[{"D", "[", RowBox[{"NN", ",", "\[Eta]"}], "]"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"FFTI", "=", RowBox[{"Inverse", "[", "FFT", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"Nx", ",", "Ny"}], "}"}], "=", RowBox[{"Transpose", "[", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"FFTI", ".", "#"}], "&"}], ",", "dNN"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"d\[CapitalOmega]", "=", RowBox[{"Det", "[", "FFT", "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"aa", "=", RowBox[{ RowBox[{"Array", "[", RowBox[{"x", ",", "nne"}], "]"}], "/.", "rule"}]}], ";", " ", RowBox[{"xx", "=", RowBox[{"NN", " ", ".", " ", "aa"}]}], ";", "\[IndentingNewLine]", RowBox[{"aa", "=", RowBox[{ RowBox[{"Array", "[", RowBox[{"y", ",", "nne"}], "]"}], "/.", "rule"}]}], ";", " ", RowBox[{"yy", "=", RowBox[{"NN", " ", ".", " ", "aa"}]}], ";", "\[IndentingNewLine]", RowBox[{"aa", "=", RowBox[{ RowBox[{"Array", "[", RowBox[{"ux", ",", "nne"}], "]"}], "/.", "rule"}]}], ";", " ", RowBox[{"\[Delta]aa", "=", RowBox[{"aa", "/.", "\[Delta]rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"uu", "=", RowBox[{"NN", " ", ".", " ", "aa"}]}], ";", " ", RowBox[{"\[Delta]uu", "=", RowBox[{"NN", " ", ".", " ", "\[Delta]aa"}]}], ";", RowBox[{"uux", "=", RowBox[{"Nx", " ", ".", " ", "aa"}]}], ";", " ", RowBox[{"\[Delta]uux", "=", RowBox[{"Nx", " ", ".", " ", "\[Delta]aa"}]}], ";", RowBox[{"uuy", "=", RowBox[{"Ny", " ", ".", " ", "aa"}]}], ";", " ", RowBox[{"\[Delta]uuy", "=", RowBox[{"Ny", " ", ".", " ", "\[Delta]aa"}]}], ";", "\[IndentingNewLine]", RowBox[{"aa", "=", RowBox[{ RowBox[{"Array", "[", RowBox[{"uy", ",", "nne"}], "]"}], "/.", "rule"}]}], ";", " ", RowBox[{"\[Delta]aa", "=", RowBox[{"aa", "/.", "\[Delta]rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"vv", "=", RowBox[{"NN", " ", ".", " ", "aa"}]}], ";", " ", RowBox[{"\[Delta]vv", "=", RowBox[{"NN", " ", ".", " ", "\[Delta]aa"}]}], ";", RowBox[{"vvx", "=", RowBox[{"Nx", " ", ".", " ", "aa"}]}], ";", " ", RowBox[{"\[Delta]vvx", "=", RowBox[{"Nx", " ", ".", " ", "\[Delta]aa"}]}], ";", RowBox[{"vvy", "=", RowBox[{"Ny", " ", ".", " ", "aa"}]}], ";", " ", RowBox[{"\[Delta]vvy", "=", RowBox[{"Ny", " ", ".", " ", "\[Delta]aa"}]}], ";", "\[IndentingNewLine]", RowBox[{"aa", "=", RowBox[{ RowBox[{"Array", "[", RowBox[{"uz", ",", "nne"}], "]"}], "/.", "rule"}]}], ";", " ", RowBox[{"\[Delta]aa", "=", RowBox[{"aa", "/.", "\[Delta]rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"ww", "=", RowBox[{"NN", " ", ".", " ", "aa"}]}], ";", " ", RowBox[{"\[Delta]ww", "=", RowBox[{"NN", " ", ".", " ", "\[Delta]aa"}]}], ";", RowBox[{"wwx", "=", RowBox[{"Nx", " ", ".", " ", "aa"}]}], ";", " ", RowBox[{"\[Delta]wwx", "=", RowBox[{"Nx", " ", ".", " ", "\[Delta]aa"}]}], ";", RowBox[{"wwy", "=", RowBox[{"Ny", " ", ".", " ", "aa"}]}], ";", " ", RowBox[{"\[Delta]wwy", "=", RowBox[{"Ny", " ", ".", " ", "\[Delta]aa"}]}], ";", "\[IndentingNewLine]", RowBox[{"aa", "=", RowBox[{ RowBox[{"Array", "[", RowBox[{"\[CapitalTheta]x", ",", "nne"}], "]"}], "/.", "rule"}]}], ";", " ", RowBox[{"\[Delta]aa", "=", RowBox[{"aa", "/.", "\[Delta]rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Phi]\[Phi]", "=", RowBox[{"NN", " ", ".", " ", "aa"}]}], ";", " ", RowBox[{"\[Delta]\[Phi]\[Phi]", "=", RowBox[{"NN", " ", ".", " ", "\[Delta]aa"}]}], ";", RowBox[{"\[Phi]\[Phi]x", "=", RowBox[{"Nx", " ", ".", " ", "aa"}]}], ";", " ", RowBox[{"\[Delta]\[Phi]\[Phi]x", "=", RowBox[{"Nx", " ", ".", " ", "\[Delta]aa"}]}], ";", RowBox[{"\[Phi]\[Phi]y", "=", RowBox[{"Ny", " ", ".", " ", "aa"}]}], ";", " ", RowBox[{"\[Delta]\[Phi]\[Phi]y", "=", RowBox[{"Ny", " ", ".", " ", "\[Delta]aa"}]}], ";", "\[IndentingNewLine]", RowBox[{"aa", "=", RowBox[{ RowBox[{"Array", "[", RowBox[{"\[CapitalTheta]y", ",", "nne"}], "]"}], "/.", "rule"}]}], ";", " ", RowBox[{"\[Delta]aa", "=", RowBox[{"aa", "/.", "\[Delta]rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[CapitalTheta]\[CapitalTheta]", "=", RowBox[{"NN", " ", ".", " ", "aa"}]}], ";", " ", RowBox[{"\[Delta]\[CapitalTheta]\[CapitalTheta]", "=", RowBox[{"NN", " ", ".", " ", "\[Delta]aa"}]}], ";", RowBox[{"\[CapitalTheta]\[CapitalTheta]x", "=", RowBox[{"Nx", " ", ".", " ", "aa"}]}], ";", " ", RowBox[{"\[Delta]\[CapitalTheta]\[CapitalTheta]x", "=", RowBox[{"Nx", " ", ".", " ", "\[Delta]aa"}]}], ";", RowBox[{"\[CapitalTheta]\[CapitalTheta]y", "=", RowBox[{"Ny", " ", ".", " ", "aa"}]}], ";", " ", RowBox[{"\[Delta]\[CapitalTheta]\[CapitalTheta]y", "=", RowBox[{"Ny", " ", ".", " ", "\[Delta]aa"}]}], ";", "\[IndentingNewLine]", RowBox[{"aa", "=", RowBox[{ RowBox[{"Array", "[", RowBox[{"\[CapitalTheta]z", ",", "nne"}], "]"}], "/.", "rule"}]}], ";", " ", RowBox[{"\[Delta]aa", "=", RowBox[{"aa", "/.", "\[Delta]rule"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Psi]\[Psi]", "=", RowBox[{"NN", " ", ".", " ", "aa"}]}], ";", " ", RowBox[{"\[Delta]\[Psi]\[Psi]", "=", RowBox[{"NN", " ", ".", " ", "\[Delta]aa"}]}], ";", RowBox[{"\[Psi]\[Psi]x", "=", RowBox[{"Nx", " ", ".", " ", "aa"}]}], ";", " ", RowBox[{"\[Delta]\[Psi]\[Psi]x", "=", RowBox[{"Nx", " ", ".", " ", "\[Delta]aa"}]}], ";", RowBox[{"\[Psi]\[Psi]y", "=", RowBox[{"Ny", " ", ".", " ", "aa"}]}], ";", " ", RowBox[{"\[Delta]\[Psi]\[Psi]y", "=", RowBox[{"Ny", " ", ".", " ", "\[Delta]aa"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"stress", " ", "resultants"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"\[Nu]21", "=", RowBox[{ RowBox[{"E2", "/", "E1"}], "*", "\[Nu]12"}]}], ";", "\[IndentingNewLine]", RowBox[{"DD", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], ")"}], "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]12", "*", "\[Nu]21"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"HH", "=", RowBox[{"tt", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]12", "*", "\[Nu]21"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Nxx", "=", RowBox[{"HH", "*", "E1", "*", RowBox[{"(", RowBox[{"uux", "+", RowBox[{"\[Nu]21", "*", "vvy"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Nyy", "=", RowBox[{"HH", "*", "E2", "*", RowBox[{"(", RowBox[{"vvy", "+", RowBox[{"\[Nu]12", "*", "uux"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Nxy", "=", RowBox[{"G12", "*", "tt", "*", RowBox[{"(", RowBox[{"vvx", "-", "\[Psi]\[Psi]"}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Nyx", "=", RowBox[{"G12", "*", "tt", "*", RowBox[{"(", RowBox[{"uuy", "+", "\[Psi]\[Psi]"}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Mxx", "=", RowBox[{"DD", "*", "E1", "*", RowBox[{"(", RowBox[{"\[CapitalTheta]\[CapitalTheta]x", "-", RowBox[{"\[Nu]21", "*", "\[Phi]\[Phi]y"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Myy", "=", RowBox[{"DD", "*", "E2", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Phi]\[Phi]y"}], "+", RowBox[{"\[Nu]12", "*", "\[CapitalTheta]\[CapitalTheta]x"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Mxy", "=", RowBox[{"G12", "*", RowBox[{ RowBox[{"tt", "^", "3"}], "/", "12"}], "*", RowBox[{"(", RowBox[{ "\[CapitalTheta]\[CapitalTheta]y", "-", "\[Phi]\[Phi]x"}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Qx", "=", RowBox[{"G13", "*", "tt", "*", RowBox[{"(", RowBox[{"wwx", "+", "\[CapitalTheta]\[CapitalTheta]"}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Qy", "=", RowBox[{"G23", "*", "tt", "*", RowBox[{"(", RowBox[{"wwy", "-", "\[Phi]\[Phi]"}], ")"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"MODE", "\[Equal]", "POSTP"}], ",", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"post", " ", "processing"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"AA", "=", RowBox[{"1", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Nu]12", "*", "\[Nu]21"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", " ", "stresses", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"sigxx", "=", RowBox[{"E1", "*", "AA", "*", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"uux", "+", RowBox[{"\[Nu]21", "*", "vvy"}]}], ")"}], "+", RowBox[{"zz", "*", RowBox[{"(", RowBox[{"\[CapitalTheta]\[CapitalTheta]x", "-", RowBox[{"\[Nu]21", "*", "\[Phi]\[Phi]y"}]}], ")"}]}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"sigyy", "=", RowBox[{"E2", "*", "AA", "*", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"vvy", "+", RowBox[{"\[Nu]12", "*", "uux"}]}], ")"}], "+", RowBox[{"zz", "*", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Phi]\[Phi]y"}], "+", RowBox[{ "\[Nu]12", "*", "\[CapitalTheta]\[CapitalTheta]x"}]}], ")"}]}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"sigxy", "=", RowBox[{"G12", "*", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"uuy", "+", "vvx"}], ")"}], "+", RowBox[{"zz", "*", RowBox[{"(", RowBox[{ "\[CapitalTheta]\[CapitalTheta]y", "-", "\[Phi]\[Phi]x"}], ")"}]}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"sigxz", "=", RowBox[{"G13", "*", RowBox[{"(", RowBox[{"wwx", "+", "\[CapitalTheta]\[CapitalTheta]"}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"sigyz", "=", RowBox[{"G23", "*", RowBox[{"(", RowBox[{"wwy", "-", "\[Phi]\[Phi]"}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "xx"}], ",", RowBox[{"y", "->", "yy"}], ",", RowBox[{"u", "\[Rule]", "uu"}], ",", RowBox[{"v", "->", "vv"}], ",", RowBox[{"w", "->", "ww"}], ",", RowBox[{"NXX", "\[Rule]", "Nxx"}], ",", RowBox[{"NXY", "->", "Nxy"}], ",", RowBox[{"NYX", "->", "Nyx"}], ",", RowBox[{"NYY", "->", "Nyy"}], ",", RowBox[{"MXX", "\[Rule]", "Mxx"}], ",", RowBox[{"MXY", "->", "Mxy"}], ",", RowBox[{"MYY", "->", "Myy"}], ",", RowBox[{"QX", "\[Rule]", "Qx"}], ",", RowBox[{"QY", "->", "Qy"}], ",", RowBox[{"SXX", "\[Rule]", "sigxx"}], ",", RowBox[{"SYY", "\[Rule]", "sigyy"}], ",", RowBox[{"SXY", "\[Rule]", "sigxy"}], ",", "\[IndentingNewLine]", RowBox[{"SXZ", "\[Rule]", "sigxz"}], ",", RowBox[{"SYZ", "\[Rule]", "sigyz"}]}], "}"}], " ", "]"}]}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"MODE", "\[Equal]", "DISP"}], ",", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"virtual", " ", "work"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]wint", "=", RowBox[{"-", RowBox[{ RowBox[{"{", RowBox[{"\[Delta]uux", ",", "\[Delta]vvy", ",", RowBox[{"\[Delta]vvx", "-", "\[Delta]\[Psi]\[Psi]"}], ",", RowBox[{"\[Delta]uuy", "+", "\[Delta]\[Psi]\[Psi]"}]}], "}"}], ".", RowBox[{"{", RowBox[{"Nxx", ",", "Nyy", ",", "Nxy", ",", "Nyx"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "+=", RowBox[{"-", RowBox[{ RowBox[{"{", RowBox[{"\[Delta]\[CapitalTheta]\[CapitalTheta]x", ",", RowBox[{"-", "\[Delta]\[Phi]\[Phi]y"}], ",", RowBox[{ "\[Delta]\[CapitalTheta]\[CapitalTheta]y", "-", "\[Delta]\[Phi]\[Phi]x"}]}], "}"}], ".", RowBox[{"{", RowBox[{"Mxx", ",", "Myy", ",", "Mxy"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wint", "+=", RowBox[{"-", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ "\[Delta]wwx", "+", "\[Delta]\[CapitalTheta]\[CapitalTheta]"}], ",", RowBox[{"\[Delta]wwy", "-", "\[Delta]\[Phi]\[Phi]"}]}], "}"}], ".", RowBox[{"{", RowBox[{"Qx", ",", "Qy"}], "}"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "=", RowBox[{ RowBox[{"{", RowBox[{"\[Delta]uu", ",", "\[Delta]vv"}], "}"}], ".", RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"fx", ",", "fy"}], "}"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "xx"}], ",", RowBox[{"y", "\[Rule]", "yy"}]}], "}"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext", "+=", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]\[Phi]\[Phi]", ",", "\[Delta]\[CapitalTheta]\[CapitalTheta]", ",", "\[Delta]\[Psi]\[Psi]"}], "}"}], ".", RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{"mx", ",", "my", ",", "mz"}], "}"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "xx"}], ",", RowBox[{"y", "\[Rule]", "yy"}]}], "}"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"QUAD", "[", RowBox[{"LINE7", ",", RowBox[{"QUAD", "[", RowBox[{"LINE7", ",", RowBox[{ RowBox[{"(", RowBox[{"\[Delta]wint", "+", "\[Delta]wext"}], ")"}], "*", "d\[CapitalOmega]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[Xi]", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "1", "}"}]}], "}"}]}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[Eta]", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "0", "}"}], ",", RowBox[{"{", "1", "}"}]}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]wext2", "=", RowBox[{"\[Delta]ww", "*", RowBox[{"(", RowBox[{ RowBox[{"fz", "[", RowBox[{"[", "1", "]"}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "xx"}], ",", RowBox[{"y", "\[Rule]", "yy"}]}], "}"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"x1", ",", "y1"}], "}"}], "=", RowBox[{"XY", "[", RowBox[{"node", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"x2", ",", "y2"}], "}"}], "=", RowBox[{"XY", "[", RowBox[{"node", "[", RowBox[{"[", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}]}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"fz", "[", RowBox[{"[", RowBox[{"2", ",", "1", ",", "1"}], "]"}], "]"}], "\[LessEqual]", "x1"}], ",", RowBox[{"\[Xi]0", "=", "0"}], ",", RowBox[{"\[Xi]0", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fz", "[", RowBox[{"[", RowBox[{"2", ",", "1", ",", "1"}], "]"}], "]"}], "-", "x1"}], ")"}], "/", RowBox[{"(", RowBox[{"x2", "-", "x1"}], ")"}]}]}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"fz", "[", RowBox[{"[", RowBox[{"2", ",", "1", ",", "2"}], "]"}], "]"}], "\[LessEqual]", "y1"}], ",", RowBox[{"\[Eta]0", "=", "0"}], ",", RowBox[{"\[Eta]0", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fz", "[", RowBox[{"[", RowBox[{"2", ",", "1", ",", "2"}], "]"}], "]"}], "-", "y1"}], ")"}], "/", RowBox[{"(", RowBox[{"y2", "-", "y1"}], ")"}]}]}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"fz", "[", RowBox[{"[", RowBox[{"2", ",", RowBox[{"-", "1"}], ",", "1"}], "]"}], "]"}], "\[GreaterEqual]", "x2"}], ",", RowBox[{"\[Xi]1", "=", "1"}], ",", RowBox[{"\[Xi]1", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fz", "[", RowBox[{"[", RowBox[{"2", ",", RowBox[{"-", "1"}], ",", "1"}], "]"}], "]"}], "-", "x1"}], ")"}], "/", RowBox[{"(", RowBox[{"x2", "-", "x1"}], ")"}]}]}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"fz", "[", RowBox[{"[", RowBox[{"2", ",", RowBox[{"-", "1"}], ",", "2"}], "]"}], "]"}], "\[GreaterEqual]", "y2"}], ",", RowBox[{"\[Eta]1", "=", "1"}], ",", RowBox[{"\[Eta]1", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"fz", "[", RowBox[{"[", RowBox[{"2", ",", RowBox[{"-", "1"}], ",", "2"}], "]"}], "]"}], "-", "y1"}], ")"}], "/", RowBox[{"(", RowBox[{"y2", "-", "y1"}], ")"}]}]}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "+=", RowBox[{"QUAD", "[", RowBox[{"LINE7", ",", RowBox[{"QUAD", "[", RowBox[{"LINE7", ",", RowBox[{"\[Delta]wext2", "*", "d\[CapitalOmega]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[Xi]", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[Xi]0", "}"}], ",", RowBox[{"{", "\[Xi]1", "}"}]}], "}"}]}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[Eta]", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[Eta]0", "}"}], ",", RowBox[{"{", "\[Eta]1", "}"}]}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", "\[Delta]WW", "]"}]}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}], " ", "/;", RowBox[{"(", RowBox[{ RowBox[{"MODE", "==", " ", "DISP"}], " ", "||", " ", RowBox[{"MODE", "==", " ", "POSTP"}]}], " ", ")"}]}]}], ";"}], "\[IndentingNewLine]", "\[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}, {3.6294628543371735`*^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}}, CellLabel-> "In[138]:=",ExpressionUUID->"21b78e0a-a635-45eb-965f-598ce75a0714"] }, Closed]], Cell[CellGroupData[{ Cell["SHELL ELEMENT defs ", "Subsection", CellChangeTimes->{{3.6303896070263977`*^9, 3.6303896080872*^9}},ExpressionUUID->"4c5b683b-05a0-4d39-a5ee-9bcaeb2e4e23"], Cell[BoxData[ RowBox[{"\[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[{"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]"}]}]], "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}, {3.6302476464502306`*^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}}, CellLabel-> "In[143]:=",ExpressionUUID->"75aebc1b-bef9-4f49-90a9-6a83763efcdc"] }, Closed]], Cell[CellGroupData[{ Cell["SOLID ELEMENT defs ", "Subsection", CellChangeTimes->{{3.629430162287647*^9, 3.6294301631768484`*^9}},ExpressionUUID->"a951088d-2efc-45c8-868e-\ 89e67a144fab"], 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]", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SOLID", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "EE_", ",", "\[Nu]\[Nu]_", ",", "\[Alpha]\[Alpha]_", ",", "kk_"}], "}"}], ",", RowBox[{"{", RowBox[{ "fX_", ",", "fY_", ",", "fZ_", ",", "ss_", ",", "\[CurlyTheta]0_"}], "}"}]}], "}"}], ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"I1_", ",", "I2_", ",", "I3_", ",", "I4_"}], "}"}], "]"}]}], "}"}], ",", "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[{"I1", ",", "I2", ",", "I3", ",", "I4"}], "}"}]}], ";", "\[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]", "]"}]}], ";"}], "\[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}}, CellLabel-> "In[145]:=",ExpressionUUID->"03ac8030-724a-407f-b1af-d0fe2dd395fc"] }, 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->"a0137111-1c1c-48db-a3dd-\ 45e6822bfa37"], 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}}, CellLabel-> "In[150]:=",ExpressionUUID->"d8f05811-c435-43b0-8866-a99cf7ca7694"] }, 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->"a3fe9042-d10d-4ce6-8f91-\ abffc26873e2"], Cell[CellGroupData[{ Cell["SOLVER defs", "Subsection",ExpressionUUID->"62e31888-f3d3-4401-8886-77b1776935f2"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"Clear", "[", "SOLVE", "]"}], ";"}], "\[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[{ 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[{ 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[{ 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]", RowBox[{ 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[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"NONL", ",", "rule_"}], "}"}], ",", 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", ",", RowBox[{"DampingFactor", "\[Rule]", "4"}], ",", RowBox[{"AccuracyGoal", "\[Rule]", "2"}], ",", RowBox[{"PrecisionGoal", "\[Rule]", "2"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", "sol", "]"}]}]}], "]"}]}], ";"}], " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", 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[{"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[{ 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]"}], "\[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[{ RowBox[{"{", RowBox[{"val", ",", "vec"}], "}"}], "=", RowBox[{"Eigensystem", "[", RowBox[{ RowBox[{"Inverse", "[", "MM", "]"}], ".", "KK"}], "]"}]}], ";"}], "*)"}], "\[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[{ 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]", "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "p_"}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "\[Delta]WW", ",", "dof", ",", "\[Delta]dof", ",", "equ", ",", "sol", ",", "KK", ",", "KK0", ",", "KK1", ",", "val", ",", "vec", ",", "modes", ",", "prule", ",", "list"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"first", " ", "ignoring", " ", "the", " ", "coupling"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"prule", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"Simplify", "[", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "prule"}], "}"}], ",", "#", ",", "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[{"prule", "=", RowBox[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{"equ", "\[Equal]", "0"}], "]"}], ",", "dof"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"then", " ", "considering", " ", "the", " ", "coupling"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Delta]WW", "=", RowBox[{"Simplify", "[", RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{ RowBox[{"{", RowBox[{"STAB", ",", "prule"}], "}"}], ",", "#", ",", "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[{"KK", " ", "=", RowBox[{"D", "[", RowBox[{"equ", ",", RowBox[{"{", "dof", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"KK0", "=", " ", RowBox[{"KK", " ", "/.", " ", RowBox[{"p", "\[Rule]", "0"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"KK1", " ", "=", RowBox[{"D", "[", RowBox[{"KK", " ", ",", "p"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"val", ",", "vec"}], "}"}], "=", RowBox[{"Simplify", "[", RowBox[{"Eigensystem", "[", RowBox[{ RowBox[{"Inverse", "[", "KK0", "]"}], ".", "KK1"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"list", "=", RowBox[{"Select", "[", RowBox[{ RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{"val", ",", "vec"}], "}"}], "]"}], ",", RowBox[{ RowBox[{"Not", "[", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], "===", "0"}], "]"}], "&"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"p", "[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "\[Rule]", RowBox[{ RowBox[{"-", "1"}], "/", 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}}, CellLabel-> "In[155]:=",ExpressionUUID->"238ce239-4374-4fc9-b278-90ffdd52d472"] }, 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->"9b0e61aa-18e2-44e2-9e0c-\ 9a1ec126de58"], Cell[CellGroupData[{ Cell["LINK RULE 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}},ExpressionUUID->"2f278e47-8352-44fb-a02b-\ 1d00ed264fcf"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"LINK", "[", RowBox[{"{", RowBox[{"I1_", ",", "I2_"}], "}"}], "]"}], ":=", "\[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]"}]], "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}, CellLabel-> "In[170]:=",ExpressionUUID->"58408154-0068-40bf-abd1-f54e461cb711"] }, Closed]], Cell[CellGroupData[{ Cell["TOOL defs", "Subsection",ExpressionUUID->"33730347-6ba2-4e0c-820c-45645621c710"], 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[171]:=",ExpressionUUID->"2c23a70f-f643-4a73-8234-932f9829f2c7"] }, Closed]], Cell[CellGroupData[{ Cell["REFINE defs", "Subsection", CellChangeTimes->{{3.7555369693812027`*^9, 3.7555369706487265`*^9}},ExpressionUUID->"8e45a61d-9be5-4264-80ec-\ 530880c7b4d5"], 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[{"{", "ff_", "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"EE", " ", "/.", "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[{"EE", " ", "/.", "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[{"{", 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[{ 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[{"{", 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", ",", 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[{"Triangle", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"TWODIM", ",", "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[{"TWODIM", ",", "mat", ",", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"n4", ",", "n2", ",", RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"TWODIM", ",", "mat", ",", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"n6", ",", "n5", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"TWODIM", ",", "mat", ",", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"n4", ",", "n5", ",", "n6"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"REF", "[", RowBox[{"{", RowBox[{"PLANE", ",", "mat_", ",", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", 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]", 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_", ",", "n4_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", "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[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n5", ",", "n2", ",", "n9", ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n4"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n8", ",", "n9", ",", "n3", ",", RowBox[{"n7", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n4"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLANE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n9", ",", "n6", ",", "n7", ",", "n4"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[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[{"PLATE", ",", "mat_", ",", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}]}], "}"}], "]"}], ":=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLATE", ",", "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[{"PLATE", ",", "mat", ",", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"n4", ",", "n2", ",", RowBox[{"n5", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n3"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", "mat", ",", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"n6", ",", "n5", ",", "n3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", "mat", ",", RowBox[{"Triangle", "[", 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[{"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[{"n5", ",", "n2", ",", "n9", ",", RowBox[{"n6", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n2", ",", "n4"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n8", ",", "n9", ",", "n3", ",", RowBox[{"n7", "=", RowBox[{"NEWNODE", "[", RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"n3", ",", "n4"}], "}"}], "]"}], "]"}]}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"PLATE", ",", "mat", ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n9", ",", "n6", ",", "n7", ",", "n4"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[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[{"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]", RowBox[{"{", RowBox[{"SOLID", ",", "mat", ",", RowBox[{"Tetrahedron", "[", RowBox[{"{", RowBox[{"n5", ",", "n8", ",", "n9", ",", "n10"}], "}"}], "]"}]}], "}"}]}], "\[IndentingNewLine]", " ", "}"}]}], ";"}], "\[IndentingNewLine]", "\[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[{"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]"}]}]], "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}}, CellLabel-> "In[175]:=",ExpressionUUID->"8cb28c0c-5bf5-4bbc-ba39-397bb5765537"] }, Closed]], Cell[CellGroupData[{ Cell["FORMAT defs", "Subsection", CellChangeTimes->{{3.687518097184434*^9, 3.687518099119545*^9}},ExpressionUUID->"cf156b2c-5cd2-49a1-ac11-\ e390717af027"], Cell[BoxData[ RowBox[{"\[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[{"ele_", ",", "fun_"}], "}"}], "]"}], ":=", RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "DISP", "}"}], ",", 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[{"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[{"{", "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[{ RowBox[{"{", RowBox[{"STAB", ",", "Null"}], "}"}], ",", "#", ",", "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]", 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[{"{", "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", "]"}]}], ";", 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]", "\[IndentingNewLine]", RowBox[{ RowBox[{"SHAPERULES", ":=", RowBox[{"{", RowBox[{ RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}], "\[RuleDelayed]", RowBox[{"{", RowBox[{ RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3"}], "}"}], "]"}], ",", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"n3", ",", "n2", ",", "n4"}], "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[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[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Last", "[", "#", "]"}], "&"}], ",", "ele"}], "]"}], " ", "/.", "SHAPERULES"}]}], "]"}]}], ";", "\[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[{"STYLE", "[", "a_", "]"}], ":=", "None"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STYLE", "[", "BEAM", "]"}], ":=", "Red"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STYLE", "[", "BAR", "]"}], ":=", "Green"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STYLE", "[", "RIGID", "]"}], ":=", "Black"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STYLE", "[", "FORCE", "]"}], ":=", "Black"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STYLE", "[", "SOLID", "]"}], ":=", "Gray"}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"DISP", "[", 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[{ RowBox[{"fun", "[", RowBox[{"[", RowBox[{";;", ",", "1", ",", "crds"}], "]"}], "]"}], "+", RowBox[{"fun", "[", RowBox[{"[", RowBox[{";;", ",", "2", ",", "crds"}], "]"}], "]"}]}], " ", ",", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Style", "[", RowBox[{ RowBox[{"Last", "[", "#", "]"}], ",", RowBox[{"STYLE", "[", RowBox[{"First", "[", "#", "]"}], "]"}]}], "]"}], "&"}], ",", "ele"}], "]"}], " ", "/.", "SHAPERULES"}]}], "]"}]}], ";", "\[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]", "All"}], ",", RowBox[{"SphericalRegion", "\[Rule]", "True"}]}], "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"STRESS", "[", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}], "]"}], ":=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], "===", "PLANE"}], ",", 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_"}], "}"}], ",", "elements_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "pick", ",", "labs", ",", "crds", ",", "stress", ",", "min", ",", "max", ",", "rule"}], "}"}], ",", "\[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[{"stress", " ", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"\[Delta]W", "[", RowBox[{"STRES", ",", "#", ",", "fun"}], "]"}], "&"}], ",", "ele"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"min", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Min", "[", RowBox[{"stress", "[", RowBox[{"[", RowBox[{";;", ",", RowBox[{"el", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"el", "[", RowBox[{"[", "2", "]"}], "]"}]}], " ", "]"}], "]"}], " ", "]"}], ",", RowBox[{"{", RowBox[{"el", ",", "elements"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"max", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Max", "[", RowBox[{"stress", "[", RowBox[{"[", RowBox[{";;", ",", RowBox[{"el", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"el", "[", RowBox[{"[", "2", "]"}], "]"}]}], " ", "]"}], "]"}], " ", "]"}], ",", RowBox[{"{", RowBox[{"el", ",", "elements"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"rule", " ", ":=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}], "\[RuleDelayed]", " ", RowBox[{"Triangle", "[", 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[{ RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "}"}], "]"}], "\[RuleDelayed]", " ", RowBox[{"Polygon", "[", 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[{"Table", "[", RowBox[{ RowBox[{"Show", "[", RowBox[{ RowBox[{"Graphics", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"COLORFUNCTION", "[", " ", RowBox[{ RowBox[{"min", "[", RowBox[{"[", "i", "]"}], "]"}], ",", RowBox[{"max", "[", RowBox[{"[", "i", "]"}], "]"}]}], "]"}], "[", RowBox[{"stress", "[", RowBox[{"[", RowBox[{"e", ",", RowBox[{"elements", "[", RowBox[{"[", RowBox[{"i", ",", "1"}], "]"}], "]"}], ",", RowBox[{"elements", "[", RowBox[{"[", RowBox[{"i", ",", "2"}], "]"}], "]"}]}], " ", "]"}], "]"}], " ", "]"}], ",", RowBox[{ RowBox[{"ele", "[", RowBox[{"[", RowBox[{"e", ",", "3"}], "]"}], "]"}], "/.", "rule"}]}], "}"}], ",", RowBox[{"{", RowBox[{"e", ",", "1", ",", RowBox[{"Length", "[", "ele", "]"}]}], "}"}]}], "]"}], "]"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"FrameLabel", "\[Rule]", "labs"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", RowBox[{"Length", "[", "elements", "]"}]}], "}"}]}], "]"}]}]}], " ", "\[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}}, CellLabel-> "In[200]:=",ExpressionUUID->"57817736-8cd5-4a82-9931-ff5ab8a99821"] }, Closed]], Cell[CellGroupData[{ Cell["POST defs", "Subsection",ExpressionUUID->"aaba6671-2f74-4543-a33d-188243a04d7c"], 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->"35b1ec2a-c74b-4377-aff5-\ 3f5da70010e2"] }, Closed]], Cell[CellGroupData[{ Cell["Pre needs 1005", "Subsection", CellChangeTimes->{{3.6337757022685537`*^9, 3.6337757351784363`*^9}, { 3.734064727558645*^9, 3.73406474989952*^9}, {3.7451438105166326`*^9, 3.745143811840375*^9}},ExpressionUUID->"a33dd732-f4fa-4999-a9bb-\ 507040049e63"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"enrich", " ", RowBox[{"Line", "[", RowBox[{"{", "a__", "}"}], "]"}]}], "-", "objects"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Clear", "[", RowBox[{"ENRICH", ",", "EXTRUDE"}], "]"}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", 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]", RowBox[{"(*", RowBox[{ RowBox[{"extrude", " ", "a", " ", "cross"}], "-", RowBox[{"section", " ", "in", " ", "z"}], "-", "direction"}], "*)"}], "\[IndentingNewLine]", 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]", 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]", 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->{{3.633673923685915*^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}}, CellLabel-> "In[221]:=",ExpressionUUID->"21df03e4-b4f1-45e8-b446-93bc1053ed8d"] }, 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}},ExpressionUUID->"3448e918-2634-476a-a298-\ 6aad0ef6b2ca"], 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[{ 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"}], "}"}], ",", 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[{"MESH3D", "[", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}], "]"}], ":=", RowBox[{"SHOW3D", "[", RowBox[{"MESH", ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SHOW3D", "[", RowBox[{"MESH", ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{ RowBox[{"Graphics3D", "[", " ", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{"MESH", ",", "#", ",", "fun"}], " ", "]"}], "&"}], ",", "ele"}], "]"}], ",", "1"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}]}], ",", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"SphericalRegion", "\[Rule]", "True"}], ",", RowBox[{"Lighting", "\[Rule]", "\"\\""}]}], "]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SHOW3D", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"ele_", ",", "fun_"}], "}"}]}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{ RowBox[{"Graphics3D", "[", " ", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale"}], "}"}], ",", "#", ",", "fun"}], " ", "]"}], "&"}], ",", "ele"}], "]"}], ",", "1"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}]}], ",", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"SphericalRegion", "\[Rule]", "True"}], ",", RowBox[{"Lighting", "\[Rule]", "\"\\""}]}], "]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"ad", " ", "hoc", " ", "geometry"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", 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[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"CORNERE", ",", "dat_", ",", "nod_"}], "}"}], ",", "fun_"}], "]"}], ":=", "0"}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", 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[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"PIVOTA", ",", "dat_", ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_"}], "}"}], "]"}]}], "}"}], ",", "fun_"}], "]"}], ":=", "0"}], ";"}], "\[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[{"\[Delta]W", "[", RowBox[{"DISP", ",", RowBox[{"{", RowBox[{"SLEEVEA", ",", "dat_"}], "}"}], ",", "fun_"}], "]"}], ":=", "0"}], ";"}], "\[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[{ "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]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"BEAM", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", RowBox[{"d_Real", ",", "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[{"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[{"force", " ", "element"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", 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[{"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]", RowBox[{ RowBox[{ RowBox[{"GRAPHICS", "[", RowBox[{ RowBox[{"{", RowBox[{"DISP", ",", "scale_"}], "}"}], ",", RowBox[{"{", RowBox[{"PLATE", ",", RowBox[{"{", RowBox[{"mat_", ",", RowBox[{"{", "t_", "}"}], ",", "for_"}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"n1_", ",", "n2_", ",", "n3_", ",", "n4_"}], "}"}], "]"}]}], "}"}], ",", "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"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"NN", "=", RowBox[{"LAGRANGE", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "\[Alpha]"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "\[Beta]"}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"r0", "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], ",", "1"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"u", ",", "v", ",", "w"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], ",", "2"}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"\[Phi]", ",", "\[Theta]", ",", "\[Psi]"}], "}"}], "=", RowBox[{"NN", ".", RowBox[{"fun", "[", RowBox[{"[", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", "n2", ",", "n3", ",", "n4"}], "}"}], ",", "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[{ RowBox[{ RowBox[{"-", "t"}], "/", "2"}], "+", RowBox[{"en", "*", "\[Gamma]", "*", "t"}]}]}], ";", "\[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]", ",", "\[Gamma]"}], "}"}], "\[Rule]", "#"}], "]"}]}], "&"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "1"}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Gray", ",", RowBox[{"Opacity", "[", "0.5", "]"}], ",", RowBox[{"EdgeForm", "[", "]"}], ",", RowBox[{"Hexahedron", "[", "pp", "]"}], ",", "Blue", ",", RowBox[{"PointSize", "[", "Tiny", "]"}], ",", RowBox[{"Point", "[", "pp", "]"}]}], "}"}]}]}], " ", "]"}]}], ";"}], "\[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}, 3.734064961166012*^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}}, CellLabel-> "In[227]:=",ExpressionUUID->"ce5a6d71-b118-4f01-aee3-41780e32359c"] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Non-linear analysis (week 5)", "Chapter", 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, {3.7554410408893995`*^9, 3.755441045372862*^9}, {3.7561874728636427`*^9, 3.756187479099147*^9}, { 3.756800970295746*^9, 3.7568009765599184`*^9}, {3.757391032232335*^9, 3.7573910408865547`*^9}},ExpressionUUID->"5aad174e-f21b-4f96-88eb-\ a7b170e89253"], Cell[CellGroupData[{ Cell["Example 4.1 (Green-Lagrange)", "Subsubsection", CellChangeTimes->{{3.4957958636017337`*^9, 3.4957958737573338`*^9}, 3.69408382394532*^9, 3.694084089815693*^9, {3.6940841484257746`*^9, 3.694084150185777*^9}, {3.7254167515801773`*^9, 3.7254167541669474`*^9}, { 3.725416987103789*^9, 3.7254169906767716`*^9}, 3.725619282059034*^9},ExpressionUUID->"8803f6c4-92ba-4717-8bd8-\ d6494db0421e"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"u", "=", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", "\[Alpha]", "]"}], ",", RowBox[{"-", RowBox[{"Sin", "[", "\[Alpha]", "]"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Sin", "[", "\[Alpha]", "]"}], ",", RowBox[{"Cos", "[", "\[Alpha]", "]"}]}], "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "\[Epsilon]"}], ")"}], "x"}], ",", "y"}], "}"}]}], "-", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"Du", "=", RowBox[{"Transpose", "[", RowBox[{"D", "[", RowBox[{"u", ",", RowBox[{"{", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], "}"}]}], "]"}], "]"}]}], ";"}], " ", RowBox[{"(*", RowBox[{"gradient", " ", "of", " ", "u"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ee", " ", "=", " ", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"(", RowBox[{"Du", "+", RowBox[{"Transpose", "[", "Du", "]"}]}], ")"}], "/", "2"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"EE", " ", "=", " ", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"(", RowBox[{"Du", "+", RowBox[{"Transpose", "[", "Du", "]"}], "+", RowBox[{"Du", ".", RowBox[{"Transpose", "[", "Du", "]"}]}]}], ")"}], "/", "2"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"MatrixForm", "[", "ee", "]"}], "\[IndentingNewLine]", RowBox[{"MatrixForm", "[", "EE", "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.495713474266*^9, 3.4957134770428*^9}, 3.495713597974*^9, {3.4957194436786003`*^9, 3.4957194470638*^9}, 3.495795893194934*^9, {3.4957959444409337`*^9, 3.495796192746134*^9}, { 3.4957962416677337`*^9, 3.4957962923989334`*^9}, 3.694084081585681*^9, 3.694084242045906*^9, {3.694084289345972*^9, 3.6940843583160686`*^9}, { 3.6940844069261365`*^9, 3.694084439306182*^9}, {3.6940844961662617`*^9, 3.6940845097762804`*^9}, {3.694084642923224*^9, 3.6940846568036976`*^9}, { 3.6940847436238194`*^9, 3.6940847683238535`*^9}, {3.6940848043249044`*^9, 3.69408481552492*^9}, {3.7253630581342545`*^9, 3.7253631520878797`*^9}, { 3.725363205624776*^9, 3.725363236894071*^9}, {3.725363401957974*^9, 3.725363424991701*^9}, 3.725416765702466*^9, {3.7574854011577168`*^9, 3.757485434921479*^9}, {3.757485475942367*^9, 3.7574854976639504`*^9}, { 3.7574855307019567`*^9, 3.7574855486872835`*^9}}, CellLabel-> "In[497]:=",ExpressionUUID->"c8ba1c59-a822-4e43-b8a2-35651811f7c3"] }, Closed]], Cell[CellGroupData[{ Cell["Example 4.2 (truss)", "Subsubsection", CellChangeTimes->{ 3.560218382980301*^9, 3.62311554059295*^9, {3.6937172119879804`*^9, 3.6937172178979883`*^9}, {3.6937211383542433`*^9, 3.6937211426242495`*^9}, 3.693721197964327*^9, 3.6938966537217274`*^9, {3.694084104105713*^9, 3.694084119395734*^9}, 3.725367865956423*^9, 3.7254169957392054`*^9, 3.725619293450783*^9},ExpressionUUID->"3ab24f61-e0b0-481e-bc07-\ 5674655e5498"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{"Sin", "[", "\[Alpha]", "]"}]}], ",", RowBox[{"Cos", "[", "\[Alpha]", "]"}], ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{ RowBox[{"Sin", "[", "\[Alpha]", "]"}], ",", RowBox[{"Cos", "[", "\[Alpha]", "]"}], ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"FORCE", ",", RowBox[{"{", RowBox[{"0", ",", "F", ",", "0"}], "}"}], ",", RowBox[{"Point", "[", RowBox[{"{", "2", "}"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ 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[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"values", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"A", "->", "0.01"}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"F", "\[Rule]", RowBox[{"-", "0.1"}]}], ",", RowBox[{"\[Alpha]", "\[Rule]", RowBox[{"Pi", "/", "3"}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", RowBox[{"NONL", ",", "ALL"}], "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", " ", "values"}]}], "]"}], "\[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}, { 3.7574855757248087`*^9, 3.757485594710279*^9}, {3.757505699791664*^9, 3.7575057187517214`*^9}, {3.757505806756074*^9, 3.757505817791669*^9}, { 3.7575058693821335`*^9, 3.7575058794393673`*^9}, {3.757505914172347*^9, 3.75750592024364*^9}, {3.7575059985860023`*^9, 3.757506039292043*^9}, 3.7575061532808533`*^9, {3.757506970806711*^9, 3.7575069907894077`*^9}, 3.7575070233789244`*^9}, CellLabel-> "In[283]:=",ExpressionUUID->"e1456d6c-ebba-41da-803e-3e854b1079b8"] }, Closed]], Cell[CellGroupData[{ Cell["Example 4.3 (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}},ExpressionUUID->"b9ca64d6-1993-4c9b-8464-\ 704989cc4f12"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "1"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", 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[{"values", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"A", "->", "0.01"}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"F", "->", "0.05"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "/.", "values"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{"DISP", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "/.", "values"}], " ", "/.", "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}, {3.757507056562605*^9, 3.7575070756264515`*^9}}, CellLabel-> "In[289]:=",ExpressionUUID->"988eb08f-3ade-4d78-b8ae-d1c77489fa7b"] }, Closed]], Cell[CellGroupData[{ Cell["Example 4.4 (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},ExpressionUUID->"d193f69f-223f-4843-8fe4-\ c57ff78467a5"], 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]"}], "\[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}, 3.7575074757602773`*^9},ExpressionUUID->"2f3e27f2-ca50-4781-b2f1-\ d12789d1032a"] }, Closed]], Cell[CellGroupData[{ Cell["Example 4.5 (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}, { 3.757510705049321*^9, 3.7575107076105695`*^9}},ExpressionUUID->"0db6022b-5465-48b6-be07-\ 4c120ac5e4a7"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", 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", "[", "0", "]"}], " ", "L"}], ",", RowBox[{ RowBox[{"a", "[", "0", "]"}], " ", "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[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"values", "=", 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]", RowBox[{"sol", "=", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "values"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{"DISP", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "values"}], " ", "/.", "sol"}], "]"}], "\[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}, {3.7575106980353403`*^9, 3.7575107267165956`*^9}, {3.757510760631243*^9, 3.757510776083911*^9}}, CellLabel-> "In[327]:=",ExpressionUUID->"e682bfa7-76d4-4984-a23e-9a3fa08356b0"] }, Closed]], Cell[CellGroupData[{ Cell["Example 4.6 (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},ExpressionUUID->"b16ed357-d398-45c5-9561-\ 958de94bda30"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "1"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", 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[{"values", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"A", "->", "0.01"}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"F", "->", "0.05"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "/.", "values"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"DISP", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "values"}], " ", "/.", "sol"}], "]"}], "\[IndentingNewLine]"}], "\[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}, {3.7575108265834846`*^9, 3.7575108770153513`*^9}, {3.7575117127215357`*^9, 3.7575117136466274`*^9}}, CellLabel-> "In[339]:=",ExpressionUUID->"77a43020-854e-4d7d-98e9-5d669cb6cfbc"] }, Closed]], Cell[CellGroupData[{ Cell["Example 4.7 (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},ExpressionUUID->"fbb3fd70-575d-46fc-8da6-\ edfa4eff0023"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", " ", RowBox[{ RowBox[{"A", "/", RowBox[{"Sqrt", "[", "2", "]"}]}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "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", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "0", ",", "L"}], " ", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"a", "[", "1", "]"}], " ", "L"}], ",", "0", ",", RowBox[{ RowBox[{"a", "[", "2", "]"}], " ", "L"}]}], "}"}], ",", 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[{ RowBox[{"values", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"A", "->", "0.01"}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"F", "->", "0.05"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "values"}]}], "]"}], " ", "\[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}, { 3.757511605569745*^9, 3.7575116659081635`*^9}, {3.7575117737933874`*^9, 3.7575117756223545`*^9}}, CellLabel-> "In[346]:=",ExpressionUUID->"82cd5ab3-f384-40df-ac9a-a7c7c7d889df"] }, Closed]], Cell["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}},ExpressionUUID->"ccf9e7cd-485b-4963-9cfb-\ 555d708665f1"], Cell[CellGroupData[{ Cell["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}},ExpressionUUID->"4001f0ca-949c-4907-95f9-\ c70dfd95ab98"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", 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}}, CellLabel->"In[22]:=",ExpressionUUID->"10e8bc68-6fcf-49f0-9673-d71aac7f5c0d"] }, Closed]], Cell[CellGroupData[{ Cell["Problem 3 (bar)", "Subsubsection", CellChangeTimes->{ 3.560218382980301*^9, 3.62311554059295*^9, {3.693819973244685*^9, 3.6938199838982944`*^9}, 3.725511564062546*^9, 3.7256253111624565`*^9},ExpressionUUID->"9d2a2055-06cf-4421-93bd-\ 9e01fcba7ecc"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", 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[{"values", "=", 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"}], "}"}], " ", "/.", "values"}]}], "]"}], "\[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},ExpressionUUID->"6cb3221f-8ce1-42a9-85fa-\ 65660b20dbbc"] }, Closed]], Cell[CellGroupData[{ Cell["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},ExpressionUUID->"08286fdf-1eb2-48d1-beb4-\ 396b77a4974c"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[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[{ 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[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"values", "=", 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"}], "}"}], " ", "/.", "values"}]}], "]"}], "\[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}}, CellLabel->"In[38]:=",ExpressionUUID->"723c585c-26a6-48c6-876a-37180b0fbda0"] }, Closed]], Cell[CellGroupData[{ Cell["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},ExpressionUUID->"50d6e35d-30f9-4a25-a35f-\ f2656f5d44ed"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "\[Rho]"}], " ", "g", " ", "A"}], ",", "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[{ RowBox[{"a", "[", "0", "]"}], "*", "L"}], ",", "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[{"values", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"A", "\[Rule]", RowBox[{"1", "/", "100"}]}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"g", "\[Rule]", "10."}], ",", RowBox[{"\[Rho]", "->", "1"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "values"}]}], "]"}], "\[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}}, CellLabel->"In[80]:=",ExpressionUUID->"c7a81e93-b874-4543-a2a4-0ab05cb26f87"] }, Closed]], Cell[CellGroupData[{ Cell["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},ExpressionUUID->"f0678385-61ed-4f97-970d-\ 2f4b6a06ba7d"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"3", ",", "1"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "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[{ 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[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"values", "=", 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"}], "}"}], " ", "/.", "values"}]}], "]"}], "\[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}}, CellLabel->"In[86]:=",ExpressionUUID->"d37d7648-9eec-42cc-a586-f100c102d178"] }, Closed]], Cell[CellGroupData[{ Cell["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}},ExpressionUUID->"812e3da1-23ec-4593-9f56-\ 8569fdb86824"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "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[{ 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[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"values", "=", 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]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "values"}]}], "]"}], "\[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}}, CellLabel->"In[92]:=",ExpressionUUID->"9c434215-4f66-42d0-beec-b44b00d54972"] }, Closed]], Cell[CellGroupData[{ Cell["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},ExpressionUUID->"e18e99d3-44ed-4fd5-936a-\ 12edb4bbd633"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", 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[{ 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[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"values", "=", 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]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "values"}]}], "]"}], "\[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}}, CellLabel->"In[98]:=",ExpressionUUID->"465c6e6d-c663-4f21-bb18-0a2d310bd100"] }, Closed]], Cell[CellGroupData[{ Cell["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}},ExpressionUUID->"7e5bb597-5850-4964-b951-\ 779ff16f3889"], Cell[BoxData[{ RowBox[{ 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[{ 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[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"values", "=", 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]", RowBox[{"sol", "=", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "values"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{"DISP", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "values"}], " ", "/.", "sol"}], "]"}], "\[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}}, CellLabel-> "In[104]:=",ExpressionUUID->"e778529a-7dc5-45a8-b4ea-a9b53b2a2eda"] }, Closed]], Cell[CellGroupData[{ Cell["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}},ExpressionUUID->"b6803274-623a-4f0a-8344-\ 191c468975e8"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "0"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4"}], "}"}], "]"}]}], "}"}], ",", "\[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[{ RowBox[{"a", "[", "0", "]"}], "L"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "\[IndentingNewLine]", "}"}]}], ";"}], "\[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[{"values", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"t", "\[Rule]", RowBox[{"1", "/", "10"}]}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"F", "\[Rule]", RowBox[{"1", "/", "2."}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "values"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{"DISP", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "values"}], " ", "/.", "sol"}], "]"}]}], "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}}, CellLabel-> "In[118]:=",ExpressionUUID->"d35a5555-9972-49dd-ab9e-a5cbaba44da7"] }, 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->"f3f80333-e18a-43f3-bb63-\ 19d66e1bdf24"], 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[{ RowBox[{ RowBox[{"-", "\[Rho]"}], " ", "g", " ", "A"}], ",", "0", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"2", ",", "1"}], "}"}], "]"}]}], "}"}], "}"}]}], ";"}], "\[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", ",", 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[{ RowBox[{"values", "=", RowBox[{"{", RowBox[{ RowBox[{"L", " ", "->", "1"}], ",", " ", RowBox[{"A", "\[Rule]", RowBox[{"1", "/", "100"}]}], ",", " ", RowBox[{"\[CapitalEpsilon]", "->", "100"}], ",", " ", RowBox[{"g", "\[Rule]", "10."}], ",", RowBox[{"\[Rho]", "->", "1"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "values"}]}], "]"}], "\[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}}, CellLabel-> "In[143]:=",ExpressionUUID->"b677149f-5050-4cb1-a704-6a1ea7a10d93"] }, 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->"84e97302-83d1-486b-be56-\ 94c2b7b01a97"], Cell[BoxData[{ RowBox[{ 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[{"{", RowBox[{"0", ",", "0", ",", "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[{"{", RowBox[{"0", ",", "0", ",", "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[{ 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[{ RowBox[{"FORMATTED", "[", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"STANDARDFORM", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"values", "=", 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]", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "values"}]}], "]"}]}], "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}}, CellLabel-> "In[182]:=",ExpressionUUID->"a4ee1c99-6171-4745-b646-4b7aa387021d"] }, 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->"fa96934c-4048-4a91-86fb-\ e6f085c276b4"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"PLANE", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[CapitalEpsilon]", ",", "\[Nu]"}], "}"}], ",", RowBox[{"{", "t", "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}], ",", 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[{ 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[{"values", "=", 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]", RowBox[{"sol", "=", RowBox[{"SOLVE", "[", RowBox[{ RowBox[{"{", "NONL", "}"}], ",", RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "values"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{"DISP", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"ele", ",", "fun"}], "}"}], " ", "/.", "values"}], " ", "/.", "sol"}], "]"}]}], "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}, CellLabel-> "In[202]:=",ExpressionUUID->"53fbd711-9876-4730-945c-ba0e2f8e4cc4"] }, Closed]], Cell[CellGroupData[{ Cell["Lecture assignment 1 (strain measures)", "Subsubsection", CellChangeTimes->{{3.4957958636017337`*^9, 3.4957958737573338`*^9}, 3.69408382394532*^9, 3.694084089815693*^9, {3.6940841484257746`*^9, 3.694084150185777*^9}, {3.7254167515801773`*^9, 3.7254167541669474`*^9}, { 3.725416987103789*^9, 3.7254169906767716`*^9}, 3.725619282059034*^9, { 3.7574830940774183`*^9, 3.7574831088662863`*^9}},ExpressionUUID->"edb29f16-cfce-4b77-96e7-\ 6981b22b136b"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"rr", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "\[Epsilon]"}], ")"}], RowBox[{"Cos", "[", "\[Alpha]", "]"}]}], ",", RowBox[{"-", RowBox[{"Sin", "[", "\[Alpha]", "]"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "\[Epsilon]"}], ")"}], RowBox[{"Sin", "[", "\[Alpha]", "]"}]}], ",", RowBox[{"Cos", "[", "\[Alpha]", "]"}]}], "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"II", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"FF", "=", RowBox[{"D", "[", RowBox[{"rr", ",", RowBox[{"{", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ee", " ", "=", " ", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"(", RowBox[{"FF", "+", RowBox[{"Transpose", "[", "FF", "]"}], "-", RowBox[{"2", "II"}]}], ")"}], "/", "2"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"EE", " ", "=", " ", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"Transpose", "[", "FF", "]"}], ".", "FF"}], "-", "II"}], ")"}], "/", "2"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"MatrixForm", "[", "FF", "]"}], "\[IndentingNewLine]", RowBox[{"MatrixForm", "[", "ee", "]"}], "\[IndentingNewLine]", RowBox[{"MatrixForm", "[", "EE", "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.495713474266*^9, 3.4957134770428*^9}, 3.495713597974*^9, {3.4957194436786003`*^9, 3.4957194470638*^9}, 3.495795893194934*^9, {3.4957959444409337`*^9, 3.495796192746134*^9}, { 3.4957962416677337`*^9, 3.4957962923989334`*^9}, 3.694084081585681*^9, 3.694084242045906*^9, {3.694084289345972*^9, 3.6940843583160686`*^9}, { 3.6940844069261365`*^9, 3.694084439306182*^9}, {3.6940844961662617`*^9, 3.6940845097762804`*^9}, {3.694084642923224*^9, 3.6940846568036976`*^9}, { 3.6940847436238194`*^9, 3.6940847683238535`*^9}, {3.6940848043249044`*^9, 3.69408481552492*^9}, {3.7253630581342545`*^9, 3.7253631520878797`*^9}, { 3.725363205624776*^9, 3.725363236894071*^9}, {3.725363401957974*^9, 3.725363424991701*^9}, 3.725416765702466*^9, {3.757483163034631*^9, 3.757483438333089*^9}, {3.7574838805294495`*^9, 3.7574838866334352`*^9}}, CellLabel-> "In[226]:=",ExpressionUUID->"15476152-f879-499e-ac66-f07d05c81d89"] }, 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->"72876b4d-aa49-4022-b869-\ e52d40741674"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"ele", "=", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"BAR", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "\[CapitalEpsilon]", "}"}], ",", RowBox[{"{", RowBox[{"A", ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"-", "1"}]}], "}"}]}], "}"}], ",", 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", ",", "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}, CellLabel-> "In[234]:=",ExpressionUUID->"33d66911-0c09-4eda-81f2-32d5906855e2"] }, Closed]] }, Open ]] }, AutoGeneratedPackage->Automatic, WindowSize->{1221, 596}, WindowMargins->{{-34, Automatic}, {-43, Automatic}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, PrivateNotebookOptions->{"VersionedStylesheet"->{"Default.nb"[8.] -> False}}, Magnification:>2. Inherited, FrontEndVersion->"11.3 for Microsoft Windows (64-bit) (March 6, 2018)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[567, 22, 1384, 21, 230, "Chapter",ExpressionUUID->"f9c2c148-a01a-4dcf-b5a2-59c8faa291c7", InitializationCell->True], Cell[CellGroupData[{ Cell[1976, 47, 914, 15, 8444, "Section",ExpressionUUID->"e3a7af86-4b21-4f7c-818a-4f3ab57ac50c"], Cell[CellGroupData[{ Cell[2915, 66, 156, 2, 300988, "Subsection",ExpressionUUID->"a4d44395-72a1-4756-8608-684d4c13df83"], Cell[3074, 70, 35633, 846, 2147483647, "Input",ExpressionUUID->"ed2ed2d9-b99d-448f-86da-4386184d8516", InitializationCell->True], Cell[38710, 918, 154, 3, 2147483647, "Input",ExpressionUUID->"159472bf-417f-4070-aad8-5406fd42698c"] }, Closed]], Cell[CellGroupData[{ Cell[38901, 926, 88, 0, 198396, "Subsection",ExpressionUUID->"dbc33de8-90b2-471d-b3b5-959be2de0621"], Cell[38992, 928, 33129, 973, 2147483647, "Input",ExpressionUUID->"b47a83a3-02c6-481a-b0dc-20c1e7dd8763", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[72158, 1906, 87, 0, 198396, "Subsection",ExpressionUUID->"8266d6dd-1c96-4d34-8a50-ec145ea0115d"], Cell[72248, 1908, 29756, 785, 2147483647, "Input",ExpressionUUID->"af4563ad-fa9d-4f51-a4b2-3a24f6978422", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[102041, 2698, 92, 0, 198396, "Subsection",ExpressionUUID->"a127969d-25ad-4bec-83a1-b69315f3f613"], Cell[102136, 2700, 7120, 206, 2147483647, "Input",ExpressionUUID->"828a39db-754e-4b24-8574-97a4b4b24377", InitializationCell->True] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[109305, 2912, 1004, 16, 6396, "Section",ExpressionUUID->"5a669127-ee0a-4eb5-ae91-329d0652de0d"], Cell[CellGroupData[{ Cell[110334, 2932, 171, 3, 6396, "Subsection",ExpressionUUID->"e7500266-a0d0-49fb-8baa-660b6426cd64"], Cell[110508, 2937, 17126, 448, 2147483647, "Input",ExpressionUUID->"ec855259-b181-4621-bff6-5b06692ed070", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[127671, 3390, 340, 5, 4220, "Subsection",ExpressionUUID->"d7faebba-7395-4e68-ab54-f492589db395"], Cell[128014, 3397, 25175, 648, 2147483647, "Input",ExpressionUUID->"c6d3c1cf-f70a-4ff4-a688-e8af531ec381", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[153226, 4050, 203, 4, 4220, "Subsection",ExpressionUUID->"b7e0fb49-27d0-4286-aad7-5e4f444291fb", InitializationCell->True], Cell[153432, 4056, 44636, 963, 2147483647, "Input",ExpressionUUID->"6c2cad90-e06d-4e59-8532-520f3d2b4ff1", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[198105, 5024, 204, 4, 4220, "Subsection",ExpressionUUID->"f2915892-cf02-4b47-a282-bce92178c7c9", InitializationCell->True], Cell[198312, 5030, 21959, 435, 264736256, "Input",ExpressionUUID->"d6d4fa4d-302f-4234-b1e0-4992bce4f95c", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[220308, 5470, 255, 5, 4220, "Subsection",ExpressionUUID->"dab2a20e-37b0-46fe-a9da-bb15afd82a63", InitializationCell->True], Cell[220566, 5477, 12438, 188, 2147483647, "Input",ExpressionUUID->"fc4bc255-0184-4db9-9632-2475e5a9fab7", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[233041, 5670, 255, 5, 4220, "Subsection",ExpressionUUID->"06e798ca-1dd4-40a4-a05a-ff4b895a2b95", InitializationCell->True], Cell[233299, 5677, 16951, 317, 2147483647, "Input",ExpressionUUID->"71233d3c-e96a-40ba-8291-d489cc54cc36", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[250287, 5999, 310, 5, 4220, "Subsection",ExpressionUUID->"189929f0-3d23-4124-9e22-07173e3f9540", InitializationCell->True], Cell[250600, 6006, 18402, 342, 2147483647, "Input",ExpressionUUID->"1315eef7-3f98-48f3-a5f1-93f83f9a04ff", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[269039, 6353, 177, 3, 15228, "Subsection",ExpressionUUID->"0b4ce7e2-c37d-4aa4-be76-85624d17acf7"], Cell[269219, 6358, 173388, 3628, 2147483647, "Input",ExpressionUUID->"62be5c9d-13e2-4eb6-bfe3-f354e8ffe2e2", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[442644, 9991, 178, 3, 15228, "Subsection",ExpressionUUID->"7b50e1e5-43b3-48dd-ab3c-7f7fab53534c"], Cell[442825, 9996, 347471, 7572, 2147483647, "Input",ExpressionUUID->"e31fa415-db4b-408c-bea5-a9ffaf7481fc", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[790333, 17573, 233, 4, 15228, "Subsection",ExpressionUUID->"3c1cc687-9e5c-4f89-bb45-0c546743d3b9"], Cell[790569, 17579, 68994, 1264, 2147483647, "Input",ExpressionUUID->"10195547-9e08-4de6-b8ba-6f68b277fa39", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[859600, 18848, 234, 4, 15228, "Subsection",ExpressionUUID->"91adccb2-269e-4a19-9a4a-91ccc1e79579"], Cell[859837, 18854, 420063, 9118, 2147483647, "Input",ExpressionUUID->"06e3e177-9d54-4611-b583-2e9378b34b1d", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[1279937, 27977, 96, 0, 15228, "Subsection",ExpressionUUID->"b0e0c39c-1804-43da-be7d-9b95f8708dba"], Cell[1280036, 27979, 179353, 4370, 20425724, "Input",ExpressionUUID->"6a0e0d0d-c6ce-4720-9792-13f58dcffffc", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[1459426, 32354, 179, 3, 15228, "Subsection",ExpressionUUID->"cac1f4d2-6abb-4583-9715-def566f4dcfc"], Cell[1459608, 32359, 28992, 590, 524860, "Input",ExpressionUUID->"4ef5f2d0-fa25-49ec-acf2-77ac9741a235", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[1488637, 32954, 243, 4, 15228, "Subsection",ExpressionUUID->"3a7fcb2c-809c-491e-8008-ff44eaa4ff92"], Cell[1488883, 32960, 40413, 889, 884860, "Input",ExpressionUUID->"af7a02fa-7ee0-4fd9-a30b-c90bf1abbac8", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell[1529333, 33854, 222, 4, 23100, "Subsection",ExpressionUUID->"d80eaf00-72a4-4ce4-bc60-d25c0abc146d"], Cell[1529558, 33860, 282830, 6492, 2147483647, "Input",ExpressionUUID->"21b78e0a-a635-45eb-965f-598ce75a0714", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[1812425, 40357, 165, 2, 15228, "Subsection",ExpressionUUID->"4c5b683b-05a0-4d39-a5ee-9bcaeb2e4e23"], Cell[1812593, 40361, 55972, 1125, 2147483647, "Input",ExpressionUUID->"75aebc1b-bef9-4f49-90a9-6a83763efcdc", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[1868602, 41491, 169, 3, 15228, "Subsection",ExpressionUUID->"a951088d-2efc-45c8-868e-89e67a144fab"], Cell[1868774, 41496, 112119, 2661, 2147483647, "Input",ExpressionUUID->"03ac8030-724a-407f-b1af-d0fe2dd395fc", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[1980930, 44162, 269, 4, 15228, "Subsection",ExpressionUUID->"a0137111-1c1c-48db-a3dd-45e6822bfa37"], Cell[1981202, 44168, 114093, 2662, 2147483647, "Input",ExpressionUUID->"d8f05811-c435-43b0-8866-a99cf7ca7694"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[2095344, 46836, 1057, 17, 6396, "Section",ExpressionUUID->"a3fe9042-d10d-4ce6-8f91-abffc26873e2"], Cell[CellGroupData[{ Cell[2096426, 46857, 88, 0, 300988, "Subsection",ExpressionUUID->"62e31888-f3d3-4401-8886-77b1776935f2"], Cell[2096517, 46859, 61162, 1427, 27040636, "Input",ExpressionUUID->"238ce239-4374-4fc9-b278-90ffdd52d472", InitializationCell->True] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[2157728, 48292, 1007, 16, 6396, "Section",ExpressionUUID->"9b0e61aa-18e2-44e2-9e0c-9a1ec126de58"], Cell[CellGroupData[{ Cell[2158760, 48312, 383, 6, 300988, "Subsection",ExpressionUUID->"2f278e47-8352-44fb-a02b-1d00ed264fcf"], Cell[2159146, 48320, 4155, 82, 2147483647, "Input",ExpressionUUID->"58408154-0068-40bf-abd1-f54e461cb711", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[2163338, 48407, 86, 0, 198396, "Subsection",ExpressionUUID->"33730347-6ba2-4e0c-820c-45645621c710"], Cell[2163427, 48409, 15190, 404, 2147483647, "Input",ExpressionUUID->"2c23a70f-f643-4a73-8234-932f9829f2c7", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[2178654, 48818, 163, 3, 198396, "Subsection",ExpressionUUID->"8e45a61d-9be5-4264-80ec-530880c7b4d5"], Cell[2178820, 48823, 105826, 2527, 479526972, "Input",ExpressionUUID->"8cb28c0c-5bf5-4bbc-ba39-397bb5765537", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[2284683, 51355, 159, 3, 198396, "Subsection",ExpressionUUID->"cf156b2c-5cd2-49a1-ac11-e390717af027"], Cell[2284845, 51360, 36902, 861, 2147483647, "Input",ExpressionUUID->"57817736-8cd5-4a82-9931-ff5ab8a99821", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[2321784, 52226, 86, 0, 198396, "Subsection",ExpressionUUID->"aaba6671-2f74-4543-a33d-188243a04d7c"], Cell[2321873, 52228, 49163, 1259, 2147483647, "Input",ExpressionUUID->"35b1ec2a-c74b-4377-aff5-3f5da70010e2"] }, Closed]], Cell[CellGroupData[{ Cell[2371073, 53492, 262, 4, 198396, "Subsection",ExpressionUUID->"a33dd732-f4fa-4999-a9bb-507040049e63"], Cell[2371338, 53498, 24901, 599, 2147483647, "Input",ExpressionUUID->"21df03e4-b4f1-45e8-b446-93bc1053ed8d", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[2396276, 54102, 361, 6, 198396, "Subsection",ExpressionUUID->"3448e918-2634-476a-a298-6aad0ef6b2ca"], Cell[2396640, 54110, 128723, 3345, 2147483647, "Input",ExpressionUUID->"ce5a6d71-b118-4f01-aee3-41780e32359c", InitializationCell->True] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[2525424, 57462, 1169, 16, 110, "Chapter",ExpressionUUID->"5aad174e-f21b-4f96-88eb-a7b170e89253"], Cell[CellGroupData[{ Cell[2526618, 57482, 408, 6, 87, "Subsubsection",ExpressionUUID->"8803f6c4-92ba-4717-8bd8-d6494db0421e"], Cell[2527029, 57490, 2949, 71, 27772, "Input",ExpressionUUID->"c8ba1c59-a822-4e43-b8a2-35651811f7c3"] }, Closed]], Cell[CellGroupData[{ Cell[2530015, 57566, 443, 7, 67, "Subsubsection",ExpressionUUID->"3ab24f61-e0b0-481e-bc07-5674655e5498"], Cell[2530461, 57575, 7193, 166, 2824, "Input",ExpressionUUID->"e1456d6c-ebba-41da-803e-3e854b1079b8"] }, Closed]], Cell[CellGroupData[{ Cell[2537691, 57746, 471, 8, 67, "Subsubsection",ExpressionUUID->"b9ca64d6-1993-4c9b-8464-704989cc4f12"], Cell[2538165, 57756, 7415, 175, 3296, "Input",ExpressionUUID->"988eb08f-3ade-4d78-b8ae-d1c77489fa7b"] }, Closed]], Cell[CellGroupData[{ Cell[2545617, 57936, 624, 10, 67, "Subsubsection",ExpressionUUID->"d193f69f-223f-4843-8fe4-c57ff78467a5"], Cell[2546244, 57948, 4478, 100, 2260, "Input",ExpressionUUID->"2f3e27f2-ca50-4781-b2f1-d12789d1032a"] }, Closed]], Cell[CellGroupData[{ Cell[2550759, 58053, 486, 8, 67, "Subsubsection",ExpressionUUID->"0db6022b-5465-48b6-be07-4c120ac5e4a7"], Cell[2551248, 58063, 4357, 115, 2772, "Input",ExpressionUUID->"e682bfa7-76d4-4984-a23e-9a3fa08356b0"] }, Closed]], Cell[CellGroupData[{ Cell[2555642, 58183, 423, 7, 67, "Subsubsection",ExpressionUUID->"b16ed357-d398-45c5-9561-958de94bda30"], Cell[2556068, 58192, 6768, 166, 3380, "Input",ExpressionUUID->"77a43020-854e-4d7d-98e9-5d669cb6cfbc"] }, Closed]], Cell[CellGroupData[{ Cell[2562873, 58363, 445, 7, 67, "Subsubsection",ExpressionUUID->"fbb3fd70-575d-46fc-8da6-edfa4eff0023"], Cell[2563321, 58372, 5836, 135, 2984, "Input",ExpressionUUID->"82cd5ab3-f384-40df-ac9a-a7c7c7d889df"] }, Closed]], Cell[2569172, 58510, 300, 5, 67, "Subsubsection",ExpressionUUID->"ccf9e7cd-485b-4963-9cfb-555d708665f1"], Cell[CellGroupData[{ Cell[2569497, 58519, 363, 6, 67, "Subsubsection",ExpressionUUID->"4001f0ca-949c-4907-95f9-c70dfd95ab98"], Cell[2569863, 58527, 4567, 110, 30076, "Input",ExpressionUUID->"10e8bc68-6fcf-49f0-9673-d71aac7f5c0d"] }, Closed]], Cell[CellGroupData[{ Cell[2574467, 58642, 265, 5, 67, "Subsubsection",ExpressionUUID->"9d2a2055-06cf-4421-93bd-9e01fcba7ecc"], Cell[2574735, 58649, 4391, 107, 35260, "Input",ExpressionUUID->"6cb3221f-8ce1-42a9-85fa-65660b20dbbc"] }, Closed]], Cell[CellGroupData[{ Cell[2579163, 58761, 287, 5, 67, "Subsubsection",ExpressionUUID->"08286fdf-1eb2-48d1-beb4-396b77a4974c"], Cell[2579453, 58768, 5132, 129, 39804, "Input",ExpressionUUID->"723c585c-26a6-48c6-876a-37180b0fbda0"] }, Closed]], Cell[CellGroupData[{ Cell[2584622, 58902, 315, 6, 67, "Subsubsection",ExpressionUUID->"50d6e35d-30f9-4a25-a35f-f2656f5d44ed"], Cell[2584940, 58910, 4232, 101, 32320, "Input",ExpressionUUID->"c7a81e93-b874-4543-a2a4-0ab05cb26f87"] }, Closed]], Cell[CellGroupData[{ Cell[2589209, 59016, 294, 5, 67, "Subsubsection",ExpressionUUID->"f0678385-61ed-4f97-970d-2f4b6a06ba7d"], Cell[2589506, 59023, 4381, 117, 39804, "Input",ExpressionUUID->"d37d7648-9eec-42cc-a586-f100c102d178"] }, Closed]], Cell[CellGroupData[{ Cell[2593924, 59145, 479, 8, 67, "Subsubsection",ExpressionUUID->"812e3da1-23ec-4593-9f56-8569fdb86824"], Cell[2594406, 59155, 3979, 104, 36732, "Input",ExpressionUUID->"9c434215-4f66-42d0-beec-b44b00d54972"] }, Closed]], Cell[CellGroupData[{ Cell[2598422, 59264, 493, 8, 67, "Subsubsection",ExpressionUUID->"e18e99d3-44ed-4fd5-936a-12edb4bbd633"], Cell[2598918, 59274, 5075, 133, 42108, "Input",ExpressionUUID->"465c6e6d-c663-4f21-bb18-0a2d310bd100"] }, Closed]], Cell[CellGroupData[{ Cell[2604030, 59412, 476, 8, 67, "Subsubsection",ExpressionUUID->"7e5bb597-5850-4964-b951-779ff16f3889"], Cell[2604509, 59422, 5193, 125, 38268, "Input",ExpressionUUID->"e778529a-7dc5-45a8-b4ea-a9b53b2a2eda"] }, Closed]], Cell[CellGroupData[{ Cell[2609739, 59552, 537, 9, 67, "Subsubsection",ExpressionUUID->"b6803274-623a-4f0a-8344-191c468975e8"], Cell[2610279, 59563, 4869, 125, 42684, "Input",ExpressionUUID->"d35a5555-9972-49dd-ab9e-a5cbaba44da7"] }, Closed]], Cell[CellGroupData[{ Cell[2615185, 59693, 325, 6, 67, "Subsubsection",ExpressionUUID->"f3f80333-e18a-43f3-bb63-19d66e1bdf24"], Cell[2615513, 59701, 4334, 103, 34428, "Input",ExpressionUUID->"b677149f-5050-4cb1-a704-6a1ea7a10d93"] }, Closed]], Cell[CellGroupData[{ Cell[2619884, 59809, 382, 6, 67, "Subsubsection",ExpressionUUID->"84e97302-83d1-486b-be56-94c2b7b01a97"], Cell[2620269, 59817, 6035, 152, 40508, "Input",ExpressionUUID->"a4ee1c99-6171-4745-b646-4b7aa387021d"] }, Closed]], Cell[CellGroupData[{ Cell[2626341, 59974, 540, 9, 67, "Subsubsection",ExpressionUUID->"fa96934c-4048-4a91-86fb-e6f085c276b4"], Cell[2626884, 59985, 5132, 125, 643, "Input",ExpressionUUID->"53fbd711-9876-4730-945c-ba0e2f8e4cc4"] }, Closed]], Cell[CellGroupData[{ Cell[2632053, 60115, 472, 7, 67, "Subsubsection",ExpressionUUID->"edb29f16-cfce-4b77-96e7-6981b22b136b"], Cell[2632528, 60124, 3073, 77, 29372, "Input",ExpressionUUID->"15476152-f879-499e-ac66-f07d05c81d89"] }, Closed]], Cell[CellGroupData[{ Cell[2635638, 60206, 326, 6, 67, "Subsubsection",ExpressionUUID->"72876b4d-aa49-4022-b869-e52d40741674"], Cell[2635967, 60214, 3684, 83, 24892, "Input",ExpressionUUID->"33d66911-0c09-4eda-81f2-32d5906855e2"] }, Closed]] }, Open ]] } ] *)