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  • Reading assignments and Lecture notes [2021]


    First words

    This course have a very dense content and six weeks is short, but what you take with you is worth.

    The weekly homework topics and the associated readings will be the 'GPS' guiding the student through the necessary material to learn.

    Therefore, the lectures will concentrate on the key topics and on the invariant fundaments while illustrating all that through examples.   

    Therefore, first we address the physics (mechanics) of instability phenomena (observation) then we try to find the minimum number of degrees of freedom to describe mathematically the problem using first principles (posing or setting the problem) and thirdly, we try to find practical solutions of importance for understanding and doing quality structural design.
    We will not hide the phenomena behind unnecessary complexe mathematics: First comes the physics then the mathematics follows as an instrument of thoughts (ajattekuväline) to obtain handels which gives us the buckling equations. (our mathematics will be the theorem: at a STABLE equilibrium the total potential energy has a local minimum for a conservative system)

    The student is encouraged to prepare for lectures and homework cessions, at least, by doing the reading assignments on time from references [1] and [2], below. You are working for yourself. Doing actively homework assignments will help you to deepen and consolidate what you have learnt.

    Please, do not concentrate to much on subjective workload-concept only since “workload” is just the amount of personal time each one invests in studying new skills and knowledge. Think that you are training to be among the best ... engineers. "What we can gain?" is the correct question not the price in hours. (of course, the work should be doable in six-seven week… and it is)

    D.B, 2021

    ------

    List of the six homework and assignments to be done during this course:

    1.       week 1:- Fundaments of Elastic Stability

    2.       week 2: - Flexural stability loss

    3.       week 3:  Lateral torsional, pure torsional and combined flexural-torsional buckling

    4.       week 4 - Computational Stability Analysis. Application example: Lateral torsional buckling & post-buckling

    5.       week 5 - Buckling of plates

    6.       week 6  - Buckling of shells (only one exercise)



    Weekly reading assignments and additional free material from lectures

    =======================================================

      BEGIN WEEK 1-2 =======================================================

     Week 1-2:  [2] Chapter 1, from 1.1  till  section 1.12.1 (the link below in blue):

                              The fundaments of Elastic Stability

                                (I provide the pdf I have written. This stability key topics are missing in the course textbook!)

     

    Week 1-2 topics   

    [PDF Slides] :  version 2021:  updated 2/3/2021 https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Lecture_Week1_DBA_2021.pdf?time=1614683734927

    The detailed content of the first lecture

    • Introduction
    •        What is stability? Phenomenon, elastic stability
    •        Structural design and stability – some standards
    • Basic concepts
    •         Equilibrium, equilibrium paths
    •         Critical points: bifurcation, limit point
    •         Stability of equilibrium (branches)
    • Energy criteria of stability
    • About post-buckling analysis
    • Types of bifurcational instabilities
    • Sensitivity to imperfections
    • Illustrative examples

    ======================================================

    You can also from e-textbook ----- read 

     Week 1-2:  [1] Chapter 1: Buckling of columns   ...

                             & especially, section 1.6: Introduction to calculus of variation (variaatiolaskenta)

                          Chapter 2:  (only 2.1 --2.7) Energy Methods,    

                                            Principle of minimum Potential Energy

                                                   Stability criteria.,

                                                   Rayleigh-Ritz method, Rayleigh-quotient,

    =================================================================================  END WEEK 1-2 =================================================================================  

    Week 2 topics   - Flexural buckling

    [PDF Slides] :

     update: 8/3/2021: https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Lecture_Week2_DBA_2021.pdf?time=1615161890268

    update: 9/3/2021:  Energy principles and Applications for Flexural Buckling

    https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Lecture_Week2_DBA_2021.pdf?time=1615275301008


    update 10 Mars 2021: (minor editorial corrections):  https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Lecture_Week2_DBA_2021.pdf?time=1615387995668


    Content for week 2:

    % -----------------------------------------------------------

    •  Trefftz stability criteria

    •  General Energy criteria of stability

    •  Recall Finite deformations (strains)

    •  Flexural buckling

    •  Buckling of beam-column

    •  Timoshenko column

    •   Effects of imperfections

    •   Ayreton-Perry formula & Eurocode buckling curves

    •    Linear buckling analysis

    •    Post-buckling analysis

    •   Buckling of beam-column on elastic foundation

    •   Finite element method – a hand version for buckling analysis

    % -------------------------------

    You can also from e-textbook ----- read 

     Week 2:  [1] Chapter 1 ,  2,   3 and 4  About flexural buckling, energy principles ...

    ************************************************

    WEEK 3 [BEGIN] =================================================================================  

    Week 3 topics   - Buckling of beams having thin-walled open cross-sections

    Notez Bien: this topic is the most time-demanding since it contains fundamental concepts not necessaryly known to students as for instance warping phenomena --- Vlassov theory of warping - poikkileikkauksen käyristyminen) and this  even before addressing the stability aspects. However, it is simply not feasible, in two lectures, to learn neither to teach, warping torsion of beams having thin-walled open cross-section and their stability. 

    No worry,there is a solution and it is doable for you and for me:  we will adress stability questions in these two lectures and cover them correctly.

    We will use two key parameters, needed for stability, taken from tables. Namely, the location of the center of shear (or rotation) and the warrping rigidity.Naturally, we will demostrate the physics of warping than move to stability questions.

    • Lateral torsional buckling (kiepahdus)
    • torsional buckling (vääntönurjahdus)
    • combined flexural-torsional buckling (avaruusnurjahdus)

    [PDF lecturer's Slides updated] : 

    1) update 31/3/2021:  https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Lecture_Week3_DBA_2021.pdf?time=1617216644423

    1 Bis) numerical simulation: I-profile post-buckling analysis    (a tiny lateral force H acts as a perturbation)  : https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/1_Torsional_Lateral_post_critical_I_Beam_DBA2019_BW_slower.avi   (by D. Baroudi, 2018)

    [You will also do such numerical GNA as a homework]

    2) : Example Matlab script to solve symbolically the lateral-torsional buckling of cantilever beam under end-load

    shown in the lecture:  https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Lateral_buckling_symbolic_2021.m

    3) Mechanics of warrping (free reading):      https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Warping_mechanics_short.pdf  (Vlassov theory)

    By Emir. Prof. Juha Paavola.

    [The PDF: (Lecturer's text 15.3.2019, part 1-2-3) UPDATED version]:
    [CRITICAL reading is encouraged... ]
    [PDF-material by Emeritus prof. J. Paavaola:
     torsion of open thin-walled beams]: https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/1__cross_section_omega_secctorial_computeJP.pdf

    MUST READ: Vlassov torsion

    Faster  and concise reading:  from the lecturer's-pdf:  Chapter 2: Torsion of opn thin-walled beams

    Naturally, you can read also from your textbook if you wish.

    [1] CHAI H. YOO &  SUNG C. LE .    Chapters 6 and 7.

     

    WEEK 3 [END]

    ============================================

     

     

    Week 4-5 topics   -  Buckling of plates

    • Introductory example
    • Cylindrical plate buckling
    • Deriving the Equation of loss of stability
      • simply supported rectangular plate under one-side compression
      • simply supported rectangular plate under in-plane bending and compression
      • Shear buckling of a rectangular plate
    • FEA linear buckling example
    • FEA post-buckling example

    [PDF lecturer's Slides   23.3.2021]:    https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Lecture_Week4_DBA_2021.pdf?time=1616485375309

    version 10/4/2021:  https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Lecture_Week4_DBA_2021.pdf?time=1618048214587

    Matlab script (buckling of plates, energy method - symbolic) : https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Plate_buckling_sybolic_Matlab.m

    ---------------------

    From the e-textbook:

     

    • Chapter 8. Buckling  of Plate Elements  (weeks 4 and 5)

    Week 5-6 topics : Buckling of Thin Cylindrical Shell 

    Note that lectures 5-6 are gathered in one lecture slide series called Lecture_Week6_DBA_2021.pdf and that 5th-lecture slides does not exist.

    • Chapter 9.  Buckling of Thin Cylindrical Shell  Elements (for last weeks 5 and 6)

    see: Lecturer (D. Baroudi) additional material: lectures-notes:  (may be updated weekly)

       

    NB. only cylindrical shell buckling belongs to the course.

    =================================================================================

    special assignment   For all weeks --- BEGIN WEEK 1-6 =================================================================================

     

    Week 1-6 MUST reading: [1] Chapter 5: Torsion in Structures

    The topics of uniform and non-uniform torsion of structure is practically not treated at the Bachelor level (= St-Venant’s torsion  and Vlassov torsion with restrained warping).

    The torsion of members with solid cross-sections, open and closed thin-walled sections deserves, for its importance and its complexity, a full six-week complete course. This is especially true when addressing the restrained warping torsion of members with such open thin-walled sections.

    In the current stability course (6 weeks), the torsional and flexural torsional buckling of beams having open thin-walled cross-section is only one subtopic from six others. It is unrealistic to both correctly teach Vlassov torsion theory and stability. This is one reason, why, I will concentrate during the lectures on the key phenomenon of warping and its relation to stability aspects. We will, together, derive the almost ‘iconic sectorial coordinate and its relation to deplanation, and consequently, the warping stiffness, and the strain energy stored in warping That is all. However, read the Chapter 5 of the textbook..

    Consequently, the students should also try its best and self-read the maximum from the assigned chapter (Chapter 5) of our textbook. If any you have questions related to the content of the chapter, , please let me know.

    =================================================================================

    special assignment   For all weeks --- END  WEEK 1-6 =================================================================================

     

    ===========================================

    Literature

    • [1] CHAI H. YOO &  SUNG C. LE .    STABILITY OF STRUCTURES - Principles and Applications,2011 Elsevier e-textbook (our course main textbook)
    • [2] Lecturer (D. Baroudi) additional material: lectures-notes:  (may be updated weekly or weakly)

    1) https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/158920/Lecturer_written_long_materal_stabililty_2020.pdf (version 2019-2020)

    2) https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Main_book_Structural_Mechanics_2020_STAB_version_2_Optimized.pdf  (version 2021)

    3) version 22 Febrary 2021:  [version 17/02/2021]:  

     New https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Main_book_Structural_Mechanics_2020_STAB._home_Optimized%20-%2022FEv2021.pdf

    4) Version 25.2.2021:  https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Main_book_Structural_Mechanics_2020_STAB._home_Optimized_25FEV2021.pdf

    5) Version 27 FEB 2021:  https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Main_book_Structural_Mechanics_2020_STAB._home_Optimized_27FEV2021_PM.pdf

    6) Version 7/3/2021: https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Main_book_Structural_Mechanics_2020_STAB._home_Optimized_7Mars2021.pdf

    7) Version 9/3/2021  https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Main_book_Structural_Mechanics_2020_STAB._home_Optimized_9_3_2021.pdf

    8) Version 11/3/2021: https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Main_book_Structural_Mechanics_2020_STAB._home_Optimized_11_3_2021.pdf        (I added some dynamic stability examples)

    9) Version 12/3/2021:    https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Main_book_Structural_Mechanics_2020_STAB._home_Optimized_12_3_2021.pdf 

    10)  Version 15/3/2021:  https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Main_book_Structural_Mechanics_2020_STAB._home_Optimized_15_3_2021.pdf

    11) version 23/3/2021:   https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Main_book_Structural_Mechanics_2020_STAB._home_Optimized_23_3_2021.pdf

    12) version 31/3/2021:  https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Main_book_Structural_Mechanics_2020_STAB._home_Optimized_31_3_2021.pdf

    24/4/2021: Last version:   https://mycourses.aalto.fi/pluginfile.php/1260824/course/section/173429/Main_book_Structural_Mechanics_2020_STAB._home_Optimized_13_4_2021.pdf

    Additinal reading:

    • [3] S.P. Timoshenko & J.M. Gere.   Theory of Elastic Stability.  2nd Ed., 1985.  (Classical textbook)
    • [7] Stability Of Structures: Elastic, Inelastic, Fracture And Damage Theories
      Etukansi
      World Scientific, 16.8.2010 - 1040 pages

    *********

     

     


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