Stability, Bifurcation and Postbuckling Analysis

  • M. Pignataro
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 379)


Liapunov theory is first presented and discrete mechanical systems are in particular analysed. Then buckling and postbuckling analysis of continuous mechanical systems due to Koiter are discussed in some detail following Budiansky presentation. Finally, the influence of multiple interactive buckling modes on postbuckling behaviour is analysed in some detail in thin-walled members.


Equilibrium Path Initial Imperfection Liapunov Function Buckling Mode Postbuckling Behaviour 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Poincaré, H.: Sur l’Equilibre d’une Masse Fluide Animée d’un Mouvement de Rotation, Acta Math., 7 (1885), 259.CrossRefMathSciNetGoogle Scholar
  2. [2]
    Liapunov, A.M.: Problème Génerâl de la Stabilité du Mouvement (in Russian), Karkov, 1892; French Translation in Ann. Fac. Sci. Univ. Tolouse, 9 (1907); English Translation: Stability of Motion, Academic Press, New York 1966.Google Scholar
  3. [3]
    La Salle, J. and Lefschetz, S.: Stability by Liapunov’s Direct Method with Applications, Academic Press, New York 1961.Google Scholar
  4. [4]
    Pontriaguine, L.: Equations Differentielles Ordinaires, MIR, Moscow 1969.Google Scholar
  5. [5]
    Gantmacher, F.: Lectures in Analytical Mechanics, MIR, Moscow 1970.Google Scholar
  6. [6]
    Budiansky, B.: Theory of Buckling and Post-Buckling Behaviour of Elastic Structures, in: Advances in Applied Mechanics, Vol. 14, (Ed. Chia-Shun Yih ), Academic Press, New York 1974, 1–65.Google Scholar
  7. [7]
    Koiter, W.T. and Skaloud, M.: Interventions Comportment Postcritique des Plaques Utilisées en Construction Metallique, Mem. Soc. R. Sci. Liège, [5] 8(5), (1963), 64–68, 103, 104.Google Scholar
  8. [8]
    Van der Neut, A.: The Interaction of Local Buckling and Column Failure of Thin-Walled Compression Members, in: Proceedings 12th International Congress of Applied Mechanics, Springer-Verlag, Berlin 1969.Google Scholar
  9. [9]
    Graves-Smith, T.R.: The Ultimate Strength of Locally Buckled Columns of Arbitrary Length, in: Thin-Walled Steel Construction (Eds. K.C. Rochey and H.V. Hill ), Crosy Lockwood, London 1967.Google Scholar
  10. [10]
    Rizzi, N. and Pignataro, M.: The Effect of Multiple Buckling Modes on the Post-buckling Behaviour of Plane Elastic Frames. Part I: Symmetric Frames. Part II: Asymmetric Frames, J. Struct. Mech., 10 (1982), 437–458 and 459–474.Google Scholar
  11. [11]
    Pignataro, M. and Rizzi, N.: On the Interaction Between Local and Overall Buckling of an Asymmetric Portal Frame, Meccanica, 18 (1983), 92–96.CrossRefMATHGoogle Scholar
  12. [12]
    Grimaldi, A. and Pignataro, M.: Postbuckling Behaviour of Thin-Walled Open Cross Section Compression Members, J. Struct. Mech., 7 (1979), 143–159.CrossRefGoogle Scholar
  13. [13]
    Tvergaard, V.: Imperfection Sensitivity of a Wide Integrally Stiffened Panel Under Compression, Int. J. Solids Struct., 9 (1973), 177–192.CrossRefMATHGoogle Scholar
  14. [14]
    Koiter, W.T. and Pignataro, M.: An Alternative Approach to the Interaction Between Local and Overall Buckling in Stiffened Panels, in: IUTAM Symposium, Cambridge, 1974, (Ed. B. Budiansky ), Springer-Verlag, Berlin 1976, 133–148.Google Scholar
  15. [15]
    Koiter, W.T. and Pignataro, M.: A General Theory of the Interaction Between Local and Overall Buckling of Stiffened Panels, Technical Report of the Univ. of Delft, WTHD 83, 1976.Google Scholar
  16. [16]
    Byskov, E. and Hutchinson, J.W.: Mode Interaction in Axially Stiffened Cylindrical Shells, AIAA J., 15 (1977), 941–948.CrossRefGoogle Scholar
  17. [17]
    Hancock, G.J.: Nonlinear Analysis of Thin Sections in Compression, Proc. ASCE, 107, ST3 (1981), 455–471.Google Scholar
  18. [18]
    Bradford, M.A. and Hancock, G.J.: Elastic Interaction of Local and Lateral Buckling in Beams, Thin-Walled Structures, 2 (1984), 1–25.CrossRefGoogle Scholar
  19. [19]
    Sridharan, S.: Doubly Symmetric Interactive Buckling of Plate Structures, Int. J. Solids Struct., 19 (1983), 625–641.CrossRefMATHGoogle Scholar
  20. [20]
    Sridharan, S. and Benito, R.: Columns: Static and Dynamic Interactive Buckling, in: Proceedings 12th International Congress of Applied Mechanics, ASCE, 110, EM1 (1984), 49–65.Google Scholar
  21. [21]
    Benito, R. and Sridharan, S.: Mode Interaction in Thin-Walled Structural Members, J. Struct. Mech., 12 (1984–85), 517–542.CrossRefGoogle Scholar
  22. [22]
    Sridharan, S. and Ali, A.: Interactive Buckling in Thin-Walled Beam Columns, in: Proceedings 12th International Congress of Applied Mechanics, ASCE, 111, EM12 (1985), 1470–1486.Google Scholar
  23. [23]
    Pignataro, M., Luongo, A. and Rizzi, N.: On the Effect of the Local-Overall Interaction on the Postbuckling of Uniformly Compressed Channels, Thin-Walled Structures, 3 (1985), 293–321.CrossRefGoogle Scholar
  24. [24]
    Pignataro, M. and Luongo, A.: Asymmetric Interactive Buckling of Thin-Walled Columns with Initial Imperfections, Thin-Walled Structures, 5 (1987), 365–386.CrossRefGoogle Scholar
  25. [25]
    Byskov, E.: Elastic Buckling Problem with Infinitely Many Local Modes, Rep. No. 327, Technical University of Denmark, Lyngby (Denmark ) 1986.Google Scholar
  26. [26]
    Luongo, A. and Pignataro, M.: Multiple Interaction and Localization Phenomenon in Postbuckling of Compressed Thin-Walled Members, AIAA J., 26 (1988), 1395–1400.CrossRefMATHGoogle Scholar
  27. [27]
    Tvergaard, V. and Needleman, A.: On the Localization of Buckling Patterns, J. Appl. Mech., 47 (1980), 613–619.CrossRefGoogle Scholar
  28. [28]
    Potier-Ferry, M.: Wavelength Selection and Pattern Localization in Buckling Problems,in: Cellular Structures in Instability Problems (Eds. J.E. Wesfreid, S. Zalesky ), Lecture Notes in Physics, Springer-Verlag, Berlin 1984.Google Scholar
  29. [29]
    Moxham, K.E.: Buckling Tests on Individual Welded Steel Plates in Compression, Cambridge University Engineering Department Report CUED/CStructures/TR3, 1971.Google Scholar
  30. [30]
    Koiter, W.T.: Over de Stabiliteit van het Elastisch Evenwicht (in Dutch), PhD Thesis, H. J. Paris, Amsterdam, 1945; English Translation as NASA TT F-10, 833, 1957 and AFFDL Report TR 70–25, 1970.Google Scholar
  31. [31]
    Plank, R.J. and Wittrick, W.H.: Buckling Under Combined Loading of Thin, Flat-Walled Structures by a Complex Finite Strip Method, Int. J. Num. Meth. Engng., 8 (1974), 323–339.CrossRefMATHGoogle Scholar
  32. [32]
    Graves-Smith, T.R. and Sridharan, S.: A Finite Strip Method For The Buckling of Plate Structures under Arbitrary Loading, Int. J. Mech. Sci., 20 (1978), 685–693.CrossRefGoogle Scholar
  33. [33]
    Hancock, G.J.: Local, Distorsional and Lateral Buckling of I-Beams, Proc. ASCE, 104, ST11 (1978), 1787–1798.Google Scholar
  34. [34]
    Yoshida, H. and Maegawa, K.: Local and Member Buckling of H-Columns, J. Struct. Mech., 6 (1978), 1–27.CrossRefGoogle Scholar
  35. [35]
    Plank, R.J.: Developments in the Finite Strip Method for the Buckling Analysis of Compression Members, in: Trosième Colloque International “Stabilité des Structures Metalliques”, Paris 1983.Google Scholar
  36. [36]
    Benito, R.: Static and Dynamic Buckling of Plate Assemblies, PhD Thesis, Washington University in St Louis 1983.Google Scholar
  37. [37]
    Benito, R. and Sridharan, S.: Interactive Buckling. A Novel Approach and some New Results, Proc. of Third Intern. Colloq. on Stability of Metal Structures, Toronto (1983), 91–111.Google Scholar
  38. [38]
    Luongo, A. and Pignataro, M.: On the Use of Finite Strip Method in the Analysis of Nontraditional Problems of Thin-Walled Members, in: Proc. VII Italian Congress of Theoretical and Applied Mechanics AIMETA (in Italian) 1984, 193–204.Google Scholar
  39. [39]
    Luongo, A. and Pignataro, M.: Buckling and Post-buckling Analysis of Stiffened Channels under Uniform Compression, Costruzioni Metalliche, 4 (1986), 242–249.Google Scholar

Copyright information

© Springer-Verlag Wien 1998

Authors and Affiliations

  • M. Pignataro
    • 1
  1. 1.University of Roma “La Sapienza”RomaItaly

Personalised recommendations