Computational asymptotic post-buckling analysis of slender elastic structures

  • Raffaele Casciaro
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 470)


The lectures provide an introduction to the computational treatment of Koiter’s asymptotic strategy for post-buckling analysis of thin elastic structures.

The analysis of slender structures characterized by complex buckling and post-buckling phenomena and by a strong imperfection sensitivity, suffers from a lack of adequate computational tools. Standard algorithms, based on incremental-iterative approaches, are computationally expensive: it is practically impossible to perform the large number of successive runs necessary for the sensitivity analysis, that is, to evaluate the reduction in load due to all possible imperfections. Finite element implementations of Koiter’s perturbation method give a convenient alternative for that purpose. The analysis is very fast, of the same order as a linearized stability analysis and new analyses for different imperfections only require a fraction of the first analysis time.

The main objective of the present course is to show that finite element implementations of Koiter’s method can be both accurate and reliable.


Limit Load Equilibrium Path Nonlinear Eigenvalue Problem Asymptotic Approach Euler Beam 
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.


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  1. Antman S.S., ‘Bifurcation problems for nonlinearly elastic structures’, Rabinowitz ed., Application of Bifurcation Theory, Academic Press, New York, 1977.Google Scholar
  2. Aristodemo M., ‘A High-Continuity Finite Element Model for Two-Dimensional Elastic Problems’, Computer and Structures, Vol.21, 987–993, 1985.MATHCrossRefGoogle Scholar
  3. Bilotta A., Garcea G., Trunfio G.A., Casciaro R., ‘Postcritical analysis of thin-walled structures by KASP (Koiter Analysis of Slender Panels) code’, Report APRICOS-DE-1.3-03-1/UNICAL, Sept. 1997.Google Scholar
  4. Brezzi F., Cornalba M., Di Carlo A., ‘How to get around a simple quadratic fold’, Numer. Math., Vol.48, pp.417–427, 1986.MATHCrossRefMathSciNetGoogle Scholar
  5. Budiansky B., ‘Theory of buckling and post-buckling of elastic structures’, Advances in Applied Mechanics, Vol.14, Academic Press, New York, 1974.Google Scholar
  6. Casciaro R., Di Carlo A., Pignataro M., ‘A finite element technique for bifurcation analysis’, Proc. 14th IUTAM Congress, Delft, The Netherlands, august–sept. 1976.Google Scholar
  7. Casciaro R., Aristodemo M., ‘Perturbation analysis of geometrically nonlinear structures’, Proc. Int. Conference on Finite Elements Nonlinear Solid and Structural Mechanics, Geilo, Norway, august–sept. 1977.Google Scholar
  8. Casciaro R., Lanzo A.D., Salerno G.,‘Computational problems in elastic structural stability’, in Nonlinear Problems in engineering, C. Carmignani, G. Maino eds., World Scientific publ., Singapore, 1991.Google Scholar
  9. Casciaro R., Salerno G., Lanzo A.D., ‘Finite Element Asymptotic Analysis of Slender Elastic Structures: a Simple Approach’, Int. J. Numer. Meth. Eng., Vol.35, pages 1397–1426, 1992.MATHCrossRefGoogle Scholar
  10. Casciaro R., ‘Un algoritmo per il problema non lineare agli autovalori’ 13th AIMETA Congress of Theoretical and Applied Mechanics, Brescia, Italy, November 13–15, 2000.Google Scholar
  11. Casciaro R., Garcea, Attanasio G., Giordano F., ‘Pertubative approach to elastic post-buckling analysis’, International Journal of Computer & Structure, Vol.66, 585–595, 1998.MATHCrossRefGoogle Scholar
  12. Casciaro R., Mancusi G., Formica G., ‘Analisi post-critica in presenza di instabilità locali accoppiate’, 16th AIMETA Congress of Theoretical and Applied Mechanics, Ferrara, Italy, Sept. 9–13, 2003.Google Scholar
  13. Gallagher R. H., ‘Perturbation procedures in nonlinear finite element analysis’, Int. Conference on Computation Methods in Nonlinear Mechanics, Texas (USA), 1974.Google Scholar
  14. Garcea G., Trunfio G.A., Casciaro R., ‘Mixed formulation and locking in path following nonlinear analysis’, Comput. Meth. Appl. Mech. Engrg., 1651–4, pp. 247–272, 1998.MATHCrossRefMathSciNetGoogle Scholar
  15. Garcea G., Bilotta A., Trunfio G.A., Casciaro R., ‘Mixed implementation in Koiter nonlinear analysis of thin-walled structures: KASP implementation’, Report APRICOS-DE-1.3-10/UNICAL, Sept. 1998.Google Scholar
  16. Garcea G., Salerno G., Casciaro R., ‘Sanitizing of locking in Koiter perturbation analysis through mixed formulation’, Computer Methods in Applied Mechanics and Engineering, Vol.180, 137–167, 1999.MATHCrossRefGoogle Scholar
  17. Garcea G., ‘Mixed formulation in Koiter nonlinear analysis of thin-walled beam’, Computer Methods in Applied Mechanics and Engineering, Vol. 190/26–27,3369–3399, marzo 2001.MATHCrossRefGoogle Scholar
  18. Ho D., ‘The influence of imperfections on systems with coincident buckling loads’, Int. J. Nonlinear Mech. Vol.7, 311–321, 1972.CrossRefMATHGoogle Scholar
  19. Ho D., ‘Buckling load of nonlinear systems with multiple eigenvalues’, Int. J. Solids Struct., Vol.10, 1315–1333, 1974.CrossRefMATHGoogle Scholar
  20. Koiter W.T., Current Trends in the Theory of Buckling, In Buckling of structures, B. Budiansky ed., Proc.of IUTAM symposium, Cambridge, Cambridge, June 17–21, 1974, Springer-Verlag, Berlin, 1976.Google Scholar
  21. Koiter W.T., Elastic stability, Koiter’s course 1978–79, Technologic University of Delft, manuscript transcription by A.M.A. v.d. Heijden.Google Scholar
  22. Lanzo A.D., Garcea G., Casciaro R., ‘Asymptotic post-buckling analysis of rectangular plates by HC finite elements’, International Journal of Numerical Methods in Engineering, Vol.38, 2325–2345, 1995.MATHCrossRefGoogle Scholar
  23. Lanzo A.D., Garcea G., ‘Koiter’s analysis of thin-walled structures by s finite element approach’, International Journal of Numerical Methods in Engineering, Vol.39, 3007–303, 1996.MATHCrossRefGoogle Scholar
  24. Livesley R.K., Matrix Methods of Structural Analysis, 2nd ed., Pergamon Press.Google Scholar
  25. Lopez S., Fortino S., Casciaro R., “An adaptive multigrid solver for plate vibration and buckling problems”, Computer & Structure, Vol. 69, pp. 625–637, 1998.MATHCrossRefGoogle Scholar
  26. Noor A.K., ‘Recent advances in reduction methods for nonlinear problems’, Computers & Structures, Vol.13, pp.31–44, 1981.MATHCrossRefMathSciNetGoogle Scholar
  27. Noor A.K., Peters J.M., ‘Recent advances in reduction methods for instability analysis of structures’, Computers & Structures, Vol.16, No. 1–4, pp.67–80, 1983.MATHCrossRefGoogle Scholar
  28. Noor A.K., ‘Recent advances and application of reduction methods’, Appl. Mech. Rev., Vol.5, 125–146, May 1994.CrossRefGoogle Scholar
  29. Pignataro M., Di Carlo A., Casciaro R., ‘On nonlinear beam model from the point of view of computational postbuckling analysis’, Int. J. Solids & Structures, Vol.18, pp. 327–347, 1982.MATHCrossRefGoogle Scholar
  30. Salerno G., ‘How to recognize the order ofinfinitesimal mechanism: a numerical approach’, International Journal of Numerical Methods in Engineering, Vol.35, 1351–1395, 1992.MATHCrossRefGoogle Scholar
  31. Salerno G., Colletta G., Casciaro R., ‘Attractive post-critical paths and stochastic imperfection sensitivity analysis of nonlinear elastic structures within an FEM context’, 2nd ECCOMAS Conference on Numerical Methods in Engineering, Paris, France, Sept. 9–13, 1996.Google Scholar
  32. Salerno G., Casciaro R., ‘Mode jumping and attrative paths in multimode elastic buckling’, International Journal for Numerical Methods in Engineering, Vol.40, 833–861, 1997.MATHCrossRefMathSciNetGoogle Scholar
  33. Salerno G., Lanzo A.D., ‘A nonlinear beam finite element for the post-buckling analysis of plane frames by Koiter’s pertubation approach’, Comp. Meth. Appl. Engng., Vol.146, pp. 325–349, 1997.MATHCrossRefGoogle Scholar
  34. Timoshenko S.P., Gere J.M., Theory of Elastic Stability, Mc Graw Hill.Google Scholar
  35. W.H. Wittrick, F.W. Williams, ‘An algorithm for computing critical buckling loads of elastic structures’, J. Struct. Mech., 1(4), pp.497–518, 1973.Google Scholar
  36. M. A. Ali and S. Sridharan, ‘A versatile model for interactive buckling of columns and beam-columns’, Int. J. Solids Struct, 24(5), 481–496 (1988).MATHCrossRefGoogle Scholar
  37. G. M. van Erp, ‘Advanced buckling analyses of beam with arbitrary cross section’, Ph.D. Thesis, Eindhoven University of Technology (1989).Google Scholar

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© CISM, Udine 2005

Authors and Affiliations

  • Raffaele Casciaro
    • 1
  1. 1.Department of StructureUniversity of CalabriaRendeItaly

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