Nonlinear Dynamics

, Volume 66, Issue 3, pp 389–401 | Cite as

Dynamic buckling analysis of composite cylindrical shells using a finite element based perturbation method

  • T. Rahman
  • E. L. JansenEmail author
  • Z. Gürdal
Original Paper


In this paper a finite element formulation of a reduction method for dynamic buckling analysis of imperfection-sensitive shell structures is presented. The reduction method makes use of a perturbation approach, initially developed for static buckling and later extended to dynamic buckling analysis. The implementation of a single-mode dynamic buckling analysis in a general purpose finite element code is described. The effectiveness of the approach is illustrated by application to the dynamic buckling of composite cylindrical shells under axial and radial step loads. Results of the reduction method are compared with results available in the literature. The results are also compared with full model finite element explicit dynamic analysis, and a reasonable agreement is obtained.


Dynamic buckling Thin-walled structures Finite elements Perturbation method Reduction method 


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  1. 1.
    Lindberg, H.E., Florence, A.L.: Dynamic Pulse Buckling. Nijhoff, Dordrecht (1987) zbMATHCrossRefGoogle Scholar
  2. 2.
    Simitses, G.J.: Dynamic Stability of Suddenly Loaded Structures. Springer, Berlin (1990) zbMATHCrossRefGoogle Scholar
  3. 3.
    Pellicano, F., Amabili, M.: Dynamic instability and chaos of empty and fluid-filled circular cylindrical shells under periodic axial loads. J. Sound Vib. 293, 227–252 (2006) CrossRefGoogle Scholar
  4. 4.
    Amabili, M.: Nonlinear Vibrations and Stability of Shells and Plates. Cambridge University Press, Cambridge (2008) zbMATHCrossRefGoogle Scholar
  5. 5.
    Gonçalves, P.B., Del Prado, Z.J.G.N.: Low-dimensional Galerkin models for nonlinear vibration and instability analysis of cylindrical shells. Nonlinear Dyn. 41, 129–145 (2005) zbMATHCrossRefGoogle Scholar
  6. 6.
    Mallon, N.J., Fey, R.H.B., Nijmeijer, H.: Dynamic stability of a thin cylindrical shell with top mass subjected to harmonic base-acceleration. Int. J. Solids Struct. 45, 1587–1613 (2008) zbMATHCrossRefGoogle Scholar
  7. 7.
    Jansen, E.L.: Dynamic stability problems of anisotropic cylindrical shells via a simplified analysis. Nonlinear Dyn. 39, 349–367 (2005) zbMATHCrossRefGoogle Scholar
  8. 8.
    Budiansky, B., Roth, R.S.: Axisymmetric dynamic buckling of clamped shallow spherical shells. Technical report TN D-1510, NASA, 1962 Google Scholar
  9. 9.
    Kounadis, A.: Nonlinear dynamic buckling of discrete dissipative or nondissipative systems under step loading. AIAA J. 29, 280–289 (1991) CrossRefGoogle Scholar
  10. 10.
    Roth, R., Klosner, J.: Nonlinear response of cylindrical shells subjected to dynamic axial loads. AIAA J. 2, 1788–1794 (1964) MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Tamura, Y.S., Babcock, C.D.: Dynamic stability of cylindrical shells under step loading. J. Appl. Mech. 42, 190–194 (1975) zbMATHCrossRefGoogle Scholar
  12. 12.
    Saigal, S., Yang, T.Y., Kapania, R.K.: Dynamic buckling of imperfection sensitive shell structures. J. Aircr. 24(10), 718–725 (1987) CrossRefGoogle Scholar
  13. 13.
    Ganapathi, M., Gupta, S.S., Patel, B.P.: Nonlinear axisymmetric dynamic buckling of laminated angle-ply composite spherical caps. Compos. Struct. 59, 89–97 (2003) CrossRefGoogle Scholar
  14. 14.
    Yaffe, R., Abramovich, H.: Dynamic buckling of cylindrical stringer stiffened shells. Comput. Struct. 81, 1031–1039 (2003) CrossRefGoogle Scholar
  15. 15.
    Bisagni, C.: Dynamic buckling of fiber composite shells under impulsive axial compression. Thin-Walled Struct. 43, 499–514 (2005) CrossRefGoogle Scholar
  16. 16.
    Spottswood, S.M., Hollkamp, J.J., Eason, T.G.: On the use of reduced-order models for a shallow curved beam under combined loading. In: Proceedings of the 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Schaumburg, IL (2008) Google Scholar
  17. 17.
    Gordon, R.W., Hollkamp, J.J.: Reduced-order modeling of the random response of curved beams using implicit condensation. In: Proceedings of the 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Newport, RI (2006) Google Scholar
  18. 18.
    Przekop, A., Rizzi, S.A.: Nonlinear reduced order random response analysis of structures with shallow curvature. AIAA J. 44(8), 1767–1778 (2006) CrossRefGoogle Scholar
  19. 19.
    Tiso, P., Jansen, E.L., Abdalla, M.M.: A reduction method for finite element nonlinear dynamic analysis of shells. In: Proceedings of the 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Newport, RI (2006) Google Scholar
  20. 20.
    Olesen, J.F., Byskov, E.: Accurate determination of asymptotic postbuckling stresses by the finite element method. Comput. Struct. 15, 157–163 (1982) zbMATHCrossRefGoogle Scholar
  21. 21.
    Peek, R., Kheyrkhahan, M.: Postbuckling behavior and imperfection sensitivity of elastic structures by the Lyapunov–Schmidt–Koiter approach. Comput. Methods Appl. Mech. Eng. 108, 261–279 (1993) MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Garcea, G., Casciaro, R., Attanasio, G., Giordano, F.: Perturbation approach to elastic post-buckling analysis. Comput. Struct. 66, 585–595 (1998) zbMATHCrossRefGoogle Scholar
  23. 23.
    Menken, C.M., Schreppers, G.M.A., Groot, W.J., Petterson, R.: Analyzing buckling mode interactions in elastic structures using an asymptotic approach; theory and experiment. Comput. Struct. 64, 473–480 (1997) CrossRefGoogle Scholar
  24. 24.
    Kheyrkhahan, M., Peek, R.: Postbuckling analysis and imperfection sensitivity of general shells by the finite element method. Int. J. Solids Struct. 36, 2641–2681 (1999) zbMATHCrossRefGoogle Scholar
  25. 25.
    Rahman, T., Jansen, E.L.: Finite element based coupled mode initial post-buckling analysis of a composite cylindrical shell. Thin-Walled Struct. 48, 25–32 (2010) CrossRefGoogle Scholar
  26. 26.
    Budiansky, B.: Dynamic buckling of elastic structures: Criteria and estimates. In: Dynamic Stability of Structures. Pergamon, Elmsford (1967) Google Scholar
  27. 27.
    Byskov, E., Hutchinson, J.W.: Mode interaction in axially stiffened cylindrical shells. AIAA J. 15, 941–948 (1977) CrossRefGoogle Scholar
  28. 28.
    Chen, H., Virgin, L.N.: Finite element analysis of post-buckling dynamics in plates—Part I: An asymptotic approach. Int. J. Solids Struct. 43, 3983–4007 (2006) zbMATHCrossRefGoogle Scholar
  29. 29.
    Teter, A.: Dynamic, multimode buckling of thin-walled columns subjected to in-plane pulse loading. Int. J. Non-Linear Mech. 45, 207–218 (2010) CrossRefGoogle Scholar
  30. 30.
    Schokker, A., Sridharan, S., Kasagi, A.: Dynamic buckling of composite shells. Comput. Struct. 59, 43–53 (1996) zbMATHCrossRefGoogle Scholar
  31. 31.
    DIANA User’s Manual—Release 9.2. Delft, The Netherlands (2007) Google Scholar
  32. 32.
    Schweizerhof, K., Ramm, E.: Displacement dependent pressure loads in nonlinear finite element analyses. Comput. Struct. 18(6), 1099–1114 (1984) zbMATHCrossRefGoogle Scholar
  33. 33.
    Arbocz, J., Hol, J.M.A.M.: Koiter’s stability theory in a computer-aided engineering (CAE) environment. Int. J. Solids Struct. 26, 945–975 (1990) zbMATHCrossRefGoogle Scholar
  34. 34.
    Jansen, E.L.: A perturbation method for nonlinear vibrations of imperfect structures: Application to cylindrical shell vibrations. Int. J. Solids Struct. 45, 1124–1145 (2008) zbMATHCrossRefGoogle Scholar
  35. 35.
    Booton, M.: Buckling of imperfect anisotropic cylinders under combined loading. Technical report 203, UTIAS (1976) Google Scholar
  36. 36.
    ABAQUS Analysis User’s Manual—Version 6.8 (2008) Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.TNO DIANA BVDelftThe Netherlands
  2. 2.Institut für Statik und DynamikLeibniz Universität HannoverHannoverGermany
  3. 3.Faculty of Aerospace EngineeringDelft University of TechnologyHS DelftThe Netherlands

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