Abstract
Localized buckling in structures has been extensively studied in the context of simple nonlinear models which capture the essence of the phenomenon near the lowest critical load. In this study we apply a non-periodic Rayleigh–Ritz procedure to track localizations into the far post-buckling regime where the structure regains stability after the initial destabilization. The results are compared against independent numerical solutions and good agreement is found.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. Fox, An Introduction to the Calculus of Variations. London: Oxford University Press (1963) 271pp.
J. M. T. Thompson and G. W. Hunt, A General Theory of Elastic Stability. London: Wiley (1987) 322pp.
G. W. Hunt, H. M. Bolt and J. M. T. Thompson, Structural localization phenomena and the dynamical phase-space analogy. Proc. R. Soc. London A 425 (1989) 245-267.
G. W. Hunt and M. K. Wadee, Comparative lagrangian formulations for localized buckling. Proc. R. Soc. London A 434 (1991) 485-502.
M. K. Wadee, G. W. Hunt and A. I. M. Whiting, Asymptotic and Rayleigh-Ritz routes to localized buckling solutions in an elastic instability problem. Proc. R. Soc. London A 453 (1997) 2085-2107.
G. W. Hunt, M. K. Wadee and N. Shiacolas, Localized elasticæ for the strut on the linear foundation. Trans. ASME J. Appl. Mech. 60 (1993) 1033-1038.
M. K. Wadee, The elastic strut on an elastic foundation: A model localized buckling problem. In: A. R. Champneys, G. W. Hunt and J. M. T. Thompson (eds.), Localization and Solitary Waves in Solid Mechanics. Singapore World Scientific (1999). To appear.
G. J. Lord, A. R. Champneys and G. W. Hunt, Computation of localized post buckling in long axially compressed cylindrical shells. Phil. Trans. R. Soc. London A 355 (1997) 2137-2150.
P. D. Woods and A. R. Champneys, Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian Hopf bifurcation. Physica D (1999) Volume 129, pp. 147-170.
M. K. Wadee, Elements of a Langrangian Theory of Localized Buckling. PhD thesis: Imperial College of Science, Technology and Medicine, London (1993) 245pp.
G. W. Hunt, M. A. Peletier, A. R. Champneys, P. D. Woods, M. A.Wadee, C. J. Budd and G. J. Lord, Cellular buckling in long structures. Nonlinear Dynamics (1999) to appear.
T.-S. Yang and T. R. Akylas, On asymmetric gravity-capillary solitary waves. J. Fluid Mech. 330 (1997) 215-232.
A. R. Champneys and J. F. Toland, Bifurcation of a plethora of multi-modal homoclinic orbits for Hamiltonian systems. Nonlinearity 6 (1993) 665-721.
M. K. Wadee and A. P. Bassom, Effects of exponentially small terms in the perturbation approach to localized buckling. Proc. R. Soc. London A (1999). Volume 455, pp. 2351-2370.
Wolfram Research Inc., MATHEMATICA: A System for doing Mathematics by Computer. Champaign, Illinois: Wolfram Research, Inc. (1995) 749pp.
W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vetterling, Numerical Recipes in C. The Art of Scientific Programming. New York: Cambridge University Press (1992) 994pp.
E. J. Doedel, A. R. Champneys, T. F. Fairgrieve, Y. A. Kuznetsov, B. Sandstede and X. Wang, AUTO 97: Continuation and bifurcation software for ordinary differential equations. (1997). Available via anonymous ftp from ftp://ftp.cs.concordia.ca/pub/doedel/auto.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Khurram Wadee, M., Bassom, A.P. Restabilization in structures susceptible to localized buckling: an approximate method for the extended post-buckling regime. Journal of Engineering Mathematics 38, 77–90 (2000). https://doi.org/10.1023/A:1004611005185
Issue Date:
DOI: https://doi.org/10.1023/A:1004611005185