Restabilization in structures susceptible to localized buckling: An approximate method for the extended post-buckling regime

Journal of Engineering Mathematics

Volumn 38, Issue 1, 2000, Pages 77-90

  Wadee, M Khurram ^a   Bassom, Andrew P ^a,b  

^a UNIVERSITY OF EXETER   (United Kingdom)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Double scale perturbation; Dynamical systems; Homoclinic and heteroclinic orbits; Non periodic Rayleigh Ritz analysis; Structural localization

Indexed keywords

BUCKLING;

EID: 0034047035     PISSN: 00220833     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004611005185     Document Type: Article

References (17)

1. C. Fox, An Introduction to the Calculus of Variations. London: Oxford University Press (1963) 271pp.
2. J. M. T. Thompson and G. W. Hunt, A General Theory of Elastic Stability. London: Wiley (1987) 322pp.
3. 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.
4. G. W. Hunt and M. K. Wadee, Comparative lagrangian formulations for localized buckling. Proc. R. Soc. London A 434 (1991) 485-502.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. M. K. Wadee, Elements of a Langrangion Theory of Localized Buckling. PhD thesis: Imperial College of Science, Technology and Medicine, London (1993) 245pp.
11. 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.
12. T.-S. Yang and T. R. Akylas, On asymmetric gravity-capillary solitary waves. J. Fluid Mech. 330 (1997) 215-232.
13. A. R. Champneys and J. F. Toland, Bifurcation of a plethora of multi-modal homoclinic orbits for Hamiltonian systems. Nonlinearity 6 (1993) 665-721.
14. 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.
15. Wolfram Research Inc., MATHEMATICA: A System for doing Mathematics by Computer. Champaign, Illinois: Wolfram Research, Inc. (1995) 749pp.
16. 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.
17. 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.