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On truncation of the structural potential function

Published online by Cambridge University Press:  24 October 2008

G. W. Hunt  and
K. A. J. Williams
G. W. Hunt
Affiliation:
Department of Civil Engineering, Imperial College, London
K. A. J. Williams
Affiliation:
Department of Civil Engineering, Imperial College, London
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Abstract

Two, essentially different, criteria for truncating a potential function of a conservative structural system are reviewed, one based on deflection considerations and the other on the mathematical concept of determinacy. Formulations in which they give different results are discussed; most importantly, these include Koiter's 1976 form for mode interaction in stiffened structure [11], which exhibits Thorn's parabolic umbilic catastrophe [15]. For this case, two alternative schemes of perturbation analysis are presented, each describing asymptotically the post-buckling response. The more obvious approach turns out to be the less successful, being linked to an indeterminate, too severely truncated, form of the potential function.

The second, determinacy linked, approach generates as a first-order response a distinctive looping pattern of equilibrium paths, which has recently been identified in a simple model due to Budiansky and Hutchinson[1], by exact, closed-form, solution [8]. The convergence of each asymptotic scheme to the exact solution is briefly reviewed for this simple model, by plotting first and second order results.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 3 , May 1984 , pp. 495 - 510
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

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