Inhomogeneities and localised buckling patterns

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

The aim of this paper is to re-examine the phenomenon of localisation in the classical problem of buckling of the elastica on a linear elastic foundation. Largely speaking, our efforts are concentrated on certain spatial variations of the mechanical characteristics of the foundation. This new feature changes the spectral properties of the linearised bifurcation problem and leads to linear localised eigenmodes; the expressions of these buckling modes are found with the help of a complex WKB approximation. By considering numerical simulations of the full non-linear problem, we then investigate the evolution of the instability patterns in the post-buckling regime. In contrast to other recent studies on similar problems, the approach taken here is conducted upon the assumption of finite length for the system under discussion.

LanguageEnglish
Pages133-152
Number of pages20
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume71
Issue number1
DOIs
Publication statusPublished - 1 Feb 2006
Externally publishedYes

Fingerprint

Buckling
Inhomogeneity
Complex Approximation
Elastica
WKB Approximation
Elastic Foundation
Postbuckling
Spectral Properties
Nonlinear Problem
Bifurcation
Numerical Simulation
Computer simulation

Cite this

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abstract = "The aim of this paper is to re-examine the phenomenon of localisation in the classical problem of buckling of the elastica on a linear elastic foundation. Largely speaking, our efforts are concentrated on certain spatial variations of the mechanical characteristics of the foundation. This new feature changes the spectral properties of the linearised bifurcation problem and leads to linear localised eigenmodes; the expressions of these buckling modes are found with the help of a complex WKB approximation. By considering numerical simulations of the full non-linear problem, we then investigate the evolution of the instability patterns in the post-buckling regime. In contrast to other recent studies on similar problems, the approach taken here is conducted upon the assumption of finite length for the system under discussion.",
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Inhomogeneities and localised buckling patterns. / Coman, Ciprian D.

In: IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), Vol. 71, No. 1, 01.02.2006, p. 133-152.

Research output: Contribution to journalArticle

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