CUED Publications database

Stable Spatially Localized Configurations in a Simple Structure—A Global Symmetry-Breaking Approach

Pandurangi, SS and Elliott, RS and Healey, TJ and Triantafyllidis, N (2020) Stable Spatially Localized Configurations in a Simple Structure—A Global Symmetry-Breaking Approach. Journal of Elasticity, 142. pp. 163-199. ISSN 0374-3535

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Abstract

We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in many applications in mechanics. Instead of a numerical search for such solutions using arbitrary imperfections, we propose a systematic search using branch-following and bifurcation techniques along with group-theoretic methods to find all the bifurcated solution orbits (primary, secondary, etc.) of the system and to examine their stability and hence their observability. Unlike previously proposed methods that use multi-scale perturbation techniques near the critical load, we show that to obtain a spatially localized deformation equilibrium path for the perfect structure, one has to consider the secondary bifurcating path with the longest wavelength and follow it far away from the critical load. The novel use of group-theoretic methods here illustrates a general methodology for the systematic analysis of structures with a high degree of symmetry.

Item Type: Article
Subjects: UNSPECIFIED
Divisions: Div C > Materials Engineering
Depositing User: Cron Job
Date Deposited: 28 Oct 2020 20:19
Last Modified: 18 May 2021 01:54
DOI: 10.1007/s10659-020-09794-5