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Happy catastrophe: Recent progress in analysis and exploitation of elastic instability

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Title: Happy catastrophe: Recent progress in analysis and exploitation of elastic instability
Authors: Champneys, AR
Dodwell, TJ
Groh, RMJ
Hunt, GW
Neville, RM
Pirrera, A
Sakhaei, AH
Schenk, M
Wadee, MA
Item Type: Journal Article
Abstract: A synthesis of recent progress is presented on a topic that lies at the heart of both structural engineering and nonlinear science. The emphasis is on thin elastic structures that lose stability subcritically — without a nearby stable post-buckled state — a canonical example being a uniformly axially-loaded cylindrical shell. Such structures are hard to design and certify because imperfections or shocks trigger buckling at loads well below the threshold of linear stability. A resurgence of interest in structural instability phenomena suggests practical stability assessment require stochastic approaches and imperfection maps. This article surveys a different philosophy; the buckling process and ultimate post-buckled state are well described by the perfect problem. The significance of the Maxwell load is emphasised, where energy of the unbuckled and fully developed buckle patterns are equal, as is the energetic preference of localised states, stable and unstable versions of which connect in a snaking load-deflection path. The state of the art is presented on analytical, numerical and experimental methods. Pseudo15 arclength continuation (path-following) of a finite-element approximation computes families of complex localised states. Numerical implementation of a mountain-pass energy method then predicts the energy barrier through which the buckling process occurs. Recent developments also indicate how such procedures can be replicated experimentally; unstable states being accessed by careful control of constraints, and stability margins assessed by shock sensitivity experiments. Finally, the fact that subcritical instabilities can be robust, not being undone by reversal of the loading path, opens up potential for technological exploitation. Several examples at different length scales are discussed; a cable-stayed prestressed column, two examples of adaptive structures inspired by morphing aeroelastic surfaces, and a model for a functional auxetic material.
Issue Date: 30-Jul-2019
Date of Acceptance: 3-Jul-2019
URI: http://hdl.handle.net/10044/1/71848
DOI: https://dx.doi.org/10.3389/fams.2019.00034
ISSN: 2297-4687
Journal / Book Title: Frontiers in Applied Mathematics and Statistics
Copyright Statement: © 2019 Hunt, Champneys, Dodwell, Groh, Neville, Pirrera, Sakhaei, Schenk and Wadee. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
Publication Status: Accepted
Online Publication Date: 2019-07-07
Appears in Collections:Faculty of Engineering
Civil and Environmental Engineering



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