Happy Catastrophe: recent progress in analysis and exploitation of elastic instability
dc.contributor.author | Dodwell, T | |
dc.contributor.author | Hunt, G | |
dc.contributor.author | Champneys, A | |
dc.contributor.author | Groh, R | |
dc.contributor.author | Neville, R | |
dc.contributor.author | Pirrera, A | |
dc.contributor.author | Sakhaei, A | |
dc.contributor.author | Schenk, M | |
dc.contributor.author | Wadee, A | |
dc.date.accessioned | 2019-07-08T11:55:53Z | |
dc.date.issued | 2019-07-30 | |
dc.description.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 assessments 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. Pseudoarclength 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. | en_GB |
dc.description.sponsorship | Alan Turing Institute | en_GB |
dc.description.sponsorship | Royal Academy of Engineering | en_GB |
dc.description.sponsorship | Engineering and Physical Sciences Research Council | en_GB |
dc.identifier.citation | Vol. 5 (34). Published online 30 July 2019. | en_GB |
dc.identifier.doi | 10.3389/fams.2019.00034 | |
dc.identifier.grantnumber | EP/N510129/1 | en_GB |
dc.identifier.grantnumber | RF\201718\17178 | en_GB |
dc.identifier.grantnumber | EP/M013170/1 | en_GB |
dc.identifier.grantnumber | EP/N509619/1 | en_GB |
dc.identifier.uri | http://hdl.handle.net/10871/37888 | |
dc.language.iso | en | en_GB |
dc.publisher | Frontiers Media S.A. | en_GB |
dc.rights | © 2019 Champneys, Dodwell, Groh, Hunt, Neville, Pirrera, Sakhaei, Schenk and Wadee. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) (http://creativecommons.org/licenses/by/4.0/). 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. | |
dc.subject | instability | en_GB |
dc.subject | Elastic | en_GB |
dc.subject | buckling | en_GB |
dc.subject | Sub-critical | en_GB |
dc.subject | localisation | en_GB |
dc.subject | path-following | en_GB |
dc.subject | Mountain-pass | en_GB |
dc.title | Happy Catastrophe: recent progress in analysis and exploitation of elastic instability | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2019-07-08T11:55:53Z | |
dc.description | This is the author accepted manuscript. The final version is available from Frontiers Media via the DOI in this record. | en_GB |
dc.identifier.eissn | 2297-4687 | |
dc.identifier.journal | Frontiers in Applied Mathematics and Statistics | en_GB |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en_GB |
dcterms.dateAccepted | 2019-07-03 | |
rioxxterms.version | AM | en_GB |
rioxxterms.licenseref.startdate | 2019-07-03 | |
rioxxterms.type | Journal Article/Review | en_GB |
refterms.dateFCD | 2019-07-05T22:39:17Z | |
refterms.versionFCD | AM | |
refterms.dateFOA | 2019-07-30T08:07:02Z | |
refterms.panel | B | en_GB |
Files in this item
This item appears in the following Collection(s)
Except where otherwise noted, this item's licence is described as © 2019 Champneys, Dodwell, Groh, Hunt, Neville, Pirrera, Sakhaei, Schenk and Wadee. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) (http://creativecommons.org/licenses/by/4.0/). 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.