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Happy Catastrophe: Recent Progress in Analysis and Exploitation of Elastic Instability

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Happy Catastrophe : Recent Progress in Analysis and Exploitation of Elastic Instability. / Champneys, Alan; Dodwell, Timothy; Groh, Rainer; Hunt, Giles; Neville, Robin; Pirrera, Alberto; Sakhaei, Amir; Schenk, Mark; Wadee, Ahmer.

In: Frontiers in Applied Mathematics and Statistics, Vol. 5, No. 34, 30.07.2019.

Research output: Contribution to journalArticle

Harvard

Champneys, A, Dodwell, T, Groh, R, Hunt, G, Neville, R, Pirrera, A, Sakhaei, A, Schenk, M & Wadee, A 2019, 'Happy Catastrophe: Recent Progress in Analysis and Exploitation of Elastic Instability', Frontiers in Applied Mathematics and Statistics, vol. 5, no. 34. https://doi.org/10.3389/fams.2019.00034

APA

Champneys, A., Dodwell, T., Groh, R., Hunt, G., Neville, R., Pirrera, A., ... Wadee, A. (2019). Happy Catastrophe: Recent Progress in Analysis and Exploitation of Elastic Instability. Frontiers in Applied Mathematics and Statistics, 5(34). https://doi.org/10.3389/fams.2019.00034

Vancouver

Champneys A, Dodwell T, Groh R, Hunt G, Neville R, Pirrera A et al. Happy Catastrophe: Recent Progress in Analysis and Exploitation of Elastic Instability. Frontiers in Applied Mathematics and Statistics. 2019 Jul 30;5(34). https://doi.org/10.3389/fams.2019.00034

Author

Champneys, Alan ; Dodwell, Timothy ; Groh, Rainer ; Hunt, Giles ; Neville, Robin ; Pirrera, Alberto ; Sakhaei, Amir ; Schenk, Mark ; Wadee, Ahmer. / Happy Catastrophe : Recent Progress in Analysis and Exploitation of Elastic Instability. In: Frontiers in Applied Mathematics and Statistics. 2019 ; Vol. 5, No. 34.

Bibtex

@article{3641bfcb322a42cf8d996e9a94472161,
title = "Happy Catastrophe: Recent Progress in Analysis and Exploitation of Elastic Instability",
abstract = "A synthesis of recent progress is presented on a topic that lies at the heart of both structural engineering and non-linear 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 emphasized, where energy of the unbuckled and fully-developed buckle patterns are equal, as is the energetic preference of localized 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. Pseudo-arclength continuation (path-following) of a finite-element approximation computes families of complex localized 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.",
keywords = "instability, elastic, buckling, sub-critical, localization, path-following, mountain-pass",
author = "Alan Champneys and Timothy Dodwell and Rainer Groh and Giles Hunt and Robin Neville and Alberto Pirrera and Amir Sakhaei and Mark Schenk and Ahmer Wadee",
year = "2019",
month = "7",
day = "30",
doi = "10.3389/fams.2019.00034",
language = "English",
volume = "5",
journal = "Frontiers in Applied Mathematics and Statistics",
issn = "2297-4687",
publisher = "Frontiers Media S.A.",
number = "34",

}

RIS - suitable for import to EndNote

TY - JOUR

T1 - Happy Catastrophe

T2 - Recent Progress in Analysis and Exploitation of Elastic Instability

AU - Champneys, Alan

AU - Dodwell, Timothy

AU - Groh, Rainer

AU - Hunt, Giles

AU - Neville, Robin

AU - Pirrera, Alberto

AU - Sakhaei, Amir

AU - Schenk, Mark

AU - Wadee, Ahmer

PY - 2019/7/30

Y1 - 2019/7/30

N2 - A synthesis of recent progress is presented on a topic that lies at the heart of both structural engineering and non-linear 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 emphasized, where energy of the unbuckled and fully-developed buckle patterns are equal, as is the energetic preference of localized 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. Pseudo-arclength continuation (path-following) of a finite-element approximation computes families of complex localized 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.

AB - A synthesis of recent progress is presented on a topic that lies at the heart of both structural engineering and non-linear 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 emphasized, where energy of the unbuckled and fully-developed buckle patterns are equal, as is the energetic preference of localized 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. Pseudo-arclength continuation (path-following) of a finite-element approximation computes families of complex localized 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.

KW - instability

KW - elastic

KW - buckling

KW - sub-critical

KW - localization

KW - path-following

KW - mountain-pass

U2 - 10.3389/fams.2019.00034

DO - 10.3389/fams.2019.00034

M3 - Article

VL - 5

JO - Frontiers in Applied Mathematics and Statistics

JF - Frontiers in Applied Mathematics and Statistics

SN - 2297-4687

IS - 34

ER -