On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities

Coman, Ciprian D. (2018) On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities. Acta Mechanica, 229 (3). pp. 1099-1109. ISSN 1619-6937

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Abstract

Weakly clamped uniformly stretched thin elastic plates can experience edge buckling when subjected to a transverse pressure. This situation is revisited here for a circular plate, under the assumption of finite rotations and negligible bending stiffness in the pre-buckling range. The eigenproblem describing this instability is formulated in terms of two singularly perturbed fourth-order differential equations involving the non-dimensional bending stiffness ε>0. By using an extension of the asymptotic reduction technique proposed by Coman and Haughton (Acta Mech 55:179–200, 2006), these equations are formally reduced to a simple second-order ordinary differential equation in the limit ε→0+. It is further shown that the predictions of this reduced problem are in excellent agreement with the direct numerical simulations of the original bifurcation equations.

Item Type: Article
Additional Information: This is a post-peer-review, pre-copyedit version of an article published in Acta Mechanica. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00707-017-2036-8.
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1007/s00707-017-2036-8
Depositing User: Eprints, Support
Date Deposited: 04 Jan 2018 15:50
Last Modified: 10 Apr 2018 16:24
URI: http://eprints.nottingham.ac.uk/id/eprint/48940

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