Wrinkling structures at the rim of an initially stratched circular thin plate subjected to transverse pressure

Coman, Ciprian D. and Bassom, Andrew P. (2018) Wrinkling structures at the rim of an initially stratched circular thin plate subjected to transverse pressure. SIAM Journal on Applied Mathematics, 78 (2). pp. 1009-1029. ISSN 1095-712X

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Abstract

Short-wavelength wrinkles that appear on an initially stretched thin elastic plate under transverse loading are examined. As the degree of loading is increased so wrinkles appear and their structure at the onset of buckling takes on one of three distinct forms depending on the size of the imposed stretching. With relatively little stretching, the wrinkles sit off the rim of the plate at a location which is not known a priori, but which is determined via a set of consistency conditions. These take the form of constraints on the solutions of certain coupled nonlinear differential equations that are solved numerically. As the degree of stretching grows, so an asymptotic solution of the consistency conditions is possible which heralds the structure that governs a second regime. Now the wrinkle sits next to the rim where its detailed structure can be described by the solution of suitably scaled Airy equations. In each of these first two regimes the Föppl–von Kármán bifurcation equations remain coupled, but as the initial stretching becomes yet stronger the governing equations separate. Further use of singular-perturbation arguments allows us to identify the wavelength wrinkle which is likely to be preferred in practice.

Item Type: Article
Additional Information: © 2018 Society for Industrial and Applied Mathematics
Keywords: thin films; wrinkling; Föppl–von Kármán plate equations; asymptotic methods
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1137/17M1155193
Depositing User: Eprints, Support
Date Deposited: 16 Feb 2018 13:07
Last Modified: 11 Jun 2018 21:28
URI: http://eprints.nottingham.ac.uk/id/eprint/49827

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