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

Citation

Coman, C and Bassom, AP, Wrinkling structures at the rim of an initially stretched circular thin plate subjected to transverse pressure, SIAM Journal on Applied Mathematics, 78, (2) pp. 1009-1029. ISSN 0036-1399 (2018) [Refereed Article]


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Copyright Statement

Copyright © 2018 Society for Industrial and Applied Mathematics

DOI: doi:10.1137/17M1155193

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, 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, 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 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 Details

Item Type:Refereed Article
Keywords:wrinkling
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Theoretical and Applied Mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Bassom, AP (Professor Andrew Bassom)
ID Code:125147
Year Published:2018
Deposited By:Mathematics and Physics
Deposited On:2018-03-30
Last Modified:2018-05-10
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