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

Coman, Ciprian D.; Bassom, Andrew P.

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


Authors

Ciprian D. Coman

Andrew P. Bassom



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.

Citation

Coman, C. D., & Bassom, A. P. (in press). Wrinkling structures at the rim of an initially stratched circular thin plate subjected to transverse pressure. SIAM Journal on Applied Mathematics, 78(2), https://doi.org/10.1137/17M1155193

Journal Article Type Article
Acceptance Date Jan 30, 2018
Online Publication Date Mar 29, 2018
Deposit Date Feb 16, 2018
Publicly Available Date Mar 29, 2024
Journal SIAM Journal on Applied Mathematics
Print ISSN 0036-1399
Electronic ISSN 1095-712X
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 78
Issue 2
DOI https://doi.org/10.1137/17M1155193
Keywords thin films; wrinkling; Föppl–von Kármán plate equations; asymptotic methods
Public URL https://nottingham-repository.worktribe.com/output/922474
Publisher URL https://epubs.siam.org/doi/10.1137/17M1155193
Additional Information © 2018 Society for Industrial and Applied Mathematics

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