Ciprian D. Coman
Wrinkling structures at the rim of an initially stratched circular thin plate subjected to transverse pressure
Coman, Ciprian D.; Bassom, Andrew P.
Authors
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 |
Files
siam_COMAN2018.pdf
(1.5 Mb)
PDF
17m1155193.pdf
(1.3 Mb)
PDF
Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf
Downloadable Citations
About Repository@Nottingham
Administrator e-mail: digital-library-support@nottingham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search