Wrinkling Structures at the Rim of an Initially Stretched Circular Thin Plate Subjected to Transverse Pressure

Ciprian D. Coman, Andrew P. Bassom

Research output: Contribution to journalArticle

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 F oppl-von K arman 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.

LanguageEnglish
Pages1009-1029
Number of pages21
JournalSIAM Journal on Applied Mathematics
Volume78
Issue number2
DOIs
Publication statusPublished - 29 Mar 2018
Externally publishedYes

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Wrinkling
Circular Plate
Thin Plate
Stretching
Consistency Conditions
Transverse
Wavelength
Elastic Plate
Asymptotics of Solutions
Singular Perturbation
Buckling
Nonlinear Differential Equations
Governing equation
Bifurcation
Likely
Distinct
Differential equations
Form

Cite this

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Wrinkling Structures at the Rim of an Initially Stretched Circular Thin Plate Subjected to Transverse Pressure. / Coman, Ciprian D.; Bassom, Andrew P.

In: SIAM Journal on Applied Mathematics, Vol. 78, No. 2, 29.03.2018, p. 1009-1029.

Research output: Contribution to journalArticle

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