Singular behaviour in a generalized boundary eigenvalue problem for annular plates in tension

Ciprian D. Coman, Andrew P. Bassom

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

A novel application of boundary-layer asymptotic techniques to a generalized linear eigenvalue problem is presented. Our investigation is concerned with a bifurcation equation that governs the formation of wrinkles in thin annular plates subjected to in-plane tensile loading on the inner boundary. If η denotes the ratio of the inner and outer radii of the annulus, then the critical wrinkling load satisfies Λ = ΛC(η), where the function ΛC is available only numerically. It is known that there is a critical value ̂η such that Λ → ∞ as η → ̂η but, until now, little has been understood about this singular behaviour. Asymptotic methods enable us to capture accurately and describe the nature of this blow-up phenomenon which we show is sensitive to the forms of the boundary conditions imposed at the edges of the annular plate. Our analytical findings are complemented by a series of comparisons with direct numerical simulations that shed further light on the singular behaviour.

LanguageEnglish
Pages319-336
Number of pages18
JournalQuarterly Journal of Mechanics and Applied Mathematics
Volume60
Issue number3
Early online date6 Jul 2007
DOIs
Publication statusPublished - Aug 2007
Externally publishedYes

Fingerprint

annular plates
Direct numerical simulation
Boundary Problem
Eigenvalue Problem
Boundary layers
eigenvalues
Boundary conditions
Wrinkling
wrinkling
asymptotic methods
annuli
Asymptotic Methods
Ring or annulus
direct numerical simulation
Blow-up
Critical value
Boundary Layer
boundary layers
Bifurcation
Radius

Cite this

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abstract = "A novel application of boundary-layer asymptotic techniques to a generalized linear eigenvalue problem is presented. Our investigation is concerned with a bifurcation equation that governs the formation of wrinkles in thin annular plates subjected to in-plane tensile loading on the inner boundary. If η denotes the ratio of the inner and outer radii of the annulus, then the critical wrinkling load satisfies Λ = ΛC(η), where the function ΛC is available only numerically. It is known that there is a critical value ̂η such that Λ → ∞ as η → ̂η but, until now, little has been understood about this singular behaviour. Asymptotic methods enable us to capture accurately and describe the nature of this blow-up phenomenon which we show is sensitive to the forms of the boundary conditions imposed at the edges of the annular plate. Our analytical findings are complemented by a series of comparisons with direct numerical simulations that shed further light on the singular behaviour.",
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Singular behaviour in a generalized boundary eigenvalue problem for annular plates in tension. / Coman, Ciprian D.; Bassom, Andrew P.

In: Quarterly Journal of Mechanics and Applied Mathematics, Vol. 60, No. 3, 08.2007, p. 319-336.

Research output: Contribution to journalArticle

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