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


Coman, CD and Bassom, AP, Singular behaviour in a generalized boundary eigenvalue problem for annular plates in tension, Quarterly Journal of Mechanics and Applied Mathematics, 60, (3) pp. 319-336. ISSN 0033-5614 (2007) [Refereed Article]

DOI: doi:10.1093/qjmam/hbm009


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<

Item Details

Item Type:Refereed Article
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
UTAS Author:Bassom, AP (Professor Andrew Bassom)
ID Code:107354
Year Published:2007
Web of Science® Times Cited:7
Deposited By:Mathematics and Physics
Deposited On:2016-03-11
Last Modified:2016-07-08

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