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Wrinkles around the inner hole of a uniformly tensioned annulus with applied in-plane uniform circumferential displacement at the inner radius

Ciprian D. Coman (1) and Andrew P. Bassom (2)
(1) Department of Mathematics, University of Glasgow University Gardens, Glasgow G12 8QW, UK
(2) School of Mathematics and Statistics, University of Western Australia
Crawley 6009, Australia

“Boundary layers and stress concentration in the circular shearing of annular thin films”, Proceedings of the Royal Society A, Vol. 463, No. 2087, pp. 3037-3053, November 2007, DOI: 10.1098/rspa.2007.0106

ABSTRACT: This work addresses a generalization of Dean's classical problem, which sought to explain how an annular thin elastic plate buckles under uniform shearing forces applied around its edges. We adapt the original setting by assuming that the outer edge is radially stretched while the inner rim undergoes in-plane rotation through some small angle. Boundary-layer methods are used to investigate analytically the deformation pattern which is set up and localized around the inner hole when this angle reaches a well-defined critical wrinkling value. Linear stability theory enables us to identify both the critical load and the preferred number of wrinkles appearing in the deformed configuration. Our asymptotic results are compared with a number of direct numerical simulations.

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