The Mathematical Institute, University of Oxford, Eprints Archive

Axisymmetric buckling of a spherical shell embedded in an elastic medium under uniaxial stress at infinity

Jones, G. W. and Chapman, S. J. and Allwright, D. J. (2007) Axisymmetric buckling of a spherical shell embedded in an elastic medium under uniaxial stress at infinity. The Quarterly Journal of Mechanics and Applied Mathematics . (Submitted)

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Abstract

The problem of a thin spherical linearly-elastic shell, perfectly bonded to an infinite linearly-elastic medium is considered. A constant axisymmetric stress field is applied at infinity in the matrix, and the displacement and stress fields in the shell and matrix are evaluated by means of harmonic potential functions. In order to examine the stability of this solution, the buckling problem of a shell which experiences this deformation is considered. Using Koiter's nonlinear shallow shell theory, restricting buckling patterns to those which are axisymmetric, and using the Rayleigh–Ritz method by expanding the buckling patterns in an infinite series of Legendre functions, an eigenvalue problem for the coefficients in the infinite series is determined. This system is truncated and solved numerically in order to analyse the behaviour of the shell as it undergoes buckling, and to identify the critical buckling stress in two cases — namely where the shell is hollow and the stress at infinity is either uniaxial or radial.

Item Type:Article
Subjects:H - N > Mechanics of deformable solids
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:670
Deposited By:Gareth Wyn Jones
Deposited On:20 Nov 2007
Last Modified:20 Jul 2009 14:23

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