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)

PDF
538kB 
Abstract
The problem of a thin spherical linearlyelastic shell, perfectly bonded to an infinite linearlyelastic 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:  29 May 2015 18:26 
Repository Staff Only: item control page