Stress Distributions Analyzed in Bispherical Co-Ordinates

Abstract

Boussinesq-Papkovich potentials are used in conjunction with the bispherical co-ordinate system to analyze three problems in the classical theory of linear elasticity: (a) The extension of the Boussinesq point-load problem to that in which the half-space contains a spherical cavity; (b) the determination of the stress distribution in an eccentric spherical shell under uniform internal pressure; (c) the determination of the stress distribution in a half-space containing a uniformly pressurized spherical cavity. Numerical results are presented for representative configurations and load distributions in each case.