On the Problem of the Theory of Elasticity for a Region Containing more than Two Spherical Cavities

Abstract

A method of solution is proposed to solve the problem of the theory of elasticity for a region containing more than two spherical cavities, extending the method utilized by A. E. Green for plates with circular holes. The method consists of the simple expression of harmonic function referred to a spherical coordinate by the sequences of those referred to another spherical coordinate. The solution is based upon the Boussinesq stress-function approach, and a series solution is obtained for the problem of elasticity for a region containing more than two spherical cavities whose centres lie on a straight line. Numerical evaluations are given for the stress distributions along the boundaries of cavities when the elastic body is under a uniform tension in the direction of a centre line.