Three-Dimentsional Stress Concentration around a Spherical Cavity in a Semi-Infinite Elastic Body

Abstract

This paper contains a three-dimensional solution for the stresses and deformations arising in a semi-infinite body with a spherical cavity stressed at infinity.Formerly, such a problem approached by means of spherical dipolar co-ordinates. The method used here is based on the Boussinesq's stress-function approach referred to the cylindrical and spherical co-ordinates.The problem can be reduced to one in two simply connected domains, i.e., a semi-infinite region and an infinite region excluding the cavity. The two stress functions in each region are given by simple expressions of the cylindrical and spherical harmonics.The boundary conditions on the face of the semi-infinite body and the surface of the cavity are satisfied by the relations between the cylindrical and spherical harmonics.Numerical results are given for six different radii of the cavity.