A Boussinesq's Problem of an Elastic Half Space with an Elastic Spherical Inclusion

Abstract

The problem of determing of stresses and displacements of an elastic half space subjected to a concentrated force acting at a point of the plane surface is called Boussinesq's problem. This paper deals with Boussinesq's problems of an elastic half space with an elastic spherical inclusion. We use a body force distribution method for the stress concentration problem. For this purpose, we apply the Green's functions for axisymmetric body force problems of an elastic half space and the fundamental solution for axisymmetric body force problems of elasticity. The problem is formulated by an integral equation with unknown functions corresponding to the intensities of distributed body forces. Stress distributions around the inclusion are shown by numerical calculations and influences of elastic moduli on the stresses are also investigated.