Spherical cavity in a semi-infinite solid with its free surface rigidly clamped (Q1071538)

The present paper contains an approach to deal with distribution of stresses and deformation in a stressed semi-infinite solid containing a spherical cavity and the free surface of the solid is rigidly clamped. The problem can be reduced to one of two simply connected domains, namely a semi-infinite region and an infinite region excluding the cavity. The two stress functions in each region are expressed in cylindrical and spherical harmonics. The prescribed boundary conditions on the free surface of semi-infinite body and on the surface of the cavity are satisfied with the relation between cylindrical and spherical harmonics. Numerical results are given for quantities of physical interest by taking different radii of the cavity and the distance of the centre of cavity from the free surface is assumed as the unit of measurement.