Stresses in a Semi-Infinite Body Subjected to Uniform Pressure on the Surface of a Cavity and the Plane Boundary

抄録

In this paper, the three-dimensional solutions for the stresses and displacements in a semi-infinite body having a spherical cavity are given for the case of a uniform pressure applied to the plane boundary and to the surface of the cavity. In analysis, the method of Boussinesq's two harmonic stress functions are used. The two stress functions are given by simple expressions of the cylindrical and spherical harmonics. The boundary conditions both on the face of the plane and on the surface of a cavity are satisfied with the aid of Hankel transform and the relations between the two harmonics. Further, numerical calculations are carried out for four different values of the radius of a cavity.