On the Stress Concentration around Hemi-oblate Spheroidal Pit in a Semi-infinite Body

Abstract

This paper contains a three-dimensional solution for the stresses in a semi-infinite body having a hemi-oblate spheroidal pit under all-around tension parallel to the free surface. In the analysis, Boussinesq's two harmonic stress functions approach is used. The solution is presented by three sets of oblate spheroidal harmonics. These are chosen so as to satisfy the boundary conditions on the free surface and at infinity automatically. The remaining boundary conditions on the surface of the pit are satisfied with the aid of half-range expansions of Legendre functions. Numerical calculations are carried out for four shape ratios of the oblate spheroidal pit.