Stress Concentration around a Prolate Spheroidal Cavity in a Semi-infinite Elastic Body Under All -round Tension

Abstract

This paper presents an exact three-dimensional solution for the stresses arising in a semi-infinite elastic body having a prolate spheroidal cavity under all-round tension. The solution is based upon Boussinesq's stress function approach and is deduced by making use of the cylindrical and prolate spheroidal harmonics. The boundary conditions on the surfaces of the semi-infinite body and of the cavity are well satisfied with the aid of the relations between the cylindrical and prolate spheroidal harmonics. Numerical results are given for some different major semiaxes and shape ratios and the stress distributions around the cavity are shown graphically.