The Stress Field in an Elastic Half Space Having a Spheroidal Inhomogeneity Under All-Around Tension Parallel to the Plane Boundary

Abstract

Stress distributions are evaluated for a semi-infinite elastic body having a spheroidal inhomogeneity under an all-around tension (axisymmetric uniform tension) at infinity. Boussinesq’s potential functions are used for the analysis. A special technique is employed for the traction-free condition on the free surface, where the ordinary Legendre functions are expressed in terms of the Bessel functions in cylindrical coordinates. A closed-form expression for the stress concentration factor is found for a special case of a needlelike inhomogeneity.