Elastic analysis of an axisymmetric stress field perturbed by a spheroidal inhomogeneity

Abstract

An infinite elastic medium contains an elastic spheroidal inclusion. Both materials are transversely isotropic. Assuming that the stress field in the absence of any inhomogeneity is prescribed, it is desired to calculate the modification caused by the inclusion. This paper presents a general solution to this elasticity problem with the restriction that the prescribed stress field is axisymmetric. The analysis is based upon some new identities in Legendre functions, which are derived in this paper. The solution is in the form of combinations of Legendre functions. An example of a spheroidal cavity in a tension field is given.