On Some Problems in Spherically Isotropic Elastic Materials

Abstract

In this paper, we study the elasticity problem of a spherically isotropic elastic medium bounded by two concentric spherical surfaces. General solutions in terms of infinite series are presented. Specifically, we consider some axisymmetric problems such as: concentrated force in an infinite medium, stress concentration due to a spherical cavity, and a steadily rotating shell. In all these cases, the infinite series terminate, and closed-form solutions are possible. Steady-state thermal stress problems are also considered.