RADIAL DEFORMATIONS OF NONHOMOGENEOUS SPHERICALLY ANISOTROPIC ELASTIC MEDIA

Abstract

This paper deals with the elasticity problem of a spherically anisotropic elastic medium bounded by two concentric spherical surfaces subjected to normal pressures. The material of the structure is spherically anisotropic and, in addition, is  continuously inhomogeneous with mechanical properties varying exponentially along the radius. An exact solution of the problem in terms of Whittaker functions is presented. The St. Venant's solution in the case of homogeneous material and Lame's solution in the case of homogeneous isotropic material are derived here from the general solution. The problem of a solid sphere of the same medium under the external pressure is also solved as a particular case of the above problem. Lastly. the displacements and stresses of a composite sphere consisting of a solid spherical body made of homogeneous material and a nonhomogeneous concentric spherical shell covering the inclusion, both of them being spherically anisotropic, are obtained when the sphere is under uniform compression.