Radial deformation and stresses in anisotropic nonhomogeneous elastic media

Abstract

In this paper we study the elasticity problem of a cylindrically- anisotropic, elastic medium bounded by two axisymmetric cylindrical surfaces subjected to normal pressures (plane-strain). The material of the structure is ortbotropic with cylindrical anisotropy and, in addition, is continuously inhomogeneous with mechanical properties varying along the radius. General solutions in terms of Whittaker functions are presented. The results obtained by St. Venant for a homogeneous cylindrically-anisotropic medium can be deduced from the general solutions. Problems of the type covered in this paper are encountered in nuclear reactor design.