The radially inhomogeneous isotropic elastic equal thickness spherical shell

Abstract

The axisymmetric elastostatic problem with axisymmetric geometry and loading is analyzed for a radially inhomogeneous equal thickness spherical shell, in linear elasticity. Considering that the stress field, the displacement field and the stiffness matrix have radial dependence, after a series of admissible functional manipulations, the general differential system which solves the isotropic linear elastic problem is developed in spherical coordinates. For the isotropic axisymmetric elastostatic problem, a differential equation in terms of the radial coordinate of the displacement field is derived. Exact analytical solution in spherical coordinates, is developed for a radially inhomogeneous equal thickness spherical shell of exponential varying Young's modulus and constant Poisson's ratio. In addition in the case that the Young's modulus is expressed by power law, the displacements and stress fields are deduced. An application has been made for a radially inhomogeneous equal thickness spherical shell where the stress and displacement fields are determined.