The radially nonhomogeneous isotropic spherical shell under a radially varying temperature field

Abstract

The axisymmetric thermoelastic problem, with axisymmetric geometry and loading under a radially varying temperature field is analyzed for a radially nonhomogeneous equal thickness spherical shell, by means of linear elasticity. Considering that the stress field, the displacements field and the stiffness matrix have radial dependence, after a series of admissible functional manipulations, the general differential system by solving the isotropic linear thermoelastic problem is developed in spherical coordinates. The contribution of this paper is that a basic constitutive nonhomogeneous differential equation is derived for the first time in the case of an isotropic axisymmetric thermoelastic problem. Based on the proposed constitutive differential equation, exact analytical solutions in spherical coordinates, are developed for a radially nonhomogeneous equal thickness spherical shell with an exponential either a power law varying Young's modulus and a radially varying temperature field. In these cases the displacements and stress fields are deduced. Applications have been made for different varying temperature fields and different pressures.