ABSTRACT
This chapter shows how one-, two-, and three-dimensional thermoelastic problems are treated in the spherical coordinate system. Some illustrative examples cover a solid sphere, a hollow sphere, and an infinite body with a spherical cavity or a spherical inclusion. Thermoelastic problems in spherical coordinates are presented. One-dimensional steady state and transient thermal stresses are discussed for the cases of a hollow and a solid sphere, and for infinite bodies with a spherical cavity. Moreover, two-dimensional (axisymmetric) problems are expressed in terms of the Goodier's thermoelastic displacement potential and the Boussinesq harmonic functions and, in this context, the solid sphere, the hollow sphere, and the infinite body with a spherical cavity are discussed for a steady temperature field. The chapter considers heat conduction problems in the spherical coordinate system. It also considers practical problems of axisymmetric thermoelastic deformation in the spherical coordinate system such as a solid sphere, a hollow sphere, and an infinite body with a spherical cavity.
