Axisymmetric temperature distributions on a transversely isotropic semi-infinite solid

An exact static solution for the axisymmetric boundary value problem of a transversely isotropic semispace subjected to a point heat source is constructed by similarity transformations. The closed-form expressions for the temperature and components of displacements and stresses are derived. In the particular cases of uniform and parabolic-type temperature distributions on a circular area of the surface, the expressions far the displacements and stresses at a distance z beneath the surface are determined The Mathematica software is used, and the numerical results are presented on graphs depicting the spatial variation of the displacements and stresses in a semispace of cobalt material.