Method for calculating nonstationary temperature stresses in a thermosensitive half-space

On the basis of a model of a thermosensitive body, we propose an analytic-numerical method for the construction of the solution of an axisymmetric quasistationary problem of thermoelasticity for a half-space heated by an instantaneous linear heat source and exchanging heat through a bounding surface by convective heat transfer with the environment. Using the perturbation method, we reduce the problem to the solution of a sequence of boundary-value problems for the Poisson equations, whose solutions are constructed in the form of rapidly convergent series for each approximation by using expansions in multiple probability integrals.