Analysis of the nonstationary spatial propagation of elastic waves from cavities subject to mechanical and thermal loads

A numerical analytic method is proposed to solve nonstationary coupled problems of thermoelasticity with regard to the finite velocity of thermal waves. The method is used to analyze the nonstationary spatial propagation of elastic waves from a cavity subjected on its surface to mechanical and thermal loads. The ray theory of propagation of wavefield discontinuities is used. To determine the time dependence of the field parameters behind the wavefront and to account for the relationship between the mechanical and thermal fields with prescribed accuracy, a numerical iterative procedure that employs the properties of characteristics is used. Plots are presented for the nonstationary stresses and temperature near a prolate spheroidal cavity subject to step mechanical loading and near an elliptical cylindrical cavity subject to thermal shock