Mixed Problems of Stationary Heat Conduction and Elasticity Theory for a Semiinfinite Layer

Abstract

We obtain analytic solutions of problems of stationary heat conduction and elasticity theory for a semiinfinite layer under the conditions of smooth contacts at the end face. The method used for the solution is based on the reduction of the Lame equations to two jointly solvable equations and to a separately solvable equation. The application of integral transforms to the obtained equations of equilibrium enables us to obtain the exact solution of the problem in the space of transforms. The method of calculation of multiple integrals containing oscillating functions is developed. The temperature and stress fields in a semiinfinite layer depending on the parameters of the area, where the load is applied, and the conditions on the lower boundary of the layer are studied.