Andriychuk R. Thermoelastic state of half-spaces for heat generation or heat insulation in flat domains.

The work is devoted to the research of heat conduction and thermoelasticity problems for a piecewise-homogenous bodies or half-spaces under the action of plane heat-generating or heat-proof inclusions. Using the harmonic potentials of a simple and double layer, the problems of stationary heat conduction for a piecewise-homogeneous formed by two ideally contacting half-spaces, with heat-generating or heat-proof disk inclusion parallel or perpendicular to its boundary in one of them, are solved. Under the action of heat sources or thermal dipoles, Green's functions of the thermoelasticity problems for half-space with a free, hardly, smoothly or flexibly clamped boundary, on which zero temperature or thermal insulation is given, are constructed. The potentials of thermoelastic displacements, Biharmonic Love’s functions and Boussinesq’s functions are used in solving thermoelasticity problem. Explicit expressions for temperature, displacements and stresses that are used to determine the thermoelastic state of half-space due to heat sources or dipoles distributed in a circular domain parallel to the boundary are given.