Two-Dimensional Problem of Thermoelasticity for a Half Space Whose Boundary is Either Free or Rigidly, Smoothly, or Flexibly Fastened with Heat Insulation in a Ribbon-Like Domain Parallel to the Boundary

Abstract

We construct Green’s functions for the problems of stationary heat conduction and thermoelasticity posed for a semiinfinite body subjected to the action of a thermal dipole under plane-strain conditions with either free or rigidly, smoothly, or flexibly fastened boundary kept at a temperature equal to zero. To solve the problem of heat conduction, we use the logarithmic double-layer potential. In the problem of thermoelasticity, we use a thermoelastic potential of displacements in the infinite body with heat dipoles specularly located relative to the boundary of the half space. To satisfy the boundary conditions on the boundary of the body, we construct the Boussinesq functions. We present explicit expressions for temperature, displacements, and stresses that can be used to determine the thermoelastic state of the half space caused by the perturbations of a given heat flux by a heatproof ribbon-like domain parallel to the boundary.