The thermally stressed state of an elastic half-plane heated by a uniformly moving heat source (Q1361959)

We construct a solution of the plane problem of the motion of a heat source with constant velocity along the boundary of an elastic half-plane. It is assumed that the boundary of the half-plane is stress-free, and that heat exchange with the surrounding medium occurs in accordance with Newton's law. It is further assumed that the source velocity of motion is small, so that the inertial effects in the half-plane can be ignored. A Fourier integral transform, the inversion of which is performed by contour integration methods, is used to solve the problems of heat conduction and thermoelasticity.