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

Abstract

A solution of the plane problem of the motion of a heat source with constant velocity along the boundary of an elastic half-plane is constructed in a development of the method proposed previously in [1] for finding fundamental thermoelastic solutions in the case of problems of this type. 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, by virtue of which inertial effects in the half-plane are ignored. The assumption is also made that the physicomechanical properties of the half-plane are independent of the temperature and that the effect of thermoelastic connectivity can be neglected. 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 in question. As a result, formulae are obtained for the temperature of the half-plane and the stresses and strains in it. Results of calculations are presented.