The conjugate problem of the thermal elasticity theory with imperfect heat contact between substances

In this paper, the one-dimensional mathematical formulation of the conjugate coupling problem of the thermal elasticity theory with non-ideal contact between substances is suggested. The approximate analytical solution of the problem is received for both quasi-static and dynamic formulations. The integral transformation method of Laplace is used together with asymptotic representation of solution in the transformation space. The fields of the temperatures, stresses, strains and displacements are found. It is demonstrated with the help of some examples that the region near the interface may be the cause of the localization of stresses. The numerical solution of the quasi-static problem is in a qualitative agreement with the analytical estimations.