Nieustalone Naprężenia Temperaturowe w Nieograniczonej Warstwie Sprężystej, Wywołane Ogrzaniem Części jej Powierzchni - Kajdarow, K.K. (Engineering Transactions, 1974)
On some finite part of the upper surface of the infinite layer the temperature is given as a function of place and time, on the remaining part and on the lower surface the temperature equals zero. The general solution of the thermoelastic problem for this layer is obtained. The symmetric and antisymmetric temperature fields are considered separately. The quasi-static approximation and the solution of the dynamic problem are derived by means of integral transforms and thermoelastic potential. The boundary conditions are corrected on solving the homogeneous Lamé equations with the aid of Lurie's method of initial functions. Heating of rectangular and circular regions constituting parts of planes bounding the layer is considered as an example. In the dynamic case the solution is expressed by the inverse Laplace transforms.