An inverse temperature field problem of the theory of thermal stresses

Unlike the investigations reported in the literature, which are restricted to the inverse problems of heat conduction, the current study presents an analytical approximate solution to an inverse problem of temperature field in the thermal stresses theory. Based upon the so-called internal responses of a different kind, an approximate form of surface temperature for a slab is predicted. To get the approximate solution - and also the exact one - the Laplace transform techniques are used. The theoretical considerations are carried out in the following way: (1) solution of a direct-initial-boundary-problem of the thermal stresses theory is exploited to obtain the transformed form of a formal solution of the problem, (2) conditions for the admissible internal responses are settled, (3) functions describing the internal responses are constructed, and (4) approximate solution of the considered problem is found and discussed. It appears that a step function is admissible for description of an internal response. The form of solution is convenient to numerical evaluation. Several numerical examples are presented as an indication of the accuracy of the theoretical results. (orig.)