THE METHOD OF CONCENTRATED SOURCES IN SOLVING THERMAL STRESS PROBLEMS

Abstract

In [1] the application of a method of concentrated sources to heat conduction problems was presented. In the present paper, the method is extended to include thermal displacements and stresses. The method is applicable to direct and inverse problems as well. The extension of the method to thermoelasticity consists in introducing, besides “fictitious” concentrated heat sources, “fictitious” concentrated mechanical forces outside a considered region. In a direct problem of heat conduction theory (or thermoelasticity), we look for a solution to partial differential equations subject to suitable initial-boundary conditions. In an inverse problem of heat conduction, we look for a boundary temperature (among other things), assuming that a temperature is prescribed on a subregion of the body and for each time. In the case of an inverse thermoelastic problem, we may look for a boundary thermomechanical load when some of the thermomechanical fields, such as temperature, displacement, or stress, are prescribed over a subregion of the body and for each time.