An exact solution of the stationary thermoelasticity problem about interfacial circular absolutely rigid inclusion, which is in the smooth contact conditions in a piecewise homogeneous transversely homogeneous space, is constructed. The task with the help of the constructed discontinuous solution, by the method of singular integral relations, is reduced to a system of singular integral equations (SIE). An exact solution has been built for the specified SIE, as a result, dependences of translational displacement of the inclusion on temperature, the resultant load, main moment and thermomechanical characteristics of transversely isotropic materials have been obtained.
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