An exact solution of the stationary thermoelasticity problem is constructed for the interfacial circular absolutely rigid inclusion, while it is in the smooth contact conditions in a piecewise homogeneous transversely homogeneous space. With the help of the constructed discontinuous solution, by the method of singular integral relations, the task is reduced to a system of singular integral equations (SIE).An exact solution has been built for the specified SIE, and 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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An exact solution to the problem of thermoelasticity about interfacial circular inclusion, which is in complete adhesion with different transversely isotropic half-spaces, is constructed. Analytical dependencies are obtained between the parameters of the linear displacement of the inclusion and the characteristics of the force and temperature fields. The order of the singularity of surges and displacements near the inclusion is determined. Expressions are obtained for the stress intensity factor at the inclusion boundary, as well as the numerical dependences of these coefficients on the polar angle, temperature, and load.

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