Interphase Circular Inclusion in a Piecewise-Homogeneous Transversely Isotropic Space Under the Action of a Heat Flux

In the space of generalized functions of slow growth \( {\Im }^{{\prime }} ({\mathbb{R}}^{3} ) \) a discontinuous solution of the stationary thermoelasticity problem for a piecewise homogeneous transversally isotropic space is constructed in the case of arbitrary loading. Using the constructed discontinuous solution and the properties of the functions from \( {\Im }^{{\prime }} ({\mathbb{R}}^{3} ) \), two-dimensional singular integral relations are obtained which allow the problem of interphase defects in an inhomogeneous transversely isotropic space allow to reduce to systems of two-dimensional singular integral equations (SIE) with kernels that are expressed in terms of elementary functions. An exact solution of the thermoelasticity problem for interphase circular inclusion is constructed, which is in complete coupling with different transversely isotropic half-spaces. Expressions for the jumps of the normal and tangential stresses are obtained and the dependences of the translational displacements of the inclusion on the temperature, the resultant load, the main moment, and the thermomechanical characteristics of transversely isotropic materials are obtained.