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The problem of construction of the fundamental solutions for a piecewise-homogeneous transversely isotropic space is reduced to a matrix Riemann problem in the space of slowly increasing distributions. We propose a method for the solution of this problem. As a result, in the explicit form, we obtain expressions for the components of the vector of fundamental solution and simple representations for the components of the stress tensor and the vector of displacements in the plane of joint of transversely isotropic elastic half spaces subjected to the action of concentrated normal and tangential forces. We study the fields of stresses and displacements in the plane of joint of the half spaces. In particular, for some combinations of materials, we present the numerical values of the coefficients of influence of concentrated forces on the stresses and displacements. We also establish conditions under which the normal displacements are absent in the plane of joint of transversely isotropic elastic half spaces.

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An exact solution of the stationary thermoelasticity problem about interfacial circular absolutely rigid inclusion, which is under conditions of complete adhesion and under conditions of smooth contact with transversely homogeneous spaces, 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 systems of two-dimensional singular integral equations. As a result, dependences jumps of stresses and displacement on temperature, equivalent load, main moments and thermomechanical characteristics of transversally isotropic materials. The influence of the type of contact interaction on the behavior of the solutions is established. In particular, it has been shown that the stresses in the neighborhood of the inclusion with a smooth contact have a root singularity, and with complete coupling, the root singularity, which is amplified by oscillation. The behavior of the generalized intensity coefficient (GCIN) was studied for the combination of various transversely isotropic materials at different power and temperature loads.

The problem of constructing fundamental solutions to the thermoelasticity problem for a piecewise-homogeneous transversely isotropic space is reduced to the matrix Riemann problem in the space of generalized slow growth functions. As a result of the solution of which, were obtained expressions in explicit form for the components of the stress tensor and the displacement vector in plane of connection of transversely isotropic elastic half-spaces containing concentrated stationary heat sources. The temperature distribution is investigated depending on the thermophysical characteristics of the half-space materials.