Thermally active interphase inclusion in a smooth contact conditions with transversely isotropic half-spaces

Abstract

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.

The fundamental solution of the problem of thermoelasticity for a piecewise homogeneous transversely isotropic elastic space

“…The problem is reduced to hypersingular integral equations of the first and second kind, for which exact solutions are obtained.In [3][4][5][6][7][8][9] non-axisymmetric problems of elasticity and thermoelasticity for piecewise-homogeneous transversely isotropic spaces containing interfacial stress concentrators, such as cracks or rigid inclusions, using the method of singular integral relations (SIR) [10] reduced to systems of two-dimensional singular integral equations (SIR) and proposed a method for their solution. A similar approach was applied in [11][12][13][14][15] to solving problems of interfacial and internal defects in piecewise homogeneous anisotropic media.…”