Dobryak D. The solution of thermoelastic problems for piecewise-homogeneous anisotropic plates with holes and cracks

In this work with the use of generalized complex potentials the technique of solving problems of thermoelasticity for multiply connected piecewise-homogeneous anisotropic plates with holes, cracks and foreign inclusions was proposed. With the use of conformal mapping, expansions of functions in Laurent series and of Faber polynomials the problems to overdetermined systems of linear algebraic equations were reduced. This systems using singular value decomposition were solved. The exact solutions of problems for an anisotropic plate with elliptical hole, with a thin absolutely rigid ring, with absolutely soft, absolutely rigid or elastic elliptical inclusion under the uniform heat flow and for an isotropic plate with a circular ring were received. Some problems for a plate with a finite number of inclusions (cores or rings), holes and cracks with a periodic system of elastic inclusions were solved. For each of the problems detailed numerical studies of thermo-stressed state (TSS) was carried out. New physical-mechanical patterns of influence of holes, cracks and inclusions geometrical characteristics, their number, mix and location, the thermophysical properties of plates and inclusions materials on their TSS were established. In particular, the stresses in the plate and their distribution depend strongly on the thermophysical constants of the material was found. At stresses much influence of material inclusions relative thermal conductivity parameter, less influence of relative deformability parameter and very little influence of relative thermal expansion parameter. In the case of linear elastic inclusions, if the deformability parameter is enclosed within interval (0.1, 10), the values of SIF is small. Convergence of elastic inclusions with each other leads to an increase of stress concentration in the plate. The investigations results presented in the thesis have both theoretical and practical importance. The proposed methods can be used for а wide variety of engineering problems solving.