Kachan J. The two-dimensional problem of the theory of elasticity for piecewise homogeneous bodies with holes and cracks

On the thesis found subsequent development methods of solutions of boundary problems in the theory of elasticity and their applications to problems of the study of stressedly-deformed state of piecewise homogeneous anisotropic or isotropic body and half-space with holes, inclusions, plain (linear) cracks, rigid and elastic inclusions. These methods based on the solution of problems of linear coupling for cuts on the multiconnected domain or on the using of classic complex potentials with eduction of the singularities on the ends of plain stress concentrators and method of the least squares. In case of half-space the method of Cauchy integrals was applied to the conditions on the plane boundary. In the dissertation especially widely combined method is represented, which permits to solve problems for any number, combination and order of holes, cracks and inclusions. This method consist on using complex potentials with eduction singularities in the ends of plain stress concentrators, on using method of computational finding of stress intensity factors and discrete method of the least squares for determination of unknown constants, which appears in compex potentials. High effectiveness of developed methods, stability of founded results and their agreement with well-known ones in literature is shown using computational investigations. Series of practically important new problems for anisotropic body and half-space, for piecewise-homogeneous isotropic plate is solved. New regularities of influence on stressedly-deformed state of geometrical forms, their numbers, positional relations and combinations, elastic properties of materials of considered body-matrix and inclusions is discovered.