Moysyeyenok O. 2D boundary problems about the interaction of plane non-stationary elastic waves with thin inclusions.

The method of the research of the stress concentration in elastic bodies near strip inclusions as a result of the non-stationary elastic waves is constructed in the thesis. Different types of interaction between a matrix and an inclusion are considered: full coupling, partial exfoliating on one side, and partial exfoliating on both sides. Taking into consideration small thickness of the inclusion the boundary conditions are formulated concerning its middle plane. In the case of the elastic inclusion the bent and shift displacements of this plane are defined from the equations of the theory of thin plates. The method of the solution of the formulated boundary problems is based on the use of the discontinuous solutions of the Helmholts and Lame equations in the space of the Laplace images. To define the unknown images of jumps the integral equations or their systems which are numerically solved by the collocation method are obtained through the satisfaction of the boundary conditions. For the conversionof the Laplace transformation used the numerical methods founded on the replacement of the Mellin integral by the Fourier series. The analysis of the dependence of the SIF on linear mass and relative rigidity of inclusion and conditions of interaction of the inclusion and the matrix is carried out.