Vasilev K. Elastic equilibrium of limited by plane surfaces piecewise homogeneous bodies with thin defects at longitudinal shear

In the thesis, using a known method of investigation of longitudinal shear of layer structures with thin inclusions and a generalized scheme of the collocation method, a number of new problems for the layer, half-layer, two- and three-layer structures has been solved. To obtain explicit formulas of integral representations of the stress state of the layered structure regarding the jump functions the recurrence relations which were tested on the examples of one-, two-, three-, four- and five-layer structures have been proposed. New methods for solving the problems of longitudinal shear of bodies bounded by plane surfaces with thin inhomogeneities of structure - a method of direct cutting and a method of direct full cutting - have been proposed. Approbation of the methods has been carried out on the problems of longitudinal shear of bodies with thin defects - a half-layer, a layer at ideal contact with the half-space, a wedge, a two-wedge structure and a square bar. A method of additional concentrated factors to study the bodies with multilink cracks or absolutely rigid inclusions has been proposed. The problem for an elastic two-link inclusion in the space as well as three-link inhomogeneity has been investigated. Numerical analysis of the stress intensity factor for all above stated problems has been made.