Opanasovych V. Mathematical models and methods of the deformation of analysis of plate structures with cracks under contact of their faces

In the thesis mathematical models are formulated and analytical and analytical-numerical methods of solving problems of bending of piecewise-homogeneous plates with through-the-thickness cracks with a smooth band or linear contact of the cracks faces, based on the methods of the theory of complex variable and complex potential. Solving of studied problems is presented in the form of superposition of solutions of two interrelated problems: a plane problem with unknown contact efforts on the faces of cracks and solution of the bend problem with unknown bending moments on the faces of cracks and a given external load applied to the plate. Classic or one of the refined theories of plate bending sixfoldare used for describing of bending.The features of the distributions of contact force between the faces of cracks, the intensity factor of efforts, moments and transverse forces, the limit load for different geometrical parameters of the problem and ways of loading were studied in details. The conditions of existence of solutions of problems in this setting were studied.