Yatsyk I. The bending of Reissner’s plate with rectilinear cracks, taking into account the two-dimensional contact zone of their faces

The dissertation is related with the study of the stress-strain state of isotropic plates is subjected to the bending loading with straight through-the-thickness cracks which faces are contacted along the region of constant width, and the slits. Using the defining relations of the elasticity theory plane problem and Reissner theory of plates bending and methods of a complex variable functions theory, the problem of bending the plate with the system of arbitrarily oriented cracks and slits is reduced to solving a system of singular integral equations, which is solved numerically using the method of mechanical quadratures. Cases are considered: plates with one crack, two, three, periodic system of coaxial cracks, two parallel, unassembled and displaced cracks, coaxial crack and slit. The graphic dependences of the reduced contact forces between the faces of the cracks, the bending and torsion moments, transverse forces intensity factors for different types of loading and under various geometric and mechanical parameters of the problem are constructed. The regularities of the plate thickness and the width of the contact area influence on the stress-strain state of the plate with cracks and slits are revealed. A comparative analysis of the problems studied with the case of the interaction absence between the cracks faces and the case of linear contact between their faces near one of the plate bases of has been carried out. The limiting loading that the plate can withstand is identified.