Contact of Interfacial Cut Faces Between Plate with Hole and Closed Elastic Rib

The statement and method for solving the problem of frictionless contact of the interfacial cut faces between an infinite isotropic plate with a curvilinear hole and a closed elastic rib are proposed. Modeling the reinforcing rib by a closed elastic rod of large curvature, the mathematical model of the problem is developed as a system of singular integral-differential equations with the Hilbert kernels to determine the contact forces between the plate and the rib. The structure of the forces at the ends of the interfaces and smooth contact sections between the plate and the rib is established. Using the methods of mechanical quadrature and collocation, the case of full closure of the cut faces, the effect on the stress state of the plate, and the increase in the relative stiffness of the rib are studied.