THE MATHEMATICAL MODEL OF AN INTERPHASE FRACTURE IN A PLATE WITH A REINFORCED CIRCULAR PROFILE DURING ITS BENDING

Abstract

Under the conditions of cylindrical bending, a mixed contact problem for an infinite isotropic plate with a circular opening, the profile of which has been reinforced by a closed elastic ring (rib) with a stable rectangular cross section, provided that at the connection border there are the materials of interphase section, the margins of which do not contact in the process of deformation, has been considered. The components of bending and torsion deformation at the profile of the plate opening are presented through integral relations with the Hilbertian kernels from the contact moments in the area where the plate and the ring are connected. The main equations, defining the stressed and deformed state of the rib have been recorded when modelling the reinforcement with an elastic line which has a bending and torsional stiffness. The problem’s mathematical model has been created in form of a system of integral and differential equations for defining the contact moments between the plate and the rib, inner moments of the reinforcement and the initial parameters of a statistically indefinite rib. A structure of the values being searched at the ends of the area where the plates and the rib are connected, has been established. An approximate solution of the problem has been created using the method of mechanic quadratures and collocation, using which the influence of the type of the external bending load and the relative stiffness of the reinforcing rib on the stressed state of the plate structure, has been studied.  It has been established, that all the components of the stressed state f the rib are limited.