INTERFACIAL FRACTURE IN ISOTROPIC PLATE WITH REINFORCED CIRCULAR OPENING

Abstract

An approximate solution to the problem of amplifying the contour of a circular opening in an infinite isotropic plate is constructed by a resilient rib of a stable rectangular cross section in the presence of a phase-cross section shores of which are not contacted. The plate is in a homogeneous stressed state at infinity. By conditional separation of the rib from the plate, replacing the action of one body on the other by normal and tangent contact forces, the first main task for the plate with a curved opening and resilient rib is considered. The rib is modeled by a closed curved beam, the  contact line of which with the contour of the opening of the plate does not coincide with its geometric axis. Deformations of the rib by contact forces are described by the basic equations of the one-dimensional theory of curvilinear rods of large curvature. The boundary conditions of the contact of the plate and the rib are formulated in the form of the equality of the relative elongations of the common filaments and the corners of a turning of the normal on the contact area. Taking into account the hypothesis of flat cross sections and the absence of pressure between the longitudinal filaments of a beam, a system of integral differential equations with the Hilbert cores was constructed to determine the contact forces between the plate and rib and the internal forces factors in the rib. The structure of functions describing the contact forces determines the characteristic part of the received integral equations. An approximate solution to the problem is given using Lagrange’s interpolation polynomials. By the method of mechanical quadratures and collocation, the effect of the relative rigidity of the rib on the distribution of tensions in the plate and rib is investigated.