THE MIXED CONTACT PROBLEM FOR THE ISOTROPIC PLATE WITH CIRCULAR HOLE AND ELASTIC DISK

Abstract

The numeric solution of an contact task for an infinite isotropic plate with a circular of hole and an elastic isotropic disk is proposed. The plate with a circular hole and the elastic isotropic disk on one part of the common contour are soldered together. On the rest of the contour between them there is a through unsymmetrical interphase section. Under the action of concentrated force applied in the center of the elastic disk, the edges of the section of the plate structure are contacted partially or completely. The friction force in the contact area of the isotropic plate and the elastic disk is absent. The solution to this problem involves determining the size and position of the contact area. And also the determination of contact and ring forces on the material separation line. The boundary conditions of the problem in the contact zone are chosen in the form of the equality of the normal displacements of the contour points of the plate and the disk.

The boundary conditions of the problem in zone of solder are chosen in the form of equality of their displacements. The relations between the components of the vector offset of the contour points of the plate and the disk and the contact stresses are written in the form of integral dependences with logarithmic kernels. Substituting these expressions into boundary conditions of the problem, a system of singular integral equations was constructed to determine the functions through which the contact forces in the zone contact and solder regions are expressed. The conditions of balance of the disk must be fulfilled. The numeric approximate solution of the problem is realized by the method of mechanical quadratures and collocation. The size and position of the zone contact are determined by the dichotomy method. The results of the numerical calculation of the problem are presented in the table and illustrated in the figures.