THE CONTACT BETWEEN 2 PLATES, ONE OF WHICH CONTAINS A CRACK

The problem of the contact between two plates, one of which has a vert ical crack which reaches the outer edge, is considered. It is assumed that, in the natural state, the plates are a specified distance from o ne another. The displacements of points on the plates satisfy two cons traints of the inequality type. One of these describes the condition o f non-penetration between the plates and is specified at internal poin ts of the region, while the other describes the mutual non-penetration of the edges of the crack and is specified on the boundary of the reg ion. The presence of a crack means that, first, the solution of the pr oblem is sought in a region with a non-smooth boundary, and, second, t he boundary conditions on the boundary of the region are given in the form of inequalities. It is proved that the equilibrium problem is sol vable. Additional smoothness of the solution up to internal points of the crack is established. It is shown that the problem of controlling external loads with an objective functional, characterizing the openin g of the crack, is solvable. For cracks of zero opening it is shown th at the solution belongs to class C-infinity in the region of the bound ary for smooth external data. The convergence of the solutions of opti mal-control problems as the thickness of the plates approaches zero is analysed. (C) 1998 Elsevier Science Ltd. All rights reserved.