The method of boundary equations of the hammerstein-type for contact problems of the theory of elasticity when the regions of contact are not known

Abstract

Novel formulations are given for the classical and non-classical, three-dimensional contact problems. The inequality-type constraints do not appear in the formulations as they do in the method of varational inequalities /1–8/ and in existing formulations of the contact problems /9– 13/. The complete system of equations of a contact problem consists of one boundary, equation of the Hammerstein-type and the usual equations of equilibrium for the compressive force and moments acting on the bodies. If the mutual rotations of the bodies and their closeness are known, the solution of the boundary Hammerstein-type equation readily yields the contact pressure and region of contact. By formulating the problem in this manner and using modern methods of the theory of operator equations we can investigate the existence and uniqueness of the solutions and some of their properties in very general cases (e.g. those of the multiConnectivity of the regions of contact sought). Moreover, the possibility arises of solving the problem using existing methods of solving Hammerstein-type equations /14–17/. Two types of problems, one of them classical, are used to study the correctness of the formulation of the contact problem.