Contact problem for a layer with two stamps: PMM vol. 42, no. 6, 1978, pp. 1068–1073

Abstract

A problem of impressing coaxial stamps of circular cross section into the upper and lower surface of a homogeneous elastic layer is studied. The bases of the stamps have axial symmetry. The parts of the layer surfaces lying oustide the contact zone are stress-free, there is no friction or coupling between the layer and the stamps. A system of two integral equations with two unknown functions is obtained, and provides a solution of the problem. The method of separating the singularities provides the way of reducing this system to the Fredholm equations of second kind. An approximate solution of the equations is obtained for the case of flat stamps under the assumptions that the two parameters entering the system are sufficiently small. Problems of a layer with various boundary conditions were formulated and solved in many papers and books, e.g. [1, 2]. However, to the best of the author's knowledge, in all these problems the conditions at the boundary were assumed different only on one side of the layer; in the present problem the boundary conditions are mixed at both sides of the layer, and this results in a system of two integral equations.