The contact problem for an elastic semi-infinite layer

Abstract

It is solved the contact problem on the action of a circular stamp with an extra-central power on the elastic semi-infinite layer. On the lateral and lower side of the layer the conditions of the smooth contact are given. The solution of the elastic problem for the semi-infinite layer when concentrated force was situated on the upper side of the layer was used. This problem was solved by the new method which is based on the reduction of Lame’s equations system to two together and one independent solved equations relatively to the new unknown functions associated with the displacements. Using of the integral transformations reduces the problem to a one-dimensional vector boundary value problem that to be solved exactly by the apparatus of the matrix differential calculus. The singular integral equation with respect to unknown contact pressure was obtained. The problem was reduced to the singular integral equation which was solved by the method of the orthogonal polynomials and was reduced to the infinite two-dimensional system of algebraic equations. These equations were solved by the reduction method. As a result the eccentricity and precipitation of the stamp that provide its forward movement were determined.