The frictionless contact problem for an elastic layer resting on an elastic half-space

Abstract

The frictionless contact problem for an elastic layer lying on an elastic half space is considered. It is assumed that, in addition to the main applied load P, the layer is subjected to a uniform vertical body force because of the effect of gravity in the layer. It is also assumed that the contact between the layer and the half space is frictionless and that only compressive normal tractions can be transmitted through the interface. Thus, up to a certain magnitude of the applied load the between the layer and the foundation is continuous. For the values of teh load ec-xceeding this critical value, the layer is partially separated from the subspace. The separation area increases with the increasing magnitude of the load. First, the problem of continuous contact is solved and the value Por is determined. Then the discontinuous contact problem is formulated in terms of a singular integral equation. The problem is formulated as a mixed boundary value problem and solved by using a treatment similar to the crack problems. The separation area along the interface is evaluated as a function of a dimensionless load parameter. The contact stress distribution is obtained for various values of corresponding to both continuous and discontinuous contact along the interface. Numerical results for Por, contact stress distribution, and separation regions are given for various material combinations.