Plane Contact Problems

Abstract

In the previous chapter, we considered problems in which the infinite wedge was loaded on its faces or solely by tractions on the infinite boundary. A related problem of considerable practical importance concerns the wedge with traction-free faces, loaded by a concentrated force F at the vertex, as shown in Figure 12.1.

An important characteristic of this problem is that there is no inherent length scale. An enlarged photograph of the problem would look the same as the original. The solution must therefore share this characteristic and hence, for example, contours of the stress function φ must have the same geometric shape at all distances from the vertex. Problems of this type — in which the solution can be mapped into itself after a change of length scale — are described as self-similar.

For a more detailed discussion of elastic contact problems, see K.L.Johnson, Contact Mechanics, Cambridge University Press, 1985 and G.M.L.Gladwell, Contact Problems in the Classical Theory of Elasticity, Sijthoff and Noordhoff, Alphen aan den Rijn, 1980.