Interaction of Punches of Canonical Shape with an Elastic Foundation with Two Bedding Coefficients

We solve the problem of contact interaction of the punches of canonical (cylindrical, elliptic, or hyperbolic) shape with an elastic foundation with two bedding coefficients (plane problem). The problem is reduced to the solution of Fredholm integral equations of the first kind, and its analytic solution is obtained. We perform the numerical analyses of contact pressure, the displacements of the punch, the displacements in the elastic foundation, and the dependence of width of the contact zone on the level of loading of the contact pair and the shape of the punch. The accumulated results are compared with the results obtained for similar problems in the case of elastic half plane.