Three-dimensional contact problem for a two-layered extra loaded elastic base

The three-dimensional Galin’s type contact problem for a two-layered elastic base (a layer completely attached to a half-space from another material) is investigated when an extra loading (concentrated force) is applied outside the contact area. The contact zone is supposed to be unknown. The punch foot form is an elliptic paraboloid. The problem is reduced to an integral equation with respect to the unknown contact pressure distributed in the unknown contact zone. Galanov’s method of nonlinear boundary integral equations is used to determine the contact pressure and the contact zone simultaneously. Calculations made for various values of elastic and geometric parameters allow estimating an extra force input to the dependence between the punch settlement and the force applied to the punch. The problem is important for the strength analysis of coated surfaces of various elastic solids subjected to contact and extra loadings. The solution can be also useful in the frame of the discrete contact theory for bodies with rough surfaces.