Elementary solution of contact problems for a transversely isotropic elastic layer bonded to a rigid foundation

The contact problem for an arbitrary punch acting on a transversely isotropic elastic layer bonded to a rigid foundation is solved by the generalized images method developed by the author earlier. The problem is reduced to that of an electrostatic problem of infinite row of coaxial charged disks in the shape of the domain of contact. The solution can be obtained by the method of iteration, collocations or any other standard procedure for solving integral equations. Exact inversion can be obtained in the case of a circular domain of contact. The mean value theorem can be used for estimation of the resultant force and tilting moment acting on a punch of arbitrary shape and circular domain of contact. A limiting case of general solution gives the solution for an isotropic layer.