Application of the generalized images method to contact problems for a transversely isotropic elastic layer

The idea of image charges, widely used in electrostatics, is applied to solution of a contact problem for an arbitrary punch acting on a transversely isotropic elastic layer resting on a rigid smooth foundation. The governing integral equation obtained is mathematically equivalent to that of an electrostatic problem of infinite row of coaxial charged discs in the shape of the domain of contact. Since the charge sign varies, each truncation gives either the upper or the lower bound to the exact solution. Simple and accurate engineering formulae are obtained for estimation of the resultant force and tilting moment acting on a punch of arbitrary shape and circular domain of contact. The case of isotropy is considered as well.