An approximate analytical solution of the integral equations of non-axisymmetric contact problems for a ring-shaped domain

An algorithm is developed for solving the integral equations of the first and third kind to which non-axisymmetric mixed problems in continuum mechanics and mathematical physics reduce on replacing the boundary conditions in a ring-shaped domain. The use of the Bubnov–Galerkin procedure in conjunction with addition theorems for Bessel functions is the basis of this method. In the final stage of solving integral equations corresponding to arbitrary harmonics of a mixed problem for a ring-shaped domain, the method enables the coefficients of the linear algebraic systems to be represented in the form of simple quadratures that are convenient for numerical implementation. The discussion is carried out using the example of a contact problem in the theory of elasticity for a linearly deformable base of a general type strengthened by a thin coating along its boundary. The effect of the relative thickness of the coating, its stiffness and the shape of the bottom of a ring-shaped punch on the basic contact characteristics is investigated. Publications on the known results are available in the special case of axisymmetric problems and the problem of an inclined ring-shaped punch.