Analytical solution for a concentrated force on the free surface of a coated material

Based on the general solution of the displacement method for isotropic plane problems, the analytical solution for the plane problem of coated materials subjected to an arbitrary concentrated force on the free surface has been derived explicitly by using the image point method.The displacement functions are assumed to be the infinite series of the harmonic functions defined in the local coordinate systems with their origins placed at different image points.The harmonic functions corresponding to the higher-order image points can be deduced from those to the lower-order points by the recurrence formulae presented in this paper, and the first two harmonic functions are the displacement functions for the solution of a semi-infinite plane subjected to a concentrated force on the free surface.The theoretical formulae have been confirmed by numerical, finite-element-based, results in a special coated material.