A New Solution Method for the Contact Mechanics of Graded Coatings

This paper attempts to solve analytically for the stresses present in a graded elastic solid resulting from pressure applied to its surface by computing the Airy stress function. The horizontal dimensions of the solid are assumed finite and hence we form the solution of the stress function as a Fourier series rather than an inverse Fourier transform. Finally, a selection of contour plots is presented to exhibit the behavior of this new model.