The solution of a certain class of dual integral equations with the right-hand side in the form of a Fourier series and its application to the solution of contact problems for inhomogeneous media

Using the bilateral asymptotic method, a semi-analytical solution of a dual integral equation with its right-hand side in the form of a Fourier series is constructed. This equation arises in the solution of a number of contact problems of elasticity theory for bodies with inhomogeneous coatings. The efficiency of the method is illustrated in the example of the solution of the plane contact problem on bending of a beam lying on a functionally graded strip with arbitrary variation of the elastic moduli with depth. It is assumed that the strip is perfectly bonded to an elastic half-plane. Numerical results are presented for a strip whose Young's modulus varies harmonically with depth. In this case, Young's modulus of the substrate is 100 times greater than at the lower boundary of the coating.