Solution of a dual integral equation arising in the contact problems of elasticity theory with the full Fourier series as the right-hand side

Abstract

A class of dual integral equations is analyzed which arises in solution of a wide range of plane and antiplane contact problems of elasticity theory for a half-plane with functionally graded coating. In particular, a similar equation arises in solution of the contact problem on indentation in the presence of tangential stresses on a surface. The solution of the dual integral equation is sought in the form of a sum of even and odd functions. It makes possible to reduce the problem to independent solution of two dual integral equations over odd and even functions. Kernel transform of these equations is approximated by a product of fractional quadratic functions. The solution of dual integral equations is constructed in approximated analytical form by the bilateral asymptotic method. The expressions obtained are asymptotically exact for small and large values of a characteristic geometrical parameter.