Double receding contact plane problem between a functionally graded layer and an elastic layer

This paper studies the plane problem of a smooth double receding contact between a functionally graded layer and an elastic layer when they are pressed together. We assume the functionally graded layer is isotropic, and the shear modulus of this layer is assumed to vary exponentially along the thickness direction. By using the Fourier integral transform and the boundary conditions, the problem is reduced to a system of singular integral equations in which the receding contact half-widths and the contact pressures are unknown. The system of singular integral equations is solved numerically by using the Gauss-Chebychev integration formulas. Numerical results for the contact pressures and the contact areas are given for various dimensionless quantities.