Frictional receding contact problem of a functionally graded orthotropic layer / orthotropic interlayer / isotropic half plane system

Abstract

A frictional receding contact problem of a functionally graded (FG) orthotropic layer / homogeneous orthotropic interlayer / homogeneous isotropic half plane system is considered. The FG layer is loaded by a rigid cylindrical punch with normal and frictional forces. While the lower layer and half plane fully bonded to each other, receding contact occurs between the upper and lower layers. It is assumed that the elastic stiffness constants for the FG layer vary exponentially in the depth direction and the Poisson’s ratios of the system are constant. The problem is converted into a system of Cauchy type singular integral equations in which the unknowns are the contact stresses on the contact areas between the punch and the FG layer, and between the FG layer and the homogeneous layer. The Gauss–Jacobi quadrature is used to discretize and collocate the singular integral equations leading to a system of algebraic equations about unknowns. Thus, the effects of some parameters such as the friction coefficient, inhomogeneity parameter, indentation load, punch radius, thickness of the upper layer on the contact areas, and the contact stresses, are presented by the results of parametric analysis.