Contact problems between a functionally graded layer and a rigid support

Abstract

In this study, frictionless contact problem for a functionally graded (FG) layer is considered. The FG layer is subjected to load with a rigid stamp and the FG layer is bonded on a rigid foundation. The graded layer is modeled as a non-homogenous medium with a constant Poisson’s ratio and exponentially varying shear modules. It is assumed that the contact between all surfaces is frictionless and the effect of gravity force is neglected. The problem is solved analytically using plane elasticity and integral transform techniques. The problem is reduced to a singular integral equation using plane elasticity and integral transform techniques. Obtained singular integral equation is solved numerically using Gauss-Jacobi integration formulation and obtain the contact pressure and contact length. The contact length and contact pressures between the FG layer and the rigid stamp are analyzed for various material properties and loading. Aim of thepaper is to investigatethe effect of the non-homogeneity parameter of the graded layer on the contact pressures and lengths.