Contact problem of a functionally graded layer resting on an elastic half plane

In this study, contact problem of a functionally graded (FG) layer resting on an elastic half-plane, which is symmetrically loaded by two uniform distributed load is solved with the aid of the theory of elasticity. Shear modulus of the FG layer is assumed to vary exponentially through the thickness. The elastic half-plane is considered as homogeneous. In solution, the body forces of the FG layer and elastic half-plane are neglected. Besides, all surfaces are assumed to be frictionless. In the first chapter, some studies which are made on the contact problems of FG layers are summarized. In addition, general expressions of stress and displacement fields are obtained for the FG layer and the half- plane by using fundamental equations of theory of elasticity and integral transform techniques. In the second chapter, boundary conditions of given and an integral equation is obtained. The singular integral equation is solved numerically by using the Gauss-Jacobi integration formulation, and then contact areas and the contact pressure are determined. In the third chapter, a parametric study is performed to investigate the effect of the non-homogenity parameter and the load width. The results are given in tabular and and graphical form and discussed. In the fourth chapter, conclusions drawn from this study and some recommendations are given.