Analytical Solution of Discontinuous Contact Problem in Functionally Graded Layer and Homogeneous Layer

In the study, the problem of discontinuous contact in two layers, one of which is functionally graded is solved using the theory of elasticity. In this problem functionally graded (FG) layer resting on homogeneous layer and loaded with two different rigid flat blocks. In addition, homogeneous layer is resting on a rigid plane. Frictions on all surfaces are neglected. The heights of the FG layer and the homogeneous layer are h1 and h2, respectively. When solving the problem, displacement and stress equations are substituted in the boundary conditions. Then the problem is demained to singular integral equations. Wherein unknown functions are the contact stresses under the two rigid flat blocks and the slope of the separation. These singular integral equations are solved numerically using the Gauss- Chebyshev integration formulas. The analyzes were performed for different inhomogeneity parameter (βh1), shear modulus ratio (μ2/μ-h1). distance between the rigid blocks ((a3-a2)/h1) and density parameter (γh1). Consequently, the stress distributions and starting and ending points of the separation area between the FG layer and homogeneous layer are determined for several dimensionless quantities.