Continuous contact problem of two functionally graded layers resting on an elastic half plane and loaded by two rigid blocks

In this study, the solution of the continuous contact problem of two functionally graded (FG) layers resting on an elastic half plane and loaded by means of two flat rigid blocks is solved using the theory of elasticity. The upper FG layer is loaded with two rigid flat blocks with widths (b-a) and (d-c) on its upper surface and external loads P and Q. The lower FG layer is resting on an elastic half plane. In the first section, studies in the literature related to contact problems were investigated, and with the help of elasticity theory and integral transformation techniques, general equations of FG layers and elastic half plane were obtained. In the second section, the continuous contact case is considered and the boundary conditions related to the problem are determined. Then, two integral equations are obtained by using the condition that the derivative of the vertical displacement function between the rigid blocks and the upper FD layer is equal to zero. These equations are solved by appropriate Gauss-Chebyshev integration methods. In addition, for the continuous contact case, the contact stresses formed under the blocks, the stresses formed in the layers, the initial separation load that will cause separation on the lower surfaces of the layers and the separation distances are investigated. In the last section, numerical solutions were made with the finite element method (FEM) for the problem by means of ANSYS Mechanical APDL package program. In the last part of the study, the analytical solutions obtained were compared with the SEM solution and similar studies in the literature, the results were presented with graphs and tables, and the findings were discussed in detail. It was seen that the analytical and SEM solutions and the findings in the literature were quite compatible with each other.