Examining the contact problem of a functionally graded layer supported by an elastic half-plane with the analytical and numerical methods

This study offers a comparative study of the analytical and numerical methods for investigating a contact problem. The contact problem comprises a functionally graded layer supported by a half-plane and loaded with a distributed load from the top surface. First, the analytical and numerical solutions to the problem are acquired by utilizing a theory of elasticity and finite element method, respectively. The problem is transformed into a system of integral equations in which the contact stress is an unknown function. The solution of the integral equation was achieved with Gauss-Jacobi integration formulation. The finite element model of the problem is created using ANSYS software, and the two-dimensional analysis of the problem is performed. Results were obtained from the samples for different material properties and loading conditions. The distributed load width and non-homogeneity parameters significantly impact on contact mechanics. The results indicate that the contact area and the contact stress obtained from finite element method (FEM) are close to the analytical results. As a result, acceptable error rates were obtained. Finally, this study provides evidence of a good agreement between the two methods.