Evaluation of the contact problem of two layers one of functionally graded, loaded by circular rigid block and resting on a Pasternak foundation by analytical and numerical (FEM and MLP) methods

In this paper, the frictionless contact problem of layers on a Pasternak foundation is addressed using various methods, such as the analytical method, finite element method (FEM), and multilayer perceptron (MLP). The problem consists of two layers: The upper layer is homogeneous (HOM), while the lower layer is functionally graded (FG). The upper layer is loaded by a circular rigid block that applies a concentrated force, and Poisson's ratios of the layers are kept constant. In the solution, the weights of both layers are neglected, and stress due to pressure is considered. First, the problem is solved analytically using the theory of elasticity and integral transformation techniques. In this method, the equations governing the stress and displacement components of the layers are transformed into a system of two singular integral equations involving unknown contact pressures and contact lengths using Fourier transform techniques and boundary conditions. The integral equations are solved numerically using the Gauss-Chebyshev integration formula. Then, the finite element solution of the problem was performed using the ANSYS package program, which is based on the finite element method. Finally, the problem was solved with a multilayer perceptron (MLP), an artificial neural network for different problem parameters. The results obtained with all three methods were compared and interpreted. It is clear from the results that the contact pressure and contact length vary depending on various parameters such as block radius, stiffness parameter, shear modulus ratios, and Pasternak soil parameters.