Analysis of the contact problem functionally graded layer placed on a Pasternak foundation

Abstract

This paper uses analytical and numerical methods to investigate the frictionless receding contact problem of two layers, one functionally graded (FG), loaded by a circular rigid block and resting on a Pasternak foundation. The upper layer loaded by the circular punch has homogeneous properties and contains a single shear modulus, while the shear modulus of the bottom layer is changed depending on an exponential function, making it an FG layer. In the solution, Poisson's ratios of both layers are assumed to be constant, and their weights are neglected. First, the overview of the topic, the existing studies in the literature, and the gaps in these studies are discussed. Then, an analytical solution is performed using the theory of elasticity and the Fourier integral transform techniques. The problem is modeled, and a numerical solution is obtained using the ANSYS package program based on the finite element method (FEM). Finally, the two methods are compared, and the results are presented using tables and graphs. Comparing analytical and numerical (FEM) solutions for the frictionless receding contact problem involving a FG layer resting on a Pasternak foundation is the main goal of this study.