Numerical Analysis On Contact Problems Of Layered Solid

In this paper we are mainly concerning on contact problems of layered solid. A methodology for the contact problems of layered solid based on stress function method are developed. Stress function method is a simple and straight approach for stress or mixed boundary value problems, such as solids under contact. In this work, the generalized plane strain problem of the contact of a rigid punch and a layered elastic solid is reduced to an integral equation by using Fourier Transforms. A numerical scheme involving matrix inversion is used to obtain the approximate solution to the integral equation. The problems under consideration are divided into two categories: conforming contact and non-conforming contact, according to the geometry of the elastic solids. Both single-layered and multi-layered structures studied in each contact setting. The distribution of contact pressure and the relationship between the total load and the indentation depth are obtained for each case. The effects of the thickness of layers, the elastic modulus ratios between layer and substrate and the ratio of contact width to layer thickness are investigated. The results are helpful to analyze the failure modes of layered elastic solid and provide useful guidance in the design and analysis of such under localized loadings.