Contact problems between a rigid punch and a layered elastic solid

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 method is general enough to deal with punch problems with various arrangements of layered structures. The problems under consideration are divided into two categories: conforming contact and non-conforming contact, according to the geometry of the rigid punches. Both single-layered and multi-layered structures are 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 layer geometry and the material properties on the responses of the structure are examined in details. The results provide useful guidance in the design and analysis of such structures under localized loadings.