Continuous and discontinuous contact problem for a layered composite resting on simple supports

The frictionless contact problem for a layered composite which consists of two elastic layershaving different elastic constants and heights resting on two simple supports is considered. The externalload is applied to the layered composite through a rigid stamp. For values of the resultant compressiveforce P acting on the stamp vertically which are less than a critical value Pcr and for small flexibility ofthe layered composite, the continuous contact along the layer - the layer and the stamp - the layeredcomposite is maintained. However, if the flexibility of the layered composite increases and if tensiletractions are not allowed on the interface, for P > Pcr, a separation may be occurred between the stampand the layered composite or two elastic layers interface along a certain finite region. The problem isformulated and solved for both cases by using Theory of Elasticity and Integral Transform Technique.Numerical results for Pcr, separation initiation distance, contact stresses, distances determining theseparation area, and the vertical displacement in the separation zone between two elastic layers are given.