The contact problem for two elastic layers loaded by means of two rigid rectangle blocks and resting on an elastic half infinite plan

In this study, the analytical solution is derived according to the theory of elasticity for the continuous and discontinuous contact problems in two homogeneous and isotropic layers with different thicknesses and elastic properties; the layers are underlain by an elastic semi-infinite plane and are loaded with two rectangular blocks. Analytical solution results are then compared with numerical solutions using ANSYS. The study consists of four chapters. Chapter I briefly reviews the historical development of contact problems and provides the general expressions for stresses and displacements of the two layers and the underlying plane using fundamental equations of elasticity and integral transform techniques. Chapter II provides the analytical solution derived for the continuous and discontinuous contact problems and provides the base for numerical computation in ANSYS. First, the continuous contact case is covered. Stress and displacement expressions are substituted into the boundary conditions, and the problem is reduced to singular integral equations, where the contact stresses are the unknown function. The solution of singular integral equations is obtained using Gauss- Chebyshev integration formulas. The load which causes the first separation and the point where the separation starts are obtained for the interfaces. Second, the discontinuous contact case is examined in two parts. First for the interface between the bottom layer and the semi-infinite plane, and then for the interface between the two layers. The same procedure as in continuous contact problem is followed for the discontinuous contact problem, except the number of singular integral equations become three with the third unknown being the slope at the separation region. By solving these three integral equations, one can easily obtain the separation between the interfaces, contact stresses under the blocks, and stress components at every point of interfaces.