Contact problem of functionally graded layers resting on a rigid plane and loaded via rigid blocks

In this thesis, the contact problem of two functionally graded layers resting on a rigid plane and loaded with two rigid flat blocks is investigated according to the theory of elasticity. The PhD. thesis consists of four sections. In the first section, a literature study on contact problems is given and the stress and displacement expressions of Functionally Graded (FG) layers are obtained. In the second section, the boundary conditions for continuous and discontinuous contact are substituted into the stress and displacement expressions for the FD layers. For the continuous contact case, the problem is reduced to two singular integral equations, where the contact stresses are unknown, and for the discontinuous contact case, the slopes of the separation between the contact surfaces of the FD layers are also unknown. The numerical solutions of the integral equations are carried out using the Gauss-Chebyshev integration method. In the third section, the contact stresses for the continuous contact case, the stresses σx, σy, and τxy occurring in the layers, the initial separation loads, and the initial separation distances are obtained. In the discontinuous contact case, the separation between the FG layers and the separation between the lower FG layer and the rigid plane are considered separately. The starting and ending points of the separations, the stresses in the layers and the openings in the contact surfaces are obtained. In addition, the problem is analyzed with the finite element method with the help of the ANSYS program. The results obtained in the fourth section and the recommendations for this study are presented in the final section.