Continuous and discontinuous contact problem of a functionally graded orthotrop layer lying on an isotropic layer bonded to a rigid substrate

In this study, continuous and discontinuous contact problem of a a functionally graded orthotropic layer lying on an isotropic layer bonded to a rigid substrate is solved by using elasticity theory and a finite element method, and the results obtained from both solutions are compared. In the first chapter, some studies on contact problems are mentioned. The stress and displacement expressions of the isotropic layer and functionally graded orthotropic layer have been obtained by using basic equations of elasticity and integral transformation techniques. In the second chapter, the problem is defined for continuous and discontinuous cases and boundary conditions for both cases are written. The problem is reduced to the singular integral equation system by applying boundary conditions to the stress and displacement expressions in continuous and discontinuous case. Using Gauss-Chebyshev formulation the singular integral equation system is reduced to the algebraic equation system. Also, the problem was modelled with the ANSYS package program and finite element solutions are performed. In the third chapter, the inhomogeneity of orthotropic material under the effect of mass forces; the results revealing the effects on the dimensionless contact lengths, contact stresses, initial separation loads, initial separation distances, and opening regions between the layers were obtained.