Contact problems of two functionally graded layers of elastic semi-infinite plane exposed to distributed load

In this study, the frictionless contact problem of two functionally graded layers with different heights and properties of elastic semi-infinite plane exposed to uniform distributed load was investigated according to the Theory of Elasticity. The weights of the layers were omitted and it was thought that the Poisson ratios did not change. In the first chapter, the studies on the contact problems are summarized. In addition, general equations are obtained for functionally graded layers and elastic semi-infinite plane. For this, general equations of elasticity and integral transformation techniques are used. In second chapter, the problems and boundary conditions are defined and boundary conditions are applied to the obtained stress and displacement expressions. The problem is reduced to a system with two integral equations where the stresses on the plane contact surfaces between layers are unknown. Then the solution of the integral equation system was realized by using Gauss-Chebshev integration formulation and the contact lengths were obtained with unknown contact stresses. In the third part, numerical application of the problem for various dimensionless magnitudes is made. Contact stresses and contact lengths between layers under uniformly distributed load; different material properties were calculated for layer heights. The results are analyzed with the help of tables and graphs. In the fourth chapter, the results obtained from this study are given.