Student:	Murat YAYLACI
Supervisor:	Prof. Dr. Ahmet BİRİNCİ
Department:	İnşaat Mühendisliği
Institution:	Graduate School of Natural and Applied Sciences
University:	Karadeniz Technical University Turkey

Title of the Thesis:	RECEDING CONTACT PROBLEM OF TWO ELASTIC LAYERS SUPPORTED BY TWO ELASTIC QUARTER PLANES
Level:	Ph.D.
Acceptance Date:	12/9/2013
Number of Pages:	113
Registration Number:	Di988

Summary:

In this study, a receding contact problem for two elastic layers whose elastic constants and heights

are different supported by two elastic quarter planes and subjected to a uniformly distributed load is

considered according to the theory of elasticity. Besides, this problem has been developed based on

the Finite Element Method using ANSYS software. In the first chapter, the historical developments

of contact problems are mentioned and some studies which are done on contact problems are

summarized. In addition, to this general expressions of stresses and displacements for the cartesian

and polar coordinates are obtained by using the fundamental equations of theory of elasticity and

integral transformation technique of layers and quarter planes. Beside this, it has been given

information about finite elements method. In the second chapter, the problem is described and

firstly the problem is formulated and solved by using Theory of Elasticity. Stress and displacement

expressions are substituted into the boundary conditions of the problem, the problem is reduced to a

system of singular integral equations. The system of singular integral equations is solved

numerically by using Gauss-Jacobi integration formulation and the contact areas, the contact

pressures, normal stresses and shear stresses are determined. Furthermore in this section, a receding

contact problem in literature is investigated via Finite Element Method to verify the suitability of

the mesh structure and component types used in the software. Subsequently the contact problem of

elastic layers supported by elastic quarter planes which are mentioned above is also numerical

analyzed by finite element method. In the third chapter, the numerical applications of the problem

given in the previous chapter for various dimensionless quantities such as load width, distance

between two quarter planes, height of layers and material properties are obtained and results are

shown and discussed in graphics and tables. In the fourth chapter, the conclusions and

recommendation drawn from this study are given.

Key Words: Theory of Elasticity, Contact mechanics, Contact pressure, Contact area, Integral

transform technique, Quarter plane, Finite elements method, ANSYS