2 nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana, Albania 458 Receding contact problem for two elastic layers resting on a Winkler foundation Erdal Öner 1 , Murat Yaylacı 2 , Ahmet Birinci 3 1 Department of Civil Engineering, Bayburt University, Turkey 2 Department of Naval Architecture and Marine Engineering, Karadeniz Technical University, Turkey 3 Department of Civil Engineering, Karadeniz Technical University, Turkey Abstract In this study, receding contact problem for two elastic layers resting on a Winkler foundation and loaded by means of a rigid circular punch is considered. The elastic layers have different heights and elastic constants. External load is applied to the upper elastic layer by means of a rigid circular punch and the lower elastic layer rests on a Winkler foundation. The problem is solved under the assumptions that the contact between elastic layers, and between the rigid punch and the upper elastic layer are frictionless and the effect of gravity forces is neglected. Since the contact between two bodies is assumed to be frictionless, then only compressive normal tractions can be transmitted in the contact areas. General equations of stresses and displacements which are required for the solution of the problem are obtained by using the theory of elasticity and the integral transform techniques. Using integral transform technique and boundary conditions of the problem, the problem is reduced to a system of singular integral equations in which the contact stresses and areas are the unknown functions. The system of singular integral equations is solved numerically by making use of appropriate Gauss-Chebyshev integration formulas and an iterative scheme is employed to obtain the correct contact half-areas that satisfies the equilibrium conditions. Numerical results for the contact stresses and the contact areas are given for various dimensionless quantities. Introduction Contact problems have a long history in solid mechanics and have been subject of many investigations due to their practical interest such as foundation grillages, pavements of highway and airfield, railway ballast, rolling mills. A contact problem is named as receding contact if the contact zone shrinks as the bodies are deformed [1]. Alternatively, it is possible to define a problem for which the contact surface in the loaded configuration is contained within the initial contact surface [2]. There is a large body of literature associated with receding contact problems both numerically and analytically. Among the analytical studies on receding contact problems, the following studies can be seen in the literature. The smooth receding contact between an elastic layer and a half space when two bodies are pressed together by considering both plane and axisymmetric cases was considered by [3]. The smooth receding contact problem between an elastic layer and a half space when the layer is compressed by a frictionless semi-infinite elastic cylinder was examined by [4]. A frictionless contact problem for two elastic layers supported by a Winkler foundation was considered by [5]. A frictionless receding contact problem between an anisotropic elastic layer and an anisotropic elastic half plane when the two bodies are pressed together by a rigid circular stamp was examined by [6]. Rhimi at al. [7-8] solved the ax symmetric problem of a frictionless receding contact between an elastic