Comparison between Analytical and ANSYS Calculations for a Receding Contact Problem Murat Yaylacı 1 ; Erdal Öner 2 ; and Ahmet Birinci 3 Abstract: This paper considers a receding contact problem for two elastic layers (with different elastic constants and heights) supported by two elastic quarter planes. The lower layer is supported by two elastic quarter planes, and the upper elastic layer is subjected to a symmetrical dis- tributed load whose length is 2a on its top surface. It is assumed that contact between all surfaces is frictionless, and the effect of gravity force is neglected. First, the problem is formulated and solved using the theory of elasticity and integral transform technique. Using the integral transform technique and boundary conditions of the problem, the problem is reduced to a system of singular integral equations in which contact pressures and contact areas are unknown. The system of singular integral equations is solved numerically by using the Gauss-Jacobi integration formulation. Second, the receding contact problem has been developed based on the FEM ANSYS software. Two-dimensional analysis of the problem is carried out. The ANSYS and analytical results for the contact pressures, contact areas, and normal stresses (s x and s y ) along the axis of symmetry are given for various dimensionless quantities. The ANSYS results are verified by comparison with analytical results. DOI: 10.1061/ (ASCE)EM.1943-7889.0000781. © 2014 American Society of Civil Engineers. Author keywords: Receding contact; ANSYS; Quarter plane; Finite-element method (FEM); Integral equation. Introduction In the literature, there are many studies about problems involving the contact of two separate bodies pressed against each other as a result of their practical importance. In these problems, the lengths of the contact zone and contact pressure, which is zero at the ends of the contact segment, are the primary unknowns of the problem. Al- though in most cases the contact zone increases after the application of the load, in some cases the final contact zone is smaller than the original. This kind of problem is referred to by the generic name of receding contact (Garrido and Lorenzana 1998). In another defini- tion (Johnson 1985), a receding contact is one where the contact surface in the loaded configuration is contained within the initial contact surface. There is a large body of literature associated with receding contact problems both numerically and analytically. The latest nu- merical studies on this type of contact problem were either based on the FEM or boundary element method (Chan and Tuba 1971; Jing and Liao 1990; Satish Kumar et al. 1996; Andersson 1981; Garrido et al. 1991; Paris et al. 1992, 1995; Graciani et al. 2005). The following analytical studies on receding contact problems are available in the literature. Stippes et al. (1962) analyzed a contact stress problem for a smooth disk in an infinite plate. Weitsman (1969) investigated the unbounded contact between plates and an elastic half-space. The unbounded contact between plates and an elastic half-space was considered by Pu and Hussain (1970). The smooth receding contact between an elastic layer and a half-space when two bodies were pressed together by considering both the plane and axisymmetric cases was examined by Keer et al. (1972). Gladwell (1976) solved the same problem by treating the layer as a simple beam in bending. The plane smooth contact problem for an elastic layer lying on an elastic half-space with a compressive load applied to the layer through a frictionless rigid stamp was studied by Ratwani and Erdogan (1973). Civelek and Erdogan (1974) in- vestigated the general axisymmetric double-contact problem for an elastic layer pressed against a half-space by an elastic stamp. The smooth receding contact problem between an elastic layer and a half- space when the layer was compressed by a frictionless semiinfinite elastic cylinder was examined by Gecit (1986). Comez et al. (2004) solved the plane double receding contact for a rigid stamp and two elastic layers having different elastic constants and heights. A re- ceding contact plane problem between a functionally graded layer and a homogeneous half-space when two bodies were pressed to- gether was analyzed by El-Borgi et al. (2006). Kahya et al. (2007) studied a frictionless receding contact problem between an aniso- tropic elastic layer and an anisotropic elastic half-plane when the two bodies were pressed together by a rigid circular stamp. The Hertzian contact problem, coupled Volterra integral equations, and a linear complementarity problem were investigated by Gauthier et al. (2007). Rhimi et al. (2009) considered the axisymmetric problem of a frictionless receding contact between an elastic functionally graded layer and a homogeneous half-space when the two bodies were pressed together. Rhimi et al. (2011) also studied a double receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate. A general solution of the axisym- metric contact problem for biphasic cartilage layers was investigated by Argatov (2011). Adibnazari et al. (2012) studied contact of an asymmetrical rounded apex wedge with a half-plane. Chidlow et al. (2013) analyzed the two-dimensional solution of both adhesive and nonadhesive contact problems involving functionally graded mate- rials. Bagault et al. (2013) investigated contact analyses for an an- isotropic half-space coated with an anisotropic layer. 1 Research Assistant, Dept. of Naval Architecture and Marine Engineer- ing, Karadeniz Technical Univ., Trabzon 61080, Turkey (corresponding author). E-mail: muratyaylaci@ktu.edu.tr 2 Research Assistant, Civil Engineering Dept., Bayburt Univ., Bayburt, 69000, Turkey. E-mail: eoner@bayburt.edu.tr 3 Professor, Civil Engineering Dept., Karadeniz Technical Univ., Trab- zon 61080, Turkey. E-mail: birinci@ktu.edu.tr Note. This manuscript was submitted on June 17, 2013; approved on February 13, 2014; published online on March 14, 2014. Discussion period open until August 14, 2014; separate discussions must be submitted for individual papers. This paper is part of the Journal of Engineering Mechanics, © ASCE, ISSN 0733-9399/04014070(10)/$25.00. © ASCE 04014070-1 J. Eng. Mech. J. Eng. Mech. Downloaded from ascelibrary.org by Karadeniz Technical University on 03/26/14. Copyright ASCE. 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