B.E.M. applied to receding contact problems with friction

117

In this paper, we consider the plane problem of a frictionless receding contact between an elastic functionally graded layer and a homogeneous half-space, when the two bodies are pressed together. The graded layer is modeled as a nonhomogeneous medium with an isotropic stress-strain law and over a certain segment of its top surface is subjected to normal tractions while the rest of this surface is free of tractions. Since the contact between the two bodies is assumed to be frictionless, then only compressive normal tractions can be transmitted in the contact area. Using integral transforms, the plane elasticity equations are converted analytically into a singular integral equation in which the unknowns are the contact pressure and the receding contact half-length. The global equilibrium condition of the layer is supplemented to solve the problem. The singular integral equation is solved numerically using Chebychev polynomials and an iterative scheme is employed to obtain the correct receding contact half-length that satisfies the global equilibrium condition. The main objective of the paper is to study the effect of the material nonhomogeneity parameter and the thickness of the graded layer on the contact pressure and on the length of the receding contact.

Section: Introductionmentioning

confidence: 99%

A receding contact plane problem between a functionally graded layer and a homogeneous substrate

El-Borgi

Abdelmoula

Keer

2006

117

“…The latest numerical studies on this type of contact problems were either based on the finite element method (Chan and Tuba, 1971;Francavilla and Zienkiewicz, 1975;Jing and Liao, 1990) or on the boundary element method (Anderson, 1982;Garrido et al, 1991;Garrido and Lorenzana, 1998;Paris et al, 1995).…”

Section: Introductionmentioning

confidence: 99%

A receding contact problem for an anisotropic elastic medium consisting of a layer and a half plane

Kahya

Özşahin

Birinci

et al. 2007

This paper considers a frictionless receding contact problem between an anisotropic elastic layer and an anisotropic elastic half plane, when the two bodies are pressed together by means of a rigid circular stamp. The problem is reduced to a system of singular integral equations in which the contact stresses and lengths are the unknown functions. Numerical results for the contact stresses and the contact lengths are given by depending on various fibre orientations.

“…The latest numerical studies on this type of contact problems were either based on the finite element method (e.g., Jing andLiao, 1990, Satish Kumar et al, 1996) or on the boundary element method (Anderson, 1982;Garrido et al, 1991;Garrido and Lorenzana, 1998;Parí s et al, 1992Parí s et al, , 1995Graciani et al, 2005).…”

Section: Introductionmentioning

confidence: 99%

A receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate

Rhimi

El-Borgi

Said

et al. 2009

a b s t r a c tIn this paper, we consider the axisymmetric problem of a frictionless receding contact between an elastic functionally graded layer and a homogeneous half-space, when the two bodies are pressed together. The graded layer is modeled as a nonhomogeneous medium with an isotropic stress-strain law and is subjected over a part of its top surface to normal tractions while the rest of it is free of tractions. Since the contact between the two bodies is assumed to be frictionless, then only compressive normal tractions can be transmitted in the contact area. Using Hankel transform, the axisymmetric elasticity equations are converted analytically into a singular integral equation in which the unknowns are the contact pressure and the receding contact radius. The global equilibrium condition of the layer is supplemented to solve the problem. The singular integral equation is solved numerically using orthogonal Chebychev polynomials and an iterative scheme is employed to obtain the correct receding contact length that satisfies the global equilibrium condition. The main objective of the paper is to study the effect of the material nonhomogeneity parameter and the thickness of the graded layer on the contact pressure and on the length of the receding contact.