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Plane receding contact problem for a functionally graded layer supported by two quarter-planes

Çömez İ., Kahya V., Erdöl R.

Archives of Mechanics

2018

Vol. 70, nr 6

485--504

In this study, the plane receding contact problem for a functionally graded (FG) layer resting on two quarter-planes is considered by using the theory of linear elasticity. The layer is indented by a rigid cylindrical punch that applies a concentrated force in the normal direction. While the Poisson’s ratio is kept constant, the shear modulus is assumed to vary exponentially through-the-thickness of the layer. It is assumed that the contact at the layer-punch interface and the layer-substrate interface is frictionless, and only the normal tractions can be transmitted along the contact regions. Applying the Fourier integral transform, the plane elasticity equations are converted to a system of two singular integral equations, in which the contact stresses and the contact widths are unknowns. The singular integral equations are solved numerically by Gauss–Jacobi integration formula. Effects of the material inhomogeneity, the distance between quarter-planes and the punch radius on the contact stresses, the contact widths, and the stress intensity factors at the sharp edges are shown. Although the theoretical analysis is formulated with respect to elastic quarter planes, the numerical studies are carried out only for rigid ones.

Double contact analysis of multilayered elastic structures involving functionally graded materials

Yan J., Mi C.

Archives of Mechanics

2017

Vol. 69, nr 3

199--221

This paper analyzes the frictionless double contact problem of a two-layer laminate pressed against a homogeneous half-plane substrate by a rigid punch. The laminate is composed of a homogeneous elastic strip and a functionally graded layer, perfectly bonded along their interface. The mechanical properties of the graded layer are modeled by an exponentially varying shear modulus and constant Poisson’s ratio. Both the governing equations and the boundary conditions of the double contact problem are converted into a pair of singular integral equations by Fourier integral transforms, which are numerically integrated by Chebyshev–Gauss quadrature. The contact pressure and the contact size at both the advancing and the receding contact interface are eventually obtained by an iterative algorithm, developed from the method of steepest descent. Extensive parametric studies suggest that it is possible to control contact stress and contact size by introducing functionally graded materials into multilayered elastic structures.