Continuous and Discontinuous Contact Problems of a Functionally Graded Layer

Year 2017, Volume: 3 Issue: 2, 12 - 14, 01.11.2017

Gökhan Adıyaman

Abstract

In
this study, the continuous and discontinuous contact problem of a functionally
graded (FG) layer resting on a rigid foundation is considered. The top of the
FG layer is subjected to normal tractions over a finite segment. The graded
layer is modeled as a non-homogenous medium with a constant Poisson’ ratio and
exponentially varying shear modules and density. For continuous contact, the
problem is solved analytically using plane elasticity and integral transform
techniques. The critical load that causes first separation for various material
properties is investigated.  The problem
is reduced to a singular integral equation using plane elasticity and integral
transform techniques in case of discontinuous contact. Obtained singular
integral equation is solved numerically using Gauss-Jacobi integral formulation
and an iterative scheme is employed to obtain the correct separation distance.
The separation distance between the FG layer and the foundation is analyzed.
The results are shown in tables and figures. It is seen that decreasing
stiffness and density at the top of the layer results an increment  in critical load and the lowest pressure
occurs on the symmetry axis in case of continuous contact. In addition, the
separation distance increases with decreasing stiffness and density at the top
of the layer in case of discontinuous contact.

Keywords

Gauss-Jacobi, Functionally graded layer, Discontinuous contact

References

• [1] M.B. Civelek, F. Erdogan, “Frictionless Contact Problem for an Elastic Layer under Gravity”, Journal of Applied Mechanics-Transactions of the Asme 42 (1975) 136-140.
• [2] A. Birinci, R. Erdol, “A frictionless contact problem for two elastic layers supported by a Winkler foundation”, Structural Engineering and Mechanics 15 (2003) 331-344.
• [3] E. Oner, A. Birinci, “Continuous Contact Problem for Two Elastic Layers Resting on an Elastic Half-Infinite Plane”, Journal of Mechanics of Materials and Structures 9 (2014) 105-119. DOI: 10.2140/jomms.2014.9.105.
• [4] S. El-Borgi, R. Abdelmoula, L. Keer, “A receding contact plane problem between a functionally graded layer and a homogeneous substrate”, International Journal of Solids and Structures 43 (2006) 658-674. DOI: 10.1016/j.ijsolstr.2005.04.017.
• [5] J. Yang, L.L. Ke, “Two-dimensional contact problem for a coating-graded layer-substrate structure under a rigid cylindrical punch”, International Journal of Mechanical Sciences 50 (2008) 985-994. DOI: 10.1016/j.ijmecsci.2008.03.002.
• [6] M. Turan, G. Adiyaman, V. Kahya, A. Birinci, “Axisymmetric analysis of a functionally graded layer resting on elastic substrate”, Structural Engineering and Mechanics 58 (2016) 423-442. DOI: 10.12989/sem.2016.58.3.423.