Analytical solution of discontinuous contact problem in functionally graded layer and homogeneous layer

Yusuf Kaya , Alper Polat , Talat Şűkrű Őzşahin , Pınar Bora

Abstract

In the study, the problem of discontinuous contact in two layers, one of which is functionally graded is solved using the theory of elasticity. In this problem functionally graded (FG) layer resting on homogeneous layer and loaded with two different rigid flat blocks. In addition, homogeneous layer is resting on a rigid plane. Frictions on all surfaces are neglected. The heights of the FG layer and the homogeneous layer are h1 and h2, respectively. When solving the problem, displacement and stress equations are substituted in the boundary conditions. Then the problem is demained to singular integral equations. Wherein unknown functions are the contact stresses under the two rigid flat blocks and the slope of the separation. These singular integral equations are solved numerically using the Gauss-Chebyshev integration formulas. The analyzes were performed for different inhomogeneity parameter (βh1), shear modulus ratio (μ2/μ-h1). distance between the rigid blocks ((a3-a2)/h1) and density parameter (γh1). Consequently, the stress distributions and starting and ending points of the separation area between the FG layer and homogeneous layer are determined for several dimensionless quantities.

Key Words

discontinuous contact problem; functionally graded layer; rigid plane; separation; theory of elasticity

Address

(1) Yusuf Kaya — Department of Civil Engineering, Gumuhane University, Gumushane 29100, Turkey
(2) Alper Polat — Department of Civil Engineering, Munzur University, Tunceli 62000, Turkey
(3) Talat Şűkrű Őzşahin — Department of Civil Engineering, Karadeniz Technical University, Trabzon 61080, Turkey
(4) Pınar Bora — Department of Civil Engineering, Sivas Cumhuriyet University, Sivas 58140, Turkey.

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