Continuous and Discontinuous Contact Problems of a Functionally Graded Layer

Yıl 2017, Cilt: 3 Sayı: 2, 12 - 14, 01.11.2017

Gökhan Adıyaman

Öz

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.

Anahtar Kelimeler

Gauss-Jacobi, Functionally graded layer, Discontinuous contact

Kaynakça

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