scholarly journals Discussion: “The Frictionless Contact Problem for an Elastic Layer Under Gravity” (Civelek, M. B., and Erdogan, F., 1975, ASME J. Appl. Mech., 42, pp. 136–140)

1975 ◽  
Vol 42 (4) ◽  
pp. 909-909
Author(s):  
M. Ratwani
Keyword(s):  
Contact Problem ◽  
Elastic Layer ◽  
Frictionless Contact

A semianalytical and finite-element solution to the unbonded contact between a frictionless layer and an FGM-coated half-plane

2017 ◽  
Vol 24 (2) ◽  
pp. 448-464 ◽  
Author(s):  
Jie Yan ◽  
Changwen Mi ◽  
Zhixin Liu
Keyword(s):  
Integral Equation ◽  
Finite Element ◽  
Singular Integral Equation ◽  
Contact Problem ◽  
Singular Integral ◽  
Material Properties ◽  
Elastic Layer ◽  
Coated Substrate ◽  
Receding Contact ◽  
Contact Size

In this work, we examine the receding contact between a homogeneous elastic layer and a half-plane substrate reinforced by a functionally graded coating. The material properties of the coating are allowed to vary exponentially along its thickness. A distributed traction load applied over a finite segment of the layer surface presses the layer and the coated substrate against each other. It is further assumed that the receding contact between the layer and the coated substrate is frictionless. In the absence of body forces, Fourier integral transforms are used to convert the governing equations and boundary conditions of the plane receding contact problem into a singular integral equation with the contact pressure and contact size as unknowns. Gauss–Chebyshev quadrature is subsequently employed to discretize both the singular integral equation and the force equilibrium condition at the contact interface. An iterative algorithm based on the method of steepest descent has been proposed to numerically solve the system of algebraic equations, which is linear for the contact pressure but nonlinear for the contact size. Extensive case studies are performed with respect to the coating inhomogeneity parameter, geometric parameters, material properties, and the extent of the indentation load. As a result of the indentation, the elastic layer remains in contact with the coated substrate over only a finite interval. Exterior to this region, the layer and the coated substrate lose contact. Nonetheless, the receding contact size is always larger than that of the indentation traction. To validate the theoretical solution, we have also developed a finite-element model to solve the same receding contact problem. Numerical results of finite-element modeling and theoretical development are compared in detail for a number of parametric studies and are found to agree very well with each other.

The Frictionless Contact Problem for an Elastic Layer Under Gravity

1975 ◽  
Vol 42 (1) ◽  
pp. 136-140 ◽  
Author(s):  
M. B. Civelek ◽  
F. Erdogan
Keyword(s):  
Elastic Layer ◽  
Mixed Boundary ◽  
Contact Problems ◽  
Simple Problem ◽  
Frictionless Contact ◽  
Continuous Contact ◽  
Crack Problems ◽  
Contact Stress Distribution ◽  
Length Of Separation ◽  
Clamping Pressure

The paper presents a technique for solving the plane frictionless contact problems in the presence of gravity and/or uniform clamping pressure. The technique is described by applying it to a simple problem of lifting of an elastic layer lying on a horizontal, rigid, frictionless subspace by means of a concentrated vertical load. First, the problem of continuous contact is considered and the critical value of the load corresponding to the initiation of interface separation is determined. Then the mixed boundary-value problem of discontinuous contact is formulated in terms of a singular integral equation by closely following a technique developed for crack problems. The numerical results include the contact stress distribution and the length of separation region. One of the main conclusions of the study is that neither the separation length nor the contact stresses are dependent on the elastic constants of the layer.

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