Two-Dimensional Contact on an Anisotropic Elastic Half-Space

1994 ◽  
Vol 61 (2) ◽  
pp. 250-255 ◽  
Author(s):  
Hui Fan ◽  
L. M. Keer
Keyword(s):  
Eigenvalue Problem ◽  
Contact Problem ◽  
Half Space ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Solution Procedure ◽  
Elastic Half Space ◽  
Two Dimensional ◽  
Anisotropic Elastic ◽  
The One

The two-dimensional contact problem for a semi-infinite anisotropic elastic media is reconsidered here by using the formalism of Es he I by et al. (1953) and Stroh (1958). The approach of analytic function continuation is employed to investigate the half-space contact problem with various mixed boundary conditions applied to the half-space. A key point of the solution procedure suggested in the present paper is its dependence on a general eigenvalue problem involving a Hermitian matrix. This eigenvalue problem is analogous to the one encountered when investigating the behavior of an interface crack (Ting, 1986). As an application, the interaction between a dislocation and a contact strip is solved. The compactness of the results shows their potential for utilization to solve the problem of contact of a damaged anisotropic half-space.

A Torsional Contact Problem for an Indented Half-Space

1996 ◽  
Vol 63 (1) ◽  
pp. 1-6 ◽  
Author(s):  
R. Y. S. Pak ◽  
F. Abedzadeh
Keyword(s):  
Stress Distribution ◽  
Boundary Value Problem ◽  
Contact Problem ◽  
Half Space ◽  
Contact Stress ◽  
Mixed Boundary ◽  
Elastic Half Space ◽  
Torsional Stiffness ◽  
Mixed Boundary Value Problem ◽  
Contact Stress Distribution

This paper is concerned with the torsion of a rigid disk bonded to the bottom of a cylindrical indentation on an elastic half-space. By virtue of Fourier sine and cosine transforms, the mixed boundary value problem in classical elastostatics is shown to be reducible to a pair of integral equations, of which one possesses a generalized Cauchy singular kernel. With the aid of the theory of analytic functions, the inherent fractional-order singularity in the contact problem is rendered explicit. Illustrative results on the torsional stiffness of the base of the indentation and the corresponding contact stress distribution are presented for engineering applications.

Shrink fit of an elastic half-space with a cylindrical cavity

1995 ◽  
Vol 448 (1932) ◽  
pp. 81-88 ◽  
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Cylindrical Cavity ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Elastic Half Space ◽  
Series Method ◽  
Dual Integral Equations ◽  
Axisymmetric Contact Problem ◽  
Shrink Fit

This paper deals with the axisymmetric contact problem for an elastic half-space with a cylindrical cavity when mixed boundary conditions are prescribed on the surface of the cavity. The problem is simplified to that of finding the solution of dual integral equations arising from the mixed boundary conditions. The solution is obtained by the series method, and quantities of physical interest are calculated.

Multiple Region Contact Solutions for a Flat Indenter on a Layered Elastic Half Space: Plane-Strain Case

1989 ◽  
Vol 56 (2) ◽  
pp. 251-262 ◽  
Author(s):  
T. W. Shield ◽  
D. B. Bogy
Keyword(s):  
Plane Strain ◽  
Half Space ◽  
Contact Region ◽  
Integral Transforms ◽  
Elastic Half Space ◽  
Geometrical Parameters ◽  
Restricted Range ◽  
Complete Contact ◽  
The One ◽  
Layered Half Space

The plane-strain problem of a smooth, flat rigid indenter contacting a layered elastic half space is examined. It is mathematically formulated using integral transforms to derive a singular integral equation for the contact pressure, which is solved by expansion in orthogonal polynomials. The solution predicts complete contact between the indenter and the surface of the layered half space only for a restricted range of the material and geometrical parameters. Outside of this range, solutions exist with two or three contact regions. The parameter space divisions between the one, two, or three contact region solutions depend on the material and geometrical parameters and they are found for both the one and two layer cases. As the modulus of the substrate decreases to zero, the two contact region solution predicts the expected result that contact occurs only at the corners of the indenter. The three contact region solution provides an explanation for the nonuniform approach to the half space solution as the layer thickness vanishes.

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