Unbonded Contact of a Square Plate on an Elastic Half-Space or a Winkler Foundation

1988 ◽  
Vol 55 (2) ◽  
pp. 430-436 ◽  
Author(s):  
Hui Li ◽  
J. P. Dempsey
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Contact Region ◽  
Elastic Half Space ◽  
Unilateral Contact ◽  
Winkler Foundation ◽  
Vertical Loading ◽  
Centrally Symmetric ◽  
Receding Contact ◽  
Square Plate

The unbonded frictionless receding contact problem of a thin plate placed under centrally symmetric vertical loading while resting on an elastic half-space or a Winkler foundation is solved in this paper. The problem is transformed into the solution of two-coupled integral-series equations over an unknown contact region. The problem is nonlinear by virtue of unilateral contact and therefore needs to be solved iteratively. Special attention is given to the edge and corner contact pressure singularities for the plate on the elastic half-space. Comparison is made with other relevant numerical results available.

A Rigid Punch on an Elastic Half-Space Under the Effect of Friction: A Finite Difference Solution

2008 ◽  
Author(s):  
Avraham Dorogoy ◽  
Leslie Banks-Sills
Keyword(s):  
Finite Difference ◽  
Contact Problem ◽  
Half Space ◽  
Contact Zone ◽  
Contact Problems ◽  
Elastic Half Space ◽  
Rigid Punch ◽  
Normal Loading ◽  
Receding Contact ◽  
Stationary Contact

The accuracy of the finite difference technique in solving frictionless and frictional advancing contact problems is investigated by solving the problem of a rigid punch on an elastic halfspace subjected to normal loading. Stick and slip conditions between the elastic and the rigid materials are added to an existing numerical algorithm which was previously used for solving frictionless and frictional stationary and receding contact problems. The numerical additions are first tested by applying them in the solution of receding and stationary contact problems and comparing them to known solutions. The receding contact problem is that of an elastic slab on a rigid half-plane; the stationary contact problem is that of a flat rigid punch on an elastic half-space. In both cases the influence of friction is examined. The results are compared to those of other investigations with very good agreement observed. Once more it is verified that for both receding and stationary contact, load steps are not required for obtaining a solution if the loads are applied monotonically, whether or not there is friction. Next, an advancing contact problem of a round rigid punch on an elastic half-space subjected to normal loading, with and without the influence of friction is investigated. The results for frictionless advancing contact, which are obtained without load steps, are compared to analytical results, namely the Hertz problem; excellent agreement is observed. When friction is present, load steps and iterations for determining the contact area within each load step, are required. Hence, the existing code, in which only iterations to determine the contact zone were employed, was modified to include load steps, together with the above mentioned iterations for each load step. The effect of friction on the stress distribution and contact length is studied. It is found that when stick conditions appear in the contact zone, an increase in the friction coefficient results in an increase in the stick zone size within the contact zone. These results agree well with semianalytical results of another investigation, illustrating the accuracy and capabilities of the finite difference technique for advancing contact.

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.

Contact Stress Analysis of a Layered Transversely Isotropic Half-Space

1992 ◽  
Vol 114 (2) ◽  
pp. 253-261 ◽  
Author(s):  
C. H. Kuo ◽  
L. M. Keer
Keyword(s):  
Half Space ◽  
Mixed Boundary ◽  
Contact Region ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Stress Components ◽  
Contact Failure

The three-dimensional problem of contact between a spherical indenter and a multi-layered structure bonded to an elastic half-space is investigated. The layers and half-space are assumed to be composed of transversely isotropic materials. By the use of Hankel transforms, the mixed boundary value problem is reduced to an integral equation, which is solved numerically to determine the contact stresses and contact region. The interior displacement and stress fields in both the layer and half-space can be calculated from the inverse Hankel transform used with the solved contact stresses prescribed over the contact region. The stress components, which may be related to the contact failure of coatings, are discussed for various coating thicknesses.

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