Elementary solution of contact problems for a transversely isotropic elastic layer bonded to a rigid foundation

2006 ◽  
Vol 57 (3) ◽  
pp. 464-490 ◽  
Author(s):  
V. I. Fabrikant
Keyword(s):  
Elastic Layer ◽  
Transversely Isotropic ◽  
Contact Problems ◽  
Elementary Solution ◽  
Rigid Foundation

Solution of contact problems for a transversely isotropic elastic layer bonded to an elastic half-space

2009 ◽  
Vol 223 (11) ◽  
pp. 2487-2499 ◽  
Author(s):  
V I Fabrikant
Keyword(s):  
Half Space ◽  
Elastic Layer ◽  
Integral Transform ◽  
Transversely Isotropic ◽  
Contact Problems ◽  
Integral Transforms ◽  
Elastic Half Space ◽  
Electrostatic Problem ◽  
Crack Problems ◽  
New Interpretation

The idea, first used by the author for the case of crack problems, is applied here to solve a contact problem for a transversely isotropic elastic layer bonded to an elastic halfspace, made of a different transversely isotropic material. A rigid punch of arbitrary shape is pressed against the layer's free surface. The governing integral equation is derived; it is mathematically equivalent to that of an electrostatic problem of an infinite row of coaxial charged discs in the shape of the domain of contact. As a comparison, the method of integral transforms is also used to solve the problem. The main difference of our integral transform approach with the existing ones is in separating of our half-space solution from the integral transform terms. It is shown that both methods lead to the same results, thus giving a new interpretation to the integral transform as a sum of an infinite series of generalized images.

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.

Contact problems for the elastic layer of small thickness

1964 ◽  
Vol 28 (2) ◽  
pp. 425-427 ◽  
Author(s):  
V.M. Aleksandrov ◽  
I.I. Vorovich
Keyword(s):  
Elastic Layer ◽  
Contact Problems ◽  
Small Thickness

Some contact problems for the elastic layer

1963 ◽  
Vol 27 (4) ◽  
pp. 1164-1174 ◽  
Author(s):  
V.M Aleksandrov
Keyword(s):  
Elastic Layer ◽  
Contact Problems
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