A semi-analytical approach to three-dimensional normal contact problems with friction |
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Authors: | Li J Berger E J |
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Affiliation: | (1) Department of Mechanical Engineering, University of Cincinnati, P.O. Box 210072, Cincinnati, Ohio 45221-0072 e-mail: ed.berger@uc.edu, |
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Abstract: | We present a semi-analytical approach for three-dimensional elastostatic normal contact problems with friction. The numerical
approach to iteration on contact area and stick zone size is supported by an underlying analytical solution relating normal
and tangential surface tractions to surface displacements in three coordinate directions. The governing equations are fully
coupled. The analytical surface displacement solutions for a basic loading element have been derived elsewhere (Li and Berger
2001), and the total surface displacements are constructed as a superposition of deflections due to overlapping pyramid load
segments. This approach requires no interpolation scheme for the field variables, which distinguishes it from other numerical
techniques such as the FEM, BEM, and meshless methods. A background grid is defined only on the contact surfaces, and iteration
approaches are used to determine a convergent configuration for contact domain and stick zone size. The approach is exercised
on several normal contact problems, with and without friction, and the results compare favorably to existing analytical and
numerical solutions.
Received: 10 July 2002 / Accepted: 3 December 2002
The authors appreciate the support of the UC Department of Mechanical Engineering and the UC Office of the Vice President
for Research, who jointly provided funds for this work. |
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Keywords: | Contact Friction Elasticity Semi-analytical methods |
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