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TECHNICAL PAPERS

Boundary Element Methods for Steady-State Thermal-Mechanical Problems of Counterformal Contact

[+] Author and Article Information
Michael J. Rodgers, Shuangbiao Liu, Q. Jane Wang, Leon M. Keer

Northwestern University, Center for Surface Engineering and Tribology, Evanston, IL 60208

J. Tribol 126(3), 443-449 (Jun 28, 2004) (7 pages) doi:10.1115/1.1757492 History: Received March 28, 2003; Revised December 09, 2003; Online June 28, 2004
Copyright © 2004 by ASME
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Figures

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The general case shows the nondimensional normal u3 displacement versus the nondimensional radius. The solid line shows the analytical solution for pressure only (with neither friction nor heating) 9. The results are not axisymmetric, due to the frictional effect (see Fig. 2).
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The geometry for appendix B
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The nondimensional heat factor Qf influences (a) the nondimensional normal u3 and radial ur displacement and (b) the nondimensional temperature rise. The solid line in (a) shows the analytical solution for pressure only (without heating) 9. The results from both (a) and (b) are axisymmetric.
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The nondimensional normal u3 and radial ur displacement are plotted versus the nondimensional radius of the pressure and frictional shear. The solid line shows the analytical solution for pressure only (without friction) 9. The results are not axisymmetric, and thus the variation of the results at different radii are caused by the variation as a function of the polar angle.
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The nondimensional normal u3 and radial ur displacement are plotted versus the nondimensional radius of the pressure over a circle. The solid line shows the analytical solution 9. The normal displacement is the higher curve, and u3 positive means the solid is depressed.
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Loading for Examples 2–5 and Mesh for BEM-Tri. One quarter of the loaded region is shown as the quarter circle. One wedge (10°) of the BEM-Tri mesh is shown with the nodes (corners) of each element. The BEM-Tri mesh (468 elements, 253 nodes) is axisymmetric with this wedge copied by rotation over a circle of radius 3.3.
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Meshes and Loading for Ex. 1. The loaded region is shown as the 5×5 element square in the center of the meshed region. The DC-FFT mesh (before the necessary doubling to avoid wrap-around error) is shown with the collocation points at the center of each pictured element. The BEM-Quad mesh is the same as the DC-FFT mesh, but the points shown are the nodes (corners) of each element; the element lines are not shown. The unfilled points are part of the BEM-Quad mesh but not part of the DC-FFT mesh.
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Description of the physical domain and coordinates. The surface of the halfspace is ∂Ω={x3=0}. The generalized surface load P is P=(p1 p2 p3 q)T, where pj is the traction in the xj direction and q is the normal heat flux directed into the elastic solid.

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