This paper presents a concise boundary integral equation framework for relating the thermal-mechanical surface load (the three traction components and the normal heat flux) to the thermal-mechanical response (the three quasi-static displacement components and the steady-state temperature). This uncoupled thermoelastic framework allows the simultaneous calculation of displacement and temperature—without subsurface discretization—because it is based on classical Green’s functions for displacement and for temperature and on newly derived Green’s functions for thermoelastic displacement. In general, the boundary element method (BEM) can be applied with this framework to finite geometry problems of steady-state thermal-mechanical contact. Here, example calculations are performed for counterformal contact problems, which can be modeled as contact on a halfspace. A linear element BEM is developed and compared with the constant element BEM for speed and accuracy. The linear element BEM uses newly derived influence coefficients for constant loads over an arbitrary triangular element, and these closed form expressions are used to improve the accuracy of the numerical algorithm. The constant element BEM uses the discrete convolution fast Fourier transform (DC-FFT) algorithm, which is based on influence coefficients for constant loads over rectangular elements. The quasi-static surface displacements and the steady-state surface temperature are calculated from an applied semi-ellipsoidal pressure with accompanying frictional heating effects. The surface thermal-mechanical behavior of the counterformal contact is shown in graphs vs. the radius, and the deviations from axisymmetry are highlighted.
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e-mail: mrodgers@uncc.edu
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July 2004
Technical Papers
Boundary Element Methods for Steady-State Thermal-Mechanical Problems of Counterformal Contact
Michael J. Rodgers,
e-mail: mrodgers@uncc.edu
Michael J. Rodgers
Northwestern University, Center for Surface Engineering and Tribology, Evanston, IL 60208
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Shuangbiao Liu,
Shuangbiao Liu
Northwestern University, Center for Surface Engineering and Tribology, Evanston, IL 60208
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Q. Jane Wang,
Q. Jane Wang
Northwestern University, Center for Surface Engineering and Tribology, Evanston, IL 60208
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Leon M. Keer
Leon M. Keer
Northwestern University, Center for Surface Engineering and Tribology, Evanston, IL 60208
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Michael J. Rodgers
Northwestern University, Center for Surface Engineering and Tribology, Evanston, IL 60208
e-mail: mrodgers@uncc.edu
Shuangbiao Liu
Northwestern University, Center for Surface Engineering and Tribology, Evanston, IL 60208
Q. Jane Wang
Northwestern University, Center for Surface Engineering and Tribology, Evanston, IL 60208
Leon M. Keer
Northwestern University, Center for Surface Engineering and Tribology, Evanston, IL 60208
Contributed by the Tribology Division for publication in the ASME JOURNAL OF TRIBOLOGY. Manuscript received by the Tribology Division March 28, 2003 revised manuscript received December 9, 2003. Associate Editor: C. H. Venner.
J. Tribol. Jul 2004, 126(3): 443-449 (7 pages)
Published Online: June 28, 2004
Article history
Received:
March 28, 2003
Revised:
December 9, 2003
Online:
June 28, 2004
Citation
Rodgers, M. J., Liu , S., Wang , Q. J., and Keer , L. M. (June 28, 2004). "Boundary Element Methods for Steady-State Thermal-Mechanical Problems of Counterformal Contact ." ASME. J. Tribol. July 2004; 126(3): 443–449. https://doi.org/10.1115/1.1757492
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