Boundary element method (BEM) applied to the rough surface contact vs. BEM in computational mechanics

Abstract

In the numerical study of rough surfaces in contact problem, the flexible body beneath the roughness is commonly assumed as a half-space or a half-plane. The surface displacement on the boundary, the displacement components and state of stress inside the half-space can be determined through the convolution of the traction and the corresponding influence function in a closed-form. The influence function is often represented by the Boussinesq-Cerruti solution and the Flamant solution for three-dimensional elasticity and plane strain/stress, respectively. In this study, we rigorously show that any numerical model using the above mentioned half-space solution is a special form of the boundary element method (BEM). The boundary integral equations (BIEs) in the BEM is simplified to the Flamant solution when the domain is strictly a half-plane for the plane strain/stress condition. Similarly, the BIE is degraded to the Boussinesq-Cerruti solution if the domain is strictly a half-space. Therefore, the numerical models utilizing these closed-form influence functions are the special BEM where the domain is a half-space (or a half-plane). This analytical work sheds some light on how to accurately simulate the non-half-space contact problem using the BEM.

Contributors

Yang XU:

Bio :

Yang XU. He is a research engineer at Caterpillar Inc. He received his M.S and Ph.D. degrees in mechanical engineering at Auburn University, AL, USA. He has research interests in the area of rough surface contact using analytical, numerical and experimental methodologies, lubrication modeling, and surface metrology.

Robert L. JACKSON:

Bio :

Robert L. JACKSON. He is the director of the Tribology Program and a professor of mechanical engineering at Auburn University. He received his PhD degree in mechanical engineering, at the Georgia Institute of Technology in Atlanta, GA, USA. He has research interests in the areas of rough surface contact mechanics, contact resistance, multiphysics modeling, hydrodynamic lubrication, and nanoparticle lubricant additives. In 2012, Prof. Jackson also initiated one of the first undergraduate minors in the field of Tribology. Prof. Jackson received the 2011 ASME Burt L. Newkirk Award for notable contributions to the field of Tribology as indicated by significant publications before reaching the age of 40, the 2009 STLE Captain Alfred E. Hunt Memorial Award for the best paper in the field of lubrication, and the 2009 Shobert Paper Award at the Holm Conference on Electrical Contacts. He was also named the best reviewer for the ASME Journal of Tribology in 2008 and 2009.

Journal

Journal ID (publisher-id): Friction

Title: Friction

Publisher: Tsinghua University Press (Beijing/Hong Kong )

ISSN (Electronic): 2223-7704

ISSN (Print): 2223-7690

Publication date (Print): 01 August 2019

Publication date (Electronic): 01 October 2019

Volume: 7

Issue: 4

Pages: 359-371

Affiliations

¹Mechanical Engineering Department, Auburn University, AL 36849, USA

Author notes

*Corresponding author: Yang XU, E-mail: yang.xu@ 123456auburn.edu

Article

Publisher ID: s40544-018-0229-3

DOI: 10.1007/s40544-018-0229-3

Copyright statement: Copyright © Journals of Tsinghua University Press

License:

This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 Unported License (CC BY-NC 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. See https://creativecommons.org/licenses/by-nc/4.0/.

Product

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Categories

Subject: Research Articles