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

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 conv...

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Vydáno v:	Friction Ročník 7; číslo 4; s. 359 - 371
Hlavní autoři:	Xu, Yang, Jackson, Robert L.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Beijing Tsinghua University Press 01.08.2019 Springer Nature B.V
Témata:	Boundary element method Boundary integral method Boussinesq equations Boussinesq-Cerruti solution Closed form solutions Computational mechanics Computer simulation Convolution Corrosion and Coatings Elasticity Engineering Exact solutions Flamant solution Flexible bodies Half spaces half-plane half-space Influence functions Integral equations Mathematical analysis Mathematical models Mechanical Engineering Nanotechnology Nonlinear programming Physical Chemistry Plane strain Research Article rough surface contact Stresses Surfaces and Interfaces Thin Films Tribology Flamant solution boundary element method Boussinesq-Cerruti solution half-space rough surface contact half-plane
ISSN:	2223-7690, 2223-7704
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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.
AbstractList	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. 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.
Author	Xu, Yang Jackson, Robert L.
Author_xml	– sequence: 1 givenname: Yang surname: Xu fullname: Xu, Yang email: yang.xu@auburn.edu organization: Mechanical Engineering Department, Auburn University – sequence: 2 givenname: Robert L. surname: Jackson fullname: Jackson, Robert L. organization: Mechanical Engineering Department, Auburn University
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Snippet	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... 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...
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SubjectTerms	Boundary element method Boundary integral method Boussinesq equations Boussinesq-Cerruti solution Closed form solutions Computational mechanics Computer simulation Convolution Corrosion and Coatings Elasticity Engineering Exact solutions Flamant solution Flexible bodies Half spaces half-plane half-space Influence functions Integral equations Mathematical analysis Mathematical models Mechanical Engineering Nanotechnology Nonlinear programming Physical Chemistry Plane strain Research Article rough surface contact Stresses Surfaces and Interfaces Thin Films Tribology
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Title	Boundary element method (BEM) applied to the rough surface contact vs. BEM in computational mechanics
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