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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-11-01
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| Series: | Friction |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/s40544-018-0229-3 |
| _version_ | 1819072354929606656 |
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| author | Yang Xu Robert L. Jackson |
| author_facet | Yang Xu Robert L. Jackson |
| author_sort | Yang Xu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-21T17:36:24Z |
| format | Article |
| id | doaj.art-7cbb0341f52448b69f11309f014bae39 |
| institution | Directory Open Access Journal |
| issn | 2223-7690 2223-7704 |
| language | English |
| last_indexed | 2024-12-21T17:36:24Z |
| publishDate | 2018-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Friction |
| spelling | doaj.art-7cbb0341f52448b69f11309f014bae392022-12-21T18:55:45ZengSpringerOpenFriction2223-76902223-77042018-11-017435937110.1007/s40544-018-0229-3Boundary element method (BEM) applied to the rough surface contact vs. BEM in computational mechanicsYang Xu0Robert L. Jackson1Mechanical Engineering Department, Auburn UniversityMechanical Engineering Department, Auburn UniversityAbstract 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.http://link.springer.com/article/10.1007/s40544-018-0229-3boundary element methodrough surface contacthalf-spacehalf-planeFlamant solutionBoussinesq-Cerruti solution |
| spellingShingle | Yang Xu Robert L. Jackson Boundary element method (BEM) applied to the rough surface contact vs. BEM in computational mechanics Friction boundary element method rough surface contact half-space half-plane Flamant solution Boussinesq-Cerruti solution |
| title | Boundary element method (BEM) applied to the rough surface contact vs. BEM in computational mechanics |
| title_full | Boundary element method (BEM) applied to the rough surface contact vs. BEM in computational mechanics |
| title_fullStr | Boundary element method (BEM) applied to the rough surface contact vs. BEM in computational mechanics |
| title_full_unstemmed | Boundary element method (BEM) applied to the rough surface contact vs. BEM in computational mechanics |
| title_short | Boundary element method (BEM) applied to the rough surface contact vs. BEM in computational mechanics |
| title_sort | boundary element method bem applied to the rough surface contact vs bem in computational mechanics |
| topic | boundary element method rough surface contact half-space half-plane Flamant solution Boussinesq-Cerruti solution |
| url | http://link.springer.com/article/10.1007/s40544-018-0229-3 |
| work_keys_str_mv | AT yangxu boundaryelementmethodbemappliedtotheroughsurfacecontactvsbemincomputationalmechanics AT robertljackson boundaryelementmethodbemappliedtotheroughsurfacecontactvsbemincomputationalmechanics |