Analysis of the Unilateral Contact Problem for Biphasic Cartilage Layers with an Elliptic Contact Zone and Accounting for Tangential Displacements
A three-dimensional unilateral contact problem for articular cartilage layers attached to subchondral bones shaped as elliptic paraboloids is considered in the framework of the biphasic cartilage model. The main novelty of the study is in accounting not only for the normal (vertical), but also for t...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2016-09-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/838 |
| _version_ | 1830339229117317120 |
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| author | Sergei Rogosin Gennady Mishuris Anna Koroleva Anastasiya Vinakurava |
| author_facet | Sergei Rogosin Gennady Mishuris Anna Koroleva Anastasiya Vinakurava |
| author_sort | Sergei Rogosin |
| collection | DOAJ |
| description | A three-dimensional unilateral contact problem for articular cartilage layers attached to subchondral bones shaped as elliptic paraboloids is considered in the framework of the biphasic cartilage model. The main novelty of the study is in accounting not only for the normal (vertical), but also for tangential vertical (horizontal) displacements of the contacting surfaces. Exact general relationships have been established between the contact approach and some integral characteristics of the contact pressure, including the contact force. Asymptotic representations for the contact pressure integral characteristics are obtained in terms of the contact approach and some integral characteristics of the contact zone. The main result is represented by the first-order approximation problem. We supply the theoretical description of the asymptotic method by numerical analysis of the model. Our calculations demonstrate good convergence of the numerical scheme in determination of the parameters. In particular, it is shown that accounting for the tangential displacement is important in cases where the contact zone is non-circular. |
| first_indexed | 2024-12-19T20:54:10Z |
| format | Article |
| id | doaj.art-60cdfb3c393e4fc1a96648ca245896b7 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-19T20:54:10Z |
| publishDate | 2016-09-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-60cdfb3c393e4fc1a96648ca245896b72022-12-21T20:06:01ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102016-09-0121510.3846/13926292.2016.1196249Analysis of the Unilateral Contact Problem for Biphasic Cartilage Layers with an Elliptic Contact Zone and Accounting for Tangential DisplacementsSergei Rogosin0Gennady Mishuris1Anna Koroleva2Anastasiya Vinakurava3Department of Economics, Belarusian State University, Nezavisimosti ave 4, BY-220030 Minsk, Belarus; IMPACS, Aberystwyth University, Penglais, SY23 3BZ Aberystwyth, UKIMPACS, Aberystwyth University, Penglais, SY23 3BZ Aberystwyth, UKDepartment of Economics, Belarusian State University, Nezavisimosti ave 4, BY-220030 Minsk, BelarusDepartment of Mechanical Engineering and Aeronautics, Rzeszow University of Technology, Powstancow Warszawy al. 12, 35-959 Rzeszow, PolandA three-dimensional unilateral contact problem for articular cartilage layers attached to subchondral bones shaped as elliptic paraboloids is considered in the framework of the biphasic cartilage model. The main novelty of the study is in accounting not only for the normal (vertical), but also for tangential vertical (horizontal) displacements of the contacting surfaces. Exact general relationships have been established between the contact approach and some integral characteristics of the contact pressure, including the contact force. Asymptotic representations for the contact pressure integral characteristics are obtained in terms of the contact approach and some integral characteristics of the contact zone. The main result is represented by the first-order approximation problem. We supply the theoretical description of the asymptotic method by numerical analysis of the model. Our calculations demonstrate good convergence of the numerical scheme in determination of the parameters. In particular, it is shown that accounting for the tangential displacement is important in cases where the contact zone is non-circular.https://journals.vgtu.lt/index.php/MMA/article/view/838articular cartilage layersbiphasic modelasymptotic representationelliptic contact zonetangential displacement |
| spellingShingle | Sergei Rogosin Gennady Mishuris Anna Koroleva Anastasiya Vinakurava Analysis of the Unilateral Contact Problem for Biphasic Cartilage Layers with an Elliptic Contact Zone and Accounting for Tangential Displacements Mathematical Modelling and Analysis articular cartilage layers biphasic model asymptotic representation elliptic contact zone tangential displacement |
| title | Analysis of the Unilateral Contact Problem for Biphasic Cartilage Layers with an Elliptic Contact Zone and Accounting for Tangential Displacements |
| title_full | Analysis of the Unilateral Contact Problem for Biphasic Cartilage Layers with an Elliptic Contact Zone and Accounting for Tangential Displacements |
| title_fullStr | Analysis of the Unilateral Contact Problem for Biphasic Cartilage Layers with an Elliptic Contact Zone and Accounting for Tangential Displacements |
| title_full_unstemmed | Analysis of the Unilateral Contact Problem for Biphasic Cartilage Layers with an Elliptic Contact Zone and Accounting for Tangential Displacements |
| title_short | Analysis of the Unilateral Contact Problem for Biphasic Cartilage Layers with an Elliptic Contact Zone and Accounting for Tangential Displacements |
| title_sort | analysis of the unilateral contact problem for biphasic cartilage layers with an elliptic contact zone and accounting for tangential displacements |
| topic | articular cartilage layers biphasic model asymptotic representation elliptic contact zone tangential displacement |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/838 |
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