A non-conforming monolithic finite element method for problems of coupled mechanics
In this study, a Lagrange multiplier technique is developed to solve problems of coupled mechanics and is applied to the case of a Newtonian fluid coupled to a quasi-static hyperelastic solid. Based on theoretical developments in [57], an additional Lagrange multiplier is used to weakly impose displ...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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2010
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| _version_ | 1797103238867058688 |
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| author | Nordsletten, D Kay, D Smith, N |
| author_facet | Nordsletten, D Kay, D Smith, N |
| author_sort | Nordsletten, D |
| collection | OXFORD |
| description | In this study, a Lagrange multiplier technique is developed to solve problems of coupled mechanics and is applied to the case of a Newtonian fluid coupled to a quasi-static hyperelastic solid. Based on theoretical developments in [57], an additional Lagrange multiplier is used to weakly impose displacement/velocity continuity as well as equal, but opposite, force. Through this approach, both mesh conformity and kinematic variable interpolation may be selected independently within each mechanical body, allowing for the selection of grid size and interpolation most appropriate for the underlying physics. In addition, the transfer of mechanical energy in the coupled system is proven to be conserved. The fidelity of the technique for coupled fluid-solid mechanics is demonstrated through a series of numerical experiments which examine the construction of the Lagrange multiplier space, stability of the scheme, and show optimal convergence rates. The benefits of non-conformity in multi-physics problems is also highlighted. Finally, the method is applied to a simplified elliptical model of the cardiac left ventricle. © 2010 Elsevier Inc. |
| first_indexed | 2024-03-07T06:17:15Z |
| format | Journal article |
| id | oxford-uuid:f17dda76-2603-4e6f-82a2-ea7bc51ce96d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:17:15Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:f17dda76-2603-4e6f-82a2-ea7bc51ce96d2022-03-27T11:56:26ZA non-conforming monolithic finite element method for problems of coupled mechanicsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f17dda76-2603-4e6f-82a2-ea7bc51ce96dEnglishSymplectic Elements at Oxford2010Nordsletten, DKay, DSmith, NIn this study, a Lagrange multiplier technique is developed to solve problems of coupled mechanics and is applied to the case of a Newtonian fluid coupled to a quasi-static hyperelastic solid. Based on theoretical developments in [57], an additional Lagrange multiplier is used to weakly impose displacement/velocity continuity as well as equal, but opposite, force. Through this approach, both mesh conformity and kinematic variable interpolation may be selected independently within each mechanical body, allowing for the selection of grid size and interpolation most appropriate for the underlying physics. In addition, the transfer of mechanical energy in the coupled system is proven to be conserved. The fidelity of the technique for coupled fluid-solid mechanics is demonstrated through a series of numerical experiments which examine the construction of the Lagrange multiplier space, stability of the scheme, and show optimal convergence rates. The benefits of non-conformity in multi-physics problems is also highlighted. Finally, the method is applied to a simplified elliptical model of the cardiac left ventricle. © 2010 Elsevier Inc. |
| spellingShingle | Nordsletten, D Kay, D Smith, N A non-conforming monolithic finite element method for problems of coupled mechanics |
| title | A non-conforming monolithic finite element method for problems of coupled mechanics |
| title_full | A non-conforming monolithic finite element method for problems of coupled mechanics |
| title_fullStr | A non-conforming monolithic finite element method for problems of coupled mechanics |
| title_full_unstemmed | A non-conforming monolithic finite element method for problems of coupled mechanics |
| title_short | A non-conforming monolithic finite element method for problems of coupled mechanics |
| title_sort | non conforming monolithic finite element method for problems of coupled mechanics |
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