A Hybridized Mixed Approach for Efficient Stress Prediction in a Layerwise Plate Model
Building upon recent works devoted to the development of a stress-based layerwise model for multilayered plates, we explore an alternative finite-element discretization to the conventional displacement-based finite-element method. We rely on a mixed finite-element approach where both stresses and di...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/10/1711 |
| _version_ | 1797498135854972928 |
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| author | Lucille Salha Jeremy Bleyer Karam Sab Joanna Bodgi |
| author_facet | Lucille Salha Jeremy Bleyer Karam Sab Joanna Bodgi |
| author_sort | Lucille Salha |
| collection | DOAJ |
| description | Building upon recent works devoted to the development of a stress-based layerwise model for multilayered plates, we explore an alternative finite-element discretization to the conventional displacement-based finite-element method. We rely on a mixed finite-element approach where both stresses and displacements are interpolated. Since conforming stress-based finite-elements ensuring traction continuity are difficult to construct, we consider a hybridization strategy in which traction continuity is relaxed by the introduction of an additional displacement-like Lagrange multiplier defined on the element facets. Such a strategy offers the advantage of uncoupling many degrees of freedom so that static condensation can be performed at the element level, yielding a much smaller final system to solve. Illustrative applications demonstrate that the proposed mixed approach is free from any shear-locking in the thin plate limit and is more accurate than a displacement approach for the same number of degrees of freedom. As a result, this method can be used to capture efficiently strong intra- and inter-laminar stress variations near free-edges or cracks. |
| first_indexed | 2024-03-10T03:29:08Z |
| format | Article |
| id | doaj.art-9a35230771fb4921977f00d6e2b1fe6c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:29:08Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9a35230771fb4921977f00d6e2b1fe6c2023-11-23T12:01:18ZengMDPI AGMathematics2227-73902022-05-011010171110.3390/math10101711A Hybridized Mixed Approach for Efficient Stress Prediction in a Layerwise Plate ModelLucille Salha0Jeremy Bleyer1Karam Sab2Joanna Bodgi3Laboratoire Navier, Ecole des Ponts ParisTech, University Gustave Eiffel, CNRS, 6-8 Av. Blaise Pascal, Cité Descartes, 77455 Champs-sur-Marne, FranceLaboratoire Navier, Ecole des Ponts ParisTech, University Gustave Eiffel, CNRS, 6-8 Av. Blaise Pascal, Cité Descartes, 77455 Champs-sur-Marne, FranceLaboratoire Navier, Ecole des Ponts ParisTech, University Gustave Eiffel, CNRS, 6-8 Av. Blaise Pascal, Cité Descartes, 77455 Champs-sur-Marne, FranceFaculté des Sciences, Université Saint Joseph, Mar Roukos-Dekwaneh, Beyrouth 1104 2020, LebanonBuilding upon recent works devoted to the development of a stress-based layerwise model for multilayered plates, we explore an alternative finite-element discretization to the conventional displacement-based finite-element method. We rely on a mixed finite-element approach where both stresses and displacements are interpolated. Since conforming stress-based finite-elements ensuring traction continuity are difficult to construct, we consider a hybridization strategy in which traction continuity is relaxed by the introduction of an additional displacement-like Lagrange multiplier defined on the element facets. Such a strategy offers the advantage of uncoupling many degrees of freedom so that static condensation can be performed at the element level, yielding a much smaller final system to solve. Illustrative applications demonstrate that the proposed mixed approach is free from any shear-locking in the thin plate limit and is more accurate than a displacement approach for the same number of degrees of freedom. As a result, this method can be used to capture efficiently strong intra- and inter-laminar stress variations near free-edges or cracks.https://www.mdpi.com/2227-7390/10/10/1711laminateslayerwise plate modelmixed finite elementhybridization |
| spellingShingle | Lucille Salha Jeremy Bleyer Karam Sab Joanna Bodgi A Hybridized Mixed Approach for Efficient Stress Prediction in a Layerwise Plate Model Mathematics laminates layerwise plate model mixed finite element hybridization |
| title | A Hybridized Mixed Approach for Efficient Stress Prediction in a Layerwise Plate Model |
| title_full | A Hybridized Mixed Approach for Efficient Stress Prediction in a Layerwise Plate Model |
| title_fullStr | A Hybridized Mixed Approach for Efficient Stress Prediction in a Layerwise Plate Model |
| title_full_unstemmed | A Hybridized Mixed Approach for Efficient Stress Prediction in a Layerwise Plate Model |
| title_short | A Hybridized Mixed Approach for Efficient Stress Prediction in a Layerwise Plate Model |
| title_sort | hybridized mixed approach for efficient stress prediction in a layerwise plate model |
| topic | laminates layerwise plate model mixed finite element hybridization |
| url | https://www.mdpi.com/2227-7390/10/10/1711 |
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