Numerical approximations of thin structure deformations
We review different models for thin structures using bending as principal mechanism to undergo large deformations. Each model consists of minimizing a fourth order energy, potentially subject to a nonconvex constraint. Equilibrium deformations are approximated using local discontinuous Galerkin fini...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-08-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.201/ |
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| author | Bonito, Andrea Guignard, Diane Morvant, Angelique |
| author_facet | Bonito, Andrea Guignard, Diane Morvant, Angelique |
| author_sort | Bonito, Andrea |
| collection | DOAJ |
| description | We review different models for thin structures using bending as principal mechanism to undergo large deformations. Each model consists of minimizing a fourth order energy, potentially subject to a nonconvex constraint. Equilibrium deformations are approximated using local discontinuous Galerkin finite elements. The discrete energies relies on a discrete Hessian operator defined on discontinuous functions with better approximation properties than the piecewise Hessian. Discrete gradient flows are used to drive the minimization process. They are chosen for their robustness and ability to preserve the nonconvex constraint. Several numerical experiments are presented to showcase the variety of shapes achievable with these models. |
| format | Article |
| id | doaj-art-aa51ad5e0a384ed5b7b2d51bd94d3a3e |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2023-08-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-aa51ad5e0a384ed5b7b2d51bd94d3a3e2025-02-07T13:46:20ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342023-08-01351S118121710.5802/crmeca.20110.5802/crmeca.201Numerical approximations of thin structure deformationsBonito, Andrea0Guignard, Diane1Morvant, Angelique2Department of Mathematics, Texas A&M University, College Station, TX 77845, USA.Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON K1N 6N5, Canada.Department of Mathematics, Texas A&M University, College Station, TX 77845, USA.We review different models for thin structures using bending as principal mechanism to undergo large deformations. Each model consists of minimizing a fourth order energy, potentially subject to a nonconvex constraint. Equilibrium deformations are approximated using local discontinuous Galerkin finite elements. The discrete energies relies on a discrete Hessian operator defined on discontinuous functions with better approximation properties than the piecewise Hessian. Discrete gradient flows are used to drive the minimization process. They are chosen for their robustness and ability to preserve the nonconvex constraint. Several numerical experiments are presented to showcase the variety of shapes achievable with these models.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.201/Nonlinear elasticityplate deformationfoldingprestrain metricdiscontinuous Galerkinreconstructed Hessiannumerical simulations |
| spellingShingle | Bonito, Andrea Guignard, Diane Morvant, Angelique Numerical approximations of thin structure deformations Comptes Rendus. Mécanique Nonlinear elasticity plate deformation folding prestrain metric discontinuous Galerkin reconstructed Hessian numerical simulations |
| title | Numerical approximations of thin structure deformations |
| title_full | Numerical approximations of thin structure deformations |
| title_fullStr | Numerical approximations of thin structure deformations |
| title_full_unstemmed | Numerical approximations of thin structure deformations |
| title_short | Numerical approximations of thin structure deformations |
| title_sort | numerical approximations of thin structure deformations |
| topic | Nonlinear elasticity plate deformation folding prestrain metric discontinuous Galerkin reconstructed Hessian numerical simulations |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.201/ |
| work_keys_str_mv | AT bonitoandrea numericalapproximationsofthinstructuredeformations AT guignarddiane numericalapproximationsofthinstructuredeformations AT morvantangelique numericalapproximationsofthinstructuredeformations |