A continuous-stress tetrahedron for finite strain problems
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10174/25865 https://doi.org/10.1016/j.finel.2019.07.003 |
Resumo: | A finite-strain tetrahedron with continuous stresses is proposed and analyzed. The complete stress tensor is now a nodal tensor degree-of-freedom, in addition to displacement. Specifically, stress conjugate to the relative Green-Lagrange strain is used within the framework of the Hellinger-Reissner variational principle. This is an extension of the Dunham and Pister element to arbitrary constitutive laws and finite strain. To avoid the excessive continuity shortcoming, outer faces can have null stress vectors. The resulting formulation is related to the nonlocal approaches popularized as smoothed finite element formulations. In contrast with smoothed formulations, the interpolation and integration domain is retained. Sparsity is also identical to the classical mixed formulations. When compared with variational multiscale methods, there are no parameters. Very high accuracy is obtained for four-node tetrahedra with incompressibility and bending benchmarks being successfully solved. Although the ad-hoc factor is removed and performance is highly competitive, computational cost is high, as each tetrahedron has 36 degrees-of-freedom. Besides the inf-sup test, four benchmark examples are adopted, with exceptional results in bending and compression with finite strains. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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A continuous-stress tetrahedron for finite strain problemsA finite-strain tetrahedron with continuous stresses is proposed and analyzed. The complete stress tensor is now a nodal tensor degree-of-freedom, in addition to displacement. Specifically, stress conjugate to the relative Green-Lagrange strain is used within the framework of the Hellinger-Reissner variational principle. This is an extension of the Dunham and Pister element to arbitrary constitutive laws and finite strain. To avoid the excessive continuity shortcoming, outer faces can have null stress vectors. The resulting formulation is related to the nonlocal approaches popularized as smoothed finite element formulations. In contrast with smoothed formulations, the interpolation and integration domain is retained. Sparsity is also identical to the classical mixed formulations. When compared with variational multiscale methods, there are no parameters. Very high accuracy is obtained for four-node tetrahedra with incompressibility and bending benchmarks being successfully solved. Although the ad-hoc factor is removed and performance is highly competitive, computational cost is high, as each tetrahedron has 36 degrees-of-freedom. Besides the inf-sup test, four benchmark examples are adopted, with exceptional results in bending and compression with finite strains.Elsevier2019-09-19T14:03:04Z2019-09-192019-07-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10174/25865http://hdl.handle.net/10174/25865https://doi.org/10.1016/j.finel.2019.07.003porFinite Elements in Analysis and Design, Vol. 165, pp 52-64pmaa@uevora.pttimon.rabczuk@uni-weimar.deflc@uevora.ptcarrilho@uevora.pt334Areias, PedroRabczuk, TimonCarapau, FernandoLopes, José Carrilhoinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-03T19:19:51Zoai:dspace.uevora.pt:10174/25865Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:16:08.748713Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
A continuous-stress tetrahedron for finite strain problems |
title |
A continuous-stress tetrahedron for finite strain problems |
spellingShingle |
A continuous-stress tetrahedron for finite strain problems Areias, Pedro |
title_short |
A continuous-stress tetrahedron for finite strain problems |
title_full |
A continuous-stress tetrahedron for finite strain problems |
title_fullStr |
A continuous-stress tetrahedron for finite strain problems |
title_full_unstemmed |
A continuous-stress tetrahedron for finite strain problems |
title_sort |
A continuous-stress tetrahedron for finite strain problems |
author |
Areias, Pedro |
author_facet |
Areias, Pedro Rabczuk, Timon Carapau, Fernando Lopes, José Carrilho |
author_role |
author |
author2 |
Rabczuk, Timon Carapau, Fernando Lopes, José Carrilho |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Areias, Pedro Rabczuk, Timon Carapau, Fernando Lopes, José Carrilho |
description |
A finite-strain tetrahedron with continuous stresses is proposed and analyzed. The complete stress tensor is now a nodal tensor degree-of-freedom, in addition to displacement. Specifically, stress conjugate to the relative Green-Lagrange strain is used within the framework of the Hellinger-Reissner variational principle. This is an extension of the Dunham and Pister element to arbitrary constitutive laws and finite strain. To avoid the excessive continuity shortcoming, outer faces can have null stress vectors. The resulting formulation is related to the nonlocal approaches popularized as smoothed finite element formulations. In contrast with smoothed formulations, the interpolation and integration domain is retained. Sparsity is also identical to the classical mixed formulations. When compared with variational multiscale methods, there are no parameters. Very high accuracy is obtained for four-node tetrahedra with incompressibility and bending benchmarks being successfully solved. Although the ad-hoc factor is removed and performance is highly competitive, computational cost is high, as each tetrahedron has 36 degrees-of-freedom. Besides the inf-sup test, four benchmark examples are adopted, with exceptional results in bending and compression with finite strains. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-09-19T14:03:04Z 2019-09-19 2019-07-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10174/25865 http://hdl.handle.net/10174/25865 https://doi.org/10.1016/j.finel.2019.07.003 |
url |
http://hdl.handle.net/10174/25865 https://doi.org/10.1016/j.finel.2019.07.003 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
Finite Elements in Analysis and Design, Vol. 165, pp 52-64 pmaa@uevora.pt timon.rabczuk@uni-weimar.de flc@uevora.pt carrilho@uevora.pt 334 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799136643429433344 |