Finite strain quadrilateral shell using least-squares fit of relative Lagrangian in-plane strains
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10174/16757 https://doi.org/@article{Areias201526, title = "Finite strain quadrilateral shell using least-squares fit of relative Lagrangian in-plane strains ", journal = "Finite Elements in Analysis and Design ", volume = "98", number = "", pages = "26 - 40", year = "2015", note = "", issn = "0168-874X", doi = "http://dx.doi.org/10.1016/j.finel.2015.01.004", url = "http://www.sciencedirect.com/science/article/pii/S0168874X15000050", author = "P. Areias and T. Rabczuk and J.M. César de Sá and J.E. Garção", keywords = "Finite strains", keywords = "Shell elements", keywords = "Pian–Sumihara stress modes", keywords = "Finite strain plasticity", keywords = "Least-square assumed strain ", https://doi.org/10.1016/j.finel.2015.01.004 |
Resumo: | This work presents a finite strain quadrilateral element with least-squares assumed in-plane shear strains (in covariant/contravariant coordinates) and classical transverse shear assumed strains. It is an alternative to enhanced-assumed-strain (EAS) formulation and, in contrast to this, produces an element satisfying ab initio the Patch-test. No additional degrees-of-freedom are present, unlike EAS. Least-squares fit allows the derivation of invariant finite strain elements which are both in-plane and out-of-plane shear-locking free and amenable to standardization in commercial codes. With that goal, we use automatically generated code produced by AceGen and Mathematica to obtain novel finite element formulations. The corresponding exact linearization of the internal forces was, until recently, a insurmountable task. We use the tangent modulus in the least-squares fit to ensure that stress modes are obtained from a five-parameter strain fitting. This reproduces exactly the in-plane bending modes. The discrete equations are obtained by establishing a four-field variational principle (a direct extension of the Hu–Washizu variational principle). The main achieved goal is coarse-mesh accuracy for distorted meshes, which is adequate for being used in crack propagation problems. In addition, as an alternative to spherical interpolation, a consistent director normalization is performed. Metric components are fully deduced and exact linearization of the shell element is performed. Full linear and nonlinear assessment of the element is performed, showing similar performance to more costly approaches, often on-par with the best available shell elements. |
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Finite strain quadrilateral shell using least-squares fit of relative Lagrangian in-plane strainsFinite strainsshell elementsPian–Sumihara stress modesFinite strain plasticityLeast-squares assumed strainThis work presents a finite strain quadrilateral element with least-squares assumed in-plane shear strains (in covariant/contravariant coordinates) and classical transverse shear assumed strains. It is an alternative to enhanced-assumed-strain (EAS) formulation and, in contrast to this, produces an element satisfying ab initio the Patch-test. No additional degrees-of-freedom are present, unlike EAS. Least-squares fit allows the derivation of invariant finite strain elements which are both in-plane and out-of-plane shear-locking free and amenable to standardization in commercial codes. With that goal, we use automatically generated code produced by AceGen and Mathematica to obtain novel finite element formulations. The corresponding exact linearization of the internal forces was, until recently, a insurmountable task. We use the tangent modulus in the least-squares fit to ensure that stress modes are obtained from a five-parameter strain fitting. This reproduces exactly the in-plane bending modes. The discrete equations are obtained by establishing a four-field variational principle (a direct extension of the Hu–Washizu variational principle). The main achieved goal is coarse-mesh accuracy for distorted meshes, which is adequate for being used in crack propagation problems. In addition, as an alternative to spherical interpolation, a consistent director normalization is performed. Metric components are fully deduced and exact linearization of the shell element is performed. Full linear and nonlinear assessment of the element is performed, showing similar performance to more costly approaches, often on-par with the best available shell elements.Elsevier B. V.2016-01-19T12:03:27Z2016-01-192015-06-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10174/16757https://doi.org/@article{Areias201526, title = "Finite strain quadrilateral shell using least-squares fit of relative Lagrangian in-plane strains ", journal = "Finite Elements in Analysis and Design ", volume = "98", number = "", pages = "26 - 40", year = "2015", note = "", issn = "0168-874X", doi = "http://dx.doi.org/10.1016/j.finel.2015.01.004", url = "http://www.sciencedirect.com/science/article/pii/S0168874X15000050", author = "P. Areias and T. Rabczuk and J.M. César de Sá and J.E. Garção", keywords = "Finite strains", keywords = "Shell elements", keywords = "Pian–Sumihara stress modes", keywords = "Finite strain plasticity", keywords = "Least-square assumed strain ",http://hdl.handle.net/10174/16757https://doi.org/10.1016/j.finel.2015.01.004engFinite Elements in Analysis and Designpmaa@uevora.pttimon.rabczuk@uni-weimar.decesarsa@fe.up.ptjesg@uevora.pt287Areias, PedroRabczuk, TimonCésar de Sá, JoséGarção, Joséinfo: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:RCAAP2024-01-03T19:03:52Zoai:dspace.uevora.pt:10174/16757Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:09:05.497203Repositório 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 |
Finite strain quadrilateral shell using least-squares fit of relative Lagrangian in-plane strains |
title |
Finite strain quadrilateral shell using least-squares fit of relative Lagrangian in-plane strains |
spellingShingle |
Finite strain quadrilateral shell using least-squares fit of relative Lagrangian in-plane strains Areias, Pedro Finite strains shell elements Pian–Sumihara stress modes Finite strain plasticity Least-squares assumed strain |
title_short |
Finite strain quadrilateral shell using least-squares fit of relative Lagrangian in-plane strains |
title_full |
Finite strain quadrilateral shell using least-squares fit of relative Lagrangian in-plane strains |
title_fullStr |
Finite strain quadrilateral shell using least-squares fit of relative Lagrangian in-plane strains |
title_full_unstemmed |
Finite strain quadrilateral shell using least-squares fit of relative Lagrangian in-plane strains |
title_sort |
Finite strain quadrilateral shell using least-squares fit of relative Lagrangian in-plane strains |
author |
Areias, Pedro |
author_facet |
Areias, Pedro Rabczuk, Timon César de Sá, José Garção, José |
author_role |
author |
author2 |
Rabczuk, Timon César de Sá, José Garção, José |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Areias, Pedro Rabczuk, Timon César de Sá, José Garção, José |
dc.subject.por.fl_str_mv |
Finite strains shell elements Pian–Sumihara stress modes Finite strain plasticity Least-squares assumed strain |
topic |
Finite strains shell elements Pian–Sumihara stress modes Finite strain plasticity Least-squares assumed strain |
description |
This work presents a finite strain quadrilateral element with least-squares assumed in-plane shear strains (in covariant/contravariant coordinates) and classical transverse shear assumed strains. It is an alternative to enhanced-assumed-strain (EAS) formulation and, in contrast to this, produces an element satisfying ab initio the Patch-test. No additional degrees-of-freedom are present, unlike EAS. Least-squares fit allows the derivation of invariant finite strain elements which are both in-plane and out-of-plane shear-locking free and amenable to standardization in commercial codes. With that goal, we use automatically generated code produced by AceGen and Mathematica to obtain novel finite element formulations. The corresponding exact linearization of the internal forces was, until recently, a insurmountable task. We use the tangent modulus in the least-squares fit to ensure that stress modes are obtained from a five-parameter strain fitting. This reproduces exactly the in-plane bending modes. The discrete equations are obtained by establishing a four-field variational principle (a direct extension of the Hu–Washizu variational principle). The main achieved goal is coarse-mesh accuracy for distorted meshes, which is adequate for being used in crack propagation problems. In addition, as an alternative to spherical interpolation, a consistent director normalization is performed. Metric components are fully deduced and exact linearization of the shell element is performed. Full linear and nonlinear assessment of the element is performed, showing similar performance to more costly approaches, often on-par with the best available shell elements. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015-06-01T00:00:00Z 2016-01-19T12:03:27Z 2016-01-19 |
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/10174/16757 https://doi.org/@article{Areias201526, title = "Finite strain quadrilateral shell using least-squares fit of relative Lagrangian in-plane strains ", journal = "Finite Elements in Analysis and Design ", volume = "98", number = "", pages = "26 - 40", year = "2015", note = "", issn = "0168-874X", doi = "http://dx.doi.org/10.1016/j.finel.2015.01.004", url = "http://www.sciencedirect.com/science/article/pii/S0168874X15000050", author = "P. Areias and T. Rabczuk and J.M. César de Sá and J.E. Garção", keywords = "Finite strains", keywords = "Shell elements", keywords = "Pian–Sumihara stress modes", keywords = "Finite strain plasticity", keywords = "Least-square assumed strain ", http://hdl.handle.net/10174/16757 https://doi.org/10.1016/j.finel.2015.01.004 |
url |
http://hdl.handle.net/10174/16757 https://doi.org/@article{Areias201526, title = "Finite strain quadrilateral shell using least-squares fit of relative Lagrangian in-plane strains ", journal = "Finite Elements in Analysis and Design ", volume = "98", number = "", pages = "26 - 40", year = "2015", note = "", issn = "0168-874X", doi = "http://dx.doi.org/10.1016/j.finel.2015.01.004", url = "http://www.sciencedirect.com/science/article/pii/S0168874X15000050", author = "P. Areias and T. Rabczuk and J.M. César de Sá and J.E. Garção", keywords = "Finite strains", keywords = "Shell elements", keywords = "Pian–Sumihara stress modes", keywords = "Finite strain plasticity", keywords = "Least-square assumed strain ", https://doi.org/10.1016/j.finel.2015.01.004 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Finite Elements in Analysis and Design pmaa@uevora.pt timon.rabczuk@uni-weimar.de cesarsa@fe.up.pt jesg@uevora.pt 287 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Elsevier B. V. |
publisher.none.fl_str_mv |
Elsevier B. V. |
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 |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799136574014750720 |