A NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approach

Autores
da Rosa Espath, Luis Felipe; Braun, A.L.; Awruch, A.M.; Dalcin, Lisandro Daniel
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A numerical model to deal with nonlinear elastodynamics involving large rotations within the framework of the finite element based on NURBS (Non-Uniform Rational B-Spline) basis is presented. A comprehensive kinematical description using a corotational approach and an orthogonal tensor given by the exact polar decomposition is adopted. The state equation is written in terms of corotational variables according to the hypoelastic theory, relating the Jaumann derivative of the Cauchy stress to the Eulerian strain rate.The generalized-α method (Gα) method and Generalized Energy-Momentum Method with an additional parameter (GEMM+ξ) are employed in order to obtain a stable and controllable dissipative time-stepping scheme with algorithmic conservative properties for nonlinear dynamic analyses.The main contribution is to show that the energy-momentum conservation properties and numerical stability may be improved once a NURBS-based FEM in the spatial discretization is used. Also it is shown that high continuity can postpone the numerical instability when GEMM+ξ with consistent mass is employed; likewise, increasing the continuity class yields a decrease in the numerical dissipation. A parametric study is carried out in order to show the stability and energy budget in terms of several properties such as continuity class, spectral radius and lumped as well as consistent mass matrices.
Fil: da Rosa Espath, Luis Felipe. Universidade Federal do Rio Grande do Sul; Brasil
Fil: Braun, A.L.. Universidade Federal do Rio Grande do Sul; Brasil
Fil: Awruch, A.M.. Universidade Federal do Rio Grande do Sul; Brasil
Fil: Dalcin, Lisandro Daniel. King Abdullah University Of Science And Technology; . Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina
Materia
Isogeometric Analysis
Generalized-Αlpha Method
Generalized Energy?Momentum Method
Corotational Kinematics
Nurbs
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/38228
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/38228
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approachda Rosa Espath, Luis FelipeBraun, A.L.Awruch, A.M.Dalcin, Lisandro DanielIsogeometric AnalysisGeneralized-Αlpha MethodGeneralized Energy?Momentum MethodCorotational KinematicsNurbsA numerical model to deal with nonlinear elastodynamics involving large rotations within the framework of the finite element based on NURBS (Non-Uniform Rational B-Spline) basis is presented. A comprehensive kinematical description using a corotational approach and an orthogonal tensor given by the exact polar decomposition is adopted. The state equation is written in terms of corotational variables according to the hypoelastic theory, relating the Jaumann derivative of the Cauchy stress to the Eulerian strain rate.The generalized-α method (Gα) method and Generalized Energy-Momentum Method with an additional parameter (GEMM+ξ) are employed in order to obtain a stable and controllable dissipative time-stepping scheme with algorithmic conservative properties for nonlinear dynamic analyses.The main contribution is to show that the energy-momentum conservation properties and numerical stability may be improved once a NURBS-based FEM in the spatial discretization is used. Also it is shown that high continuity can postpone the numerical instability when GEMM+ξ with consistent mass is employed; likewise, increasing the continuity class yields a decrease in the numerical dissipation. A parametric study is carried out in order to show the stability and energy budget in terms of several properties such as continuity class, spectral radius and lumped as well as consistent mass matrices.Fil: da Rosa Espath, Luis Felipe. Universidade Federal do Rio Grande do Sul; BrasilFil: Braun, A.L.. Universidade Federal do Rio Grande do Sul; BrasilFil: Awruch, A.M.. Universidade Federal do Rio Grande do Sul; BrasilFil: Dalcin, Lisandro Daniel. King Abdullah University Of Science And Technology; . Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; ArgentinaJohn Wiley & Sons Ltd2015-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/38228da Rosa Espath, Luis Felipe ; Braun, A.L.; Awruch, A.M.; Dalcin, Lisandro Daniel; A NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approach; John Wiley & Sons Ltd; International Journal for Numerical Methods in Engineering; 102; 13; 6-2015; 1839-18680029-5981CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1002/nme.4870info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:11:13Zoai:ri.conicet.gov.ar:11336/38228instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:11:13.989CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approach
title A NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approach
spellingShingle A NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approach
da Rosa Espath, Luis Felipe
Isogeometric Analysis
Generalized-Αlpha Method
Generalized Energy?Momentum Method
Corotational Kinematics
Nurbs
title_short A NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approach
title_full A NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approach
title_fullStr A NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approach
title_full_unstemmed A NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approach
title_sort A NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approach
dc.creator.none.fl_str_mv da Rosa Espath, Luis Felipe
Braun, A.L.
Awruch, A.M.
Dalcin, Lisandro Daniel
author da Rosa Espath, Luis Felipe
author_facet da Rosa Espath, Luis Felipe
Braun, A.L.
Awruch, A.M.
Dalcin, Lisandro Daniel
author_role author
author2 Braun, A.L.
Awruch, A.M.
Dalcin, Lisandro Daniel
author2_role author
author
author
dc.subject.none.fl_str_mv Isogeometric Analysis
Generalized-Αlpha Method
Generalized Energy?Momentum Method
Corotational Kinematics
Nurbs
topic Isogeometric Analysis
Generalized-Αlpha Method
Generalized Energy?Momentum Method
Corotational Kinematics
Nurbs
dc.description.none.fl_txt_mv A numerical model to deal with nonlinear elastodynamics involving large rotations within the framework of the finite element based on NURBS (Non-Uniform Rational B-Spline) basis is presented. A comprehensive kinematical description using a corotational approach and an orthogonal tensor given by the exact polar decomposition is adopted. The state equation is written in terms of corotational variables according to the hypoelastic theory, relating the Jaumann derivative of the Cauchy stress to the Eulerian strain rate.The generalized-α method (Gα) method and Generalized Energy-Momentum Method with an additional parameter (GEMM+ξ) are employed in order to obtain a stable and controllable dissipative time-stepping scheme with algorithmic conservative properties for nonlinear dynamic analyses.The main contribution is to show that the energy-momentum conservation properties and numerical stability may be improved once a NURBS-based FEM in the spatial discretization is used. Also it is shown that high continuity can postpone the numerical instability when GEMM+ξ with consistent mass is employed; likewise, increasing the continuity class yields a decrease in the numerical dissipation. A parametric study is carried out in order to show the stability and energy budget in terms of several properties such as continuity class, spectral radius and lumped as well as consistent mass matrices.
Fil: da Rosa Espath, Luis Felipe. Universidade Federal do Rio Grande do Sul; Brasil
Fil: Braun, A.L.. Universidade Federal do Rio Grande do Sul; Brasil
Fil: Awruch, A.M.. Universidade Federal do Rio Grande do Sul; Brasil
Fil: Dalcin, Lisandro Daniel. King Abdullah University Of Science And Technology; . Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina
description A numerical model to deal with nonlinear elastodynamics involving large rotations within the framework of the finite element based on NURBS (Non-Uniform Rational B-Spline) basis is presented. A comprehensive kinematical description using a corotational approach and an orthogonal tensor given by the exact polar decomposition is adopted. The state equation is written in terms of corotational variables according to the hypoelastic theory, relating the Jaumann derivative of the Cauchy stress to the Eulerian strain rate.The generalized-α method (Gα) method and Generalized Energy-Momentum Method with an additional parameter (GEMM+ξ) are employed in order to obtain a stable and controllable dissipative time-stepping scheme with algorithmic conservative properties for nonlinear dynamic analyses.The main contribution is to show that the energy-momentum conservation properties and numerical stability may be improved once a NURBS-based FEM in the spatial discretization is used. Also it is shown that high continuity can postpone the numerical instability when GEMM+ξ with consistent mass is employed; likewise, increasing the continuity class yields a decrease in the numerical dissipation. A parametric study is carried out in order to show the stability and energy budget in terms of several properties such as continuity class, spectral radius and lumped as well as consistent mass matrices.
publishDate 2015
dc.date.none.fl_str_mv 2015-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/38228
da Rosa Espath, Luis Felipe ; Braun, A.L.; Awruch, A.M.; Dalcin, Lisandro Daniel; A NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approach; John Wiley & Sons Ltd; International Journal for Numerical Methods in Engineering; 102; 13; 6-2015; 1839-1868
0029-5981
CONICET Digital
CONICET
url http://hdl.handle.net/11336/38228
identifier_str_mv da Rosa Espath, Luis Felipe ; Braun, A.L.; Awruch, A.M.; Dalcin, Lisandro Daniel; A NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approach; John Wiley & Sons Ltd; International Journal for Numerical Methods in Engineering; 102; 13; 6-2015; 1839-1868
0029-5981
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1002/nme.4870
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv John Wiley & Sons Ltd
publisher.none.fl_str_mv John Wiley & Sons Ltd
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1844614009432571904
score 13.070432

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