Geometrically exact beam finite element formulated on the special Euclidean group SE(3)

Autores
Sonneville, V.; Cardona, Alberto; Brüls, O.
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper describes a dynamic formulation of a straight beam finite element in the setting of the special Euclidean group SE(3). First, the static and dynamic equilibrium equations are derived in this framework from variational principles. Then, a non-linear interpolation formula using the exponential map is introduced. It is shown that this framework leads to a natural coupling in the interpolation of the position and rotation variables. Next, the discretized internal and inertia forces are developed. The semi-discrete equations of motion take the form of a second-order ordinary differential equation on a Lie group, which is solved using a Lie group time integration scheme. It is remarkable that no parameterization of the nodal variables needs to be introduced and that the proposed Lie group framework leads to a compact and easy-to-implement formulation. Some important numerical and theoretical aspects leading to a computationally efficient strategy are highlighted and discussed. For instance, the formulation leads to invariant tangent stiffness and mass matrices under rigid body motions and a locking free element. The proposed formulation is successfully tested in several numerical static and dynamic examples.
Fil: Sonneville, V.. Université de Liège; Bélgica
Fil: Cardona, Alberto. Universidad Nacional del Litoral; Argentina. 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
Fil: Brüls, O.. Université de Liège; Bélgica
Materia
Dynamic Beam
Finite Element
Lie Group
Special Euclidean Group
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:11336/78602
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Geometrically exact beam finite element formulated on the special Euclidean group SE(3)Sonneville, V.Cardona, AlbertoBrüls, O.Dynamic BeamFinite ElementLie GroupSpecial Euclidean Grouphttps://purl.org/becyt/ford/2.3https://purl.org/becyt/ford/2This paper describes a dynamic formulation of a straight beam finite element in the setting of the special Euclidean group SE(3). First, the static and dynamic equilibrium equations are derived in this framework from variational principles. Then, a non-linear interpolation formula using the exponential map is introduced. It is shown that this framework leads to a natural coupling in the interpolation of the position and rotation variables. Next, the discretized internal and inertia forces are developed. The semi-discrete equations of motion take the form of a second-order ordinary differential equation on a Lie group, which is solved using a Lie group time integration scheme. It is remarkable that no parameterization of the nodal variables needs to be introduced and that the proposed Lie group framework leads to a compact and easy-to-implement formulation. Some important numerical and theoretical aspects leading to a computationally efficient strategy are highlighted and discussed. For instance, the formulation leads to invariant tangent stiffness and mass matrices under rigid body motions and a locking free element. The proposed formulation is successfully tested in several numerical static and dynamic examples.Fil: Sonneville, V.. Université de Liège; BélgicaFil: Cardona, Alberto. Universidad Nacional del Litoral; Argentina. 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; ArgentinaFil: Brüls, O.. Université de Liège; BélgicaElsevier Science Sa2014-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/78602Sonneville, V.; Cardona, Alberto; Brüls, O.; Geometrically exact beam finite element formulated on the special Euclidean group SE(3); Elsevier Science Sa; Computer Methods in Applied Mechanics and Engineering; 268; 3-2014; 451-4740045-7825CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.cma.2013.10.008info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:06:42Zoai:ri.conicet.gov.ar:11336/78602instacron: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:34982025-09-10 13:06:43.213CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Geometrically exact beam finite element formulated on the special Euclidean group SE(3)
title Geometrically exact beam finite element formulated on the special Euclidean group SE(3)
spellingShingle Geometrically exact beam finite element formulated on the special Euclidean group SE(3)
Sonneville, V.
Dynamic Beam
Finite Element
Lie Group
Special Euclidean Group
title_short Geometrically exact beam finite element formulated on the special Euclidean group SE(3)
title_full Geometrically exact beam finite element formulated on the special Euclidean group SE(3)
title_fullStr Geometrically exact beam finite element formulated on the special Euclidean group SE(3)
title_full_unstemmed Geometrically exact beam finite element formulated on the special Euclidean group SE(3)
title_sort Geometrically exact beam finite element formulated on the special Euclidean group SE(3)
dc.creator.none.fl_str_mv Sonneville, V.
Cardona, Alberto
Brüls, O.
author Sonneville, V.
author_facet Sonneville, V.
Cardona, Alberto
Brüls, O.
author_role author
author2 Cardona, Alberto
Brüls, O.
author2_role author
author
dc.subject.none.fl_str_mv Dynamic Beam
Finite Element
Lie Group
Special Euclidean Group
topic Dynamic Beam
Finite Element
Lie Group
Special Euclidean Group
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.3
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv This paper describes a dynamic formulation of a straight beam finite element in the setting of the special Euclidean group SE(3). First, the static and dynamic equilibrium equations are derived in this framework from variational principles. Then, a non-linear interpolation formula using the exponential map is introduced. It is shown that this framework leads to a natural coupling in the interpolation of the position and rotation variables. Next, the discretized internal and inertia forces are developed. The semi-discrete equations of motion take the form of a second-order ordinary differential equation on a Lie group, which is solved using a Lie group time integration scheme. It is remarkable that no parameterization of the nodal variables needs to be introduced and that the proposed Lie group framework leads to a compact and easy-to-implement formulation. Some important numerical and theoretical aspects leading to a computationally efficient strategy are highlighted and discussed. For instance, the formulation leads to invariant tangent stiffness and mass matrices under rigid body motions and a locking free element. The proposed formulation is successfully tested in several numerical static and dynamic examples.
Fil: Sonneville, V.. Université de Liège; Bélgica
Fil: Cardona, Alberto. Universidad Nacional del Litoral; Argentina. 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
Fil: Brüls, O.. Université de Liège; Bélgica
description This paper describes a dynamic formulation of a straight beam finite element in the setting of the special Euclidean group SE(3). First, the static and dynamic equilibrium equations are derived in this framework from variational principles. Then, a non-linear interpolation formula using the exponential map is introduced. It is shown that this framework leads to a natural coupling in the interpolation of the position and rotation variables. Next, the discretized internal and inertia forces are developed. The semi-discrete equations of motion take the form of a second-order ordinary differential equation on a Lie group, which is solved using a Lie group time integration scheme. It is remarkable that no parameterization of the nodal variables needs to be introduced and that the proposed Lie group framework leads to a compact and easy-to-implement formulation. Some important numerical and theoretical aspects leading to a computationally efficient strategy are highlighted and discussed. For instance, the formulation leads to invariant tangent stiffness and mass matrices under rigid body motions and a locking free element. The proposed formulation is successfully tested in several numerical static and dynamic examples.
publishDate 2014
dc.date.none.fl_str_mv 2014-03
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/11336/78602
Sonneville, V.; Cardona, Alberto; Brüls, O.; Geometrically exact beam finite element formulated on the special Euclidean group SE(3); Elsevier Science Sa; Computer Methods in Applied Mechanics and Engineering; 268; 3-2014; 451-474
0045-7825
CONICET Digital
CONICET
url http://hdl.handle.net/11336/78602
identifier_str_mv Sonneville, V.; Cardona, Alberto; Brüls, O.; Geometrically exact beam finite element formulated on the special Euclidean group SE(3); Elsevier Science Sa; Computer Methods in Applied Mechanics and Engineering; 268; 3-2014; 451-474
0045-7825
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cma.2013.10.008
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 Elsevier Science Sa
publisher.none.fl_str_mv Elsevier Science Sa
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
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score 12.993085

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