Lie Group Generalized-α Time Integration of Constrained Flexible Multibody Systems

Autores
Brüls, Olivier; Cardona, Alberto; Arnold, Martín Alejandro
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper studies a Lie group extension of the generalized-α time integration method for the simulation of flexible multibody systems. The equations of motion are formulated as an index-3 differential-algebraic equation (DAE) on a Lie group, with the advantage that rotation variables can be taken into account without the need of introducing any parameterization. The proposed integrator is designed to solve this equation directly on the Lie group without index reduction. The convergence of the method for DAEs is studied in detail and global second-order accuracy is proven for all solution components, i.e. for nodal translations, rotations and Lagrange multipliers. The convergence properties are confirmed by three benchmarks of rigid and flexible systems with large rotation amplitudes. The Lie group method is compared with a more classical updated Lagrangian method which is also formulated in a Lie group setting. The remarkable simplicity of the new algorithm opens interesting perspectives for real-time applications, model-based control and optimization of multibody systems.
Fil: Brüls, Olivier. University of Liège; Bélgica
Fil: Cardona, Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina
Fil: Arnold, Martín Alejandro. Martin Luther University Halle-Wittenberg; Alemania
Materia
Flexible Multibody System;
Time Integration;
Generalized-Α Method;
Dae;
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:11336/18837
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/18837
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Lie Group Generalized-α Time Integration of Constrained Flexible Multibody SystemsBrüls, OlivierCardona, AlbertoArnold, Martín AlejandroFlexible Multibody System;Time Integration;Generalized-Α Method;Dae;https://purl.org/becyt/ford/2.3https://purl.org/becyt/ford/2This paper studies a Lie group extension of the generalized-α time integration method for the simulation of flexible multibody systems. The equations of motion are formulated as an index-3 differential-algebraic equation (DAE) on a Lie group, with the advantage that rotation variables can be taken into account without the need of introducing any parameterization. The proposed integrator is designed to solve this equation directly on the Lie group without index reduction. The convergence of the method for DAEs is studied in detail and global second-order accuracy is proven for all solution components, i.e. for nodal translations, rotations and Lagrange multipliers. The convergence properties are confirmed by three benchmarks of rigid and flexible systems with large rotation amplitudes. The Lie group method is compared with a more classical updated Lagrangian method which is also formulated in a Lie group setting. The remarkable simplicity of the new algorithm opens interesting perspectives for real-time applications, model-based control and optimization of multibody systems.Fil: Brüls, Olivier. University of Liège; BélgicaFil: Cardona, Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Arnold, Martín Alejandro. Martin Luther University Halle-Wittenberg; AlemaniaElsevier2012-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18837Brüls, Olivier; Cardona, Alberto; Arnold, Martín Alejandro; Lie Group Generalized-α Time Integration of Constrained Flexible Multibody Systems; Elsevier; Mechanism And Machine Theory; 48; 2-2012; 121-1370094-114XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0094114X11001510info:eu-repo/semantics/altIdentifier/doi/10.1016/j.mechmachtheory.2011.07.017info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:02:01Zoai:ri.conicet.gov.ar:11336/18837instacron: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:34982025-10-22 11:02:02.134CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Lie Group Generalized-α Time Integration of Constrained Flexible Multibody Systems
title Lie Group Generalized-α Time Integration of Constrained Flexible Multibody Systems
spellingShingle Lie Group Generalized-α Time Integration of Constrained Flexible Multibody Systems
Brüls, Olivier
Flexible Multibody System;
Time Integration;
Generalized-Α Method;
Dae;
title_short Lie Group Generalized-α Time Integration of Constrained Flexible Multibody Systems
title_full Lie Group Generalized-α Time Integration of Constrained Flexible Multibody Systems
title_fullStr Lie Group Generalized-α Time Integration of Constrained Flexible Multibody Systems
title_full_unstemmed Lie Group Generalized-α Time Integration of Constrained Flexible Multibody Systems
title_sort Lie Group Generalized-α Time Integration of Constrained Flexible Multibody Systems
dc.creator.none.fl_str_mv Brüls, Olivier
Cardona, Alberto
Arnold, Martín Alejandro
author Brüls, Olivier
author_facet Brüls, Olivier
Cardona, Alberto
Arnold, Martín Alejandro
author_role author
author2 Cardona, Alberto
Arnold, Martín Alejandro
author2_role author
author
dc.subject.none.fl_str_mv Flexible Multibody System;
Time Integration;
Generalized-Α Method;
Dae;
topic Flexible Multibody System;
Time Integration;
Generalized-Α Method;
Dae;
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 studies a Lie group extension of the generalized-α time integration method for the simulation of flexible multibody systems. The equations of motion are formulated as an index-3 differential-algebraic equation (DAE) on a Lie group, with the advantage that rotation variables can be taken into account without the need of introducing any parameterization. The proposed integrator is designed to solve this equation directly on the Lie group without index reduction. The convergence of the method for DAEs is studied in detail and global second-order accuracy is proven for all solution components, i.e. for nodal translations, rotations and Lagrange multipliers. The convergence properties are confirmed by three benchmarks of rigid and flexible systems with large rotation amplitudes. The Lie group method is compared with a more classical updated Lagrangian method which is also formulated in a Lie group setting. The remarkable simplicity of the new algorithm opens interesting perspectives for real-time applications, model-based control and optimization of multibody systems.
Fil: Brüls, Olivier. University of Liège; Bélgica
Fil: Cardona, Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina
Fil: Arnold, Martín Alejandro. Martin Luther University Halle-Wittenberg; Alemania
description This paper studies a Lie group extension of the generalized-α time integration method for the simulation of flexible multibody systems. The equations of motion are formulated as an index-3 differential-algebraic equation (DAE) on a Lie group, with the advantage that rotation variables can be taken into account without the need of introducing any parameterization. The proposed integrator is designed to solve this equation directly on the Lie group without index reduction. The convergence of the method for DAEs is studied in detail and global second-order accuracy is proven for all solution components, i.e. for nodal translations, rotations and Lagrange multipliers. The convergence properties are confirmed by three benchmarks of rigid and flexible systems with large rotation amplitudes. The Lie group method is compared with a more classical updated Lagrangian method which is also formulated in a Lie group setting. The remarkable simplicity of the new algorithm opens interesting perspectives for real-time applications, model-based control and optimization of multibody systems.
publishDate 2012
dc.date.none.fl_str_mv 2012-02
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/11336/18837
Brüls, Olivier; Cardona, Alberto; Arnold, Martín Alejandro; Lie Group Generalized-α Time Integration of Constrained Flexible Multibody Systems; Elsevier; Mechanism And Machine Theory; 48; 2-2012; 121-137
0094-114X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18837
identifier_str_mv Brüls, Olivier; Cardona, Alberto; Arnold, Martín Alejandro; Lie Group Generalized-α Time Integration of Constrained Flexible Multibody Systems; Elsevier; Mechanism And Machine Theory; 48; 2-2012; 121-137
0094-114X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0094114X11001510
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.mechmachtheory.2011.07.017
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
publisher.none.fl_str_mv Elsevier
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 12.982451

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