A Dimensional Reduction Algorithm and Software for Acyclically Dependent Constraints
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/10174/24498 https://doi.org/10.1080/15502287.2019.1566284 |
Resumo: | For discrete equations of motion with acyclic equality constraints and within the context of the null-space method, an original Algorithm is introduced. By first permuting and then topologically ordering the degrees-of-freedom in the constraint gradient matrix, the saddle point problem can be solved with a sparse triangular system for the constraint equations. In this work, we show that saddle problems resulting from constrained (nonlinear) mechanical problems can always be set in this form, with constraint pivots being selected a priori. Given n discrete motion equations and m equality constraints, the original square sparse (n+m)2 ( n + m ) 2 system is replaced by a sparse system (n−m)2 ( n − m ) 2 and a sparse triangular solve with m2 coefficients and n – m right-hand sides. This triangular solve, which involves three sparse matrices (in existing literature only two of the three matrices are sparse), is here discussed in detail. Seven sparse operations are addressed (five standard and two nonstandard) in addition to some specific ad-hoc operations. Algorithms, source code and examples are presented in this work. |
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A Dimensional Reduction Algorithm and Software for Acyclically Dependent ConstraintsCoupling Of Multibody Dynamics And Finite ElementsEquality ConstraintsNONLINEAR PROBLEMSSPARSE MATRICESFor discrete equations of motion with acyclic equality constraints and within the context of the null-space method, an original Algorithm is introduced. By first permuting and then topologically ordering the degrees-of-freedom in the constraint gradient matrix, the saddle point problem can be solved with a sparse triangular system for the constraint equations. In this work, we show that saddle problems resulting from constrained (nonlinear) mechanical problems can always be set in this form, with constraint pivots being selected a priori. Given n discrete motion equations and m equality constraints, the original square sparse (n+m)2 ( n + m ) 2 system is replaced by a sparse system (n−m)2 ( n − m ) 2 and a sparse triangular solve with m2 coefficients and n – m right-hand sides. This triangular solve, which involves three sparse matrices (in existing literature only two of the three matrices are sparse), is here discussed in detail. Seven sparse operations are addressed (five standard and two nonstandard) in addition to some specific ad-hoc operations. Algorithms, source code and examples are presented in this work.INTERNATIONAL JOURNAL FOR COMPUTATIONAL METHODS IN ENGINEERING SCIENCE AND MECHANICS2019-02-07T15:38:51Z2019-02-072019-02-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10174/24498http://hdl.handle.net/10174/24498https://doi.org/10.1080/15502287.2019.1566284porP. Areias, A. Vidinha-Alves, M. Pereira dos Santos & J. Carrilho Lopes (2019) A Dimensional Reduction Algorithm and Software for Acyclically Dependent Constraints, International Journal for Computational Methods in Engineering Science and Mechanics, DOI: 10.1080/15502287.2019.1566284GEOPMAA@UEVORA.PTndMPSANTOS@UEVORA.PTCARRILHO@UEVORA.PT450AREIAS, P.VIDINHA-ALVES, A.PEREIRA DOS SANTOS, M.CARRILHO LOPES, J.info: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:RCAAP2024-01-03T19:17:40Zoai:dspace.uevora.pt:10174/24498Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:15:12.435400Repositório 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 Dimensional Reduction Algorithm and Software for Acyclically Dependent Constraints |
title |
A Dimensional Reduction Algorithm and Software for Acyclically Dependent Constraints |
spellingShingle |
A Dimensional Reduction Algorithm and Software for Acyclically Dependent Constraints AREIAS, P. Coupling Of Multibody Dynamics And Finite Elements Equality Constraints NONLINEAR PROBLEMS SPARSE MATRICES |
title_short |
A Dimensional Reduction Algorithm and Software for Acyclically Dependent Constraints |
title_full |
A Dimensional Reduction Algorithm and Software for Acyclically Dependent Constraints |
title_fullStr |
A Dimensional Reduction Algorithm and Software for Acyclically Dependent Constraints |
title_full_unstemmed |
A Dimensional Reduction Algorithm and Software for Acyclically Dependent Constraints |
title_sort |
A Dimensional Reduction Algorithm and Software for Acyclically Dependent Constraints |
author |
AREIAS, P. |
author_facet |
AREIAS, P. VIDINHA-ALVES, A. PEREIRA DOS SANTOS, M. CARRILHO LOPES, J. |
author_role |
author |
author2 |
VIDINHA-ALVES, A. PEREIRA DOS SANTOS, M. CARRILHO LOPES, J. |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
AREIAS, P. VIDINHA-ALVES, A. PEREIRA DOS SANTOS, M. CARRILHO LOPES, J. |
dc.subject.por.fl_str_mv |
Coupling Of Multibody Dynamics And Finite Elements Equality Constraints NONLINEAR PROBLEMS SPARSE MATRICES |
topic |
Coupling Of Multibody Dynamics And Finite Elements Equality Constraints NONLINEAR PROBLEMS SPARSE MATRICES |
description |
For discrete equations of motion with acyclic equality constraints and within the context of the null-space method, an original Algorithm is introduced. By first permuting and then topologically ordering the degrees-of-freedom in the constraint gradient matrix, the saddle point problem can be solved with a sparse triangular system for the constraint equations. In this work, we show that saddle problems resulting from constrained (nonlinear) mechanical problems can always be set in this form, with constraint pivots being selected a priori. Given n discrete motion equations and m equality constraints, the original square sparse (n+m)2 ( n + m ) 2 system is replaced by a sparse system (n−m)2 ( n − m ) 2 and a sparse triangular solve with m2 coefficients and n – m right-hand sides. This triangular solve, which involves three sparse matrices (in existing literature only two of the three matrices are sparse), is here discussed in detail. Seven sparse operations are addressed (five standard and two nonstandard) in addition to some specific ad-hoc operations. Algorithms, source code and examples are presented in this work. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-02-07T15:38:51Z 2019-02-07 2019-02-01T00:00:00Z |
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/10174/24498 http://hdl.handle.net/10174/24498 https://doi.org/10.1080/15502287.2019.1566284 |
url |
http://hdl.handle.net/10174/24498 https://doi.org/10.1080/15502287.2019.1566284 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
P. Areias, A. Vidinha-Alves, M. Pereira dos Santos & J. Carrilho Lopes (2019) A Dimensional Reduction Algorithm and Software for Acyclically Dependent Constraints, International Journal for Computational Methods in Engineering Science and Mechanics, DOI: 10.1080/15502287.2019.1566284 GEO PMAA@UEVORA.PT nd MPSANTOS@UEVORA.PT CARRILHO@UEVORA.PT 450 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
INTERNATIONAL JOURNAL FOR COMPUTATIONAL METHODS IN ENGINEERING SCIENCE AND MECHANICS |
publisher.none.fl_str_mv |
INTERNATIONAL JOURNAL FOR COMPUTATIONAL METHODS IN ENGINEERING SCIENCE AND MECHANICS |
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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1799136633536118784 |