GFEM STABILIZATION TECHNIQUES APPLIED TO TRANSIENT DYNAMIC ANALYSIS
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Revista Interdisciplinar de Pesquisa em Engenharia |
Texto Completo: | https://periodicos.unb.br/index.php/ripe/article/view/21368 |
Resumo: | In the context of dynamic analysis of structures, one of the limitations of the Finite Element Method (FEM) is the difficulty of approaching the high frequencies. This lack of precision becomes more significant as the loading excite modes with higher frequencies. Aiming at address this problem one may use the Finite Element Method Generalized / Extended (GFEM /XFEM) to enrich the approximation space and better represent these high frequency modes. Despite the excellent properties of GFEM / XFEM as high accuracy, application versatility and excellent convergence rates, there are aspects that still limit its applicability as the numerical instability associated with this enrichment process even in well-placed boundary value problems. GFEM/XFEM matrices may be ill-conditioned, which may result in a accuracy loss, and even resulting in numerically singular matrices. In this work two proposals are presented to circumvent the GFEM sensitivity problem. Examples of one-dimensional transient analysis are presented and results are discussed analyzing the effects of adopting the preconditioning of enrichment functions strategy. |
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GFEM STABILIZATION TECHNIQUES APPLIED TO TRANSIENT DYNAMIC ANALYSISDynamic Analysis. GFEM. Partition of Unity. Conditioning. SGFEM.In the context of dynamic analysis of structures, one of the limitations of the Finite Element Method (FEM) is the difficulty of approaching the high frequencies. This lack of precision becomes more significant as the loading excite modes with higher frequencies. Aiming at address this problem one may use the Finite Element Method Generalized / Extended (GFEM /XFEM) to enrich the approximation space and better represent these high frequency modes. Despite the excellent properties of GFEM / XFEM as high accuracy, application versatility and excellent convergence rates, there are aspects that still limit its applicability as the numerical instability associated with this enrichment process even in well-placed boundary value problems. GFEM/XFEM matrices may be ill-conditioned, which may result in a accuracy loss, and even resulting in numerically singular matrices. In this work two proposals are presented to circumvent the GFEM sensitivity problem. Examples of one-dimensional transient analysis are presented and results are discussed analyzing the effects of adopting the preconditioning of enrichment functions strategy.Programa de Pós-Graduação em Integridade de Materiais da Engenharia2017-01-30info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://periodicos.unb.br/index.php/ripe/article/view/2136810.26512/ripe.v2i14.21368Revista Interdisciplinar de Pesquisa em Engenharia; Vol. 2 No. 14 (2016): DEVELOPMENTS AND APPLICATIONS OF SPECIAL ENRICHMENT METHODS AND INNOVATE DISCRETIZATION TECHNIQUES; 156-170Revista Interdisciplinar de Pesquisa em Engenharia; v. 2 n. 14 (2016): DEVELOPMENTS AND APPLICATIONS OF SPECIAL ENRICHMENT METHODS AND INNOVATE DISCRETIZATION TECHNIQUES; 156-1702447-6102reponame:Revista Interdisciplinar de Pesquisa em Engenhariainstname:Universidade de Brasília (UnB)instacron:UNBenghttps://periodicos.unb.br/index.php/ripe/article/view/21368/19711Copyright (c) 2019 Revista Interdisciplinar de Pesquisa em Engenharia - RIPEinfo:eu-repo/semantics/openAccessWeinhardt, Paulo de OliveiraArndt, MarcosMachado, Roberto Dalledone2019-06-16T02:35:07Zoai:ojs.pkp.sfu.ca:article/21368Revistahttps://periodicos.unb.br/index.php/ripePUBhttps://periodicos.unb.br/index.php/ripe/oaianflor@unb.br2447-61022447-6102opendoar:2019-06-16T02:35:07Revista Interdisciplinar de Pesquisa em Engenharia - Universidade de Brasília (UnB)false |
dc.title.none.fl_str_mv |
GFEM STABILIZATION TECHNIQUES APPLIED TO TRANSIENT DYNAMIC ANALYSIS |
title |
GFEM STABILIZATION TECHNIQUES APPLIED TO TRANSIENT DYNAMIC ANALYSIS |
spellingShingle |
GFEM STABILIZATION TECHNIQUES APPLIED TO TRANSIENT DYNAMIC ANALYSIS Weinhardt, Paulo de Oliveira Dynamic Analysis. GFEM. Partition of Unity. Conditioning. SGFEM. |
title_short |
GFEM STABILIZATION TECHNIQUES APPLIED TO TRANSIENT DYNAMIC ANALYSIS |
title_full |
GFEM STABILIZATION TECHNIQUES APPLIED TO TRANSIENT DYNAMIC ANALYSIS |
title_fullStr |
GFEM STABILIZATION TECHNIQUES APPLIED TO TRANSIENT DYNAMIC ANALYSIS |
title_full_unstemmed |
GFEM STABILIZATION TECHNIQUES APPLIED TO TRANSIENT DYNAMIC ANALYSIS |
title_sort |
GFEM STABILIZATION TECHNIQUES APPLIED TO TRANSIENT DYNAMIC ANALYSIS |
author |
Weinhardt, Paulo de Oliveira |
author_facet |
Weinhardt, Paulo de Oliveira Arndt, Marcos Machado, Roberto Dalledone |
author_role |
author |
author2 |
Arndt, Marcos Machado, Roberto Dalledone |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Weinhardt, Paulo de Oliveira Arndt, Marcos Machado, Roberto Dalledone |
dc.subject.por.fl_str_mv |
Dynamic Analysis. GFEM. Partition of Unity. Conditioning. SGFEM. |
topic |
Dynamic Analysis. GFEM. Partition of Unity. Conditioning. SGFEM. |
description |
In the context of dynamic analysis of structures, one of the limitations of the Finite Element Method (FEM) is the difficulty of approaching the high frequencies. This lack of precision becomes more significant as the loading excite modes with higher frequencies. Aiming at address this problem one may use the Finite Element Method Generalized / Extended (GFEM /XFEM) to enrich the approximation space and better represent these high frequency modes. Despite the excellent properties of GFEM / XFEM as high accuracy, application versatility and excellent convergence rates, there are aspects that still limit its applicability as the numerical instability associated with this enrichment process even in well-placed boundary value problems. GFEM/XFEM matrices may be ill-conditioned, which may result in a accuracy loss, and even resulting in numerically singular matrices. In this work two proposals are presented to circumvent the GFEM sensitivity problem. Examples of one-dimensional transient analysis are presented and results are discussed analyzing the effects of adopting the preconditioning of enrichment functions strategy. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-01-30 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://periodicos.unb.br/index.php/ripe/article/view/21368 10.26512/ripe.v2i14.21368 |
url |
https://periodicos.unb.br/index.php/ripe/article/view/21368 |
identifier_str_mv |
10.26512/ripe.v2i14.21368 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://periodicos.unb.br/index.php/ripe/article/view/21368/19711 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2019 Revista Interdisciplinar de Pesquisa em Engenharia - RIPE info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2019 Revista Interdisciplinar de Pesquisa em Engenharia - RIPE |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Programa de Pós-Graduação em Integridade de Materiais da Engenharia |
publisher.none.fl_str_mv |
Programa de Pós-Graduação em Integridade de Materiais da Engenharia |
dc.source.none.fl_str_mv |
Revista Interdisciplinar de Pesquisa em Engenharia; Vol. 2 No. 14 (2016): DEVELOPMENTS AND APPLICATIONS OF SPECIAL ENRICHMENT METHODS AND INNOVATE DISCRETIZATION TECHNIQUES; 156-170 Revista Interdisciplinar de Pesquisa em Engenharia; v. 2 n. 14 (2016): DEVELOPMENTS AND APPLICATIONS OF SPECIAL ENRICHMENT METHODS AND INNOVATE DISCRETIZATION TECHNIQUES; 156-170 2447-6102 reponame:Revista Interdisciplinar de Pesquisa em Engenharia instname:Universidade de Brasília (UnB) instacron:UNB |
instname_str |
Universidade de Brasília (UnB) |
instacron_str |
UNB |
institution |
UNB |
reponame_str |
Revista Interdisciplinar de Pesquisa em Engenharia |
collection |
Revista Interdisciplinar de Pesquisa em Engenharia |
repository.name.fl_str_mv |
Revista Interdisciplinar de Pesquisa em Engenharia - Universidade de Brasília (UnB) |
repository.mail.fl_str_mv |
anflor@unb.br |
_version_ |
1798315226120060928 |