COMPARATIVE STUDY OF THE WEAK-FORM COLLOCATION MESHLESS FORMULATION AND OTHER MESHLESS METHODS
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/21472 |
Resumo: | This paper is concerned with the numerical comparison of the weak-form collocation, a new local meshless method, and other meshless methods, for the solution of two-dimensional problems in linear elasticity. Four methods are compared, namely, the Generalized-Strain Mesh-free (GSMF) formulation, the Rigid-body Displacement Mesh-free (RBDMF) formulation, the Element-free Galerkin (EFG) and the Meshless Local Petrov-Galerkin Finite Volume Method (MLPG FVM). While the RBDMF, EFG and MLPG FVM rely on integration and quadrature process to obtain the stiffness matrix, the GSMF is completely integration free, working as a weighted-residual weak-form collocation. This weak-form collocation readily overcomes the well-known difficulties of the strong-form collocation, such as low accuracy and instability of the solution. A numerical example was analyzed with these methods, in order to assess the accuracy and the computational effort. The results obtained are in agreement with those of the available analytical solution. The numerical results show that the GSMF, when compared to the other methods, is superior not only regarding the computational efficiency, but also regarding the accuracy. |
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COMPARATIVE STUDY OF THE WEAK-FORM COLLOCATION MESHLESS FORMULATION AND OTHER MESHLESS METHODSLocal Meshless. Generalized-strain. Weak-form collocation. Local work theorem. Comparative study.This paper is concerned with the numerical comparison of the weak-form collocation, a new local meshless method, and other meshless methods, for the solution of two-dimensional problems in linear elasticity. Four methods are compared, namely, the Generalized-Strain Mesh-free (GSMF) formulation, the Rigid-body Displacement Mesh-free (RBDMF) formulation, the Element-free Galerkin (EFG) and the Meshless Local Petrov-Galerkin Finite Volume Method (MLPG FVM). While the RBDMF, EFG and MLPG FVM rely on integration and quadrature process to obtain the stiffness matrix, the GSMF is completely integration free, working as a weighted-residual weak-form collocation. This weak-form collocation readily overcomes the well-known difficulties of the strong-form collocation, such as low accuracy and instability of the solution. A numerical example was analyzed with these methods, in order to assess the accuracy and the computational effort. The results obtained are in agreement with those of the available analytical solution. The numerical results show that the GSMF, when compared to the other methods, is superior not only regarding the computational efficiency, but also regarding the accuracy.Programa de Pós-Graduação em Integridade de Materiais da Engenharia2017-01-19info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://periodicos.unb.br/index.php/ripe/article/view/2147210.26512/ripe.v2i6.21472Revista Interdisciplinar de Pesquisa em Engenharia; Vol. 2 No. 6 (2016): BOUNDARY ELEMENT AND MESH REDUCED METHODS (I); 60-78Revista Interdisciplinar de Pesquisa em Engenharia; v. 2 n. 6 (2016): BOUNDARY ELEMENT AND MESH REDUCED METHODS (I); 60-782447-6102reponame:Revista Interdisciplinar de Pesquisa em Engenhariainstname:Universidade de Brasília (UnB)instacron:UNBenghttps://periodicos.unb.br/index.php/ripe/article/view/21472/19800Copyright (c) 2019 Revista Interdisciplinar de Pesquisa em Engenharia - RIPEinfo:eu-repo/semantics/openAccessOliveira, Tiago da SilvaPortela, Artur2019-06-07T18:05:58Zoai:ojs.pkp.sfu.ca:article/21472Revistahttps://periodicos.unb.br/index.php/ripePUBhttps://periodicos.unb.br/index.php/ripe/oaianflor@unb.br2447-61022447-6102opendoar:2019-06-07T18:05:58Revista Interdisciplinar de Pesquisa em Engenharia - Universidade de Brasília (UnB)false |
dc.title.none.fl_str_mv |
COMPARATIVE STUDY OF THE WEAK-FORM COLLOCATION MESHLESS FORMULATION AND OTHER MESHLESS METHODS |
title |
COMPARATIVE STUDY OF THE WEAK-FORM COLLOCATION MESHLESS FORMULATION AND OTHER MESHLESS METHODS |
spellingShingle |
COMPARATIVE STUDY OF THE WEAK-FORM COLLOCATION MESHLESS FORMULATION AND OTHER MESHLESS METHODS Oliveira, Tiago da Silva Local Meshless. Generalized-strain. Weak-form collocation. Local work theorem. Comparative study. |
title_short |
COMPARATIVE STUDY OF THE WEAK-FORM COLLOCATION MESHLESS FORMULATION AND OTHER MESHLESS METHODS |
title_full |
COMPARATIVE STUDY OF THE WEAK-FORM COLLOCATION MESHLESS FORMULATION AND OTHER MESHLESS METHODS |
title_fullStr |
COMPARATIVE STUDY OF THE WEAK-FORM COLLOCATION MESHLESS FORMULATION AND OTHER MESHLESS METHODS |
title_full_unstemmed |
COMPARATIVE STUDY OF THE WEAK-FORM COLLOCATION MESHLESS FORMULATION AND OTHER MESHLESS METHODS |
title_sort |
COMPARATIVE STUDY OF THE WEAK-FORM COLLOCATION MESHLESS FORMULATION AND OTHER MESHLESS METHODS |
author |
Oliveira, Tiago da Silva |
author_facet |
Oliveira, Tiago da Silva Portela, Artur |
author_role |
author |
author2 |
Portela, Artur |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Oliveira, Tiago da Silva Portela, Artur |
dc.subject.por.fl_str_mv |
Local Meshless. Generalized-strain. Weak-form collocation. Local work theorem. Comparative study. |
topic |
Local Meshless. Generalized-strain. Weak-form collocation. Local work theorem. Comparative study. |
description |
This paper is concerned with the numerical comparison of the weak-form collocation, a new local meshless method, and other meshless methods, for the solution of two-dimensional problems in linear elasticity. Four methods are compared, namely, the Generalized-Strain Mesh-free (GSMF) formulation, the Rigid-body Displacement Mesh-free (RBDMF) formulation, the Element-free Galerkin (EFG) and the Meshless Local Petrov-Galerkin Finite Volume Method (MLPG FVM). While the RBDMF, EFG and MLPG FVM rely on integration and quadrature process to obtain the stiffness matrix, the GSMF is completely integration free, working as a weighted-residual weak-form collocation. This weak-form collocation readily overcomes the well-known difficulties of the strong-form collocation, such as low accuracy and instability of the solution. A numerical example was analyzed with these methods, in order to assess the accuracy and the computational effort. The results obtained are in agreement with those of the available analytical solution. The numerical results show that the GSMF, when compared to the other methods, is superior not only regarding the computational efficiency, but also regarding the accuracy. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-01-19 |
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/21472 10.26512/ripe.v2i6.21472 |
url |
https://periodicos.unb.br/index.php/ripe/article/view/21472 |
identifier_str_mv |
10.26512/ripe.v2i6.21472 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://periodicos.unb.br/index.php/ripe/article/view/21472/19800 |
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. 6 (2016): BOUNDARY ELEMENT AND MESH REDUCED METHODS (I); 60-78 Revista Interdisciplinar de Pesquisa em Engenharia; v. 2 n. 6 (2016): BOUNDARY ELEMENT AND MESH REDUCED METHODS (I); 60-78 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 |
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1798315226249035776 |