[RETRACTED ARTICLE] On the sparsity of linear systems of equations for a new stress basis applied to three-dimensional Hybrid-Trefftz stress finite elements
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Latin American journal of solids and structures (Online) |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252020000700506 |
Resumo: | Abstract Hybrid-Trefftz finite elements have been applied to the analysis of several types of structures successfully. It is based on two different sets of approximations applied simultaneously: stresses in the domain and displacements on its boundary. This method presents very large linear systems of equations to be solved. To overcome this issue, most authors have been careful in the choice of the approximation fields in order to have highly sparse linear systems. The natural choice for the stress basis has been linearly independent, hierarchical and orthogonal polynomials which typically result in more than 90% of sparsity in 3-D finite elements. Functions derived from associated Legendre and Chebyshev orthogonal polynomials have been used with success for this purpose. In this work the non-orthogonal polynomials available in the Pascal pyramid are proposed to derive a harmonic and complete set of polynomial basis as an alternative to the above-cited functions. Numerical tests show this basis produces accurate results. No significant differences were found when comparing the sparsity of the linear system of equations for both functions. |
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Latin American journal of solids and structures (Online) |
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[RETRACTED ARTICLE] On the sparsity of linear systems of equations for a new stress basis applied to three-dimensional Hybrid-Trefftz stress finite elementshybrid-TrefftzsparsityFinite Element Methodstress elementAbstract Hybrid-Trefftz finite elements have been applied to the analysis of several types of structures successfully. It is based on two different sets of approximations applied simultaneously: stresses in the domain and displacements on its boundary. This method presents very large linear systems of equations to be solved. To overcome this issue, most authors have been careful in the choice of the approximation fields in order to have highly sparse linear systems. The natural choice for the stress basis has been linearly independent, hierarchical and orthogonal polynomials which typically result in more than 90% of sparsity in 3-D finite elements. Functions derived from associated Legendre and Chebyshev orthogonal polynomials have been used with success for this purpose. In this work the non-orthogonal polynomials available in the Pascal pyramid are proposed to derive a harmonic and complete set of polynomial basis as an alternative to the above-cited functions. Numerical tests show this basis produces accurate results. No significant differences were found when comparing the sparsity of the linear system of equations for both functions.Associação Brasileira de Ciências Mecânicas2020-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252020000700506Latin American Journal of Solids and Structures v.17 n.7 2020reponame:Latin American journal of solids and structures (Online)instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)instacron:ABCM10.1590/1679-78256124info:eu-repo/semantics/openAccessBusinaro,Felipe AlvarezBussamra,Flávio Luiz de Silvaeng2021-06-22T00:00:00Zoai:scielo:S1679-78252020000700506Revistahttp://www.scielo.br/scielo.php?script=sci_serial&pid=1679-7825&lng=pt&nrm=isohttps://old.scielo.br/oai/scielo-oai.phpabcm@abcm.org.br||maralves@usp.br1679-78251679-7817opendoar:2021-06-22T00:00Latin American journal of solids and structures (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)false |
dc.title.none.fl_str_mv |
[RETRACTED ARTICLE] On the sparsity of linear systems of equations for a new stress basis applied to three-dimensional Hybrid-Trefftz stress finite elements |
title |
[RETRACTED ARTICLE] On the sparsity of linear systems of equations for a new stress basis applied to three-dimensional Hybrid-Trefftz stress finite elements |
spellingShingle |
[RETRACTED ARTICLE] On the sparsity of linear systems of equations for a new stress basis applied to three-dimensional Hybrid-Trefftz stress finite elements Businaro,Felipe Alvarez hybrid-Trefftz sparsity Finite Element Method stress element |
title_short |
[RETRACTED ARTICLE] On the sparsity of linear systems of equations for a new stress basis applied to three-dimensional Hybrid-Trefftz stress finite elements |
title_full |
[RETRACTED ARTICLE] On the sparsity of linear systems of equations for a new stress basis applied to three-dimensional Hybrid-Trefftz stress finite elements |
title_fullStr |
[RETRACTED ARTICLE] On the sparsity of linear systems of equations for a new stress basis applied to three-dimensional Hybrid-Trefftz stress finite elements |
title_full_unstemmed |
[RETRACTED ARTICLE] On the sparsity of linear systems of equations for a new stress basis applied to three-dimensional Hybrid-Trefftz stress finite elements |
title_sort |
[RETRACTED ARTICLE] On the sparsity of linear systems of equations for a new stress basis applied to three-dimensional Hybrid-Trefftz stress finite elements |
author |
Businaro,Felipe Alvarez |
author_facet |
Businaro,Felipe Alvarez Bussamra,Flávio Luiz de Silva |
author_role |
author |
author2 |
Bussamra,Flávio Luiz de Silva |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Businaro,Felipe Alvarez Bussamra,Flávio Luiz de Silva |
dc.subject.por.fl_str_mv |
hybrid-Trefftz sparsity Finite Element Method stress element |
topic |
hybrid-Trefftz sparsity Finite Element Method stress element |
description |
Abstract Hybrid-Trefftz finite elements have been applied to the analysis of several types of structures successfully. It is based on two different sets of approximations applied simultaneously: stresses in the domain and displacements on its boundary. This method presents very large linear systems of equations to be solved. To overcome this issue, most authors have been careful in the choice of the approximation fields in order to have highly sparse linear systems. The natural choice for the stress basis has been linearly independent, hierarchical and orthogonal polynomials which typically result in more than 90% of sparsity in 3-D finite elements. Functions derived from associated Legendre and Chebyshev orthogonal polynomials have been used with success for this purpose. In this work the non-orthogonal polynomials available in the Pascal pyramid are proposed to derive a harmonic and complete set of polynomial basis as an alternative to the above-cited functions. Numerical tests show this basis produces accurate results. No significant differences were found when comparing the sparsity of the linear system of equations for both functions. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-01-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252020000700506 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252020000700506 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/1679-78256124 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Associação Brasileira de Ciências Mecânicas |
publisher.none.fl_str_mv |
Associação Brasileira de Ciências Mecânicas |
dc.source.none.fl_str_mv |
Latin American Journal of Solids and Structures v.17 n.7 2020 reponame:Latin American journal of solids and structures (Online) instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM) instacron:ABCM |
instname_str |
Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM) |
instacron_str |
ABCM |
institution |
ABCM |
reponame_str |
Latin American journal of solids and structures (Online) |
collection |
Latin American journal of solids and structures (Online) |
repository.name.fl_str_mv |
Latin American journal of solids and structures (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM) |
repository.mail.fl_str_mv |
abcm@abcm.org.br||maralves@usp.br |
_version_ |
1754302890454810624 |