The weak patch test for nonhomogeneous materials modeled with graded finite elements
Autor(a) principal: | |
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Data de Publicação: | 2007 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online) |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1678-58782007000100010 |
Resumo: | Functionally graded materials have an additional length scale associated to the spatial variation of the material property field which competes with the usual geometrical length scale of the boundary value problem. By considering the length scale of nonhomogeneity, this paper presents the weak patch test (rather than the standard one) of the graded element for nonhomogeneous materials to assess convergence of the finite element method (FEM). Both consistency (as the size of elements approach zero, the FEM approximation represents the exact solution) and stability (spurious mechanisms are avoided) conditions are addressed. The specific graded elements considered here are isoparametric quadrilaterals (e.g. 4, 8 and 9-node) considering two dimensional plane and axisymmetric problems. The finite element approximate solutions are compared with exact solutions for nonhomogeneous materials. |
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Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online) |
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The weak patch test for nonhomogeneous materials modeled with graded finite elementsfinite element method (FEM)patch testweak patch testfunctionally graded material (FGM)graded elementFunctionally graded materials have an additional length scale associated to the spatial variation of the material property field which competes with the usual geometrical length scale of the boundary value problem. By considering the length scale of nonhomogeneity, this paper presents the weak patch test (rather than the standard one) of the graded element for nonhomogeneous materials to assess convergence of the finite element method (FEM). Both consistency (as the size of elements approach zero, the FEM approximation represents the exact solution) and stability (spurious mechanisms are avoided) conditions are addressed. The specific graded elements considered here are isoparametric quadrilaterals (e.g. 4, 8 and 9-node) considering two dimensional plane and axisymmetric problems. The finite element approximate solutions are compared with exact solutions for nonhomogeneous materials.Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM2007-03-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1678-58782007000100010Journal of the Brazilian Society of Mechanical Sciences and Engineering v.29 n.1 2007reponame:Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online)instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)instacron:ABCM10.1590/S1678-58782007000100010info:eu-repo/semantics/openAccessPaulino,Glaucio H.Kim,Jeong-Hoeng2007-09-04T00:00:00Zoai:scielo:S1678-58782007000100010Revistahttps://www.scielo.br/j/jbsmse/https://old.scielo.br/oai/scielo-oai.php||abcm@abcm.org.br1806-36911678-5878opendoar:2007-09-04T00:00Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)false |
dc.title.none.fl_str_mv |
The weak patch test for nonhomogeneous materials modeled with graded finite elements |
title |
The weak patch test for nonhomogeneous materials modeled with graded finite elements |
spellingShingle |
The weak patch test for nonhomogeneous materials modeled with graded finite elements Paulino,Glaucio H. finite element method (FEM) patch test weak patch test functionally graded material (FGM) graded element |
title_short |
The weak patch test for nonhomogeneous materials modeled with graded finite elements |
title_full |
The weak patch test for nonhomogeneous materials modeled with graded finite elements |
title_fullStr |
The weak patch test for nonhomogeneous materials modeled with graded finite elements |
title_full_unstemmed |
The weak patch test for nonhomogeneous materials modeled with graded finite elements |
title_sort |
The weak patch test for nonhomogeneous materials modeled with graded finite elements |
author |
Paulino,Glaucio H. |
author_facet |
Paulino,Glaucio H. Kim,Jeong-Ho |
author_role |
author |
author2 |
Kim,Jeong-Ho |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Paulino,Glaucio H. Kim,Jeong-Ho |
dc.subject.por.fl_str_mv |
finite element method (FEM) patch test weak patch test functionally graded material (FGM) graded element |
topic |
finite element method (FEM) patch test weak patch test functionally graded material (FGM) graded element |
description |
Functionally graded materials have an additional length scale associated to the spatial variation of the material property field which competes with the usual geometrical length scale of the boundary value problem. By considering the length scale of nonhomogeneity, this paper presents the weak patch test (rather than the standard one) of the graded element for nonhomogeneous materials to assess convergence of the finite element method (FEM). Both consistency (as the size of elements approach zero, the FEM approximation represents the exact solution) and stability (spurious mechanisms are avoided) conditions are addressed. The specific graded elements considered here are isoparametric quadrilaterals (e.g. 4, 8 and 9-node) considering two dimensional plane and axisymmetric problems. The finite element approximate solutions are compared with exact solutions for nonhomogeneous materials. |
publishDate |
2007 |
dc.date.none.fl_str_mv |
2007-03-01 |
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=S1678-58782007000100010 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1678-58782007000100010 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S1678-58782007000100010 |
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 Engenharia e Ciências Mecânicas - ABCM |
publisher.none.fl_str_mv |
Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM |
dc.source.none.fl_str_mv |
Journal of the Brazilian Society of Mechanical Sciences and Engineering v.29 n.1 2007 reponame:Journal of the Brazilian Society of Mechanical Sciences and Engineering (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 |
Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online) |
collection |
Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online) |
repository.name.fl_str_mv |
Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM) |
repository.mail.fl_str_mv |
||abcm@abcm.org.br |
_version_ |
1754734680929730560 |