Successive linear approximation for finite elasticity

Detalhes bibliográficos
Autor(a) principal: Liu,I-Shih
Data de Publicação: 2010
Outros Autores: Cipolatti,Rolci A, Rincon,Mauro A
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000300008
Resumo: A method of successive Lagrangian formulation of linear approximation for solving boundary value problems of large deformation in finite elasticity is proposed. Instead of solving the nonlinear problem, by assuming time steps small enough and the reference configuration updated at every step, we can linearize the constitutive equation and reduce it to linear boundary value problems to be solved successively with incremental boundary data. Moreover, nearly incompressible elastic body is considered as an approximation to account for the condition of incompressibility. For the proposed method, numerical computations of pure shear of a square block for Mooney-Rivlin material are considered and the results are compared with the exact solutions. Mathematical subject classification: Primary: 65C20; Secondary: 74B20.
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spelling Successive linear approximation for finite elasticitylarge deformationnonlinear elastic materialssuccessive Lagrangian formulationboundary value problemincremental methodnumerical computationA method of successive Lagrangian formulation of linear approximation for solving boundary value problems of large deformation in finite elasticity is proposed. Instead of solving the nonlinear problem, by assuming time steps small enough and the reference configuration updated at every step, we can linearize the constitutive equation and reduce it to linear boundary value problems to be solved successively with incremental boundary data. Moreover, nearly incompressible elastic body is considered as an approximation to account for the condition of incompressibility. For the proposed method, numerical computations of pure shear of a square block for Mooney-Rivlin material are considered and the results are compared with the exact solutions. Mathematical subject classification: Primary: 65C20; Secondary: 74B20.Sociedade Brasileira de Matemática Aplicada e Computacional2010-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000300008Computational & Applied Mathematics v.29 n.3 2010reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S1807-03022010000300008info:eu-repo/semantics/openAccessLiu,I-ShihCipolatti,Rolci ARincon,Mauro Aeng2010-11-22T00:00:00Zoai:scielo:S1807-03022010000300008Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2010-11-22T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv Successive linear approximation for finite elasticity
title Successive linear approximation for finite elasticity
spellingShingle Successive linear approximation for finite elasticity
Liu,I-Shih
large deformation
nonlinear elastic materials
successive Lagrangian formulation
boundary value problem
incremental method
numerical computation
title_short Successive linear approximation for finite elasticity
title_full Successive linear approximation for finite elasticity
title_fullStr Successive linear approximation for finite elasticity
title_full_unstemmed Successive linear approximation for finite elasticity
title_sort Successive linear approximation for finite elasticity
author Liu,I-Shih
author_facet Liu,I-Shih
Cipolatti,Rolci A
Rincon,Mauro A
author_role author
author2 Cipolatti,Rolci A
Rincon,Mauro A
author2_role author
author
dc.contributor.author.fl_str_mv Liu,I-Shih
Cipolatti,Rolci A
Rincon,Mauro A
dc.subject.por.fl_str_mv large deformation
nonlinear elastic materials
successive Lagrangian formulation
boundary value problem
incremental method
numerical computation
topic large deformation
nonlinear elastic materials
successive Lagrangian formulation
boundary value problem
incremental method
numerical computation
description A method of successive Lagrangian formulation of linear approximation for solving boundary value problems of large deformation in finite elasticity is proposed. Instead of solving the nonlinear problem, by assuming time steps small enough and the reference configuration updated at every step, we can linearize the constitutive equation and reduce it to linear boundary value problems to be solved successively with incremental boundary data. Moreover, nearly incompressible elastic body is considered as an approximation to account for the condition of incompressibility. For the proposed method, numerical computations of pure shear of a square block for Mooney-Rivlin material are considered and the results are compared with the exact solutions. Mathematical subject classification: Primary: 65C20; Secondary: 74B20.
publishDate 2010
dc.date.none.fl_str_mv 2010-01-01
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=S1807-03022010000300008
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000300008
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S1807-03022010000300008
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 Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv Computational & Applied Mathematics v.29 n.3 2010
reponame:Computational & Applied Mathematics
instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron_str SBMAC
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reponame_str Computational & Applied Mathematics
collection Computational & Applied Mathematics
repository.name.fl_str_mv Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
repository.mail.fl_str_mv ||sbmac@sbmac.org.br
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