An efficient coupled polynomial interpolation scheme to eliminate material-locking in the Euler-Bernoulli piezoelectric beam finite element
Autor(a) principal: | |
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Data de Publicação: | 2015 |
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=S1679-78252015000100153 |
Resumo: | The convergence characteristic of the conventional two-noded Euler-Bernoulli piezoelectric beam finite element depends on the configuration of the beam cross-section. The element shows slower convergence for the asymmetric material distribution in the beam cross-section due to 'material-locking' caused by extension-bending coupling. Hence, the use of conventional Euler-Bernoulli beam finite element to analyze piezoelectric beams which are generally made of the host layer with asymmetrically surface bonded piezoelectric layers/patches, leads to increased computational effort to yield converged results. Here, an efficient coupled polynomial interpolation scheme is proposed to improve the convergence of the Euler-Bernoulli piezoelectric beam finite elements, by eliminating ill-effects of material-locking. The equilibrium equations, derived using a variational formulation, are used to establish relationships between field variables. These relations are used to find a coupled quadratic polynomial for axial displacement, having contributions from an assumed cubic polynomial for transverse displacement and assumed linear polynomials for layerwise electric potentials. A set of coupled shape functions derived using these polynomials efficiently handles extension-bending and electromechanical couplings at the field interpolation level itself in a variationally consistent manner, without increasing the number of nodal degrees of freedom. The comparison of results obtained from numerical simulation of test problems shows that the convergence characteristic of the proposed element is insensitive to the material configuration of the beam cross-section. |
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Latin American journal of solids and structures (Online) |
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An efficient coupled polynomial interpolation scheme to eliminate material-locking in the Euler-Bernoulli piezoelectric beam finite elementCoupled fieldfinite elementspiezoelectricsmart structure.The convergence characteristic of the conventional two-noded Euler-Bernoulli piezoelectric beam finite element depends on the configuration of the beam cross-section. The element shows slower convergence for the asymmetric material distribution in the beam cross-section due to 'material-locking' caused by extension-bending coupling. Hence, the use of conventional Euler-Bernoulli beam finite element to analyze piezoelectric beams which are generally made of the host layer with asymmetrically surface bonded piezoelectric layers/patches, leads to increased computational effort to yield converged results. Here, an efficient coupled polynomial interpolation scheme is proposed to improve the convergence of the Euler-Bernoulli piezoelectric beam finite elements, by eliminating ill-effects of material-locking. The equilibrium equations, derived using a variational formulation, are used to establish relationships between field variables. These relations are used to find a coupled quadratic polynomial for axial displacement, having contributions from an assumed cubic polynomial for transverse displacement and assumed linear polynomials for layerwise electric potentials. A set of coupled shape functions derived using these polynomials efficiently handles extension-bending and electromechanical couplings at the field interpolation level itself in a variationally consistent manner, without increasing the number of nodal degrees of freedom. The comparison of results obtained from numerical simulation of test problems shows that the convergence characteristic of the proposed element is insensitive to the material configuration of the beam cross-section.Associação Brasileira de Ciências Mecânicas2015-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252015000100153Latin American Journal of Solids and Structures v.12 n.1 2015reponame:Latin American journal of solids and structures (Online)instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)instacron:ABCM10.1590/1679-78251401info:eu-repo/semantics/openAccessSulbhewar,Litesh N.Raveendranath,P.eng2015-06-02T00:00:00Zoai:scielo:S1679-78252015000100153Revistahttp://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:2015-06-02T00:00Latin American journal of solids and structures (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)false |
dc.title.none.fl_str_mv |
An efficient coupled polynomial interpolation scheme to eliminate material-locking in the Euler-Bernoulli piezoelectric beam finite element |
title |
An efficient coupled polynomial interpolation scheme to eliminate material-locking in the Euler-Bernoulli piezoelectric beam finite element |
spellingShingle |
An efficient coupled polynomial interpolation scheme to eliminate material-locking in the Euler-Bernoulli piezoelectric beam finite element Sulbhewar,Litesh N. Coupled field finite elements piezoelectric smart structure. |
title_short |
An efficient coupled polynomial interpolation scheme to eliminate material-locking in the Euler-Bernoulli piezoelectric beam finite element |
title_full |
An efficient coupled polynomial interpolation scheme to eliminate material-locking in the Euler-Bernoulli piezoelectric beam finite element |
title_fullStr |
An efficient coupled polynomial interpolation scheme to eliminate material-locking in the Euler-Bernoulli piezoelectric beam finite element |
title_full_unstemmed |
An efficient coupled polynomial interpolation scheme to eliminate material-locking in the Euler-Bernoulli piezoelectric beam finite element |
title_sort |
An efficient coupled polynomial interpolation scheme to eliminate material-locking in the Euler-Bernoulli piezoelectric beam finite element |
author |
Sulbhewar,Litesh N. |
author_facet |
Sulbhewar,Litesh N. Raveendranath,P. |
author_role |
author |
author2 |
Raveendranath,P. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Sulbhewar,Litesh N. Raveendranath,P. |
dc.subject.por.fl_str_mv |
Coupled field finite elements piezoelectric smart structure. |
topic |
Coupled field finite elements piezoelectric smart structure. |
description |
The convergence characteristic of the conventional two-noded Euler-Bernoulli piezoelectric beam finite element depends on the configuration of the beam cross-section. The element shows slower convergence for the asymmetric material distribution in the beam cross-section due to 'material-locking' caused by extension-bending coupling. Hence, the use of conventional Euler-Bernoulli beam finite element to analyze piezoelectric beams which are generally made of the host layer with asymmetrically surface bonded piezoelectric layers/patches, leads to increased computational effort to yield converged results. Here, an efficient coupled polynomial interpolation scheme is proposed to improve the convergence of the Euler-Bernoulli piezoelectric beam finite elements, by eliminating ill-effects of material-locking. The equilibrium equations, derived using a variational formulation, are used to establish relationships between field variables. These relations are used to find a coupled quadratic polynomial for axial displacement, having contributions from an assumed cubic polynomial for transverse displacement and assumed linear polynomials for layerwise electric potentials. A set of coupled shape functions derived using these polynomials efficiently handles extension-bending and electromechanical couplings at the field interpolation level itself in a variationally consistent manner, without increasing the number of nodal degrees of freedom. The comparison of results obtained from numerical simulation of test problems shows that the convergence characteristic of the proposed element is insensitive to the material configuration of the beam cross-section. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015-01-01 |
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=S1679-78252015000100153 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252015000100153 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/1679-78251401 |
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.12 n.1 2015 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_ |
1754302887723270144 |