Trusses Nonlinear Problems Solution with Numerical Methods of Cubic Convergence Order

Detalhes bibliográficos
Autor(a) principal: SOUZA,L.A.F.
Data de Publicação: 2018
Outros Autores: CASTELANI,E.V., SHIRABAYASHI,W.V.I., ALIANO FILHO,A., MACHADO,R.D.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000100161
Resumo: ABSTRACT A large part of the numerical procedures for obtaining the equilibrium path or load-displacement curve of structural problems with nonlinear behavior is based on the Newton-Raphson iterative scheme, to which is coupled the path-following methods. This paper presents new algorithms based on Potra-Pták, Chebyshev and super-Halley methods combined with the Linear Arc-Length path-following method. The main motivation for using these methods is the cubic order convergence. To elucidate the potential of our approach, we present an analysis of space and plane trusses problems with geometric nonlinearity found in the literature. In this direction, we will make use of the Positional Finite Element Method, which considers the nodal coordinates as variables of the nonlinear system instead of displacements. The numerical results of the simulations show the capacity of the computational algorithm developed to obtain the equilibrium path with force and displacement limits points. The implemented iterative methods exhibit better efficiency as the number of time steps and necessary accumulated iterations until convergence and processing time, in comparison with classic methods of Newton-Raphson and Modified Newton-Raphson.
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spelling Trusses Nonlinear Problems Solution with Numerical Methods of Cubic Convergence OrderArc-LengthPositional Finite ElementChebyshevPotra-Pt´akGeometric NonlinearityABSTRACT A large part of the numerical procedures for obtaining the equilibrium path or load-displacement curve of structural problems with nonlinear behavior is based on the Newton-Raphson iterative scheme, to which is coupled the path-following methods. This paper presents new algorithms based on Potra-Pták, Chebyshev and super-Halley methods combined with the Linear Arc-Length path-following method. The main motivation for using these methods is the cubic order convergence. To elucidate the potential of our approach, we present an analysis of space and plane trusses problems with geometric nonlinearity found in the literature. In this direction, we will make use of the Positional Finite Element Method, which considers the nodal coordinates as variables of the nonlinear system instead of displacements. The numerical results of the simulations show the capacity of the computational algorithm developed to obtain the equilibrium path with force and displacement limits points. The implemented iterative methods exhibit better efficiency as the number of time steps and necessary accumulated iterations until convergence and processing time, in comparison with classic methods of Newton-Raphson and Modified Newton-Raphson.Sociedade Brasileira de Matemática Aplicada e Computacional2018-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000100161TEMA (São Carlos) v.19 n.1 2018reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2018.019.01.0161info:eu-repo/semantics/openAccessSOUZA,L.A.F.CASTELANI,E.V.SHIRABAYASHI,W.V.I.ALIANO FILHO,A.MACHADO,R.D.eng2018-05-24T00:00:00Zoai:scielo:S2179-84512018000100161Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2018-05-24T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse
dc.title.none.fl_str_mv Trusses Nonlinear Problems Solution with Numerical Methods of Cubic Convergence Order
title Trusses Nonlinear Problems Solution with Numerical Methods of Cubic Convergence Order
spellingShingle Trusses Nonlinear Problems Solution with Numerical Methods of Cubic Convergence Order
SOUZA,L.A.F.
Arc-Length
Positional Finite Element
Chebyshev
Potra-Pt´ak
Geometric Nonlinearity
title_short Trusses Nonlinear Problems Solution with Numerical Methods of Cubic Convergence Order
title_full Trusses Nonlinear Problems Solution with Numerical Methods of Cubic Convergence Order
title_fullStr Trusses Nonlinear Problems Solution with Numerical Methods of Cubic Convergence Order
title_full_unstemmed Trusses Nonlinear Problems Solution with Numerical Methods of Cubic Convergence Order
title_sort Trusses Nonlinear Problems Solution with Numerical Methods of Cubic Convergence Order
author SOUZA,L.A.F.
author_facet SOUZA,L.A.F.
CASTELANI,E.V.
SHIRABAYASHI,W.V.I.
ALIANO FILHO,A.
MACHADO,R.D.
author_role author
author2 CASTELANI,E.V.
SHIRABAYASHI,W.V.I.
ALIANO FILHO,A.
MACHADO,R.D.
author2_role author
author
author
author
dc.contributor.author.fl_str_mv SOUZA,L.A.F.
CASTELANI,E.V.
SHIRABAYASHI,W.V.I.
ALIANO FILHO,A.
MACHADO,R.D.
dc.subject.por.fl_str_mv Arc-Length
Positional Finite Element
Chebyshev
Potra-Pt´ak
Geometric Nonlinearity
topic Arc-Length
Positional Finite Element
Chebyshev
Potra-Pt´ak
Geometric Nonlinearity
description ABSTRACT A large part of the numerical procedures for obtaining the equilibrium path or load-displacement curve of structural problems with nonlinear behavior is based on the Newton-Raphson iterative scheme, to which is coupled the path-following methods. This paper presents new algorithms based on Potra-Pták, Chebyshev and super-Halley methods combined with the Linear Arc-Length path-following method. The main motivation for using these methods is the cubic order convergence. To elucidate the potential of our approach, we present an analysis of space and plane trusses problems with geometric nonlinearity found in the literature. In this direction, we will make use of the Positional Finite Element Method, which considers the nodal coordinates as variables of the nonlinear system instead of displacements. The numerical results of the simulations show the capacity of the computational algorithm developed to obtain the equilibrium path with force and displacement limits points. The implemented iterative methods exhibit better efficiency as the number of time steps and necessary accumulated iterations until convergence and processing time, in comparison with classic methods of Newton-Raphson and Modified Newton-Raphson.
publishDate 2018
dc.date.none.fl_str_mv 2018-01-01
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=S2179-84512018000100161
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000100161
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.5540/tema.2018.019.01.0161
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 TEMA (São Carlos) v.19 n.1 2018
reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
instname:Sociedade Brasileira de Matemática Aplicada e Computacional
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional
instacron_str SBMAC
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reponame_str TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
collection TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
repository.name.fl_str_mv TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacional
repository.mail.fl_str_mv castelo@icmc.usp.br
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