Application of the Complex Variable Semi-analytical Method for Improved Displacement Sensitivity Evaluation in Geometrically Nonlinear Truss Problems
Autor(a) principal: | |
---|---|
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=S1679-78252015000500980 |
Resumo: | AbstractThe application of gradient-based methods to structural optimization problems usually requires the determination of displacement sensitivities with respect to design variables. In this regard, it is important to have at hand comprehensive methods for sensitivity analysis, which show stability, efficiency and accuracy. Particularly, application of the semi-analytical method for linear and nonlinear problems is generally a good trade-off between formulation simplicity and accuracy. In spite of that, semi-analytical methods are known to behave pathologically for shape design variables when the structure is subjected to rigid rotations. A large number of solutions for this problem have been presented in last years, although the formulation involved is generally not trivial, especially in the nonlinear case. A recent method, which adopts the semi-analytical approach and uses complex variables has rendered very promising results for all the aforementioned aspects: stability, efficiency and accuracy. Additionally, it is simple to codify. The present contribution is concerned with the application of this sensitivity analysis method to geometrically nonlinear truss problems. To this end, a finite element formulation is presented and displacement sensitivities are evaluated with respect to material and shape design variables. The results are compared to those obtained using the semi-analytical method with real variables and to global finite differences. An example demonstrates the potentiality of this new approach. |
id |
ABCM-1_6048e22030e16c184ae33383312bccbf |
---|---|
oai_identifier_str |
oai:scielo:S1679-78252015000500980 |
network_acronym_str |
ABCM-1 |
network_name_str |
Latin American journal of solids and structures (Online) |
repository_id_str |
|
spelling |
Application of the Complex Variable Semi-analytical Method for Improved Displacement Sensitivity Evaluation in Geometrically Nonlinear Truss ProblemsStructural optimizationSensitivity analysisFinite element methodNonlinear analysesAbstractThe application of gradient-based methods to structural optimization problems usually requires the determination of displacement sensitivities with respect to design variables. In this regard, it is important to have at hand comprehensive methods for sensitivity analysis, which show stability, efficiency and accuracy. Particularly, application of the semi-analytical method for linear and nonlinear problems is generally a good trade-off between formulation simplicity and accuracy. In spite of that, semi-analytical methods are known to behave pathologically for shape design variables when the structure is subjected to rigid rotations. A large number of solutions for this problem have been presented in last years, although the formulation involved is generally not trivial, especially in the nonlinear case. A recent method, which adopts the semi-analytical approach and uses complex variables has rendered very promising results for all the aforementioned aspects: stability, efficiency and accuracy. Additionally, it is simple to codify. The present contribution is concerned with the application of this sensitivity analysis method to geometrically nonlinear truss problems. To this end, a finite element formulation is presented and displacement sensitivities are evaluated with respect to material and shape design variables. The results are compared to those obtained using the semi-analytical method with real variables and to global finite differences. An example demonstrates the potentiality of this new approach.Associação Brasileira de Ciências Mecânicas2015-05-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252015000500980Latin American Journal of Solids and Structures v.12 n.5 2015reponame:Latin American journal of solids and structures (Online)instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)instacron:ABCM10.1590/1679-78251911info:eu-repo/semantics/openAccessHaveroth,Geovane AugustoStahlschmidt,JoânessonMuñoz-Rojas,Pablo Andréseng2015-09-28T00:00:00Zoai:scielo:S1679-78252015000500980Revistahttp://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:2015-09-28T00:00Latin American journal of solids and structures (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)false |
dc.title.none.fl_str_mv |
Application of the Complex Variable Semi-analytical Method for Improved Displacement Sensitivity Evaluation in Geometrically Nonlinear Truss Problems |
title |
Application of the Complex Variable Semi-analytical Method for Improved Displacement Sensitivity Evaluation in Geometrically Nonlinear Truss Problems |
spellingShingle |
Application of the Complex Variable Semi-analytical Method for Improved Displacement Sensitivity Evaluation in Geometrically Nonlinear Truss Problems Haveroth,Geovane Augusto Structural optimization Sensitivity analysis Finite element method Nonlinear analyses |
title_short |
Application of the Complex Variable Semi-analytical Method for Improved Displacement Sensitivity Evaluation in Geometrically Nonlinear Truss Problems |
title_full |
Application of the Complex Variable Semi-analytical Method for Improved Displacement Sensitivity Evaluation in Geometrically Nonlinear Truss Problems |
title_fullStr |
Application of the Complex Variable Semi-analytical Method for Improved Displacement Sensitivity Evaluation in Geometrically Nonlinear Truss Problems |
title_full_unstemmed |
Application of the Complex Variable Semi-analytical Method for Improved Displacement Sensitivity Evaluation in Geometrically Nonlinear Truss Problems |
title_sort |
Application of the Complex Variable Semi-analytical Method for Improved Displacement Sensitivity Evaluation in Geometrically Nonlinear Truss Problems |
author |
Haveroth,Geovane Augusto |
author_facet |
Haveroth,Geovane Augusto Stahlschmidt,Joânesson Muñoz-Rojas,Pablo Andrés |
author_role |
author |
author2 |
Stahlschmidt,Joânesson Muñoz-Rojas,Pablo Andrés |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Haveroth,Geovane Augusto Stahlschmidt,Joânesson Muñoz-Rojas,Pablo Andrés |
dc.subject.por.fl_str_mv |
Structural optimization Sensitivity analysis Finite element method Nonlinear analyses |
topic |
Structural optimization Sensitivity analysis Finite element method Nonlinear analyses |
description |
AbstractThe application of gradient-based methods to structural optimization problems usually requires the determination of displacement sensitivities with respect to design variables. In this regard, it is important to have at hand comprehensive methods for sensitivity analysis, which show stability, efficiency and accuracy. Particularly, application of the semi-analytical method for linear and nonlinear problems is generally a good trade-off between formulation simplicity and accuracy. In spite of that, semi-analytical methods are known to behave pathologically for shape design variables when the structure is subjected to rigid rotations. A large number of solutions for this problem have been presented in last years, although the formulation involved is generally not trivial, especially in the nonlinear case. A recent method, which adopts the semi-analytical approach and uses complex variables has rendered very promising results for all the aforementioned aspects: stability, efficiency and accuracy. Additionally, it is simple to codify. The present contribution is concerned with the application of this sensitivity analysis method to geometrically nonlinear truss problems. To this end, a finite element formulation is presented and displacement sensitivities are evaluated with respect to material and shape design variables. The results are compared to those obtained using the semi-analytical method with real variables and to global finite differences. An example demonstrates the potentiality of this new approach. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015-05-01 |
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=S1679-78252015000500980 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252015000500980 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/1679-78251911 |
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.5 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_ |
1754302888005337088 |