Modal P-delta – simplified geometric nonlinear method by using modal and buckling analysis
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Revista IBRACON de Estruturas e Materiais |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1983-41952023000200205 |
Resumo: | Abstract Recent works show that in structures, there is a relationship between the natural period of vibration and global second-order effects. This relationship occurs because both depend on the stiffness matrix and the mass matrix of the structure. In this work, a non-linear geometric method - modal P-delta – is proposed that takes advantage of the relationship between the dynamic parameters and the non-linear effects. The methodology establishes an association between the buckling instability modes and the structural vibration modes. An interpolation of the vibration modes without axial loading and vibration modes with critical axial loading is proposed to approximate the vibration modes and frequencies of the loaded structure. In this way, through a simple formulation, the vibration modes and the natural frequencies of the loaded structure can be used to evaluate the displacements of the structures including the non-linear effects. Several numerical examples were simulated in regular structures in the plane, such as a free-fixed column and a plane frame with two different loading configurations. The results generated with the modal P-delta method provide information about the nonlinear behavior of the pre-buckling equilibrium path. These results are different from the findings in the literature, where the relationship between dynamic parameters and non-linear effects is used as a simple indicator or amplification factors to determine non-linear effects. Furthermore, our results indicate that the modal P-delta reduces the computational time spent considerably compared to the traditional P-delta iterative method. |
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Modal P-delta – simplified geometric nonlinear method by using modal and buckling analysisgeometric non-linearitymodal analysisstructural stabilityp-delta Abstract Recent works show that in structures, there is a relationship between the natural period of vibration and global second-order effects. This relationship occurs because both depend on the stiffness matrix and the mass matrix of the structure. In this work, a non-linear geometric method - modal P-delta – is proposed that takes advantage of the relationship between the dynamic parameters and the non-linear effects. The methodology establishes an association between the buckling instability modes and the structural vibration modes. An interpolation of the vibration modes without axial loading and vibration modes with critical axial loading is proposed to approximate the vibration modes and frequencies of the loaded structure. In this way, through a simple formulation, the vibration modes and the natural frequencies of the loaded structure can be used to evaluate the displacements of the structures including the non-linear effects. Several numerical examples were simulated in regular structures in the plane, such as a free-fixed column and a plane frame with two different loading configurations. The results generated with the modal P-delta method provide information about the nonlinear behavior of the pre-buckling equilibrium path. These results are different from the findings in the literature, where the relationship between dynamic parameters and non-linear effects is used as a simple indicator or amplification factors to determine non-linear effects. Furthermore, our results indicate that the modal P-delta reduces the computational time spent considerably compared to the traditional P-delta iterative method.IBRACON - Instituto Brasileiro do Concreto2023-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1983-41952023000200205Revista IBRACON de Estruturas e Materiais v.16 n.2 2023reponame:Revista IBRACON de Estruturas e Materiaisinstname:Instituto Brasileiro do Concreto (IBRACON)instacron:IBRACON10.1590/s1983-41952023000200009info:eu-repo/semantics/openAccessFerreira,Wagner AlmeidaCordova De La Cruz,Jeffer RoussellAraujo,Iván Darío GómezGarcia Sánchez,Jesús Antonioeng2022-09-14T00:00:00Zoai:scielo:S1983-41952023000200205Revistahttp://www.revistas.ibracon.org.br/index.php/riemhttps://old.scielo.br/oai/scielo-oai.phpeditores.riem@gmail.com||arlene@ibracon.org.br1983-41951983-4195opendoar:2022-09-14T00:00Revista IBRACON de Estruturas e Materiais - Instituto Brasileiro do Concreto (IBRACON)false |
dc.title.none.fl_str_mv |
Modal P-delta – simplified geometric nonlinear method by using modal and buckling analysis |
title |
Modal P-delta – simplified geometric nonlinear method by using modal and buckling analysis |
spellingShingle |
Modal P-delta – simplified geometric nonlinear method by using modal and buckling analysis Ferreira,Wagner Almeida geometric non-linearity modal analysis structural stability p-delta |
title_short |
Modal P-delta – simplified geometric nonlinear method by using modal and buckling analysis |
title_full |
Modal P-delta – simplified geometric nonlinear method by using modal and buckling analysis |
title_fullStr |
Modal P-delta – simplified geometric nonlinear method by using modal and buckling analysis |
title_full_unstemmed |
Modal P-delta – simplified geometric nonlinear method by using modal and buckling analysis |
title_sort |
Modal P-delta – simplified geometric nonlinear method by using modal and buckling analysis |
author |
Ferreira,Wagner Almeida |
author_facet |
Ferreira,Wagner Almeida Cordova De La Cruz,Jeffer Roussell Araujo,Iván Darío Gómez Garcia Sánchez,Jesús Antonio |
author_role |
author |
author2 |
Cordova De La Cruz,Jeffer Roussell Araujo,Iván Darío Gómez Garcia Sánchez,Jesús Antonio |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Ferreira,Wagner Almeida Cordova De La Cruz,Jeffer Roussell Araujo,Iván Darío Gómez Garcia Sánchez,Jesús Antonio |
dc.subject.por.fl_str_mv |
geometric non-linearity modal analysis structural stability p-delta |
topic |
geometric non-linearity modal analysis structural stability p-delta |
description |
Abstract Recent works show that in structures, there is a relationship between the natural period of vibration and global second-order effects. This relationship occurs because both depend on the stiffness matrix and the mass matrix of the structure. In this work, a non-linear geometric method - modal P-delta – is proposed that takes advantage of the relationship between the dynamic parameters and the non-linear effects. The methodology establishes an association between the buckling instability modes and the structural vibration modes. An interpolation of the vibration modes without axial loading and vibration modes with critical axial loading is proposed to approximate the vibration modes and frequencies of the loaded structure. In this way, through a simple formulation, the vibration modes and the natural frequencies of the loaded structure can be used to evaluate the displacements of the structures including the non-linear effects. Several numerical examples were simulated in regular structures in the plane, such as a free-fixed column and a plane frame with two different loading configurations. The results generated with the modal P-delta method provide information about the nonlinear behavior of the pre-buckling equilibrium path. These results are different from the findings in the literature, where the relationship between dynamic parameters and non-linear effects is used as a simple indicator or amplification factors to determine non-linear effects. Furthermore, our results indicate that the modal P-delta reduces the computational time spent considerably compared to the traditional P-delta iterative method. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-01-01 |
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=S1983-41952023000200205 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1983-41952023000200205 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/s1983-41952023000200009 |
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 |
IBRACON - Instituto Brasileiro do Concreto |
publisher.none.fl_str_mv |
IBRACON - Instituto Brasileiro do Concreto |
dc.source.none.fl_str_mv |
Revista IBRACON de Estruturas e Materiais v.16 n.2 2023 reponame:Revista IBRACON de Estruturas e Materiais instname:Instituto Brasileiro do Concreto (IBRACON) instacron:IBRACON |
instname_str |
Instituto Brasileiro do Concreto (IBRACON) |
instacron_str |
IBRACON |
institution |
IBRACON |
reponame_str |
Revista IBRACON de Estruturas e Materiais |
collection |
Revista IBRACON de Estruturas e Materiais |
repository.name.fl_str_mv |
Revista IBRACON de Estruturas e Materiais - Instituto Brasileiro do Concreto (IBRACON) |
repository.mail.fl_str_mv |
editores.riem@gmail.com||arlene@ibracon.org.br |
_version_ |
1754193606969655296 |