Mecânica do dano concentrado expandida para meios bidimensionais: elemento finito para problemas de localização de deformações em chapas
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFS |
Texto Completo: | https://ri.ufs.br/jspui/handle/riufs/14310 |
Resumo: | In engineering, the representation of structures using mathematical models has a fundamental importance. Through them, together with computational tools, it is possible to simulate the behaviour of structural elements, allowing for various analyses. Thus, the development of increasingly precise models that includes a greater number of phenomena observed in reality becomes crucial. The main current models are based on plasticity theory, damage mechanics and fracture mechanics. As it is well known, upon reaching the softening zone, classic damage models lead to mesh dependency in a finite element analysis whenever a localized solution is chosen. The so-called phenomenon of localization in these models leads to infinite possible solutions and obviously needs some regularization criteria to obtain the correct solution. This paper presents a new finite element formulation for the analysis of a tensile plate regarding strain localization problems, based mainly on the previous work by Amorim et al. (2018). The new model is not based on modern approaches to damage mechanics that use nonlocal or gradient models to circumvent the localization problem. It is an expansion of Concentrated Damage Mechanics, or MDC, into two-dimensional continuum. This more general formulation of the theory is here referred to as Expanded Concentrated Damage Mechanics, or MDCX. MDC uses key ideas of fracture mechanics and damage mechanics in conjunction with the concept of plastic hinges. Until then, in terms of concrete applicability, the MDC models were limited to analysis of frames and arches, demonstrating objective results for these cases. For these models, the finite element is given by combining an elastic bar element with two inelastic hinges at the ends. In the case of a two-dimensional medium, such as plate elements, inelastic hinges become localization bands. The finite element proposed in this work consists of joining a four-node elastic element with a set of locating bands on the sides and also within the element. Damage evolution laws that describe the behaviour of each location band are introduced in the model formulation and the proposed element is then implemented in a finite element analysis program. The convergence of numerical results to a single solution as the mesh is refined is demonstrated through examples and related problems are discussed. The results are presented graphically along with the final configuration of the problem structure, highlighting the formation of the localization bands. |
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Oliveira, João Marcos de JesusAmorim, David Leonardo Nascimento de Figueiredo2021-06-07T12:26:38Z2021-06-07T12:26:38Z2020-01-30OLIVEIRA, João Marcos de Jesus. Mecânica do dano concentrado expandida para meios bidimensionais: elemento finito para problemas de localização de deformações em chapas. 2020. 113 f. Dissertação (Mestrado em Engenharia Civil) - Universidade Federal de Sergipe, São Cristóvão, SE, 2020.https://ri.ufs.br/jspui/handle/riufs/14310In engineering, the representation of structures using mathematical models has a fundamental importance. Through them, together with computational tools, it is possible to simulate the behaviour of structural elements, allowing for various analyses. Thus, the development of increasingly precise models that includes a greater number of phenomena observed in reality becomes crucial. The main current models are based on plasticity theory, damage mechanics and fracture mechanics. As it is well known, upon reaching the softening zone, classic damage models lead to mesh dependency in a finite element analysis whenever a localized solution is chosen. The so-called phenomenon of localization in these models leads to infinite possible solutions and obviously needs some regularization criteria to obtain the correct solution. This paper presents a new finite element formulation for the analysis of a tensile plate regarding strain localization problems, based mainly on the previous work by Amorim et al. (2018). The new model is not based on modern approaches to damage mechanics that use nonlocal or gradient models to circumvent the localization problem. It is an expansion of Concentrated Damage Mechanics, or MDC, into two-dimensional continuum. This more general formulation of the theory is here referred to as Expanded Concentrated Damage Mechanics, or MDCX. MDC uses key ideas of fracture mechanics and damage mechanics in conjunction with the concept of plastic hinges. Until then, in terms of concrete applicability, the MDC models were limited to analysis of frames and arches, demonstrating objective results for these cases. For these models, the finite element is given by combining an elastic bar element with two inelastic hinges at the ends. In the case of a two-dimensional medium, such as plate elements, inelastic hinges become localization bands. The finite element proposed in this work consists of joining a four-node elastic element with a set of locating bands on the sides and also within the element. Damage evolution laws that describe the behaviour of each location band are introduced in the model formulation and the proposed element is then implemented in a finite element analysis program. The convergence of numerical results to a single solution as the mesh is refined is demonstrated through examples and related problems are discussed. The results are presented graphically along with the final configuration of the problem structure, highlighting the formation of the localization bands.Dentro da engenharia, a representação das estruturas por meio de modelos matemáticos é de fundamental importância. Através deles, em conjunto com ferramentas computacionais, consegue-se simular o comportamento dos elementos estruturais, possibilitando diversas análises. Com isso, torna-se determinante a elaboração de modelos cada vez mais precisos e que englobem um maior número de fenômenos observados na realidade. Os principais modelos atuais são baseados na teoria da plasticidade, na mecânica do dano e na mecânica da fratura. Sabidamente, ao se atingir a zona de amolecimento, modelos de dano clássicos levam a dependência de malha em uma análise por elementos finitos sempre que uma solução localizada é escolhida. O chamado fenômeno da localização, nesses modelos, leva a uma infinidade de soluções possíveis e, obviamente, necessita de algum critério de regularização para que se obtenha a solução correta. Este trabalho apresenta uma nova formulação de elemento finito para a análise de problemas de localização de deformações em chapas, baseado principalmente no trabalho anterior de Amorim et al. (2018). O novo modelo não se baseia nas modernas abordagens da mecânica do dano que se utilizam de modelos não locais ou por gradiente para contornar o problema da localização. Trata-se de uma expansão da mecânica do dano concentrado, ou MDC, para meios bidimensionais. Essa formulação mais geral da teoria é aqui chamada de mecânica do dano concentrado expandida, ou MDCX. A MDC utiliza ideias chave da mecânica da fratura e da mecânica do dano em união com o conceito de rótulas plásticas. Até então, em termos de aplicabilidade concreta, os modelos da MDC estavam limitados a análise de pórticos e arcos, demonstrando resultados objetivos para esses casos. Para esses modelos, o elemento finito é dado pela combinação de um elemento de barra elástico com duas rótulas inelásticas nas extremidades. No caso de um meio bidimensional, como em elementos de chapa, as rótulas inelásticas se transformam em bandas de localização. O elemento finito proposto neste trabalho consiste na união de um elemento elástico de quatro nós com um conjunto de bandas de localização nos lados e também no interior do elemento. Leis de evolução de dano que descrevem o comportamento de cada banda de localização são introduzidas na formulação do modelo e o elemento proposto é então implementado em um programa de análise por elementos finitos. A convergência dos resultados numéricos para uma solução única, na medida em que se refina a malha, é demonstrada através de exemplos e problemas relacionados são discutidos. Os resultados são apresentados de maneira gráfica junto à configuração final da estrutura do problema, destacando a formação das bandas de localização.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESSão Cristóvão, SEporEngenharia civilModelos matemáticosMecânica do danoDeformaçõesElementos finitosTwo dimensionalStrain localizationMesh independencyFinite elementsENGENHARIAS::ENGENHARIA CIVILMecânica do dano concentrado expandida para meios bidimensionais: elemento finito para problemas de localização de deformações em chapasinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisPós-Graduação em Engenharia CivilUniversidade Federal de Sergipereponame:Repositório Institucional da UFSinstname:Universidade Federal de Sergipe (UFS)instacron:UFSinfo:eu-repo/semantics/openAccessTEXTJOAO_MARCOS_JESUS_OLIVEIRA.pdf.txtJOAO_MARCOS_JESUS_OLIVEIRA.pdf.txtExtracted texttext/plain204679https://ri.ufs.br/jspui/bitstream/riufs/14310/3/JOAO_MARCOS_JESUS_OLIVEIRA.pdf.txtc1f9c3f27c74f69c68451bab069675a2MD53THUMBNAILJOAO_MARCOS_JESUS_OLIVEIRA.pdf.jpgJOAO_MARCOS_JESUS_OLIVEIRA.pdf.jpgGenerated Thumbnailimage/jpeg1303https://ri.ufs.br/jspui/bitstream/riufs/14310/4/JOAO_MARCOS_JESUS_OLIVEIRA.pdf.jpg83bd682cb8e412381a01612e9534b98eMD54LICENSElicense.txtlicense.txttext/plain; charset=utf-81475https://ri.ufs.br/jspui/bitstream/riufs/14310/1/license.txt098cbbf65c2c15e1fb2e49c5d306a44cMD51ORIGINALJOAO_MARCOS_JESUS_OLIVEIRA.pdfJOAO_MARCOS_JESUS_OLIVEIRA.pdfapplication/pdf1922779https://ri.ufs.br/jspui/bitstream/riufs/14310/2/JOAO_MARCOS_JESUS_OLIVEIRA.pdf846dfa96c881892f729185435a9db7f8MD52riufs/143102021-06-07 09:28:28.97oai:ufs.br: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Repositório InstitucionalPUBhttps://ri.ufs.br/oai/requestrepositorio@academico.ufs.bropendoar:2021-06-07T12:28:28Repositório Institucional da UFS - Universidade Federal de Sergipe (UFS)false |
dc.title.pt_BR.fl_str_mv |
Mecânica do dano concentrado expandida para meios bidimensionais: elemento finito para problemas de localização de deformações em chapas |
title |
Mecânica do dano concentrado expandida para meios bidimensionais: elemento finito para problemas de localização de deformações em chapas |
spellingShingle |
Mecânica do dano concentrado expandida para meios bidimensionais: elemento finito para problemas de localização de deformações em chapas Oliveira, João Marcos de Jesus Engenharia civil Modelos matemáticos Mecânica do dano Deformações Elementos finitos Two dimensional Strain localization Mesh independency Finite elements ENGENHARIAS::ENGENHARIA CIVIL |
title_short |
Mecânica do dano concentrado expandida para meios bidimensionais: elemento finito para problemas de localização de deformações em chapas |
title_full |
Mecânica do dano concentrado expandida para meios bidimensionais: elemento finito para problemas de localização de deformações em chapas |
title_fullStr |
Mecânica do dano concentrado expandida para meios bidimensionais: elemento finito para problemas de localização de deformações em chapas |
title_full_unstemmed |
Mecânica do dano concentrado expandida para meios bidimensionais: elemento finito para problemas de localização de deformações em chapas |
title_sort |
Mecânica do dano concentrado expandida para meios bidimensionais: elemento finito para problemas de localização de deformações em chapas |
author |
Oliveira, João Marcos de Jesus |
author_facet |
Oliveira, João Marcos de Jesus |
author_role |
author |
dc.contributor.author.fl_str_mv |
Oliveira, João Marcos de Jesus |
dc.contributor.advisor1.fl_str_mv |
Amorim, David Leonardo Nascimento de Figueiredo |
contributor_str_mv |
Amorim, David Leonardo Nascimento de Figueiredo |
dc.subject.por.fl_str_mv |
Engenharia civil Modelos matemáticos Mecânica do dano Deformações Elementos finitos |
topic |
Engenharia civil Modelos matemáticos Mecânica do dano Deformações Elementos finitos Two dimensional Strain localization Mesh independency Finite elements ENGENHARIAS::ENGENHARIA CIVIL |
dc.subject.eng.fl_str_mv |
Two dimensional Strain localization Mesh independency Finite elements |
dc.subject.cnpq.fl_str_mv |
ENGENHARIAS::ENGENHARIA CIVIL |
description |
In engineering, the representation of structures using mathematical models has a fundamental importance. Through them, together with computational tools, it is possible to simulate the behaviour of structural elements, allowing for various analyses. Thus, the development of increasingly precise models that includes a greater number of phenomena observed in reality becomes crucial. The main current models are based on plasticity theory, damage mechanics and fracture mechanics. As it is well known, upon reaching the softening zone, classic damage models lead to mesh dependency in a finite element analysis whenever a localized solution is chosen. The so-called phenomenon of localization in these models leads to infinite possible solutions and obviously needs some regularization criteria to obtain the correct solution. This paper presents a new finite element formulation for the analysis of a tensile plate regarding strain localization problems, based mainly on the previous work by Amorim et al. (2018). The new model is not based on modern approaches to damage mechanics that use nonlocal or gradient models to circumvent the localization problem. It is an expansion of Concentrated Damage Mechanics, or MDC, into two-dimensional continuum. This more general formulation of the theory is here referred to as Expanded Concentrated Damage Mechanics, or MDCX. MDC uses key ideas of fracture mechanics and damage mechanics in conjunction with the concept of plastic hinges. Until then, in terms of concrete applicability, the MDC models were limited to analysis of frames and arches, demonstrating objective results for these cases. For these models, the finite element is given by combining an elastic bar element with two inelastic hinges at the ends. In the case of a two-dimensional medium, such as plate elements, inelastic hinges become localization bands. The finite element proposed in this work consists of joining a four-node elastic element with a set of locating bands on the sides and also within the element. Damage evolution laws that describe the behaviour of each location band are introduced in the model formulation and the proposed element is then implemented in a finite element analysis program. The convergence of numerical results to a single solution as the mesh is refined is demonstrated through examples and related problems are discussed. The results are presented graphically along with the final configuration of the problem structure, highlighting the formation of the localization bands. |
publishDate |
2020 |
dc.date.issued.fl_str_mv |
2020-01-30 |
dc.date.accessioned.fl_str_mv |
2021-06-07T12:26:38Z |
dc.date.available.fl_str_mv |
2021-06-07T12:26:38Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
OLIVEIRA, João Marcos de Jesus. Mecânica do dano concentrado expandida para meios bidimensionais: elemento finito para problemas de localização de deformações em chapas. 2020. 113 f. Dissertação (Mestrado em Engenharia Civil) - Universidade Federal de Sergipe, São Cristóvão, SE, 2020. |
dc.identifier.uri.fl_str_mv |
https://ri.ufs.br/jspui/handle/riufs/14310 |
identifier_str_mv |
OLIVEIRA, João Marcos de Jesus. Mecânica do dano concentrado expandida para meios bidimensionais: elemento finito para problemas de localização de deformações em chapas. 2020. 113 f. Dissertação (Mestrado em Engenharia Civil) - Universidade Federal de Sergipe, São Cristóvão, SE, 2020. |
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openAccess |
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Pós-Graduação em Engenharia Civil |
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Universidade Federal de Sergipe |
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