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Felício Bruzzi Barroshttp://lattes.cnpq.br/9765621436381704Sérgio Persival Baroncini ProençaRoque Luiz da Silva PitangueiraSamuel Silva PennaRafael Marques Linshttp://lattes.cnpq.br/8574495645474747Gabriela Marinho Fonseca2023-08-31T16:45:45Z2023-08-31T16:45:45Z2023-07-12http://hdl.handle.net/1843/58365O Método dos Elementos Finitos Generalizados com enriquecimento global-local (MEFGgl) tem se consolidado, nos últimos anos, como importante ferramenta para a solução de problemas contendo descontinuidades e/ou singularidades. Sua formulação se baseia na decomposição da solução em duas escalas de análise: uma escala grosseira (global), buscando representar a parcela suave da solução, e uma escala refinada (local), na qual são inseridas as particularidades do problema estudado. Apesar dos avanços já alcançados na aplicação desse método numérico, verificam-se lacunas no que diz respeito ao controle dos erros da simulação. Nesse sentido, o presente trabalho propõe, pela primeira vez, estimadores de erro a posteriori e procedimentos adaptativos para o MEFGgl, aplicados a problemas bidimensionais da Mecânica da Fratura Linear Elástica. Formulam-se medidas de erro nas duas escalas de análise (problema local e problema global), tendo como base a norma energia e, ainda, um estimador orientado ao objetivo especialmente concebido para o fator de intensidade de tensão. Tais medidas são empregadas em procedimentos adaptativos com o objetivo de aprimorar a solução aproximada e diminuir a dependência em relação ao usuário do sistema computacional. As simulações numéricas são desenvolvidas no sistema INSANE (INteractive Structural ANalysis Environment), um projeto de software livre desenvolvido no Departamento de Engenharia de Estruturas da Universidade Federal de Minas Gerais.The Generalized Finite Element Method with global-local enrichments (GFEMgl) has been consolidated, in recent years, as an important tool for solving problems containing discontinuities and singularities. The formulation is based on a two-scale decomposition of the solution: a coarse scale (global), capable of representing the smooth component of the solution, and a fine scale (local), where the special features of the problem are inserted. Despite the advances in the application of this numerical method, there is a lack of studies concerning approximation errors. Therefore, the present work proposes, for the first time, a posteriori error estimators and adaptive procedures for the GFEMgl, considering two-dimensional Linear Elastic Fracture Mechanics problems. Error measures are formulated in the two solution scales (local and global problems) based on the energy norm and, additionally, a goal-oriented error estimator specially designed for the stress intensity factors. These measures are employed in adaptive procedures to improve the approximate solution and reduce the dependence on the user of the computational platform. The numerical simulations are performed in INSANE (INteractive Structural ANalysis Environment), a free software project developed at the Department of Structural Engineering of the Federal University of Minas Gerais.CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorporUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em Engenharia de EstruturasUFMGBrasilENG - DEPARTAMENTO DE ENGENHARIA ESTRUTURASEngenharia de estruturasMétodo dos elementos finitosMecânica da fraturaMétodos numéricosMetodos de simulaçãoMétodo dos elementos finitos generalizadosEnriquecimento global-localEstimador de erro a posterioriAdaptatividadeMecânica da fratura linear elásticaEstimadores de erro a posteriori e estratégias adaptativas para o método dos elementos finitos generalizados com enriquecimento global-local aplicado a problemas da mecânica da fraturainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGLICENSElicense.txtlicense.txttext/plain; charset=utf-82118https://repositorio.ufmg.br/bitstream/1843/58365/4/license.txtcda590c95a0b51b4d15f60c9642ca272MD54ORIGINALTese_Gabriela VersãoFinal.pdfTese_Gabriela VersãoFinal.pdfapplication/pdf54920084https://repositorio.ufmg.br/bitstream/1843/58365/3/Tese_Gabriela%20Vers%c3%a3oFinal.pdf8f8507b81e7836c15347c826ce41ff0fMD531843/583652023-08-31 13:45:46.324oai:repositorio.ufmg.br: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ório InstitucionalPUBhttps://repositorio.ufmg.br/oaiopendoar:2023-08-31T16:45:46Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false
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