Elementos de Contorno para Análise Isogeométrica de Sólidos Elásticos com Vincos
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFMS |
Texto Completo: | https://repositorio.ufms.br/handle/123456789/3990 |
Resumo: | The boundary element method (BEM) is an important alternative applied to the numerical solution of various problems derived from continuum mechanics. In solids mechanics, more specifically, the method is attractive as it may require only a discretization of the surfaces of the bodies under analysis, with a consequent decrease in the dimensionality of the discrete system. In the context of isogeometric analysis (IGA), the BEM is even more naturally attractive, since the idea behind IGA is to use the geometric model of an object - generally defined by NURBS surface patches generated from a CAD tool - as the analysis model, without the employment of a particular process of mesh generation. Recently, several papers demonstrating the feasibility of IGA can be found in the literature. However, there are still several limitations that prevent the practical use of IGA, mainly due to the difficulty of imposing non-homogeneous boundary conditions. In this thesis, a study of those limitations is carried out, and a solution based on the MEC for isogeometric analysis of elastic solids is proposed. The resulting framework allows the modeling of traction discontinuities by using discontinuous elements and/or multiple nodes, where the multiplicity of a node is given by surface regions delimited by crease curves. The boundary elements are defined as Bézier patches associated with the faces of the elemental mesh of a T-spline surface. T-splines are employed instead of NURBS since they allow non-structured control point meshes, with T-joints and extraordinary points, without the need for trimming curves. Nevertheless, any geometric representation that can be transformed into Bézier patches is supported. A Bézier extraction procedure for generic T-splines with creases and a robust numerical integration scheme for the boundary integral equation are introduced. The framework is implemented in C ++. A prototype in MATLAB allows the interactive selection of groups of elements for specifying boundary conditions that represent generic constraints and uniformly distributed tractions, pressures, and torques, as well as the numerical analysis and visualization of results. |
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2021-09-17T20:13:03Z2021-09-30T19:55:34Z2021https://repositorio.ufms.br/handle/123456789/3990The boundary element method (BEM) is an important alternative applied to the numerical solution of various problems derived from continuum mechanics. In solids mechanics, more specifically, the method is attractive as it may require only a discretization of the surfaces of the bodies under analysis, with a consequent decrease in the dimensionality of the discrete system. In the context of isogeometric analysis (IGA), the BEM is even more naturally attractive, since the idea behind IGA is to use the geometric model of an object - generally defined by NURBS surface patches generated from a CAD tool - as the analysis model, without the employment of a particular process of mesh generation. Recently, several papers demonstrating the feasibility of IGA can be found in the literature. However, there are still several limitations that prevent the practical use of IGA, mainly due to the difficulty of imposing non-homogeneous boundary conditions. In this thesis, a study of those limitations is carried out, and a solution based on the MEC for isogeometric analysis of elastic solids is proposed. The resulting framework allows the modeling of traction discontinuities by using discontinuous elements and/or multiple nodes, where the multiplicity of a node is given by surface regions delimited by crease curves. The boundary elements are defined as Bézier patches associated with the faces of the elemental mesh of a T-spline surface. T-splines are employed instead of NURBS since they allow non-structured control point meshes, with T-joints and extraordinary points, without the need for trimming curves. Nevertheless, any geometric representation that can be transformed into Bézier patches is supported. A Bézier extraction procedure for generic T-splines with creases and a robust numerical integration scheme for the boundary integral equation are introduced. The framework is implemented in C ++. A prototype in MATLAB allows the interactive selection of groups of elements for specifying boundary conditions that represent generic constraints and uniformly distributed tractions, pressures, and torques, as well as the numerical analysis and visualization of results.O método dos elementos de contorno (MEC) é uma importante alternativa para solução numérica de diversos problemas derivados da mecânica do contínuo. Em mecânica dos sólidos, mais especificamente, o método é atrativo pois pode requerer somente uma discretização das superfícies dos corpos em análise, com consequente diminuição da dimensionalidade do sistema discreto. No contexto de análise isogeométrica (IGA), o MEC é ainda mais naturalmente atrativo, uma vez que a ideia da IGA é utilizar o modelo geométrico de um objeto - geralmente definido por retalhos de superfícies NURBS produzidos por uma ferramenta CAD - como o próprio modelo de análise, sem emprego de um processo particular de geração de malhas. Recentemente, vários trabalhos que comprovam a viabilidade da IGA podem ser encontrados na literatura. Contudo, ainda há uma série de limitações que impedem a utilização prática da IGA, decorrentes principalmente da dificuldade de imposição de condições de contorno não homogêneas. Nesta tese, efetua-se um estudo dessas limitações e propõe-se uma solução baseada no MEC para análise isogeométrica de sólidos elásticos. O arcabouço resultante permite a modelagem de descontinuidades de forças de superfície através de elementos descontínuos e/ou nós múltiplos, sendo a multiplicidade de um nó dada por regiões da superfície delimitadas por curvas de vincos. Os elementos de contorno são definidos como retalhos de Bézier associados às faces da malha elementar de uma superfície T-spline. T-splines foram empregadas no lugar de NURBS por permitirem malhas de pontos de controle não estruturadas com junções em T e pontos extraordinários, sem necessidade de curvas de recorte, mas qualquer representação da qual se possa extrair retalhos de Bézier pode ser adotada. Um procedimento de extração de Bézier para superfícies T-splines genéricas com vincos e um esquema robusto de integração numérica dos termos da equação integral de contorno são introduzidos. O arcabouço é implementado em C++. Um protótipo em MATLAB permite a seleção interativa de grupos de elementos para especificação de condições de contorno representando vínculos genéricos e carregamentos uniformemente distribuídos, pressões e torques, bem como a análise numérica e visualização dos resultados.Fundação Universidade Federal de Mato Grosso do SulUFMSBrasilanálise isogeométrica, método dos elementos de contorno, T-splinesElementos de Contorno para Análise Isogeométrica de Sólidos Elásticos com Vincosinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisPaulo Aristarco PagliosaMarcio Artacho Peresinfo:eu-repo/semantics/openAccessporreponame:Repositório Institucional da UFMSinstname:Universidade Federal de Mato Grosso do Sul (UFMS)instacron:UFMSTHUMBNAILTese Márcio Artacho Peres 09.2021.pdf.jpgTese Márcio Artacho Peres 09.2021.pdf.jpgGenerated Thumbnailimage/jpeg1045https://repositorio.ufms.br/bitstream/123456789/3990/3/Tese%20M%c3%a1rcio%20Artacho%20Peres%2009.2021.pdf.jpg913325505ac937e676a833938b75f846MD53TEXTTese Márcio Artacho Peres 09.2021.pdf.txtTese Márcio Artacho Peres 09.2021.pdf.txtExtracted texttext/plain277133https://repositorio.ufms.br/bitstream/123456789/3990/2/Tese%20M%c3%a1rcio%20Artacho%20Peres%2009.2021.pdf.txt095f4467e360933dd29911d70c67f6cdMD52ORIGINALTese Márcio Artacho Peres 09.2021.pdfTese Márcio Artacho Peres 09.2021.pdfapplication/pdf6455973https://repositorio.ufms.br/bitstream/123456789/3990/1/Tese%20M%c3%a1rcio%20Artacho%20Peres%2009.2021.pdf36c4f2ef21f3756578a2f77fce6cb467MD51123456789/39902021-09-30 15:55:34.887oai:repositorio.ufms.br:123456789/3990Repositório InstitucionalPUBhttps://repositorio.ufms.br/oai/requestri.prograd@ufms.bropendoar:21242021-09-30T19:55:34Repositório Institucional da UFMS - Universidade Federal de Mato Grosso do Sul (UFMS)false |
dc.title.pt_BR.fl_str_mv |
Elementos de Contorno para Análise Isogeométrica de Sólidos Elásticos com Vincos |
title |
Elementos de Contorno para Análise Isogeométrica de Sólidos Elásticos com Vincos |
spellingShingle |
Elementos de Contorno para Análise Isogeométrica de Sólidos Elásticos com Vincos Marcio Artacho Peres análise isogeométrica, método dos elementos de contorno, T-splines |
title_short |
Elementos de Contorno para Análise Isogeométrica de Sólidos Elásticos com Vincos |
title_full |
Elementos de Contorno para Análise Isogeométrica de Sólidos Elásticos com Vincos |
title_fullStr |
Elementos de Contorno para Análise Isogeométrica de Sólidos Elásticos com Vincos |
title_full_unstemmed |
Elementos de Contorno para Análise Isogeométrica de Sólidos Elásticos com Vincos |
title_sort |
Elementos de Contorno para Análise Isogeométrica de Sólidos Elásticos com Vincos |
author |
Marcio Artacho Peres |
author_facet |
Marcio Artacho Peres |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Paulo Aristarco Pagliosa |
dc.contributor.author.fl_str_mv |
Marcio Artacho Peres |
contributor_str_mv |
Paulo Aristarco Pagliosa |
dc.subject.por.fl_str_mv |
análise isogeométrica, método dos elementos de contorno, T-splines |
topic |
análise isogeométrica, método dos elementos de contorno, T-splines |
description |
The boundary element method (BEM) is an important alternative applied to the numerical solution of various problems derived from continuum mechanics. In solids mechanics, more specifically, the method is attractive as it may require only a discretization of the surfaces of the bodies under analysis, with a consequent decrease in the dimensionality of the discrete system. In the context of isogeometric analysis (IGA), the BEM is even more naturally attractive, since the idea behind IGA is to use the geometric model of an object - generally defined by NURBS surface patches generated from a CAD tool - as the analysis model, without the employment of a particular process of mesh generation. Recently, several papers demonstrating the feasibility of IGA can be found in the literature. However, there are still several limitations that prevent the practical use of IGA, mainly due to the difficulty of imposing non-homogeneous boundary conditions. In this thesis, a study of those limitations is carried out, and a solution based on the MEC for isogeometric analysis of elastic solids is proposed. The resulting framework allows the modeling of traction discontinuities by using discontinuous elements and/or multiple nodes, where the multiplicity of a node is given by surface regions delimited by crease curves. The boundary elements are defined as Bézier patches associated with the faces of the elemental mesh of a T-spline surface. T-splines are employed instead of NURBS since they allow non-structured control point meshes, with T-joints and extraordinary points, without the need for trimming curves. Nevertheless, any geometric representation that can be transformed into Bézier patches is supported. A Bézier extraction procedure for generic T-splines with creases and a robust numerical integration scheme for the boundary integral equation are introduced. The framework is implemented in C ++. A prototype in MATLAB allows the interactive selection of groups of elements for specifying boundary conditions that represent generic constraints and uniformly distributed tractions, pressures, and torques, as well as the numerical analysis and visualization of results. |
publishDate |
2021 |
dc.date.accessioned.fl_str_mv |
2021-09-17T20:13:03Z |
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2021-09-30T19:55:34Z |
dc.date.issued.fl_str_mv |
2021 |
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info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/doctoralThesis |
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doctoralThesis |
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https://repositorio.ufms.br/handle/123456789/3990 |
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por |
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info:eu-repo/semantics/openAccess |
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openAccess |
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Fundação Universidade Federal de Mato Grosso do Sul |
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UFMS |
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Brasil |
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Fundação Universidade Federal de Mato Grosso do Sul |
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