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Master's Dissertation
DOI
Document
Author
Full name
Gianluca Marchiori
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Gay Neto, Alfredo (President)
Alves, Marcilio
Bittencourt, Marco Lucio
Title in Portuguese
Análise isogeométrica aplicada a elementos de vigas planas.
Keywords in Portuguese
Estruturas (Análise)
Método dos Elementos Finitos
Vigas
Abstract in Portuguese
A análise isogeométrica (AIG) de estruturas consiste em construir a geometria exata ou aproximada de um modelo computacional a partir de funções criadas por meio de tecnologias de Computer Aided Design (CAD), tais como B-Splines, NURBS (Non-Uniform Rational BSplines) e T-splines, e aplicar o conceito de análise isoparamétrica, ou seja, representar o espaço de solução para as variáveis independentes em termos das mesmas funções que representam a geometria. O presente trabalho visa o estudo da análise isogeométrica aplicada a vigas planas, com a utilização de B-Splines e NURBS para aproximação de deslocamentos. São desenvolvidos modelos isogeométricos de vigas planas baseados nas hipóteses de Bernoulli- Euler e Timoshenko, e alguns exemplos de aplicação são realizados a fim de comparar os resultados numéricos com soluções analíticas, mostrando boa concordância. Uma questão pertinente à AIG corresponde à imposição de vínculos em pontos do domínio em que as funções básicas não sejam interpolatórias ou os vínculos desejados não forem diretamente relacionados aos graus de liberdade do elemento, que é o caso do elemento de viga de Bernoulli-Euler, já que as rotações geralmente não são tidas como graus de liberdade mas há a necessidade de se prescrever condições de contorno/conexão nas mesmas para descrever problemas físicos. Essa questão é tratada no presente trabalho através dos Métodos de Lagrange e de penalidade. São realizados exemplos de aplicação construídos com elementos de viga de Bernoulli-Euler utilizando os métodos de Lagrange e de penalidade na imposição de vínculos e na conexão entre pontos de regiões de domínio.
Title in English
Isogeometric analysis applied to 2D beam elements.
Keywords in English
Beam
Finite Element Method
Isogeometric analysis
Lagrange method
Multi-region
Penalty method
Splines
Abstract in English
Isogeometric analysis (IGA) consists on building the geometry of the computational model with functions created by Computer Aided Design (CAD) technologies, such as B-Splines, NURBS (Non-Uniform Rational B-Splines) and T-Splines. Then, isoparametric concept is employed, that is, the solution space is represented by means of the same functions used to describe the geometry. The aim of the present contribution is the study of isogeometric analysis applied to 2D beams with interpolation via B-splines and NURBS. Two-dimensional isogeometric beam formulations based on Bernoulli-Euler and Timoshenko assumptions are presented. Some examples of application are given and results are compared to analytical solutions, showing good agreement. An important issue about IGA corresponds to the imposition of constraints at points of domain in which the shape functions are not interpolatory, or the desired constraints are not directly related to the degrees of freedoms. This may occur for Bernoulli-Euler beams since rotations are not usually defined as degrees of freedom, but they need to be assessed for prescription of some boundary/connection conditions. This is done in present contribution by employing both Lagrange and penalty methods. Some examples of structures composed by 2D isogeometric Bernoulli-Euler beam elements are solved by using Lagrange and Penalty methods to impose constraints and to make the connection between domain regions.
 
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Publishing Date
2019-05-08
 
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