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Otimização de Topologia de Treliças considerando Encurvadura
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Assim, neste trabalho, foi estudada a introdução de imperfeições geométricas tanto na estrutura como nos elementos que a constituem, de forma a suavizar a transição do domínio estável para instável. Aos elementos barra foram aplicados empenos e às treliças aplicados deslocamentos nas posições dos nós.
Para conseguir aplicar empeno nas barras, cada barra foi modelada por 3 elementos viga utilizando a formulação corrotacional. Foi utilizado o método de análise incremental-iterativa que alia o método de Newton-Raphson a um aumento gradual de carregamento. Para fazer a otimização estrutural, utilizou-se o método de ground structure, tendo sido utilizado o algoritmo SQP com a formulação de minimizar a flexibilidade (compliance), sujeito a um constrangimento de volume. Tudo isto foi implementado com recurso aos algoritmos constituintes do programa PROAES_NL.
Inicialmente foi atestado o bom funcionamento tanto do programa PROAES como do programa PROAES_NL. Verificou-se que o programa é tanto capaz de efetuar o cálculo de gradientes por análise de sensibilidades como por diferenças finitas.
Após terem sido criados os algoritmos, foram testados vários exemplos, de forma a testar a aplicabilidade da metodologia e a influência em cada parâmetro, utilizando o PROAES_NL. Os resultados foram positivos, aproximando-se dos obtidos na literatura.
The present thesis follows the work developed by Ana Silva [1], who included the non linear sensitivity analysis to the program PROAES_NL and validated its performance. The goal is to create an algorithm for the topology optimization of trusses, where a method is used to consider the problem of buckling in bars. This phenomenon is critical in structure design and controlling it by performing a linear analysis is highly complex, requiring the use of non linear analysis. However, due to the nature of the phenomenon, the transition between the stable and the unstable domains often occurs in an abruptly way and prevents the convergence of the solutions. Therefore, in this work, the introduction of geometrical imperfections was studied both for the structure and the elements that compose the structure, in order to smoothen the transition from stable domain to the unstable one. A warp was applied to bar elements and a displacement was applied to the nodes positions. To achieve an initial deformation in the bars, each bar was modelled by 3 beam elements using the corotational method. An iterative-incremental analysis method was used, which joins the Newton-Raphson method to a gradual increase of the load. In order to perform the structural optimization, the ground structure method was applied, using the SQP algorithm with minimum compliance while subjected to volume constraints. All this was implemented using the algorithms contained within the PROAES_NL program. The performance of both PROAES and PROAES_NL was initially checked. The program proved to be able to calculate the gradients by sensitivity analysis and by finite differences. After the creation of the algorithms, several examples were tested to demonstrate the method and the influence of each parameter, using PROAES_NL. The results were positive, being similar to those found on the literature.
The present thesis follows the work developed by Ana Silva [1], who included the non linear sensitivity analysis to the program PROAES_NL and validated its performance. The goal is to create an algorithm for the topology optimization of trusses, where a method is used to consider the problem of buckling in bars. This phenomenon is critical in structure design and controlling it by performing a linear analysis is highly complex, requiring the use of non linear analysis. However, due to the nature of the phenomenon, the transition between the stable and the unstable domains often occurs in an abruptly way and prevents the convergence of the solutions. Therefore, in this work, the introduction of geometrical imperfections was studied both for the structure and the elements that compose the structure, in order to smoothen the transition from stable domain to the unstable one. A warp was applied to bar elements and a displacement was applied to the nodes positions. To achieve an initial deformation in the bars, each bar was modelled by 3 beam elements using the corotational method. An iterative-incremental analysis method was used, which joins the Newton-Raphson method to a gradual increase of the load. In order to perform the structural optimization, the ground structure method was applied, using the SQP algorithm with minimum compliance while subjected to volume constraints. All this was implemented using the algorithms contained within the PROAES_NL program. The performance of both PROAES and PROAES_NL was initially checked. The program proved to be able to calculate the gradients by sensitivity analysis and by finite differences. After the creation of the algorithms, several examples were tested to demonstrate the method and the influence of each parameter, using PROAES_NL. The results were positive, being similar to those found on the literature.
Descrição
Palavras-chave
Instabilidade Encurvadura Imperfeições Geométricas Ground Structure Análise Não-Linear Otimização de Topologia