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Otimização de Topologia de Estruturas Não Lineares
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Resumo(s)
A presente dissertação surge no seguimento do trabalho realizado por Ana Silva em
dissertação de mestrado [1] na qual validou o programa PROAES_NL, tendo-lhe adicionado
o cálculo de sensibilidades não lineares.
O principal objetivo consiste na criação de uma metodologia que realize a otimização
de topologia de treliças usando o conceito de Ground Structure e considerando a possibilida-
de de encurvadura.
Esta temática é muito interessante, uma vez que o desenvolvimento desta metodologia
com sucesso permite aproximar a fase de otimização da fase de fabrico.
É crucial ter em consideração, durante o projeto, o fenómeno da encurvadura pois o
mesmo leva a grandes deslocamentos transversais e à perda de rigidez da estrutura.
Recorreu-se à análise não linear pelo método corrotacional e à imposição de imperfei-
ções, locais e globais, de forma a não ser necessário a imposição de constrangimentos de en-
curvadura. Implementou-se com sucesso no programa, através da metodologia criada, a pos-
sibilidade de maximizar a força aplicada, tendo como constrangimento um valor máximo
para o deslocamento num determinado nó da estrutura, definido pelo utilizador aquando do
projeto.
Aplicou-se o método de Newton Raphson para controlar o valor das forças aplicadas e
o Method of Moving Asymptotes, ou MMA, para a otimização estrutural.
Replicaram-se os exemplos apresentados no artigo tido como base da autoria de Ma-
dah e Amir [2] de acordo com a metodologia criada, e os resultados obtidos foram posteri-
ormente comparados com os obtidos através do software de elementos finitos ANSYS, ten-
do-se verificado um erro pequeno entre ambos e consequentemente validado a presente me-
todologia.
The present dissertation follows the work carried out by Ana Silva in her master's the- sis [1] in which she validated the PROAES_NL program, having added the calculation of non-linear sensitivities. The main objective consists in the creation of a methodology that successfully performs the topology optimization of trusses using the concept of Ground Structure and considering the possibility of buckling. This topic is very interesting since the successful development of this methodology al- lows the optimization phase to get closer to the manufacturing one. It is crucial to consider buckling phenomenon, during the project, as it leads to large transversal displacements and loss of stiffness in the structure. Non-linear analysis using the corotational method and the imposition of local and global imperfections was used to avoid the need to impose buckling constraints. Through the created methodology, the possibility of maximizing the applied force was successfully im- plemented in the program, having as constraint a maximum value for displacement at a cer- tain point of the structure, defined by the user during the project. Newton Raphson's method was used to control the value of the forces applied and the Method of Moving Asymptotes, or MMA, used for structural optimization. The examples presented in the article authored by Madah and Amir [2] were replicated according to the methodology created, and the results obtained were later compared with those obtained using the finite element software ANSYS, having verified a small relative error between both. Consequently, the present methodology was validated.
The present dissertation follows the work carried out by Ana Silva in her master's the- sis [1] in which she validated the PROAES_NL program, having added the calculation of non-linear sensitivities. The main objective consists in the creation of a methodology that successfully performs the topology optimization of trusses using the concept of Ground Structure and considering the possibility of buckling. This topic is very interesting since the successful development of this methodology al- lows the optimization phase to get closer to the manufacturing one. It is crucial to consider buckling phenomenon, during the project, as it leads to large transversal displacements and loss of stiffness in the structure. Non-linear analysis using the corotational method and the imposition of local and global imperfections was used to avoid the need to impose buckling constraints. Through the created methodology, the possibility of maximizing the applied force was successfully im- plemented in the program, having as constraint a maximum value for displacement at a cer- tain point of the structure, defined by the user during the project. Newton Raphson's method was used to control the value of the forces applied and the Method of Moving Asymptotes, or MMA, used for structural optimization. The examples presented in the article authored by Madah and Amir [2] were replicated according to the methodology created, and the results obtained were later compared with those obtained using the finite element software ANSYS, having verified a small relative error between both. Consequently, the present methodology was validated.
Descrição
Palavras-chave
Encurvadura Imperfeições Otimização Topológica Treliças Força Deslocamento