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Symmetry of solutions in discrete and continuous structural topology optimization

par Richardson, James ;Adriaenssens, Sigrid;Bouillard, Philippe ;Filomeno Coelho, Rajan
Référence Civil-Comp Proceedings, 99
Publication Publié, 2012

Article révisé par les pairs

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Résumé :

In this paper symmetry and asymmetry of optimal solutions in symmetric structural topology optimization problems are investigated, based on the choice of variables. A group theory approach is used to formally define the symmetry of the structural problems. This approach allows the set of symmetric structures to be described and related to the entire search space. It is shown that, given a symmetric problem with continuous variables, an optimal symmetric solution (if any) necessarily exists. However, it is shown that this does not hold for the discrete case. Finally a number of examples are investigated to demonstrate the findings of the research. © Civil-Comp Press, 2012.