Symmetry and asymmetry of solutions in discrete variable structural optimization

Symmetry and asymmetry of solutions in discrete variable structural optimization

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Article ID: iaor20133002
Volume: 47
Issue: 5
Start Page Number: 631
End Page Number: 643
Publication Date: May 2013
Journal: Structural and Multidisciplinary Optimization
Authors: , , ,
Keywords: optimization
Abstract:

In this paper symmetry and asymmetry of optimal solutions in symmetric structural optimization problems is investigated, based on the choice of variables. A group theory approach is used to define the symmetry of the structural problems in a general way. This approach allows the set of symmetric structures to be described and related to the entire search space of the problem. A relationship between the design variables and the likelihood of finding symmetric or asymmetric solutions to problems is established. It is shown that an optimal symmetric solution (if any) does not necessarily exist in the case of discrete variable problems, regardless of the size of the discrete, countable set from which variables can be chosen. Finally a number of examples illustrate these principles on simple truss structures with discrete topology and sizing variables.

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