### Abstract

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.

Original language | English (US) |
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Title of host publication | Proceedings of the 11th International Conference on Computational Structures Technology, CST 2012 |

Publisher | Civil-Comp Press |

Volume | 99 |

ISBN (Print) | 9781905088546 |

State | Published - Jan 1 2012 |

Event | 11th International Conference on Computational Structures Technology, CST 2012 - Dubrovnik, Croatia Duration: Sep 4 2012 → Sep 7 2012 |

### Other

Other | 11th International Conference on Computational Structures Technology, CST 2012 |
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Country | Croatia |

City | Dubrovnik |

Period | 9/4/12 → 9/7/12 |

### All Science Journal Classification (ASJC) codes

- Environmental Engineering
- Civil and Structural Engineering
- Computational Theory and Mathematics
- Artificial Intelligence

### Keywords

- Asymmetric topology
- Group theory
- Structural topology optimization
- Symmetric topology
- Symmetry operation
- Truss topology optimization

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## Cite this

*Proceedings of the 11th International Conference on Computational Structures Technology, CST 2012*(Vol. 99). Civil-Comp Press.