### 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.

Original language | English (US) |
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Pages (from-to) | 631-643 |

Number of pages | 13 |

Journal | Structural and Multidisciplinary Optimization |

Volume | 47 |

Issue number | 5 |

DOIs | |

State | Published - May 1 2013 |

### All Science Journal Classification (ASJC) codes

- Software
- Control and Systems Engineering
- Computer Science Applications
- Computer Graphics and Computer-Aided Design
- Control and Optimization

### Keywords

- Asymmetric topology
- Discrete variable optimization
- Symmetric topology
- Symmetry operation
- Truss topology optimization

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## Cite this

*Structural and Multidisciplinary Optimization*,

*47*(5), 631-643. https://doi.org/10.1007/s00158-012-0871-8