A group-theoretic approach to computational bifurcation problems with symmetry
Computer Methods in Applied Mechanics and Engineering
Bifurcation analysis of symmetric structures using block-diagonalization
Computer Methods in Applied Mechanics and Engineering
Design of truss-structures for minimum weight using genetic algorithms
Finite Elements in Analysis and Design
On symmetry and non-uniqueness in exact topology optimization
Structural and Multidisciplinary Optimization
Discussion on symmetry of optimum topology design
Structural and Multidisciplinary Optimization
Multiobjective topology optimization of truss structures with kinematic stability repair
Structural and Multidisciplinary Optimization
Some symmetry results for optimal solutions in structural optimization
Structural and Multidisciplinary Optimization
| Hi-index | 0.00 |
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.