A computational method for automated detection of engineering structures with cyclic symmetries

In general, for a complex engineering structure with a large number of nodes or members, the inherent symmetry is not easily recognizable. Even though someone succeeds in recognizing certain symmetry properties of the structure, these might be partial ones, and the others will be possibly unnoticed. To overcome this difficulty and enable the integration of computational analysis and symmetry methods, we propose an automated detection method for engineering structures with cyclic symmetries. Only the nodes and the connectivity patterns of the members are needed for implementing this algorithm. Using group theory, we first describe different cyclic groups of symmetries and their symmetry operations. In order to establish a group-theoretic algorithm for automated symmetry detection, several theorems and corollaries are presented. Then, on the basis of matrix representations of symmetry operations, the equivalence of the nodes and members of a structure is evaluated. Hence, the inherent symmetry operations of the structure are identified one by one. Illustrative examples show that the proposed automated symmetry detection method is robust and applicable to both 2D and 3D structures. Highly symmetric structures are recognized accurately and effectively. In addition, asymmetric structures and 2D structures can be recognized in a very small number of iterations.