Automatic and Exact Symmetry Recognition of Structures Exhibiting High-Order Symmetries

Abstract

Symmetry analysis is common and important, and the involved symmetry is in general self evident or manually recognized. However, for a structure with high-order symmetry or complex geometry, it becomes very difficult to perform manual recognition. Even though some symmetry properties are detected, the others might be undetected. Thus, computer-aided recognition methods are preferred. Here, the authors proposed an automatic symmetry recognition approach for engineering structures with either cubic or dihedral symmetries. It took only nodal coordinates and connectivity patterns of members as input. Without assuming any prior symmetries, the configuration can be expressed in an arbitrary three-dimensional (3D) coordinate system. Then, on the basis of matrix representations of five types of symmetry operations, equivalence of the geometric configuration of a structure was evaluated. Hence, the inherent symmetry can be identified, with all the unshifted components and feasible symmetry axes and planes detected in succession. Illustrative examples show that the proposed approach can accurately and effectively recognize the symmetries of various engineering structures.