THE ANALYSIS OF CYCLICALLY SYMMETRIC STRUCTURES – HISTORICAL REMARKS

Abstract

This paper aims to review and explain the path of evolution of the concepts and techniques to analyze symmetric structures. First domes designed by Schwedler imply a new theory of spatial truss system in the static analysis of determinate and indeterminate problems. The system of equilibrium equations obtained has a circulant determinant. This specific form conducted to complex numbers and some savings appeared. The development of methods to exploit the symmetry properties have depended on achievements in mathematics and informatics. The use of electronic computers within the development of finite element structural analysis package had a spectacular increased at work done in this area. Two main advanced approaches in the analysis of symmetric structures have used: the discrete Fourier transformation (DFT) for rotational symmetry, and group representation theory to exploit any type of symmetry.