An introduction to the analysis of symmetric structures

This paper aims to review and explain the techniques used to analyse symmet ric structures subject to a general loading. After an extensive review of p revious work in this field, the paper introduces the most general way of de scribing the full symmetry properties of a structure, based on group repres entation theory, and shows how this approach can be used to systematically simplify a structural analysis. A technique which is better known to struct ural engineers, known as the Fourier method, is also presented, but it is s hown that this method is a special case of the group representation theory method. For both methods the techniques that are used to block-diagonalize the full stiffness matrix of a structure are presented, and it is also show n that substructuring techniques can be used so that the full stiffness mat rix never needs to be generated. (C) 1999 Elsevier Science Ltd. All rights reserved.