An introduction to the analysis of symmetric structures

This paper aims to review and explain the techniques used to analyse symmetric structures subject to a general loading. After an extensive review of previous work in this field, the paper introduces the most general way of describing the full symmetry properties of a structure, based on group representation theory, and shows how this approach can be used to systematically simplify a structural analysis. A technique which is better known to structural engineers, known as the Fourier method, is also presented, but it is shown 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 shown that substructuring techniques can be used so that the full stiffness matrix never needs to be generated. (C) 1999 Elsevier Science Ltd. All rights reserved.