An introduction to the analysis of symmetric structures

摘要

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 anaylsis. 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.