A group-theoretic approach to computational bifurcation problems with symmetry

Abstract

Bifurcation of solution branches in static or steady problems of nonlinear mechanics is often associated with the underlying symmetry of the physical system. The use of group-theoretic methods in local bifurcation theory for problems with symmetry is well known. In this paper it is shown that the exploitation of symmetry via group invariance also yields an efficient computational approach to global bifurcation problems. These techniques are illustrated in the analysis of a lattice-dome structure with hexagonal symmetry. The methodology leads to a drastic reduction in numerical effort in the determination of several global solution branches, and enables the accurate computation of numerous singular points.