On the best choice of symmetry group for group-theoretic computational schemes in solid and structural mechanics

Abstract

Abstract Group theory has been used for many years to study phenomena in various branches of physics and chemistry, such as quantum mechanics, crystallography and molecular structure. Within engineering mechanics, it has found application in simplifying the analysis of systems exhibiting symmetry properties, and has been particularly effective in studying vibration, bifurcation and kinematic phenomena. Symmetry properties of physical systems are described by symmetry groups. Given a physical system with multiple symmetry properties, the question arises as to which of the various possible symmetry groups is the most appropriate for computational purposes. This question is particularly relevant for configurations belonging to symmetry groups of high order, which typically are associated with several subgroups. The aim of this paper is to highlight the computational implications of choice of symmetry group, and to present, for the first time, a rational criterion for identifying the most computationally efficient symmetry group for a given problem. The criterion is applied to the problem of a cubic configuration with octahedral symmetry.