Group-Theoretic Applications in Solid and Structural Mechanics: A Review

This paper is a review of applications of symmetry groups and associated representation theory in the analysis and study of problems involving symmetry within the fields of solid and structural mechanics. Such techniques are very well-established in various branches of physics and chemistry, but the need for a more systematic and thorough exploitation of symmetry in tackling problems within solid and structural mechanics has provided the impetus over the past 30 years for the development of group-theoretic methods. This paper traces the advances made in the exploitation of group theory in areas such as bifurcation analysis, vibration analysis and finite-element analysis, and outlines the various schemes of implementation currently available. In all cases, it is shown that through the characteristic vector-space decomposition, group-theoretic methods afford considerable simplifications and reductions in computational effort in comparison with conventional methods, and render the computations amenable to the use of parallel processors.