Abstract

The presentation will outline some of the work carried out at the University of Cape Town on symmetry in structural mechanics, and explain how group theory has been applied to simplify computations, study the physical properties of structural systems, and explore new possibilities. These studies have included (i) the static analysis of space frames, (ii) the vibration behaviour of grids, cable nets, plates and shells, (iii) the buckling of space trusses, rigid frames, plates and shells, (iv) the development of group-theoretic numerical formulations, and (v) the innovative use of group theory in creating novel configurations of space structures. After outlining basic concepts of symmetry and group theory, the talk will illustrate the group-theoretic approach by reference to the vibration of a double-layer cable net. Through a numerical example, the talk will highlight the usefulness of group theory in predicting the behaviour of the structure prior to any detailed calculations, and in simplifying the computation of key structural properties.