[Univ of Cambridge] [Dept of Engineering]
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Simon Guest: Symmetry


Structures and mechanisms that are symmetric often have interesting properties that depend on their symmetries. For instance, many structures/mechanisms have finite mechanisms, even though they are apparently overconstrained; in many cases this paradox can be explained by the symmetry of the system.

Together with Patrick Fowler of the University of Sheffield, R. Pandia Raj, Riki Kangwai and Hannes Schmidt at Cambridge, Jingyao Zhang of the University of Kyoto, and following initial inspiration from Sergio Pellegrino, I have looked at both the tools of symmetry analysis, working out new methods of applying group-theoretical techniques to structural analysis, and also the application of symmetry to various systems with interesting properties.

Tools of symmetry analysis

Our early work was concerned with applying group-theoretical techniques to new areas of structural analysis, particularly equilibrium relationships between applied loads and internal forces. One important outcome was that it proved to be possible to show the finite nature of many mechanisms, simply based on a local first-order analysis, and symmetry.

Recent work with Patrick Fowler has focussed on using representation theory to expand simple counting rules for structural analysis to consider the symmetries, as well as number, of various quantities. We have developed a symmetry-adapted form of both Maxwell's rule for the determinacy of truss structures, and the mobility criterion for the determination of the number of degrees of freedom of a mechanism.

Further work is concentrating on applying symmetry methods to understand and devise new tensegrity structures.

Applications of symmetry analysis

We have applied our knowledge of symmetry and structural analysis to a number of different systems:

Relevant Publications

Guest, S.D. and Fowler, P.W. (2006), "Symmetry conditions and finite mechanisms", accepted for publication in the Journal of Mechanics of Materials and Structures. (pdf preprint)

Zhang, J.Y., Guest, S.D. and Ohsaki, M. (2006) "Symmetric Prismatic Tensegrity Structures". Presented at IASS-2006, Beijing, China, October 16-19, 2006. (pdf copy)

Pandia Raj, R. and Guest, S.D. (2006) "Using Symmetry for Tensegrity Formfinding". Presented at IASS-2006, Beijing, China, October 16-19, 2006. (pdf copy)

Guest, S.D. and Fowler, P.W. (2005), "A symmetry-extended mobility rule." Mechanism and Machine Theory. 40, 1002-1014 (pdf preprint) / doi:10.1016/j.mechmachtheory.2004.12.017

Fowler, P.W. and Guest, S.D. (2005), "A symmetry analysis of mechanisms in rotating rings of tetrahedra." Proceedings of the Royal Society: Mathematical, Physical & Engineering Sciences. 461(2058), 1829-1846 (pdf preprint) / doi:10.1098/rspa.2004.1439

Fowler, P.W. and Guest, S.D. (2002). "Symmetry Analysis of the double banana and related indeterminate structures", in New Approaches to Structural Mechanics, Shells and Biological Structures, Drew H.R. and Pellegrino, S. eds., Kluwer, 91-101.

Fowler, P.W. and Guest, S.D. (2002), "Symmetry and states of self stress in triangulated toroidal frames." International Journal of Solids and Structures. 39(17), 4385-4393.doi:10.1016/S0020-7683(02)00350-5

Guest, S.D. (2000). "Tensegrities and rotating rings of tetrahedra: a symmetry viewpoint of structural mechanics." Philosophical Transactions of the Royal Society of London, Series A, Millennium Issue 358(1765), 229-243. http://www.journals.royalsoc.ac.uk/link.asp?id=w3huwr0et12hlr3d

Fowler, P.W. and Guest, S.D. (2000). "A Symmetry Extension of Maxwell's Rule for Rigidity of Frames" International Journal of Solids and Structures 37, 1793-1804. doi:10.1016/S0020-7683(98)00326-6

Kangwai, R.D. and Guest, S.D. (2000). "Symmetry Adapted Equilibrium Matrices." International Journal of Solids and Structures 37, 1525-1548. doi:10.1016/S0020-7683(98)00318-7

Guest, S.D. (1999). "Mechanisms of the Icosahedral Compound of Ten Tetrahedra." 4th Geometry Festival, Eotvos University, Budapest, November 1999 Periodica Mathematica Hungarica 39(1-3), 213-223. doi:10.1023/A:1004863511981

Kangwai, R.D. and Guest, S.D. (1999). "Detection of Finite Mechanisms in Symmetric Structures." International Journal of Solids and Structures 36, 5507-5527. doi:10.1016/S0020-7683(98)00234-0

Kangwai, R.D., Guest, S.D. and Pellegrino, S. (1999). "Introduction to the Analysis of Symmetric Structures." Computers & Structures 71(2), 671-688. doi:10.1016/S0045-7949(98)00234-X

Last updated on the 25th of October, 2006

S.D. Guest - sdg@eng.cam.ac.uk