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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 19
DEVELOPMENTS IN COMPUTATIONAL ENGINEERING MECHANICS
Edited by: B.H.V. Topping
Paper IX.4

Group-Theory Considerations of Finite-Difference Plate Eigenvalue Problems

A. Zingoni*, M.N. Pavlovic*, D. Lloyd Smith* and G.M. Zlokovic+

*Department of Civil Engineering, Imperial College of Science, Technology & Medicine, London, England
+Faculty of Architecture, University of Belgrade, Yugoslavia

Full Bibliographic Reference for this paper
A. Zingoni, M.N. Pavlovic, D. Lloyd Smith, G.M. Zlokovic, "Group-Theory Considerations of Finite-Difference Plate Eigenvalue Problems", in B.H.V. Topping, (Editor), "Developments in Computational Engineering Mechanics", Civil-Comp Press, Edinburgh, UK, pp 243-256, 1993. doi:10.4203/ccp.19.9.4
Abstract
Group theory provides a systematic means of exploiting the physical symmetry of a structure in the course of analysis, with the result that all the symmetry elements of the configuration are taken into account. This is achieved by a decomposition of the vector space of the arbitrary functions of the problem, into mutually-independent subspaces of symmetry-adapted functions, within each of which the number of unknowns is only a fraction of those of the original problem. Consequently, substantial reductions in computational effort can be achieved. In the present paper, the method is applied to the determination of eigenvalues of a plate by the well-known numerical technique of finite differences, thereby illustrating the significant computational gains of a group-theoretic approach over conventional methods, whenever the physical configuration of the plate structure (or sub-structure) exhibits symmetry properties.

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