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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 26
ADVANCES IN COMPUTATIONAL MECHANICS
Edited by: M. Papadrakakis and B.H.V. Topping
Paper IV.1

Symmetry and the Direct Stiffness Method in Structural Analysis: A Formulation based on Group Theory

A. Zingoni*, M.N. Pavlovic# and G.M. Zlokovic**

*Department of Civil Engineering, University of Zimbabwe, Harare, Zimbabwe
#Department of Civil Engineering, Imperial College, London, United Kingdom
**Faculty of Architecture, University of Belgrade, Belgrade, Yugoslavia

Full Bibliographic Reference for this paper
A. Zingoni, M.N. Pavlovic, G.M. Zlokovic, "Symmetry and the Direct Stiffness Method in Structural Analysis: A Formulation based on Group Theory", in M. Papadrakakis, B.H.V. Topping, (Editors), "Advances in Computational Mechanics", Civil-Comp Press, Edinburgh, UK, pp 107-115, 1994. doi:10.4203/ccp.26.4.1
Abstract
Group theory provides an efficient and systematic means for exploiting the full symmetry of physical systems, resulting in a substantial simplification of the quantitative analysis of their properties. For a given problem exhibiting symmetry properties, this simplification is achieved by a decomposition of the vector space of its arbitrary functions into a number of mutually-independent subspaces each spanned by a set of symmetry-adapted functions, such that within each subspace, the number of unknowns (i.e. symmetry-adapted functions) is only a fraction of that associated with a conventional analysis of the problem. In the present paper, the technique is applied to the structural analysis of symmetrical plane frames by the well-known direct stiffness method, and the computational superiority of the group-theoretic procedure over its conventional counterpart is shown through a simple illustrative example.

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