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DEVELOPMENTS IN COMPUTATIONAL ENGINEERING MECHANICS
Edited by: B.H.V. Topping
Conditioning of Structural Stiffness Matrices
A. Kaveh and I. Ghaderi
Department of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran
A. Kaveh, I. Ghaderi, "Conditioning of Structural Stiffness Matrices", in B.H.V. Topping, (Editor), "Developments in Computational Engineering Mechanics", Civil-Comp Press, Edinburgh, UK, pp 39-45, 1993. doi:10.4203/ccp.19.1.5
The popularity of the stiffness method of structural analysis is due to its simplicity and amenability to a computer. In this method special cut set basis, known as cocycle basis, is usually employed for constructing equilibrium equations. However, when a structure contains members of widely different stiffnesses, the corresponding stiffness matrix becomes ill-conditioned due to the creation of large off-diagonal entries. Although there are various algebraic approaches for modifying the conditioning, however, more efficient methods based on graph theory can be used.
In this paper methods are developed for generating special cut set bases leading to well-conditioned stiffness matrices. A simple approach is provided for assembling the stiffness matrices when such bases are used in place of traditional cocycle bases. The efficiency of the developed methods are illustrated using some examples chosen from truss structures.
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