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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 33
DEVELOPMENTS IN COMPUTATIONAL TECHNIQUES FOR STRUCTURAL ENGINEERING
Edited by: B.H.V. Topping
Paper X.2

The Theorems of Structural Variation for Solid Cubic Elements

M.P. Saka

Civil Engineering Department, University of Bahrain, Bahrain

Full Bibliographic Reference for this paper
M.P. Saka, "The Theorems of Structural Variation for Solid Cubic Elements", in B.H.V. Topping, (Editor), "Developments in Computational Techniques for Structural Engineering", Civil-Comp Press, Edinburgh, UK, pp 261-272, 1995. doi:10.4203/ccp.33.10.2
Abstract
The theorems of structural variation predict the forces and displacements throughout a structure without need of fresh analysis when the physical properties of one or more of its elements are altered. It has been shown that by means of these theorems the elastic, non-linear elastic and elastic-plastic analysis of number of related frame structures can be obtained from the simple elastic analysis of a parent structure. They are later extended to cover the triangular and quadrilateral finite element structures. In this paper, it is shown that these theorems can also be applied to three dimensional finite element structures. For this purpose eight nodded solid cubic element structures are considered. The unit loading cases required to study the modification of a single element are derived. They are later used to obtain the variation factors. These factors are utilized to predict the behavior of a cubic element structure when one or more of its element are modified or totally removed. It is verified that the accuracy of the results is the same as the original finite element discritization of the parent structure.

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