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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 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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