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Showing 2 results for Flexibility Matrix

H. Rahami, A. Kaveh, M. Ardalan Asl, S. R. Mirghaderi,
Volume 11, Issue 4 (12-2013)
Abstract

In the process of structural analysis we often come to structures that can be analyzed with simpler methods than the standard approaches. For these structures, known as regular structures, the matrices involved are in canonical forms and their eigen-solution can be performed in a simple manner. However, by adding or removing some elements or nodes, such methods cannot be utilized. Here, an efficient method is developed for the analysis of irregular structures in the form a regular structure with additional or missing nodes or with additional or missing supports. In this method, the saving in computational time is considerable. The power of the method becomes more apparent when the analysis should be repeated very many times as it is the case in optimal design or non-linear analysis.
A. Kaveh, M.s. Massoudi ,
Volume 12, Issue 2 (6-2014)
Abstract

Formation of a suitable null basis is the main problem of finite elements analysis via force method. For an optimal analysis, the selected null basis matrices should be sparse and banded corresponding to sparse, banded and well-conditioned flexibility matrices. In this paper, an efficient method is developed for the formation of the null bases of finite element models (FEMs) consisting of tetrahedron elements, corresponding to highly sparse and banded flexibility matrices. This is achieved by associating special graphs with the FEM and selecting appropriate subgraphs and forming the self-equilibrating systems (SESs) on these subgraphs. Two examples are presented to illustrate the simplicity and effectiveness of the presented graph-algebraic method.

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