Volume 12, Issue 2 And A (Transaction A: Civil Engineering, June 2014)
IJCE 2014, 12(2 And A): 249-269 |
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Kaveh A, Massoudi M. Efficient finite element analysis using graph-theoretical force method tetrahedron elements. IJCE 2014; 12 (2) :249-269
URL: http://ijce.iust.ac.ir/article-1-1123-en.html
URL: http://ijce.iust.ac.ir/article-1-1123-en.html
Abstract: (46557 Views)
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.
Keywords: hree dimensional elements, Tetrahedron elements, Higher order elements, Finite element method, Force method, Null basis matrix, Flexibility matrix, Graph Theory.
Type of Study: Research Paper |
Subject:
Structure-Steel
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