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COMPUTATIONAL METHODS FOR ENGINEERING TECHNOLOGY
Edited by: B.H.V. Topping and P. Iványi
Recent Advances in the Finite Element Force Method
A. Kaveh and M.S. Massoudi
Centre of Excellence for Fundamental Studies in Structural Engineering, School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran
A. Kaveh, M.S. Massoudi, "Recent Advances in the Finite Element Force Method", in B.H.V. Topping and P. Iványi, (Editor), "Computational Methods for Engineering Technology", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 12, pp 305-324, 2014. doi:10.4203/csets.35.12
Keywords: finite element force method, graph theory, rectangular element, triangular element, tetrahedron element, hexahedron element, null basis matrix.
Formation of a suitable null basis for an equilibrium matrix is the main problem of finite elements analysis using the 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, efficient methods are developed for the formation of null bases of finite element models (FEMs) consisting of triangular, rectangular, tetrahedron, and hexahedron elements with various orders, 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.
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