Efficient Graph-Theoretical Force Method: Wedge-Shaped Finite Element

Abstract

Formation of a suitable null basis (static basis) for equilibrium matrix is the main part of finite element analysis via force method. For an optimal analysis, the selected null basis matrices should be sparse, well-structured, e.g., banded, and well-conditioned flexibility matrices. In this paper, an efficient method is developed for the formation of null bases of wedge element, 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 on these subgraphs. The efficiency of the presented method is illustrated through three examples.

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Correspondence to M. S. Massoudi.

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Haji Ebrahim Araghi, F., Massoudi, M.S. & Kaveh, A. Efficient Graph-Theoretical Force Method: Wedge-Shaped Finite Element. Iran J Sci Technol Trans Civ Eng 45, 1121–1138 (2021). https://doi.org/10.1007/s40996-020-00395-9

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Keywords

  • Finite element force method
  • Null (static) basis
  • Flexibility matrix
  • Graph theory
  • Wedge elements