Efficient finite element analysis using graph-theoretical force method; hexahedron elements

• Formation of a suitable null basis for equilibrium matrix is the main problem in force method.
• An efficient method is developed for the formation of null bases consisting of hexahedron elements.
• corresponding flexibility matrices are highly sparse and banded.
• special graphs are defined for selecting appropriate subgraphs for forming localized SESs.

Formation of a suitable null basis for equilibrium matrix 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 null bases of finite element models (FEMs) consisting of hexahedron 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.