Efficient finite element analysis using graph-theoretical force method; rectangular plane stress and plane strain Lagrange family elements

Formation of a suitable null basis for equilibrium matrix is the main part 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 rectangular plane stress and plane strain Lagrange family 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. The efficiency of the present method is illustrated through three examples.