Efficient finite element analysis by graph-theoretical force method; triangular and rectangular plate bending elements

Abstract

The calculation of 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. There are many algorithms for the formation of null bases among which the algebraic methods benefit from the generality. However, the efficiency of these methods is highly dependent on the size of problems, and their computational times are very high for such problems. In this paper, a graph-theoretical method is presented for the formation of sparse, banded and highly accurate null basis matrices for finite element models with triangular and rectangular plate bending elements. These bases are generated much faster than those obtained by the algebraic methods. The efficiency of the present method is illustrated through some examples.