A comparative study of combinatorial and algebraic force methods

Abstract

In this paper the computation of sparse statical (null) bases is studied for use in the force method of structural analysis. A comparative study of combinatorial methods and algebraic approaches is made. Combinatorial methods employ the graph theory and construct statical bases on the elements of selected cycle bases of the structural models. Algebraic methods use matrix algebra for direct formulation of statical bases from the equilibrium equations. The sparsity of the selected bases generated by three combinatorial methods and three algebraic approaches, and the running time, are compared through many examples.