Recent Developments in the Force Method of Structural Analysis

Abstract

The development of the force method of structural analysis has been hindered by the difficulty of generating a suitable maximal set of independent self-equilibrating stress systems, known as statical or null basis. Recent developments to overcome this problem can be classified as topological, combinatorial, algebraic, mixed and integrated force methods. Combinatorial methods are efficient and provide insight to the problems involved, however, further research is needed before a unified formulation can be made. Algebraic methods are simple and general in nature, however, their automation requires considerable amount of operations and storage. The insight to the problems are not present in these methods. Mixed methods incorporate the efficiency of the existing combinatorial methods and generality of the algebraic approaches. In this paper, the progress made in the analysis of structures by means of the force method is reviewed, and directions required for further advances are specified. It is hoped that such advances will make the force method competitive to the displacement approach in fields such as non-linear analysis and optimization of structures. This will hopefully put the force method as an efficient counterpart to the displacement approach in computational mechanics.