Integrated force method versus displacement method for finite element analysis

A novel formulation termed the ‘integrated force method’ (IFM) has been developed in recent years for analyzing structures. In this method all the internal forces are taken as independent variables, and the system equilibrium equations (EEs) are integrated with the global compatability conditions (CCs) to form the governing set of equations. In IFM the CCs are obtained from the strain formulation of St. Venant, and no choices of redundant load systems have to be made, in contrast to the standard force method (SFM). This property of IFM allows the generation of the governing equation to be automated straightforwardly, as it is in the popular stiffness method (SM). In this paper IFM and SM are compared relative to the structure of their respective equations, their conditioning, required solution methods, overall computational requirements, and convergence properties as these factors influence the accuracy of the results. Overall, this new version of the force method produces more accurate results than the stiffness method for comparable computational cost.