An Automated Bipartite Graph-based Force Method for Efficient Analysis of Planar Trusses

Abstract

Efficient analysis of structures refers to the methods which reduce the computational cost of the structural analysis. To achieve this, the structural matrices should have some specific attributes. For this purpose, a graph theoretical force method is employed in this study, which leads to a sparse flexibility matrices. In this method, the bipartite graph corresponding to the equivalent graph of the original structural model is constructed. A cycle basis of the bipartite graph corresponds to subgraphs of the structural model on which localized self-equilibrating stress systems can be formed, referred to as a generalized cycle basis of the structure. This enabled the authors of this study to develop a fully automated procedure for the efficient analysis of planar trusses using a graph-theoretical force method. The proposed approach combines classical structural mechanics with the concepts of graph theory. In other words, a bipartite graph approach is employed for a systematic identification of self-equilibrating stress systems in the truss structures. The entire procedure is implemented in MATLAB, allowing all steps to be performed automatically and three different planar trusses are solved using proposed method.