Cycle Bases of Graphs for the Analysis of Frames Structures Using Force Method

Abstract

The formation of suitable cycle bases corresponding to sparse flexibility matrices for the force method of frame analysis has always been an interesting problem in structural mechanics. These cycle bases are needed for the formation of static bases for efficient force method of structural analysis. Similarly, such bases are required in the mesh analysis of other networks. This paper reviews methods for the cycle basis selection by utilizing different embeddings on higher dimensional topological spaces, and using the ideas and concept from this study, graph theory algorithms are developed for efficient computational algorithms for the formation of subminimal, and minimal cycle bases.