Analysis of frames with semi-rigid joints: A graph-theoretical approach

For an efficient force method of frame analysis, special cycle bases should be generated for the formation of localized self-equilibrating systems, leading to sparse flexibility matrices. In this paper, an algorithm is presented using a fundamental cycle basis, where the selected cycles are improved via an algebraic exchange approach. Optimal analysis is performed for frames with semi-rigid joints. s method, flexibility matrices are generated which are highly sparse. An ordering algorithm is also used for profile reduction to acquire an efficient method for the solution of the corresponding equations.