A Study on the Bandwidth Reduction of the Stiffness Matrix of a Framed Structure

Abstract

How to give the numerical number for joints of a framed structure in order to reduce the bandwidth of its stiffness matrix, has been studied and a number of methods have been proposed already. Though the minimum bandwidth is wholly governed by the connectivity relationship between joints, only a few studies have taken that fact into the consideration. The connectivity relationship of a framed structure can be sufficiently shown by the use of a linear graph, which is composed of nodes and lines. Its characteristics can be understood by introducing the concept of graph theory. In this paper, the authors propose a graphical method to obtain the minimum bandwidth of tree structures. This is a kind of statically determinate system including no closed path, by the application of some definitions in graph theory. By use of the this sequential file method, all the nodal sequences are efficiently filed along the longest nodal sequence among the graph. The number of rows of filed nodal sequences present the bandwidth of the original structure.