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

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

Structural Analysis and Design of Rigid Frames Based on Plastic Theorem

This paper is concerned with the plastic analysis and the design problems of multistory rigid frames by use of the linear programming technique. The objective of this work is to develop the plastic analysis and design of rigid frames, paying attention to the graph theory, and to reduce the computer core size and also to save the execution time by using a decomposition technique. A few examples are presented to illustrate the method proposed here

A Network-Topological Study on Statical Analysis of Rigid Framed Structure

After the studies of G.H. Kron, who applied the network theory to structural analysis, many investigations in this field were done. They are the analysis by analogy of framed structures to electrical circuits, and the purpose of these studies is to establish the effective formulations of framed structural analysis, with respect to the Network-Topological properties of structures which are suited to the numerical analysis by use of the digital computer which requires systematic notation- and calculation methods. In the network-topological analysis of electrical circuits, there are two basic different methods, i.e. “Node Method” and “Mesh Method”. As a variation of “Node Method”, the “Tree Method” exists. In the structural analysis, the two basic methods are already formulated as “Displacement Method” and “Force Method” respectively, but the last one is not used. When these methods are used for the analysis of large structures by use of computer, there arise many problems, which are the problems of the capacity of the computer and also that of calculation-time. To decrease the difficulties of these problems, the method of tearing and interconnecting of the structure is used. In this paper, a tearing and interconnecting method by an information, which is got from Incidence Matrix, is presented. And the application of Tree Method in the problems of electric circuits to the structural analysis and a tearing and interconnecting method for it by successive application of the Housholder's formula is also considered