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

Abstract

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.