The matrix force method of structural analysis and some new applications

Abstract

Summary.--The purpose of this paper is : (a) to summarise the basic principles of the matrix force method of structural analysis given in Ref. 1 and to present also some new applications of the general theory ; (b) to establish and illustrate on simple examples the special method of cut-outs developed in Ref. 1. In this procedure the stresses in a structure with cut-outs are derived from the simpler analysis of the corresponding structure without cut-outs under the same loads and/or temperature distribution ; (c) to present a method for the determination of the stresses in a structure, some of whose components have been modified subsequent to an initial stress analysis. This procedure, not included in Ref. 1, is, in fact, a generalisation of the cut-out method (b) and gives the stresses in the modified system solely in terms of the stresses of the original system subject to the same loads and temperature distribution. The theory is illustrated on some simple examples which show clearly the extreme simplicity of the powerful techniques (b) and (c). We emphasise that the application of these methods requires only one stress analysis : that of tile continuous structure under the same external loads, as the modified structure. No additional stress analysis due to other, e.g., perturbation, loads is involved.