Topological Aspects of Structural Linear Analysis: Improving the Conditioning of the Equations of Compatibility of a Multi‐Member Skeletal Structure by Use of the Knowledge of Topology

The selection of a system of cut releases which would render a continuous skeletal structure statically determinate is governed principally by the topological and geometric characteristics of the structure, and to a lesser extent by its material properties. Only the topological aspects will be considered here, the other factors being purposely excluded. It is shown how the knowledge of the topology of the structure can be exploited to improve the conditioning of the associated equations of compatability. Owing to difficulties inherent in the design of any automatic procedure for the reduction to a canonical form, a method of condensation has been evolved for complex multi‐member structures. In this way the large scale features of the structure are taken into account without neglecting the effect of local characteristics.