Network Analysis of Structures

When applied to structures, the node and mesh methods of a network theory are special cases of, respectively, the displacement and force methods of analysis, with connectivity, in the topological sense, efficiently introduced. One of the primary differences between these methods is the way in which the configuration geometry, which is not relevant in electrical networks, is accounted for. In this formulation, the physical variables (actual joint displacements and member forces) are retained, making it necessary to include geometric as well as topological information in the structural analogues of the incidence matrices. A structural network theory is developed using only well known structural theorems. First, an existing node method is reformulated using forces at a single branch end as branch variables. This allows a mesh method to be simply developed. It is finally shown how the theory obtained is analogous to that for electrical networks and implicitly contains a generalization of graph theory appropriate to structural networks. A simple numerical example is included.