Network-Topological Formulation of Structural Analysis

Structural analysis is formulated using topological and algebraic laws which are counterparts of those used in treating electric network problems. The structural problem has three aspects: Topological interconnections, geometric relationship, and mechanical properties of members. Formulation as a network problem follows directly once these aspects have been identified and characterized by matrix equations. Thus, a unified and generalized approach to structural analysis is obtained. Geometric manipulations and load-deflection relationships of structural members are reviewed, and abstract topological and algebraic properties of the network problem are described. Then, equilibrium, continuity, and load-deflection relationships are shown to correspond to basic network properties. Force and displacement methods of analyzing linear, framed structures are developed as counterparts of mesh and node methods of network analysis. This formulation, adaptable to a digital computer, paves the way for applying to structural problems many existing and future developments in network analysis, design, and synthesis. Specifically, it permits the use of Kron's method of piecewise analysis.