Mathematical similarities in engineering network analysis

Abstract

This paper examines the proposition that structural trusses and pipe networks for water supply are closely related in a mathematical sense. It shows that in terms of representation, physical quantities, constitutive equations, analysis problem formulations and methods of analysis they both belong to the same class of nonlinear potentiated networks, the truss being a special linear case for problems of analysis. The analysis of nonlinear potentiated networks may therefore be efficiently performed by linearization of the relevant nonlinear quantities and the iterative use of well-known truss analysis methods. The commonality established between structural trusses and water supply systems has potential for exploitation in respect of other network-related problems of optimum design, reliability evaluation and design for resilience.