Load-path optimisation of funicular networks

Abstract

This paper describes the use of load-path optimisation for discrete, doubly curved, compression-only structures, represented by thrust networks. The load-path of a thrust network is defined as the sum of the internal forces in the edges multiplied by their lengths. The presented approach allows for the finding of the funicular solution for a network layout defined in plan, that has the lowest volume for the given boundary conditions. The compression-only thrust networks are constructed with Thrust Network Analysis by assigning force densities to the network’s independent edges. By defining a load-path function and deriving its associated gradient and Hessian functions, optimisation routines were used to find the optimum independent force densities that minimised the load-path function subject to compression-only constraints. A selection of example cases showed a dependence of the optimum load-path and force distribution on the network topology. Appropriate selection of the network pattern encouraged the flow of compression forces by avoiding long network edges with high force densities. A general, non-orthogonal network example showed that structures of high network indeterminacy can be investigated both directly for weight minimisation, and for the understanding of efficient thrust network patterns within the structure.