Constrained Force Density Method optimisation for compression-only shell structures

Abstract

The Force Density Method is a powerful tool for the design of efficient long-spanning shells and gridshells, as it can generate structural forms that utilise membrane action. However, force density distributions are defined by the user, which does not lead to the most effective structure with regards to material usage, or in enabling the control of member lengths. This paper presents a Constrained Force Density Method (CFDM) optimisation, that assembles the force density distribution for the user, and allows constraints on forces, force densities, lengths and the spatial movements of vertices. The focus is on shell and gridshell type structures, with compression-only internal force states. The optimisation algorithm’s objective function combines the minimisation of the total volume of material in the structure and control of the member lengths. Described is a computational implementation that efficiently solves the constrained non-linear programming problem, by exploiting symmetry, fast solvers, and analytical gradient functions. Results of three practical case studies show that the CFDM can lead to material savings of between 21% to 66% when compared to uniform force density distributions, while providing full control on the lengths of the structural elements and the spatial movement of vertices. It opens up possibilities in engineering design, enabling the exploration of many new lightweight structural forms, and offering many sustainability, fabrication and construction advantages.