A Framework for Comparing Form Finding Methods

This paper discusses existing form finding methods in the context of a research project on fabric formworks. The stiffness matrix, force density, surface stress density and dynamic relaxation form finding methods are discussed by mathematically structuring and presenting them in the same way. Based on this, a single computational framework using a sparse branch-node data structure is presented. It is shown how each method defines the internal forces and stiffness of the network, both for linear elements and triangular surface elements, and which solver is used. This single framework marginalizes any differences related to operating platforms, programming language and style, offering a better baseline for comparison of performance. As an example, the minimal surface of a cable-net is calculated, followed by a comparison of the time and iterations required per method. Implications of these results and the framework itself are discussed.