Load‐Finding: a Form‐Finding Method for Plane‐Faced Funicular Gridshells

Gridshells and shells are geometrical objects that must comply with mechanical and manufacturing constraints. Being funicular, and having planar panels (for discretized structures) is a combination of constraints often searched and studied in the literature. The study of funicular structures is the subject of graphic statics, with the panel planarity constraint added in methods using the Airy stress function. It is proposed in this paper to reverse the existing procedures and to present a “load‐finding” method: rather than creating structures with almost flat panels, we design almost funicular grids with perfectly flat panels. We hence use lifting methods with strict control over geometrical properties and we prescribe heights and forces at the boundary to calculate the load under which the structure operates without bending, i.e. the funicular load associated with the structure. We can then optimize the lift to find the load which will be the closest to a target distribution. We hence get a space of planar faced polyhedra in equilibrium under a certain load that projects onto the input mesh, and which is controlled by heights and forces defined on guide curves. The funicular load deviation is a purely static tool for locating and quantifying loads that cause moments in the structure. A finite element analysis of the structures produced opens a discussion on the influence of the parameters and metric chosen in our method, as well as on certain biases introduced by our method and a method using an elastic calculation.