Statics Aware Grid Shells

We introduce a framework for the generation of polygonal grid-shell architectural structures, whose topology is designed in order to excel in static performances. We start from the analysis of stress on the input surface and we use the resulting tensor field to induce an anisotropic non-Euclidean metric over it. This metric is derived by studying the relation between the stress tensor over a continuous shell and the optimal shape of polygons in a corresponding grid-shell. Polygonal meshes with uniform density and isotropic cells under this metric exhibit variable density and anisotropy in Euclidean space, thus achieving a better distribution of the strain energy over their elements. Meshes are further optimized taking into account symmetry and regularity of cells to improve aesthetics. We experiment with quad meshes and hex-dominant meshes, demonstrating that our grid-shells achieve better static performances than state-of-the-art grid-shells.