Quad Meshes as Optimized Architectural Freeform Structures

Abstract

This thesis tackles the design of freeform surface-like and load-bearing structures realized with cladding panels and supported by a framework substructure, often called gridshells. The actual fabrication of freeform gridshells is a challenging task, and easily leads to unsustainable costs. A well known strategy to realize a gridshell is to use as layout a so-called principal mesh. This is a quadrilateral mesh whose edges follow the principal curvature directions of a continuous surface. We achieve in this way flat cladding panels and a substructure with simplified connections. This thesis shows that quadrilateral meshes, besides allowing manufacturing simplification, are also optimal solutions both for static performance and smooth visual appearance. In particular, we show that the best static performance is achieved for quad meshes discretizing membranes along principal stress lines, and we get an absolute minimum on such membranes where the integral of absolute principal stresses is minimal. We also show that the best smooth visual appearance is achieved for principal meshes; the absolute minimum is now reached for principal meshes discretizing surfaces where the integral of absolute principal curvatures is minimal. Therefore, from membranes where stress and curvature directions are aligned, and where the total absolute stress is minimal, we can extract principal meshes with the best static performance and with optimal visual appearance. We present then computational tools for the design of such highly efficient gridshells.