Presentation
NURBS-Based Grid Shell Form Finding on Domains with Topologically Arbitrary Boundaries
DescriptionShell structures are thin curved surface structures in architectural design that efficiently carry loads through in-plane stresses, rather than relying on bending. The process of determining their shape—called form finding—ensures that shells remain structurally efficient. Some computational methods solve this using discrete meshes, while others approach it through continuum mechanics, where the Airy stress function plays a central role. An Airy stress function is a smooth surface that encodes internal stress distributions in its curvatures. Earlier methods, including work by Miki et al. (2022), applied this approach to mixed tension–compression shells and solved the equilibrium equation using the Variable Projection method (VarPro). In 2024, they further extended the method to design bending-free metal–glass grid shells with flat panels by aligning stress and curvature directions through a bilinear partial differential equation (PDE). However, these methods struggle with complex geometries, particularly where boundaries are topologically disjoint but mechanically interactive. This limitation arises not from the numerical methods themselves but from the Airy stress function, which cannot model stress fields that transmit net forces across such boundaries. To address this, we revive an overlooked supplementary stress function from Schaefer (1953) and Gurtin (1963), which, when combined with the Airy function, can represent any stress state, regardless of boundary complexity. Using the same computational framework, VarPro, we demonstrate that this extension can solve problems involving topologically complex shapes through various examples, including a Stanford bunny grid shell. Our method ensures alignment between conjugate curvature and stress directions, and also aligns the resulting grid layout with the boundary curves, enhancing both structural efficiency and architectural expression. Optionally, one can make the resulting grid strictly orthogonal, resulting in lines of curvature-principal stress alignment. Moreover, we present a variant of VarPro in which the computational efficiency and the memory usage are both significantly improved.
Event Type
Technical Papers
TimeTuesday, 16 December 20254:51pm - 5:02pm HKT
LocationMeeting Room S426+S427, Level 4