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DTSTART:19911015T033000
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BEGIN:VEVENT
DTSTAMP:20251218T030656Z
LOCATION:Meeting Room S426+S427\, Level 4
DTSTART;TZID=Asia/Hong_Kong:20251216T165100
DTEND;TZID=Asia/Hong_Kong:20251216T170200
UID:siggraphasia_SIGGRAPH Asia 2025_sess130_papers_1147@linklings.com
SUMMARY:NURBS-Based Grid Shell Form Finding on Domains with Topologically 
 Arbitrary Boundaries
DESCRIPTION:Masaaki Miki (University of Tokyo) and Toby Mitchell (Thornton
  Tomasetti)\n\nShell structures are thin curved surface structures in arch
 itectural design that efficiently carry loads through in-plane stresses, r
 ather than relying on bending. The process of determining their shape—call
 ed form finding—ensures that shells remain structurally efficient. Some co
 mputational methods solve this using discrete meshes, while others approac
 h it through continuum mechanics, where the Airy stress function plays a c
 entral role. An Airy stress function is a smooth surface that encodes inte
 rnal stress distributions in its curvatures. Earlier methods, including wo
 rk by Miki et al. (2022), applied this approach to mixed tension–compressi
 on shells and solved the equilibrium equation using the Variable Projectio
 n method (VarPro). In 2024, they further extended the method to design ben
 ding-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 w
 here boundaries are topologically disjoint but mechanically interactive. T
 his limitation arises not from the numerical methods themselves but from t
 he Airy stress function, which cannot model stress fields that transmit ne
 t forces across such boundaries. To address this, we revive an overlooked 
 supplementary stress function from Schaefer (1953) and Gurtin (1963), whic
 h, when combined with the Airy function, can represent any stress state, r
 egardless of boundary complexity. Using the same computational framework, 
 VarPro, we demonstrate that this extension can solve problems involving to
 pologically 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 e
 xpression. 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.\n\nRegistration Category: F
 ull Access, Full Access Supporter\n\nSession Chair: Daniel Ritchie (Brown 
 University)\n\n
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