Design of Self-Supporting Surfaces with Isogeometric Analysis

Yang Xia (1, 2) , Angelos Mantzaflaris (3, 4) , Bert Jüttler (5) , Hao Pan (6) , Ping Hu (1) , Wenping Wang (7)

1 Dalian University of Technology
2 HKU - The University of Hong Kong
3 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)
4 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
5 Institute of Applied Geometry [Linz]
6 Microsoft Research Asia
7 CSE - Department of Computer Science and Engineering [HKUST]

Self-supporting surfaces are widely used in contemporary architecture, but their design remains a challenging problem. This paper aims to provide a heuristic strategy for the design of complex self-supporting surfaces. In our method, non-uniform rational B-spline (NURBS) surfaces are used to describe the smooth geometry of the self-supporting surface. The equilibrium state of the surface is derived with membrane shell theory and Airy stresses within the surfaces are used as tunable variables for the proposed heuristic design strategy. The corresponding self-supporting shapes to the given stress states are calculated by the nonlinear isogeometric analysis (IGA) method. Our validation using analytic catenary surfaces shows that the proposed method finds the correct self-supporting shape with a convergence rate one order higher than the degree of the applied NURBS basis function. Tests on boundary conditions show that the boundary's influence propagates along the main stress directions in the surface. Various self-supporting masonry structures, including models with complex topology, are constructed using the presented method. Compared with existing methods such as thrust network analysis and dynamic relaxation, the proposed method benefits from the advantages of NURBS-based IGA, featuring smooth geometric description, good adaption to complex shapes and increased efficiency of computation.

Mots clés: Equilibrium approach; Isogeometric analysis; Masonry structure; Self-supporting; Architectural geometry

Domaines: Analyse numérique [math.NA]; Modélisation et simulation; Calcul formel [cs.SC]

Yang Xia, Angelos Mantzaflaris, Bert Jüttler, Hao Pan, Ping Hu, et al.. Design of Self-Supporting Surfaces with Isogeometric Analysis. Computer Methods in Applied Mechanics and Engineering, 2019, 353, pp.328-347. ⟨10.1016/j.cma.2019.05.030⟩. ⟨hal-02138360⟩