Linear‐Weingarten membranes with funicular boundaries

• Published in: Structural concrete : journal of the FIB Vol. 21; no. 6; pp. 2293 - 2306
• Main Authors: Tellier, Xavier, Douthe, Cyril, Hauswirth, Laurent, Baverel, Olivier
• Format: Journal Article
• Language: English
• Published: Weinheim WILEY‐VCH Verlag GmbH & Co. KGaA 01.12.2020; Wiley Subscription Services, Inc; Wiley
• Subjects: Arches; architectural geometry; Boundaries; Cables; Civil Engineering; Design; Differential Geometry; Engineering Sciences; Fabricability; fabrication‐aware design; funicular structures; Mathematics; Mechanical properties; Mechanics; Membranes; minimal surfaces; planar quad meshes; static equilibrium; structural design; Structures; Vaults; membranes; Structural design; fabrication-aware design; architectural geometry; static equilibrium; Linear-Weingarten surfaces; funicular structures; minimal surfaces; planar quad meshes
• ISSN: 1464-4177; 1751-7648
• DOI: 10.1002/suco.202000030

Designing a curved architectural envelope is a challenging task, as it requires a balance between structural efficiency, fabricability, and architectural requirements. In this article, we introduce a new conceptual design tool: Linear‐Weingarten membranes, with boundaries either simply supported or realized as funicular cables or arches. We present a generation method for these surfaces, with a focus on how to treat free funicular boundaries. The method uses a surface discretization by triangular meshes, and computes a shape iteratively by a combination of dynamic relaxation and guided projections. The method can be used to generate the shape of self‐stressed membranes, funicular vaults, and gridshells. For gridshells, the method allows to find geometries that combine mechanical performance and ease of fabrication. For membranes, the method allows for an exploration of a rich design space, with very limited preprocessing work required for the designer: it is hence well suited as a conceptual design tool.