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Linear‐Weingarten membranes with funicular boundaries
Author(s) -
Tellier Xavier,
Douthe Cyril,
Hauswirth Laurent,
Baverel Olivier
Publication year - 2020
Publication title -
structural concrete
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.912
H-Index - 34
eISSN - 1751-7648
pISSN - 1464-4177
DOI - 10.1002/suco.202000030
Subject(s) - dynamic relaxation , architectural geometry , polygon mesh , computer science , conceptual design , focus (optics) , envelope (radar) , discretization , surface (topology) , computation , structural engineering , geometry , engineering , algorithm , mathematics , computer graphics (images) , mathematical analysis , physics , programming language , telecommunications , software construction , radar , software , optics , software system , human–computer interaction
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.