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Vol. 56 (2015) No. 4 December n. 186


Hangai Prize Papers for 2015: Buckled Double-Curved Surface Using a Controlled Pattern of In-Plane Strain

< Table of Contents for Vol. 56 (2015) No. 4 December n. 186
  • Journal Name: Journal of the International Association for Shell and Spatial Structures (J. IASS)
  • ISSN: (Electronic Version) 1996-9015
  • ISSN: (Print Version) 1028-365X
  • Issue: Vol. 56 (2015) No. 4 December n. 186
  • Pages: 239-247
  • Title: Hangai Prize Papers for 2015: Buckled Double-Curved Surface Using a Controlled Pattern of In-Plane Strain
  • Author(s): Y. Takahashi and T. Tachi
  • Keywords: computational design, double-curved surface, dynamic relaxation, conformal map, self-organization
Abstract
In this paper, we propose a method to design a double-curved surface that is self-organized through the buckling of a thin material due to a controlled pattern of in-plane strain. We assume that the in-plane strain of a thin material is isotropic. Therefore, the intrinsic deformation is described by the distribution of the scalar value of a local scale factor, which can be obtained by calculating a conformal map from the initial state to the given 3D state. The construction of the pattern is as follows. We calculate the conformal map from the given shape to the original sheet. The map is calculated as the equilibrium state of a mass-spring (angular and length) model with defined rest angles and lengths to discretize a conformal map. We obtain the scale-factor distribution pattern from the conformal map. Using this pattern, we simulate the buckling deformation process and observe its behavior. We note additional geometric conditions needed to make the generated shape approximate the given 3D shape.

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