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Title: Optimization method for shape design of Auxetic Bending-Active Gridshells using discrete differential geometry
Authors: Sakai, Yusuke
Ohsaki, Makoto
Author's alias: 堺, 雄亮
大﨑, 純
Keywords: Auxetic structure
Bending-active gridshell
Discrete differential geometry
Particle swarm optimization
Issue Date: Dec-2021
Publisher: Elsevier BV
Journal title: Structures
Volume: 34
Start page: 1589
End page: 1602
Abstract: The purpose of this paper is to propose an optimization method for shape design of Auxetic Bending-Active Gridshells (ABAGs). A 2-dimensional auxetic structure has negative Poisson’s ratio for in-plane deformation. Positive Gaussian curvature distributed on a curved surface of ABAG is obtained by out-of-plane deformation of the initial flat grid composed of reentrant structural units. We introduce discrete differential geometry into shape design of the surface of ABAG, which can be easily discretized into triangular meshes in accordance with the discrete member locations. The objective function of the proposed optimization problem is formulated using discrete Gaussian curvature, which is defined as the angle defect at node. In addition, discrete mean curvature vector is used for specifying the direction of convexity. We use particle swarm optimization for solving the problem. It is shown in the numerical examples, that surfaces with specified distribution of convex region on an ABAG can be obtained using the proposed method.
Rights: © 2021. This manuscript version is made available under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International license.
The full-text file will be made open to the public on 1 December 2022 in accordance with publisher's 'Terms and Conditions for Self-Archiving'.
This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。
DOI(Published Version): 10.1016/j.istruc.2021.08.067
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