Elastica surface generation of curved-crease origami
Elastica surface generation of curved-crease origami
复制标题
DOI：
10.1016/j.ijsolstr.2017.11.029
复制
发表时间：
2018-04-01
影响因子：
3.6
通讯作者：
Gattas, Joseph M.
中科院分区：
文献类型：
--
作者：
Lee, Ting-Uei;You, Zhong;Gattas, Joseph M.
弯曲折纸折纸在工程和建筑领域的许多新颖应用中得到了研究，因为它们是可开发的，但在折叠时具有非零主曲率和相应的能量存储能力。然而，几何建模技术是有限的，大多数方法需要对目标曲面进行数值离散，以允许在顶点处强制实施可展性约束。离散表面可以通过松弛最小弯曲能量来近似物理表面，但是这种方法很麻烦并且其准确性很大程度上未知。本文提出了一种用于弯曲折痕折纸的分析几何构造方法，避免了表面离散化的需要。新方法将大弹性弯曲变形的一维弹性解与直折纸投影和反射过程相结合；因此，它可以简洁、准确地捕捉弹性弯曲折痕折纸的主表面曲率和展开特性。使用 3D 扫描物理原型的表面误差分析来验证模型，结果显示，对于一系列弹性表面轮廓的 2 毫米厚模型，该模型的精确度在片材厚度的 +/- 50% 范围内。还探讨了模型的局限性，包括最大压缩极限的推导；折叠运动数值模拟精度研究；以及对某些折纸形式中发生的自由边缘扭曲行为的研究。 (C) 2017 Elsevier Ltd. 保留所有权利。
Curved-crease origami are studied for many novel applications across engineering and architecture, as they are developable but possess a non-zero principal curvature and a corresponding energy storage capability when folded. However, geometric modelling techniques are limited, with most methods requiring numerical discretisation of a target curved surface to allow developability constraints to be enforced at vertices. The discretised surface can approximate a physical surface through relaxation for minimum bending energy, however such methods are cumbersome and their accuracy is largely unknown. This paper presents an analytical geometric construction method for curved-crease origami that avoids the need for surface discretisation. The new method combines a 1D elastica solution for large elastic bending deformation with a straight-crease origami projection and reflection process; it can thus concisely and accurately capture the principal surface curvature and developability characteristics of elastically-bent curved-crease origami. A surface error analysis of 3D scanned physical prototypes is used to validate the model, which is shown to be accurate to within +/- 50% of the sheet thickness for a 2 mm thick model for a range of elastica surface profiles. Limitations of the model are also explored including the derivation of a maximum compressibility limit; investigation of accuracy of numerical folding motion simulation; and an investigation of a free edge distortion behaviour which occurs in certain origami forms. (C) 2017 Elsevier Ltd. All rights reserved.