论文标题
编织纸带，用于设计具有几何弹性的一般弯曲表面
Weaving paper strips for designing of general curved surface with geometrical elasticity
论文作者
论文摘要
这项研究提出“ amigami”作为创建一般弯曲表面的新方法。它根据riemannian歧管上的非线性弹性理论进行编织纸条的形状优化。通过将培养基及其坐标切割成小曲线，将目标表面分成小弯曲条，并将每个条带嵌入平坦的纸板中，以最大程度地减少平面内变形，使应变能功能最小化。弱形式平衡方程是从带有虚拟位移矢量场的Lie衍生物得出的，并且使用具有非均匀B-Spline歧管的Galerkin方法来求解该方程。作为示范，我们制作了连链球和螺旋型表面，这些表面是通过挥舞54个纸条制成的。 Papercraft使我们想起了从类螺旋的等轴测转换，反之亦然。我们还提供了具有严格数学证明的纸带的应变估计。这个估计过程是将Euler-Bernoulli的经典束理论概括为现代的几何弹性。
This study proposes 'amigami' as a new method of creating a general curved surface. It conducts the shape optimization of weaving paper strips based on the theory of nonlinear elasticity on Riemannian manifolds. The target surface is split into small curved strips by cutting the medium along with its coordinates, and each strip is embedded into a flat paper sheet to minimize a strain energy functional due to the in-plane deformation. The weak form equilibrium equation is derived from a Lie derivative with the virtual displacement vector field, and the equation is solved numerically using the Galerkin method with a non-uniform B-spline manifold. As a demonstration, we made catenoid and helicoid surfaces which are made by waving 54 paper strips. The papercraft reminds us of the isometric transformation from the catenoid to the helicoid and vice versa. We also provide strain estimates for paper strips with rigorous mathematical proof. This estimating process is a generalization of the classical beam theory of Euler-Bernoulli to a modern geometrical elasticity.
