Department of Engineering Mechanics and Center for Nano and Micro Mechanics, AML, Tsinghua University, Beijing 100084, China.
Columbia Nanomechanics Research Center, Department of Earth and Environmental Engineering, Columbia University, New York, NY 10027, USA.
Sci Rep. 2016 Sep 14;6:33312. doi: 10.1038/srep33312.
Origami structures enrich the field of mechanical metamaterials with the ability to convert morphologically and systematically between two-dimensional (2D) thin sheets and three-dimensional (3D) spatial structures. In this study, an in-plane design method is proposed to approximate curved surfaces of interest with generalized Miura-ori units. Using this method, two combination types of crease lines are unified in one reprogrammable procedure, generating multiple types of cylindrical structures. Structural completeness conditions of the finite-thickness counterparts to the two types are also proposed. As an example of the design method, the kinematics and elastic properties of an origami-based circular cylindrical shell are analysed. The concept of Poisson's ratio is extended to the cylindrical structures, demonstrating their auxetic property. An analytical model of rigid plates linked by elastic hinges, consistent with numerical simulations, is employed to describe the mechanical response of the structures. Under particular load patterns, the circular shells display novel mechanical behaviour such as snap-through and limiting folding positions. By analysing the geometry and mechanics of the origami structures, we extend the design space of mechanical metamaterials and provide a basis for their practical applications in science and engineering.
折纸结构通过在二维（2D）薄片和三维（3D）空间结构之间形态和系统地转换，丰富了机械超材料领域。在这项研究中，提出了一种基于广义村正折纸单元的面内设计方法，用于逼近感兴趣的曲面。使用这种方法，两种类型的折线在一个可重新编程的过程中统一起来，生成了多种类型的圆柱结构。还提出了两种类型的有限厚度对应物的结构完整性条件。作为设计方法的一个示例，对基于折纸的圆柱壳的运动学和弹性特性进行了分析。将泊松比的概念扩展到圆柱结构，展示了它们的负泊松比特性。采用由弹性铰链连接的刚性板的解析模型，与数值模拟一致，用于描述结构的力学响应。在特定的载荷模式下，圆形壳体会显示出一些新颖的力学行为，如突跳和极限折叠位置。通过分析折纸结构的几何形状和力学特性，我们扩展了机械超材料的设计空间，并为它们在科学和工程中的实际应用提供了基础。
