MSC折纸结构设计及其双稳态解析与实验

折纸是一门古老艺术，其本质是将平面材料沿着事先设计好的折痕进行折叠，进而形成一个复杂的三维结构．柔性折纸结构是实现三维结构轻量化的重要途径．因此，解析折纸结构几何特性和力学性质十分必要．本文以MSC(Magic Spiral Cube)为研究对象，通过实际折痕和虚拟折痕的方法，建立了该结构的几何模型，确定了实现完全展开和完全折叠对刚性面和可变形面的设计条件，在虚拟折痕上引入了扭转刚度，证明了该扭转刚度与柔性面变形的等效性，从而得到了MSC 折纸结构的弹性势能，得到了使结构变形的力与位移本构．通过力学特性分析，发现了MSC折纸结构具有双稳态特性，这种特性是由面内变形诱发的，与虚拟折痕刚度与弹性折痕刚度的比值有直接的关系．最后，我们对MSC折纸结构进行设计和制备，通过实验，验证了理论 模型的准确性．本文的研究结果不仅进一步加深了我们对于MSC折纸结构力学特性的认识，同时也为其工程应用提供理论基础．

Design,Analysis and Experiment of Bistable MSC Origami Structurey

Origami is an ancient art, the essence of which is to fold flat materials along pre-designed folds, thus forming a complex three-dimensional structure. Flexible origami structures are an important way to achieve lightweight three-dimensional structures. Therefore, it is necessary to analyze the geometric properties and mechanical properties of the origami structure. In this paper, with MSC (Magic Spiral Cube) as the research object, the geometric model of this structure is established by the method of the actual crease and virtual crease. The design conditions of achieving fully unfolded and fully folded rigid and deformable surfaces are determined. The torsional stiffness is introduced to the virtual crease. The equivalence of this torsional stiffness and the deformation of the flexible surface is proved. Therefore, the elastic potential energy of the MSC origami structure is obtained, and the forcedisplacement constitutive relations of deforming the structure are obtained. The mechanical characterization reveals that the MSC origami structure has a bistable property, which is induced by the in-plane deformation and is directly related to the ratio of the virtual crease stiffness to the elastic crease stiffness. Finally, we design and prepare the MSC origami structure, and verify the accuracy of the theoretical model through experiments. The results of this paper not only further deepen our understanding of the mechanical properties of MSC origami structure, but also provide the theoretical basis for their engineering applications.