Corrugations offer a convenient way to make thin, lightweight sheets into stiff structures. However, traditional, v-shaped corrugations made from straight creases result in highly anisotropic stiffness which leads to undesirable flexibility in some directions of loading. In this paper, we explore the bending stiffness of curved-crease corrugations with a planar midsurface—developable corrugations made by folding thin sheets about curves and without linerboard covers on the top or bottom. The curved-crease corrugations break symmetry in the pattern and can redistribute stiffness to resist bending deformations in multiple directions. To study these systems, we formulate a framework for predicting the bending stiffness of any planar-midsurface corrugation from its multiple geometric features at different scales. We use the framework to create two predictive methods that provide valuable insight into the global stiffness of corrugations without a detailed analysis. Results from these methods match well with experimental, three-point bending tests of five corrugation geometries made from polyester film. We found that corrugations with elliptical or parabolic curved-creases that intersect with one edge of the pattern are best at redistributing stiffness in multiple directions. While a straight-crease pattern has a stiffness of about 4 N/mm in one direction and about 0 N/mm in the other, a parabolic crease pattern has a stiffness of about 2.5 N/mm in both directions. These curved-crease corrugations can enable the self-assembly and fabrication of practical, stiff structures from simple, developable sheets.

中文翻译：

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弯曲折痕重新分布波纹中的整体弯曲刚度：理论和实验

波纹提供了一种将薄而轻的板材制成坚硬结构的便捷方法。然而，由直折痕制成的传统 V 形波纹会导致高度各向异性的刚度，从而导致在某些加载方向上出现不良的柔韧性。在本文中，我们探讨了具有平面中间表面的弯曲折痕波纹的弯曲刚度 - 可展开波纹是通过围绕曲线折叠薄片制成的，并且顶部或底部没有挂面纸覆盖物。弯曲的折痕波纹破坏了图案的对称性，可以重新分配刚度以抵抗多个方向的弯曲变形。为了研究这些系统，我们制定了一个框架，用于根据不同尺度的多个几何特征预测任何平面中表面波纹的弯曲刚度。我们使用该框架创建了两种预测方法，无需详细分析即可提供对波纹整体刚度的宝贵见解。这些方法的结果与由聚酯薄膜制成的五种波纹几何形状的实验性三点弯曲测试非常吻合。我们发现，与图案的一个边缘相交的带有椭圆形或抛物线弯曲折痕的波纹最适合在多个方向上重新分配刚度。直线折痕图案在一个方向上的刚度约为 4 N/mm，而在另一个方向上的刚度约为 0 N/mm，而抛物线折痕图案在两个方向上的刚度约为 2.5 N/mm。这些弯曲的折痕波纹可以实现从简单、可开发的板材自组装和制造实用、坚固的结构。