零泊松比手风琴蜂窝等效模量

柔性蒙皮是变形机翼和风力机叶片的关键组成部分。一维变形的柔性蒙皮不仅要求其支撑结构具有良好的面内变形和面外承载能力，还需要具有零泊松比特性。手风琴蜂窝具有零泊松比特性，可用作一维变形柔性蒙皮支撑。为全面分析其面内外弹性变形特性，综合考虑结构的内力弯矩、轴力和剪力，通过卡氏第二定理对其x向等效弹性模量和x-y面内等效剪切模量进行了推导；利用最小余能原理和最小势能原理确定了x-z面内的等效剪切模量；此外还推导了其y和z向的等效弹性模量以及y-z面内的等效剪切模量；然后通过ANSYS有限元仿真对等效模量理论公式进行了验证；最后将本文理论模型与现有模型进行了比较。结果表明，理论公式和有限元仿真吻合较好，在结构设计时采用较大的斜梁高度系数h和斜梁间距系数g，较小的厚度系数t以及较大的竖直梁厚度系数η，有望获得具有较小面内刚度和较大面外刚度的手风琴蜂窝结构。该结果可用于手风琴蜂窝面内外等效模量的快速预测，为一维变形柔性蒙皮的结构设计提供相应的参考。此外，本文理论模型相比传统模型更为精确且具有更加广泛的应用范围。

Equivalent Moduli of Accordion Honeycomb with Zero Poisson’s Ratio

Flexible skin is an essential component of morphing wing and morphing wind turbine blade. The support structure of the flexible skin undergoing one-dimensional morphing is required of good in-plane morphing capability and good out-of-plane load-bearing capability as well as zero Poisson’s ratio. To overcome these problems, an accordion honeycomb with zero Poisson’s ratio was proposed as a potential candidate for support structure of one-dimensional morphing flexible skin. To comprehensively analyze the in-plane and out-of-plane elastic properties of the proposed structure, the equivalent elastic modulus in the x-direction and the equivalent shear modulus in the x-y plane were derived by the Castigliano’s second theorem considering the internal bending moment, axial force and shear force; the equivalent shear modulus in the x-z plane was determined by principle of minimum complementary energy and principle of minimum potential energy; besides, the equivalent elastic moduli in the y and z direction, and the equivalent shear modulus in the y-z plane were also obtained by conventional derivation methods. The theoretical formulas were then verified by finite element analysis in ANSYS. Finally, comparisons with several conventional theoretical models were carried out to show the superiority of the theoretical model adopted in this paper. Results show that theoretical formulas are of good agreement with finite element analysis, proving the validity of the derivation. Accordion honeycomb of lower in-plane stiffness and higher out-of-plane stiffness will be obtained by employing larger height ratio of inclined beam h, spacing ratio of inclined beam g, thickness ratio of vertical beam η, and smaller thickness ratio t. These results can be used for rapid predictions of the mechanical properties of the accordion honeycomb, providing corresponding reference for structural design of one-dimensional morphing flexible skin. Furthermore, the theoretical model proposed in this paper is more accurate and has a wider range of application on the analyses of similar cellular honeycomb structures than conventional models.