新型零泊松比蜂窝结构的设计与面内力学性能

A novel honeycomb structure for zero Poisson's ratio: design and in-plane mechanical properties

  • 摘要: 为解决变形机翼蒙皮芯层在保证高面外承载能力的同时实现高面内柔顺性所面临的结构设计矛盾,设计了一种新型零泊松比蜂窝结构,并对其面内弹性性能进行了系统分析。蜂窝结构由弯曲韧带、圆环节点与水平韧带三种子结构组成。基于Castigliano第二定理推导出无因次解析表达式,同时在Ansys中开展有限元均质化模拟,结合FDM打印试件的标准拉伸试验进行验证,通过三路径互证构建参数-性能映射关系。结果表明,新型零泊松比蜂窝结构的面内横向模量Ex对水平韧带参数ξ高度敏感,ξ从0.10增至0.14时Ex提升约36%。面内轴向模量Ey与剪切模量Gxy主要由弯曲韧带主导变形,两者随壁厚增大而提高,随圆心角增大而下降。三者偏差均小于10%,验证了方法可靠性。在相同密度下与反四手性蜂窝对比,新型结构横向模量Ex提升约8.8倍,剪切模量提高约20%,同时泊松比近乎为零,综合面内性能显著提升。

     

    Abstract: To address the structural design conflict of morphing wing skin cores, which require high out-of-plane load-bearing capacity while maintaining high in-plane compliance, a new zero Poisson’s ratio honeycomb structure is proposed, and its in-plane elastic properties are systematically investigated. The honeycomb architecture consists of three fundamental substructures: curved ligaments, circular ring nodes, and horizontal ligaments. Based on Castigliano's second theorem, dimensionless analytical expressions were derived. Finite element homogenization simulations were conducted in Ansys and validated against standard tensile tests performed on FDM-printed specimens. The triangulation of these three independent approaches established a comprehensive parameter-to-performance mapping. The results demonstrate that the in-plane moduli of the novel zero Poisson's ratio honeycomb structure are sensitive to geometric parameters. The transverse elastic modulus Ex is highly sensitive to the horizontal ligament parameter ξ, increasing by approximately 36% as ξ rises from 0.10 to 0.14. The axial modulus Ey and the equivalent shear modulus Gxy are primarily governed by the curved ligaments, enhancing with increasing wall thickness but diminishing with a larger central angle of the curved ligaments. The deviations among the theoretical, numerical, and experimental results are all below 10%, validating the reliability of the methodologies employed. Under identical relative density conditions, compared with the anti-tetrachiral honeycomb, the new structure demonstrates a remarkable enhancement: its transverse elastic modulus Ex exhibits an approximately 8.8-fold increase, and its shear modulus shows a roughly 20% improvement, while maintaining a near-zero Poisson's ratio. This signifies a significantly improved overall in-plane mechanical performance.

     

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