负泊松比可变弧角曲边内凹蜂窝结构的力学性能

在环形蜂窝结构的基础上，提出了一种具有负泊松比效应的可变弧角曲边内凹蜂窝结构。分析了刚架结构的弯曲内力，利用能量法给出了曲边内凹蜂窝结构的横/纵向等效弹性模量和等效泊松比的解析公式。当弧角为180°时，所提出的曲边内凹蜂窝结构可退化为已有的环形蜂窝结构。所得解析解、已有理论解和有限元结果三者有较好的吻合度，表明了所提出方法的有效性。基于所得解析解讨论了微结构几何参数对等效弹性模量和等效泊松比的影响，研究结果表明：等效弹性模量受弧角的影响显著；等效泊松比受弧角、竖直壁板长度和两竖直壁板间宽度的影响较为明显，而受连接部分长度的影响不明显。

Mechanics Properties of Negative Poisson's Ratio Honeycomb Structures with Variable Arc Angle Curved Concave Sides

A variable arc angle curved concave honeycomb structure with negative Poisson's ratio effect was proposed based on the circular honeycomb structure.The bending internal forces of the rigid frame structures were analyzed and the analytical formulas of the transverse/longitudinal equivalent elastic modulus and the equivalent Poisson's ratio were obtained by using the energy method. The proposed curved concave honeycomb structure might be degenerated into the existing circular honeycomb structure when the arc angle is as 180°. The present analytical solutions were in agreement with the existing theoretical solutions and finite element results, which showed the validity of the present method. Based on the obtained analytical solutions, the effects of the microstructure geometric parameters on the equivalent elastic modulus and the equivalent Poisson's ratio were discussed.The research results show that the equivalent elastic modulus is significantly affected by the arc angles. The equivalent Poisson's ratio is also obviously affected by the arc angles, the lengths of vertical walls and the widths between two vertical walls, while the influences of the connected part lengths are not obvious.