负泊松比手性结构圆薄板的参数设计

薄膜张紧在曲线边界上必然产生反枕效应，这会降低网状可展开天线的型面精度。为了减少影响，通常采用增加径向肋或者网面牵引索等措施，但这些方法会增加可展开天线的复杂程度。王一鸣、黄鹏飞提出了一种弱刚度复合膜，通过调整厚度使其具有一定的弯曲刚度降低反枕效应的影响，但厚度的增加会增加天线的质量。根据薄板的弯曲刚度方程可知，为了在不改变材料厚度的情况下改变弯曲刚度，通过调节材料的泊松比可以达到这个目的。文章利用等效法计算了伞天线反射面形成时两肋间材料需要施加的位移；将天线反射面等效为薄板，计算了在此位移下为消除反枕效应圆薄板所需的弯曲刚度；选取了合适的负泊松比结构，即手性结构，计算了为实现这一弯曲刚度所需的手性结构胞元的几何参数；最后，利用有限元对胞元进行强度校核，以保证设计的手性结构能满足后续实验加载需求。

Parameter design of a circular thin plate with Negative Poisson’s ratio

For an umbrella like deployable mesh reflector, the metal mesh exhibits properties of a thin film when tensioned on curved boundaries,pillowing effects arise and this inevitably leads to the deterioration of the surface accuracy of the reflector,and further jeopardizes the performances of the antenna. Increasing the numbers of ribs of the reflector, or applying cable net structures between adjacent ribs can effectively reduce the negatives of pillowing effects,the complexity of the reflector design, however, increases at the same time, adding mass and reducing deployment reliability.A weak stiffness composite film concept was proposed by WANG Y M and HUANG P F, which is expected to relieve the pillowing effects by conferring a degree of bending stiffness to the film. The magnitude of bending stiffness is determined mainly by the thickness of the film, resulting in increase of mass when higher bending stiffness is required. A new proposal is suggested in this paper, that the bending stiffness of the film is not tuned by changing its thickness, but its Poisson''s ratio, while keeping the possibility of not increasing the mass dramatically.The relationships between the Poisson''s ratio and the effects of easing pillowing effects are investigated with a circular thin plate subjects lateral concentrated force at the center, and the results are presented.Key words:circular thin plate; Negative Poisson’s ratio; antenna reflector; surface accuracy; hexagonal chiral structure