轴对称分布多集中载荷作用下的圆薄板变形  

Deformation analysis of circular thin plates under axisymmetricdistributed concentrated lateral loads

作　　者：王一鸣 宋燕平[1] 王辉[1] WANG Yiming;SONG Yanping;WANG Hui(China Academy of Space Technology(Xi’an),Xi’an 710000,China)

机构地区：[1]中国空间技术研究院西安分院,西安710000

出　　处：《空间电子技术》2021年第3期80-90,共11页Space Electronic Technology

基　　金：国家自然科学基金(编号:51775406)。

摘　　要：传统的设计与分析中,大型网状可展开天线的金属网都作为薄膜看待。当薄膜张紧在曲线边界上时,必然形成负高斯曲率曲面,即反枕效应,使天线反射面型面精度降低。为了减少反枕效应的影响,通常的方法是减小曲线边界所围区域的面积,例如增加径向肋天线肋的数量,或者增大张力索网天线的网格密度,这些措施都增加了天线的复杂程度,带来重量的增加、加工难度的增大和展开可靠性的降低。在曲线边界所围区域中对金属网施加横向集中载荷,可以缓解反枕效应的影响,但由于金属网的薄膜特性,载荷施加点附近的曲面仍为负高斯曲率曲面,使的反射面型面精度的改善受到限制。文章研究一种具有一定弯曲刚度的薄膜材料,力求使用较少的牵引点达到良好的型面精度。分析采用弹性力学和板壳理论的基本理论,首先建立圆薄板在横向受到轴对称载荷作用下的变形方程,结合边界条件求出挠曲线的精确解析解。改变薄板的弯曲刚度,研究不同弯曲刚度的圆薄板在不同载荷分布下的挠曲线,并与标准抛物线进行比较。研究结果对提高网状可展开天线型面精度提供了一种新的选择。As for the design and analysis of large deployable mesh antenna,an approach of treating the metal mesh as thin film is always adopted.When a film is stressed over a curved boundary,a surface with negative Gaussian Curvature is formed-“pillowing effect”as mentioned in some literatures.The consequence of this effect is the degradation of surface accuracy of the antenna reflector.Previous approaches to improve the surface accuracy include increasing the number of radial ribs in umbrella type reflectors or,increasing the grid density of stressed cords in AstroMesh type reflectors,both result in complexity increasing,mass adding,assembly difficulty,and lowering in reliability.It is expected that the surface accuracy will be improved,when concentrated lateral loads are applied to the mesh.The improvement is limited however,as the surface adjacent to the loading point is still with a negative Gaussian Curvature.If the mesh possesses certain bending stiffness,by making it a kind of composite material,the surface adjacent to the loading point will featuring a positive Gaussian Curvature,this will result in a better surface with fewer loading points.Classical theory of Elasticity,and theory of Plates and Shells are applied to predict the deformation of a circular thin plates under axisymmetric distributed concentrated lateral loads.Deflection equation was first established,and then its analytical solution was obtained by assuming appropriate boundary conditions.A survey of the relationship between the bending stiffness of the composite film and the deformation under different load conditions was made,and the resulting surfaces were compared to the paraboloid.Conclusion given in the end of this work provides a new option to improve the surface accuracy of deployable mesh antenna reflectors.

关 键 词：圆薄板 轴对称载荷 天线反射面 型面精度 

分 类 号：V474[航空宇航科学与技术—飞行器设计]