非对称环形桁架索网天线预张力设计解析算法

An analytic algorithm for pretension design of asymmetrical ring truss cable-net antennas

摘要:

为便于工程应用,提出一种非对称环形桁架空间索网天线预张力设计的解析算法. 给出主网在与环形桁架中心线垂直的平面内平衡预张力的投影方程,再根据平面索网结构预张力优化的极小范数法计算公式求出主网绳索中的预张力；根据主网节点的张力纵向平衡方程计算出张力阵绳索预张力；将主网绳索中的预张力分别与特定的系数相乘,即可得到副网中对应绳索的预张力. 分别用理论分析、非线性有限元数值仿真以及与其他索网结构预张力优化算法相比较的方式证明了所提算法的正确性、可行性和有效性.

Abstract:

For convenience of application, an analytic algorithm was proposed to design the pretensions of asymmetrical ring truss cable-net space-borne antennas. The projection equations of the main net in the plane perpendicular to the central line of the ring truss were given at first, and then the pretensions of the main net were obtained using the formula of the minimal norm method that is used to optimize the pretensions of a planar cable-net. The pretensions of the tension ties were calculated according to the vertical equilibrium equations of the points of the main net. A set of equilibrium pretensions of the auxiliary net were obtained by letting the tensions of the main net multiply the special coefficients respectively. The accuracy, validity and feasibility of the algorithm were proved by theoretical analysis, nonlinear finite element numerical simulations and comparisons with other pretension optimization algorithms. The algorithm can be used to design the pretensions of the asymmetrical or symmetrical ring truss cable-net space-borne antennas.