【摘要】 索-膜组合结构预张力会通过边界索力作用到支撑桁架上导致桁架变形，桁架变形又会改变索-膜组合结构的边界形状和预张力分布，这是索-膜-桁架之间的力-形耦合问题。针对索-膜-桁架天线中普遍存在的这种力-形耦合问题，提出了基于改进力密度法和非线性有限元法的形态优化设计方法进行解决。首先推导了索-膜组合结构的改进力密度平衡方程，利用力密度迭代方法确定边界固定时的索-膜组合结构初始形态，作为形态优化的初始值。然后推导了索-膜-桁架组合结构的非线性有限元平衡方程，并以索和薄膜预张力为设计变量、薄膜反射面的最佳拟合形面精度为优化目标、索-膜组合结构不松弛或褶皱为约束条件建立形态优化模型。最后通过对某口径5米索-膜-桁架天线和某口径20米的偏置索-膜-桁架天线进行形态优化设计仿真，验证了提出方法的有效性。设计完成的某口径5米的索-膜-桁架天线，实物模型测量取得了预期结果。更多还原

【Abstract】 The pre-tension of the cable-membrane composite structure will act on the supporting truss through the boundary cable force to cause the truss deformation, and the deformation of the truss will change the boundary shape and pre-tension distribution of the cable-membrane composite structure. This is the force-shape coupling problem of the cable-membrane-truss structure. Aiming at the force-shape coupling problem that is common in cable-membrane-truss antennas, a shape-state optimal design method based on improved force density method and nonlinear finite element method is proposed. First, the improved force density balance equation of the cable-membrane composite structure is derived, and the initial shape of the cable-membrane composite structure when the boundary is fixed is determined by the force density iteration method as the initial value of the shape-state optimal design. Then the nonlinear finite element balance equation of the cable-membrane-truss composite structure is derived, and the pretension of the cable and the membrane is used as the design variable, the best fitting shape accuracy of the membrane reflective surface is the optimization goal, and the cable-membrane composite structure is not slacked or wrinkled are constraints to establish the shape-state optimal design model. Finally, the effectiveness of the proposed method is verified by shape-state optimal design simulation of a 5m cable-membrane-truss antenna and a 20m offset cable-membrane-truss antenna. The design of a cable-membrane-truss antenna with a diameter of 5 meters has been measured by a physical model and the expected results have been obtained.更多还原