In the current pretension design of mesh reflector antennas based on the equilibrium matrix method (EMM), the truss and hinge deformation cannot be accurately captured, which will deteriorate the shape accuracy of the antenna. To solve this problem, this paper proposes a new EMM-based pretension design method. In this method, the rod of the truss is modeled as Euler-Bernoulli beam, and the joint of the hinge is treated as the spring with six degrees of freedom. Based on the beams and springs, the systematic equilibrium equation of the mesh reflector antenna is established considering the flexibility of rods and hinges. Then, the mesh reflector antenna is divided into the inner cable network and boundary cable-truss-hinge assembly. The equilibrium equation of the boundary cable-truss-hinge assembly is solved by the force density method to calculate the truss and hinge deformation. The equilibrium equation of the inner cable network is solved by the EMM to fix all free nodes at desired positions. Combined with the active-set optimization algorithm, the required cable tensions are obtained by taking the mean tension ratio of the cable network as the objective function, thus ensuring high shape accuracy. Lastly, the proposed method is applied to the mesh reflector antenna and verified by ABAQUS.

在目前基于平衡矩阵法（EMM）的网状反射面天线预紧设计中，无法准确捕获桁架和铰链变形，这会降低天线的形状精度。针对这一问题，本文提出了一种新的基于EMM的预紧设计方法。在该方法中，桁架的杆被建模为欧拉-伯努利梁，铰链的关节被视为具有六个自由度的弹簧。基于梁和弹簧，系统平衡方程考虑到杆和铰链的灵活性，建立了网状反射器天线。然后，将网状反射面天线分为内部索网和边界索-桁架-铰链组件。采用力密度法求解边界索-桁架-铰链组合体的平衡方程，计算桁架和铰链变形。内部电缆网络的平衡方程由 EMM 求解，以将所有自由节点固定在所需位置。结合主动集优化算法，以索网平均张力比为目标函数得到所需的索力，从而保证了较高的形状精度。最后，将所提方法应用于网状反射面天线，并通过ABAQUS进行了验证。