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中文摘要：
结合大射电望远镜中索网主动反射面实例给出了一种基于最小二乘优化模型求解索网结构初始平衡状态的方法．该模型以悬索长度和节点外力载荷为设计变量，在一定的约束条件下追求索网的平衡状态与指定的几何形状最为接近．根据悬索悬链线解析表达式推导出索端位置和索端拉力与悬索长度之间的关系，从而可以得到优化所需的敏度信息．数值算例中给出了分析的详细过程，验证了算法的有效性．
英文摘要：
An approach, together with a demonstration on the active cable-mesh reflector, using the least square optimization model is presented to solve the initial equilibrium problem of cable-mesh. The optimization model,in which the corresponding cable length and external nodal force are considered as design variables,is established to seek a certain equilibrium configuration closest to the given structure geometry. The relationship among end node position, end force and cable length is derived based on the precise analytical catenary equation,and following it, we can obtain the relative sensitivity information to be utilized in the optimization. Detailed analysis procedure and the efficiency of the proposed method are demonstrated with a numerical example.
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