索网主动反射面的形状精度调整研究

ANALYSIS ON SHAPE ACCURACY ADJUSTMENT OF AN ACTIVE CABLE-MESH REFLECTOR

根据柔索的悬链线方程,推导出索端张力与索端位移之间的线性增量关系,据此可对索网结构进行精确的力学分析。采用偏差分布向量来描述网面节点相对于设计抛物面的偏差,以便能够反映出网面上任一节点偏离其理想位置的方向和大小。提出了一种形状精度调整算法,将设计抛物面的顶点位置和非照明部分的节点位移同时进行优化,这样既可以满足照明部分的形状精度要求,又保证调整过程中所做的功最少。数值算例表明:该文提出的调整方法具有很好的收敛性。

The linear incremental relationship between the end force and the end displacement of a cable is deduced based on the analytical catenary in order to construct a rigorous mechanical model for cable-mesh structures. The error distribution vector is introduced to represent the distribution of the shape error with respect to the design paraboloid, thus the direction and magnitude of the divergence of each node on the surface from its ideal position can be reflected. A shape adjustment algorithm is presented in which the position of the vertex of the design paraboloid and the displacement of the nodes out of the illuminated area are optimized. The optimization algorithm guarantees both the shape accuracy within the illuminated area and the minimal work during the adiustment. The numerical example shows that the method proposed achieves a good convergence.