索网结构初始平衡状态的优化设计

Optimization Design of Initial Equilibrium State of Cable-Net Structures

结合索网主动反射面结构,采用优化方法研究了考虑自重影响时索网面在调整索牵引下的初始平衡状态.该方法以索段长度为设计变量,以索网节点的不平衡力最小为优化目标,并针对调整索和网面张力引入相应的约束条件,能够在已知结构几何形状和边界条件的前提下方便地求解出索网中索段的初始长度.文中采用弹性悬链线解析方程来精确描述自重作用下柔索的力学特性,在此基础上推导出优化模型的敏度信息.最后,以索网主动反射面为例给出了分析的详细过程,得到了索段的初始长度和张力分布,结果表明该方法是有效的.

Proposed in this paper is an optimization-based method to solve the initial equilibrium problem of the cable-net surface tensioned with adjustable cables,with the effect of cable self weight being considered and with the active cable-net reflector structure being employed.In this method,the cable length is considered as the design variable,the minimum unbalanced force of cable-net nodes is taken as the optimization objective,and the corresponding constraints on the tensions of adjustable cables and cable-net surface are introduced.Thus,it can easily determine the initial cable length when the structural geometry and the boundary conditions are known.Moreover,the mechanical characteristics of cables considering their self weight are analyzed according to the analytical expression of elastic catenary,based on which the sensitivity of the optimization model is obtained.Finally,a detailed analysis procedure is presented with the numerical example of the active cable-net reflector,and the initial cable length and the tension distribution of the structure are obtained.The results demonstrate that the proposed method is effective.