位形优化部分，介绍了决定索网位形关键参数的选取策略。首先基于理论双曲抛物面方程建立索网位形的数学描述；然后证明了正交正放双曲抛物面索网每个网格的四个角点共面，该特性使屋面模块可以按照平面设计和加工，显著降低加工和安装难度，从工程实施角度提出了索网位形控制的需求。之后根据几何约束条件，提炼出决定索网位形的关键参数，并通过参数分析，综合考虑JGJ 257—2012《索结构技术规程》建议范围、环桁架受力、预应力水平、刚度与用索量等因素，分别选取承重索垂度和稳定索拱度为8.25 m和7 m，进而确定索网的目标位形。
This paper teases apart the key issues in the cable net form-finding of the National Speed Skating Oval (NSSO) of China which will serve the 2022 Beijing Winter Olympics. The topics include the geometry optimization, the form-finding under fixed boundary condition and the form control considering supporting structure flexibility.
The determination of the key parameter that dominates the geometry of the cable net is set forth in the part of geometry optimization. Firstly, a hyperbolic paraboloid formula is employed to mathematically describe the geometry of the cable net. The four corners of each spatial quadrilateral grid of the cable net with a square projection prove to be coplanar. This feature enables the roof modules to be designed and manufactured as a plane, significantly reducing the level of difficulty in the fabrication of the roofing system and raising the necessity of maintaining the roof cable net in its target geometry after erection. Then the key parameter that dominates the geometry is extracted according to the geometrical constraint condition and a parametric analysis is conducted to determine the target geometry considering the recommendation in the national technical specification of China, the performance of the truss ring, the pretension level, the structural rigidity as well as the cable consumption. The sag of the suspending cable and the rise of the stabilizing cable are finally determined as 8.25 m and 7 m, respectively.
The form control of the cable net is preliminarily realized in the part of form-finding under fixed boundary condition. The form-finding, in which the cooperative influence of the boundary shape, the topology, the cable tensioning and the distribution of the roof weight is taken into consideration, limits the maximum deviation of the cable net geometry in the initial state within 5 mm from the theoretical hyperbolic paraboloid. Meanwhile, the orthogonality of the projection of the cable net in the initial state is realized, guaranteeing that the four corners of each grid are coplanar. The form-finding also enables the adjustment of the pretension level without varying the target geometry, making it possible to modify the percentages of the pretension in the cable envelope force and the geometrical stiffness in the global stiffness, by which the optimal comprehensive structural performance can be achieved.
The form control of the cable net considering the supporting structure flexibility sets the final goal of the form-finding. The impact of the supporting structure deflection due to cable tensioning on the form of the cable net is firstly analyzed, in which the maximum deviations from the results under fixed boundary condition are found to be 502 mm for the geometry and 11.1% and 7.3% for the cable pretensions of the suspending cables and stabilizing cables, respectively. Afterwards, the form control of the cable net considering the supporting structure flexibility is realized using a calibrating algorithm involving pre-deformation of the truss ring and modification of the initial strains from the fixed-boundary form-finding. In the initial state of the primary steel structure, not only the form of the cable net is identical to that under fixed boundary condition, but also the geometry of the truss ring and the forces of the stay cables reach their targets.