Method of Force-Finding Analysis Based on Ratio Updating for Cable Domes
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摘要:为了快速高效求解索穹顶结构的预应力分布，提出了一种基于比值更新的找力新方法. 以不断更新的索预应力比值来分配拉索预应力，以索力和位形作为收敛控制参数，迭代得到满足精度要求的预应力分布. 基于此，首先对索穹顶结构进行了不考虑重力影响的找力分析，验证了该方法的正确性；其次当考虑重力影响且每个索段划分为多个单元时，可引入沿索长的索水平分力这一不变量，将索力的比值替换为索水平分力的比值. 结果表明：基于比值更新的找力分析方法计算速度快，位形偏差小，精度高；考虑重力影响的找力分析结果与不考虑重力影响相差较大（最大为19.34%），索穹顶结构的找力分析宜考虑重力的影响；将每个索段划分为单个单元和多个单元的找力分析结果相差甚微（最大仅0.05%），当索预应力较大且索长较短时，可将每个索段划分为单个单元以简化求解预应力分布.
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关键词:
- 索穹顶结构/
- 找力分析/
- 基于比值更新的找力分析方法/
- 索水平分力
Abstract:In order to determine the prestress distribution of cable domes efficiently, a new method of force-finding analysis based on ratio updating was proposed. In this method, values of cable prestresses are pre-assumed and then constantly adjusted according to the continuously updated ratio of cable prestress; the precise prestress distribution of cable dome is acquired by iterations using the cable force and geometric shape as convergence control parameters. In this way, a force-finding analysis of cable domes is first conducted without considering the gravity effect, which verifies the effectiveness of this method. When the gravity is considered, each cable segment is divided into multiple units. An invariant, the cable force’s horizontal component along the length is introduced and the ratio of cable force is then replaced by that of the horizontal component force to deal with the situation with gravity. The results show that the method of force-finding analysis based on ratio updating is characterized by fast computational speed, small geometric shape deviation, and high precision. The results of force-finding analysis considering the influence of gravity are significantly different from those without considering gravity, and the maximum deviation reaches 19.34%. Thus, the influence of gravity should be taken into account in force-finding analysis of cable domes. In addition, whether each cable segment is divided into one unit or multiple units, the results of force-finding analysis make little difference (0.05% maximum deviation). Therefore, in cases when the cable prestress is large and cable length is short, each cable segment could be divided into only one unit to simplify the solving process of prestress distribution. -
表 1截面参数
Table 1.Section parameter
索杆编号 截面面积/mm2 索杆编号 截面面积/mm2 JS1 2 494.03 HS1 5 202.03 JS2 3 271.03 SLH 1 424.03 JS3 3 671.03 XLH 2 494.03 XS3 1 669.03 YG1 6 633.03 XS2 3 671.03 YG2 3 280.03 XS1 4 195.03 YG3 2 749.03 HS2 3 671.03 
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表 2预应力分布对比
Table 2.Comparison of prestress distributions
索杆编号 预应力 预应力比值 文献[18]/kN 本文方法/kN 偏差/% 文献[18] 本文方法 偏差/% JS1 435.33 435.33 0.00 1.000 1.000 0.00 JS2 715.33 715.09 −0.03 1.643 1.643 0.00 JS3 1 492.00 1 491.26 −0.05 3.427 3.426 −0.03 XS3 276.00 275.75 −0.09 0.634 0.633 −0.16 XS2 764.33 764.02 −0.04 1.756 1.755 −0.06 XS1 1 001.00 1 000.39 −0.06 2.299 2.298 −0.04 HS2 1 451.67 1 451.14 −0.04 3.335 3.333 −0.06 HS1 1 819.33 1 818.41 −0.05 4.179 4.177 −0.05 SLH 834.00 833.49 −0.06 1.916 1.915 −0.05 XLH 521.00 520.93 −0.01 1.197 1.197 0.00 YG1 −339.00 −338.83 −0.05 −0.779 −0.778 −0.13 YG2 −140.33 −140.23 −0.07 −0.322 −0.322 0.00 YG3 −57.67 −57.53 −0.24 −0.132 −0.132 0.00 下载:
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表 3找力后控制点竖向位置与设计初始态偏差值
Table 3.Deviation of the control point’s vertical position after force finding from that in the initial state of design
节点编号 控制点偏差/mm B 0.045 C 0.045 D 0.097 E 0.097 F 0.030 G 0.030 下载:
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表 4找力后控制点竖向位置与设计初始态偏差值
Table 4.Deviation of the control point’s vertical position after force finding from that in the initial state of design
mm 节点编号 划分为 1 个单元 划分为 3 个单元 B 0.028 0.047 C 0.028 0.047 D 0.104 0.085 E 0.104 0.085 F 0.031 0.025 G 0.031 0.025 下载:
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表 5找力分析结果对比
Table 5.Comparison of force-finding analysis results
索杆编号 节点编号 不考虑重力影响/kN 考虑重力影响 偏差3/% 划分为 1 个单元/kN 偏差1/% 划分为 3 个单元/kN 偏差2/% JS1 D 435.33 435.35 0.00 435.19 −0.03 −0.04 F 435.33 435.35 0.00 435.45 0.03 0.02 JS2 B 715.09 735.73 2.89 735.40 2.84 −0.04 D 715.09 735.73 2.89 735.97 2.92 0.03 JS3 A 1 491.26 1 619.21 8.58 1 618.81 8.55 −0.02 B 1 491.26 1 619.21 8.58 1 619.46 8.60 0.02 XS3 D 275.75 296.43 7.50 296.56 7.55 0.04 G 275.75 296.43 7.50 296.28 7.45 −0.05 XS2 B 764.02 870.19 13.90 870.42 13.93 0.03 E 764.02 870.19 13.90 869.90 13.86 −0.03 XS1 A 1 000.39 1 193.29 19.28 1 193.83 19.34 0.05 C 1 000.39 1 193.29 19.28 1 192.67 19.22 −0.05 HS2 E 1 451.14 1 652.77 13.89 1 652.73 13.89 0.00 E1 1 451.14 1 652.77 13.89 1 652.73 13.89 0.00 HS1 C 1 818.41 2 169.04 19.28 2 168.97 19.28 0.00 C1 1 818.41 2 169.04 19.28 2 168.97 19.28 0.00 SLH F 833.49 833.50 0.00 833.46 0.00 0.00 F1 833.49 833.50 0.00 833.46 0.00 0.00 XLH G 520.93 559.98 7.50 559.97 7.49 0.00 G1 520.93 559.98 7.50 559.97 7.49 0.00 YG1 −338.83 −392.08 −15.72 −392.08 −15.72 0.00 YG2 −140.23 −153.91 −9.76 −153.91 −9.76 0.00 YG3 −57.53 −59.82 −3.98 −59.82 −3.98 0.00 注：偏差1、2 分别表示将每根索段划分为 1 和 3 个单元时，考虑重力影响的找力分析结果与不考虑重力影响的找力分 析结果之间的偏差；偏差 3 表示将每根索段划分为 1 及 3 个单元时，考虑重力影响的找力分析结果之间的偏差；E1、 C1、F1、G1分别为水平构件 HS2、HS1、SLH、XLH 的另一端. 下载:
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