HIGH-PRECISION THREE-DIMENSIONAL FINITE ELEMENT METHOD FOR ANALYSIS OF SLIDING CABLE STRUCTURES
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摘要: 针对现有滑移索结构分析方法适用范围有限、精度不高的缺点，提出了一种通用、高精度的三维滑移索单元法。基于悬链线理论和Euler-Eytelwein公式，同时考虑了温度效应和滑动摩擦，分别建立了已知单元无应力索长和已知张拉力的三维滑移索单元的基本方程组；利用矩阵微分从单元基本方程组导出了单元的切线刚度矩阵；建立了滑移索结构从张拉到后期加载的全过程精细化分析流程，可实现自动调用建立的各类索单元，准确分析各滑移点的摩擦；通过3个算例的计算及与现有理论解、数值解和试验结果的比较来验证该文所提出方法的可靠性和有效性。结果表明，该文提出的三维有限元法准确可靠，计算效率较高，适用于工程中各种滑移索结构的高精度非线性分析。Abstract: To overcome the shortcomings of limited application range and low precision in the existing analysis methods for sliding cable structures, a general and high-precision three-dimensional finite element method for sliding cables is proposed. Based on the catenary theory and Euler-Eytelwein equation, the governing equations of the three-dimensional sliding cable elements with known unstressed cable length and with known tensile forces are respectively developed, accounting for the thermal effect and sliding friction. The tangent stiffness matrix of the element is derived directly from the governing equations by using matrix differential. A refined analysis procedure of sliding cable structures for the whole process from tensioning to later loadings is proposed, with the capability of automatically using all types of cable elements and accurately analyzing the friction at each sliding point. The reliability and effectiveness of the proposed method are verified by three computational examples and, by the comparison with the pertinent existing theoretical solutions and, with the pertinent numerical results and experimental ones. The computational results show that the three-dimensional finite element method proposed is accurate and reliable with high computational efficiency and is very suitable for the high-precision nonlinear analysis of various sliding cable structures in engineering practice.
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Keywords:
- sliding cable structures /
- friction /
- temperature /
- geometric nonlinearity /
- finite element method
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图 1 一种穹顶结构空间型滑移索节点的构造
Figure 1. Composition of a spatial sliding cable joint in the suspen-dome structure
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图 2 两节点三维悬链线索单元示意图
Figure 2. Schematic diagram of the two-node three-dimensional catenary cable element
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图 4 三维滑移索单元内部受力图
Figure 4. Internal forces of the three-dimensional sliding cable element
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图 9 无摩擦的两跨三维滑移索数值和试验结果
Figure 9. Numerical and experimental results of the two span three-dimensional sliding cable without friction
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图 10 考虑摩擦的两跨三维滑移索数值和试验结果
Figure 10. Numerical and experimental results of the two-span three-dimensional sliding cable with friction
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图 12 索力与张拉力关系的比较
Figure 12. Comparison of the relationship between cable force and tensile force
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图 13 上弦中心上拱量与张拉力关系的比较
Figure 13. Comparison of the relationship between the camber on the center of the top chord and tensile force
表 1 不考虑温度效应的平面移动索-轮体系的平衡构型
Table 1 Equilibrium configurations of the plan transport pulley system without thermal effect
平衡构型 方法 滑移点索力(T/g)/kg 坐标xo/m 无应力索长s1/m C1 文献[15] 1478.000 47.6700 111.070 文献[22] 1481.230 47.2500 110.833 文献[21] 1479.510 47.2530 110.830 本文 1481.180 47.3300 110.957 C2 文献[15] 1830.000 282.810 446.370 文献[22] 1833.020 283.150 447.295 文献[21] 1830.780 283.155 447.300 本文 1833.440 283.125 447.226 C3 文献[22] 1083.680 136.530 221.518 文献[21] 1082.770 136.540 221.530 本文 1083.920 136.519 221.497 C4 文献[15] 278 059.0 199.960 219.780 本文 264 225.8 200.197 220.174 
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表 2 考虑温度效应的平面移动索-轮体系的平衡构型
Table 2 Equilibrium configurations of the plan transport pulley system with thermal effect
平衡构型 方法 滑移点索力(T/g)/kg 坐标xo/m 无应力索长s1/m C1 本文 1481.190 47.2930 110.907 C2 本文 1833.270 283.136 447.245 C3 本文 1083.770 136.532 221.512 C4 本文 259 396.3 200.201 220.177
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表 3 三维移动索-轮的平衡构型
Table 3 Equilibrium configurations of the three-dimensional transport pulley system
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表 4 施加后期荷载后的结构响应(相对初始态)
Table 4 Structural response under later loadings (relative to the initial state)
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