滑移索结构分析的精确三维有限元法

陈诗再; 杨孟刚

doi:10.6052/j.issn.1000-4750.2021.08.0642

滑移索结构分析的精确三维有限元法

doi: 10.6052/j.issn.1000-4750.2021.08.0642

陈诗再^{1, 2,},
杨孟刚^1, ,

1.
中南大学土木工程学院，湖南，长沙 410075
2.
广东省交通规划设计研究院集团股份有限公司，广东，广州 523136

基金项目: 国家自然科学基金项目(51978667)

详细信息

作者简介:
陈诗再(1994−)，男，福建泉州人，硕士，主要从事桥梁结构几何非线性研究(E-mail: chensz7@163.com)

通讯作者:
杨孟刚(1976−)，男，江西安义人，教授，博士，主要从事桥梁抗震减震及结构几何非线性研究(E-mail: mgyang@csu.edu.cn)

中图分类号: TU311
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- HTML全文浏览量: 160
- PDF下载量: 79
- 被引次数: 0
出版历程
- 收稿日期: 2021-08-17
- 修回日期: 2021-11-28
- 录用日期: 2021-12-14
- 网络出版日期: 2021-12-14
- 刊出日期: 2023-02-01

HIGH-PRECISION THREE-DIMENSIONAL FINITE ELEMENT METHOD FOR ANALYSIS OF SLIDING CABLE STRUCTURES

CHEN Shi-zai^{1, 2
,},
YANG Meng-gang^{1
, ,}

1.
School of Civil Engineering, Central South University, Changsha, Hu’nan 410075, China
2.
Guangdong Communication Planning and Design Institute Group Co, Ltd, Guangzhou, Guangdong 523136, China

摘要

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。
- 滑移索结构 /
- 摩擦 /
- 温度 /
- 几何非线性 /
- 有限元法
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.
- sliding cable structures /
- friction /
- temperature /
- geometric nonlinearity /
- finite element method

HTML全文

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 3 三维滑移索单元示意图

Figure 3. Diagram of the three-dimensional sliding 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 5 滑移索结构的精细化分析流程

Figure 5. Refined analysis process of sliding cable structures

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图 6 平面移动索-轮体系　/m

Figure 6. Plan transport pulley system

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图 7 空间移动索-轮体系　/m

Figure 7. Three-dimensional transport pulley system

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图 8 两跨三维滑移索　/m

Figure 8. Two span three-dimensional sliding cable

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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 11 预应力钢桁架　/m

Figure 11. Prestressed steel truss

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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

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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x_o/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
C₄	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x_o/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

平衡构型	方法	滑移点索力(T/g)/kg	坐标x_o/m	无应力索长s₁/m
C₁	文献[22]	1439.66	56.290	126.122
C₁	本文	1439.54	56.3850	126.269
C₂	文献[22]	1099.43	134.240	219.983
C₂	本文	1099.72	134.217	219.956
C₃	文献[22]	1775.31	274.460	424.757
C₃	本文	1775.69	274.422	424.659

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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)

方法	张拉端索力/kN	左滑移点左侧索力/kN	左滑移点右侧索力/kN	锚固端索力/kN	上弦中心上拱量/cm
文献[13]-不计静摩擦	701.083	700.844	638.647	581.958	0.57
文献[6]-不计静摩擦	720.181	719.943	650.753	588.432	0.99
本文-不计静摩擦	701.081	700.843	638.654	582.210	0.64
本文-考虑静摩擦	618.855	618.617	659.078	600.890	1.08

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