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滑移索结构分析的精确三维有限元法

陈诗再 杨孟刚

陈诗再, 杨孟刚. 滑移索结构分析的精确三维有限元法[J]. 工程力学, 2023, 40(2): 135-144, 189. doi: 10.6052/j.issn.1000-4750.2021.08.0642
引用本文: 陈诗再, 杨孟刚. 滑移索结构分析的精确三维有限元法[J]. 工程力学, 2023, 40(2): 135-144, 189. doi: 10.6052/j.issn.1000-4750.2021.08.0642
CHEN Shi-zai, YANG Meng-gang. HIGH-PRECISION THREE-DIMENSIONAL FINITE ELEMENT METHOD FOR ANALYSIS OF SLIDING CABLE STRUCTURES[J]. Engineering Mechanics, 2023, 40(2): 135-144, 189. doi: 10.6052/j.issn.1000-4750.2021.08.0642
Citation: CHEN Shi-zai, YANG Meng-gang. HIGH-PRECISION THREE-DIMENSIONAL FINITE ELEMENT METHOD FOR ANALYSIS OF SLIDING CABLE STRUCTURES[J]. Engineering Mechanics, 2023, 40(2): 135-144, 189. 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
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

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

  • 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。
  • 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

    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

    图  3  三维滑移索单元示意图

    Figure  3.  Diagram of the three-dimensional sliding cable element

    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

    图  5  滑移索结构的精细化分析流程

    Figure  5.  Refined analysis process of sliding cable structures

    图  6  平面移动索-轮体系 /m

    Figure  6.  Plan transport pulley system

    图  7  空间移动索-轮体系 /m

    Figure  7.  Three-dimensional transport pulley system

    图  8  两跨三维滑移索 /m

    Figure  8.  Two span three-dimensional sliding cable

    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

    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

    图  11  预应力钢桁架 /m

    Figure  11.  Prestressed steel truss

    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

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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xo/m无应力索长s1/m
    C1文献[22]1439.6656.290126.122
    本文1439.5456.3850126.269
    C2文献[22]1099.43134.240219.983
    本文1099.72134.217219.956
    C3文献[22]1775.31274.460424.757
    本文1775.69274.422424.659
    下载: 导出CSV

    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
    701.083700.844638.647581.9580.57
    文献[6]-不计
    静摩擦
    720.181719.943650.753588.4320.99
    本文-不计
    静摩擦
    701.081700.843638.654582.2100.64
    本文-考虑
    静摩擦
    618.855618.617659.078600.8901.08
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-08-17
  • 录用日期:  2021-12-14
  • 修回日期:  2021-11-28
  • 网络出版日期:  2021-12-14
  • 刊出日期:  2023-02-01

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