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波形腹板钢箱-混凝土箱梁桥的有限元模型修正

冀伟 邵天彦

冀伟, 邵天彦. 波形腹板钢箱-混凝土箱梁桥的有限元模型修正[J]. 西南交通大学学报, 2021, 56(1): 1-11. doi: 10.3969/j.issn.0258-2724.20191198
引用本文: 冀伟, 邵天彦. 波形腹板钢箱-混凝土箱梁桥的有限元模型修正[J]. 西南交通大学学报, 2021, 56(1): 1-11. doi: 10.3969/j.issn.0258-2724.20191198
JI Wei, SHAO Tianyan. Finite Element Model Updating of Box Girder Bridges with Corrugated Steel Webs[J]. Journal of Southwest Jiaotong University, 2021, 56(1): 1-11. doi: 10.3969/j.issn.0258-2724.20191198
Citation: JI Wei, SHAO Tianyan. Finite Element Model Updating of Box Girder Bridges with Corrugated Steel Webs[J]. Journal of Southwest Jiaotong University, 2021, 56(1): 1-11. doi: 10.3969/j.issn.0258-2724.20191198

波形腹板钢箱-混凝土箱梁桥的有限元模型修正

doi: 10.3969/j.issn.0258-2724.20191198
基金项目: 国家自然科学基金(51708269,51868039);中国博士后科学基金(2018M643766)
详细信息
    作者简介:

    冀伟(1982—),男,教授,研究方向为组合箱梁桥设计,E-mail:jiwei1668@163.com

  • 中图分类号: U441

Finite Element Model Updating of Box Girder Bridges with Corrugated Steel Webs

  • 摘要: 为了缩小波形钢腹钢箱-混凝土组合箱梁桥有限元值与实测值之间的偏差,提出了采用响应面法和Fmincon算法相结合的桥梁有限元模型修正方法. 以甘肃景中机场连接线的一座波形钢腹钢箱-混凝土组合箱梁桥为研究对象,首先对其进行静、动载试验,获得其弯曲振动频率、挠度及应变的实测值;其次分别采用实体和板壳模式的有限元建模获得该桥相应的弯曲振动频率、挠度及应变的计算值,通过与实测值对比分析后,选取较为精确的实体模式有限元模型作为修正的初始有限元模型;随后在合理选择设计参数的基础上,通过中心复合试验设计得到相应的结构响应,采用最小二乘法拟合得到结构响应和设计参数之间的二次多项式回归方程,并构造目标响应与相应响应实测值差值的目标函数;最后运用Fmincon算法对目标函数进行迭代计算,获得参数修正值及该桥的基准有限元模型. 研究结果表明:采用响应面法和Fmincon算法相结合的方法对波形钢腹钢箱-混凝土组合箱梁桥的有限元模型进行修正切实可行,具有修正过程简单、计算收敛速度快等特点,计算时间在0.25~0.75 s内,一阶弯曲振动频率相对误差由4.85%依据不同响应组合修正到1.62%~2.91%不等;通过对遗传算法和Fmincon算法的比较发现,Fmincon算法显著提高了模型修正效率,可为实际工程中该类桥梁的有限元建模分析及力学性能分析提供参考.

     

  • 图 1  波形腹板钢箱-混凝土组合箱梁

    Figure 1.  Box girder bridges with corrugated steel webs

    图 2  两种工况加载位置示意

    Figure 2.  Loading placements for the two loading tests

    图 3  测点布置

    Figure 3.  Arrangement of measuring points

    图 4  桥梁的有限元模型

    Figure 4.  FE models of elements of bridge

    图 5  两种工况挠度对比

    Figure 5.  Comparison of the deflections in two conditions

    图 6  两种工况应变对比

    Figure 6.  Comparison of the strains in two conditions

    图 7  不同初始值对优化结果的影响

    Figure 7.  Influence of different initial values on optimization results

    图 8  计算10次后两种算法的对比

    Figure 8.  Comparison of the two algorithms after ten calculations

    图 9  工况2挠度修正前后比对

    Figure 9.  Deflection comparison before and after updating in condition 2

    图 10  工况2应变修正前后比对

    Figure 10.  Strain comparison before and after updating in condition 2

    图 11  工况1挠度修正前后比对

    Figure 11.  Deflection comparison before and after updating in condition 1

    图 12  工况1应变修正前后比对

    Figure 12.  Strain comparison before and after updating in condition 1

    图 13  工况2不同目标响应组合挠度比对

    Figure 13.  Comparison of deflections for different response combinations in condition 2

    图 14  工况2不同目标响应组合应变比对

    Figure 14.  Comparison of strains fordifferent response combinations in condition 2

    表  1  材料属性

    Table  1.   Material properties

    材料种类密度/(kg•m−3弹性模量/GPa泊松比
    C55混凝土2 54935.50.20
    钢材7 850206.00.30
    下载: 导出CSV

    表  2  一阶弯曲振动频率对比

    Table  2.   Comparison of the first-order bending vibration frequency

    名称一阶弯曲振动频率/Hz相对误差/%
    实测值3.09
    实体模式2.944.85
    板壳模式2.4520.71
    下载: 导出CSV

    表  3  设计参数

    Table  3.   Design parameters

    因素名称参数初值单位变化
    程度/%
    x1桥面板弹性模量/GPa35.540
    x2桥面板密度/(kg•m−3254920
    x3波形钢腹板弹性模量/GPa20630
    x4钢底板弹性模量/GPa20630
    x5箱间横联弹性模量/GPa20630
    下载: 导出CSV

    表  4  5因素参数设计试验

    Table  4.   Five-factors parameter design test

    试验组合参数值
    x1/GPax2/(kg•m−3x3/GPax4/GPax5/GPa
    1 21.3 2039.2 144.2 144.2 267.8
    2 49.7 3058.8 144.2 144.2 144.2
    3 21.3 2039.2 144.2 144.2 144.2
    4 49.7 3058.8 144.2 144.2 267.8
    5 21.3 2039.2 267.8 144.2 144.2
    6 49.7 3058.8 267.8 144.2 267.8
    7 21.3 2039.2 267.8 144.2 267.8
    8 49.7 3058.8 267.8 144.2 144.2
    9 21.3 2039.2 144.2 267.8 144.2
    10 49.7 3058.8 144.2 267.8 267.8
    11 21.3 2039.2 144.2 267.8 267.8
    12 49.7 3058.8 144.2 267.8 144.2
    13 21.3 2039.2 267.8 267.8 267.8
    14 49.7 3058.8 267.8 267.8 144.2
    15 21.3 2039.2 267.8 267.8 144.2
    16 49.7 3058.8 267.8 267.8 267.8
    17 7.1 2549.0 206.0 206.0 206.0
    18 63.9 2549.0 206.0 206.0 206.0
    19 35.5 1529.4 206.0 206.0 206.0
    20 35.5 3568.6 206.0 206.0 206.0
    21 35.5 2549.0 82.4 206.0 206.0
    22 35.5 2549.0 329.6 206.0 206.0
    23 35.5 2549.0 206.0 82.4 206.0
    24 35.5 2549.0 206.0 329.6 206.0
    25 35.5 2549.0 206.0 206.0 82.4
    26 35.5 2549.0 206.0 206.0 329.6
    27 35.5 2549.0 206.0 206.0 206.0
    28 35.5 2549.0 206.0 206.0 206.0
    29 35.5 2549.0 206.0 206.0 206.0
    30 35.5 2549.0 206.0 206.0 206.0
    下载: 导出CSV

    表  5  频率-挠度响应组合修正结果

    Table  5.   Updated results of the frequency-deflection response combination

    因素名称 上边界 下边界设计值修正后
    x1 49.700 21.300 35.500 38.903
    x2 30.588 20.392 25.490 20.786
    x3 26.780 14.420 20.600 14.475
    x4 26.780 14.420 20.600 20.600
    x5 26.780 14.420 20.600 20.600
    下载: 导出CSV

    表  6  两种算法约束条件下的修正结果

    Table  6.   Updated results under the constraint of two algorithms

    因素名称约束1约束2
    x1 38.903 48.470
    x2 20.786 25.733
    x3 14.475 20.654
    x4 20.600 20.600
    x5 20.600 20.600
    下载: 导出CSV

    表  7  修正前后频率比对

    Table  7.   Frequency comparison before and after updating

    项目一阶弯曲振动频率/Hz相对误差/%
    实测值 3.09
    修正前 2.94 4.85
    约束 1 3.14 1.62
    约束 2 3.02 2.27
    下载: 导出CSV

    表  8  不同目标响应组合频率比对

    Table  8.   Comparison of frequencies of different response combinations

    响应组合一阶弯曲振动频率/Hz相对误差/%
    实测值 3.09
    修正前 2.94 4.85
    频率 3.04 1.62
    挠度 3.04 1.62
    应变 3.00 2.91
    频率-挠度 3.02 2.27
    频率-应变 3.00 2.91
    挠度-应变 3.02 2.27
    频率-挠度-应变 3.02 2.27
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-12-25
  • 修回日期:  2020-05-07
  • 网络出版日期:  2020-05-22
  • 刊出日期:  2021-02-01

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