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Hamilton力学下框筒结构剪滞翘曲位移模式研究

胡启平 陈哲 周娟

胡启平,陈哲,周娟. Hamilton力学下框筒结构剪滞翘曲位移模式研究 [J]. 应用数学和力学,2022,43(4):374-381 doi: 10.21656/1000-0887.420088
引用本文: 胡启平,陈哲,周娟. Hamilton力学下框筒结构剪滞翘曲位移模式研究 [J]. 应用数学和力学,2022,43(4):374-381 doi: 10.21656/1000-0887.420088
HU Qiping, CHEN Zhe, ZHOU Juan. Research on Shear Lag Warping Displacement Modes of Frame-Tube Structures Based on the Hamiltonian Mechanics[J]. Applied Mathematics and Mechanics, 2022, 43(4): 374-381. doi: 10.21656/1000-0887.420088
Citation: HU Qiping, CHEN Zhe, ZHOU Juan. Research on Shear Lag Warping Displacement Modes of Frame-Tube Structures Based on the Hamiltonian Mechanics[J]. Applied Mathematics and Mechanics, 2022, 43(4): 374-381. doi: 10.21656/1000-0887.420088

Hamilton力学下框筒结构剪滞翘曲位移模式研究

doi: 10.21656/1000-0887.420088
基金项目: 河北省自然科学基金(E2016402110)
详细信息
    作者简介:

    胡启平(1963—),男,教授,硕士,硕士生导师(E-mail:huqiping@hebeu.edu.cn

    周娟(1982—),女,讲师,硕士(通讯作者. E-mail:41249061@qq.com)

  • 中图分类号: O39; TU311.4

Research on Shear Lag Warping Displacement Modes of Frame-Tube Structures Based on the Hamiltonian Mechanics

  • 摘要:

    以等效连续化方法为基础,在Hamilton力学体系下进行框筒结构剪滞翘曲位移函数精度研究。选用不同类型的函数描述翼缘板的剪滞翘曲位移,考虑等效板的剪切变形以及纵向翘曲,得到不同位移函数下结构的总势能及对应的Lagrange函数。区别于传统变分法,该文在Hamilton力学体系下进行问题研究,导出框筒结构弯曲问题的Hamilton正则方程并利用精细积分法求解,进而计算出柱轴力并进行精度分析。算例验证结果表明:使用该方法分析框筒结构的剪力滞后效应是简单可行的;不同翘曲位移函数的选择对侧移计算结果影响不大,对轴力求解结果影响较大,二次抛物线最能反映等效翼缘板的实际翘曲位移;对比不同形式荷载作用下等效翼缘板中应力分布可知,随着外荷载合力作用点位置的升高,结构顶部负剪力滞后效应逐渐减弱至消失。

  • 图  1  等效筒模型

    Figure  1.  The equivalent tube model

    图  2  算例平面图

    Figure  2.  The plan of the example

    图  3  等效筒底部应力对比

    Figure  3.  Stress comparison at the bottom of the equivalent tube

    图  4  不同翘曲函数下结构侧移曲线

    Figure  4.  Curves of structural lateral displacements with different warping functions

    图  5  工况①下不同高度处翼缘应力分布

    Figure  5.  Flange stress distributions at different heights under working condition ①

    图  6  工况②下不同高度处翼缘应力分布

    Figure  6.  Flange stress distributions at different heights under working condition ②

    图  7  工况③下不同高度处翼缘应力分布

    Figure  7.  Flange stress distributions at different heights under working condition ③

    表  1  工况①下结构底层柱轴力计算值及相对误差

    Table  1.   The axial force values and relative errors of the bottom floor column under working condition ①

    column numberref. [1] N/kNfunction type N/kNrelative error δ1/%
    quadratic functioncosine functioncatenary functionexponential functionquadratic functioncosine functioncatenary functionexponential function
    1000000000
    248.9051.3250.0852.0147.974.952.426.36−1.90
    3105.80108.53106.07109.85102.202.580.263.83−3.40
    4178.80177.51173.87179.36168.94−0.72−2.760.31−5.52
    5275.90264.15259.38266.35254.44−4.26−6.00−3.46−7.78
    6698.00644.80636.71647.67629.60−7.62−8.78−7.21−9.80
    7304.50283.86291.09278.81288.19−6.78−4.41−8.44−5.36
    8223.00210.29220.09204.51223.82−5.70−1.30−8.300.37
    9159.60153.06159.13150.16169.32−4.10−0.29−5.926.09
    10114.40112.19112.36113.11123.20−1.94−1.79−1.137.69
    1187.2087.6682.9591.5784.150.53−4.875.01−3.50
    1278.1079.4972.9284.5058.691.77−6.638.20−24.85
    下载: 导出CSV

    表  2  工况①下结构最大侧移值及相对误差

    Table  2.   Maximum side shift values and relative errors of the structure under working condition ①

    ref. [1] u/cmfunction type u/cmrelative error δ2/%
    quadratic functioncosine functioncatenary functionexponential functionquadratic functioncosine functioncatenary functionexponential function
    0.750.76850.76630.76910.76382.472.172.551.84
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-04-06
  • 录用日期:  2021-06-17
  • 修回日期:  2021-06-17
  • 网络出版日期:  2022-03-10
  • 刊出日期:  2022-04-01

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