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基于剪切效应纤维梁单元的结构非线性有限元数值模拟

李嘉钰 陈梦成 王开心

李嘉钰,陈梦成,王开心. 基于剪切效应纤维梁单元的结构非线性有限元数值模拟 [J]. 应用数学和力学,2022,43(1):34-48 doi: 10.21656/1000-0887.420032
引用本文: 李嘉钰,陈梦成,王开心. 基于剪切效应纤维梁单元的结构非线性有限元数值模拟 [J]. 应用数学和力学,2022,43(1):34-48 doi: 10.21656/1000-0887.420032
LI Jiayu, CHEN Mengcheng, WANG Kaixin. Nonlinear Numerical Simulation of Finite Elements Based on Fiber Beam Elements With Shear Effects for Structures[J]. Applied Mathematics and Mechanics, 2022, 43(1): 34-48. doi: 10.21656/1000-0887.420032
Citation: LI Jiayu, CHEN Mengcheng, WANG Kaixin. Nonlinear Numerical Simulation of Finite Elements Based on Fiber Beam Elements With Shear Effects for Structures[J]. Applied Mathematics and Mechanics, 2022, 43(1): 34-48. doi: 10.21656/1000-0887.420032

基于剪切效应纤维梁单元的结构非线性有限元数值模拟

doi: 10.21656/1000-0887.420032
基金项目: 国家自然科学基金 (51878275)
详细信息
    作者简介:

    李嘉钰(1996—),男,硕士生(E-mail:531782112@qq.com

    陈梦成(1962—),男,教授,博士生导师(通讯作者. E-mail:mcchen@ecjtu.edu.cn

  • 中图分类号: O344.3

Nonlinear Numerical Simulation of Finite Elements Based on Fiber Beam Elements With Shear Effects for Structures

  • 摘要:

    基于Euler-Bernoulli梁理论的经典纤维模型忽略了剪切变形给截面带来的影响,为了得到更加精确的梁单元模型,该文基于考虑剪切效应的纤维梁单元,根据Timoshenko梁理论,推导了该纤维梁单元的刚度矩阵,并结合弹塑性增量理论,同时考虑了几何非线性和材料非线性的双重影响,建立了压弯剪复杂应力状态下结构非线性有限元分析理论。该文最后利用MATLAB编制了相关计算程序,对钢筋混凝土和矩形钢管混凝土的典型压弯剪构件进行有限元数值模拟,得到了构件的荷载-位移非线性全过程曲线。典型算例的验证结果表明:该文建立的非线性有限元分析理论是通用、可行和正确的。

  • 图  1  纤维梁单元

    Figure  1.  The fiber beam element

    图  2  增量理论应力更新流程图

    Figure  2.  The flow chart for stress updating with the incremental theory

    图  3  钢筋混凝土柱(单位:mm)

    Figure  3.  The reinforced concrete column (unit: mm)

    图  4  纤维单元截面

    Figure  4.  The fiber element section

    图  5  混凝土本构模型

    Figure  5.  The constitutive model of concrete

    图  6  钢筋双折线本构模型

    Figure  6.  The constitutive model of steel reinforcement

    图  7  荷载-位移关系曲线

    Figure  7.  The load-displacement curves

    图  8  矩形钢管混凝土压弯剪试件计算模型

    Figure  8.  The calculation model for the rectangular CFST column under the compression-bending-shear loading condition

    图  9  矩形钢管混凝土试件V-R曲线

    Figure  9.  V-R curves of the rectangular CFST column

    表  1  计算参数

    Table  1.   Calculation parameters

    parametervalue
    compressive strength of concrete $ f_{\rm{c}}^\prime = 32.1\;{\text{MPa}} $
    Poisson’s ratio of concrete $ {\nu _{\rm{c}}} = 0.2 $
    yield strength of rebar $ {f_{\rm{y}}} = 510\;{\text{MPa}} $
    sectional shear coefficient $ {\kappa _y} = {\kappa _z} = 6/5 $
    elastic modulus of concrete $ {E_{\rm{c}}} = 2.64 \times {10^4}\;{\text{MPa}} $
    Poisson’s ratio of rebar $ {\nu _{\rm{s}}} = 0.3 $
    elastic modulus of rebar $ {E_{\rm{s}}} = 2 \times {10^5}\;{\text{MPa}} $
    peak compressive strain of the member $ \varepsilon {\text{ = }}0.005\;2 $
    shear modulus of concrete $ {G_{\rm{c}}} = 1.1 \times {10^4}\;{\text{MPa}} $
    moment of inertia $ I = 7.63 \times {10^{ - 3}}\;{{\text{m}}^4} $
    shear modulus of rebar $ {G_{\rm{s}}} = 7.7 \times {10^4}\;{\text{MPa}} $
    equivalent weight of the element $ P = 3\;539.25\;{\text{kN}} $
    下载: 导出CSV

    表  2  数值模拟结果

    Table  2.   Numerical simulation results

    displacement u/mmref. [15] FR/kNnumerical simulation FN/kNerror δ/%
    2167.16156.026.66
    4313.14294.855.84
    6417.97409.751.97
    8490.91487.480.70
    10540.35537.670.50
    12568.83558.611.80
    14577.99570.971.22
    16573.22555.433.10
    18562.80534.984.94
    20552.04515.576.61
    22538.23497.127.64
    24517.62479.597.35
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-01-28
  • 修回日期:  2021-05-05
  • 刊出日期:  2022-01-01

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