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基于复合材料层合箱梁改进解析模型计算等效刚度

朱秀杰 熊超 殷军辉 尹德军 邓辉咏 李宝晨

朱秀杰, 熊超, 殷军辉, 等. 基于复合材料层合箱梁改进解析模型计算等效刚度[J]. 复合材料学报, 2020, 37(6): 1483-1495. doi: 10.13801/j.cnki.fhclxb.20190706.001
引用本文: 朱秀杰, 熊超, 殷军辉, 等. 基于复合材料层合箱梁改进解析模型计算等效刚度[J]. 复合材料学报, 2020, 37(6): 1483-1495. doi: 10.13801/j.cnki.fhclxb.20190706.001
ZHU Xiujie, XIONG Chao, YIN Junhui, et al. Equivalent stiffness calculation based on refined analytical model of composite laminated box beam[J]. Acta Materiae Compositae Sinica, 2020, 37(6): 1483-1495. doi: 10.13801/j.cnki.fhclxb.20190706.001
Citation: ZHU Xiujie, XIONG Chao, YIN Junhui, et al. Equivalent stiffness calculation based on refined analytical model of composite laminated box beam[J]. Acta Materiae Compositae Sinica, 2020, 37(6): 1483-1495. doi: 10.13801/j.cnki.fhclxb.20190706.001

基于复合材料层合箱梁改进解析模型计算等效刚度

doi: 10.13801/j.cnki.fhclxb.20190706.001
基金项目: 省部级重点攻关项目(ZS2015070132A12002)
详细信息
    通讯作者:

    熊超,博士,副教授,硕士生导师,研究方向为兵器新材料技术及应用 E-mail:xiongchao@tsinghua.org.cn

  • 中图分类号: TB330.1

Equivalent stiffness calculation based on refined analytical model of composite laminated box beam

  • 摘要: 提出了基于复合材料层合箱梁改进解析模型的等效刚度计算方法。在考虑三维应变效应的同时用复合材料单层的二维折算模量分量来表示三维折算模量分量,简化了复合材料层合箱梁等效刚度系数的计算,得到了由梁横截面几何尺寸和层合板刚度系数表达的等效抗弯刚度和等效抗扭刚度的解析式。该解析式适用于环向刚度一致的复合材料层合箱梁,并充分考虑了弯曲-剪切耦合和扭转-拉伸耦合效应对等效刚度的影响。通过三点弯试验和扭转试验,验证了解析式的正确性;通过与分层等效叠加法、有限元法进行对比,分析了解析式的计算精度。结合经典层合板理论,研究了铺层方式对等效刚度产生的影响及原因,预测了不同铺层复合材料层合箱梁等效刚度的变化规律。

     

  • 图  1  复合材料层合箱梁几何尺寸和坐标系

    Figure  1.  Geometry and coordinate system of composite laminated box beam

    图  2  复合材料层合箱梁位移场

    Figure  2.  Displacement field of composite laminated box beam

    图  3  三点弯试验

    Figure  3.  Three-point bending test

    图  4  试验和理论计算的T300/QY8911矩形截面管载荷-应变曲线

    Figure  4.  Experimental and theoretical calculated load-strain curves for T300/QY8911 rectangular section tube

    图  5  扭转试验

    Figure  5.  Torsion test

    图  6  试验和理论计算的T300/QY8911矩形截面管扭矩-扭转角曲线

    Figure  6.  Experimental and theoretical calculated torque-torsional angle curves for T300/QY8911 rectangular section tube

    图  7  复合材料层合箱梁的有限元模型

    Figure  7.  Finite element model of composite laminated box beam

    图  8  T300/QY8911复合材料层合箱梁等效抗弯刚度随铺层角度变化规律

    Figure  8.  Variation of equivalent bending stiffness of T300/QY8911 composite laminated box beam with ply angle

    图  9  T300/QY8911复合材料层合箱梁等效抗扭刚度随铺层角度变化规律

    Figure  9.  Variation of equivalent torsion stiffness of T300/QY8911 composite laminated box beam with ply angle

    图  10  各向同性材料箱梁的抗弯刚度和抗扭刚度随厚高比的变化曲线

    Figure  10.  Curves of bending stiffness and torsional stiffness with thickness-to-height ratio of thin-walled box beam with isotropic materials

    图  11  不同宽高比和厚高比的各向同性材料箱梁抗弯刚度的比值k

    Figure  11.  Variation of ratio of bending stiffness k with different aspect ratios and different thickness-to-height ratios of thin-walled box beam with isotropic materials

    图  12  不同铺层方式复合材料层合箱梁等效抗弯刚度

    Figure  12.  Equivalent bending stiffness of composite laminated box beams with different types of lay-up

    图  13  不同铺层方式复合材料层合箱梁等效抗扭刚度

    Figure  13.  Equivalent torsional stiffness of composite laminated box beams with different types of lay-up

    图  14  不同铺层方式复合材料层合箱梁的等效刚度随铺层角度θ的变化规律

    Figure  14.  Variation of equivalent stiffness with ply angle θ of composite laminated box beams with different lay-ups

    表  2  复合材料矩形截面管铺层参数和几何尺寸

    Table  2.   Layup parameters and geometric dimensions of composite rectangular section tube

    Group Specimen Lay-ups b/mm h/mm T/mm L/mm
    B BCS1 [30]6 20 20 1.00 200
    BCS2 [0/90]32020 0.98 200
    BCS4 [30/−30/30]s2020 1.01 200
    BCS5 [02/±30/±60] 2020 1.02 200
    T TCS1 [30]6 2020 1.00 200
    TCS3 [04/±45] 2020 0.99 200
    TCS4 [30/−30/30]s 2020 1.01 200
    TCS5 [02/±30/±60] 20 20 1.02 200
    Notes: In BCS1 and TCS1, B represents the bending test, T represents the torsion test, CS represents the carbon fiber reinforced resin composite square tube, and 1 is the specimen number; b—Width of the section; h—Height of the section; T—Wall thickness; L—Length of the tube.
    下载: 导出CSV

    表  1  T300/QY8911材料力学性能参数

    Table  1.   Mechanical properties parameters of T300/QY8911

    Material propertyValue
    E1/GPa135
    E2=E3/GPa8.8
    G12=G13/GPa4.47
    G23/GPa3.0
    v12=v130.33
    v230.33
    下载: 导出CSV

    表  3  T300/QY8911矩形截面管等效抗弯刚度理论值与试验值对比

    Table  3.   Comparisons between theoretical and experimental values of equivalent bending stiffness for T300/QY8911 rectangular section tube

    No.Experiment/TheoryBending stiffness/(N·mm2)Error/%
    BCS1Experiment54 580 205
    <Kx>45 536 750−16.6
    Kx58 547 2507.3
    BCS2Experiment162 759 101
    <Kx>169 383 5314.1
    Kx168 580 5033.6
    BCS4Experiment74 004 918
    <Kx>45 536 750−38.5
    Kx78 930 3676.7
    BCS5Experiment139 189 698
    <Kx>125 002 347−10.2
    Kx143 815 8663.3
    Note: <Kx> and Kx are bending stiffnesses calculated by Eqs.(19) and Eqs.(12),respectively.
    下载: 导出CSV

    表  4  T300/QY8911矩形截面管等效抗扭刚度理论值与试验值对比

    Table  4.   Comparisons between theoretical and experimental values of equivalent torsional stiffness for T300/QY8911 rectangular section tube

    No.Experiment/TheoryTorsional stiffness/(N·mm2)Error/%
    TCS1Experiment44 087 964-
    <Kz>106 484 765141.53
    Kz45 815 3453.92
    TCS3Experiment92 078 987-
    <Kz>108 910 04818.28
    Kz96 489 3934.78
    TCS4Experiment159 784 264-
    <Kz>165 162 2373.36
    Kz165 162 2373.36
    TCS5Experiment126 678 364-
    <Kz>144 476 62614.04
    Kz129 924 2772.56
    Note: <Kz> and Kz are torsional stiffnesses calculated by Eqs.(20) and Eqs.(13),respectively.
    下载: 导出CSV

    表  5  复合材料的层合箱梁5种铺层方式

    Table  5.   Five kinds of lay-up methods for composite laminated box beam

    No.Lay-ups
    CRL1[0/(±θ/04)4]s
    CRL2[90/(04θ)4]s
    CRL3[0/(904θ)4]s
    CRL4[90/(±45)11θ]s
    CRL5[90/(±45/±θ)4]s
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-05-23
  • 录用日期:  2019-06-26
  • 网络出版日期:  2019-07-09
  • 刊出日期:  2020-06-15

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