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吸湿老化影响下天然纤维增强复合圆柱壳屈曲分析的辛方法

张俊霖 倪一文 李庆东 仝真真 周震寰 徐新生

张俊霖,倪一文,李庆东,仝真真,周震寰,徐新生. 吸湿老化影响下天然纤维增强复合圆柱壳屈曲分析的辛方法 [J]. 应用数学和力学,2021,42(12):1238-1247 doi: 10.21656/1000-0887.420018
引用本文: 张俊霖,倪一文,李庆东,仝真真,周震寰,徐新生. 吸湿老化影响下天然纤维增强复合圆柱壳屈曲分析的辛方法 [J]. 应用数学和力学,2021,42(12):1238-1247 doi: 10.21656/1000-0887.420018
ZHANG Junlin, NI Yiwen, LI Qingdong, TONG Zhenzhen, ZHOU Zhenhuan, XU Xinsheng. A Symplectic Approach for Buckling Analysis of Natural Fiber Reinforced Composite Shells Under Hygrothermal Aging[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1238-1247. doi: 10.21656/1000-0887.420018
Citation: ZHANG Junlin, NI Yiwen, LI Qingdong, TONG Zhenzhen, ZHOU Zhenhuan, XU Xinsheng. A Symplectic Approach for Buckling Analysis of Natural Fiber Reinforced Composite Shells Under Hygrothermal Aging[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1238-1247. doi: 10.21656/1000-0887.420018

吸湿老化影响下天然纤维增强复合圆柱壳屈曲分析的辛方法

doi: 10.21656/1000-0887.420018
基金项目: 国家自然科学基金(12002071);中国航空科学基金(2018ZC63003)
详细信息
    作者简介:

    张俊霖(1997—),男,博士(E-mail:junlin_zhang@mail.dlut.edu.cn

    仝真真(1986—),女,讲师,博士(通讯作者. E-mail:tongzhzh@163.com

  • 中图分类号: O343.9

A Symplectic Approach for Buckling Analysis of Natural Fiber Reinforced Composite Shells Under Hygrothermal Aging

  • 摘要:

    针对一类天然纤维增强复合(natural fiber reinforced composite, NFRC)圆柱壳的屈曲问题展开研究,基于Reissner壳体理论和辛方法,建立了轴压NFRC圆柱壳在Hamilton体系下的屈曲控制方程。将原问题归结为辛空间下的辛本征问题,通过求解辛本征值和本征解可以直接获得高精度的临界载荷和解析的屈曲模态。数值算例分析了NFRC材料的吸湿老化过程对辛本征解表达式的影响,并详细讨论了老化时间、纤维含量和几何参数对NFRC圆柱壳屈曲行为的影响。

  • 图  1  NFRC圆柱壳示意图

    Figure  1.  The geometry of a NFRC cylindrical shell

    图  2  不同纤维含量NFRC圆柱壳临界载荷随老化时间的变化曲线

    Figure  2.  Variations of critical loads for NFRC cylindrical shells with various f values vs. the aging time

    图  3  纤维含量f = 0.15时NFRC圆柱壳屈曲模态图

    Figure  3.  Buckling mode shapes of NFRC cylindrical shells with f = 0.15

    图  4  不同纤维含量NFRC圆柱壳临界载荷随壳体厚度变化曲线

    注 为了解释图中的颜色,读者可以参考本文的电子网页版本,后同。

    Figure  4.  Variations of critical loads for NFRC cylindrical shells with various f values vs. the shell thickness

    图  5  不同纤维含量NFRC圆柱壳临界载荷随壳体长度变化曲线

    Figure  5.  Variations of critical loads for NFRC cylindrical shells with various f values vs. the shell length

    表  1  两端简支FGM圆柱壳的临界载荷(单位:MPa)

    Table  1.   Critical loads of an S-S FGM cylindrical shell (unit: MPa)

    h / R1/5001/4001/3001/2001/100
    present163.938204.581273.089409.309818.942
    ref. [14]164.148205.185273.580410.371820.741
    下载: 导出CSV

    表  2  两端固支时NFRC圆柱壳的本征函数表达详解

    Table  2.   Detailed eigen function expressions of the C-C NFRC cylindrical shell

    ft/h$ {{\boldsymbol{\xi}} } $σcr/MPa
    case$ \pm {\lambda _{1,2}} $$ \pm {\lambda _{3,4}} $$ \pm {\lambda _{5,6}} $$ \pm {\lambda _{7,8}} $
    0.05 0 iii 4.595i 4.249i 4.041−2.325i 4.041+2.325i 3.985
    250 i 6.875i 6.505i 5.379 8.590 3.274
    500 iii 6.264i 5.752i 4.733−4.109i 4.733+4.109i 3.155
    0.10 0 i 4.525i 4.359i 1.770 11.45 4.374
    250 i 5.898i 5.734i 2.818 12.28 3.031
    500 iii 4.512i 4.274i 4.121−2.089i 4.121+2.089i 2.857
    0.15 0 ii 10.39i 9.425i 0.835 1i 0.530 4i 4.850
    250 i 3.717i 3.508i 1.038 12.83 1.232
    500 i 2.976i 2.796i 0.7722 11.08 0.9117
    下载: 导出CSV

    表  3  两端简支时NFRC圆柱壳的本征函数表达详解

    Table  3.   Detailed eigen function expressions of the S-S NFRC cylindrical shell

    ft/h$ {{\boldsymbol{\xi}} } $σcr/MPa
    case$ \pm {\lambda _{1,2}} $$ \pm {\lambda _{3,4}} $$ \pm {\lambda _{5,6}} $$ \pm {\lambda _{7,8}} $
    0.05 0 i 6.283i 4.212i 2.984 9.209 3.271
    250 iii 6.283i 5.502i 5.011−3.477i 5.011+3.477i 2.763
    500 iii 6.283i 5.735i 4.734−4.108i 4.734+4.108i 2.671
    0.10 0 i 4.742i 3.142i 1.839 8.509 3.842
    250 i 6.283i 4.214i 2.988 9.203 2.567
    500 i 5.165i 5.035i 2.900 9.315 2.383
    0.15 0 i 4.128i 3.975i 1.375 12.22 4.028
    250 i 3.258i 3.040i 0.9613 10.63 1.056
    500 i 3.386i 3.231i 0.8493 13.13 0.8091
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-01-18
  • 录用日期:  2021-01-18
  • 修回日期:  2021-11-14
  • 网络出版日期:  2021-11-29
  • 刊出日期:  2021-12-01

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