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一般宏观应力状态下凹角蜂窝结构的屈曲性能分析

周世奇 侯秀慧 邓子辰

周世奇,侯秀慧,邓子辰. 一般宏观应力状态下凹角蜂窝结构的屈曲性能分析 [J]. 应用数学和力学,2023,44(1):12-24 doi: 10.21656/1000-0887.430202
引用本文: 周世奇,侯秀慧,邓子辰. 一般宏观应力状态下凹角蜂窝结构的屈曲性能分析 [J]. 应用数学和力学,2023,44(1):12-24 doi: 10.21656/1000-0887.430202
ZHOU Shiqi, HOU Xiuhui, DENG Zichen. Buckling Analysis of Re-Entrant Honeycomb Structures Under General Macroscopic Stress States[J]. Applied Mathematics and Mechanics, 2023, 44(1): 12-24. doi: 10.21656/1000-0887.430202
Citation: ZHOU Shiqi, HOU Xiuhui, DENG Zichen. Buckling Analysis of Re-Entrant Honeycomb Structures Under General Macroscopic Stress States[J]. Applied Mathematics and Mechanics, 2023, 44(1): 12-24. doi: 10.21656/1000-0887.430202

一般宏观应力状态下凹角蜂窝结构的屈曲性能分析

doi: 10.21656/1000-0887.430202
基金项目: 国家自然科学基金(11972287;11872303)
详细信息
    作者简介:

    周世奇(1995—),男,硕士生(E-mail:zhoushiqi@mail.nwpu.edu.cn

    侯秀慧(1983—),女,副教授(通讯作者. E-mail:houxiuhui@nwpu.edu.cn

    邓子辰(1963—),男,教授(E-mail:dweifan@nwpu.edu.cn

  • 中图分类号: O34

Buckling Analysis of Re-Entrant Honeycomb Structures Under General Macroscopic Stress States

  • 摘要:

    基于凹角蜂窝的负Poisson比拉胀效应,对其屈曲力学性能进行了有限元仿真分析,得出区别于传统正六边形蜂窝结构的两种屈曲模态。为了研究这两种屈曲模态的屈曲强度以及产生机理,采用梁柱理论对其进行了理论分析。根据梁-柱方程和平衡关系建立包含杆端弯矩和杆端转角的方程组,利用屈曲临界条件建立稳定方程,得到屈曲强度的解析表达式。采用增材制造技术打印凹角蜂窝试件,对其屈曲性能进行实验验证。结果表明,双轴加载条件的不同会引起屈曲模态的显著变化;区别于传统蜂窝结构,凹角蜂窝的负Poisson比拉胀效应使其在双轴受拉状态下发生屈曲失稳;双轴应力状态下的屈曲失效界面分析获得了典型的屈曲分岔现象。这项研究对凹角蜂窝因失稳而破坏以及利用凹角蜂窝失稳实现特殊力学性能的研究具有一定的指导意义。

  • 图  1  凹角蜂窝的有限元模型和边界条件:(a) 沿着$ x $方向准静态压缩的边界条件;(b) 沿着$ y $方向准静态压缩的边界条件

    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  1.  The finite element model and boundary conditions for the re-entrant honeycomb: (a) boundary conditions for the quasi-static compression along the x direction; (b) boundary conditions for the quasi-static compression along the y direction

    图  2  收敛性计算结果

    Figure  2.  Convergence calculation results

    图  3  凹角蜂窝在单轴荷载作用下的前十阶屈曲模态:(a) 沿着y方向单轴压缩;(b) 沿着x方向单轴压缩

    Figure  3.  The 1st 10 buckling modes of the re-entrant honeycomb under uniaxial loading: (a) uniaxial compression along the y direction;(b) uniaxial compression along the x direction

    图  4  凹角蜂窝的第一阶模态:(a) 沿着$ x $方向准静态压缩得到屈曲模态Ⅰ;(b) 沿着$ y $方向准静态压缩得到屈曲模态Ⅱ

    Figure  4.  The 1st buckling modes of the re-entrant honeycomb: (a) buckling mode Ⅰ obtained under quasi-static compression along the $ x $ direction; (b) buckling mode Ⅱ obtained under quasi-static compression along the $ y $ direction

    图  5  不同单胞数量的凹角蜂窝的屈曲模态:(a) 3×4构型沿着y方向单轴压缩;(b) 3×4构型沿着x方向单轴压缩;(c) 7×10构型沿着y方向单轴压缩;(d) 7×10构型沿着x方向单轴压缩

    Figure  5.  Buckling modes of the re-entrant honeycomb with different numbers of unit cells: (a) the 3×4 configuration under uniaxial compression in the y direction; (b) the 3×4 configuration under uniaxial compression in the x direction; (c) the 7×10 configuration under uniaxial compression in the y direction; (d) the 7×10 configuration under uniaxial compression in the x direction

    图  6  不同单胞数量的凹角蜂窝的屈曲强度

    Figure  6.  Buckling strengths of the re-entrant honeycomb with different numbers of unit cells

    图  7  梁柱的杆端转角和杆端弯矩

    Figure  7.  End rotations and end bending moments of the beam-column

    图  8  一般宏观应力状态下的凹角蜂窝结构:(a) 凹角蜂窝整体的几何结构和应力状态;(b) 基础单胞的几何结构和应力状态

    Figure  8.  The re-entrant honeycomb structure under a general macroscopic stress state:(a) the geometric structure and the stress state of the re-entrant honeycomb; (b) the geometric structure and the stress state of the unit cell

    图  9  凹角蜂窝屈曲模态Ⅰ的单胞模态和OAOC杆的内力示意图

    Figure  9.  The unit cell modes for buckling mode Ⅰ of the re-entrant honeycomb and the internal forces of rods OA and OC

    图  10  凹角蜂窝屈曲模态Ⅱ的单胞模态和OAOB杆的内力示意图

    Figure  10.  The unit cell modes for buckling mode Ⅱ of the re-entrant honeycomb and the internal forces of rods OA and OC

    图  11  凹角蜂窝屈曲模态Ⅰ和Ⅱ的失效界面

    Figure  11.  Failure surfaces for buckling modes Ⅰ and Ⅱ of the re-entrant honeycomb

    图  12  凹角蜂窝沿着$ x $方向和$ y $方向单轴压缩的实验结果和数值结果对比

    Figure  12.  Comparison of experimental and numerical results of re-entrant honeycombs under uniaxial compression along the $ x $ and $ y $ direction

    图  13  凹角蜂窝沿着$ x $方向和$ y $方向单轴压缩的应力-应变曲线

    Figure  13.  Stress-strain curves of the re-entrant honeycomb in uniaxial compression along the $ x $ and $ y $ directions

    表  1  实验、数值和理论研究得到的凹角蜂窝屈曲强度对比

    Table  1.   Comparison of buckling strengths of re-entrant honeycombs obtained from experimental, numerical and theoretical studies

    experiment simulation theory error between
    simulation and experiment
    error between
    theory and experiment
    uniaxial compression along
    the x direction (mode I)
    3.114 8 kPa 3.162 8 kPa 2.839 5 kPa 1.51% 8.83%
    uniaxial compression along
    the y direction (mode Ⅱ)
    6.279 5 kPa 6.326 2 kPa 5.903 2 kPa 0.74% 5.99%
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-06-13
  • 修回日期:  2022-07-08
  • 网络出版日期:  2023-01-07
  • 刊出日期:  2023-01-15

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