引入Sierpinski层级特性的新型薄壁多胞管轴向冲击吸能特性

何强 王勇辉 史肖娜 顾航 陈宇

何强, 王勇辉, 史肖娜, 顾航, 陈宇. 引入Sierpinski层级特性的新型薄壁多胞管轴向冲击吸能特性[J]. 爆炸与冲击, 2020, 40(12): 123101. doi: 10.11883/bzycj-2020-0055
引用本文: 何强, 王勇辉, 史肖娜, 顾航, 陈宇. 引入Sierpinski层级特性的新型薄壁多胞管轴向冲击吸能特性[J]. 爆炸与冲击, 2020, 40(12): 123101. doi: 10.11883/bzycj-2020-0055
HE Qiang, WANG Yonghui, SHI Xiaona, GU Hang, CHEN Yu. Energy absorption of new thin-walled, multi-cellular, tubular structures with Sierpinski hierarchical characteristics under axial impact[J]. Explosion And Shock Waves, 2020, 40(12): 123101. doi: 10.11883/bzycj-2020-0055
Citation: HE Qiang, WANG Yonghui, SHI Xiaona, GU Hang, CHEN Yu. Energy absorption of new thin-walled, multi-cellular, tubular structures with Sierpinski hierarchical characteristics under axial impact[J]. Explosion And Shock Waves, 2020, 40(12): 123101. doi: 10.11883/bzycj-2020-0055

引入Sierpinski层级特性的新型薄壁多胞管轴向冲击吸能特性

doi: 10.11883/bzycj-2020-0055
基金项目: 国家自然科学基金(51705215)
详细信息
    作者简介:

    何 强(1989- ),男,博士,副教授,heqiang@just.edu.cn

  • 中图分类号: O382.2

Energy absorption of new thin-walled, multi-cellular, tubular structures with Sierpinski hierarchical characteristics under axial impact

  • 摘要:

    为提高薄壁结构的吸能能力,基于Sierpinski分形结构提出了一种具有层级特性的新型薄壁管,即Sierpinski层级管(Sierpinski hierarchical tube, SHT)。采用非线性有限元法对SHTs在轴向冲击载荷作用下的变形模式和能量吸收特性进行了数值分析,并与普通三角形薄壁管在轴向冲击载荷作用下的变形模式和能量吸收特性进行了对比。结果表明:SHTs的变形模式为轴对称渐进屈曲模式,在薄壁管中引入Sierpinski层级特性后,胞壁弯曲过程的半折叠波长减小,促使压缩过程中形成更多的塑性折叠单元,有利于提高薄壁结构能量吸收能力。进一步基于能量守恒理论和塑性铰理论对SHTs的轴向压缩应力进行理论求解,并通过有限元数值模拟验证其准确性。在相同的相对密度下,一阶、二阶及三阶SHTs的动态压缩应力较普通三角形薄壁管的动态压缩应力提高了85.8%、138.2%和183.8%。将Sierpinski层级特性引入薄壁管的设计中,能够有效提高薄壁管的耐撞性能。

  • 图  1  SHT几何结构

    Figure  1.  Geometrical structures of SHTs

    图  2  SHTs结构角单元示意图

    Figure  2.  Schematic angle elements of SHTs

    图  3  SHT轴向压缩有限元模型

    Figure  3.  A finite element model for dynamic axial compression of an SHT

    图  4  不同SHTs的轴向压缩变形

    Figure  4.  Deformation of different SHTs under axial dynamic crushing

    图  5  两类基本单元

    Figure  5.  Two kinds of basic elements

    图  6  SHTs变形机理

    Figure  6.  Folding mechanisms of SHTs

    图  7  薄壁结构在轴向冲击载荷下的变形示意图

    Figure  7.  Schematic of the buckling of a thin-walled structure under axial impact load

    图  8  基本折叠单元凸缘充分压缩示意图

    Figure  8.  Schematic full compression of a basic folding element flange

    图  9  直角角单元与V形角单元之间薄膜耗散能关系

    Figure  9.  Membrane energy relationship between the rectangular angle element and the V-angle element

    图  10  变形模式

    Figure  10.  Deformation modes

    表  1  薄壁方形管动态平均压缩力模拟结果与实验数据[14]的比较

    Table  1.   Comparison between simulated and experimental mean dynamic compressive forces[14] for thin-walled square tubes

    编号$ {P}_{{\rm{m}}}^{\rm{d}}/{\rm{k}}{\rm{N}} $误差/%
    实验[14]模拟
    S210.2610.865.8
    S315.7116.706.3
    S418.8319.473.4
    S529.8331.927.0
    下载: 导出CSV

    表  2  各采样点有限元结果与理论预测值对比

    Table  2.   Comparison of finite element results and theoretical predictions for all the sampling points

    层级级数$ \bar {\rm{\rho }} $$ {t}_{i} $/mm$ {l}_{i} $/mm$ {\sigma }_{{\rm{m}}}^{\rm{d}} $/MPa相对误差/%
    模拟理论
    0th0.0771.00901.9251.968−2.18
    0.1001.302.8402.917−2.64
    0.1231.604.1183.9823.42
    1st0.0770.67453.5773.5231.54
    0.1000.874.9485.221−5.23
    0.1231.077.0467.129−1.17
    2nd0.0770.4422.54.5864.4463.14
    0.1000.586.4076.590−2.77
    0.1230.719.1868.9982.09
    3rd0.0770.3011.255.4645.2713.67
    0.1000.397.7207.813−1.19
    0.1230.4710.97210.6692.84
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-03-03
  • 修回日期:  2020-06-07
  • 刊出日期:  2020-12-05

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