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基于单胞有限元的波纹板等效刚度特性

王远 臧勇 管奔 秦勤

王远, 臧勇, 管奔, 等 . 基于单胞有限元的波纹板等效刚度特性[J]. 北京航空航天大学学报, 2018, 44(6): 1230-1238. doi: 10.13700/j.bh.1001-5965.2017.0698
引用本文: 王远, 臧勇, 管奔, 等 . 基于单胞有限元的波纹板等效刚度特性[J]. 北京航空航天大学学报, 2018, 44(6): 1230-1238. doi: 10.13700/j.bh.1001-5965.2017.0698
WANG Yuan, ZANG Yong, GUAN Ben, et al. Equivalent stiffness property of dimpled sheet based on unit cell finite element[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(6): 1230-1238. doi: 10.13700/j.bh.1001-5965.2017.0698(in Chinese)
Citation: WANG Yuan, ZANG Yong, GUAN Ben, et al. Equivalent stiffness property of dimpled sheet based on unit cell finite element[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(6): 1230-1238. doi: 10.13700/j.bh.1001-5965.2017.0698(in Chinese)

基于单胞有限元的波纹板等效刚度特性

doi: 10.13700/j.bh.1001-5965.2017.0698
基金项目: 

中央高校基本科研业务费专项资金 FRF-TP-16-010A3

工信部2016年智能制造综合标准化与新模式应用项目 

详细信息
    作者简介:

    王远  男, 博士研究生。主要研究方向:复杂结构等效力学行为、新型塑性成形方法

    臧勇  男, 教授, 博士生导师。主要研究方向:机械装备行为分析及控制、塑性加工工艺与设备

    管奔  男, 博士, 讲师。主要研究方向:机械力学行为数值模拟与测试、现代成形工艺与设备研究

    通讯作者:

    管奔, E-mail:guanben@ustb.edu.cn

  • 中图分类号: V250.3;TB383

Equivalent stiffness property of dimpled sheet based on unit cell finite element

Funds: 

the Fundamental Research Funds for the Central Universities FRF-TP-16-010A3

Intelligent Manufacturing Comprehensive Standardized and New Model Program of Ministry of Industry and Information 2016 

More Information
  • 摘要:

    为了得到波纹板的宏观刚度特性及其与表面形貌结构参数的关系,基于单胞有限元的方法对波纹板的等效刚度特性进行了研究。首先,基于单胞有限元的周期性边界条件,计算了具有周期性排布特点的波纹板的等效刚度;然后,计算了典型形貌波纹板的等效刚度特性,并进行了分析和验证;最后,运用单胞有限元的方法分析了波纹板结构参数对等效刚度特性的影响。分析结果表明:采用单胞有限元的方法可以有效计算波纹板的等效刚度;波纹板相较于基础薄板具有更高的弯曲刚度,但拉伸刚度和剪切刚度较低。当基础薄板厚度固定时,随着波纹板相对厚度的增加,拉伸刚度和剪切刚度降低,弯曲刚度升高;随着波纹板波纹相对周期间距的增加,拉伸刚度和剪切刚度升高,弯曲刚度降低。

     

  • 图 1  波纹板单胞的选取及结构参数

    Figure 1.  Selection and structural parameters of dimpled sheet unit cell

    图 2  单胞结构轮廓示意图

    Figure 2.  Schematic diagram of unit cell profile

    图 3  波纹板单胞结构组成的梁结构

    Figure 3.  Cantilever plate with unit cells of dimpled sheet

    图 4  波纹板单胞形貌的提取

    Figure 4.  Unit cell morphology extraction of dimpled sheet

    图 5  单胞结构在6种变形情况的应力云图

    Figure 5.  Stress contours of unit cell in six deformation cases

    图 6  单胞在单向拉伸时的应力分布

    Figure 6.  Stress distribution of unit cell under uniaxial tension

    图 7  等效模型的验证

    Figure 7.  Verification of equivalent model

    图 8  不同结构参数波纹板单胞结构的形貌

    Figure 8.  Morphology of unit cell of dimpled sheet with different structural parameters

    图 9  相对厚度对等效刚度特性的影响

    Figure 9.  Effect of h/t on equivalent stiffness property

    图 10  相对厚度对刚度特性的影响

    Figure 10.  Effect of p/t on equivalent stiffness property

    表  1  单胞结构6种单位应变载荷的周期性边界条件

    Table  1.   Periodic boundary condition for six unit strain loads of unit cell

    应变 u(p, y, z)-u(0, y, z) v(p, y, z)-v(0, y, z) w(p, y, z)-w(0, y, z) u(x, p, z)-u(x, 0, z) v(x, p, z)-v(x, 0, z) w(x, p, z)-w(x, 0, z)
    =1 p 0 0 0 0 0
    =1 0 0 0 0 p 0
    =1 0 p/2 0 p/2 0 0
    =1 pz 0 -p2/2 0 0 0
    =1 0 0 0 0 pz -p2/2
    =1 0 pz/2 -py/2 pz/2 0 -px/2
    下载: 导出CSV

    表  2  波纹板与基础薄板的刚度特性

    Table  2.   Stiffness properties of dimpled sheet and base flat sheet

    刚度 波纹板 基础薄板 波纹板与基础薄板刚度比值
    A11/(N·mm-1) 24 069 38 716 0.622
    A12/(N·mm-1) -162 12 776 -0.013
    A22/(N·mm-1) 24 069 38 716 0.622
    A66/(N·mm-1) 6 558 12 970 0.506
    D11/(N·mm) 1 015 806 1.26
    D12/(N·mm) 517 266 1.944
    D22/(N·mm) 1 015 806 1.26
    D66/(N·mm) 1 165 270 4.315
    下载: 导出CSV
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出版历程
  • 收稿日期:  2017-11-13
  • 录用日期:  2017-12-29
  • 网络出版日期:  2018-06-20

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