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基于重构边界光滑离散剪切间隙法的复合材料层合板自由振动分析

李情 陈莘莘

李情,陈莘莘. 基于重构边界光滑离散剪切间隙法的复合材料层合板自由振动分析 [J]. 应用数学和力学,2022,43(10):1123-1132 doi: 10.21656/1000-0887.430109
引用本文: 李情,陈莘莘. 基于重构边界光滑离散剪切间隙法的复合材料层合板自由振动分析 [J]. 应用数学和力学,2022,43(10):1123-1132 doi: 10.21656/1000-0887.430109
LI Qing, CHEN Shenshen. Free Vibration Analysis of Laminated Composite Plates Based on the Reconstructed Edge-Based Smoothing DSG Method[J]. Applied Mathematics and Mechanics, 2022, 43(10): 1123-1132. doi: 10.21656/1000-0887.430109
Citation: LI Qing, CHEN Shenshen. Free Vibration Analysis of Laminated Composite Plates Based on the Reconstructed Edge-Based Smoothing DSG Method[J]. Applied Mathematics and Mechanics, 2022, 43(10): 1123-1132. doi: 10.21656/1000-0887.430109

基于重构边界光滑离散剪切间隙法的复合材料层合板自由振动分析

doi: 10.21656/1000-0887.430109
基金项目: 国家自然科学基金(12172131;11772129)
详细信息
    作者简介:

    李情(1986—),女,讲师,硕士(E-mail:liqing_726@163.com

    陈莘莘(1975—),男,教授,博士(通讯作者. E-mail:chenshenshen@tsinghua.org.cn

  • 中图分类号: O242; O343

Free Vibration Analysis of Laminated Composite Plates Based on the Reconstructed Edge-Based Smoothing DSG Method

  • 摘要:

    重构边界光滑离散剪切间隙(RES-DSG3)法,利用边界光滑技术将域积分转化为沿光滑域边界的边界积分,结合基于全局坐标系的非等参离散剪切间隙(DSG)法,避免了坐标映射和Jacobi矩阵的计算,同时克服了“剪切自锁”现象,提高了计算的精度。基于一阶剪切变形理论,采用该文给出的方法,从不同材料参数、边厚比、边界条件等几个方面对复合材料层合板自由振动固有频率进行了数值分析,通过典型算例的计算,验证了该方法的可行性和有效性。

  • 图  1  层合板的坐标系

    Figure  1.  The coordinate system for the laminate

    图  2  三角形单元和基于边界的光滑域

    Figure  2.  Triangular elements and smoothing domains associated with edges

    表  1  四层复合材料简支层合板的一阶无量纲固有频率

    Table  1.   The non-dimensional 1st fundamental frequency of the simply supported 4-layer laminated composite plate

    number of meshesE1/ E2=10 E1/ E2=20 E1/ E2=30
    α=0α=0.4ref. [21]α=0α=0.4ref. [21]α=0α=0.4ref. [21]
    13 × 138.2938.3098.298 9.5259.5269.567 10.25910.24610.326
    15 × 158.2938.3069.5359.52810.27510.255
    17 × 178.2948.3009.5419.53910.28510.276
    19 × 198.2948.3019.5469.54810.29310.283
    下载: 导出CSV

    表  2  三层复合材料层合板的一阶无量纲固有频率

    Table  2.   The non-dimensional 1st fundamental frequency of the 3-layer laminated composite plate

    a/hmethodSSSCCCa/hmethodSSSCCC
    2ref. [22]5.2115.2175.26310ref. [22]14.80417.19919.678
    ref.[21]5.2055.2115.257ref. [21]14.76717.17519.669
    present5.1495.5715.256present14.47517.34619.626
    5ref. [22]10.20710.65811.274100ref. [22]18.35528.16540.234
    ref. [21]10.29010.64611.266ref. [21]18.89128.50140.743
    present10.11610.67511.477present18.56528.61640.761
    下载: 导出CSV

    表  3  三层复合材料层合板前三阶无量纲固有频率(a/h=10)

    Table  3.   The non-dimensional 1st 3 fundamental frequencies of the 3-layer laminated composite plate (a/h=10)

    modelmethodSSSCCC
    1present14.38417.34619.626
    ref. [23]14.76617.17519.669
    2present22.04023.79425.187
    ref. [23]22.15823.67725.349
    3present36.52137.99638.553
    ref. [23]36.90037.72038.650
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-03-31
  • 录用日期:  2022-07-15
  • 修回日期:  2022-06-22
  • 网络出版日期:  2022-09-14
  • 刊出日期:  2022-10-31

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