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基于对流粒子域插值物质点法的壳结构分析

王长生 于传泽 张向奎

王长生, 于传泽, 张向奎. 基于对流粒子域插值物质点法的壳结构分析[J]. 应用数学和力学, 2024, 45(9): 1147-1156. doi: 10.21656/1000-0887.440286
引用本文: 王长生, 于传泽, 张向奎. 基于对流粒子域插值物质点法的壳结构分析[J]. 应用数学和力学, 2024, 45(9): 1147-1156. doi: 10.21656/1000-0887.440286
WANG Changsheng, YU Chuanze, ZHANG Xiangkui. Shell Structure Analysis Based on the Convected Particle Domain Interpolation[J]. Applied Mathematics and Mechanics, 2024, 45(9): 1147-1156. doi: 10.21656/1000-0887.440286
Citation: WANG Changsheng, YU Chuanze, ZHANG Xiangkui. Shell Structure Analysis Based on the Convected Particle Domain Interpolation[J]. Applied Mathematics and Mechanics, 2024, 45(9): 1147-1156. doi: 10.21656/1000-0887.440286

基于对流粒子域插值物质点法的壳结构分析

doi: 10.21656/1000-0887.440286
基金项目: 

国家重点研发计划 2021YFB3300603

中央高校基本科研业务费 DUT22YG232

详细信息
    作者简介:

    王长生(1984—),男,副教授,博士(E-mail: changsheng@dlut.edu.cn)

    通讯作者:

    张向奎(1976—),男,教授,博士(通讯作者. E-mail: zhangxk@dlut.edu.cn)

  • 中图分类号: O34

Shell Structure Analysis Based on the Convected Particle Domain Interpolation

  • 摘要: 物质点法(material point method, MPM)采用Lagrange质点和Euler网格双重描述,适合处理大变形和接触问题. 该文基于对流粒子域插值物质点法(CPDI2)框架分析了薄壳结构的大变形问题:使用四边形网格来离散壳体结构,通过物质点到壳单元节点再到背景网格节点的双重映射计算基函数,在背景网格上求解动量方程,基于BT壳单元理论更新物质点的内力. 数值算例将受大变形的壳结构与参考解进行了比较,验证了该文方法的准确性.
  • 图  1  物质点到背景网格的二次映射过程

    Figure  1.  The 2-step mapping process from material points to background grids

    图  2  悬臂板的受力示意图、变形过程与计算结果

    Figure  2.  The force diagram, deformation process and calculation results of the cantilever

    图  3  半球壳的受力示意图、变形结果与计算结果

    Figure  3.  The force diagram, deformation process and calculation results of the spherical shell

    图  4  方管模型和本文算法(左侧)与LS-DYNA(右侧)的计算结果对比

    Figure  4.  The steel box beam model and the comparison between the results with this method(left) and the LS-DYNA(right)

    表  1  Utip的解析解与本文算法结果对比

    Table  1.   The comparison between the result obtained with this method and the exact solution of Utip

    P/Pmax Wtip Utip this papaer solution δ/%
    0.1 1.309 0.103 0.100 2.9
    0.2 2.493 0.381 0.374 1.8
    0.3 3.488 0.763 0.749 1.8
    0.4 4.292 1.184 1.167 1.4
    0.5 4.933 1.604 1.585 1.2
    0.6 5.444 2.002 1.981 1.0
    0.7 5.855 2.370 2.345 1.1
    0.8 6.190 2.705 2.678 1.0
    0.9 6.467 3.010 2.978 1.1
    1.0 6.698 3.286 3.259 0.8
    下载: 导出CSV

    表  2  VA的解析解与本文算法结果对比

    Table  2.   The comparison between the results with this method and the exact solution of VA

    P/Pmax UB VA this papaer solution δ/%
    0.1 1.840 1.499 1.472 1.8
    0.2 3.261 2.321 2.287 1.5
    0.3 4.339 2.819 2.791 1.0
    0.4 5.196 3.158 3.104 1.7
    0.5 5.902 3.406 3.372 1.0
    0.6 6.497 3 598 3.523 2.1
    0.7 7.006 3.750 3.701 1.3
    0.8 7.448 3.875 3.872 0.1
    0.9 7.835 3.976 3.944 0.8
    1.0 8.178 4.067 4.050 0.4
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-09-20
  • 修回日期:  2024-01-15
  • 刊出日期:  2024-09-01

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