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

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

王长生^{1, 2,},
于传泽¹,
张向奎^3, ,

1.
大连理工大学机械工程学院, 辽宁大连 116023
2.
大连理工大学宁波研究院, 浙江宁波 315016
3.
大连理工大学控制科学与工程学院, 辽宁大连 116023

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
计量
- 文章访问数: 97
- HTML全文浏览量: 35
- PDF下载量: 40
- 被引次数: 0
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

Shell Structure Analysis Based on the Convected Particle Domain Interpolation

1.
School of Mechanical Engineering, Dalian University of Technology, Dalian, Liaoning 116023, P.R.China
2.
Ningbo Institute, Dalian University of Technology, Ningbo, Zhejiang 315016, P.R.China
3.
School of Control Science and Engineering, Dalian University of Technology, Dalian, Liaoning 116023, P.R.China

摘要

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.
- 对流粒子域插值物质点法 /
- BT壳单元 /
- 超弹性材料 /
- 非线性大变形
Abstract: The material point method (MPM) adopts the dual description of Lagrangian particles and Euler grids, so it can deal with large deformation and contact problems conveniently. The large deformation problem of thin shell structures was analyzed based on the framework of the convected particle domain interpolation material point method (CPDIMPM). The quadrilateral mesh was used to discretize the shell structure. The basis function was calculated by the double mapping from the material point to the shell element node and then to the background grid node. The momentum equation was solved on the background grid, and the internal force of the material point was updated based on the Belytschko-Tsay (BT) shell element theory. In the numerical example, the comparison of large deformations of the shell structure with reference solutions verifies the accuracy of the proposed method.
- CPDIMPM /
- BT shell element /
- hyperelastic material /
- nonlinear large deformation

HTML全文

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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)

下载: 全尺寸图片幻灯片

表 1 U_tip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 U_tip

P/P_max	W_tip	U_tip	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 V_A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 V_A

P/P_max	U_B	V_A	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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