基于EEP法的三维有限元超收敛计算初探

袁驷; 吴越; 徐俊杰; 邢沁妍

doi:10.6052/j.issn.1000-4750.2016.05.ST07

基于EEP法的三维有限元超收敛计算初探

1.
清华大学土木工程系, 土木工程安全与耐久教育部重点实验室, 北京 100084;
2.
中国地震局工程力学研究所, 中国地震局地震工程与工程振动重点实验室, 哈尔滨 150080

基金项目: 国家自然科学基金项目（51378293，51078199）

详细信息

作者简介:
吴越(1991-),男,江西人,博士生,从事结构工程研究(E-mail:ywu12@mails.tsinghua.edu.cn);徐俊杰(1984-),男,山东人,副研究员,博士,从事结构工程研究(E-mail:xujj@iem.ac.cn);邢沁妍(1981-),女,辽宁人,讲师,博士,从事结构工程研究(E-mail:xingqy@mail.thu.edu.cn).

通讯作者:
袁驷(1953-),男,北京人,教授,博士,中国土木工程学会副理事长,中国力学学会副理事长,从事结构工程研究(E-mail:yuans@tsinghua.edu.cn).

中图分类号: TU311.4
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出版历程
- 收稿日期: 2016-05-30
- 修回日期: 2016-08-25
- 刊出日期: 2016-09-24

EXPLORATION ON SUPER-CONVERGENT SOLUTIONS OF 3D FEM BASED ON EEP METHOD

1.
Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry, Department of Civil Engineering, Tsinghua University, Beijing 100084, China;
2.
Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China

More Information

Corresponding author:
YUAN Si: 10.6052/j.issn.1000-4750.2016.05.ST07

摘要

摘要: 二维有限元法（FEM）的超收敛计算，借助有限元线法（FEMOL）作为桥梁，分两步采用单元能量投影（EEP）法导出超收敛公式，初步形成“逐维离散、逐维恢复”的方案。然而这一思路直接应用于三维问题却遇到了困扰：一维问题的EEP解（位移和导数）均可达到相同的超收敛阶，而二维问题却难以做到。研究发现，为了得到三维问题的EEP超收敛位移，只需提供二维问题最低阶的超收敛位移即可。该文按此思路推导了非规则网格下三维六面体单元的EEP超收敛位移公式，给出了一个实施方案，并通过数值算例验证了此方案的有效性。
- 有限元法 /
- 有限元线法 /
- 超收敛 /
- 三维问题 /
- 单元能量投影 /
- 六面体单元
Abstract: In the super-convergence computation of a 2D Finite Element Method (FEM), the "discretization and recovery by dimension" scheme has basically formed by taking the Finite Element Method of Lines (FEMOL) as a bridge and iteratively by adopting the super-convergent formulas derived from the Element Energy Projection (EEP) method. However, when applying this idea to 3D problems, it occurs a puzzle that the EEP solutions (including displacements and derivatives) of 1D problems all share the same super-convergence order whereas those of 2D problems can hardly do. Recent studies show that in order to obtain the EEP super-convergent solution of a 3D problem, the displacement of a 2D problem with the least super-convergence order is merely necessary. Following this idea, this paper derives EEP super-convergent formulas for 3D hexahedron elements on irregular meshes, proposes an implementation scheme, and verifies its effectiveness with numerical examples.
- FEM /
- FEMOL /
- super-convergence /
- 3D problem /
- element energy projection /
- hexahedron element

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参考文献(10)

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施引文献(8)

期刊类型引用(4)

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2.	袁驷，蒋凯峰，邢沁妍. 膜结构极小曲面找形的一种自适应有限元分析. 工程力学. 2019(01): 15-22 . 本站查看
3.	叶康生，邱廷柱. 二阶非线性常微分方程边值问题有限元p型超收敛计算. 工程力学. 2019(12): 7-14 . 本站查看
4.	Si YUAN，Yue WU，Qinyan XING. Recursive super-convergence computation for multi-dimensional problems via one-dimensional element energy pro jection technique. Applied Mathematics and Mechanics(English Edition). 2018(07): 1031-1044 . 必应学术