一维有限元的EEP单元及其自适应分析

杨帅; 袁驷

doi:10.21656/1000-0887.450036

一维有限元的EEP单元及其自适应分析

doi: 10.21656/1000-0887.450036

杨帅^,,
袁驷

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

基金项目:

国家自然科学基金（51878383；51378293）

详细信息

作者简介:
杨帅（1997—），男，博士生(通讯作者. E-mail: s-yang20@mails.tsinghua.edu.cn)；袁驷（1953—），男，教授，博士.

通讯作者:
杨帅（1997—），男，博士生(通讯作者. E-mail: s-yang20@mails.tsinghua.edu.cn).

中图分类号: O342
计量
- 文章访问数: 14
- HTML全文浏览量: 2
- PDF下载量: 5
- 被引次数: 0
出版历程
- 收稿日期: 2024-02-18
- 修回日期: 2024-05-08

EEP Elements for the 1D Finite Element Method and the Adaptivity Analysis

YANG Shuai^,,
YUAN Si

Key Laboratory of Civil Engineering Safety and Durability, Ministry of Education, Department of Civil Engineering, Tsinghua University, Beijing 100084, P.R.China

Funds:

The National Science Foundation of China(51878383；51378293)

摘要

摘要: 对m(>1)次单元，基于单元能量投影(element energy projection，简称EEP)法提出的简约格式位移解u^*具有比常规有限元解u^h至少高一阶的精度，据此提出了EEP单元概念，并给出以EEP单元作为最终解的自适应有限元求解策略.通过编制相应的计算程序分析了一维非自伴随问题，计算结果与理论预期吻合较好，验证了自适应求解策略的有效性和可靠性.研究结果表明：该法可以给出按最大模度量、逐点满足误差限的解答，相较于常规单元，最终的求解单元数更少.
- 一维有限元 /
- 单元能量投影(EEP) /
- EEP单元 /
- 自适应有限元法
Abstract: For the elements of degree m(>1), simplified form solution u^* based on the element energy projection (EEP) method has at least 1-order higher accuracy than conventional finite element solution u^h.As a result, the EEP element, with simplified form EEP solution u^h in as the final solution, was proposed, and a corresponding adaptive finite element analysis strategy for EEP elements was developed. By means of the developed algorithm, the 1D 2-point boundary value problem was analyzed, and the computation results are in good agreement with theoretical solutions, verifying the effectiveness and reliability of the proposed adaptivity strategy. The theoretical study and numerical experiments show that, the proposed method provides an EEP element solution satisfying the preset error tolerances in the maximum norm with fewer elements and less adaptive steps compared to conventional finite elements.
- 1D problem /
- element energy projection (EEP) /
- EEP element /
- adaptive finite element method

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参考文献(21)

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