再谈从矩阵位移法看有限元位移精度的损失与恢复  

REVISITING THE LOSS AND RECOVERY OF DISPLACEMENT ACCURACY IN FEM AS SEEN FROM MATRIX DISPLACEMENT METHOD

作　　者：袁驷[1] 袁全 YUAN Si;YUAN Quan(Department of Civil Engineering,Tsinghua University,Beijing 100084,China)

机构地区：[1]清华大学土木工程系,北京100084

出　　处：《力学与实践》2020年第6期689-694,共6页Mechanics in Engineering

基　　金：国家自然科学基金资助项目(51878383,51378293)。

摘　　要：本文是文献[1]的续篇。文献[1]以一维有限元为例,揭示了其误差主要来自于各个单元的“固端解”。其后,基于这一思想的超收敛计算的单元能量投影(element energy projection,EEP)法得以创立和发展,并有效地用于自适应有限元求解。近期的反思发现,前文的思想精华还有发扬空间:既然单元“固端解”是有限元误差的主要来源,就可以用EEP公式简便地事先求出来,从而可以不经有限元计算而一举得到所需的网格划分。本文简要介绍这一最新方法的思路和机理,并给出初步的数值结果。This paper is a revisit of Ref.[1],where it is shown that the errors from one-dimensional finite element(FE)results mostly come from the element fixed-end solutions.Based on this concept,the element energy projection(EEP)method for the super-convergence calculation is developed.Moreover,when the EEP technique is applied to the adaptive FE analysis to estimate and control the errors in FE solutions,the solutions satisfying the user pre-set error tolerances in the maximum norm can be obtained.Recent introspection leads to a realization that the essence in Ref.[1]has not been fully exploited:since the element fixed-end solutions are the major source of errors,then it is possible to calculate the errors a priori by using the EEP method,immediately generating a desirable mesh without the need for the FE analysis in advance.This paper gives a brief introduction to this novel idea and some initial numerical results are given to show the validity and effectiveness of the proposed technique.

关 键 词：矩阵位移法 一维有限元法 固端解 先验定量估计 自适应网格划分 

分 类 号：O302[理学—力学]