具有最佳超收敛阶的EEP法计算格式:Ⅰ算法公式  

A SCHEME WITH OPTIMAL ORDER OF SUPER-CONVERGENCE BASED ON EEP METHOD:Ⅰ FORMULATION

作　　者：袁驷[1] 王旭[1] 邢沁妍[1] 叶康生[1] 

机构地区：[1]清华大学土木工程系结构工程与振动教育部重点实验室,北京100084

出　　处：《工程力学》2007年第10期1-5,共5页Engineering Mechanics

基　　金：国家自然科学基金资助项目(50678093)

摘　　要：对一维C0问题的高次有限元后处理中超收敛计算的EEP(单元能量投影)法提出改进的最佳超收敛计算格式,即用m次单元对足够光滑问题的有限元解答,采用该格式计算的任意一点的位移和应力都可以达到h2m阶的最佳超收敛结果。整个工作分为3个部分,分别给出算法公式、数值算例和数学证明。该文是系列工作的第一部分,针对高次单元提出了凝聚形函数的概念,并证明了相关的逼近定理和等价定理,在此基础上给出了具体的算法公式。Based on the Element Energy Projection （EEP） method, the present paper presents, for onedimensional Co FEM, an improved scheme with optimal order of super-convergence, i.e., FEM sulotions can be obtained through the scheme for the elements with sufficient smooth property and m degrees. The proposed scheme is capable of producing O（h^2m） super-convergence for both displacements and stresses at any point on an element in post-processing stage. To achieve that, the concept of condensed shape functions was developed and the associated theorems of approximation and equivalence were proved. The whole work consists of three parts, i.e., formulation, numerical results and mathematical analysis. The present paper is the first in the series and gives the formulation of the proposed scheme.

关 键 词：有限元 一维问题 超收敛 最佳收敛阶 单元能量投影 凝聚形函数 

分 类 号：TU318[建筑科学—结构工程]