具有最佳超收敛阶的EEP法计算格式:Ⅱ数值算例  

A SCHEME WITH OPTIMAL ORDER OF SUPER-CONVERGENCE BASED ON EEP METHOD: Ⅱ NUMERICAL RESULTS

作　　者：袁驷[1] 邢沁妍[1] 王旭[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11期1-6,共6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二部分,给出实施算法和数值算例,用以验证理论公式的有效性和正确性。Based on the Element Energy Projection （EEP） method, an improved scheme with optimal order of super-convergence, is presented for one-dimensional Co FEM, 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 all element in postprocessing stage. The whole work consists of three parts, i.e. formulation, numerical results and mathematical analysis. The present paper is the second in the series and gives numerical algorithm and experimental results, which support the formulation proposed in the first part of the whole work.

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]