多套函数有限元逼近与拟协调板元
Finite Element Approximations with Multiple Sets of Functions and Quasi-Conforming Elements for Plate Bending Problems
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摘要: 继[1]、[2]的工作,本文根据多套函数有限元逼近的思想,建立了唐立民等人[3]、[4]提出的拟协调板元的数学基础.Abstract: Continuing refs. [1],[2]. we try toestablish here the mathematical foundation of quasi-conforming elements suggesied by Prof. Tang Limin and his colleagues for plate bending problems [3,4]. The main theme used in this paper is the finite element approximations with multiple sets of functions.
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[1] Zhang Hong-qing,The generalized patch test and 9-parameters quasi-conforming element,Proceedings of the Sino-France Symposium on Finite Element Methods,Edited by Feng Kang and J.L.Lions,Science Press,Gordon and Breach,Science Publishers,(1983),566-583. [2] 张鸿庆,多套函数广义分片检验与12参数拟协调元,大连工学院学报,21, 3(1982), 11-19. [3] 唐立民、陈万吉、刘迎曦,有限元分析中的拟协调元,大连工学院学报,19, 2(1980), 19-35 [4] 蒋和洋,用拟协调元法推导高精度三角形板弯曲单元,大连工学院学报,20,增刊2(1981).21-28. [5] 钱伟长.《变分法与有限元》.上册.科学出版社.(1980). [6] Oden,J.T.,J.N.,Reddy,An Introdution to the Mathematical Theory of Finite Elements,Wiley-Interscience,New York(1976). [7] Stummel,F.,The generalized patch test,SIAM J.Num.Anal.16(1979),449-471. [8] Ciarlet,P.C.,The Finite Element Method for Elliptic Problems,North-Holland,Amsterdam,New York,Oxford,(1978).
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