更一般的杂交广义变分原理及有限元模型
More Generalized Hybrid Variational Principle and Corresponding Finite Element Model
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摘要: 本文根据钱伟长教授提出的更一般的广义变分原理,给出了适用于有限元法中的更广义杂交变分原理,并由此建立了新的广义杂交模理. 进一步以变厚度薄板弯曲单元为例,对基于各种不同的广义变分原理建立的各种杂交元做了比较.Abstract: According to recent studies of the generalized variational principle by Professor Chien Wei-zang,the mere generalized hybrid varialional principle for finite element method is given,from which a new kind of the generalized hybrid element model is established.Using the thin plate bending element with varying thickness as an eaample,we compare various hybrid elements based on different generalized variational principles.
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[1] 钱伟长,高阶垃氏乘子法和弹性理价中更一般的广义变分原理,应用数学与力学,4.2(1993). [2] Liang Guo-ping(梁国平)and Fu Zi-zhi(付子智),A New method fur the construction elemeat,Proceedings of the Inteuuiionul Conference On Finitc Element Lethods,Shanghai,2-6,August(1982),593-599. [3] Michael.,L,Day and T,Y,Yang,A mixed variatianal principle for finite element analysis,Int,J.Num,Methods Engng.,8(1982),1212-1230. [4] Oden,J.T.,The classical variatioml principles of mechanics,Energy bleihods in finite Element Analysis,Edited by R.Glowinsk,E.Y.Rodin.,O,C,Zienkiewicz(1979),1-31. [5] 陈万吉,杂交广义义变分原理及杂交模型,大连工学学报,4(1983). [6] 陈万吉,变厚度薄板,壳广义杂交元,力学学报(待发表). [7] 钱伟长,《变分法和有限元》,科学出版社(1980). [8] 龙驭球,弹性力学中的分区广义变分原理,上海力学,2(1981). -
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