广义弹塑性梁理论及接触问题中的时偶变分不等式<sup>*</sup>

高扬

广义弹塑性梁理论及接触问题中的时偶变分不等式^*

高扬

美国维吉尼亚理工大学数学系, VA24061

基金项目: * 美国国家科学基金

计量
- 文章访问数: 2540
- HTML全文浏览量: 273
- PDF下载量: 485
- 被引次数: 0
出版历程
- 收稿日期: 1996-02-21
- 刊出日期: 1996-10-15

Contact Problems and Dual Variational Inequality of 2-D Elastoplastic Beam Theory

Gao Yang

Department of Mathematics, Virginia Polytechnic Institute and State University,Blacksburg, VA 24061, U.S.A.

摘要

摘要: 为研究摩擦接触问题,本文建立了一个具有二类独立交量的二维弹塑性梁模型。由此提出了一个新的非线性二次互补性问题。其中的外部互补性条件定义了自由边界;而内部互补性条件则控制了弹塑性分界面。文中证明了此二次互补性问题等价于一非线性变分不等式,并导出了其对偶变分不等式。本文结果显示对偶问题较原问题有更多的优越性。应用于塑性极限分析理论中,文中最后证明了一个简单的下限定理。
- 接触问题 /
- 互补性问题 /
- 弹塑性梁理论 /
- 变分不等式
Abstract: In order to study the frictional contact problems of the elastoplastic beam theory,an extended two-dimensional beam model is established, and a second order nonlinear equilibrium problem with both internal and external complementarity conditions is proposed. The external complementarity condition provides the free boundary condition. While the internal complemententarity condition gives the interface of the elastic and plastic regions. We prove that this bicomplementarity problem is equivalent to a nonlinear variational inequality The dual variational inequality is also developed.It is shown that the dual variational inequality is much easier than the primalvariational problem. Application to limit analysis is illustrated.
- complementarity problems /
- variational inequality /
- duality theory /
- elastoplastic beam

HTML全文

参考文献(18)

[1]	J, P, Aubin,Applied Functional Analysis,Wiley-Intersicencc,New York(1979).
[2]	G.Allen, Variational inequalities, complemPntarity problems,and duality theorems,T,Math.Analy.Appl.,58(1977), 1-10.
[3]	J, Chakrabarty,Theory of Plasticity, McGraw-Hill Book Company(1987),791.
[4]	I, Ekeland and R.Temam, Convex Analysis and Yariational Problems, North-Holland(1976).
[5]	G. Fichera,Existence theorems in elasticity-boundary value problems of elasticity with unilateral constraints,in Encyclopedia of Phgsics,Ed.by S,FlÜgger,Vol.Ⅵ a/2,Mechanics of Solids(Ⅱ),Ed, by C, Truesdell, Springer Verlag (1972),347-427.
[6]	高扬,凸分析及塑性力学的数学理论,《现代数学与力学》,郭仲衡编,北京大学出版社(1987),165-185.
[7]	Guo Zhongheng,Th.Lehmann and Liang Haoyun,The abstract representation of rates of stretch tensors,Acta Mechanica Sinica,23,6 (1991).712.Ⅱ
[8]	Y,Gao,Panpenalty finite element programming for limit analysis, Computers&Structures,28 (1988). 749-755.
[9]	David Yang Gao and David L. Russell,A finite element approach to optimal control of a "smart" beam,in Int. Conf. Computational Methods in Structural and Geoteehnical Engineering,Ed,by P,K.K.Lee, L, G.Tham and Y, K.Cheuug,December 12-14,1994,Hong Kong (1994),135-140.
[10]	David Yang Gao and David L. Russell,An extended beam theory for smart materials applications,Part j .Extended beam models,duality theory and finite element simulations, J.Applied Math, and Optimization, 34(3)(1996).
[11]	R .Glowinski,K.L.Lions and R.Trémoliéres,Numerical Analysis of variationdl Inequalities, North-Holland,Amsterdam,New York,Oxford(1981).
[12]	S,Karamardian,Generalized complememtarity problems,J.of Optimization Theory and Applications,6(19)(1971),161-168.
[13]	N-Kikuchi and J.T. Oden, Contact Problems in Elasticity A Study of Yariational I nequalities and Finite Element Methods,SIAM,Philadephia(1988),495.
[14]	D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inevualities and Their Applications,Academic Press,New York (1980).
[15]	A,Klarbring,A,Mikelié and M, Shillor,Duality applied to contact problems with friction, Appl.Math, Optim,,22 (1990),211-226.
[16]	J, Lovisek,Duality in the obstacle and unilateral problem for the biharmonic operator,Aplikace Matematiky,Svazek,26 (1981),291-303.
[17]	U,Mosco,Dual variational inequalities, J, Math Anal, Appl,40(1972), 202-206.
[18]	S. T.au and Y.Gao,Obstacle. problem for von Kármán equations,Adv, Appl.Math., 13(1992),123-141.