The Problem of Inequality in Solid Mechanics

Abstract

In this paper the problem of inequality in solid mechanics, the contents of which consist of some main concepts, methods and results of the stationary and evolutionary as well as determinate and random problems in variational principle and variational inequality, is studied in detail.

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References(25)

References

[1]	Stampacchia,G.,Formes bilinéaires coercitives sur les ensembles convexes,C.R.Acad Sc.Paris,258(1964),4413-4416.
[2]	Lions,J.L.and G.Stampacchia,Variational inequalities,Comm.Pure Appl.Math.,20(1967),490-519.
[3]	Lions,J.L.,关于变分不辛式及其应用约若干问题(郭友中泽),数学进展,12,2(1983),1-29.
[4]	Kinderlehrer,D.and G.Stampacchia,《变分不等式及其应用引论》(郭友中等译),科学出版社.
[5]	Pascali,D.and S.Sburian,Nonlinear Mappings of Monotone Type,Editura Academiei(1978).
[6]	Dinca;,G.,Operatori Monotonic in Teoria Plasticitatii,Editura Academiei(1972).
[7]	Lions,J.L.and E.Magenes,Non-Homogeneous Boundary Value Problems and Applications,Springer-Verlag(1972).
[8]	Lions,J.L.,Optimal Control of Systems Governed by Partial Differential Equations,Springer-Verlag(1971).
[9]	Bensoussen,A.and J.L.Lions,Applications of Variational Inequalities in Stochastic Control,North-Holland Pub.Comp.(1982).
[10]	Duvaut,G.and J.L.Lions,Inequalities in Mechanics and Physics,Springer-Verlag(1976).
[11]	Lions,J.L.,Perturbations Singulieres dans les Problems aux Limites et en Controle Optimal,Springer-Verlag(1973).
[12]	郊友中,弹性理论中的互补变分原理,科学通报,29,10(1984),1291-1302.
[13]	Rockafellar,R.T.,Convex Analysis,Princeton Univ.Press(1970).
[14]	Panagiotopoulos,P.D.,Subdifferentials and optimal control in unilateral elasticity,Mech.Res.Comm.,3(1976),91-96.
[15]	郭友中,星域上的变分不等式,科学通报,4,1(1984),117-118.
[16]	Lax,P.D.and A.N.Milgram,Parabolic equations,Ann.of Math.Studies,33(1954),167-190.
[17]	Brezis,H.and G.Stampacchia,Sur les régularitéde la solution dinequations elliptiques,Bull.Soc.Math.France,96,1(1968),153-180.
[18]	Brezis,H.,Problems unileraux,J.Math.Pares Appl.,51(1972),1-168.
[19]	Hünlich,R.and J.Naumann,On general boundary value problems and duality in linear elasticity,Ⅰ,Ⅱ,Appl.Matematiky,23(1978),208-229;25(1980),11-32.
[20]	Ciarlet,P.G.,A justification of the von Kármán equations,Arch.Rat.Mech.Ann.,73(1980),349-389.
[21]	郭友中,Variational inequality in micro-elasto-visco-plasticity,Proceedings of ICNM(1985).
[22]	Schatzman,M.,Le systeme differentiel ∂₂u/∂t₂+∂φ(u)=f avec conditions initiales,C.R.Acad.Sc.Paris,284A(1972),603-606.
[23]	Lions,J.L.,《偏微分方程的边界问题》(李大潜译)上海科学技术出版社(1980).
[24]	Ciarlet,P.G.,《有限元法的数值分析》(蒋尔雄等译),上海科学技术出版社(1980).
[25]	Mosco,U.,《变分不等式近似解引论》(王烈衡等译),上海科学技术出版社(1985).