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The problem of inequality in solid mechanics

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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

  1. Stampacchia, G., Formes bilinéaires coercitives sur les ensembles convexes,C. R. Acad. Sc. Paris,258 (1964), 4413–4416.

    Google Scholar 

  2. Lions, J. L. and G. Stampacchia, Variational inequalities,Comm. Pure Appl. Math.,20 (1967), 490–519.

    Google Scholar 

  3. Lions, J. L.,Quelques méthodes de Résolution des Problemes aux Limites Nonlinéaires, Dunod/Gauthier-Villars (1969).

  4. Kinderlehrer, D. and G. Stampacchia,An Introduction to Variational Inequalities and Their Applications, Academic Press (1980).

  5. Pascali, D. and S. Sburian,Nonlinear Mappings of Monotone Type, Editura Academiei (1978).

  6. Dincâ, G.,Operatori Monotonic În 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. Guo You-zhong, Complementary principle in elastic theory,Kexue Tongbao,29, 10 (1984), 1291–1302.

    Google Scholar 

  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.

    Google Scholar 

  15. Guo You-zhong, Variational inequalities on star region,Kexue Tongbao,4, 1 (1984), 117–118.

    Google Scholar 

  16. Lax, P. D. and A. N. Milgram, Parabolic equations,Ann. of Math. Studies,33 (1954), 167–190.

    Google Scholar 

  17. Brezis, H. and G. Stampacchia, Sur les régularité de la solution dínequations elliptiques,Bull. Soc. Math. France,96, 1 (1968), 153–180.

    Google Scholar 

  18. Brezis, H., Problems unileraux,J. Math. Pures Appl.,51 (1972), 1–168.

    Google Scholar 

  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.

    Google Scholar 

  20. Ciarlet, P. G., A justification of the von Kármán equations,Arch. Rat. Mech. Ann.,73 (1980), 349–389.

    Google Scholar 

  21. Guo You-zhong, 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.

    Google Scholar 

  23. Lions, J. L.,Problémes aux Limites dans les équations aux Dérivées Partielles, Les Press de l'Université de Montréal (1967).

  24. Ciarlet, P. G.,The Finite Element Method for Elliptic Problems, North-Holland Pub. Co. (1978).

  25. Mosco, U., Approximation of the solutions of some variational inequalities,Ann. Sc. Norm. Sup., Pisa,21 (1967), 373–394.

    Google Scholar 

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You-zhong, G. The problem of inequality in solid mechanics. Appl Math Mech 10, 1–24 (1989). https://doi.org/10.1007/BF02018488

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