Article
MSC:
49A27,
49A29,
49A34,
49J27,
49J40,
49J99,
73k40,
74K10,
74K20,
74S30 | MR 0897834 | Zbl 0638.49003 | DOI: 10.21136/AM.1987.104261
Full entry |
PDF
(1.3 MB)
Feedback
PDF
(1.3 MB)
Feedback
Keywords:
optimal control; variational inequalities; optimal design; elasto-plastic beam; elastic plate; obstacle; convex set; thickness-function
optimal control; variational inequalities; optimal design; elasto-plastic beam; elastic plate; obstacle; convex set; thickness-function
Summary:
We deal with an optimal control problem for variational inequalities, where the monotone operators as well as the convex sets of possible states depend on the control parameter. The existence theorem for the optimal control will be applied to the optimal design problems for an elasto-plastic beam and an elastic plate, where a variable thickness appears as a control variable.
References:
[1] I. Bock J. Lovíšek: An optimal control problem for an elliptic variational inequality. Math Slovaca 33, 1983, No. 1, 23-28. MR 0689273
[2] M. Chipot: Variational inequalities and flow in porous media. Springer Verlag 1984. MR 0747637 | Zbl 0544.76095
[3] I. Hlaváček I. Bock J. Lovíšek: Optimal control of a variational inequality with applications to structural analysis. I. Optimal design of a beam with unilateral supports. Appl. Math. Optimization 11, 1984, 111-143. DOI 10.1007/BF01442173 | MR 0743922
[4] I. Hlaváček I. Bock J. Lovíšek: Optimal control of a variational inequality with applications to structural analysis. II. Local optimization of the stress in a beam. III. Optimal design of an elastic plate. Appl. Math. Optimization 13, 1985, 117-136. DOI 10.1007/BF01442202 | MR 0794174
[5] D. Kinderlehrer G. Stampacchia: An introduction to variational inequalities and their applications. Academic Press 1980. MR 0567696
[6] A. Langenbach: Monotone Potentialoperatoren in Theorie und Anwendung. VEB Deutsche Verlag der Wissenschaften, Berlin 1976. MR 0495530 | Zbl 0387.47037
[7] J. L. Lions: Quelques méthodes de résolution děs problèmes aux limites non linéaires. Dunod, Paris 1969. MR 0259693 | Zbl 0189.40603
[8] U. Mosco: Convergence of convex sets and of solutions of variational inequalities. Advances of Math. 3, 1969,510-585. MR 0298508 | Zbl 0192.49101
[9] F. Murat: L'injection du cone positif de $H^{-1}$ dans $W^{-1,2}$ est compact pour tout q < 2. J. Math. Pures Appl. 60, 1981, 309-321. MR 0633007
Search
Partner of
