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second invariant of the stress deviator; smooth regularized control problems; optimal shape design; axisymmetric shells; elliptic, linear symmetric operator; first order necessary conditions of optimality; nonsmooth; nonconvex infinite dimensional opimization problem
The optimal control problem of variational inequality with applications to axisymmetric shells is discussed. First an existence result for the solution of the optimal control problem is given. Next is presented the formulation of first order necessary conditionas of optimality for the control problem governed by a variational inequality with its coefficients as control variables.
[1] R. A. Adams: Sobolev spaces. Academic Press, New York, San Francisco, London 1975. MR 0450957 | Zbl 0314.46030
[2] H. Attouch: Convergence des solutions d'inequations variationnelles avec obstacle. Proceedings of the international meeting on recent methods in nonlinear analysis. Rome, may 1978, ed. by E. De Giorgi - E. Magenes - U. Mosco.
[3] V. Barbu: Optimal control of variational inequalities. Pitman Advanced Publishing Program, Boston, London, Melbourne 1984. MR 0742624 | Zbl 0574.49005
[4] I. Boccardo A. Dolcetta: Stabilita delle soluzioni di disequazioni variazionali ellitiche e paraboliche quasi - lineari. Ann. Universeta Ferrara, 24 (1978), 99-111.
[5] J. M. Boisserie, Glowinski: Optimization of the thickness law for thin axisymmetric shells. Computers 8. Structures, 8 (1978), 331-343. Zbl 0379.73090
[6] I. Hlaváček: Optimalization of the shape of axisymmetric shells. Aplikace matematiky 28, с. 4, pp. 269-294. MR 0710176
[7] J. L. Lions: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod Paris, 1969. MR 0259693 | Zbl 0189.40603
[8] F. Mignot: Controle dans les inéquations variationelles elliptiques. Journal Functional Analysis. 22 (1976), 130-185. DOI 10.1016/0022-1236(76)90017-3 | MR 0423155 | Zbl 0364.49003
[9] J. Nečas: Les méthodes directes en theorie des équations elliptiques. Academia, Praha, 1967. MR 0227584
[10] J. Nečas I. Hlaváček: Mathematical theory of elastic and elasto-plastic bodies. An introduction. Amsterdam, Elsevier, 1981. MR 0600655
[11] P. D. Panagiotopoulos: Inequality problems in mechanics and applications. Birkhäuser, Boston-Basel-Stuttgart, 1985. MR 0896909 | Zbl 0579.73014
[12] J. P. Yvon: Controle optimal de systémes gouvernes par des inéquations variationnelles. Rapport Laboria, February 1974.
[13] O. C. Zienkiewcz: The Finite Element Method in Engineering. Science, McGraw Hill, London, 1984.
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