Abstract
In this paper, we consider problems of optimal control involving stressed or strained states of orthotropic, noncircular cylindrical shells. It is assumed that the thickness of the shell is variable. The thickness and the radius of curvature of the directrix of the shell are assumed to be the controls. Existence of solutions for the optimal control problems considered is shown. In particular, existence of solutions for the problem of the minimal weight shell and the problem of nearest-to-equal-strength shell is shown. We present results on the approximation of the optimal control problems by a sequence of finite-dimensional problems, which may be reduced to nonlinear programming problems.
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Lurie, K. A.,Optimal Control Problems of Mathematical Physics, Nauka, Moscow, USSR, 1975.
Prager, W.,Introduction to Structural Optimization, Springer-Verlag, New York, New York, 1974.
Banichuk, N. V.,Optimization of the Form of Elastic Bodies, Nauka, Moscow, USSR, 1980.
Lurie, K. A., andCherkayev, A. V.,On the Application of the Prager Theorem to Problems of Optimal Design of Thin Plates, Izvestiya Akademii Nauk SSSR, Mekhanika Tverdogo Tela, Vol. xx, No. 6, pp. 157–159, 1976.
Lurie, K. A., Fedorov, A. V., andCherkayev, A. V.,On the Existence of Solutions of Some Problems of Optimal Design of Bars and Plates, A. F. Yoffe Physical-Technical Institute, Leningrad, USSR, Report No. 668, 1980.
Litvinov, V. G.,Some Inverse Problems for Plates in Bending, Prikladnaya Matematika i Mekhanika, Vol. 40, No. 4, pp. 682–691, 1976.
Rubezhansky, Yu. J.,Some Inverse Problems for Cylindrical Shells, Prikladnaya Mekhanika, Vol. 15, No. 9, pp. 32–36, 1979.
Lions, J. L.,Optimal Control of Systems Described by Partial Differential Equations, Mir, Moscow, USSR, 1972.
Besov, O. V., Ilyin, V. P., andNikolsky, S. M.,Integral Representation of Functions and Embedding Theorems, Nauka, Moscow, USSR, 1975.
Medvedev, N. G.,On the Possibility of Solution of Problems of the Theory of Orthotropic Noncircular Cylindrical Shells, Doklady Akademii Nauk SSR, No. 10, 1978.
Grigorenko, Ya. M., Vasilenko, A. T., andPankratova, N. D.,Design of Noncircular Cylindrical Shells, Naukova Dumka, Kiev, USSR, 1977.
Panteleyev, A. D., andMedvedev, N. G.,On the Coercitivity of the Operator of the Theory of Three-Layered Plates, Matematicheskaja Fizika, Vol. 26, pp. 121–124, 1979.
Mikhlin, S. G.,Variational Methods in Mathematical Physics, Nauka, Moscow, USSR, 1970.
Schwartz, L.,Analysis, Vol. 1, Mir, Moscow, USSR, 1972.
Goldenblatt, J. J., andKopnov, V. A.,Criteria of Strength and Plasticity of Structural Materials, Mashinostroyeniye, Moscow, USSR, 1968.
Ambartsumian, S. A.,The Theory of Anisotropic Shells, Nauka, Moscow, USSR, 1961.
Kantorowich, L. V., andAkilov, G. P.,Functional Analysis, Nauka, Moscow, USSR, 1977.
Litvinov, V. G.,Optimal Control of the Coefficients in Elliptical Systems, USSR Academy of Sciences, Institute of Mathematics, Kiev, Report No. 79-4, 1979.
Varga, R.,Functional Analysis and Approximation Theory in Numerical Analysis, Mir, Moscow, USSR, 1974.
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Communicated by K. A. Lurie
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Litvinov, V.G., Medvedev, N.G. Some optimal and inverse problems for orthotropic noncircular cylindrical shells. J Optim Theory Appl 42, 229–246 (1984). https://doi.org/10.1007/BF00934298
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DOI: https://doi.org/10.1007/BF00934298