Journal of Optimization Theory and Applications

, Volume 42, Issue 2, pp 229–246 | Cite as

Some optimal and inverse problems for orthotropic noncircular cylindrical shells

  • V. G. Litvinov
  • N. G. Medvedev
Contributed Papers


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.

Key Words

Optimization problems shells stresses strains existence of solutions finite-dimensional problems structural optimization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Lurie, K. A.,Optimal Control Problems of Mathematical Physics, Nauka, Moscow, USSR, 1975.Google Scholar
  2. 2.
    Prager, W.,Introduction to Structural Optimization, Springer-Verlag, New York, New York, 1974.Google Scholar
  3. 3.
    Banichuk, N. V.,Optimization of the Form of Elastic Bodies, Nauka, Moscow, USSR, 1980.Google Scholar
  4. 4.
    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.Google Scholar
  5. 5.
    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.Google Scholar
  6. 6.
    Litvinov, V. G.,Some Inverse Problems for Plates in Bending, Prikladnaya Matematika i Mekhanika, Vol. 40, No. 4, pp. 682–691, 1976.Google Scholar
  7. 7.
    Rubezhansky, Yu. J.,Some Inverse Problems for Cylindrical Shells, Prikladnaya Mekhanika, Vol. 15, No. 9, pp. 32–36, 1979.Google Scholar
  8. 8.
    Lions, J. L.,Optimal Control of Systems Described by Partial Differential Equations, Mir, Moscow, USSR, 1972.Google Scholar
  9. 9.
    Besov, O. V., Ilyin, V. P., andNikolsky, S. M.,Integral Representation of Functions and Embedding Theorems, Nauka, Moscow, USSR, 1975.Google Scholar
  10. 10.
    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.Google Scholar
  11. 11.
    Grigorenko, Ya. M., Vasilenko, A. T., andPankratova, N. D.,Design of Noncircular Cylindrical Shells, Naukova Dumka, Kiev, USSR, 1977.Google Scholar
  12. 12.
    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.Google Scholar
  13. 13.
    Mikhlin, S. G.,Variational Methods in Mathematical Physics, Nauka, Moscow, USSR, 1970.Google Scholar
  14. 14.
    Schwartz, L.,Analysis, Vol. 1, Mir, Moscow, USSR, 1972.Google Scholar
  15. 15.
    Goldenblatt, J. J., andKopnov, V. A.,Criteria of Strength and Plasticity of Structural Materials, Mashinostroyeniye, Moscow, USSR, 1968.Google Scholar
  16. 16.
    Ambartsumian, S. A.,The Theory of Anisotropic Shells, Nauka, Moscow, USSR, 1961.Google Scholar
  17. 17.
    Kantorowich, L. V., andAkilov, G. P.,Functional Analysis, Nauka, Moscow, USSR, 1977.Google Scholar
  18. 18.
    Litvinov, V. G.,Optimal Control of the Coefficients in Elliptical Systems, USSR Academy of Sciences, Institute of Mathematics, Kiev, Report No. 79-4, 1979.Google Scholar
  19. 19.
    Varga, R.,Functional Analysis and Approximation Theory in Numerical Analysis, Mir, Moscow, USSR, 1974.Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • V. G. Litvinov
    • 1
  • N. G. Medvedev
    • 1
  1. 1.Institute of MechanicsAcademy of Sciences of UkraineKievUSSR

Personalised recommendations