Journal of Mathematical Sciences

, Volume 96, Issue 1, pp 2930–2934 | Cite as

Optimization of vertical axisymmetric displacements of a thin circular plate under a nonstationary thermal load

  • A. V. Yasins'kii
  • R. I. Shipka
Article
  • 18 Downloads

Abstract

We study the problem of optimal control of the distribution of vertical axisymmetric thermal displacements of a thin circular plate fixed along its edge. The displacements are caused by a nonstationary heat load on one of the end surfaces. The thermal action on the other end surface is chosen as the control function. Using the Hankel and Laplace transforms in the space of continuous functions, we construct the solution of the inverse problem of thermoelasticity to which the original control problem has been reduced.

Keywords

Continuous Function Control Problem Inverse Problem Control Function Thermal Load 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    N. A. Bochkov, V. F. Gordeev, V. S. Kolesov, et al., “The parameters of geometric stability of the optical surface of laser mirrors,”Poverkhnost′: Fiz. Khim. Mekh., No. 11, 89–96 (1983).Google Scholar
  2. 2.
    V. M. Vigak,Optimal Control of Nonstationary Temperature Regimes [in Russian], Naukova Dumka, Kiev (1979).Google Scholar
  3. 3.
    V. M. Vigak,Control of Temperature Stresses and Displacements [in Russian], Naukova Dumka, Kiev (1988).Google Scholar
  4. 4.
    V. M. Vigak, V. S. Kolesov, and A. V. Yasinskii, “Optimal control of the temperature displacements of the optical surface of a laser mirror,”Fiz. Khim. Obr. Mater., No. 3, 25–30 (1985).Google Scholar
  5. 5.
    V. M. Vigak and A. V. Yasinskii, “Optimization of axisymmetric temperature displacements in a given section of an unbounded layer,”Mat. Met. Fiz. Mekh. Polya, No. 34, 55–61 (1991).Google Scholar
  6. 6.
    G. Doetsch,A Guide to Applications of the Laplace and Z-Transforms, Van Nostrand-Reinhart, New York (1971).Google Scholar
  7. 7.
    A. D. Kovalenko,Thermoelasticity [in Russian], Vishcha Shkola, Kiev (1975).Google Scholar
  8. 8.
    G. P. Tolstov,Fourier Series, Prentice-Hall, Englewood Cliffs (1962).Google Scholar
  9. 9.
    L. S. Tsesnek, O. V. Sorokin, and A. A. Zolotukhin,Metallic Mirrors [in Russian], Mashinostroenie, Moscow (1983).Google Scholar
  10. 10.
    A. V. Yasins'kii, “Optimization of vertical axisymmetric temperature displacements of a circular plate using heat sources,”Mat. Met. Fiz.-Mekh. Polya, No. 36, 105–110 (1993).Google Scholar
  11. 11.
    N. Noda, “Optimal heating problem for transient thermal stresses in a thick plate,”J. Therm. Stresses, 11, No. 2, 141–150 (1988).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • A. V. Yasins'kii
  • R. I. Shipka

There are no affiliations available

Personalised recommendations