Skip to main content
Log in

Variational Methods of Solving Problems on Control of the Intensity of a Temperature Field

  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

The possibility of effective application of variational methods to the solution of problems on optimum control of decrease in the intensity of the temperature perturbations of the surroundings of devices, attained with the use of heterogeneous laminated composition coatings, was investigated. In the process of investigating the conditions of optimum control of the intensity of a temperature field with the use of a heterogeneous laminated composition construction, qualitative relations between the parameters of such a construction, which allows one to estimate its efficiency and potentials, have been obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. V. N. Bakulin, I. F. Obraztsov, and V. A. Potopakhin, Dynamic Problems of the Nonlinear Theory of Multilayer Coatings. Action of Intensive Thermal Forces and Concentrated Energy Flows [in Russian], Nauka, Moscow (1998).

  2. G. D. Babe and E. L. Gusev, Mathematical Methods of Optimization of Interference Filters [in Russian], Nauka, Novosibirsk (1987).

  3. E. L. Gusev, Mathematical Methods of Synthesis of Layered Structures [in Russian], Nauka, Novosibirsk (1993).

  4. V. N. Bakulin, E. L. Gusev, and V. G. Markov, Methods of Optimum Designing and Calculation of Composition Constructions [in Russian], Fizmatlit, Moscow (2008).

  5. E. L. Gusev, Research methods of the limit possibilities of structurally inhomogeneous structures with a desired set of properties during wave actions in the variation statement, J. Mach. Manuf. Reliab., 44, No. 2, 148–152 (2015).

    Article  MathSciNet  Google Scholar 

  6. E. L. Gusev and V. N. Bakulin, Variation formulations of inverse problems in forecasting the residual life of composites, Dokl. Phys., 63, No. 9, 388–392 (2018).

    Article  Google Scholar 

  7. E. L. Gusev, V. N. Bakulin, and V. D. Chernykh, Development of combined search methods for efficiency indicator extreme in variation statement of forecasting tasks for determining characteristics of composite materials, J. Phys.: Conf. Ser., 1392, Article 012008 (2019).

  8. E. L. Gusev and V. N. Bakulin, Variation statement of the optimal design problem of composite constructions with the required complex of properties, Mech. Compos. Mater., 51, No. 5, 637–644 (2015).

    Article  Google Scholar 

  9. E. L. Gusev and V. N. Bakulin, Optimum design of structurally nonhomogeneous materials and constructions with required properties, J. Eng. Phys. Thermophys., 89, No. 1, 260–264 (2016).

    Article  Google Scholar 

  10. V. N. Bakulin, E. L. Gusev, and V. G. Markov, Methods of optimal designing of constructions of conventional and composite materials subjected to wave and static actions, J. Eng. Phys. Thermophys., 74, No. 6, 1426–1430 (2001).

    Article  Google Scholar 

  11. V. L. Strakhov, Yu. M. Atamanov, I. A. Kuzmin, and V. N. Bakulin, Mathematical modeling of high-temperature thermophysical characteristics of rubber-like thermal protection materials, High Temp., 55, No 4, 515–523 (2017).

    Article  Google Scholar 

  12. V. L. Strakhov, I. A. Kuz'min, and V. N. Bakulin, Complex mathematical modeling of thermal protection made of highly extended elastomers, High Temp., 57, No. 2, 250–255 (2019).

    Article  Google Scholar 

  13. V. I. Andreev and I. A. Potekhin, On the method of obtaining optimum constructions on the basis of solving inverse problems of the theory of elasticity of inhomogeneous bodies, Vestn. Otd. Stroit. Nauk RAASN, No. 11, 48–52 (2007).

  14. V. S. Zarubin, Calculation and Optimization of Thermal Insulation [in Russian], Énergoatomizdat, Moscow (1992).

  15. N. V. Banichuk, V. V. Kobelev, and R. B. Rikards, Optimization of Elements of Constructions of Composite Materials [in Russian], Mashinostroenie, Moscow (1988).

  16. N. V. Banichuk, Introduction into the Optimization of Constructions [in Russian], Nauka, Moscow (1986).

  17. N. V. Banichuk, S. Yu. Ivanova, and A. V. Sharanyuk, Dynamics of Constructions. Analysis and Optimization [in Russian], Nauka, Moscow (1980).

  18. E. L. Gusev, Optimum Designing of Multistage Systems [in Russian], Yakutsk (1985).

  19. A. V. Arguchintsev, Optimum Control of Hyperbolic Systems [in Russian], Fizmatlit, Moscow (2007).

  20. F. L. Chernous′ko, I. M. Anan′evskii, and S. A. Reshmin, Methods of Control of Nonlinear Mechanical Systems [in Russian], Fizmatlit, Moscow (2006).

  21. V. I. Matyukhin, Control of Mechanical Systems [in Russian], Fizmatlit, Moscow (2009).

  22. R. F. Gabasov and A. M. Kirillova, Constructive Optimization Methods [in Russian], Izd. “Universitetskoe,” Minsk (1984).

  23. R. F. Gabasov and A. M. Kirillova, Maximum Principle in the Theory of Optimum Control [in Russian], Izd. “URSS,” Moscow (2011).

  24. L. S. Pontryagin, Maximum Principle in the Theory of Optimum Systems [Russian translation], Izd. “URSS,” Moscow (2004).

  25. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, Mathematical Theory of Optimal Processes [Russian translation], Nauka, Moscow (1983).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 94, No. 5, pp. 1141–1147, September–October, 2021.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gusev, E.L., Bakulin, V.N. Variational Methods of Solving Problems on Control of the Intensity of a Temperature Field. J Eng Phys Thermophy 94, 1117–1123 (2021). https://doi.org/10.1007/s10891-021-02392-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-021-02392-9

Keywords

Navigation