2020, issue 1, p. 32-40
Received 21.01.2020; Revised 06.02.2020; Accepted 10.03.2020
Published 31.03.2020; First Online 26.04.2020
ON CERTAIN PROBLEMS OF IDENTIFICATION OF THERMAL DENSITY OF THE TEMPERATURE STATE OF THE HOLLOW CYLINDER SHELL
Albina Aralova 1 *
1 V.M. Glushkov Institute of Cybernetics, Kyiv, Ukraine
Introduction. In conditions of the active use of composite materials, as when accomplishing the tasks of extending the service life of existing structures, problems on recovering unknown parameters of their components under the known data on their surface arise. In [1–4], to solve the problems of identification of parameters of a wide range, it is proposed to construct explicit expressions of the gradients of residual functionals by means of the corresponding conjugate problems obtained from the theory of optimal control of the states of multicomponent distributed systems, which is the development of the corresponding researches of Zh. Lyons. In [5–7], this technology is extended to the problem of thermoelastic deformation of multicomponent bodies.
In this article some problems of optimal control of the temperature state of a cylindrical body with a cavity are considered.
The purpose of the paper is to show the algorithm for identifying the parameters of a cylindrical hollow shell, based on the theory of optimal control and using the gradient methods of Alifanov.
Results. Based on the theory of optimal control, the temperature control of a cylindrical shell is studied. To solve the problem of identifying the parameters of a hollow cylindrical shell, namely, finding the heat flux powers on its surfaces, based on [1, 2, 5–7], a direct and conjugate problem and gradients of non-viscous functionals are constructed. Discretization by the finite element method using piecewise quadratic functions is carried out and accuracy estimates for it are presented. The initial problem in the model examples presented is solved using gradient methods, where at each step of determining the (n + 1) the approximation of the solution, the direct and adjoint problems are solved using finite element method with the help piecewise quadratic functions by minimizing the corresponding energy functional.
A number of model examples solved.
Keywords: temperature state, gradient methods, cylindrical bodies.
Cite as: Aralova A. On Certain Problems of Identification of Thermal Density of the Temperature State of the Hollow Cylinder Shell. Cybernetics and Computer Technologies. 2020. 1. 32–40. (in Ukrainian) https://doi.org/10.34229/2707-451X.20.1.4
1. Sergienko I.V., Deineka V.S. System analysis of multicomponent distributed systems. Kiev: Nauk. Dumka, 2009. 640 p. (in Russian)
2. Sergienko I.V., Deineka V.S. Identification of the parameters of the stress-strain state of a multicomponent elastic body with inclusion. Prikladnaya mekhanika. 2010. 46 (4). P. 14–24.
3. Sergienko I.V., Deineka V.S. Optimal control of distributed systems with conjugation conditions. New York: Kluwer Academic Publishers, 2005. 400 p.
4. Deineka V.S. Models and methods for solving problems in heterogeneous environments. Kiev: Nauk. Dumka, 2001. 606 p. (in Russian)
5. Aralova A.A., Deineka V.S. Numerical solution of inverse boundary value problems of axisymmetric thermoelastic deformation of a long thick hollow cylinder. Komp'yuternaya matematika. 2011. 1. P. 3–12. (in Russian) http://dspace.nbuv.gov.ua/handle/123456789/84653
6. Aralova A.A., Deineka V.S. Optimal control of the hollow cylinder thermal stress. Dopovidi natsionalʹnoyi akademiyi nauk Ukrayiny. 2012. 5. P. 38–42. (in Russian) http://dspace.nbuv.gov.ua/handle/123456789/49803
7. Aralova A.A. Numerical solution of inverse problems of thermoelasticity for a composite cylinder. Cybernetics and System Analysis. 2014. 50 (5). P. 164–172. https://doi.org/10.1007/s10559-014-9670-0
8. Kovalenko A.D. Thermoelasticity. Kiev: Vishcha shkola, 1975. 216 p. (in Russian)
9. Motovilevets I.A., Kozlov V.I. The mechanics of related fields in structural elements. Vol. 1. Termouprugost'. Kiev: Nauk. Dumka, 1987. 264 p. (in Russian)
10. Lyons J.-L. Optimal control of systems described by partial differential equations. M .: Mir, 1972. 414 p. (in Russian)
11. Alifanov O.M., Artyukhin E.A., Rumyantsev S.V. Extreme methods for solving incorrect tasks. M .: Nauka, 1988. 288 p. (in Russian)
ISSN 2707-451X (Online)
ISSN 2707-4501 (Print)