DETERMINATION AND ANALYSIS OF THE TEMPERATURE FIELD IN A THREE-LAYER ISOTROPIC PLATE WITH A GIVEN INITIAL TEMPERATURE DISTRIBUTION
Abstract
An approximate system of two-dimensional heat conduction equations for a multilayer isotropic
plate is written down. Boundary conditions for a rectangular plate of finite dimensions are
formulated. A general solution of the non-stationary heat conduction problem for this plate was
found using integral Fourier transforms in spatial variables and Laplace transform in time.On the
basis of the obtained general solutions, the solution of the thermal conductivity problem for a
three-layer plate, which at the initial moment of time is heated by a temperature field linear in its
thickness, which is uniformly distributed over the surface of the plate in a rectangular region, was
analyzed. The numerical analysis of the temperature field was performed for a three-layer plate,
the middle layer of which is made of metal, and the outer layers are made of ceramics.
References
EncyclopediaofThermalStresses/R. Hetnarski (ed.). - Springer, 2014.- Vol. 11. P. 5835-6643.
Kolyano Yu.M.Metody teploprovіdnostі ta termopruzhnostі neodnorіdnykh tіl. - K.: Nauk. dumka, 1992. - 280 s.
Varelis D., Saravanos D.A. A coupled nonlinear plate finite element for thermal buckling and postbuckling of piezoelectric composite plates including thermomechanical effects // J. Thermal Stresses. - 2022. - 45, №1. - P. 30-50. https://doi.org/10.1080/01495739.2021.2005498
ZhydykU.V.,FlyachokV.M. Termopruzhnyyanalizneodnorіdnykhanіzotropnykhplastyn // Naukovіnotatki. Lutsk: LNTU. - 2011. Vyp. 33. - S. 281-287.
Manthena V.R., Kedar G.D. On thermoelastic problem of a thermosensitive functionally graded rectangular plate with instantaneous point heat source // J. Thermal Stresses. - 2019. - 42, №7. - P. 849-862.
Ohmichi M., Noda N., Sumi N. Plane heat conduction problems in functionally graded orthotropic materials // J. Thermal Stresses. - 2017. - 40, № 6. - P. 747-764. https://doi.org/10.1080/01495739.2016.1249989
Brishetto S., Carrera E., Heat conduction and thermal analysis in multilayered plates and shells // J. Mech. Res. Commun. -2011. - 38, № 6. - P. 449-455. https://doi.org/10.1016/j.mechrescom.2011.05.016
Flyachok V. M. Rivnyannya nestatsionarnykh temperaturnykh polіv dlya bagatosharovykh anіzotropnykh obolonok z urakhuvannyam teplovoi іnertsіi. Dop. NAU. Ser. Mekhanіka. 2000.№ 2. S. 60-63.
Shvets R.M.,Flyachok V.M., Heat conduction equations for multilayer anisotropic shells// J. Therm. Stresses. - 1999. - 22, № 2.- P. 241-254. https://doi.org/10.1080/014957399280995
Zhydyk U.V., Flyachok V.M. Temperaturnі polya v pologikh obolonkakh sharuvatoi strukturi // Kvalіlogіya knigi. - 2017. - № 1 (31). - S. 94-97. https://doi.org/10.1080/0005772X.2017.1389814
Podstryhach Ya.S., Shvets R.N. Termouprugost tonkikh obolochek. - K.: Nauk. dumka, 1978. - 344 s.
FlyachokV.M.Variational theorem for the dynamical problem of coupled mechanothermodiffusion in inhomogeneous anisotropic shells with distortions // JournalofMathematicalSciences. -2016.- Vol.215, № 1.- P. 79-88 .https://doi.org/10.3917/all.215.0079
Thai H.T., Kim S.E. A review of theories for the modeling and analysis of functionally graded plates and shells // Compos. Struct. -
- 128, №1. - P. 70-86.mmhttps://doi.org/10.1016/j.compstruct.2015.03.010
Swaminathan K., Sangeetha D.M. Thermal analysis of FGM plates - a critical review of various modeling techniques and solution methods // Composite Structures. - 2017. - 160, №1. - P. 43-mhttps://doi.org/10.1016/j.compstruct.2016.10.047
Copyright (c) 2023 Роман Мусій, Уляна Жидик, Богдан Бандирський, Ольга М’яус (Автор)
This work is licensed under a Creative Commons Attribution 4.0 International License.
