1. MMC
  2. All Volumes and Issues
  3. Volume 10, Number 3, 2023
  4. Determination and analysis of the thermoelastic state of layered orthotropic cylindrical shells

Determination and analysis of the thermoelastic state of layered orthotropic cylindrical shells

MMC.
2023;
Volume 10, Number 3
: pp. 918–926
https://doi.org/10.23939/mmc2023.03.918
Received: January 11, 2023
Revised: July 25, 2023
Accepted: August 01, 2023

Mathematical Modeling and Computing, Vol. 10, No. 3, pp. 918–926 (2023)

Authors:
  1. R. Musii
  2. U. Zhydyk
  3. I. Svidrak
  4. V. Shynder
  5. N. Morska
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University
3
Lviv Polytechnic National University
4
Lviv Polytechnic National University
5
Lviv Polytechnic National University

The fundamental relations of the quasi-static problem of thermoelasticity are written for a finite layered orthotropic cylindrical shell of an antisymmetric structure.  Under convective heat transfer on the surfaces of this shell and under a linear dependence of temperature on the transverse coordinate, the basic system of equations for the integral characteristics of temperature is given.  The method is proposed for solving the formulated problems of thermoelasticity and thermal conductivity, using the double finite integral Fourier transform with respect to the corresponding coordinates of the transformation and Laplace transform with respect to the time.  The results of a numerical analysis of temperature, deflections, and stresses for the considered two-layer shell hinged at the edges under local heating by the initially specified temperature field are presented.

orthotropic
layered
cylindrical shell
temperature
thermally stressed state
heat transfer
  1. Reddy J. N.  Mechanics of laminated composite plates and shells. Theory and analysis.  New York, CRC Press (2004).
  2. Hetnarski R.  Encyclopedia of Thermal Stresses.  Springer (2014).
  3. Kolyano Yu. M.  Methods of thermal conductivity and thermoelasticity of heterogeneous bodies.  Kyiv, Naukova dumka (1992).
  4. Brischetto S., Carrera E.  Heat conduction and thermal analysis in multilayered plates and shells.  Mechanics Research Communications.  38 (6), 449–455 (2011).
  5. Kushnir R. M., Nykolyshyn M. M., Zhydyk U. V., Flyachok V. M.  On the theory of inhomogeneous anisotropic shells with initial stresses.  Journal of Mathematical Sciences.  186, 61–72 (2012).
  6. Tokovyy Y., Chyzh A., Ma C. C.  An analytical solution to the asymmetric thermoelasticity problem for a cylinder with arbitrarily varying thermomechanical properties.  Acta Mechanica.  230, 1469–1485 (2019).
  7. Ootao Y., Tanigawa Y., Miyatake K.  Transient thermal stresses of cross-ply laminated cylindrical shell using a higher-order shear deformation theory.  Journal of Thermal Stresses.  33 (1), 55–74 (2010).
  8. Zhydyk U., Nykolyshyn M., Flyachok V.  Calculation of the thermoelastic state of a layered anisotropic cylindrical shell under local heating by heat sources.  Visnyk Lviv. univer. Series: mech.-math.  73, 71–76 (2010).
  9. Fazelzadeh S. A., Rahmani S., Ghavanloo E., Marzocca P.  Thermoelastic vibration of doubly-curved nano-composite shells reinforced of doubly-curved of doubly-curved nano-composite shells reinforced.  Journal of Thermal Stresses.  42 (1), 1–17 (2019).
  10. Punera D., Kant T., Desai Y. M.  Thermoelastic analysis of laminated and functionally graded sandwich cylindrical shells with two refined higher order models.  Journal of Thermal Stresses.  41 (1), 54–79 (2018).
  11. Brischetto S., Carrera E.  Coupled thermo-mechanical analysis of one-layered and multilayered isotropic and composite shells.  Computer Modeling in Engineering & Sciences.  56 (3), 249–301 (2010).
  12. Pandey S., Pradyumna S.  Transient stress analysis of sandwich plate and shell panels with functionally graded material core under thermal shock.  Journal of Thermal Stresses.  41 (5), 543–567 (2018).
  13. Li Y., Yang L., Zhang L., Gao Y.  Exact thermoelectroelastic solution of layered one-dimensional quasicrystal cylindrical shells.  Journal of Thermal Stresses.  41 (10–12), 1450–1467 (2018).
  14. Musii R. S., Zhydyk U. V., Mokryk O. Ya., Melnyk N. B.  Functionally gradient isotropic cylindrical shell locally heated by heat sources.  Mathematical Modeling and Computing.  6 (2), 367–373 (2019).
  15. Musii R., Zhydyk U., Turchyn Ya., Svidrak I., Baibakova I.  Stressed and strained state of layered cylindrical shell under local convective heating.  Mathematical Modeling and Computing.  9 (1), 143–151 (2022).