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  4. Functionally gradient isotropic cylindrical shell locally heated by heat sources

Functionally gradient isotropic cylindrical shell locally heated by heat sources

MMC.
2019;
Volume 6, Number 2
: pp. 367–373
https://doi.org/10.23939/mmc2019.02.367
Received: September 26, 2019
Revised: July 20, 2019
Accepted: July 23, 2019

Mathematical Modeling and Computing, Vol. 6, No. 2, pp. 367–373 (2019)

Authors:
  1. R. S. Musii
  2. U. V. Zhydyk
  3. O. Ya. Mokryk
  4. N. B. Melnyk
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University
3
Danylo Halytsky Lviv National Medical University
4
Lviv Polytechnic National University

The stress-strain state of a functionally gradient isotropic thin circular cylindrical shell under local heating by a flat heat source has been investigated.  For this purpose, a mathematical model of the classical theory of inhomogeneous shells has been used.  A two-dimensional heat equation is derived under the condition of a linear dependence of the temperature on the transverse coordinate.  The solutions of the non-stationary heat conduction problem and the quasi-static thermoelasticity problem for a finite closed cylindrical pivotally supported shell have been obtained by means of methods of Fourier and Laplace integral transforms.  Numerical results are presented for the metal-ceramic composite used to restore the integrity of human tooth crowns.

thermoelasticity
functionally gradient materials
temperature load
cylindrical shell
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