Functionally gradient isotropic cylindrical shell locally heated by heat sources

: pp. 367–373
Received: September 26, 2019
Revised: July 20, 2019
Accepted: July 23, 2019

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

Lviv Polytechnic National University
Lviv Polytechnic National University
Danylo Halytsky Lviv National Medical University
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.

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