functionally gradient materials

Functionally gradient isotropic cylindrical shell locally heated by heat sources

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 meth