Document Type : Research Paper
Amirkabir University of Technology
This article presents the coupled thermoelasticity of a truncated functionally
graded conical shell under thermal shock load. The classical coupled thermoelas-
ticity theory is employed to set the partial differential equations of motion of the
conical shell. The shell governing equations are based on the first-order shear de-
formation shell theory that accounts for the transverse shear strains and rotations.
The solution is obtained by transforming the governing equations into the Laplace
domain and using the Galerkin finite element method in the Laplace domain to
calculate the displacement components. The physical displacement components in
real time domain are obtained by the numerical inversion of the Laplace transform.
Temperature distribution is assumed to be linear across the shell thickness. Radial
displacement, axial stress, axial force, and temperature versus time are calculated
and the effect of relaxation time and power law index are examined. Comparison
indicates that an increase in the radial vibration amplitude and a decrease of vi-
bration frequency occur when changing the material from ceramic to metal. The
results are validated with the known data in the literature.