Abstract: The transient thermoelastic response of thick hollow cylinder made of functionally graded material under thermal loading is studied. The generalized coupled thermoelasticity based on the Green-Lindsay model is used. The thermal and mechanical properties of the functionally graded material are assumed to be varied in the radial direction according to a power law variation as a function of the volume fractions of the constituents. The thermal and elastic governing equations are solved by using Galerkin finite element method. All the finite element calculations were done by using commercial finite element program FlexPDE. The transient temperature, radial displacement, and thermal stresses distribution through the radial direction of the cylinder are plotted.
Abstract: Thermoelastic temperature, displacement, and
stress in heat transfer during laser surface hardening are solved
in Eulerian formulation. In Eulerian formulations the heat flux
is fixed in space and the workpiece is moved through a control
volume. In the case of uniform velocity and uniform heat flux
distribution, the Eulerian formulations leads to a steady-state
problem, while the Lagrangian formulations remains transient.
In Eulerian formulations the reduction to a steady-state
problem increases the computational efficiency. In this study
also an analytical solution is developed for an uncoupled
transient heat conduction equation in which a plane slab is
heated by a laser beam. The thermal result of the numerical
model is compared with the result of this analytical model.
Comparing the results shows numerical solution for uncoupled
equations are in good agreement with the analytical solution.