Generalized thermoelastic functionally graded half space under surface absorption of a laser radiation

The subject of this paper is to study the thermoelastic behavior of a functionally graded
semi-infinite medium heated uniformly by a laser beam having temporally Gaussian distribution.
The surface of the medium is taken as traction free. The general solution is obtained
in the Laplace transform domain. The inverse of the Laplace transform is computed numerically
using the Riemann-sum approximation method. The numerical results for temperature,
displacement and stress are obtained and presented graphically for the generalized theory
of thermo-elasticity with one relaxation time.