This Paper illustrates the behaviour of a functionally graded layer under thermal shock load based on the Lord-Shulman theory. The coupled form of the equations are considered and the material properties of the layer are assumed to vary in a power law form function through the thickness of the layer. The Galerkin finite element method via the Laplace transformation is employed to solve the system of equations in the space domain. Finally, the temperature, displacement and stress fields are inverted to the physical time domain using a numerical inversion of the Laplace transform. The temperature and stress waves propagation through the thickness of the layer are investigated and the effects of material composition and the relaxation time on thermal and elastic waves propagation are studied.

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