Proceedings of ESDA2006 8th Biennial ASME Conference on Engineering Systems Design and Analysis July 4-7, 2006, Torino, Italy ESDA2006-95661 GENERALIZED COUPLED THERMOELASTICIY OF FUNCTIONALLY GRADED LAYERS A. Bagri M. R. Eslami B. A. Samsam-Shariat Department of Mechanical Engineering Amirkabir University of Technology Tehran, 15914 Iran Email: bagri.a@gmail.com ABSTRACT This Paper illustrates the behaviour of a functionally graded layer under thermal shock load based on the Lord-Shulman the- ory. 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 in- verted to the physical time domain using a numerical inversion of the Laplace transform. The temperature and stress waves prop- agation 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. NOMENCLATURE L thickness of layer N i shape function P material property T absolute temperature T 0 reference temperature T d characteristic temperature T i nodal values of temperature Address all correspondence to this author. U i nodal values of displacement c specific heat k heat conduction number of nodes in the base element n power law index q heat flux s Laplace parameter t time t 0 relaxation time proposed by lord and Shulman u displacement x position from the ceramic rich side x f position of the first node in the base element x e position of the last node in the base element β temperature-stress moduli λ Lam´ e constant μ Lam´ e constant ρ density σ xx stress in x direction ¯ dimensionless form of terms the Laplace transform of terms c ceramic properties m metal properties 1 Copyright c 2006 by ASME Proceedings of ESDA2006 8th Biennial ASME Conference on Engineering Systems Design and Analysis July 4-7, 2006, Torino, Italy ESDA2006-95661