Dynamic thermal stresses in functionally graded thick hollow cylinders by a graded finite element method and 2D axisymmetric elasticity

In this research, an axisymmetric thick hollow cylinder made of functionally graded materials under internal thermal shock based on classical theory of linear thermoelasticity is considered. The cylinder is made of a combined ceramic-metal material and its material is graded through the thickness direction according to a power law distribution. The governing equations are based on 2D-axisymmetric theory of elasticity and graded finite element method based on Rayleigh- Ritz energy formulation is used to model the problem. To obtain transient temperatures, Crank- Nicolson algorithm is used and then Newmark direct integration method is used to obtain time history of displacements and stresses. Distribution of displacements and stresses for different power law exponents is investigated. To obtain transient temperatures, Crank- Nicolson algorithm is used and then Newmark direct integration method is used to obtain time history of displacements and stresses. Distribution of displacements and