Thermoelastic Analysis in Thick FGM Cylinders with Extended Profile

An exact solution is obtained for an axisymmetric steady-state‎ ‎thermo-mechanical stresses in a thick functionally graded‎ ‎cylinder‎. ‎The material properties are graded along the radial‎ ‎direction according to an exponential function of radial‎ ‎direction with three constants‎. ‎The advantage of the proposed‎ ‎model‎, ‎compared to the models with two constants such as the‎ ‎linear‎, ‎power law‎, ‎and exponential models with two constants‎, ‎is‎ ‎that it satisfies the material boundary conditions at the inside‎ ‎and outside radiuses‎, ‎leaving one more constant to be selected to‎ ‎produce different types of material variation profiles along the‎ ‎cylinder radius‎. ‎Utilizing the assumed exponential model‎, ‎the‎ ‎analytical solution of the problem‎, ‎using the generalized Bessel‎ ‎function and the Lagrange method‎, ‎is obtained employing the energy‎‎and Navier equations.