Thermoelastic Stresses in FG-Cylinders

FGM components are generally constructed to sustain elevated temperatures and severe temperature gradients. Low thermal conductivity, low coefficient of thermal expansion and core ductility have enabled the FGM material to withstand higher temperature gradients for a given heat flux. Examples of structures undergo extremely high temperature gradients are plasma facing materials, propulsion system of planes, cutting tools, engine exhaust liners, aerospace skin structures, incinerator linings, thermal barrier coatings of turbine blades, thermal resistant tiles, and directional heat flux materials. Continuously varying the volume fraction of the mixture in the FGM materials eliminates the interface problems and mitigating thermal stress concentrations and causes a more smooth stress distribution. Extensive thermal stress studies made by Noda reveal that the weakness of the fiber reinforced laminated composite materials, such as delamination, huge residual stress, and locally large plastic deformations, may be avoided or reduced in FGM materials (Noda, 1991). Tanigawa presented an extensive review that covered a wide range of topics from thermo-elastic to thermo-inelastic problems. He compiled a comprehensive list of papers on the analytical models of thermo-elastic behavior of FGM (Tanigawa, 1995). The analytical solution for the stresses of FGM in the one-dimensional case for spheres and cylinders are given by Lutz and Zimmerman (Lutz & Zimmerman, 1996 & 1999). These authors consider the non-homogeneous material properties as linear functions of radius. Obata presented the solution for thermal stresses of a thick hollow cylinder, under a two-dimensional transient temperature distribution, made of FGM (Obata et al., 1999). Sutradhar presented a Laplace transform Galerkin BEM for 3-D transient heat conduction analysis by using the Green's function approach where an exponential law for the FGMs was used (Sutradhar et al., 2002). Kim and Noda studied the unsteady-state thermal stress of FGM circular hollow cylinders by using of Green's function method (Kim & Noda, 2002). Reddy and co-workers carried out theoretical as well as finite element analyses of the thermo-mechanical behavior of FGM cylinders, plates and shells. Geometric non-linearity and effect of coupling item was considered for different thermal loading conditions (Praveen & Reddy, 1998, Reddy & Chin, 1998, Paraveen et al., 1999, Reddy, 2000, Reddy & Cheng, 2001). Shao and Wang studied the thermo-mechanical stresses of FGM hollow cylinders and cylindrical panels with the assumption that the material properties of FGM followed simple laws, e.g., exponential law,