Exact Thermoelastic Analysis of Functionally Graded Anisotropic Hollow Cylinders with Arbitrary Material Gradation

摘要

An exact solution is presented for the thermoelastic analysis of functionally graded long hollow cylinders. The functionally graded material is assumed to have temperature-dependent cylindrical monoclinic material properties that vary as a function of the radial coordinate. Thermal and mechanical boundary conditions are specified on the inner and outer surfaces of the cylinder. In addition, the net axial force and torque acting on the cylinder are prescribed. The nonlinear steady-state heat conduction equation is solved using an iterative power-series solution procedure to obtain the temperature field. Subsequently, the three-dimensional thermoelasticity equations are solved using a power-series solution procedure to obtain the displacements and stresses. The solution procedure is applicable to hollow cylinders with an arbitrary variation of material properties in the radial direction. The convergence of the analytical solution is improved by dividing the hollow cylinder into multiple functionally graded concentric layers or sub-cylinders through the introduction of fictitious material interfaces. Results are presented for isotropic tungsten/copper functionally graded cylinders. The homogenized properties of the composite material are evaluated using the self-consistent scheme. The temperature, displacements and stresses are compared with numerical results obtained using the element-free Galerkin method and the effect of material gradation on the response of the cylinder is scrutinized. Results are also presented for a fiber-reinforced titanium/silicon carbide composite cylinder with functionally graded fiber orientation. The silicon carbide fibers are oriented in the axial direction on the inner surface and circumferential direction on the outer surface with a sigmoidal variation in between. The radial variation of temperature, displacements and stresses are investigated for different sigmoid exponents.