A functionally graded (FG) rotating disk with axisymmetric bending and steady-state thermal loading is studied. The material properties of the disk are assumed to be graded in the direction of the thickness by a power law distribution of volume fractions of the constituents. First-order shear deformation Mindlin plate and von Karman theories are employed. New set of equilibrium equations with small and large deflections are developed. Using small deflection theory an exact solution for displacement field is given. Solutions are obtained in series form in case of large deflection. Mechanical responses are compared small deflection versus large deflection as well as homogeneous versus FG disks. It is observed that for particular values of the grading index n of material properties mechanical responses in FG disk can be smaller than in a homogeneous disk. It is seen that given the non-dimensional maximum vertical displacement wmax/h close to 0.4 for a homogeneous (full-ceramic in this study) disk greater errors in the mechanical responses for FG disks would be introduced if one uses small deflection theory.

Thermo elastic analysis of a functionally graded rotating disk with small and large deflections

As a first endeavor, the nonlinear bending behavior of functionally graded carbon nanotube reinforced composite (FG-CNTRC) annular plates with variable thickness on an elastic foundation is scrutinized in this research. The nonlinear governing equations are established according to the third-order shear deformation theory (TSDT) in conjunction with the nonlinear von Karman strain field. A Pasternak elastic foundation is assumed to be in contact with the annular plate during deformation. To discretize the nonlinear governing equations and boundary conditions, the generalized differential quadrature method (GDQM) is adopted and the nonlinear system of equations is solved via the Newton-Raphson iterative method. Through the numerical results, effects of the elastic foundation, geometrical parameters, boundary conditions, CNT dispersion and volume fraction, thickness-to-radius ratio and thickness profile are investigated in detail. It is shown that CNT volume fraction and dispersion have a remarkable effect on improving bending behavior of the annular plate. It is found that thickness profile plays an essential role in the bending response of the annular plate.

C.L. Haung

Papers

Nonlinear axisymmetric bending of annular plates with varying thickness