Stress analysis of rotating nano-disks of variable thickness made of functionally graded materials

This paper presents the stress analysis of rotating nano-disk made of functionally graded materials with nonlinearly varying thickness based on strain gradient theory. The equilibrium equation and corresponding boundary conditions of nano-disk were obtained using Hamilton's principle. Because of the complexity of governing equations and boundary conditions, the equations are solved using numerical methods. Fixed boundary conditions are considered, in the numerical examples. This analysis is general and can be reduced to classical elasticity. The effect of various parameters such as graded index and thickness profile on stresses and high-order stresses were examined. Values of stresses at inner and outer radial are not zero, because stresses at inner and outer radius accumulate with stresses caused by strain gradient theory. Results show that the effects of thickness parameters are greater than the effect of graded index and the difference between the stress predicted by the classical theory and the strain gradient theory is large when the thickness of nano-disk is small.