Multilayer heterostructure power-law inhomogeneous model for the functionally graded cylinders and annular disks with rotation effect for arbitrarily material property with the parametric uncertainty

Abstract

This study comprehensively investigates the influence of the rotation effect on the elastic field of functionally graded (FG) hollow cylinders and annular disks with considering uncertainty and fluctuation in material parameters. The multilayer heterostructure power-law inhomogeneous (MHPI) model is introduced, where the radial change in Young's modulus and density are approximated by multiple sublayers with power-law functionally graded materials (FGMs). The analytical solutions for rotating FG hollow cylinders and annular disks are derived by considering continuity between the layers and six different boundary conditions. Numerical examples are conducted using various classical gradient assumptions, including property profile gradient models (power, linear, and exponential laws, etc.) and the volume fractional gradient model (volume fractional gradient and homogenization schemes). Comparison of the MHPI model with the finite difference method (FDM) and the multilayer heterostructure homogeneous (MHH) model demonstrates its validity. Additionally, the study analyzes the impact of the gradient parameter, rotation effect, and elastic foundation effect on the elastic field of rotating FG hollow cylinders and annular disks. The results show that the MHPI model effectively overcomes the oscillation problem of the circumferential stress calculated by the MHH model, and the accuracy is very high, with an error of about 5‰ in the case of the number of sublayers N = 10. The solution of the problem for different boundary conditions such as stress-free or displacement-fixed can be obtained by adjusting the elastic foundation parameters. In addition, based on the reliable and efficient MHPI model, how the uncertainties in the material parameters E and ρ affect the mechanical response of rotating FG hollow cylinders and annular disks is analyzed, which contributes to a deeper understanding of their mechanical behavior.