Thermoelastic analysis of rotating functionally graded micro/nanodisks of variable thickness

Abstract

In this study, stress distribution in a functionally graded nanodisk of variable thickness is investigated based on the strain gradient theory. It is assumed that nanodisk is subjected to thermal and mechanical loads while it is rotating with a constant angular velocity. The equilibrium equation and the corresponding boundary conditions are deduced using Hamilton's principle. A numerical scheme is used to solve the problem. The effects of angular velocity, thickness profile, material inhomogeneity parameter, external loads and temperature are investigated on the total stresses as well as radial displacements. A close examination of the results based on strain gradient and classical theories predict the same trend for variation in radial displacements along the nanodisk radius. Additionally, results show that selection of a variable thickness reduces the radial stresses. Due to coupling effect between radial stress, σr, and high-order stresses which appear in strain gradient theory, total radial stresses at the inner and outer radii are nonzero despite the zero external loads applied at the two corresponding surfaces. Moreover, Due to very small radius of the nanodisk, the centrifugal forces due to angular velocity ω are negligible and hence, the total radial stresses are barely affected by their magnitudes.