Analysis of functionally graded nanodisks under thermoelastic loading based on the strain gradient theory

In this paper, the thermoelastic behavior of a functionally graded nanodisk is studied based on the strain gradient theory. It is assumed that the nanodisk thickness is constant, and a power-law model is adopted to describe the variation of functionally graded material properties. Furthermore, the nanodisk angular acceleration is taken to be zero while it is subjected to an axisymmetric loading. Also, it is assumed that any variation in temperature occurs only in the radial direction. The equilibrium equation and the boundary conditions are deduced from Hamilton's principle. The obtained results are compared with those of classical theory. These results show that both theories predict the same trend for the variation in radial displacements. The differences between the stresses obtained from classical and strain gradient theories are clearly highlighted. Increasing the value of the material inhomogeneity parameter, n, considerably affects the magnitudes and the corresponding peak values of the high-order stress ${\overline{\tau }}_{rrr}$. Any rise in temperature at the outside radius has a direct effect on the total stresses and radial displacements in the nanodisk. Also, the effects of external load at the inner and outer radii on radial displacement as well as stress components are fully investigated.