Static and free vibration analysis of functionally graded annular plates using stress-driven nonlocal theory

This study presents analytical and numerical solutions of the bending and the free vibration analysis of a functionally graded annular nanoplate based on the stress-driven nonlocal theory. The nonlocal equation is obtained using the classical plate theory; the power law distribution is assumed to model changes in material properties throughout the thickness. The governing differential equation is analytically solved for different types of edge supports. The explicit analytical solution is obtained in terms of special functions, namely, hypergeometric and Meijer functions. Furthermore, based on the Galerkin technique, a finite element method is introduced to figure out the nanoplate's flexural deformation and natural frequencies. The analytical and numerical solutions are compared with those available in the literature. The size effects in the nonlocal theory and FGM's gradient properties have been discussed, considering clamped and simply supported boundary conditions. According to the stress-driven nonlocal model, size-dependent flexural responses of the plate demonstrate stiffening behavior with increasing nonlocal parameters. Which, in general, leads to a decrease in the value of transversal deformation and an increase in natural frequencies when compared to the plate's local solutions.

Automated summary

This study investigates the bending and free vibration analysis of a functionally graded annular nanoplate using the stress-driven nonlocal theory. Analytical solutions are obtained for different boundary conditions and the explicit form is expressed in terms of special functions. A finite element method based on the Galerkin technique is also employed to calculate the flexural deformation and natural frequencies. The results are compared with existing literature and indicate a stiffening behavior with increasing nonlocal parameters, resulting in decreased transversal deformation and increased natural frequencies compared to local solutions.