Bending and buckling analysis of functionally graded mindlin nano-plate model based on strain gradient elasticity theory

چکیده مقاله

In this article, the bending and buckling analysis of functionally graded nano-plate with simply support boundary conditions using Mindlin theory are investigated. First strain-displacement relations are derived using Mindlin theory, and then the governing equations of equilibrium are obtained using energy method and Hamilton's principle. Analytical method is used to solve these equations. To satisfy the boundary conditions of plate, the Navier's type solution is employed that is assumed to be a trigonometric. In order to consider the small scale effect, the strain gradient elasticity theory is considered. Finally, the effects of aspect ratio, material length scale parameter and power law index on deflection and critical buckling load of functionally graded Mindlin nano-plate are investigated. The results show that the obtained critical buckling load from the strain gradient theory is larger than that of from the classical and modified coupled stress theories, and vice versa for the deflection. It is observed from the result that with an increase in the length scale parameter and aspect ratio, the critical buckling load reduces, while the deflection of functionally graded nano-plate increases. Also, with increasing of the power law index, the critical buckling load decreases and vice versa for the deflection of Mindlin nano-plate.