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

In this article, the bending and buckling analysis of functionally graded nano-plate with simply supportboundary conditions using Mindlin theory are investigated. First strain-displacement relations are derived usingMindlin theory, and then the governing equations of equilibrium are obtained using energy method and Hamilton'sprinciple. Analytical method is used to solve these equations. To satisfy the boundary conditions of plate, theNavier's type solution is employed that is assumed to be a trigonometric. In order to consider the small scale effect,the strain gradient theory is considered. Finally, the effects of material length scale parameter and power law indexon deflection and critical buckling load of functionally graded Mindlin nano-plate are investigated. The resultsshow that the obtained critical buckling load from the strain gradient theory is larger than that of from the classicaland modified coupled stress theories, and vice versa for the deflection.

Keywords:

Bending and buckling analysis , functionally graded nano-plate , Mindlin theory , strain gradient theory