Size Dependency in the Axial Postbuckling Behavior of Nanopanels Made of Functionally Graded Material Considering Surface Elasticity

Size-dependent modeling and analysis for the nonlinear postbuckling response of functionally graded (FG) cylindrical nanopanels under axial compressive load are presented based on the surface elasticity theory. The non-classical formulations are developed on the basis of the Gurtin-Murdoch elasticity theory within the framework of the classical shell theory. In order to capture the large deflections associated with the postbuckling regime, the geometrical nonlinearity is considered in von Karman sense. The material properties are supposed to be graded across the panel thickness in accordance with a simple power law function of the volume fractions of the silicon and aluminum constituents with considering the physical neutral plane position. To satisfy the balance conditions on the free surface layers, it is assumed that the bulk normal stress along the thickness direction varies linearly between those values of surface stress components at the inner and outer layers. A boundary layer theory of shell buckling is extended to the case of size-dependent FG nanopanels, and then, a singular perturbation technique is put to use to solve the nonlinear problem. It is displayed that due to the stiffening influence of surface effects, the depth of the postbuckling regime for FG nanopanels with higher material gradient index decreases, as for the metal-rich nanopanel, the snap-through phenomenon approximately diminishes.