Post-buckling of Shear Deformable Nanocomposite Panels

In this paper, post-buckling equilibrium paths of nanocomposite panels reinforced by carbon-nanofillers and subjected to lateral pressure are studied using shear deformable refined theory. Three different types of nanofillers dispersion patterns are considered, including uniform (U-NFLL) and two graded (FG-V-NFLL, FG-X-NFLL) forms. The elastic materials properties of nanocomposite panels are obtained by applying the extended rule of mixture with some efficiency parameters to consider the size-dependency of nanofillers reinforcements. The equations of motion are elaborated within a refined high-order theory which includes seven kinematic variables compromising three displacements: u, v, w and two rotations \({\theta }_{x}\) , \({\theta }_{y}\) and two high-order terms of rotations \({\theta }_{x}^{h}\) , \({\theta }_{y}^{h}\) . The discretization of these variables is established using a four noded finite shell element and the resolution procedure is performed using the Newton-Raphson method with the arc length control technique. The reliability and efficiency of the formulas are validated. The effects of types of nanofillers and their volume fractions on post-buckling behavior of nanocomposite panels are studied and interpreted. It is pointed that graded nanofillers with X-form are more efficient in the enhancement of the post-buckling strength of the nanocomposite panel than other forms with an optimal value of 28% of added nanofillers.