Non-linear bending analysis of nanocomposites reinforced by graphene-nanotubes with finite shell element and membrane enhancement

The purpose of this paper is to investigate the non-linear bending behavior of functionally graded shell structures reinforced by carbon nanotubes (FG-CNTRC) using non-linear double directors shell model and membrane enhancement. This model induces a high order variation of the displacement field along the thickness direction and imposes a zero transverse shear stresses condition in the top and bottom surfaces. The effective material properties of FG-CNTRC are estimated by the modified rule of mixtures using some efficiency parameters. Uniformly (UD) and three graded distributions, known as FG-V, FG-O and FG-X, are considered to show the effects of carbon nanotubes (CNTs) profiles and their volume fractions on non-linear deflections of various shapes of shell structures. To illustrate these effects, a set of numerical examples including beams, plates, cylindrical panels and hemispherical shells are presented. The effects of some geometrical parameters are also examined. A convergence studies are carried out to validate the proposed non-linear model, then non-linear results for FG-CNTRC shell structures are provided leading hence to outline the applicability and the efficiency of the present model.