Finite rotation three and four nodes shell elements for functionally graded carbon nanotubes-reinforced thin composite shells analysis

In this paper, we address the extension of the Kirchhoff shell model to non-linear analysis of functionally graded carbon nanotubes-reinforced thin composite shells (FG-CNTRCs). The present model can bring up two levels of analysis: geometrically non-linearities and nanostructures with the possibilities of two type of discretization. Either, three and four nodes finite shell elements are implemented to analyze as well as predict the non-linear bending behavior of FG-CNTRC shell structures. Uniform (UD) and three graded distributions of carbon nanotubes (CNTs) which are FG-V, FG-O and FG-X are considered. These distributions are uniaxially aligned in the axial direction of the shell and functionally graded along the thickness direction. The material properties of CNTs are estimated using the modified rule of mixture and the size dependence of these CNTs is taken into account via the introduction of some efficiency parameters. Three numerical examples of FG-CNTRC plates, hyperboloidal and cylindrical shells are presented to highlight the applicability and effectiveness of the present finite element model notably for thin structures. The effect of CNT profiles, CNT volume fractions and others geometrical parameters on non-linear behavior of such structures are also examined.