Geometrically nonlinear postbuckling behavior of imperfect FG-CNTRC shells under axial compression using isogeometric analysis

The postbuckling and geometrically nonlinear behaviors of imperfect functionally graded carbon nanotubereinforced composite (FG-CNTRC) shells under axial compression are investigated in this paper. For the first time, a new type of instability named "snap-backward" with the presence of three limit points on the equilibrium path is proposed. A novel formulation based on non-uniform rational B-Spline (NURBS) basis functions and the first-order shear deformation shell theory (FSDT) using the von Karman assumption and considering the initial deformation of the shells is presented. In addition, the advantage of NURBS in modeling exactly geometries of shells is exploited. In numerical implementation, the discrete nonlinear equation system is iteratively solved by a modified Riks method. The rule of mixture is used to estimate the effective material properties of FG-CNTRC shells. Some benchmark problems are solved to verify the high reliability of the proposed formulation. Effects of geometrical imperfection, CNTs distribution, volume fraction, CNTs orientation, thickness, radius of shell on the postbuckling and geometrically nonlinear behaviors of FG-CNTRC shells are rigorously investigated. Especially, some new and complex load-deflection curves of imperfect FG-CNTRC shells under axial compression are first provided that could be useful for future references.