Buckling of pressurized functionally graded carbon nanotube reinforced conical shells

A linear buckling analysis is presented for nanocomposite conical shells reinforced with single walled carbon nanotubes (SWCNTs) subjected to lateral pressure. Material properties of functionally graded carbon nanotube reinforced composite (FG-CNTRC) conical shell are assumed to be graded across the thickness and are obtained based on the modified rule of mixture. Governing equilibrium equations of the shell are obtained based on the Donnell shell theory assumptions consistent with the first order shear deformation shell theory. General form of the equilibrium equations and the complete set of boundary conditions are obtained based on the concept of virtual displacement principle. Shell is assumed to be under lateral pressure. Prebuckling load of the shell is estimated based on the linear membrane analysis. Stability equations of the shell are extracted via the adjacent equilibrium criterion. Resulting stability equations are discreted by suitable trigonometric functions in circumferential direction and generalized differential quadrature method in axial direction. An eigenvalue problem is established to obtain the buckling pressure and circumferential buckling mode of the conical shell. It is shown that, CNTs volume fraction and CNTs distribution law are important factors on the buckling mode and buckling load of the FG-CNTRC conical shells.