Analytical solution for nonlinear postbuckling of functionally graded carbon nanotube-reinforced composite shells with piezoelectric layers

Abstract

This paper presents an analytical solution procedure for the nonlinear postbuckling analysis of piezoelectric functionally graded carbon nanotubes reinforced composite (FG-CNTRC) cylindrical shells subjected to combined electro-thermal loadings, axial compression and lateral loads. The carbon nanotubes are assumed to be aligned and straight with uniform and functionally graded distributions in the thickness direction. The kinematics and constitutive relations are written on the basis of the classic theory and the von Kármán nonlinear strain–displacement relations of large deformation. Applying the Ritz energy approach, analytical solutions are proposed for the nonlinear critical axial load, lateral pressure as well as the load-shortening ratio of the piezoelectric FG-CNTRC shell. Numerical results are presented to study the effects of dimensional parameters, CNT volume fraction, distribution type of the reinforcement and piezoelectric thickness on the nonlinear buckling behavior of the piezoelectric nanocomposite shell. It is revealed that the carrying capacity of the structure increases as the shell is integrated by the piezoelectric layers and reinforced by higher CNT volume fraction. Furthermore, FGX- and FGO- CNTRC piezoelectric shells are indicated to have higher and lower carrying capacities compared to UD-CNTRC piezoelectric shells, respectively.