Nonlinear impact on the buckling characteristic of functionally graded nonlocal nanotube via a couple of nonlocal strain gradient theory and a novel higher-order tube theory

Abstract

The buckling behavior of nonlocal bi-directional functionally graded and imperfect nanotube based on the first-order beam theory and a novel higher-order tube theory is investigated in this paper. The nonlocal strain gradient theory is considered to length-scale impact applying the nonlinear von-Kármán theory using the conservation energy method to derive the nonlocal governing equations and related boundary conditions. Two-dimensional functionally graded (2D-FG) material in both length and radial direction is assumed to model the FG nano-scale tubes. Finally, the nonlinear equations are solved using the generalized differential quadrature method (GDQM) coupled with the iteration technique. Eventually, the calculated results are extracted to study the influence of various parameters, such as the size-effect parameters, FG power indexes parameters, porosity parameters, nonlinear amplitude on the buckling of 2D-FG imperfect nano-scale cylindrical beams and tubes.