Imperfection sensitivity of postbuckling behaviour of functionally graded carbon nanotube-reinforced composite beams

The imperfection sensitivity of the postbuckling behaviour of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams subjected to axial compression is investigated based on the first-order shear deformation beam theory with a von Kármán geometric nonlinearity. The material properties of FG-CNTRC are assumed to vary in the beam thickness direction and are estimated according to the extended rule of mixture. The differential quadrature method is employed to discretize the governing differential equations and the modified Newton-Raphson iterative technique is used to obtain the postbuckling equilibrium paths of FG-CNTRC beams with various imperfections. Parametric studies are carried out to examine the effects of imperfection modes, half-wave number, location, and amplitude on the postbuckling response of beams. The influences of CNT distribution pattern and volume fraction, boundary conditions, and slenderness ratio are also discussed. Numerical results in graphical form show that the postbuckling behaviour is highly sensitive to the imperfection amplitude. The imperfection mode and its half-wave number also moderately affect the imperfection sensitivity of the postbuckling response, whereas the effects of other parameters are much less pronounced.