Nonlinear flexural behavior of temperature-dependent FG-CNTRC laminated beams with negative Poisson's ratio resting on the Pasternak foundation

Nanocomposite materials, such as carbon nanotube-reinforced composites (CNTRCs), have emerged as a novel engineering material. They have received growing attentions in various engineering sectors. The fabrication process has also offered the possibility to design and make this type of material to have desired features, such as being functionally graded (FG) or/and having negative Poison's ratio. This paper reports an investigation on the nonlinear flexural behavior of auxetic laminated beams with each layer is made of CNTRC. Each layer may have different CNT volume fractions and the functional grading occurs in the thickness direction of the beam in the piece-wise pattern. The extended rule of mixture model is used to evaluate the temperature-dependent material properties of CNTRCs. The governing equations for the nonlinear bending of FG-CNTRC laminated beams are derived based on the high order shear deformation beam theory. These equations include the geometrical nonlinearity in the von Karman sense and take into account the thermal effect and the beam-foundation interaction. The nonlinear bending solutions can be obtained by employing a two-step perturbation approach. The nonlinear flexural responses of FG-CNTRC laminated beams under a uniform pressure in thermal environments are revealed and examined in details through a parametric study. Results showed that the negative Poisson's ratio has a significant impact on the nonlinear flexural behavior of CNTRC laminated beams.