Theoretical solutions for auxetic laminated beam subjected to a sudden load

In the current work, the concept of auxetic structures design is introduced into carbon nanotube-reinforced composite (CNTRC) laminate. Larger values of negative Poisson's ratio (NPR) of CNTRC laminate are obtained by setting the optimal orientation. Meanwhile, a theoretical model is presented for the nonlinear dynamic response of functionally graded (FG) CNTRC beam with NPR. Using Reddy's higher order shear deformation plate theory with von Karman's strain–displacement relations, the motion equations are obtained A two-perturbation approach and the fourth-order Runge Kutta method are then used to obtain the time-deflection curve of the auxetic FG-CNTRC beam. The effects of factors such as the CNT distribution, thermal field and foundation stiffness on the dynamic characteristic of the auxetic FG-CNTRC beam are studied in details. Numerical results indicate that the thermal–mechanical behavior of FG-CNTRC beams might be significantly improved by determining a proper distribution of CNTs. Furthermore, the results show that the change of temperature and foundation stiffness have a significant effect on the dynamic characteristic of FG-CNTRC laminated beams with NPR.