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.