MESHLESS ANALYSIS OF LINEAR BENDING AND FREE VIBRATION OF FUNCTIONALLY GRADED CARBON NANOTUBE-REINFORCED COMPOSITE PLATE ON ELASTIC FOUNDATION BASED ON IMPROVED REDDY TYPE THIRD-ORDER SHEAR DEFORMATION THEORY

Based on the improved Reddy type third-order shear deformation theory (TSDT), and considering the orientation of carbon nanotubes (CNTs) and the inhomogeneity of functionally gradient materials, a meshless analysis model for the linear bending and free vibration of functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates on elastic foundation is established. The potential energy and kinetic energy of FG-CNTRC plate are derived by the improved Reddy type TSDT, and then the expression of the potential energy of elastic foundation is given, and then they are respectively superposed. The linear bending and free vibration control equations of FG-CNTRC plate on elastic foundation are derived by the principle of minimum potential energy and Hamilton principle. Stable moving Kriging interpolation (SMKI) is used to discretize the nodes in the problem domain. The construction method of the approximate shape function satisfies the Kronecker condition and can directly apply the boundary conditions. In this paper, a meshless discrete model of linear bending and free vibration of FG-CNTRC plate on elastic foundation based on the third-order shear deformation theory is presented. Then, the effectiveness and accuracy of the proposed method are studied by a benchmark example. Finally, the effects of CNTs distribution, orientation angle, volume fraction, foundation coefficient, width thickness ratio and boundary conditions on the linear bending and natural frequency of FG-CNTRC plate are numerically analyzed. The results show that the proposed method has a good accuracy in calculating the linear bending and natural frequencies of FG-CNTRC thin, medium-thick, and even thick plates. As the volume fraction of CNTs and the foundation coefficient increase, the stiffness of the FG-CNTRC plate structure gradually increases. The stiffness of the FG-CTRC plate structure is positively correlated with the width-thickness ratio, and the shear effect of increasing thickness gradually reduces the influence of the CNTs orientation angle on the plate stiffness.