Geometrically nonlinear analysis of CNT-reinforced functionally graded composite plates integrated with piezoelectric layers

The paper develops a geometrically nonlinear finite element model with large rotation based on the first-order shear deformation (FOSD) hypothesis for static and dynamic analyses of piezoelectric integrated carbon nanotube reinforced functionally graded (P-CNT-FG) composite structures. A constant electric field distribution through the thickness of plate is considered. An eight-node quadrilateral plate element with five mechanical degrees of freedom (DOFs) and one electric degree of freedom is developed for finite element analysis. Four typical forms of CNT distributions are included in the model, namely uniform, V-shaped, O-shaped, and X-shaped distributions. The nonlinear model considers fully geometrically nonlinear strain-displacement relations and large rotations of the shell direction of plate. Using the Hamilton's principle, a nonlinear dynamic model including dynamic and sensory equations is obtained. The proposed nonlinear model is validated by a frequency analysis of a simply supported P-CNT-FG composite plate. Furthermore, the effects of various parameters on the static and dynamic behavior are investigated, e.g. CNT-reinforcement orientation, CNT distribution, the number of laminate layers and volume fraction.