Piezoelectric Interaction Analysis and Load‐Deflection Prediction for Nonlinear Bending and Snap‐Through of Post‐Buckled FG Piezoelectric Beams

Abstract

Revealing the interaction effect in the nonlinear bending of post‐buckled functionally graded (FG) piezoelectric beams promotes the intelligent development of structural design. The nonlinear bending behavior of post‐buckled piezoelectric beams is studied. Based on the displacement field constructed by the refined beam model, the post‐buckling configuration is considered. The nonlinear geometric relationship and the constitutive relationship in the multi‐physical field are modeled. In the framework of the principle of minimum potential energy, the nonlinear static models of post‐buckled FG piezoelectric beams are established. The post‐buckling configuration is obtained by the extended two‐step perturbation method. To obtain the approximate solution for the static problems of the post‐buckled FG piezoelectric beam, the perturbation scheme of electric potential and generalized displacement is proposed. The detailed parametric analysis indicates the interaction mechanism in the nonlinear bending of the post‐buckled FG piezoelectric beam. The snap‐through process and its sensitive interval are further captured. The back propagation neural network (BPNN) technique developed for the nonlinear bending problem of post‐buckled FG piezoelectric beams achieves accurate prediction.