Analytical Buckling and Neural Network Prediction of FG Imperfect Piezo-MPCF

This study examines the static buckling behavior of FG piezoelectric micropipes with geometric imperfections in the presence of external disturbances. Utilizing the EBB model as well as incorporating the MCST, the dynamical model for the MPCF is formulated along with its boundary conditions through the application of Hamilton’s principle. By analyzing the static equation, the research assesses the impact of parameters such as the FG power-law exponent, bending stiffness ratio, and slenderness ratio on the static buckling configurations of both perfect and imperfect micropipes. The findings indicate that geometric imperfections significantly influence the buckling configurations of micropipes. As the power-law exponent increases, a decreasing trend is shown in the critical flow velocity associated with micropipe instability, leading to a higher propensity for buckling. In contrast, an increase in flexural stiffness ratio demonstrates an opposite trend. The aspect ratio’s impact is moderated by imperfections. To predict the complex phenomenon, the BP, RF, and RBF-NNs are used to establish the data-driven model. Compared to BP and RF-NNs, the RBF-NNs show better prediction indicators. Additionally, the SHAP analysis is carried out to determine the importance ranking of factors influencing buckling.