A Numerical Framework for Flexible–Electrical Coupled Analysis of Piezoelectric Structures with Large Deformations

Piezoelectric smart materials have been widely used in applications such as soft robotic actuation, vibration control and sensing of aerospace structures. In such contexts, the smart structures are typically subjected to significant large deformations and strong electromechanical coupling effects, which pose considerable challenges for conventional analytical approaches and classical finite element models in accurately predicting their nonlinear dynamic responses and capturing multiphysics coupling behaviors. To address these challenges in modeling and analysis, this work develops a flexible–electrical coupled computational framework with a unified mesh description based on the absolute nodal coordinate formulation (ANCF). This coupling methodology introduces a consistent high-order discretization scheme for both the structural and electric fields within the thin plate element, effectively ensuring the numerical accuracy and stability of the electromechanical coupling terms. Based on continuum mechanics and piezoelectric constitutive theory, the generalized elastic force and electromechanical coupling matrices of the flexible–electrical coupled thin plate element under geometric nonlinearity are systematically derived, and the corresponding nonlinear governing equations are formulated. Subsequently, numerical solution procedures for flexible–electrical coupled analyses are developed, enabling a systematic investigation of the bidirectional coupling mechanisms between the electric and structural fields, as well as the nonlinear dynamic behavior of the structure under large deformations. Comparisons with numerical methods are conducted to validate the accuracy and robustness of the proposed modeling framework. The present study provides a unified and high-accuracy numerical modeling approach for the strongly coupled multiphysics modeling and dynamic analysis of piezoelectric smart structures with large deformations.