RVE-based isogeometric analysis for the dynamic response of electro-mechanical coupling in piezoelectric composite materials

Abstract

Piezoelectric composite materials (PCMs) are widely used in smart devices and play a crucial role in various engineering applications. Accurate and efficient dynamic analysis is crucial for ensuring the reliability of materials. However, the finite element method (FEM) often suffers from geometric approximation errors and increased computational cost when modeling complex PCM structures, particularly in dynamic analyses involving complex geometries. To enhance numerical accuracy in the dynamic analysis of PCMs, this study proposes the representative volume element (RVE) based isogeometric analysis for piezoelectric composite materials (RVE-PCMIGA). By combining isogeometric analysis (IGA) with the homogenization method, the macroscopic effective properties of the PCM at various fiber volume fractions were computed at the mesoscale. These effective properties were integrated into the constitutive equations and boundary conditions of the PCM to derive the governing equations for RVE-PCMIGA. Compared to FEM, the proposed method significantly simplifies mesh generation during preprocessing, precisely represents curved geometries, and minimizes discretization errors. Numerical simulations were performed to evaluate the accuracy and efficiency of the proposed method. The free vibration, transient response, and harmonic response of PCM structures were investigated. Numerical simulations demonstrate that, compared to FEM, the proposed method achieves higher accuracy and robustness, maintains high accuracy with coarse meshes, and can significantly improve the convergence and accuracy for high-frequency modes. Furthermore, since frequent interactions between CAD and CAE are not required, the preprocessing of RVE-PCMIGA is easier than that of FEM for typical problems. These advantages highlight the significant potential of RVE-PCMIGA for the dynamic analysis of advanced PCM-based smart structures in future engineering applications.