A Volume Coordinates System Generalized Mixed Element for Piezoelectric Structures

Prompted by the significant aerospace applications of piezoelectric materials, a novel 8-node hexahedral generalized mixed element is introduced for analyzing such structures. The element employs a volume coordinate system for its local frame, which maintains a linear transformation to the global Cartesian coordinates. Unlike conventional displacement-based formulations, the governing equations of this mixed element simultaneously include displacement and stress field variables, facilitating the direct solution of stress components. To address potential discontinuities in in-plane stresses across layers in piezoelectric laminates, a partial mixed method is further implemented. The model is applicable to flat or large-curvature-radius piezoelectric plates. Numerical benchmarks confirm the element’s robustness to mesh distortion.