An Efficient Finite Shell Element for the Static Response of Piezoelectric Laminates

This study presents a novel finite element (FE) for shell structures including piezoelectric actuators and sensors. Based on a conventional 8-node shell formulation and the classical displacement-based variational formulation, the present element has an enriched description of the transverse kinematics in order to consistently retain the full three-dimensional (3D) piezoelectric coupling. Furthermore, a layer-wise description of the electric degrees of freedom permits to account for embedded piezoelectric actuators and sensors. The robustness of the FE is enhanced by referring to an established technique that avoids transverse shear locking and membrane locking. Numerical results are given which validate the present implementation and highlight the efficiency and accuracy of the proposed formulation. Additionally, some new reference solutions for the static behavior of piezoelectric shells are provided by means of 3D FE computations with a commercial software.