New linear and quadratic prismatic piezoelectric solid–shell finite elements

Fessal Kpeky (1) , Farid Abed-Meraim (1, 2) , El Mostafa Daya (1, 2)

1 LEM3 - Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux
2 Labex DAMAS

In this work, we propose two prismatic piezoelectric solid–shell elements based on fully three-dimensional kinematics. For this purpose, we perform electromechanical coupling, which consists in adding an electrical degree of freedom to each node of the purely mechanics-based versions of these elements. To increase efficiency, these geometrically three-dimensional elements are provided with some desirable shell features, such as a special direction, designated as the thickness, along which the integration points are located, while adopting a reduced integration rule in the other directions. To assess the performance of the proposed piezoelectric solid–shell elements, a variety of benchmark tests, both in static and vibration analysis, have been performed on multilayer structures ranging from simple beams to more complex structures involving geometric nonlinearities. Compared to conventional finite elements with the same kinematics, the evaluation results allow highlighting the higher performance of the newly developed solid–shell technology.

Mots clés: Piezoelectric effect; Vibration analysis; Prismatic geometry; Finite elements; Solid–shell

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des structures [physics.class-ph]; Sciences de l'ingénieur [physics]; Mécanique des matériaux [physics.class-ph]; Vibrations [physics.class-ph]; Mécanique [physics]

Fessal Kpeky, Farid Abed-Meraim, El Mostafa Daya. New linear and quadratic prismatic piezoelectric solid–shell finite elements. Applied Mathematics and Computation, 2018, 319, pp.355-368. ⟨10.1016/j.amc.2017.03.050⟩. ⟨hal-02388830⟩