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An advanced finite element formulation for piezoelectric shell structures


Correspondence to: W. Wagner, Institut für Baustatik, Karlsruher Institut für Technologie, Karlsruhe, Germany.



Piezoelectric materials are increasingly employed throughout the field of sensor and actuator applications. The physical description leads to a boundary value problem with electromechanically coupled differential equations that can be solved approximatively, for example, by the FEM. As the structures usually are quite thin, piezoelectric shell elements are very well suited for this task. In piezoelectric materials, the mechanical and the electrical fields are coupled by the constitutive relations. Especially for problems dominated by bending, this results in incompatibilities when using element formulations where the mechanical and the electrical DOFs are interpolated with lowest order functions. As a consequence, parasitic approximations and incorrect computation results occur. The present work proposes a concept to avoid these incompatible approximation spaces and the occurring computation errors when dealing with thin structures. The element is based on a mixed variational formulation and uses six mechanical and two electrical nodal DOFs. It employs the Reissner–Mindlin kinematics, considers strains throughout the thickness, and allows for 3D-electromechanical constitutive relations. Numerical examples show that the element formulation is electromechanically consistent and enables to analyze piezoelectric shell structures without parasitic approximations for all typical load cases. Copyright © 2013 John Wiley & Sons, Ltd.