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Advanced Shell Element Formulations for Coupled Electromechanical Systems
Author(s) -
Yang Fan,
Lammering Rolf,
MeseckeRischmann Simone
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410174
Subject(s) - piezoelectricity , finite element method , shell (structure) , electric field , displacement (psychology) , node (physics) , actuator , variational principle , electric displacement field , field (mathematics) , dielectric , quadratic equation , mathematical analysis , engineering , physics , mechanical engineering , mathematics , structural engineering , acoustics , geometry , electrical engineering , psychology , quantum mechanics , pure mathematics , psychotherapist
With the significantly increasing applications of smart structures, piezoelectric material is widely used in branches of engineering sciences. Normally, the Finite Element Method is employed in the numerical analysis of these structures [2]. In this contribution, in order to avoid the locking effects and zero energy modes, the Assumed Natural Strain (ANS) Method [4] is implemented into four‐node piezoelectric shallow shell elements, by using the two‐field variational formulation in which displacements and electric potentials serve as independent variables and the three‐field variational formulation in which the dielectric displacement is taken as an independent variable additionally [3]. Moreover, a quadratic variation of the electric potential through the thickness direction is applied in the two‐field formulation. Numerical examples of piezoelectric sensors and actuators are presented, showing the behaviour of the shell elements by using different hybrid finite element formulations. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)