Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Reliable finite elements for the analysis of piezoelectric shells

Rolf Lammering*, Fan Yang, Simone Mesecke-Rischmann
Helmut Schmidt-Universität/Universität der Bundeswehr Hamburg, Institut für Mechanik, 22043 Hamburg, Germany

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This paper presents a reliable and robust low-order finite shell element without zero energy modes or locking effects for smart structures applications, especially for layered plate and shallow shell structures with adhered piezoelectric patches serving as actuators or sensors. Four-noded finite elements are developed on the basis of the assumed natural strain (ANS) method taking into account piezoelectric material behavior. The ANS technique adapted from purely mechanical finite element formulations is combined with a two-field and a three-field variational formulation of the electromechanical problem. In contrast to the two-field variational formulation, in which displacements and electric potentials serve as independent variables, the three-field variational formulation also takes the dielectric displacement into consideration. Numerical examples are presented in which various finite elements are compared with each other.

Keywords:  Smart structures; Finite elements; Piezoelectricity; ANS method; Shallow shell; Coupled field problems

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