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

A nonlinear piezoelectric 3D-beam finite element formulation

A. Butz*, S. Klinkel, W. Wagner
Institut für Baustatik, Universität Karlsruhe, Kaiserstr. 12, 76131 Karlsruhe, Germany

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This paper presents a finite element formulation of a three-dimensional piezoelectric beam which includes geometrical and material nonlinearities. Based on the Timoshenko theory, an eccentric beam formulation is introduced which provides an efficient model of piezoelectric multilayered structures. The geometrically nonlinear assumption allows the calculation of large deformations including buckling behavior. A quadratic approximation of the electric potential through the cross section of the beam ensures the fulfilment of the charge conservation law exactly. To account for the material nonlinearities which arise in ferroelectric materials, the Preisach model is implemented in the finite element formulation.

Keywords:  Piezoelectricity, Finite beam element; Smart material; Preisach model

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