A finite element formulation for piezoelectric shell structures considering geometrical and material non-linearities

In this paper, we present a non-linear finite element formulation for piezoelectric shell structures. Based on a mixed multi-field variational formulation, an electro-mechanical coupled shell element is developed considering geometrically and materially non-linear behavior of ferroelectric ceramics. The mixed formulation includes the independent fields of displacements, electric potential, strains, electric field, stresses, and dielectric displacements. Besides the mechanical degrees of freedom, the shell counts only one electrical degree of freedom. This is the difference in the electric potential in the thickness direction of the shell. Incorporating non-linear kinematic assumptions, structures with large deformations and stability problems can be analyzed. According to a Reissner-Mindlin theory, the shell element accounts for constant transversal shear strains. The formulation incorporates a three-dimensional transversal isotropic material law, thus the kinematic in the thickness direction of the shell is considered. The normal zero stress condition and the normal zero dielectric displacement condition of shells are enforced by the independent resultant stress and the resultant dielectric displacement fields. Accounting for material non-linearities, the ferroelectric hysteresis phenomena are considered using the Preisach model. As a special aspect, the formulation includes temperature-dependent effects and thus the change of the piezoelectric material parameters due to the temperature. This enables the element to describe temperature-dependent hysteresis curves. Copyright (C) 2011 John Wiley & Sons, Ltd.