The paper is concerned with a geometrically nonlinear finite element formulation to analyze piezoelectric shell
structures. The classical shell assumptions are extended to the electromechanical coupled problem. The consideration
of geometrical nonlinearity includes the analysis of stability problems and other nonlinear effects. The
formulation is based on the mixed field functional of Hu-Washizu. The independent fields are displacements,
electric potential, strains, electric field, stresses and dielectric displacements. The mixed formulation allows an
interpolation of the strains and the electric field through the shell thickness, which is an essential advantage when
using nonlinear 3D material laws. With respect to the numerical approximation an arbitrary reference surface
of the shell is modeled with a four node element. Each node possesses six mechanical and one electrical degree
of freedom. Some simulations demonstrate the applicability of the present piezoelectric shell element.
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