A geometrically non-linear piezoelectric solid shell element based on a mixed multi-field variational formulation

This paper is concerned with a geometrically non-linear solid shell element to analyse piezoelectric structures. The finite element formulation is based on a variational principle of the Hu–Washizu type and includes six independent fields: displacements, electric potential, strains, electric field, mechanical stresses and dielectric displacements. The element has eight nodes with four nodal degrees of freedoms, three displacements and the electric potential. A bilinear distribution through the thickness of the independent electric field is assumed to fulfill the electric charge conservation law in bending dominated situations exactly. The presented finite shell element is able to model arbitrary curved shell structures and incorporates a 3D-material law. A geometrically non-linear theory allows large deformations and includes stability problems. Linear and non-linear numerical examples demonstrate the ability of the proposed model to analyse piezoelectric devices