A finite element model for laminated piezoelectric shell structures

Thin piezoelectric laminates are used for a wide range of technical applications. A four-node piezoelectric shell element is presented to analyse such structures effectively. In case of bending dominated problems incompatible approximation functions of the electrical and mechanical fields cause incorrect results. In order to overcome this problem the finite element formulation is based on a mixed variational principle implying six independent fields: displacements, electric potential, strains, electric field, mechanical stresses and dielectric displacements. This allows for an interpolation of the strains and the electric field in thickness direction independent of the bilinear interpolation functions. A piecewise quadratic approach for the shear strains in thickness direction and the corresponding electric field is proposed for arbitrarily layered shells. Regarding coupling of electrical and mechanical fields this yields to an appropriate balance of the approximation functions. Numerical examples show more precise results in contrast to standard elements with lowest order interpolation functions. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)