A family of piezoelectric MITC plate elements

Abstract

In the present paper, a class of accurate and reliable piezoelectric plate elements is presented. The formulations are based upon the Reissner–Mindlin assumptions, which makes the elements applicable to both thin and moderately thick situations. Shear locking is eliminated by employing the MITC (mixed interpolation of tensorial components) approach for the transverse shear strains. To improve the in-plane bending behaviour in the four node elements, incompatible modes are used. Regarding the assumptions for the electric field, it is shown that only a quadratic variation of the electric potential over the thickness can take into account the potential induced by the bending deformation. Two different approaches are developed that fulfil this requirement. The first formulation is based upon an analytical integration of the electric charge equation over the plate thickness, using the kinematic assumptions of the Reissner–Mindlin theory. As compared to elastic plate elements, only one additional global degree of freedom is introduced for every electrode pair, which makes the formulation very efficient. The second formulation interpolates the electric potential over the thickness, employing additional electric degrees of freedom at the mid-plane nodes. This approach is computationally more expensive than the first one, but allows a more accurate modelling of the in-plane electric field. The resulting elements are very widely applicable and can be used for both sensing and actuation. A number of numerical examples are given to compare the two approaches and demonstrate the elements’ performance.