A Finite Element for Piezoelectric Multilayered Plates: Combined Higher-order and Piecewise Linear C0 Formulation

A finite element is presented for the static and dynamic analysis of smart multilayered plates. A fourth-order expansion is combined with a piecewise linear term to describe the distribution of the in-plane displacements through the thickness. The out-of-plane displacement is assumed constant through the thickness. Both free edges and interlaminar continuity conditions are satisfied, thus reducing the number of elastic unknowns to nine whatever be the number of layers. To this aim, two redundant unknowns describing the two derivatives of the out-of-plane displacement with respect to the in-plane coordinates are introduced and related to the out-of-plane displacement by the use of penalty functions. A quadratic distribution of the electric potential is used inside each piezoelectric layer to completely account for the piezoelectric coupling effects.