A new 4-node quadrilateral FE model with variable electrical degrees of freedom for the analysis of piezoelectric laminated composite plates

A new 4-node quadrilateral finite element is developed for the analysis of laminated composite plates containing distributed piezoelectric layers (surface bonded or embedded). The mechanical part of the element formulation is based on the first-order shear deformation theory. The formulation is established by generalizing that of the high performance Mindlin plate element ARS-Q12, which was derived based on the DKQ element formulation and Timoshenko’s beam theory. The layerwise linear theory is applied to deal with electric potential. Therefore, the number of electrical DOF is a variable depending on the number of plate sub-layers. Thus, there is no need to make any special assumptions with regards to the through-thickness variation of the electric potential, which is the true situation. Furthermore, a new “partial hybrid”-enhanced procedure is presented to improve the stresses solutions, especially for the calculation of transverse shear stresses. The proposed element, denoted as CTMQE, is free of shear locking and it exhibits excellent capability in the analysis of thin to moderately thick piezoelectric laminated composite plates.