FEM modeling of adaptive composite structures using a reduced higher-order plate theory via penalty functions

This paper presents a finite element model for analyzing the composite laminates containing the piezoelectrics statistically or dynamically. First, to model the moderately thick laminated plates, a simple higher-order plate theory, which can satisfy the free conditions of transverse shear strains on the top and bottom surfaces of plates, have been adopted. To set up a C⁰-type FEM scheme, two artificial variables in the displacement field have been introduced to avoid the higher-order derivatives from the higher-order plate theory. The corresponding constraint conditions from two artificial variables have been enforced effectively through the penalty function method using the reduced integral scheme within the element area. Second, a generalized coupling FEM model for the mechanical and electric fields from the variational framework have been proposed. Finally, various examples studied in many previous researches have been employed to verify the justification, accuracy and efficiency of the present model.