Optimal design of composite structures with integrated piezoelectric laminae

A family of nine-node Lagrangian finite element models based on higher order displacement fields is applied to the optimal design of laminated composite plates with embedded and/or surface bonded piezoelectric layers and/or patches. The described formulation introduces, for the electric behavior, one electric potential degree of freedom for each piezoelectric layer in each element. In the optimal design, the design variables are the ply orientation angles in the orthotropic layers, the ply thickness of both the substrate and piezoelectric layers and the electrical potentials applied to the piezoelectric actuators. The design objectives are the minimization of structural weight and/or the minimization of specified displacements subjected to behavioral constraints.