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A finite element formulation is presented for modeling the dynamic as well as static response of laminated composites containing distributed piezoelectric ceramics subjected to both mechanical and electrical loadings. The formulation was derived from the variational principle with consideration for both the total potential energy of the structures and the electrical potential energy of the piezoceramics. An eight-node three-dimensional composite brick element was implemented for the analysis, and three-dimensional incompatible modes were introduced to take into account the global bending behavior resulting from the local deformations of the piezoceramics. Experiments were also conducted to verify the analysis and the computer simulations. Overall, the comparisons between the predictions and the data agreed fairly well. Numerical examples were also generated by coupling the analysis with simple control algorithms to control actively the response of the integrated structures in a closed loop.
Ha et al. (Sun,) studied this question.