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Because of electromechanical coupled properties and anisotropy of piezoelectric materials, it is quite a challenge to obtain analytical solution and numerical solution. In the paper, the dual form of the generalized VPs for piezoelectricity are established using the variational integral method and form the Hamilton symplectic dual system for piezoelectricity. These then provide the theoretical foundation of the finite element method for piezoelectricity.

Dual form of Generalized Variational Principles for Piezoelectricity