A new method for numerical analysis of piezoelectric smart materials

Based on the principle of minimum potential energy combined with the modified Hellinger-Reissner (H-R) variational principle, one kind of noncompatible symplectic isoparametric equation can be established that includes displacement and out-of-plane stress variables. And it can be easily extended to engineering materials containing multi-physics fields or related smart structures. The method shows better numerical performance than similar compatible element by introducing the noncompatible shape function of the displacement variable for discretisation. Since the control equation contains only two types of variables, displacement and out-plane stress, the space occupied by linear equations is less than that of the mixed method. Numerical examples show that the method with generalized displacement and generalized out-of-plane stress variables gives high accuracy and fast convergence of the force and current results obtained in this paper.