A special finite element based on the complex potential theory and hybrid variational principle is proposed for analyzing mechanical-electrical coupling field of piezoelectric materials containing an elliptical hole. In the formulation, the complex series solutions satisfying the equilibrium equations and compatibility equations are chosen as the displacement and stress fields in the element domain. The series solutions satisfy exactly the D-P condition in advance. While the displacements along the element outer boundaries vary parabolically for an eight-node special element. The element stiffness matrix is then obtained by using the Gauss quadrature method. Numerical examples verify the accuracy and efficiency of the proposed element. It is found that the relationships between the logarithm concentration factor of tangential (θ＝0) stress, electrical displacement, and electrical field at the notch tip and logarithm b/a are linear.
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