Analyses Of Crack-Tip Fields Of Plane Piezoelectric Materials By The Hybrid Stress Finite Element Method
压电材料平面裂纹尖端场的杂交应力有限元分析

A hybrid stress finite element based on the complex potential theory and hybrid variational principle is proposed for mechanical-electrical coupling analyses. The formulations are given in detail in this paper. The complex series solutions satisfying the equilibrium equations and compatibility equations are chosen as the displacement and stress fields in the element domain. Assume that the series solutions satisfy exactly the traction free and the zero normal electrical displacement boundary conditions along the crack surface in advance. While the displacements along the element outer boundaries vary parabolically. The element stiffness matrix is then obtained by using the Gauss quadrature method. Numerical examples verify the accuracy of the program and the efficiency of the proposed element. Meanwhile, the theoretical results are verified by the finite element results.