Analyses Of Crack-Tip Fields Of Plane Piezoelectric Materials By The Hybrid Stress Finite Element Method

A hybrid stress finite element based on the complexpotential theory and hybrid variational principle is proposed formechanical-electrical coupling analyses. The formulations are given indetail in this paper. The complex series solutions satisfying theequilibrium equations and compatibility equations are chosen as thedisplacement and stress fields in the element domain. Assume that the seriessolutions satisfy exactly the traction free and the zero normal electricaldisplacement boundary conditions along the crack surface in advance. Whilethe displacements along the element outer boundaries vary parabolically. Theelement stiffness matrix is then obtained by using the Gauss quadraturemethod. Numerical examples verify the accuracy of the program and theefficiency of the proposed element. Meanwhile, the theoretical results areverified by the finite element results.