Hybrid Finite Element Method Of Piezoelectric Laminate

Starting with a review on the development of the finite element method and piezoelectric material,the theory and finite element analysis of piezoelectric laminates are stressed on. On the basis of the theory of general laminate,the following topics are presented:1. Based on the theories of Hybrid/Mixed finite element method,the generalized energy functional including stress,mechanical displacement ,electric displacement ,electric field and electric potential is used ,with the electric-potential relations and the constitutive equations of piezoelectric materials constrained,hybrid energy functional including mechanical displacement,electric potential and stress is gained. Moreover,splitting in-plane components and transverse components,the mixed energy functional in which mechanical displacement,transverse stresses and electric potential as basic variables is derived. With the use of surface stress parameters of sub-elements ,the continuity of transverse stress at interfaces between layers is obtained.2. Based on the Hybrid/Mixed element method of piezoelectric laminated,A piezoelectric multilayer element is developed,In the piezoelectric multilayer element,The continuity of transverse stresses of at interfaces between layers is naturally ensured.3. By the use of iso-function method,stress modes of 8-node three-dimensional solid element made of on-axis orthotropic material are derived. By determining the zero-energy modes of piezoelectric multilayer element,eight stress modes on piezoelectric sub-element are obtained.4. A finite element program for piezoelectric laminates is developed,Examples of the piezoelectric laminates are presented to identify the accuracy and the continuity of transverse stress.