On an equivalent model of multi-layer piezoelectric actuators for facilitating finite element simulations

Abstract

Multi-layer piezoelectric actuators (MPA) are widely used precision actuators. For design and optimization of MPA-based applications with a complex structure, finite element method, which can achieve a high computation accuracy, is widely applied in finite element analysis software for computation and analysis. However, MPA are commonly made of hundreds of thin piezo layers and the piezoelectric material involves electro-mechanical coupled fields, which makes it cumbersome to directly implement them in finite element analysis software and hard to solve. In this paper, it is shown that the multi-layer and electro-mechanical coupled-field MPA can be simply considered as a homogeneous mechanical solid with a pair of equivalent forces acting on the two ends. This equivalent model can greatly facilitate the implementation of MPA in finite element analysis software and cut down computational cost for design and optimization of MPA-based applications. The rationale behind the equivalent model is unveiled and the equivalent force input is derived with respect to voltage input in terms of the standard 3D piezoelectric coefficients. The effectiveness of the equivalent model is further verified by conventional model of MPA via FE simulations in ANSYS.