Multiphysics simulation of piezoelectric bending of a laminated beam as for example can be found in actuators for MEMS (micro electro mechanical systems) devices. The model features coupled plane-stress and electrostatics physics modes with equations modified to account for the anisotropic piezo-electric coupling. The simulation results are validated against an analytical solution for the Euler-Bernoulli equation with piezo-electric displacement showing good agreement [1].
This model is available as an automated tutorial by selecting Model Examples and Tutorials… > Multiphysics > Piezo Electric Bending of a Beam from the File menu, and also as the MATLAB simulation m-script example ex_piezoelectric1. Step-by-step tutorial instructions to set up and run this model are linked below.
References
[1] C-I. Tseng, Electromechanical Dynamics of a Coupled Piezo-electric/Mechanical System Applied to Vibration Control and Distributed Sensing, Univ. of Kentucky, Lexington, July 1989.
[2] V. Pierfort, Finite Element Modeling of Piezoelectric Active Structures, ULB, Faculty of Applied Sciences, 2000.
[3] W-S. Hwang, H.C. Park, Finite Element Modeling of Piezoelectric Sensors and Actuators, AIAA Journal, Vol. 31, No. 5, May 1993.