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
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. Or alternatively, follow
the linked step-by-step instructions.
 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.
 V. Pierfort, Finite Element Modeling of Piezoelectric Active Structures,
ULB, Faculty of Applied Sciences, 2000.
 W-S. Hwang, H.C. Park, Finite Element Modeling of Piezoelectric Sensors and
Actuators, AIAA Journal, Vol. 31, No. 5, May 1993.