Piezoelectric actuator-sensor analysis using a three-dimensional assumed strain solid element

This paper presents a piezoelectric solid element that can be used for modeling thin sensors and actuators. The element has been extended from an eighteen-node assumed strain solid element that can alleviate locking in mechanical problems. For the fully coupled mechanical-piezoelectric formulation, the electric potential is regarded as a nodal degree of freedom in addition to three translations in the original element. Consequently, the induced electric potential can be calculated for a prescribed load and the actuation displacement computed for an input voltage. Since the assumed strain solid element can relieve locking, the proposed element can also be used to analyze the behavior of very thin actuators. In addition, a finite element code was developed based on the proposed formulation and typical numerical examples were solved for code validation. Parametric studies for the THUNDER actuator have been also conducted using the code, where specific combinations of materials used for the layers plus the curvature of THUNDER were both found to improve the actuation displacement.