Inclusion of piezoelectric polarization in the design of a flextensional actuator

Actuators based on smart materials generally exhibit a tradeoff between force and stroke. Researchers have surrounded piezoelectric materials (PZT's) with compliant structures to magnify either their geometric or mechanical advantage. Most of these designs are literally built around a particular piezoelectric device, so the design space consists of only the compliant mechanism. Materials scientists researchers have demonstrated the ability to pole a PZT in an arbitrary direction, and some engineers have taken advantage of this to build "shear mode" actuators. The goal of this work is to determine if the performance of compliant mechanisms improves by the inclusion of the piezoelectric polarization as a design variable. The polarization vector is varied via transformation matrixes, and the compliant actuator is modeled using the SIMP (Solid Isotropic Material with Penalization) or "power-law method." The concept of mutual potential energy is used to form an objective function to measure the piezoelectric actuator's performance. The optimal topology of the compliant mechanism and orientation of the polarization method are determined using a sequential linear programming algorithm. This paper presents a demonstration problem that shows small changes in the polarization vector have a marginal effect on the optimum topology of the mechanism, but improves actuation.