**Abstract**

Piezoelectric actuators have the obvious advantages of simple and compact structure, high precision and long stroke. However, it is difficult to satisfy the various industrial requirements. Topology optimization method can be used to find the new configurations of the compliant mechanism, and different objective function and constraint conditions can be flexibly used to determine the compliant mechanism. In the research of piezoelectric actuators, due to the advantages of compact structure, no lubrication and large displacement magnification, compliant mechanism is extremely suitable to be introduced into the design of piezoelectric actuators. In recent years, topology optimization method is frequently used to design the compliant mechanism on piezoelectric actuator, and has become a research hotspot. In this chapter, the development of topology optimization method is introduced, the design and research on the compliant mechanism of piezoelectric actuator have been summarized, and the future research direction and challenges of topology optimization design for flexure hinge type piezoelectric actuators are prospected.

**Keywords:** topology optimization, piezoelectric actuator, flexure hinge, compliant mechanism, displacement amplification
