Integrated Layout and Topology Optimization Design of Piezoelectric Smart Structure in Accurate Shape Control

Smart structures are those equipped with sensors/actuators made of smart materials, which have the capability to control structure movement in such a way that makes the design more efficient. However, due to systematic complexity and multidisciplinary objectives, the optimization design of such structures in accurate shape control becomes very challenging. This paper proposes an integrated layout and topology optimization design method for accurate shape control of smart structures with surface bonded piezoelectric actuators. The multi-point constraints (MPC) method is used to simulate the bonding connections between movable piezoelectric actuators and host supporting structures. A new weighted shape error function based on desired deflections of observation points is defined to fulfill accurate shape control of piezoelectric smart structure. Through the proposed method, the optimal position and orientation of each piezoelectric actuator as well as the topology configuration of host supporting structure are founded, which significantly improves the systematic actuating and morphing performance of piezoelectric smart structures. Further studies on the relationships of structural stiffness with shape morphing constraint and volume fraction constraint are carried out, and distortions of load carrying path in optimized designs are illustrated. With several numerical results, the proposed integrated optimization method is proved to be an efficient way to decrease the error between computed and desired surface and achieve the accurate shape control of piezoelectric smart structures.