Concurrent topology optimization of multiscale piezoelectric actuators

As an important component of smart structural devices, piezoelectric composites have strong macroscopic electromechanical coupling properties which often depend on their microstructural geometries and material parameters. Therefore, optimizing the microstructural design is crucial for achieving the desired macroscale effective properties. To this end, this paper conducts a concurrent multiscale topology optimization (TO) to optimize the material distribution of piezoelectric actuators, aiming to maximize the electrical and mechanical energy transmission to meet specific engineering requirements. Firstly, an energy method is used to homogenize the microstructures and obtain the effective parameters of the piezoelectric material. Then, the piezoelectric material with penalization and polarization (PEMAP-P) approach in conjunction with the adjoint method is employed to calculate the sensitivity of objective and constraint functions. The sensitivities at both the macroscale and microscale are obtained by considering the interscale coupling effects. Finally, the concurrent bi-level iteration based on the optimality criteria (OC) or the method of moving asymptotes (MMA) is conducted. Through this research, we have illuminated the relations between the optimized performance of the actuator and the material volume fractions at each scale. We have also compared in detail the differences between two-scale and single-scale designs, as well as the differences between the simplified half-symmetric geometric model and the full geometric model. We find that a larger volume fraction of material either at the macroscale or microscale generates a larger transmitted displacement magnitude under the same applied electric field, and for a given total material, the transmitted maximum increases with increasing microstructural volume fraction.