Topology optimization design of functionally graded bimorph-type piezoelectric actuators

The concept of a functionally graded material (FGM) is useful for engineering advanced piezoelectric actuators. For instance, it can lead to locally improved properties, and to increased lifetime of bimorph piezoelectric actuators. By selectively grading the elastic, piezoelectric, and/or dielectric properties along the thickness of a piezoceramic, the resulting gradation of electromechanical properties influences the behavior and performance of piezoactuators. In this work, topology optimization is applied to find the optimum gradation and polarization sign variation in piezoceramic domains in order to improve actuator performance measured in terms of selected output displacements. A bimorph-type actuator is emphasized, which is designed by maximizing the output displacement or output force at selected location(s) (e.g. the tip of the actuator). The numerical discretization is based on the graded finite element concept such that a continuum approximation of material distribution, which is appropriate to model FGMs, is achieved. The present results consider two-dimensional models with a plane-strain assumption. The material gradation plays an important role in improving the actuator performance when distributing piezoelectric (PZT5A) and non-piezoelectric (gold) materials in the design domain; however, the performance is not improved when distributing two types of similar piezoelectric material. In both cases, the polarization sign change did not play a significant role in the results. However, the optimizer always finds a solution with opposite polarization (as expected).