Design of functionally graded piezoelectric actuators using topology optimization

Functionally Graded Materials (FGMs) possess continuous variation of material properties and are characterized by spatially varying microstructures. Recently, the FGM concept has been explored in piezoelectric materials to improve properties and to increase the lifetime of bimorph piezoelectric actuators. Elastic, piezoelectric, and dielectric properties are graded along the thickness of a piezoceramic FGM. Thus, the gradation of piezoceramic properties can influence the performance of piezoactuators. In this work, topology optimization is applied to find the optimum gradation variation in piezoceramics in order to improve actuator performance measured in terms of output displacements. A bimorph type actuator design is investigated. The corresponding optimization problem is posed as finding the optimized gradation of piezoelectric properties that maximizes output displacement or output force at the tip of the bimorph actuator. The optimization algorithm combines the finite element method with sequential linear programming. The finite element method is based on the graded finite element concept where the properties change smoothly inside the element. This approach provides a continuum approximation of material distribution, which is appropriate to model FGMs. The present results consider gradation between two different piezoceramic properties and two-dimensional models with plane stress assumption.