Topology Optimization Applied to the Design of Functionally Graded Piezoelectric Bimorph

Functionally Graded Materials (FGMs) possess continuously graded material properties and are characterized by spatially varying microstructures. The smooth variation of properties may offer advantages such as reduction of stress concentration and increased bonding strength. Recently, this concept has been explored in piezoelectric materials to improve properties and to increase the lifetime of bimorph piezoelectric actuators. Usually, elastic, piezoelectric, and dielectric properties are graded along the thickness of a piezoceramic PGM. Thus the gradation law of piezoceramic properties can influence the performance of piezoactuators. In this work, topology optimization has been applied to find the optimum gradation variation in piezoceramic FGMs to improve actuator performance measured in terms of output displacements. A bimorph type actuator design is considered. Accordingly, the optimization problem is posed as finding the optimized gradation variation of piezoelectric properties that maximizes output displacement or output force in the tip of bimorph actuator. The optimization algorithm combines the finite element method with sequential linear programming (SLP). The finite element method applied 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 (CAMD), which is appropriate to model FGMs. The alternative FGM modelling using traditional FEM formulation and discretizing the FGM into layers gives a discontinuous stress distribution, which is not compatible with FGM behavior. The present results consider gradation between two different piezoceramic properties and consider two-dimensional models with plane stress assumption.