Piezoactuator design considering the optimum placement of FGM piezoelectric material

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 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, and an optimum gradation can be sought through optimization techniques. However, the design of these FGM piezoceramics are usually limited to simple shapes. An interesting approach to be investigated is the design of FGM piezoelectric mechanisms which essentially can be defined as a FGM structure with complex topology made of piezoelectric and non-piezoelectric material that must generate output displacement and force at a certain specified point of the domain and direction. This can be achieved by using topology optimization method. Thus, in this work, a topology optimization formulation that allows the simultaneous distribution of void and FGM piezoelectric material (made of piezoelectric and non-piezoelectric material) in the design domain, to achieve certain specified actuation movements, will be presented. The method is implemented based on the SIMP material model where fictitious densities are interpolated in each finite element, providing a continuum material distribution in the domain. The optimization algorithm employed is based on sequential linear programming (SLP) and 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. Some FGM piezoelectric mechanisms were designed to demonstrate the usefulness of the proposed method. Examples are limited to two-dimensional models, due to FGM manufacturing constraints and the fact that most of the applications for such FGM piezoelectric mechanisms are planar devices. An one-dimensional constraint of the material gradation is imposed to provide more realistic designs.