Piezoelectric actuators offer significant promise in a wide range of applications. The piezoelectric actuators considered in this work essentially consist of a flexible structure actuated by piezoceramics that must generate output displacement and force at a certain specified point of the domain and direction. The flexible structure acts as a mechanical transformer by amplifying and changing the direction of piezoceramics output displacements.
The design of these piezoelectric actuators are complex and a systematic design method, such as topology optimization has been successfully applied in the latest years, with appropriate formulation of the optimization problem to obtain optimized designs. However, in these previous design formulations, piezoceramics position are usually kept fixed in the design domain and only the flexible structure is designed by distributing only some non-piezoelectric material (Aluminum, for example). This imposes a constraint in the position of piezoelectric material in the optimization problem limiting the optimality of the solution. Thus, in this work, a formulation that allows the simultaneous search for an optimal topology of a flexible structure as well as the optimal positions of the piezoceramics in the design domain, to achieve certain specified actuation movements, will be presented. This can be achieved by allowing the simultaneous distribution of non-piezoelectric and piezoelectric material in the design domain. The optimization problem is posed as the design of a flexible structure together with optimum positions of piezoelectric material that maximizes output displacements or output forces in a certain specified direction and point of the domain. 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. Presented examples are limited to two-dimensional models, once most of the applications for such piezoelectric actuators are planar devices.