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The micro-tools considered in this work consist essentially of multi-flexible structures actuated by two or more piezoceramic devices that must generate different output displacements and forces at different specified points of the domain and on different directions. The multiflexible structure acts as a mechanical transformer by amplifying and changing the direction of the piezoceramics output displacements. Micro-tools offer significant promise in a wide range of applications such as cell manipulation, microsurgery, and micro/nanotechnology processes. Although the design of these micro-tools is complicated due to the coupling among movements generated by various piezoceramics, it can be realized by means of topology optimization concepts. Recently, the concept of functionally graded materials (FGMs) has been explored in piezoelectric materials to improve performance and increase lifetime of piezoelectric actuators. Usually for an FGM piezoceramic, elastic, piezoelectric, and dielectric properties are graded along the thickness. Thus, the objective of this work is to study the influence of piezoceramic property gradation in the design of the multiflexible structures of piezoelectric micro-tools using topology optimization. The optimization problem is posed as the design of a flexible structure that maximizes different output displacements or output forces in different specified directions and points of the domain, in response to different excited piezoceramic portions: while minimizing the effects of movement coupling. The method is implemented based on the solid isotropic material with penalization (SIMP) model where fictitious densities are interpolated in each finite element, providing a continuum material distribution in the domain. As examples, designs of a single piezoactuator and an XY nano-positioner actuated by two FGM piezoceramics are considered. The resulting designs are compared with designs considering homogeneous piezoceramics. The present examples are limited to two-dimensional models because most of the applications for such micro-tools are planar devices.
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