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.
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.
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.
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.
Multi-actuators piezoelectric devices consist of a multi-flexible
structure actuated by two or more piezoceramic portions, whose
differing output displacements and forces are tailored according to
the excitation properties of the piezoceramic materials and the
desired working locations and directions of movement. Such devices
have a wide range of application in performing biological cell
manipulation, for microsurgery, and in nanotechnology equipment, and
the like. However, the design of multi-flexible structures is a
highly complex task since the devices have many degrees of freedom
and, employ a variety of piezoceramics, but must carefully tune the
movement coupling among the device parts to prevent motion in
undesirable directions. In prior research, topology optimization
techniques have been applied to the design of devices having minimum
movement coupling among the piezoceramic parts, and in this work a
number of these devices were manufactured and experimentally
analyzed to validate the results of the topology optimization. X-Y
nanopositioners consisting of two piezoceramic portions were
addressed and designs considering low and high degrees of coupling
between desired and undesirable displacements were investigated to
evaluate the performance of the design method. Prototypes were
manufactured in aluminum using a wire EDM process, and bonded to
piezoceramics (PZT5A) polarized in the thickness direction and
working in d31 mode. Finite element simulations were carried out
using the commercial ANSYS software application. Experimental
analyses were conducted using laser interferometry to measure
displacement, while considering a quasi-static excitation. The
coupling between the X-Y movements was measured and compared with
FEM results, which showed that the coupling requirements were
adequately achieved.
Micro-tools can have a wide range of
application such as cell manipulation, microsurgery, nanotechnology
equipment,etc. Micro-tools considered in this work consist of a multiflexible structure
actuated by two or more piezoceramics that must generate different output
displacements and forces in different specified points of the domain and
directions, for different excited piezoceramics. The multiflexible structure
acts as a mechanical transform by amplifying and changing the direction of
the piezoceramics output displacements. Thus, the development of micro-tools requires to design
micromechanisms with many degrees of freedom that perform complex movements
without presence of joints and pins, due to manufacturing constraints of
MEMS scale. In addition, when many piezoceramics are involved the
coupling among movements becomes critical, that is, undesired movements
may appear. This makes the design task very complex, which
suggests that systematic design method, such as topology optimization, must
be applied. Thus, in this work the topology optimization formulation was
applied to design micro-tools actuated by many piezoceramics with minimum
movement coupling. Essentially, the topology optimization method consists of
finding the optimal material distribution in a design domain to extremize
some objective function. The topology optimization method implemented is
based on the CAMD approach where the pseudo-densities are interpolated
in each finite element, providing a continuum material
distribution in the domain. The optimization problem is posed as the
design of a flexible structure that maximizes different output displacements
(or grabbing forces) in different specified directions and points of the
domain, for different excited piezoceramics. Different types of micro-tools
can be obtained for a desired application. Among the examples, designs of
a XY nanopositioner and a micro-gripper are considered.
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