Emílio Carlos Nelli Silva

Design of piezoelectric transducers using topology optimization

Among other applications piezoelectric transducers are widely used for acoustic wave generation and as resonators. These applications require goals in the transducer design such as high electromechanical energy conversion for a certain transducer vibration mode, specified resonance frequencies and narrowband or broadband response. In this work, we have proposed a method for designing piezoelectric transducers that tries to obtain these characteristics, based upon topology optimization techniques and the finite element method (FEM). This method consists of finding the distribution of the material and void phases in the design domain that optimizes a defined objective function. The optimized solution is obtained using sequential linear programming (SLP). Considering acoustic wave generation and resonator applications, three kinds of objective function were defined: maximize the energy conversion for a specific mode or a set of modes; design a transducer with specified frequencies and design a transducer with narrowband or broadband response. Although only two-dimensional plane strain transducer topologies have been considered to illustrate the implementation of the method, it can be extended to three-dimensional topologies. Transducer designs were obtained that conform to the desired design requirements and have better performance characteristics than other common designs.

Topology optimization design of flextensional actuators

Flextensional actuators can be defined as a piezoceramic (or a stack of piezoceramics) connected to a flexible mechanical structure that converts and amplifies the output displacement of the piezoceramic. Essentially, the actuator performance depends on the distribution of stiffness and flexibility in the coupling structure and, therefore, on the coupling structure topology. In this work, we propose a general method for designing flextensional actuators with large output displacement (or generative force) by applying the topology optimization method. The goal is to design a flexible structure coupled to the piezoceramic that maximizes the output displacement (or force) in some specified direction. Static and low frequency applications are considered. To illustrate the implementation of the method, 2-D topologies of flextensional actuators are presented because of the lower computational cost; however, the method can be extended to 3-D topologies. By designing other types of coupling structures connected to the piezoceramic, new designs of flextensional actuators that produce output displacements or forces in different directions can be obtained, as shown. This method can be extended for designing flextensional hydrophones and sonars.

Optimal design of periodic piezocomposites

Abstract Application of piezoelectric materials, such as hydrophones and naval sonars, requires an improvement in their performance characteristics. This improvement can be obtained by designing new types of piezocomposite materials that possess a richer class of properties. The effective properties of a composite material depend on the topology of its unit cell (or microstructure) and the properties of its constituents. By changing the unit cell topology, better performance characteristics can be obtained in the piezocomposite. In this work, we have extended the optimal design method of piezocomposite microstructures proposed in the previous work [1] to three dimensional (3D) topologies, considering static applications such as hydrophones. This method uses topology optimization techniques and homogenization theory, and consists of finding the distribution of the material and void phases in a periodic unit cell that optimizes the performance characteristics of the piezocomposite. The optimization problem is subjected to constraints such as property symmetry and stiffness. An additional constraint was added in order to penalize the amount of intermediate densities generated in the final design. The optimized solution is obtained using Sequential Linear Programming (SLP). In order to calculate the effective properties of a unit cell with complex topology, a general homogenization method applied to piezoelectricity was implemented using the finite element method (FEM). This homogenization method has no limitations regarding volume fraction or shape of the composite constituents. The main assumption is the periodicity of the unit cell. Microstructures obtained show a large improvement in performance characteristics compared to pure piezoelectric material or simple designs of piezocomposite unit cells. Finally, a hydrophone made of one layer of the unit cells obtained by using microstructure design is suggested. An FEM analysis is done to evaluate the performance improvement of such transducer.

Design optimization method for compliant mechanisms and material microstructure

A design methodology based on the global-local modeling method is described along with its application to the design of the optimum layout of compliant mechanisms and the microstructure of composite materials.

Optimization methods applied to material and flextensional actuator design using the homogenization method

Abstract The design method based on the extended fixed domain method and global-local modeling (or homogenization) theory is applied to the design of elastic, thermoelastic, and piezoelectric composite materials, and flextensional actuators. rights reserved.

Dynamic Design of Piezoelectric Laminated Sensors and Actuators using Topology Optimization

Sensors and actuators based on piezoelectric plates have shown increasing demand in the field of smart structures, including the development of actuators for cooling and fluid-pumping applications and transducers for novel energy-harvesting devices. This project involves the development of a topology optimization formulation for dynamic design of piezoelectric laminated plates aiming at piezoelectric sensors, actuators and energy-harvesting applications. It distributes piezoelectric material over a metallic plate in order to achieve a desired dynamic behavior with specified resonance frequencies, modes, and enhanced electromechanical coupling factor (EMCC). The finite element employs a piezoelectric plate based on the MITC formulation, which is reliable, efficient and avoids the shear locking problem. The topology optimization formulation is based on the PEMAP-P model combined with the RAMP model, where the design variables are the pseudo-densities that describe the amount of piezoelectric material at each finite element and its polarization sign. The design problem formulated aims at designing simultaneously an eigenshape, i.e., maximizing and minimizing vibration amplitudes at certain points of the structure in a given eigenmode, while tuning the eigenvalue to a desired value and also maximizing its EMCC, so that the energy conversion is maximized for that mode. The optimization problem is solved by using sequential linear programming. Through this formulation, a design with enhancing energy conversion in the low-frequency spectrum is obtained, by minimizing a set of first eigenvalues, enhancing their corresponding eigenshapes while maximizing their EMCCs, which can be considered an approach to the design of energy-harvesting devices. The implementation of the topology optimization algorithm and some results are presented to illustrate the method.

Topology optimization design of functionally graded bimorph-type piezoelectric actuators

The concept of a functionally graded material (FGM) is useful for engineering advanced piezoelectric actuators. For instance, it can lead to locally improved properties, and to increased lifetime of bimorph piezoelectric actuators. By selectively grading the elastic, piezoelectric, and/or dielectric properties along the thickness of a piezoceramic, the resulting gradation of electromechanical properties influences the behavior and performance of piezoactuators. In this work, topology optimization is applied to find the optimum gradation and polarization sign variation in piezoceramic domains in order to improve actuator performance measured in terms of selected output displacements. A bimorph-type actuator is emphasized, which is designed by maximizing the output displacement or output force at selected location(s) (e.g. the tip of the actuator). The numerical discretization is based on the graded finite element concept such that a continuum approximation of material distribution, which is appropriate to model FGMs, is achieved. The present results consider two-dimensional models with a plane-strain assumption. The material gradation plays an important role in improving the actuator performance when distributing piezoelectric (PZT5A) and non-piezoelectric (gold) materials in the design domain; however, the performance is not improved when distributing two types of similar piezoelectric material. In both cases, the polarization sign change did not play a significant role in the results. However, the optimizer always finds a solution with opposite polarization (as expected).

Design of piezoelectric multi-actuated microtools using topology optimization

Microtools offer significant promise in a wide range of applications such as cell manipulation, microsurgery, nanotechnology processes, and many other fields. The development of these microtools is still in the initial stages and it can be strongly enhanced by using design tools. The microtools considered in this paper essentially consist of a multi-flexible structure actuated by two or more piezoceramic devices such that when each piezoceramic is actuated, it generates an output displacement and force in a specified point of the domain and direction. The multi-flexible structure acts as a mechanical transform by amplifying and changing the direction of the piezoceramic output displacements. Thus, the development of microtools requires the design of actuated flexible structures that can perform complex movements. In addition, when multiple piezoceramic devices are involved, coupling effects in their movements become critical, especially the appearance of undesired movements, which makes the design task very complex. One way to avoid such undesirable effects is the use of a systematic design method, such as topology optimization, with appropriate formulation of the optimization problem. Here, a topology optimization formulation is developed for the design of microtools actuated by multiple piezoceramics that minimizes the effects of movement coupling. This method is implemented based on the CAMD (continuous approximation of material distribution) approach where fictitious densities are interpolated in each finite element, providing a continuum material distribution in the domain. In addition, in previous piezoelectric actuator topology optimization works the piezoceramics were excited by charge, which is not realistic, even though it simplifies the sensitivity analysis. In this work, the piezoceramics are excited by voltage and the corresponding sensitivity analysis is presented. Different types of microtools required for various applications are designed to demonstrate the usefulness of the proposed method. Although the presented examples are limited to two-dimensional models, this is appropriate since most of the applications for such microtools are planar devices.

Design of Functionally Graded Structures Using Topology Optimization

The concept of functionally graded materials (FGMs) is closely related to the concept of topology optimization, which consists in a design method that seeks a continuum optimum material distribution in a design domain. Thus, in this work, topology optimization is applied to design FGM structures considering a minimum compliance criterion. The present approach applies the so-called “continuous topology optimization” formulation where a continuous change of material properties is considered inside the design domain by using the graded finite element concept. A new design is obtained where distribution of the graded material itself is considered in the design domain, and the material properties change in a certain direction according to a specified variation, leading to a structure with asymmetric stiffness properties.

Three-Dimensional Electrical Impedance Tomography: A Topology Optimization Approach

Electrical impedance tomography is a technique to estimate the impedance distribution within a domain, based on measurements on its boundary. In other words, given the mathematical model of the domain, its geometry and boundary conditions, a nonlinear inverse problem of estimating the electric impedance distribution can be solved. Several impedance estimation algorithms have been proposed to solve this problem. In this paper, we present a three-dimensional algorithm, based on the topology optimization method, as an alternative. A sequence of linear programming problems, allowing for constraints, is solved utilizing this method. In each iteration, the finite element method provides the electric potential field within the model of the domain. An electrode model is also proposed (thus, increasing the accuracy of the finite element results). The algorithm is tested using numerically simulated data and also experimental data, and absolute resistivity values are obtained. These results, corresponding to phantoms with two different conductive materials, exhibit relatively well-defined boundaries between them, and show that this is a practical and potentially useful technique to be applied to monitor lung aeration, including the possibility of imaging a pneumothorax.