Design of compliant mechanisms considering thermal effect compensation and topology optimization

Compliant mechanisms can achieve a specified motion as a mechanism without relying on the use of joints and pins. They have broad application in precision mechanical devices and Micro-Electro Mechanical Systems (MEMS) but may lose accuracy and produce undesirable displacements when subjected to temperature changes. These undesirable effects can be reduced by using sensors in combination with control techniques and/or by applying special design techniques to reduce such undesirable effects at the design stage, a process generally termed ""design for precision"". This paper describes a design for precision method based on a topology optimization method (TOM) for compliant mechanisms that includes thermal compensation features. The optimization problem emphasizes actuator accuracy and it is formulated to yield optimal compliant mechanism configurations that maximize the desired output displacement when a force is applied, while minimizing undesirable thermal effects. To demonstrate the effectiveness of the method, two-dimensional compliant mechanisms are designed considering thermal compensation, and their performance is compared with compliant mechanisms designs that do not consider thermal compensation. (C) 2010 Elsevier B.V. All rights reserved.

Layout and material gradation in topology optimization of functionally graded structures: a global-local approach

By means of continuous topology optimization, this paper discusses the influence of material gradation and layout in the overall stiffness behavior of functionally graded structures. The formulation is associated to symmetry and pattern repetition constraints, including material gradation effects at both global and local levels. For instance, constraints associated with pattern repetition are applied by considering material gradation either on the global structure or locally over the specific pattern. By means of pattern repetition, we recover previous results in the literature which were obtained using homogenization and optimization of cellular materials.

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.

Integral Piezoactuator System with Optimum Placement of Functionally Graded Material - A Topology Optimization Paradigm

Piezoactuators consist of compliant mechanisms actuated by two or more piezoceramic devices. During the assembling process, such flexible structures are usually bonded to the piezoceramics. The thin bonding layer(s) between the compliant mechanism and the piezoceramic may induce undesirable behavior, including unusual interfacial nonlinearities. This constitutes a drawback of piezoelectric actuators and, in some applications, such as those associated to vibration control and structural health monitoring (e. g., aircraft industry), their use may become either unfeasible or at least limited. A possible solution to this standing problem can be achieved through the functionally graded material concept and consists of developing `integral piezoactuators`, that is those with no bonding layer(s) and whose performance can be improved by tailoring their structural topology and material gradation. Thus, a topology optimization formulation is developed, which allows simultaneous distribution of void and functionally graded piezoelectric materials (including both piezo and non-piezoelectric materials) in the design domain in order to achieve certain specified actuation movements. Two concurrent design problems are considered, that is the optimum design of the piezoceramic property gradation, and the design of the functionally graded structural topology. Two-dimensional piezoactuator designs are investigated because the applications of interest consist of planar devices. Moreover, material gradation is considered in only one direction in order to account for manufacturability issues. To broaden the range of such devices in the field of smart structures, the design of integral Moonie-type functionally graded piezoactuators is provided according to specified performance requirements.

Topology optimization for designing strain-gauge load cells

Load cells are used extensively in engineering fields. This paper describes a novel structural optimization method for single- and multi-axis load cell structures. First, we briefly explain the topology optimization method that uses the solid isotropic material with penalization (SIMP) method. Next, we clarify the mechanical requirements and design specifications of the single- and multi-axis load cell structures, which are formulated as an objective function. In the case of multi-axis load cell structures, a methodology based on singular value decomposition is used. The sensitivities of the objective function with respect to the design variables are then formulated. On the basis of these formulations, an optimization algorithm is constructed using finite element methods and the method of moving asymptotes (MMA). Finally, we examine the characteristics of the optimization formulations and the resultant optimal configurations. We confirm the usefulness of our proposed methodology for the optimization of single- and multi-axis load cell structures.

A simple and effective inverse projection scheme for void distribution control in topology optimization

The ability to control both the minimum size of holes and the minimum size of structural members are essential requirements in the topology optimization design process for manufacturing. This paper addresses both requirements by means of a unified approach involving mesh-independent projection techniques. An inverse projection is developed to control the minimum hole size while a standard direct projection scheme is used to control the minimum length of structural members. In addition, a heuristic scheme combining both contrasting requirements simultaneously is discussed. Two topology optimization implementations are contributed: one in which the projection (either inverse or direct) is used at each iteration; and the other in which a two-phase scheme is explored. In the first phase, the compliance minimization is carried out without any projection until convergence. In the second phase, the chosen projection scheme is applied iteratively until a solution is obtained while satisfying either the minimum member size or minimum hole size. Examples demonstrate the various features of the projection-based techniques presented.

Multi-actuated functionally graded piezoelectric micro-tools design: A multiphysics topology optimization approach

Micro-tools offer significant promise in a wide range of applications Such as cell Manipulation, microsurgery, and micro/nanotechnology processes. Such special micro-tools consist of multi-flexible structures actuated by two or more piezoceramic devices that must generate output displacements and forces lit different specified points of the domain and at different directions. The micro-tool Structure acts as a mechanical transformer by amplifying and changing the direction of the piezoceramics Output displacements. The design of these micro-tools involves minimization of the coupling among movements generated by various piezoceramics. To obtain enhanced micro-tool performance, the concept of multifunctional and functionally graded materials is extended by, tailoring elastic and piezoelectric properties Of the piezoceramics while simultaneously optimizing the multi-flexible structural configuration using multiphysics topology optimization. The design process considers the influence of piezoceramic property gradation and also its polarization sign. The method is implemented considering continuum material distribution with special interpolation of fictitious densities in the design domain. As examples, designs of a single piezoactuator, an XY nano-positioner actuated by two graded piezoceramics, and a micro-gripper actuated by three graded piezoceramics are considered. The results show that material gradation plays an important role to improve actuator performance, which may also lead to optimal displacements and coupling ratios with reduced amount of piezoelectric material. The present examples are limited to two-dimensional models because many of the applications for Such micro-tools are planar devices. Copyright (c) 2008 John Wiley & Sons, Ltd.

Piezoresistive sensor design using topology optimization

Piezoresistive materials, materials whose resistivity properties change when subjected to mechanical stresses, are widely utilized in many industries as sensors, including pressure sensors, accelerometers, inclinometers, and load cells. Basic piezoresistive sensors consist of piezoresistive devices bonded to a flexible structure, such as a cantilever or a membrane, where the flexible structure transmits pressure, force, or inertial force due to acceleration, thereby causing a stress that changes the resistivity of the piezoresistive devices. By applying a voltage to a piezoresistive device, its resistivity can be measured and correlated with the amplitude of an applied pressure or force. The performance of a piezoresistive sensor is closely related to the design of its flexible structure. In this research, we propose a generic topology optimization formulation for the design of piezoresistive sensors where the primary aim is high response. First, the concept of topology optimization is briefly discussed. Next, design requirements are clarified, and corresponding objective functions and the optimization problem are formulated. An optimization algorithm is constructed based on these formulations. Finally, several design examples of piezoresistive sensors are presented to confirm the usefulness of the proposed method.

Tailoring vibration mode shapes using topology optimization and functionally graded material concepts

Tailoring specified vibration modes is a requirement for designing piezoelectric devices aimed at dynamic-type applications. A technique for designing the shape of specified vibration modes is the topology optimization method (TOM) which finds an optimum material distribution inside a design domain to obtain a structure that vibrates according to specified eigenfrequencies and eigenmodes. Nevertheless, when the TOM is applied to dynamic problems, the well-known grayscale or intermediate material problem arises which can invalidate the post-processing of the optimal result. Thus, a more natural way for solving dynamic problems using TOM is to allow intermediate material values. This idea leads to the functionally graded material (FGM) concept. In fact, FGMs are materials whose properties and microstructure continuously change along a specific direction. Therefore, in this paper, an approach is presented for tailoring user-defined vibration modes, by applying the TOM and FGM concepts to design functionally graded piezoelectric transducers (FGPT) and non-piezoelectric structures (functionally graded structures-FGS) in order to achieve maximum and/or minimum vibration amplitudes at certain points of the structure, by simultaneously finding the topology and material gradation function. The optimization problem is solved by using sequential linear programming. Two-dimensional results are presented to illustrate the method.

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.

Topology Optimized Design, Microfabrication and Characterization of Electro-Thermally Driven Microgripper

This article presents a systematic and logical study of the topology optimized design, microfabrication, and static/dynamic performance characterization of an electro-thermo-mechanical microgripper. The microgripper is designed using a topology optimization algorithm based on a spatial filtering technique and considering different penalization coefficients for different material properties during the optimization cycle. The microgripper design has a symmetric monolithic 2D structure which consists of a complex combination of rigid links integrating both the actuating and gripping mechanisms. The numerical simulation is performed by studying the effects of convective heat transfer, thermal boundary conditions at the fixed anchors, and microgripper performance considering temperature-dependent and independent material properties. The microgripper is fabricated from a 25 mm thick nickel foil using laser microfabrication technology and its static/dynamic performance is experimentally evaluated. The static and dynamic electro-mechanical characteristics are analyzed as step response functions with respect to tweezing/actuating displacements, applied current/power, and actual electric resistance. A microgripper prototype having overall dimensions of 1mm (L) X 2.5mm (W) is able to deliver the maximum tweezing and actuating displacements of 25.5 mm and 33.2 mm along X and Y axes, respectively, under an applied power of 2.32 W. Experimental performance is compared with finite element modeling simulation results.

Design and Characterization of a Biomimetic Piezoelectric Pump Inspired on Group Fish Swimming Effect

Flow pumps are important tools in several engineering areas, such as in the fields of bioengineering and thermal management solutions for electronic devices. Nowadays, many of the new flow pump principles are based on the use of piezoelectric actuators, which present some advantages such as miniaturization potential and lower noise generation. In previous work, authors presented a study of a novel pump configuration based on placing an oscillating bimorph piezoelectric actuator in water to generate flow. It was concluded that this oscillatory behavior (such as fish swimming) yields vortex interaction, generating flow rate due to the action and reaction principle. Thus, following this idea the objective of this work is to explore this oscillatory principle by studying the interaction among generated vortex from two bimorph piezoelectric actuators oscillating inside the same pump channel, which is similar to the interaction of vortex generated by frontal fish and posterior ones when they swim together in a group formation. It is shown that parallel-series configurations of bimorph piezoelectric actuators inside the same pump channel provide higher flow rates and pressure for liquid pumping than simple parallel-series arrangements of corresponding single piezoelectric pumps, respectively. The scope of this work includes structural simulations of bimorph piezoelectric actuators, fluid flow simulations, and prototype construction for result validation.

Recycling Krylov subspaces for efficient large-scale electrical impedance tomography

Electrical impedance tomography (EIT) captures images of internal features of a body. Electrodes are attached to the boundary of the body, low intensity alternating currents are applied, and the resulting electric potentials are measured. Then, based on the measurements, an estimation algorithm obtains the three-dimensional internal admittivity distribution that corresponds to the image. One of the main goals of medical EIT is to achieve high resolution and an accurate result at low computational cost. However, when the finite element method (FEM) is employed and the corresponding mesh is refined to increase resolution and accuracy, the computational cost increases substantially, especially in the estimation of absolute admittivity distributions. Therefore, we consider in this work a fast iterative solver for the forward problem, which was previously reported in the context of structural optimization. We propose several improvements to this solver to increase its performance in the EIT context. The solver is based on the recycling of approximate invariant subspaces, and it is applied to reduce the EIT computation time for a constant and high resolution finite element mesh. In addition, we consider a powerful preconditioner and provide a detailed pseudocode for the improved iterative solver. The numerical results show the effectiveness of our approach: the proposed algorithm is faster than the preconditioned conjugate gradient (CG) algorithm. The results also show that even on a standard PC without parallelization, a high mesh resolution (more than 150,000 degrees of freedom) can be used for image estimation at a relatively low computational cost. (C) 2010 Elsevier B.V. All rights reserved.

Toward Optimal Design of Piezoelectric Transducers Based on Multifunctional and Smoothly Graded Hybrid Material Systems

This work explores the design of piezoelectric transducers based on functional material gradation, here named functionally graded piezoelectric transducer (FGPT). Depending on the applications, FGPTs must achieve several goals, which are essentially related to the transducer resonance frequency, vibration modes, and excitation strength at specific resonance frequencies. Several approaches can be used to achieve these goals; however, this work focuses on finding the optimal material gradation of FGPTs by means of topology optimization. Three objective functions are proposed: (i) to obtain the FGPT optimal material gradation for maximizing specified resonance frequencies; (ii) to design piezoelectric resonators, thus, the optimal material gradation is found for achieving desirable eigenvalues and eigenmodes; and (iii) to find the optimal material distribution of FGPTs, which maximizes specified excitation strength. To track the desirable vibration mode, a mode-tracking method utilizing the `modal assurance criterion` is applied. The continuous change of piezoelectric, dielectric, and elastic properties is achieved by using the graded finite element concept. The optimization algorithm is constructed based on sequential linear programming, and the concept of continuum approximation of material distribution. To illustrate the method, 2D FGPTs are designed for each objective function. In addition, the FGPT performance is compared with the non-FGPT one.

Optimal design of periodic functionally graded composites with prescribed properties

The computational design of a composite where the properties of its constituents change gradually within a unit cell can be successfully achieved by means of a material design method that combines topology optimization with homogenization. This is an iterative numerical method, which leads to changes in the composite material unit cell until desired properties (or performance) are obtained. Such method has been applied to several types of materials in the last few years. In this work, the objective is to extend the material design method to obtain functionally graded material architectures, i.e. materials that are graded at the local level (e.g. microstructural level). Consistent with this goal, a continuum distribution of the design variable inside the finite element domain is considered to represent a fully continuous material variation during the design process. Thus the topology optimization naturally leads to a smoothly graded material system. To illustrate the theoretical and numerical approaches, numerical examples are provided. The homogenization method is verified by considering one-dimensional material gradation profiles for which analytical solutions for the effective elastic properties are available. The verification of the homogenization method is extended to two dimensions considering a trigonometric material gradation, and a material variation with discontinuous derivatives. These are also used as benchmark examples to verify the optimization method for functionally graded material cell design. Finally the influence of material gradation on extreme materials is investigated, which includes materials with near-zero shear modulus, and materials with negative Poisson`s ratio.