Materiais piezocompósitos laminados são compostos por camadas de material piezelétrico, metálico e compósito (matriz epóxi com fibras de carbono ou de vidro), que possibilitam obter vantagens em relação aos materiais piezelétricos convencionais, permitindo obter características superiores que não podem ser conseguidas pelos seus componentes de forma isolada como, por exemplo, maior flexibilidade e resistência mecânica ou menor peso. Sob esse enfoque, este trabalho tem por objetivo o desenvolvimento de Estruturas Piezocompósitas Laminadas (EPLA) que consistem basicamente em estruturas multicamadas, através do projeto da sua resposta transiente e harmônica visando aplicações dinâmicas. Entre as potenciais aplicações dessas estruturas, tem-se atuadores, motores, sonares e dispositivos de coleta de energia (\"energy harvester\"), sendo de muito interesse a melhora das suas características dinâmicas e o seu desempenho. O projeto dinâmico de uma EPLA é complexo, porém pode ser sistematizado utilizando o Método de Otimização Topológica (MOT). O MOT é um método baseado na distribuição de material num domínio de projeto fixo com o objetivo de extremizar uma função de custo sujeita às restrições inerentes do problema, combinando algoritmos de otimização e de elementos finitos. A formulação de MOT para o projeto dinâmico de EPLA pretende determinar tanto a topologia ótima dos materiais nas diferentes camadas quanto o sinal de polarização do material piezelétrico e o ângulo da fibra na camada compósita, tendo como finalidade a maximização da amplitude de vibração em pontos determinados (em atuadores) ou da geração de energia elétrica a partir de excitações mecânicas (em coletores de energia). Além disso, é formulado um problema combinando os enfoques harmônico e transiente com o intuito de customizar a resposta da EPLA, de modo que, o nível da resposta seja o mesmo perante diferentes tipos de onda de excitação (transdutores multi-entrada). O trabalho inclui as etapas de projeto, simulação, fabricação e caracterização de protótipos. / Laminated piezocomposite materials are composed by layers of piezoelectric, metal and composite material (epoxy matrix with carbon or glass fiber), which have advantages over conventional piezoelectric materials, because of their superior characteristics, which cannot be achieved by any of its components isolated, for example, more flexibility and strength and less weight. Under this approach, this work aims at the development of Laminated Piezocomposite Structures (LAPS) what primarily consist of multi-layer structures, through the transient and harmonic response design aiming at dynamic applications. Among the potential applications of these structures it can be cited actuators, motors, sonar devices and energy harvester, being of great interest the improvement of its dynamic characteristics and performance. The dynamic design of a LAPS is complex however it can be systematized by using the Topology Optimization Method (TOM). The TOM is a method based on the distribution of material in a fixed design domain with the aim of extremizing a cost function subject to constraints inherent to the problem by means of combining the optimization algorithms and the finite element method (FEM). The TOM formulation for the LAPS dynamic project aims to determine together the optimal topology of the materials for different layers, the polarization sign of the piezoelectric material and the fiber angle of the composite layer, in order to maximize the vibration amplitude at certain points (in actuators), or the generation of electrical energy from mechanical excitations (in energy harvesters). In addition, a TOM problem combining harmonic and transient approaches is formulated with the purpose of customizing EPLA response so that the response level is the same for different excitation waveforms (multi-entry transducers). The work includes design, simulation, manufacturing and characterization of prototypes.

Cerâmicas piezelétricas possibilitam posicionamento e sensoriamento de precisão ou captação de energia mecânica valendo-se do efeito piezelétrico, capaz de converter energia mecânica em elétrica ou o contrário. Para aprimorar ou estender as aplicações dessas cerâmicas, mecanismos flexíveis podem ser acoplados a elas, formando um Dispositivo Piezelétrico Flextensional (DPF). No projeto desse tipo de estrutura, o conceito de Material com Gradação Funcional (MGF) é interessante, já que esses materiais apresentam variações graduais de suas propriedades efetivas, permitindo a alternância entre um material mais flexível e um mais rígido de acordo com a intensidade de deslocamento desejada em cada região da estrutura. Assim, neste trabalho, implementa-se o Método de Otimização Topológica (MOT) no projeto de estruturas gradadas com o intuito de identificar as vantagens e desvantagens da utilização do conceito de MGF em DPF. Esse método combina algoritmos de otimização e o Métodos dos Elementos Finitos (MEF) para distribuir material dentro de um domínio fixo através de um modelo de material, que no presente caso é o de Material Isotrópico Sólido com Penalização (MISP) adaptado a MGF. Na fabricação desses dispositivos otimizados, utiliza-se a Sinterização por Jato de Plasma (SJP) para a obtenção de tarugos gradados que são submetidos a processos de eletro-erosão e de corte a laser. Por fim, para a verificação dos resultados numéricos, utiliza-se um vibrômetro para aferir os deslocamentos dos protótipos de atuadores fabricados. / Piezoelectric devices enable precision positioning and sensing or mechanical energy harvesting based on the piezoelectric effect. In flextensional piezoelectric devices, flexible coupling structures are attached to ceramics to improve or extend the application possibilities. On the design of this kind of structure, the concept of Functionally Graded Materials (FGM) can be interesting, since it allows gradual variations of its effective properties along some direction by mixing two or more materials. Thus, in order to identify the advantages and disadvantages of using FGM, graded flexible coupling structures that maximize the performance of piezoelectric devices are obtained by implementing the Topology Optimization Method (TOM). This method combines optimization algorithms and the Finite Element Method (FEM) to distribute material inside a fixed domain. In this work, the formulation is based on the Solid Isotropic Material with Penalization (SIMP) material model adapted for the FGM concept, which can represent continuous change in material properties along the domain. Resulting optimal graded topologies of coupling structures are presented and compared with homogeneous structures. Finally, graded devices are manufactured through Spark Plasma Sintering (SPS) technique in order to be characterized, validating numerical results. The numerical results demonstrate the TOM efficacy in designing functionally graded piezoelectric devices and show, by its implementation, significant gains in graded mechanisms performance when compared with analogous homogeneous. Furthermore, the feasibility of proposed manufacturing process is confirmed, allowing the fabrication of prototypes with expected behavior.

De nos jours, les systèmes intègrent de plus en plus de fonctionnalités dans des volumes de plus en plus petits grâce aux microcomposants intégrés. L'assemblage de ces microcomposants nécessite des systèmes de manipulation précis et reproductibles. Un nombre considérable de recherches ont été menées afin de mettre au point des actionneurs et des microrobots capables d'effectuer des tâches de positionnement ou de manipulation avec des précisions microniques voire submicroniques. Les technologies piézoélectriques jouent un rôle fondamental dans les applications de positionnement à résolution nanométrique ou même inférieure. Ces matériaux permettent la conception et le développement de systèmes de positionnement avec résolution et bande passante élevées. Cependant, des effets non linéaires tels que l'hystérésis et la dérive lente affectent la précision de la position des systèmes à base piézoélectrique s'ils ne sont pas contrôlés. Souvent, des capteurs de position sont montés sur ces systèmes pour permettre un contrôle en boucle fermée et l'élimination des effets d'hystérésis et de dérive lente. Néanmoins, l'intégration de capteurs permettant un asservissement robuste et de qualité pose des problèmes spécifiques aux microrobots. Cela est particulièrement vrai lorsque le nombre de degrés de liberté augmente. En effet, les capteurs de position qui jouissent d'une bonne résolution et précision sont généralement très volumineux et coûteux. Les solutions alternatives à l’intégration de capteurs de position externes peuvent être regroupées en deux catégories: soit par contrôle en boucle ouverte, également appelé schémas de contrôle prédictifs, soit par des techniques basées sur le contrôle par auto-détection (Self-Sensing Actuation - SSA), c’est-à-dire un contrôle en boucle fermée utilisant l'actionneur piézoélectrique comme son propre capteur.Dans cette thèse, l'objectif est de concevoir et de contrôler un système de positionnement basé sur la technologie piézoélectrique avec une méthode de mesure intégrée par SSA et ayant plusieurs degrés de liberté. À cette fin, les deux classes de SSA, à savoir le SSA basé sur l’effet direct piézoélectrique et le SSA basé sur la modification des propriétés électriques de l'actionneur piézoélectrique (PEA), sont étudiées en profondeur afin de déterminer celle qui convient le mieux au contrôle de la force et de la position dans les actionneurs piézoélectriques caractérisés par le fluage et non-linéarités d'hystérésis et consacrés à des opérations précises. De plus, cette étude présente un modèle constitutif et une technique d’identification de paramètres améliorés, qui prend en compte l’effet de couplage électromécanique et les non linéarités sur les propriétés du matériau piézoélectrique (constantes élastiques et diélectriques).Une nouvelle technique d'évaluation en temps réel des propriétés électriques du PEA est développée. Cette évaluation est basée sur la mesure de l’amplitude du courant de détection résultant de l’application d’une tension d’entrée haute fréquence de faible amplitude superposée à la tension d’entrée de commande qui actionne le PEA. Ensuite, un estimateur qui utilise le courant de détection pour estimer la position du PEA est conçu. Enfin, une plate-forme microrobotique pour le positionnement planaire à haute résolution avec la mesure intégrée par SSA développée est présentée. / Currently, systems integrate more and more functionalities into smaller volumes thanks to embedded micro-components. The assembly of those components requires precise and repeatable systems of manipulation. Substantial amounts of research have been carried out for developing actuators and microrobots to perform positioning or manipulation with micron- or even submicron accuracies. Piezoelectric technologies play a fundamental role in positioning applications with nanoscale or even lower resolution. These materials make possible the design and development of positioning systems with high resolution and bandwidth. However, nonlinear effects such as hysteresis and creep affect the position accuracy of piezoelectric-based systems if not controlled. Often, position sensors are mounted to these systems to permit a feedback control and the elimination of the hysteresis and creep effects. Nonetheless, the integration of sensors to enable quality and robust servo control poses specific problems for microrobots. This is especially true when the number of degrees of freedom (DOF) increases. Precision position sensors are usually very bulky and expensive. Alternative solutions to the integration of external position sensors can be grouped into two categories: either by open-loop control, also called feedforward control schemes or by Self-Sensing Actuation (SSA) control-based techniques, that is, a feedback control that uses the piezoelectric actuator as its own sensor.In this thesis, the objective is to design and control a piezoelectric-based positioning system with an embedded measurement by SSA method and having several degrees of freedom. To this end, the two classes of SSA, namely SSA based on the piezoelectric direct effect and the SSA based on the change of electrical properties of the piezoelectric actuator (PEAs), are studied in depth to determine the more adequate for force and position control in piezoelectric actuators typified by creep and hysteresis nonlinearities and devoted to precise operations. Additionally, from this study, an improved constitutive model and parameter identification technique are presented which includes the electromechanical coupling effect on the piezoelectric material properties (elastic and dielectric constants).A novel technique for real-time evaluation of the PEA's electrical properties is developed. This evaluation is based on the measurement of the amplitude of the detection current that results from the application of high-frequency low amplitude input voltage that is superimposed to the control input voltage which actuates the PEA. Then an estimator that uses the detection current to estimate the PEA's position is designed. Finally, a microrobotics platform for planar positioning with high resolution and the developed embedded measurement by SSA is presented.

Orientador: Cláudio Kitano / Resumo: Nesta dissertação de mestrado é apresentado um vibrômetro para a medição de deslocamentos nanométricos. O vibrômetro proposto está baseado em um interferômetro de Michelson modificado, homódino e em malha fechada. A demodulação em tempo real é executada inteiramente em modo digital, utilizando uma plataforma embarcada que realiza a aquisição de dados, processamento dos sinais, controle PI (proporcional-integral) e a geração dos sinais que acionam o modulador de fase óptica (baseado em uma célula Pockels) e o atuador piezoelétrico sob estudo. Dois sinais em quadratura de fase são obtidos a partir de um único sinal interferométrico utilizando uma tensão de modulação principal e, em seguida, a conhecida técnica de multiplicação cruzada é aplicada para calcular a variação da fase óptica de interesse. A condição de quadratura é atingida pelo próprio controlador PI por meio da análise da figura de Lissajous dos sinais fora de fase. O novo vibrômetro óptico é capaz de medir deslocamentos nanométricos, e é simples, barato, exato, imune ao desvanecimento e auto-consistente. O controlador PI é robusto, uma vez que o método de demodulação é capaz de trabalhar com elevado ruído eletrônico, variações indesejáveis no ganho do amplificador e na tensão de meia-onda da célula Pockels com a temperatura e outras perturbações externas. O novo sistema foi utilizado para determinar a magnitude da resposta em frequência de dois protótipos de atuadores piezoelétricos flextensionais multiatuados. As ... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: A vibrometer to measure nanometric displacements is presented in this work. The proposed vibrometer is based on a modified closed loop homodyne Michelson interferometer. Real-time phase demodulation is carried out entirely in a digital mode, using an embedded platform that performs data acquisition, signal processing, PI (proportional-integral) control and the generation of signals that drive the electrooptic Pockels cell phase shifter and the piezoelectric actuator under test. Two phase quadrature signals are generated from a single interferometric output, using the interleaving action, in alternation, of a digitally generated principal modulating signal, and then the well-known cross-multiplication technique is applied to perform the computation of the phase shift of interest. The quadrature condition is reached by the PI control itself, using the length difference between the major axis and the minor axis of the ellipse formed by the Lissajous figure associated with the out of phase signals as the controller error signal. The new optical vibrometer is capable of measuring nanometric displacements, and is simple, inexpensive, accurate, immune to fading and self-consistent. The PI controller is robust, since the demodulation method is able to work under high electronic noise, undesirable variations in Pockels cell half-wave voltage with temperature, amplifier gain and other external entrances. The new method was used to determine the displacement frequency response curves of... (Complete abstract click electronic access below) / Mestre

Two - stage servovalves, despite being widely used in aircraft and industry because of their reliability and high performance, have a few disadvantages that are still unsolved at the state of the art, such as the power consumption caused by the quiescent flow (internal leakage) in the pilot stage, and the complexity and high number of parts of the torque motor assembly of the pilot stage. The solution to these problems can help to reduce costs, weight, power consumption, and to enhance the reliability and producibility as well as the performance of these valves. This paper presents a novel configuration of servovalve, which has the potential to overcome the above-mentioned issues. The proposed servo-valve includes a novel architecture for the pilot stage by using two piezo-electric actuators (ring benders). In this paper, the performance of this novel pilot stage is assessed. To this end, a valve prototype has been constructed and tested; the experimental results are also used to validate a numerical model obtained with the software Simscape Fluids. The results show that, acting on specific parameters, the performance of the piezo-valve can be very competitive, while ensuring very low internal leakage and complexity.

The research reported in this dissertation focuses on the development of optimization tools for the design of subsystems in a modern aircraft power distribution system. The baseline power distribution system is built around a 270V DC bus. One of the distinguishing features of this power distribution system is the presence of regenerative power from the electrically driven flight control actuators and structurally integrated smart actuators back to the DC bus. The key electrical components of the power distribution system are bidirectional switching power converters, which convert, control and condition electrical power between the sources and the loads. The dissertation is divided into three parts. Part I deals with the formulation of an optimization problem for a sample system consisting of a regulated DC-DC buck converter preceded by an input filter. The individual subsystems are optimized first followed by the integrated optimization of the sample system. It is shown that the integrated optimization provides better results than that obtained by integrating the individually optimized systems. Part II presents a detailed study of piezoelectric actuators. This study includes modeling, optimization of the drive amplifier and the development of a current control law for piezoelectric actuators coupled to a simple mechanical structure. Linear and nonlinear methods to study subsystem interaction and stability are studied in Part III. A multivariable impedance ratio criterion applicable to three phase systems is proposed. Bifurcation methods are used to obtain global stability characteristics of interconnected systems. The application of a nonlinear design methodology, widely used in power systems, to incrementally improve the robustness of a system to Hopf bifurcation instability is discussed. / Ph. D.

Microdispositivos piezelétricos tem uma vasta aplicação em mecânica de precisão, como, por exemplo, manipulação de células, microcirurgias, equipamentos de nanotecnologia e principalmente em microeletromecanismos (MEMS). Os microdispositivos piezelétricos considerados nesta tese essencialmente consistem de uma estrutura multi-flexível atuada por duas ou mais piezocerâmicas, que geram deslocamentos e forças em direções e regiões pré-determinadas do domínio, ou seja, a estrutura multi-flexível atua como um transformador mecânico amplificando e alterando os deslocamentos gerados pelas piezocerâmicas nos movimentos de atuação. O desenvolvimento destes microdispositivos piezelétricos em sua grande maioria não utiliza ferramentas sistemáticas e genéricas. A complexidade dos movimentos de atuação torna o desenvolvimento dos microdispositivos piezelétricos complexo, principalmente devido ao surgimento de movimentos indesejados ou acoplados durante a sua atuação. Portanto, é necessário um método sistemático e eficiente como o método de otimização topológica (MOT), que incorpore na sua formulação as principais exigências de projeto dos microdispositivos, como apresentado nesse trabalho. O MOT implementado é baseado na abordagem CAMD (Distribuição Contínua da Distribuição de Material), onde as pseudo-densidades são interpoladas nos nós de cada elemento finito, resultando numa distribuição contínua de material no domínio. Um método adjunto foi implementado para o cálculo das sensibilidades. São consideradas três formulações. A primeira denominada de MAPs (Multi-Atuadores Piezelétricos) considera as regiões piezocerâmicas fixas, otimizando apenas a estrutura multi-flexível no domínio de projeto. Nesta formulação materiais não-piezelétricos (como, por exemplo, Alumínio) e vazio são distribuídos no domínio de projeto, mantendo as regiões piezocerâmicas fixas e homogêneas. Para validar os resultados obtidos com essa formulação foram fabricados protótipos de nanoposicionadores $XY$, que foram caracterizados experimentalmente utilizando técnicas de interferometria laser, considerando excitação quasi-estática. No entanto, essa primeira formulação impõe restrições no problema, limitando a optimalidade da solução obtida pela otimização topológica. Assim, surgiu a necessidade de desenvolver uma segunda formulação, que permite distribuir simultaneamente material não-piezelétrico, piezelétrico e vazio no domínio de projeto, denominada de LOMPs (Localização Ótima do Material Piezelétrico). A formulação dos LOMPs obtém simultaneamente a localização do material piezelétrico na estrutura flexível otimizada pela OT, e inclui também uma variável de projeto para determinar o ângulo ótimo entre as direções de polarização e do campo elétrico. Nesta formulação como as posições dos eletrodos não são conhecidas, ``a priori\'\', é utilizado como abordagem aplicar um campo elétrico constante para determinar a localização do material piezelétrico e conseqüentemente dos eletrodos. Finalmente, foi explorado o conceito de materiais com gradação funcional (MGFs) no projeto dos MAPs. Os MGFs apresentam uma distribuição contínua de materiais na sua microestrutura, não possuindo interface entre os materiais distribuídos, o que possibilita aumentar a vida útil do dispositivo piezelétrico. Assim, foi implementado uma terceira formulação denominada de MAPs MGFs, que permite obter a gradação ótima de materiais piezelétricos e não-piezelétricos no domínio piezocerâmico dos MAPs, conjuntamente com a topologia da estrutura multi-flexível. Essa formulação foi estendida para projetar atuadores bilaminares MGFs. Todas as formulações desenvolvidas utilizam uma função multi-objetivo, que permite controlar a rigidez e a flexibilidade minimizando o movimento acoplado, de cada movimento de atuação. Os exemplos numéricos são limitados a modelos bi-dimensionais, utilizando o estado plano de tensões e deformações mecânicas e elétricas, uma vez que a grande maioria das aplicações dos microdispositivos piezelétricos são bi-dimensionais. / Microtools offer significant promise in a wide range of applications such as cell manipulation, microsurgery, nanotechnology processes, and many other fields. The microtools considered in this doctoral thesis essentially consist of a multi-flexible structure actuated by two or more piezoceramic devices that when each piezoceramic is actuated, it generates an output displacement and force at a specified point of the domain and direction. The multi-flexible structure acts as a mechanical transformer 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. The development of these microtools is still in the beginning and it can be strongly enhanced by using design tools. 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. The topology optimization method implemented is based on the CAMD (Continuous Approximation of Material Distribution) approach where fictitious densities are interpolated at each finite element, providing a continuum material distribution in the domain. The corresponding sensitivity analysis is presented using the adjoint method. Three formulations are considered. The first formulation, called Piezoelectric Multi-Actuators (PMAs), keeps fixed piezoceramic positions in the design domain and only the flexible structure is designed by distributing some non-piezoelectric material (Aluminum, for example). $XY$ Piezoelectric Nanopositioner are manufactured and experimentally analyzed to validate the results of the topology optimization obtained using this formulation. Experimental analyses are conducted using laser interferometry to measure displacement, while considering a quasi-static excitation. However, this first formulation imposes a constraint to the position of piezoelectric material in the optimization problem limiting the optimality of the solution. Thus, the second formulation presented, called LOMPs, allows the simultaneous distribution of non-piezoelectric and piezoelectric material in the design domain, to achieve certain specified actuation movements. The optimization problem is posed as the simultaneous search for an optimal topology of a flexible structure as well as the optimal position of piezoceramics in the design domain and optimal rotation angle of piezoceramic material axes that maximize output displacements or output forces at a specified point of the domain and direction. When the distribution of a non-piezoelectric conductor material and a piezoceramic material is considered in the design domain, the electrode positions are not known ``a priori\'\'. To circumvent this problem, an electric field is applied as electrical excitation. Finally, the concept of functionally graded materials (FGM) is applied to PMAs design. FGMs are special materials that possess continuously graded properties without interfaces which can increase lifetime of piezoelectric devices. Thus, a third formulation is implemented to find the optimum gradation and polarization sign variation of piezoceramic FGMs, while simultaneously optimizing the multi-flexible structural configuration. This formulation is extended to design bimorph type FGM actuators. For all developed formulations, a multi-objective function is defined that controls the stiffness and flexibility, minimizing the coupling movement of each actuated movement. The present examples are limited to two-dimensional models because most part of the applications for such micro-tools are planar devices.

Περίληψη Σκοπός της παρούσας διδακτορικής διατριβής είναι η διατύπωση µοντέλων µηχανικής και η ανάπτυξη µεθοδολογίας πεπερασµένων στοιχείων, για τηv αριθµητική επίλυση τoυ προβλήµατος της συζευγµένης µη-γραµµικής απόκρισης πιεζοηλεκτρικών κελυφών και πλακών µε εµφυτευµένα πιεζοηλεκτρικά στοιχεία. Η ανάπτυξη της παρούσας µεθόδου στηρίχθηκε σε θεωρίες µεσοµηχανικής για τη ανάλυση στρωµατοποιηµένων πιεζοηλεκτρικών κελυφών και κατά επέκταση πλακών και δοκών. Πιο συγκεκριµένα διατυπώνονται σε επίπεδο στρώσης, οι καταστατικές εξισώσεις του ηλεκτροµηχανικού πεδίου, οι εξισώσεις συµβιβαστού των παραµορφώσεων-µετατοπίσεων, που εµπεριέχουν την γεωµετρική µη γραµµικότητα, καθώς και οι γενικευµένες εξισώσεις κίνησης (εξισώσεις ισορροπίας των τάσεων στο µηχανικό και διατήρησης ηλεκτρικού φορτίου στο ηλεκτρικό πεδίο). Στη συνέχεια δύναται να γραφούν οι παραπάνω εξισώσεις κίνησης σε ολοκληρωτική µορφή, µε την βοήθεια της αρχής των φανταστικών µετατοπίσεων, ώστε να ισχύουν για ολόκληρη την πιεζοηλεκτρική πολύστρωτη δοµή. Τα παραπάνω ολοκληρώµατα όγκου υποβιβάζονται σε ολοκληρώµατα επιφάνειας µε την εισαγωγή των κινηµατικών υποθέσεων για τις ελαστικές και ηλεκτρικές µεταβλητές κατάστασης. Για την επίλυση των παραπάνω συζευγµένων µη γραµµικών ολοκληρωτικών εξισώσεων αναπτύχθηκε µέθοδος πεπερασµένων στοιχείων. ∆υο 8-κοµβα συζευγµένα µη γραµµικά ισοπαραµετρικά πεπερασµένα στοιχεία κελύφους και πλάκας αναπτύσσονται. Στο εσωτερικό των στοιχειών το παραµορφωσιακό πεδίο προσεγγίζεται µε πολυώνυµικές εξισώσεις δευτέρου βαθµού, που ονοµάζονται συναρτήσεις µορφής. Με την βοήθεια των συναρτήσεων µορφής προκύπτουν οι συζευγµένες µη γραµµικές εξισώσεις σε µητρωική µορφή, και λόγω του ότι εξαρτώνται από τη λύση δεν µπορούν να λυθούν απευθείας αλλά χρησιµοποιείται µια σταδιακή- επαναληπτική µέθοδος βασισµένη στη Newton-Raphson τεχνική. Αφού πραγµατοποιηθεί η σύνθεση των ολικών µητρώων, εφαρµοστούν οι µηχανικές και ηλεκτρικές συνοριακές συνθήκες τελικά επιλύονται οι προκύπτουσες γραµµικοποιηµένες συζευγµένες εξισώσεις σε κάθε επανάληψη εως ότου επιτευχθεί σύγκλιση της λύσης. Σε κάθε επανάληψη υπολογίζονται ταπραγµατικά και εφαπτοµενικά µη γραµµικά µητρώα καθώς επίσης και τα διανύσµατα ανισορροπίας µεταξύ των εξωτερικών και εσωτερικών δυνάµεων και ηλεκτρικών φορτίων. Τα µη γραµµικά ελαστικά και πιεζοηλεκτρικά µητρώα, που εµπεριέχουν τη γεωµετρική µη γραµµικότητα, καθώς και τα γραµµικά επιλύονται αριθµητικά µε τη µέθοδο Gauss. Η παρούσα µέθοδος µπορεί να εφαρµοστεί για τη διερεύνηση και αριθµητική επίλυση µιας σειράς προβληµάτων ευφυών πιεζοηλεκτρικών κατασκευών, όπου η γεωµετρική µη γραµµικότητα (µεγάλες µετατοπίσεις και περιστροφές σε σχέση µε το πάχος, αλλά µικρές παραµορφώσεις) παίζει σηµαντικό ή πρωτεύοντα ρόλο, µε ιδιαίτερη έµφαση στα εξής προβλήµατα: Μοντελοποίηση ευφυών κατασκευών υπό µεγάλη κάµψη. Εφαρµογές σε κατασκευές, στις οποίες επιδιώκονται µεγάλες αλλαγές στο σχήµα τους µέσω µεγάλων ενεργών µετατοπίσεων και περιστροφών, υπό την επιβολή ηλεκτρικού πεδίου στους πιεζοηλεκτρικούς διεγέρτες (morphing structures) . Πρόβλεψη κρίσιµων επίπεδων µηχανικών δυνάµεων και ηλεκτρικών τάσεων λυγισµού, οι οποίες µπορεί να οδηγήσουν τις ευφυείς πλάκες και τα κελύφη σε συνθήκες λυγισµού και απώλειας ευστάθειας. Πρόβλεψη και προσοµοίωση του λυγισµού και µετα-λυγισµού σε panel αεροναυπηγικών κατασκευών, µέσω παρακολούθησης της µεταβολής των φυσικών συχνοτήτων της κατασκευής ή της αναπτυσσόµενης ηλεκτρικής τάσης στους πιεζοηλεκτρικούς αισθητήρες. Την ενεργή µεταβολή της δυσκαµψίας (αύξηση ή µείωση) ευφυών κατασκευών µε την επιβολή κατάλληλου ηλεκτρικού δυναµικού στους πιεζοηλεκτρικούς διεγέρτες. Πρόβλεψη της µετάβασης των πιεζοηλεκτρικών κελυφών από τη µια θέση ισορροπίας σε άλλη (snap-through), υπό την επιβολή µηχανικού φορτίου ή πιεζοηλεκτρικής καµπτικής ροπής µέσω των πιεζοηλεκτρικών διεγερτών.πραγµατικά και εφαπτοµενικά µη γραµµικά µητρώα καθώς επίσης και τα διανύσµατα ανισορροπίας µεταξύ των εξωτερικών και εσωτερικών δυνάµεων και ηλεκτρικών φορτίων. Τα µη γραµµικά ελαστικά και πιεζοηλεκτρικά µητρώα, που εµπεριέχουν τη γεωµετρική µη γραµµικότητα, καθώς και τα γραµµικά επιλύονται αριθµητικά µε τη µέθοδο Gauss. Η παρούσα µέθοδος µπορεί να εφαρµοστεί για τη διερεύνηση και αριθµητική επίλυση µιας σειράς προβληµάτων ευφυών πιεζοηλεκτρικών κατασκευών, όπου η γεωµετρική µη γραµµικότητα (µεγάλες µετατοπίσεις και περιστροφές σε σχέση µε το πάχος, αλλά µικρές παραµορφώσεις) παίζει σηµαντικό ή πρωτεύοντα ρόλο, µε ιδιαίτερη έµφαση στα εξής προβλήµατα: Μοντελοποίηση ευφυών κατασκευών υπό µεγάλη κάµψη. Εφαρµογές σε κατασκευές, στις οποίες επιδιώκονται µεγάλες αλλαγές στο σχήµα τους µέσω µεγάλων ενεργών µετατοπίσεων και περιστροφών, υπό την επιβολή ηλεκτρικού πεδίου στους πιεζοηλεκτρικούς διεγέρτες (morphing structures) . Πρόβλεψη κρίσιµων επίπεδων µηχανικών δυνάµεων και ηλεκτρικών τάσεων λυγισµού, οι οποίες µπορεί να οδηγήσουν τις ευφυείς πλάκες και τα κελύφη σε συνθήκες λυγισµού και απώλειας ευστάθειας. Πρόβλεψη και προσοµοίωση του λυγισµού και µετα-λυγισµού σε panel αεροναυπηγικών κατασκευών, µέσω παρακολούθησης της µεταβολής των φυσικών συχνοτήτων της κατασκευής ή της αναπτυσσόµενης ηλεκτρικής τάσης στους πιεζοηλεκτρικούς αισθητήρες. Την ενεργή µεταβολή της δυσκαµψίας (αύξηση ή µείωση) ευφυών κατασκευών µε την επιβολή κατάλληλου ηλεκτρικού δυναµικού στους πιεζοηλεκτρικούς διεγέρτες. Πρόβλεψη της µετάβασης των πιεζοηλεκτρικών κελυφών από τη µια θέση ισορροπίας σε άλλη (snap-through), υπό την επιβολή µηχανικού φορτίου ή πιεζοηλεκτρικής καµπτικής ροπής µέσω των πιεζοηλεκτρικών διεγερτών.πραγµατικά και εφαπτοµενικά µη γραµµικά µητρώα καθώς επίσης και τα διανύσµατα ανισορροπίας µεταξύ των εξωτερικών και εσωτερικών δυνάµεων και ηλεκτρικών φορτίων. Τα µη γραµµικά ελαστικά και πιεζοηλεκτρικά µητρώα, που εµπεριέχουν τη γεωµετρική µη γραµµικότητα, καθώς και τα γραµµικά επιλύονται αριθµητικά µε τη µέθοδο Gauss. Η παρούσα µέθοδος µπορεί να εφαρµοστεί για τη διερεύνηση και αριθµητική επίλυση µιας σειράς προβληµάτων ευφυών πιεζοηλεκτρικών κατασκευών, όπου η γεωµετρική µη γραµµικότητα (µεγάλες µετατοπίσεις και περιστροφές σε σχέση µε το πάχος, αλλά µικρές παραµορφώσεις) παίζει σηµαντικό ή πρωτεύοντα ρόλο, µε ιδιαίτερη έµφαση στα εξής προβλήµατα: Μοντελοποίηση ευφυών κατασκευών υπό µεγάλη κάµψη. Εφαρµογές σε κατασκευές, στις οποίες επιδιώκονται µεγάλες αλλαγές στο σχήµα τους µέσω µεγάλων ενεργών µετατοπίσεων και περιστροφών, υπό την επιβολή ηλεκτρικού πεδίου στους πιεζοηλεκτρικούς διεγέρτες (morphing structures) . Πρόβλεψη κρίσιµων επίπεδων µηχανικών δυνάµεων και ηλεκτρικών τάσεων λυγισµού, οι οποίες µπορεί να οδηγήσουν τις ευφυείς πλάκες και τα κελύφη σε συνθήκες λυγισµού και απώλειας ευστάθειας. Πρόβλεψη και προσοµοίωση του λυγισµού και µετα-λυγισµού σε panel αεροναυπηγικών κατασκευών, µέσω παρακολούθησης της µεταβολής των φυσικών συχνοτήτων της κατασκευής ή της αναπτυσσόµενης ηλεκτρικής τάσης στους πιεζοηλεκτρικούς αισθητήρες. Την ενεργή µεταβολή της δυσκαµψίας (αύξηση ή µείωση) ευφυών κατασκευών µε την επιβολή κατάλληλου ηλεκτρικού δυναµικού στους πιεζοηλεκτρικούς διεγέρτες. Πρόβλεψη της µετάβασης των πιεζοηλεκτρικών κελυφών από τη µια θέση ισορροπίας σε άλλη (snap-through), υπό την επιβολή µηχανικού φορτίου ή πιεζοηλεκτρικής καµπτικής ροπής µέσω των πιεζοηλεκτρικών διεγερτών. / -

Η παρούσα διδακτορική διατριβή έχει ως κύριο αντικείμενο μελέτης την μοντελοποίηση και έλεγχο ενός μικρορομποτικού βραχίονα αναλυόμενου σε σφαιρικά πεπερασμένα στοιχεία σε περιβάλλον με εξωτερικές δυνάμεις Van Der Waals και συνυπολογίζοντας την τριβή. Τα κύρια σημεία είναι η εισαγωγή των εξωτερικών δυνάμεων στο μοντέλο του μικρορομπότ, η δημιουργία προσαρμοστικού ελέγχου για την επίτευξη ακολουθίας τροχιάς με αναγνώριση και ακύρωση των ισχυρών μεταβαλλόμενων εξωτερικών δυνάμεων, η αναγνώριση της θέσης και η αποφυγή εμποδίων σε άγνωστο περιβάλλον κλίμακας μικρομέτρων και ο καθορισμός τροχιάς για προσέγγιση σημείων στον χώρο εργασίας του μικρορομπότ. Προτείνεται επίσης ένα σύστημα επενέργησης σε διάταξη τένοντα με νανοκαλώδια και γίνεται μελέτη της αντοχής του σε σχέση με τις μέγιστες δυνάμεις-ροπές που παρουσιάζονται κατά τον έλεγχο. Για την αναγνώριση των εξωτερικών δυνάμεων δοκιμάζονται διαφορετικά είδη εκτιμητών και εξετάζεται η απόδοσή τους στο συνολικό σύστημα. / The present PhD thesis has a key object the modeling and control of a micro robotic manipulator, represented by spherical particles in an environment with external Van Der Waals forces and taking friction into account. The main points are a) the insertion of the external forces in the micro robot model, b) the adaptive control used in order to follow a desired trajectory, with identification and cancellation of the external forces, the position identification and avoidance of obstacles in an unstructured micrometer scale environment and the trajectory planning towards a target point in the task space of the microrobot. Also a tendon like actuation system is proposed, using nanowires and its mechanical properties are studied in order to determine the viability of its use in relation to the required torques during the control process. For the external force identification scheme, various types of estimators are proposed and their efficiency in the system is studied.

Microdispositivos piezelétricos tem uma vasta aplicação em mecânica de precisão, como, por exemplo, manipulação de células, microcirurgias, equipamentos de nanotecnologia e principalmente em microeletromecanismos (MEMS). Os microdispositivos piezelétricos considerados nesta tese essencialmente consistem de uma estrutura multi-flexível atuada por duas ou mais piezocerâmicas, que geram deslocamentos e forças em direções e regiões pré-determinadas do domínio, ou seja, a estrutura multi-flexível atua como um transformador mecânico amplificando e alterando os deslocamentos gerados pelas piezocerâmicas nos movimentos de atuação. O desenvolvimento destes microdispositivos piezelétricos em sua grande maioria não utiliza ferramentas sistemáticas e genéricas. A complexidade dos movimentos de atuação torna o desenvolvimento dos microdispositivos piezelétricos complexo, principalmente devido ao surgimento de movimentos indesejados ou acoplados durante a sua atuação. Portanto, é necessário um método sistemático e eficiente como o método de otimização topológica (MOT), que incorpore na sua formulação as principais exigências de projeto dos microdispositivos, como apresentado nesse trabalho. O MOT implementado é baseado na abordagem CAMD (Distribuição Contínua da Distribuição de Material), onde as pseudo-densidades são interpoladas nos nós de cada elemento finito, resultando numa distribuição contínua de material no domínio. Um método adjunto foi implementado para o cálculo das sensibilidades. São consideradas três formulações. A primeira denominada de MAPs (Multi-Atuadores Piezelétricos) considera as regiões piezocerâmicas fixas, otimizando apenas a estrutura multi-flexível no domínio de projeto. Nesta formulação materiais não-piezelétricos (como, por exemplo, Alumínio) e vazio são distribuídos no domínio de projeto, mantendo as regiões piezocerâmicas fixas e homogêneas. Para validar os resultados obtidos com essa formulação foram fabricados protótipos de nanoposicionadores $XY$, que foram caracterizados experimentalmente utilizando técnicas de interferometria laser, considerando excitação quasi-estática. No entanto, essa primeira formulação impõe restrições no problema, limitando a optimalidade da solução obtida pela otimização topológica. Assim, surgiu a necessidade de desenvolver uma segunda formulação, que permite distribuir simultaneamente material não-piezelétrico, piezelétrico e vazio no domínio de projeto, denominada de LOMPs (Localização Ótima do Material Piezelétrico). A formulação dos LOMPs obtém simultaneamente a localização do material piezelétrico na estrutura flexível otimizada pela OT, e inclui também uma variável de projeto para determinar o ângulo ótimo entre as direções de polarização e do campo elétrico. Nesta formulação como as posições dos eletrodos não são conhecidas, ``a priori\'\', é utilizado como abordagem aplicar um campo elétrico constante para determinar a localização do material piezelétrico e conseqüentemente dos eletrodos. Finalmente, foi explorado o conceito de materiais com gradação funcional (MGFs) no projeto dos MAPs. Os MGFs apresentam uma distribuição contínua de materiais na sua microestrutura, não possuindo interface entre os materiais distribuídos, o que possibilita aumentar a vida útil do dispositivo piezelétrico. Assim, foi implementado uma terceira formulação denominada de MAPs MGFs, que permite obter a gradação ótima de materiais piezelétricos e não-piezelétricos no domínio piezocerâmico dos MAPs, conjuntamente com a topologia da estrutura multi-flexível. Essa formulação foi estendida para projetar atuadores bilaminares MGFs. Todas as formulações desenvolvidas utilizam uma função multi-objetivo, que permite controlar a rigidez e a flexibilidade minimizando o movimento acoplado, de cada movimento de atuação. Os exemplos numéricos são limitados a modelos bi-dimensionais, utilizando o estado plano de tensões e deformações mecânicas e elétricas, uma vez que a grande maioria das aplicações dos microdispositivos piezelétricos são bi-dimensionais. / Microtools offer significant promise in a wide range of applications such as cell manipulation, microsurgery, nanotechnology processes, and many other fields. The microtools considered in this doctoral thesis essentially consist of a multi-flexible structure actuated by two or more piezoceramic devices that when each piezoceramic is actuated, it generates an output displacement and force at a specified point of the domain and direction. The multi-flexible structure acts as a mechanical transformer 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. The development of these microtools is still in the beginning and it can be strongly enhanced by using design tools. 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. The topology optimization method implemented is based on the CAMD (Continuous Approximation of Material Distribution) approach where fictitious densities are interpolated at each finite element, providing a continuum material distribution in the domain. The corresponding sensitivity analysis is presented using the adjoint method. Three formulations are considered. The first formulation, called Piezoelectric Multi-Actuators (PMAs), keeps fixed piezoceramic positions in the design domain and only the flexible structure is designed by distributing some non-piezoelectric material (Aluminum, for example). $XY$ Piezoelectric Nanopositioner are manufactured and experimentally analyzed to validate the results of the topology optimization obtained using this formulation. Experimental analyses are conducted using laser interferometry to measure displacement, while considering a quasi-static excitation. However, this first formulation imposes a constraint to the position of piezoelectric material in the optimization problem limiting the optimality of the solution. Thus, the second formulation presented, called LOMPs, allows the simultaneous distribution of non-piezoelectric and piezoelectric material in the design domain, to achieve certain specified actuation movements. The optimization problem is posed as the simultaneous search for an optimal topology of a flexible structure as well as the optimal position of piezoceramics in the design domain and optimal rotation angle of piezoceramic material axes that maximize output displacements or output forces at a specified point of the domain and direction. When the distribution of a non-piezoelectric conductor material and a piezoceramic material is considered in the design domain, the electrode positions are not known ``a priori\'\'. To circumvent this problem, an electric field is applied as electrical excitation. Finally, the concept of functionally graded materials (FGM) is applied to PMAs design. FGMs are special materials that possess continuously graded properties without interfaces which can increase lifetime of piezoelectric devices. Thus, a third formulation is implemented to find the optimum gradation and polarization sign variation of piezoceramic FGMs, while simultaneously optimizing the multi-flexible structural configuration. This formulation is extended to design bimorph type FGM actuators. For all developed formulations, a multi-objective function is defined that controls the stiffness and flexibility, minimizing the coupling movement of each actuated movement. The present examples are limited to two-dimensional models because most part of the applications for such micro-tools are planar devices.