Le Haut-Parleur Digital Matriciel (HPDM) est un moyen de transduction électroacoustique qui reçoit comme entrée un signal numérique et qui effectue la conversion vers l'analogique directement dans l'air. Il est constitué de plusieurs éléments rayonnants disposés au sein d'une matrice. Ces éléments seront désignés par le terme «speaklet» lorsqu'ils sont de tailles réduites. Le rayonnement acoustique du HPDM est en effet très sensible à la taille de la matrice, ce qui le rend tout particulièrement adapté à la technologie MEMS. Cette thèse porte sur l'étude de HPDM MEMS piézoélectriques. Après une introduction qui débute par certaines généralités jusqu'à se focaliser sur le sujet, la thèse aborde les modélisations multiphysiques des HPDM étudiés, le dimensionnement des speaklets puis les tests expérimentaux. Des modèles analytiques ainsi que des simulations numériques et par éléments finis sont mis en place et permettent de prédire le comportement mécanique des speaklets présentés, les pressions rayonnées par les HPDM et les puissances électriques consommées. Les speaklets sont ensuite dimensionnés à partir de l'empilement technologique afin de maximiser le niveau de pression qu'ils génèrent. Des tests expérimentaux permettent alors de valider la majorité des modèles ou au contraire de revenir sur certains d'entre eux pour les optimiser ou montrer leurs limitations. Les résultats ont en effet montré l'importance de la prise en compte des contraintes résiduelles, qui provoquent une déformée initiale des speaklets et modifient leurs fréquences propres, rendant alors l'utilisation de grands rayons inefficaces. En accord avec les modèles, les speaklets possèdent un comportement dynamique linéaire, ce qui permet de les caractériser à l'aide de fonctions de transfert. La théorie et les enregistrements sonores montrent alors qu'un HPDM composé de tels speaklets permet dans le meilleur des cas de produire une pression identique à celle générée par la même matrice pilotée en analogique. Dans notre cas, des taux de distorsions supérieurs ont été obtenus lors des reconstructions digitales, à cause des réponses non uniformes des speaklets, dues à des résistances d'accès différentes. Le HPDM présenté possède cependant d'autres avantages, le plus important étant la très faible consommation électrique qu'il est théoriquement possible d'atteindre en utilisant les méthodes de charges et de décharges adiabatiques. Le HPDM piézoélectrique MEMS apparait donc comme étant une technologie prometteuse. L'optimisation de notre premier prototype à l'aide des outils développés doit en effet conduire à un HPDM capable de générer une pression équivalente à celle obtenue en mode analogique, mais avec un rendement électroacoustique beaucoup plus important. Les futurs travaux devront ensuite se concentrer sur la conception de speaklets non-linéaires et sur la forme du pulse de pression qu'ils génèrent, afin de gagner en niveau sonore. / The Digital Loudspeaker Array (DLA) is an electroacoustic transducer which receives as input a digital signal and performs the analog conversion directly into the air. It consists of a plurality of radiating elements arranged in a matrix. These elements will be designated by the term “speaklet” when they are reduced in size. The acoustic radiation of a DLA is indeed very sensitive to the size of the matrix due to differences in path length, which makes it especially suitable for MEMS technology. This thesis is on the study of a piezoelectric MEMS DLA. After an introduction that is increasingly focused on the subject, the thesis addresses the multiphysics modeling of the DLA, dimensioning of the speaklets and experimental tests. Analytical formulas, numerical simulations and finite element models are developed and used to predict the mechanical behavior of the presented speaklets, the pressure radiated by the DLA and the electrical power consumption. The speaklet are then dimensioned from the technological stack (set in advance) in order to maximize the pressure level. Experimental tests involving the use of an anechoic chamber, an optical interferometer, a vibrometer and an impedancemeter validate most of the models. Otherwise, these tests are usefull for improving some of them or for showing their limitations. The results have shown the importance of the residual stresses, which cause an initial deformation of the speaklets and modify their resonance frequencies, thus rendering ineffective the use of large radii. In accordance with the models, the static deflection of the speaklets is nonlinear but their dynamic behavior is linear. This enables characterizations using transfer functions. Theory and sound recordings show that a DLA made of such speaklets can produce in the best case the same pressure to that generated by the same matrix driven in an analog way. In our case, more distortions were obtained in digital reconstructions because of non-uniform responses of the speaklets, due to different access resistances. However, the presented DLA has other advantages, the most important being the very low power consumption it is theoretically possible to achieve using the adiabatic charge principle. The piezoelectric MEMS DLA thus appears as a promising technology. The optimization of our first prototype using the developed tools should indeed lead to a DLA able to generate an equivalent presure to that obtained with analog control, but with a far greater electroacoustic efficiency. Future work should then focus on the design of nonlinear speaklets and on the shaping of the pulse of pressure they generate, in order to increase the total pressure level.

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.

Les contacteurs et les relais sont utilisés dans de très nombreux dispositifs pour le contrôleet la commande à distance. La plupart sont équipés d’actionneurs électromagnétiques qu’il est nécessairede produire en quantité importante pour réaliser ces fonctions. Les exigences environnementalessur l’efficacité et la consommation énergétiques sont de plus en plus contraignantes. La conception deces actionneurs est donc un enjeu important. Cette thèse porte sur le développement d’une plateforme deconception dédiée au pré-dimensionnement d’actionneurs électromagnétiques. Cette plateforme reposesur le développement de méthodes de modélisation très rapides et suffisamment précises. La premièrepartie est consacrée à la résolution des équations de la magnétostatique en linéaire et non-linéaire par lecouplage de la méthode des intégrales de frontières avec la méthode de réseaux de réluctances. L’évaluationdes grandeurs globales telles que le flux magnétique traversant une bobine et la force est étudiée.Les résultats sont validés sur un relais bistable en rotation. La seconde partie concerne la simulationmulti-physique du composant dans son environnement système, pour prendre en compte les aspects mécaniqueet électrique. Une étude de faisabilité par optimisation est réalisée pour le composant seul, puispour l’ensemble composant-système. Enfin, une ouverture sur une autre méthode de modélisation plusgénérale est proposée avec la présentation d’un couplage original et performant entre les méthodes deséléments finis et des intégrales de frontière. / Contactors and relays are used in many devices for monitoring and remote controlling. Mostof them are equipped with electromagnetic actuators, which are produced in large quantities. The environmentalrequirements on efficiency and energy consumption have become more and more strict. Thedesign of these actuators is therefore an important issue. This thesis focuses on the development of adesign platform dedicated to the pre-sizing of electromagnetic actuators. This platform is based on theimplementation of very fast and sufficiently accurate modeling methods. The first part is devoted to theresolution of linear and nonlinear magnetostatic equations by the coupling between boundary integralmethod and reluctance network method. The evaluation of global quantities such as the magnetic fluxflowing through a coil and the force is investigated. The results are validated on a rotating bistable relay.The second part concerns the multi-physics simulation of the component in its environment by takinginto account the mechanical and electrical aspects. A feasibility study by optimization is performed bothfor the component alone and for the whole component-system. Finally, a general modeling method isproposed with the presentation of an original and efficient coupling between the finite element methodsand boundary integrals.

La montée en puissance des systèmes de production de l'énergie électrique, à partir de centrales éoliennes ou photovoltaïques, a fait apparaître un besoin aigu en moyens de stockage de cette énergie. Les technologies d'accumulateurs électrochimiques sont à même de répondre à cette problématique, en particulier les batteries sodium chlorure de nickel, une technologie d'accumulateur à haute température. Mais afin de gérer au mieux les performances de ces batteries, il est nécessaire d'avoir une connaissance approfondie du comportement électrothermique des cellules unitaires les composant. Ce travail de thèse présente en détail le développement d'un modèle multiphysique 2D d'une cellule Na-MCl2 commerciale, à même de simuler son fonctionnement en décharge à courant constant. Ce modèle a été construit sur une étude approfondie des mécanismes électrochimiques à l'œuvre dans ce type de technologie, et des effets thermiques associés. Il repose également sur la synthèse et la critique des modèles proposés précédemment dans la littérature. Le modèle inédit proposé dans ce manuscrit permet de prendre en compte deux réactions électrochimiques simultanées, ainsi que le comportement thermique de la cellule. Le modèle a été validé en confrontant les résultats de simulations aux performances électriques réelles d'une cellule commerciale Na-MCl2 (incluant une caractérisation des phénomènes électrochimiques par voltammetrie cyclique). Ce modèle permet de simuler avec succès des décharges à courant constant à différents régimes, et à partir de différentes températures. Il est également capable de prévoir les effets électrothermiques qui seraient consécutifs à un changement de design de la cellule (design structurel et de constitution). / The growing production capacity of wind turbines or photo-voltaic plants has revealed an acute need for electric energy storage systems. Electrochemical accumulator technologies are able to address this issue, in particular sodium nickel chloride batteries, a high temperature battery system. But to enhance the energy management of these batteries, it is necessary to have a deep knowledge of the electro-thermal behavior of its unit cell component. This thesis presents the development of a comprehensive multiphysics 2D model of a commercial Na-MCl2 cell, able to simulate its operation in constant current discharge. This model was built on a thorough study of electrochemical mechanisms at work with this type of technology, and its associated thermal effects. It is also based on the synthesis of existing models, and their critique. The new model proposed in this manuscript can take into account two simultaneous electrochemical reactions, as well as the thermal behavior of the cell. The model was validated by comparison between simulation results and the actual electrical performances of a commercial Na-MCl2 cell (including the characterization of electrochemical phenomena by cyclic voltammetry). This model successfully simulates constant current discharges at different rates, and from different temperatures. It is also capable of predicting the electro-thermal effects consecutive to design changes of the cell (structural and relevant to the active material).

La fabrication additive est l’un des secteurs industriels les plus en développent ces dernières années. L’une de ces technologies de fabrication les plus prometteuses est la fusion laser sélective (SLS), et relève d’un intérêt croissant aussi bien industriel qu’académique. Néanmoins, beaucoup de phénomène mis en jeu par ce procédé demeure non encore bien compris, entravant ainsi son développement pour la production de pièces de bonne qualité pour des applications industrielles. L’objectif de cette thèse est de développer un cadre de simulation numérique permettant la simulation du procédé SLS pour des poudres de polymère afin de comprendre les multiples et complexes phénomènes physiques qui se produise lors du frittage laser et d’étudier l’influence des paramètres du procédé sur la qualité du produit final. Contrairement aux approches classiques de modélisation numérique, basées sur la définition de matériaux homogène équivalents pour la résolution des équations de bilan, nous proposons une simulation globale du procédé du frittage laser de poudres, en utilisant la méthode des Eléments Discrets (DEM). Cela consiste en un couplage entre quatre sous-modèles : transferts radiatif dans le milieu granulaire semi-transparent, conduction thermique dans les milieux discrets, coalescence puis densification. Le modèle de transferts par rayonnement concerne l’interaction du faisceau laser avec le lit de poudre. Plusieurs phénomènes sont ainsi pris en compte, notamment la réflexion, la transmission, l’absorption et la réfraction. De plus, une méthode de Monte-Carlo couplée à la méthode du Lancer de rayons est développée afin d’étudier l’influence de la réfraction sur la distribution de l’énergie du laser dans le lit de poudre. Le modèle de conduction dans des milieux discrets décrit la diffusion thermique inter-particules. Finalement, le modèle de frittage décrit les cinétiques de coalescence et de diffusion de l’air dans le polymère et densification du milieu. Cela permet de décrire les cinétiques de fusion des grains, dont l’énergie de surface et la diffusons de l’air sont les deux moteurs principaux. Le couplage entre les différents modèles nous a permis de proposer un modèle numérique global, validé grâce à des comparaisons à des résultats de simulations théoriques et expérimentales, trouvés dans la littérature. Une analyse paramétrique est alors proposée pour la validation du modèle et l’étude du procédé. L’influence de différents paramètres aussi bien du procédé que du matériau sur le champ de température, la densité relative du matériau sa structure, etc , est ainsi investiguée. Les résultats montrent une bonne précision dans la modélisation des différents phénomènes complexes inhérents à ce procédé, et ce travail constitue un potentiel réel pour la modélisation et l’optimisation des procédés de fabrication additive par matériaux granulaires. / Many industrial and academic interests concerning the additive manufacturing processes are developed in the last decades. As one of the most promising technique of additive manufacturing, the Selective Laser Sintering (SLS) has been valued by both industry and academic. However, it remains that several phenomena are still not well understood in order to properly model the process and propose quality improvement of parts made. The goal of this Ph.D. project is to develop a framework of numerical simulation in order to model the SLS process in polymer powder bed, meanwhile understanding multiple physical phenomena occurring during the process and studying the influence of process parameters on the quality of final product. In contrast to traditional approach, based on the equivalent homogeneous material in numerical modeling of partial differential equations derived from conservation laws, we propose a global model to simulate powder-based additive manufacturing by using the Discrete Element method (DEM). It consists in a coupling between four different physical models: radiative heat transfer, discrete heat conduction, sintering and granular dynamics models. Firstly, the submodel of radiative heat transfer concerns the interaction between the laser beam and powder bed. Several phenomena are considered, including the reflection, transmission, absorption and scattering. Besides, a modified Monte Carlo ray-tracing method is developed in order to study the influence of scattering on the distribution of the deposited laser energy inside the powder bed Furthermore, the submodel of discrete heat conduction describes the inter-particles heat diffusion. Moreover, the sintering submodel concerns the phenomena of coalescence and air diffusion. It describes the melting kinetics of grains, driven by surface tension and the release of entrapped gases inside powder bed. Finally, the granular dynamics submodel concerns the motions and contacts between particles when depositing a new layer of powders. The coupling between these submodels leads to propose a global numerical framework, validated by comparing the results to both simulated and experimental ones from literatures. A parametric study is then proposed for model validation and process analysis. The Influence of different material and process parameters on the evolution of temperature, relative density and materials structure and characteristics are investigated. The results exhibit accurate modeling of the complex phenomena occurring during the SLS process, and the work constitute a great potential in modeling and optimization of additive processes.

Les systèmes sur puce sont de plus en plus complexes : ils intègrent des parties numériques, desparties analogiques et des capteurs ou actionneurs. SystemC et son extension SystemC AMSpermettent aujourd’hui de modéliser à haut niveau d’abstraction de tels systèmes. Ces outilsconstituent de véritables atouts dans une optique d’étude de faisabilité, d’exploration architecturale etde vérification du fonctionnement global des systèmes complexes hétérogènes et multiphysiques. Eneffet, les durées de simulation deviennent trop importantes pour envisager les simulations globales àbas niveau d’abstraction. De plus, les simulations basées sur l’utilisation conjointe de différents outilsprovoquent des problèmes de synchronisation. Les modèles de bas niveau, une fois crées par lesspécialistes des différents domaines peuvent toutefois être abstraits afin de générer des modèles dehaut niveau simulables sous SystemC/SystemC AMS en des temps de simulation réduits. Une analysedes modèles de calcul et des styles de modélisation possibles est d’abord présentée afin d’établir unlien avec les durées de simulation, ceci pour proposer un style de modélisation en fonction du niveaud’abstraction souhaité et de l’ampleur de la simulation à effectuer. Dans le cas des circuits analogiqueslinéaires, une méthode permettant de générer automatiquement des modèles de haut niveaud’abstraction à partir de modèles de bas niveau a été proposée. Afin d’évaluer très tôt dans le flot deconception la consommation d’un système, un moyen d’enrichir les modèles de haut niveaupréalablement générés est présenté. L’attention a ensuite été portée sur la modélisation à haut niveaudes systèmes multiphysiques. Deux méthodes y sont discutées : la méthode consistant à utiliser lecircuit équivalent électrique puis la méthode basée sur les bond graphs. En particulier, nous proposonsune méthode permettant de générer un modèle équivalent au bond graph à partir d’un modèle de basniveau. Enfin, la modélisation d’un système éolien est étudiée afin d’illustrer les différents conceptsprésentés dans cette thèse. / Systems on chip are more and more complex as they now embed not only digital and analog parts, butalso sensors and actuators. SystemC and its extension SystemC AMS allow the high level modeling ofsuch systems. These tools are efficient for feasibility study, architectural exploration and globalverification of heterogeneous and multiphysics systems. At low level of abstraction, the simulationdurations are too important. Moreover, synchronization problems appear when cosimulations areperformed. It is possible to abstract the low level models that are developed by the specialists of thedifferent domains to create high level models that can be simulated faster using SystemC/SystemCAMS. The models of computation and the modeling styles have been studied. A relation is shownbetween the modeling style, the model size and the simulation speed. A method that generatesautomatically the high level model of an analog linear circuit from its low level representation isproposed. Then, it is shown how to include in the high level model some information allowing thepower consumption estimation. After that, the multiphysics systems modeling is studied. Twomethods are discussed: firstly, the one that uses the electrical equivalent circuit, then the one based onthe bond graph approach. It is shown how to generate a bond graph equivalent model from a low levelrepresentation. Finally, the modeling of a wind turbine system is discussed in order to illustrate thedifferent concepts presented in this thesis.

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.

Cette thèse porte sur le thème général de la fiabilité des circuits microélectroniques. Le but de notre travail fut de développer un outil de simulation multi-physiques pour la conception des circuits intégrés fiables qui possède les caractéristiques innovatrices suivantes : • (i) L’intégration dans un environnement de conception microélectronique standard, tel que l’environnement Cadence® ; • (ii) La possibilité de simulation, sur de longues durées, du comportement des circuits CMOS analogiques en tenant compte du phénomène de vieillissement ; • (iii) La simulation de plusieurs physiques (électrique-thermique-mécanique) couplées dans ce même environnement de CAO en utilisant la méthode de simulation directe. Ce travail de thèse a été réalisé en passant par trois grandes étapes traduites par les trois parties de ce manuscrit. / This thesis was carried out under the theme of the microelectronics Integrated Circuits Reliability. The aim of our work was to develop a multi-physics simulation tool for the design of reliable integrated circuits. This tool has the following innovative features : • (i) The integration in a standard microelectronics design environment, such as the Cadence® environment ;• (ii) The possibility of efficient simulation, over long periods, of analog CMOS circuits taking into account the aging henomenon ; • (iii) The simulation of multiple physical behaviours of ICs (electrical-thermalmechanical) coupled in the same environment using the direct simulation method. This work was carried out through three main stages detailed in the three parts of this Manuscript.

This thesis is an introduction to the modeling of electromagnetic fields in the tissue and is focused on the knowledge of electromagnetic field theory. Maxwell's equations and their solutions are described the spread of plane waves in the environment. It also discusses the exposure limit values of specific absorbed power and hygienic limits based on the standards in force in the Czech Republic on health protection against nonionizing radiation in accordance with Government Regulation No. 106/2010 Coll. It also deals with the software interface in COMSOL Multiphysics 4.2 for solving physical modeling and simulation. There is mention of the RF module, which is used for modeling. Work mentions in detail about the menu of the program and the most important part - the Model Builder.

Tématem této práce je počítačové modelování organického elektrochemického tranzistoru (OECT). Pro vytvoření modelu bylo třeba vypočítat rozložení elektrického pole a koncentrace iontů elektrolytu. Výpočet byl proveden numericky pomocí metody konečných prvků. Bylo vypočítáno rozložení elektrického potenciálu na povrchu kanálu OECT, dále byly vypočítány změny vodivosti a výstupní proud OECT. Výpočty byly provedeny na osobním počítači pomocí komerčního softwaru COMSOL Multiphysics. Kvůli nedostatečnému výpočetnímu výkonu musel být model rozdělen na části a drasticky zjednodušen. Prezentované výsledky se liší od literatury, protože se nepodařilo správně modelovat saturaci tranzistoru. Odchylky od reálného chování OECT jsou pravděpodobně způsobeny zjednodušením modelu.