The work herein is, in part, motivated by the idea of creating optimized, actuating structures using additive manufacturing processes (AM). By developing a consistent, repeatable method for designing and manufacturing multi-material compliant mechanisms, significant performance improvements can be seen in application, such as increased mechanism deflection. There are three distinct categories of research that contribute to this overall motivating idea: 1) investigation of an appropriate multi-material topology optimization process for multi-material jetting, 2) understanding the role that manufacturing constraints play in the fabrication of complex, optimized structures, and 3) investigation of an appropriate process for embedding actuating elements within material jetted parts. PolyJet material jetting is the focus of this dissertation research as it is one of the only AM processes capable of utilizing multiple material phases (e.g., stiff and flexible) within a single build, making it uniquely qualified for manufacturing complex, multi-material compliant mechanisms. However, there are two limitations with the PolyJet process within this context: 1) there is currently a dearth of understanding regarding both single and multi-material manufacturing constraints in the PolyJet process and 2) there is no robust embedding methodology for the in-situ embedding of foreign actuating elements within the PolyJet process. These two gaps (and how they relate to the field of compliant mechanism design) will be discussed in detail in this dissertation. Specific manufacturing constraints investigated include 1) "design for embedding" considerations, 2) removal of support material from printed parts, 3) self-supporting angle of surfaces, 4) post-process survivability of fine features, 5) minimum manufacturable feature size, and 6) material properties of digital materials with relation to feature size. The key manufacturing process and geometric design factors that influence each of these constraints are experimentally determined, as well as the quantitative limitations that each constraint imposes on design. / Ph. D.

Cellular mechanical metamaterials (CMMs) are a special class of materials that consist of microstructural architectures of macroscopic hierarchical frameworks that can have extraordinary properties. These properties largely depend on the topology and arrangement of the unit cells constituting the microstructure. The material hierarchy facilitates the synthesis and design of CMMs on the micro-scale to achieve enhanced properties (i.e., improved strength, toughness, low density) on the component (macro)-scale. However, designing on-demand cellular metamaterials usually requires solving a challenging inverse problem to explore the complex structure-property relations. The first part of this study (Ch. 3) proposes an experience-free and systematic design methodology for microstructures of CMMs using an advanced stochastic searching algorithm called micro-genetic algorithm (μGA). Locally, this algorithm minimizes the computational expense of the genetic algorithm (GA) with a small population size and a conditionally reduced parameter space. Globally, the algorithm employs a new search strategy to avoid local convergence induced by the small population size and the complexity of the parameter space. What's more, inspired by natural evolution in the GA, this study applies the inverse design method with the standard GA (sGA) as a sampling algorithm for intuitively mapping material-property spaces of CMMs, which requires the selection of objective properties and stochastic search of property points within the property space. The mapping methodology utilizing the sGA is proposed in the second part of the study (Ch. 4). This methodology involves a robust strategy that is shown to identify more comprehensive property spaces than traditional mapping approaches. The resulting property space allows designers to acknowledge the limitations of material performance, and select an appropriate class of CMMs based on the difficulty of the realization and fabrication of their microstructures. During the fabrication process, manufacturing defects cause uncertainty in the microstructures, and thus the structural properties. The third part of the study (Ch. 5) investigates the effects of the uncertainty stemming from manufacturing defects on the material property space. To accelerate the uncertainty quantification (UQ) via the Monte Carlo method, this study utilizes a machine learning technique to bypass the expensive simulations to compute properties. In addition to reducing the computational expense of the simulations, the deep learning method has been proven to be practical to accomplish non-intuitive design tasks. Due to the numerous combinations of properties and complex underlying geometries of metamaterials, it is numerically intractable to obtain optimal material designs that satisfy multiple user-defined performance criteria at the same time. Nevertheless, a deep learning method called conditional generative adversarial networks (CGANs) is capable of solving this many-to-many inverse problem. The fourth part of the study (Ch. 6) proposes a new inverse design framework using CGANs to overcome this challenge. Given combinations of target properties, the framework can generate a group of geometric patterns providing these target properties. Therefore, the proposed strategy provides alternative solutions to satisfy on-demand requirements while increasing the freedom in the fabrication process. Besides, with the advances in additive manufacturing (AM), the design space of an engineering material can be further enlarged by multi-scale topology optimization. As the interplay between microstructure and macrostructure drives the overall mechanical performance of engineering materials, it is necessary to develop a multi-scale design framework to optimize structural features in these two scales simultaneously. The final part of the study (Ch. 7) presents a concurrent multi-scale topology optimization method of CMMs. Structures in micro and macro scales are optimized concurrently by utilizing sequential quadratic programming (SQP) with the Solid Isotropic Material with Penalization (SIMP) method and a numerical homogenization approach. / Doctor of Philosophy / Cellular materials widely exist in natural biological systems such as honeycombs, bones, and wood. Recent advances in additive manufacturing have enabled us to fabricate these materials with high precision. Inspired by architectures in nature, cellular mechanical metamaterials (CMMs) have been introduced recently as a new class of architected systems. The materials are formed by hierarchical microstructural topologies, which have a decisive influence on the structural performance at the macro-scale. Therefore, the design of these materials primarily focuses on the geometric arrangement of their microstructures rather than the chemical composition of their base material. Tailoring the microstructures of these materials can lead to several outstanding features, such as high stiffness and strength, low density, and high energy absorption. However, it is challenging to design microstructures that satisfy user-defined requirements for properties and material costs. This is mainly due to the trade-off between the accuracy and computing times of the optimization process. In the first part of this study (Ch. 3), a design framework is proposed to overcome this issue. The framework employs a global search algorithm called the genetic algorithm (GA). With a newly designed search algorithm, the framework reduces errors between target and optimized material properties while improving computational efficiency. Inspired by the algorithm behind the GA, the second part of the study (Ch. 4) employs a similar algorithm to identify a material property chart demonstrating all possible combinations of mechanical properties of CMMs. Each axis of the material property chart corresponds to a selected mechanical property, such as Young's modulus or Poisson's ratio, along different directions. The boundary of the property space helps designers understand material performance limitations and make informed decisions in engineering practices. In the fabrication process, unexpected material properties might be achieved due to defects and tolerances in additive manufacturing (AM), such as uneven surfaces, shrinkage of pores, etc. The third part of the study (Ch. 5) investigates the uncertainty propagation on mechanical properties as a result of these manufacturing defects. To investigate the uncertainty propagation problem efficiently, the study uses a deep learning method to predict the variations (stochasticity) of properties. Consequently, the material property space boundary also varies with the uncertainty of properties. In addition to their computational efficiency, deep learning methods are beneficial for solving many-to-many inverse design problems. Traditionally, the global and local search/optimization methods retrieve alternative optimal solutions in their Pareto front set, where each solution is considered to be equally good. A deep learning method called conditional generative adversarial networks (CGANs) can bypass the property calculation to accelerate the simulation process while obtaining a group of candidates with on-demand properties. The fourth part of the study (Ch. 6) employs CGANs to build a new inverse design framework to increase flexibility in the fabrication process by generating alternative solutions for the microstructures of CMMs. Besides, as fabrication technologies have advanced, designing engineering systems has become increasingly complex. Material design is now not only focused on meeting micro-scale requirements but also addressing needs at multiple scales. The interaction between the microstructure (small-scale) and macrostructure (large-scale) significantly influences the overall performance of engineering systems. To optimize structures effectively, there is a need for a design framework that considers these two scales simultaneously. Thus, the final part of the study (Ch. 7) introduces a method called concurrent multi-scale topology optimization. To obtain the extreme performance of a multi-scale structure, this approach optimizes its structure at both micro- and macro-scales concurrently, using gradient-based optimization algorithms with density-based property determination methods in the two scales.

This thesis considers applications of gradient-based optimization algorithms to the design and control of some mechanics systems. The material distribution approach to topology optimization is applied to design two different acoustic devices, a reactive muffler and an acoustic horn, and optimization is used to control a ball pitching robot. Reactive mufflers are widely used to attenuate the exhaust noise of internal combustion engines by reflecting the acoustic energy back to the source. A material distribution optimization method is developed to design the layout of sound-hard material inside the expansion chamber of a reactive muffler. The objective is to minimize the acoustic energy at the muffler outlet. The presence or absence of material is represented by design variables that are mapped to varying coefficients in the governing equation. An anisotropic design filter is used to control the minimum thickness of materials separately in different directions. Numerical results demonstrate that the approach can produce mufflers with high transmission loss for a broad range of frequencies. For acoustic devices, it is possible to improve their performance, without adding extended volumes of materials, by an appropriate placement of thin structures with suitable material properties. We apply layout optimization of thin sound-hard material in the interior of an acoustic horn to improve its far-field directivity properties. Absence or presence of thin sound-hard material is modeled by a surface transmission impedance, and the optimization determines the distribution of materials along a “ground structure” in the form of a grid inside the horn. Horns provided with the optimized scatterers show a much improved angular coverage, compared to the initial configuration. The surface impedance is handled by a new finite element method developed for Helmholtz equation in the situation where an interface is embedded in the computational domain. A Nitschetype method, different from the standard one, weakly enforces the impedance conditions for transmission through the interface. As opposed to a standard finite-element discretization of the problem, our method seamlessly handles both vanishing and non-vanishing interface conditions. We show the stability of the method for a quite general class of surface impedance functions, provided that possible surface waves are sufficiently resolved by the mesh. The thesis also presents a method for optimal control of a two-link ball pitching robot with the aim of throwing a ball as far as possible. The pitching robot is connected to a motor via a non-linear torsional spring at the shoulder joint. Constraints on the motor torque, power, and angular velocity of the motor shaft are included in the model. The control problem is solved by an interior point method to determine the optimal motor torque profile and release position. Numerical experiments show the effectiveness of the method and the effect of the constraints on the performance.

For the purpose of numerically simulating continuum mechanical structures, different types of material may be represented by the extreme values {<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cepsilon" />,1}, where 0&lt;<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cepsilon" /><img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cll" />1, of a varying coefficient <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Calpha" /> in the governing equations. The paramter <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cepsilon" /> is not allowed to vanish in order for the equations to be solvable, which means that the exact conditions are approximated. For example, for linear elasticity problems, presence of material is represented by the value <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Calpha" /> = 1, while <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Calpha" /> = <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cepsilon" /> provides an approximation of void, meaning that material-free regions are approximated with a weak material. For acoustics applications, the value <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Calpha" /> = 1 corresponds to air and <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Calpha" /> = <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cepsilon" /> to an approximation of sound-hard material using a dense fluid. Here we analyze the convergence properties of such material approximations as <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cepsilon" />!0, and we employ this type of approximations to perform design optimization. In Paper I, we carry out boundary shape optimization of an acoustic horn. We suggest a shape parameterization based on a local, discrete curvature combined with a fixed mesh that does not conform to the generated shapes. The values of the coefficient <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Calpha" />, which enters in the governing equation, are obtained by projecting the generated shapes onto the underlying computational mesh. The optimized horns are smooth and exhibit good transmission properties. Due to the choice of parameterization, the smoothness of the designs is achieved without imposing severe restrictions on the design variables. In Paper II, we analyze the convergence properties of a linear elasticity problem in which void is approximated by a weak material. We show that the error introduced by the weak material approximation, after a finite element discretization, is bounded by terms that scale as <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cepsilon" /> and <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cepsilon" />1/2hs, where h is the mesh size and s depends on the order of the finite element basis functions. In addition, we show that the condition number of the system matrix scales inversely proportional to <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cepsilon" />, and we also construct a left preconditioner that yields a system matrix with a condition number independent of <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cepsilon" />. In Paper III, we observe that the standard sound-hard material approximation with <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Calpha" /> = <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cepsilon" /> gives rise to ill-conditioned system matrices at certain wavenumbers due to resonances within the approximated sound-hard material. To cure this defect, we propose a stabilization scheme that makes the condition number of the system matrix independent of the wavenumber. In addition, we demonstrate that the stabilized formulation performs well in the context of design optimization of an acoustic waveguide transmission device. In Paper IV, we analyze the convergence properties of a wave propagation problem in which sound-hard material is approximated by a dense fluid. To avoid the occurrence of internal resonances, we generalize the stabilization scheme presented in Paper III. We show that the error between the solution obtained using the stabilized soundhard material approximation and the solution to the problem with exactly modeled sound-hard material is bounded proportionally to <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cepsilon" />.

<div>The rapid development of topology optimization in photonics has greatly expanded the number of photonic structures with extraordinary performance. The optimization is usually solved by using a gradient-based optimization algorithm, where gradients are evaluated by the adjoint sensitivity analysis. While the adjoint sensitivity analysis has been demonstrated to provide reliable gradients for designs of dielectrics, there has not been too much success in plasmonics. The difficulty of obtaining accurate field solutions near sharp edges and corners in plasmonic structures, and the strong field enhancement jointly increase the numerical error of gradients, leading to failure of convergence for any gradient-based algorithm. </div><div> </div><div>We present a new method of calculating accurate sensitivity with the FDTD method by direct differentiation of the time-marching system in frequency domain. This new method supports general frequency-domain objective functions, does not relay on implementation details of the FDTD method, works with general isotropic materials and can be easily incorporated into both level-set-based and density-based topology optimizations. The method is demonstrated to have superior accuracy compared to the traditional continuous sensitivity. Next, we present a framework to carry out density-based topology optimization using our new sensitivity formula. We use the non-linear material interpolation to counter the rough landscape of plasmonics, adopt the filteringand-projection regularization to ensure manufacturability and perform the optimization with a continuation scheme to improve convergence. </div><div> </div><div>We give two examples involving reconstruction of near fields of plasmonic structures to illustrate the robustness of the sensitivity formula and the optimization framework. In the end, we apply our method to generate a rectangular temperature profile in the recording medium of the HAMR system. </div>

Les échangeurs de chaleur sont des dispositifs largement utilisés dans divers systèmes énergétiques. Les présents travaux de recherche s’intéressent à la conception des échangeurs bi-fluides monophasiques par des méthodes d’optimisation topologique. A la différence des méthodes conventionnelles d’optimisation de taille et de forme, ces méthodes permettent une liberté de conception plus grande et ne nécessitent aucune définition a priori de la géométrie de l’échangeur. L’optimisation topologique bi-fluide consiste donc à réorganiser librement deux fluides et un solide dans un domaine d’optimisation. Les deux fluides doivent connecter les zones d’entrée aux zones de sortie en évitant tout mélange entre fluides. Dans le cadre de cette thèse, la méthode SIMP « Solid Isotropic Material with Penalization » a été utilisée. Divers algorithmes constituant cette méthode ont été formulés et testés : la méthode des volumes finis a été choisie pour la résolution du problème direct, la méthode des adjoints discrets pour le calcul du gradient de la fonction objectif et enfin la méthode des asymptotes mobiles pour guider l’optimisation numérique. Les résultats des simulations ont permis de définir différentes formes d’échangeurs de chaleur en 2D. On a fait varier le nombre d’entrées et de sorties ainsi que les débits de chaque fluide. Les travaux montrent la capacité de cette méthode à concevoir des formes innovantes d’échangeur de chaleur. La thèse établit ainsi les bases d’une nouvelle méthode de conception des échangeurs de chaleur. / Heat exchangers are devices widely used in various energy systems. The present research work focuses on the design of single-phase bi-fluid heat exchangers by using topology optimization methods. Unlike conventional size and shape optimization methods, topology optimization methods allow greater design freedom and do not require prior definition of the exchanger geometry. Hence, bi-fluid topology optimization consists of freely reorganizing two fluids and one solid in the optimization domain. Both fluids should connect inlet sections to outlet sections while avoiding any fluid mixture inside the domain. SIMP method “Solid Isotropic Material with Penalization” is used within the framework of this thesis. This method includes various algorithms that were formulated and tested : finite volume method was selected for solving the direct physical problem, discrete adjoint method was used for the calculation of the gradient of the objective function, and the method of moving asymptotes was adopted to guide the numerical optimization. Simulation results have allowed the definition of various heat exchanger shapes in 2D. The number of inlet and outlet as well as the flow rates of each fluid have been varied. The works have shown the ability of this method to design innovative shapes of heat exchangers. Hence, the thesis establishes the basis of a new design methodology of heat exchangers.

Filtros modais permitem que se identifique a contribuição de cada modo de vibrar na resposta dinâmica de uma estrutura, o que pode simplificar o projeto de sistemas dinâmicos em diversas aplicações como controle de vibrações, controle de forma, monitoramento de integridade estrutural e aproveitamento de energia. O objetivo desta dissertação é desenvolver uma metodologia para projetar e otimizar filtros modais a partir de uma rede de sensores piezelétricos discretos. É de especial interesse a relação entre a topologia da rede de sensores e o desempenho dos filtros modais obtidos pela soma ponderada dos sinais de tensão elétrica medida por cada sensor. A modelagem estrutural, usando o método dos elementos finitos com acoplamento eletromecânico, considera uma placa retangular de alumínio com trinta e seis sensores piezelétricos, em forma de pequenas pastilhas, colados sobre uma de suas superfícies. As topologias de rede consideradas neste trabalho consistem das possíveis combinações de trinta e seis sensores tomados doze a doze. Esta estratégia permite um amplo processo de otimização topológica a partir de um único modelo de elementos finitos. Duas funções-objetivo definem os índices de desempenho de cada topologia de rede avaliada, objetivando projetar filtros modais capazes de isolar a resposta dos primeiros modos de vibrar que maximizem a faixa de frequência e minimizem o número de sensores necessários. Em uma primeira abordagem ao problema de otimização topológica combinatorial, é utilizado o método de busca extensiva em um espaço de soluções reduzido. Em seguida, o problema é codificado para o uso de um algoritmo genético. Os resultados mostram que aumentos de 25% a 50% na faixa de frequência dos filtros modais podem ser obtidos a partir da otimização topológica da rede de sensores. / Modal filters allow identifying the contribution of each vibration mode to the dynamical response of a structure, which can simplify the design of dynamical systems in several applications, such as vibration control, shape control, structural health monitoring and energy harvesting. The aim of this dissertation is to develop a methodology to design and optimize modal filters by using a discrete array of piezoelectric sensors. The relationship between the sensors array topology and the performance of the modal filters, which are obtained by means of weighted sum of the voltage signs, draws special interest. The structural modeling through the finite element method with electromechanical coupling considers a retangular aluminum plate with thirty-six patch-shaped piezoelectric sensors bonded on one of its surfaces. The array topologies considered in this work consist of the possible combinations of thirty-six sensors taken twelve at a time. This strategy allows for a broad process of topological optimization by using only one finite element model. Two objective functions define the performance index associated with each evaluated array topology, aiming to design modal filters able to isolate the response of the first vibration modes that maximize the frequency band and minimize the number of sensors needed. As a first approach to the combinatorial topology optimization problem, the extensive search method is applied to a reduced solutions space. Next, the optimization problem is codified for using a genetic algorithm. The results show that an increase from 25% to 50% in the frequency band of the modal filters can be obtained from the topology optimization of the sensors array.

Transdutores baseados em cascas piezocompósitas têm uma vasta aplicação no campo de estruturas inteligentes, principalmente como atuadores, sensores e coletores de energia. Essas estruturas piezocompósitas são geralmente compostas por dois ou mais tipos de materiais, como por exemplo materiais piezelétricos, ortotrópicos elásticos (possuem fibras de reforçamento) e isotrópicos (materiais homogêneos). Vários fatores devem ser considerados no projeto de transdutores baseados em cascas piezocompósitas, como o tamanho, a forma, a localização e a polarização do material piezelétrico, bem como a orientação das fibras do material ortotrópico. O projeto desses transdutores é complexo e trabalhos anteriores envolvendo esses tipos de materiais sugerem utilizar Método de Otimização Topológica (MOT) para aprimorar o desempenho dos transdutores distribuindo o material piezelétrico sobre substratos fixos de materiais isotrópicos e ortotrópicos, ou otimizar a orientação das fibras dos materiais ortotrópicos com material piezelétrico com tamanho, forma e localização previamente estabelecidos. Assim, nesta tese, propõe-se o desenvolvimento de uma metodologia baseada no MOT para projetar transdutores piezocompósitos de casca considerando, simultaneamente, a otimização da distribuição e do sentido de polarização do material piezelétrico, e também a otimização da orientação das fibras de materiais ortotrópicos, que é livre para assumir valores diferentes ao longo da mesma camada compósita. Utilizando essa metodologia, são obtidos resultados numéricos para atuadores e sensores em regime estático e para coletores de energia com circuito elétrico acoplado, em regime dinâmico amortecido. Para os casos dos sensores e dos coletores de energia, também são consideradas as tensões mecânicas na estrutura, as quais devem obedecer os critérios de von Mises (para materiais isotrópicos) e de Tsai-Wu (para materiais ortotrópicos) para que não haja falhas na estrutura, que está sujeita a esforços mecânicos. / Transducers based on laminated piezocomposite shell structures have a wide application in the field of smart structures, especially as actuators, sensors and energy harvesting devices. These piezocomposite structures are generally composed by two or more kinds of materials, such as piezoelectric, isotropic, and elastic orthotropic (fiber reinforcement) materials. Several factors must be considered in the design of piezocomposite transducers, such as size, shape, location and polarization of the piezoelectric material and the fiber orientation of the orthotropic material. The design of these transducers is complex and previous studies involving these types of materials suggest using \"Topology Optimization Method\" (TOM) to enhance the performance of piezoelectric transducers by distributing piezoelectric material over fixed isotropic and orthotropic substrate or to optimize the fiber orientation of orthotropic materials with piezoelectric patches previously established. Thus, this thesis proposes the development of a methodology based on the TOM to design laminated piezocomposite shell transducers by considering simultaneously the optimization of distribution and the polarization direction of the piezoelectric material, and also the optimization of the fiber orientation orthotropic material, which is free to assume different values along the same composite layer. By using this methodology, numerical results are obtained for actuators and sensors under static response, and energy harvesting devices with an electrical circuit coupled, in dynamic damped analysis. In the case of sensors and energy harvesting devices, which are subjected to mechanical loads, the mechanical stresses in the structure are also considered, which must satisfy two stress criteria to prevent failure: von Mises for isotropic materials and Tsai-Wu for orthotropic materials.

O presente trabalho trata da formulação e implementação de modelos numéricos baseados no Método dos Elementos de Contorno (MEC). Inspirando-se em problemas de engenharia, uma abordagem multidisciplinar é proposta como meio de representação numérica mais realista. Há materiais de uso corrente na engenharia que possuem resposta dependente do tempo. Nesta tese os fenômenos dependentes do tempo são abordados por meio da Mecânica Viscoelástica Linear associada a modelos reológicos. Neste trabalho, se apresenta a dedução do modelo constitutivo de Maxwell para ser utilizado via MEC. As equações deduzidas são verificadas em problemas de referência. Os resultados mostram que a formulação deduzida pode ser utilizada para representar estruturas compostas, mesmo em casos envolvendo uma junção entre materiais viscoelásticos e não viscoelásticos. Adicionalmente as formulações apresentadas se mantém estáveis na presença de fissuras de domínio e bordo. Verifica-se que a formulação clássica dual pode ser utilizada para simular o comportamento de fissuras com resposta dependente do tempo. Essa constatação serve de base para maiores investigações no campo da Mecânica da Fratura de materiais viscoelásticos. Na sequência, mostra-se como o MEC pode ser aliado a conceitos probabilísticos para fazer estimativas de comportamentos a longo prazo. Estas estimativas incluem as incertezas inerentes nos processos de engenharia. As incertezas envolvem os parâmetros materiais, de carregamento e de geometria. Por meio do conceito de probabilidade de falha, os resultados mostram que as incertezas relacionadas às estimativas das cargas atuantes apresentam maior impacto no desempenho esperado a longo prazo. Esta constatação serve para realizar estudos que colaborem para a melhoria dos processos de concepção estrutural. Outro aspecto de interesse desta tese é a busca de formas otimizadas, por meio da Otimização Topológica. Neste trabalho, um algoritmo alternativo de otimização topológica é proposto. O algoritmo é baseado no acoplamento entre o Método Level Set (MLS) e o MEC. A diferença entre o algoritmo aqui proposto, e os demais presentes na literatura, é forma de obtenção do campo de velocidades. Nesta tese, os campos normais de velocidades são obtidos por meio da sensibilidade à forma. Esta mudança torna o algoritmo propício a ser tratado pelo MEC, pois as informações necessárias para o cálculo das sensibilidades residem exclusivamente no contorno. Verifica-se que o algoritmo necessita de uma extensão particular de velocidades para o domínio a fim de manter a estabilidade. Limitando-se a casos bidimensionais, o algoritmo é capaz de obter os conhecidos casos de referência reportados pela literatura. O último aspecto tratado nesta tese retrata a maneira pela qual as incertezas geométricas podem influenciar na determinação das estruturas otimizadas. Utilizando o MEC, propõe-se um critério probabilístico que permite embasar escolhas levando em consideração a sensibilidade geométrica. Os resultados mostram que os critérios deterministas, nem sempre, conduzem às escolhas mais adequadas sob o ponto de vista de engenharia. Assim, este trabalho contribui para a expansão e difusão das aplicações do MEC em problemas de engenharia de estruturas. / The present work deals with the formulation and implementation of numerical models based on the Boundary Element Method (BEM). Inspired by engineering problems, a multidisciplinary combination is proposed as a more realistic approach. There are common engineering materials that have time-dependent response. In this thesis, time-dependent phenomena are approached through the Linear Viscoelastic Mechanics associated with rheological models. In this work, the formulation of Maxwell\'s constitutive model is presented to be used via MEC. The resultant equations are checked on reference problems. The results show that the presented formulation can be used to represent composite structures, even in cases involving a junction between viscoelastic and non-viscoelastic materials. Additionally the formulations presented remain stable in the presence of cracks. It is found that the classical DUAL-BEM formulation can be used to simulate cracks with time-dependent behaviour. This result serves as the basis for further investigations in the field of Fracture Mechanics of viscoelastic materials. In the sequence, it is shown how the BEM can be associated with probabilistic concepts to make predictions of long-term behaviour. These predictions include the inherent uncertainties in engineering processes. The uncertainties involve the material, loading and geometry parameters. Using the concept of probability of failure, the results show that the uncertainties related to the estimations of loads have important impact on the long-term expected performance. This finding serves to carry out studies that collaborate for the improvement of structural design processes. Another aspect of interest of this thesis is the search for optimized forms through Topological Optimization. In this work, an alternative topological optimization algorithm is proposed. The algorithm is based on the coupling between the Level Set Method (LSM) and BEM. The difference between the algorithm proposed here, and the others present in the literature, is a way of obtaining the velocity field. In this thesis, the normal fields of velocities are obtained by means of shape sensitivity. This change makes the algorithm adequate to be treated by the BEM, since the information necessary for the calculation of the sensitivities resides exclusively in the contour. It is found that the algorithm requires a particular velocity extension in order to maintain stability. Limiting to two-dimensional cases, the algorithm is able to obtain the known benchmark cases reported in the literature. The last aspect addressed in this thesis involves the way in which geometric uncertainties can influence the determination of optimized structures. Using the BEM, it is proposed a probabilistic criterion that takes into consideration the geometric sensitivity. The results show that deterministic criteria do not always lead to the most appropriate choices from an engineering point of view. In summary, this work contributes to the expansion and diffusion of MEC applications in structural engineering problems.

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.