Este trabalho apresenta uma metodologia de otimização topológica de atuadores piezelétricos em estruturas compostas laminada com o objetivo de atenuar as vibrações estruturais induzidas por excitações externas. Para isso, utiliza-se técnicas de controle ótimo, como o regulador linear quadrático (LQR) e o controlador linear quadrático gaussiano (LQG). Os estados não mensuráveis são estimados através do uso de observadores de estados de ordem completa, usando o filtro de Kalman para a escolha ótima da matriz de ganhos do observador de estados. O problema de otimização topológica é formulado para a localização ótima do atuador piezelétrico composto MFC (Macro Fiber Composite) na camada ativa da placa, determinando a localização mais vantajosa do material MFC através da maximização do índice de controlabilidade. Para o modelo estrutural, é proposto neste trabalho um modelo para a interação entre o atuador MFC e a estrutura. Assume-se que o MFC é uma das lâminas de material ortotrópico que sofre uma deformação inicial a partir da aplicação de um potencial elétrico e que essa deformação terá efeitos sobre o restante da estrutura. Dessa maneira, não é necessário modelar o campo elétrico gerado através dos eletrodos, uma vez que o efeito eletromecânico é considerado analiticamente. A rigidez e a massa do atuador MFC são considerados no modelo estrutural. Os resultados numéricos mostram que o modelo estrutural proposto para representar a interação entre o atuador MFC e a estrutura apresenta boa concordância com resultados experimentais e numéricos encontrados. Além disso, os resultados mostram que a partir do posicionamento ótimo do atuador MFC na estrutura, a técnica de controle implementada permite atenuar as vibrações estruturais. As simulações para uma força de um degrau unitário permitem concluir que a estratégia de controle usando o controlado LQG apresenta melhor desempenho em termos de tempo de assentamento, sobre resposta, amortecimento e sinal de controle, quando comparado com o controlador LQR. / This work presents a topologic optimization methodology of piezoelectric actuators in laminated composite structures with the objective of controlling external perturbation induced by structural vibrations. The Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) optimal control techniques are used. The states are estimated through of the full order state observers, using the Kalman filter to the observer gain matrix. The topology optimization is formulated to find the optimum localization of the Macro Fiber Composite (MFC) active piezoelectric patch, determining the most advantageous location of the MFC, through of the maximization of the controllability index. For the structural model, this work proposes a simplified MFC/structure interaction model. It is assumed that the MFC is one of the orthotropic material layers which has an initial strain arising from the application of an electric potential; this strain acts on the remainder of the structure. This way, modeling the electromechanical interaction between the piezoelectric material and the electric field is unnecessary because this effect is considered analytically. Both the stiffness and the mass of the MFC are taken into account in the structural model. Numerical results show that proposed MFC-structure interaction model presents good agreement with experiments and numerical simulations of models that uses the electromechanical effect. Actuator location optimization results show that the technique implemented improves the structural vibration damping. The response simulations to an unit step force allows to conclude that the control strategy using the LQG controller presents better performance in terms of settling time, overshoot, damping and control signal energy when compared to the LQR controller.

Cette étude fait partie d'un programme de recherche concernant la réparation de structures composites par collage de patchs externes. Les objectifs principaux de ce programme sont d'une part l'identification de l'ensemble des facteurs susceptibles d’influencer les performances à long terme de ce type de réparation, et d’autre part de déterminer dans quelle mesure l’utilisation de tels assemblages peuvent s'avérer une solution optimale. La conception d'un tel système passe obligatoirement par le développement d'un outil de simulation et de prédiction robuste du fait des divers mécanismes d’endommagement pouvant intervenir de fa?on très complexe et de la rupture finale du système résultant d’une propagation des zones endommagées. Cette étude compose d’une et d’autre l’aspect de la modélisation numérique, et l'aspect expérimental. Le dialogue entre les résultats numériques et expérimentaux permet, d’une part de comprendre les mécanismes d’endommagement et l’évolution de ce dernier dans le système réparé, d’autre part de valider le modèle numérique. En particulier, nos efforts ont été concentrés, en utilisant le logiciel LS-dyna, sur l’application des modèles de zone cohésive (MZC). Le comportement au délaminage d’un composite carbone/époxyde et de l’adhésif sont étudié avec les essais en mode I, mode II et mode mixte. Une étude paramétrique de MZC est effectuée. Le modèle de zone cohésive validé est utilisé pour modéliser le comportement en traction des composites réparés par collage de patches externes / This study is one part of a program of research with regard to the repair of composite structure with extern bonded-patches. The principal objectives of this program are, on one side, the identification of all the factors susceptible to influence the long-term performance of this type of repair, on the other, to determine the extent to which the use of such assemblage can be proved to be an optimal solution. The conception of such a system needs essentially the development of a tool of simulation and of robust prediction because various mechanisms of damage can take place in a very complex way and the final fracture of the system arise from the propagation of damage zones. This study consists of both numerical simulation and experimental aspect which can help us, on one side, understand the mechanisms of damage and its evolution in a repair structure, on the other, valid the numerical model. In particular, we concentrate in the application of cohesive zone model using LS-dyna. The behavior of delamination of carbon/epoxy composite and the adhesive is studied with the experiments in mode I, mode II and mode mixed. A parametric study is carried out. The validated cohesive zone model is used to simulate the tensile behavior of composite repaired by extern bonded-patches

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L’électronisation de l’industrie a mené à l’augmentation de la pollution électromagnétique pouvant être néfaste pour les systèmes électroniques sensibles et les êtres vivants. L’un des moyens pour limiter la propagation des champs électromagnétiques est l’utilisation d’un blindage. L’étude s’est ainsi focalisée sur l’élaboration à froid d’un composite bimétallique pour le blindage magnétique. Le composite étudié allie les propriétés physiques de l’aluminium et de l’acier via le trilame Al8011/AcierDC01/Al8011. Le trilame est élaboré par colaminage à température ambiante. Il s’est avéré que la qualité de l’adhérence des interfaces Al/Acier et l’architecture du trilame dépendent fortement des paramètres du colaminage. Une préparation minutieuse des tôles et de leurs surfaces concomitantes se révèle être tout aussi importante que le colaminage en lui-même. De plus, au cours du colaminage, la tôle d’acier s’est montrée sensible à des instabilités plastiques qui amènent par la suite à sa striction et à sa fragmentation. Ces instabilités plastiques favorisent l’adhérence grâce à des soudages Al/Al mais n’en sont pas un prérequis. Au niveau de l’efficacité de blindage, le trilame s’est révélé être particulièrement intéressant puisque, grâce à sa composition et à sa structuration, il est capable d’atténuer aussi bien les champs magnétiques basses fréquences (< 1 kHz) que les champs magnétiques de plus hautes fréquences (> 1 kHz). Dans une étude à iso-masse, le trilame a présenté une meilleure efficacité de blindage que les tôles d’Al, de Cu et d’acier. Cependant, la fragmentation de l’acier dans le trilame s’est révélée être néfaste pour le blindage magnétique, nécessitant de faire alors un compromis entre tenue mécanique et efficacité de blindage. / The growth of electronic devices has led to an increase in electromagnetic pollution that can be harmful to sensitive electronic systems and living beings. One of the means of limiting the propagation of electromagnetic fields is the use of shielding. Then, the study focused on the elaboration of a bimetallic composite for magnetic shielding. The studied composite combines the physical properties of aluminum and steel via the Al8011/SteelDC01/Al8011 trilayer. The trilayer is produced by cold roll bonding (CRB). It has been found that the adherence quality of the Al/Steel interfaces and the architecture of the composite heavily depend on the CRB parameters. Careful preparation of the sheet and their concomitant surfaces is just as important as CRB itself. Furthermore, during CRB, the steel sheet was sensitive to plastic instabilities which subsequently led to its necking and fragmentation. These plastic instabilities promote adherence through Al/Al welds but are not a prerequisite. In terms of shielding effectiveness, the bimetallic composite has proved to be particularly interesting. Thanks to its composition and its structuring, it can attenuate both low (< 1 kHz) and high frequency (> 1 kHz) magnetic fields. In an iso-mass study, the composite showed a higher shielding effectiveness than Al, Cu and steel sheets. However, the steel fragmentation in the composite proved to be detrimental to magnetic shielding, then requiring a compromise between mechanical strength and shielding effectiveness.

Les composites stratifiés à matrice organique thermodurcissable (TD) et renforts fibreux continus se sont progressivement imposés dans le monde de l’aéronautique depuis bientôt 50 ans. Ces matériaux, malgré de nombreux avantages ayant permis de remplacer les alliages métalliques précédemment utilisés, ont néanmoins un point faible majeur, à savoir une tolérance aux dommages limitée. De nombreuses solutions de renforcement ont vu le jour, dont l’ajout de polymères thermoplastiques (TP) présentant une ductilité supérieure à la matrice TD. Les travaux réalisés concernent une matrice représentative de composites stratifiés employés aujourd’hui. Elle est constituée d’un système époxy-amine menant à un réseau de haute Tg, ainsi que deux TP utilisés comme agents renforçants : un polyéthersulfone (PES) initialement soluble dans le système, et un polyamide (PA) sous forme de microparticules préformées. Un état de l’art sur les mélanges TD/TP cristallins et l’utilisation de TP comme agents renforçants dans les composites stratifiés est présenté en préambule des résultats expérimentaux. L’étude s’est focalisée sur le comportement de ces deux TP vis-à-vis du réseau époxy-amine en construction lors de la polymérisation. L’intérêt porte sur la compréhension des phénomènes reliant les différents composants du mélange entre eux. Dans un premier temps, le comportement du PES dans le système époxy-amine est étudié en fonction des conditions de polymérisation, à savoir le cycle de température appliqué. Le phénomène de séparation de phase induite par polymérisation (RIPS) ayant lieu étant en compétition avec la gélification du réseau TS, et ces deux phénomènes étant liés à la température, différents types de morphologie ont pu être obtenus. L’approche concernant le PA est différente. En effet, ce polymère initialement insoluble dans le système époxy-amine peut être compatibilisé après avoir réagi avec les monomères époxy. De plus, l’affinité physique entre le PA et le durcisseur aminé employé entraîne une modification du comportement du PA à la fusion. Des systèmes binaires modèles époxy-PA et amine-PA ont donc été étudiés pour bien découpler et comprendre toutes ces interactions. Enfin, les morphologies et propriétés résultantes du système époxy-amine modifié simultanément avec le PES et le PA ont été suivies et contrôlées grâce à un choix pertinent de différents cycles de polymérisation. La compréhension du développement d’un mélange si complexe, en termes de morphologie et de mécanismes réactionnels, a été rendue possible grâce aux études préliminaires sur systèmes modèles. / Fiber-reinforced thermosetting (TS) matrix-based composites, and more particularly laminates, have progressively imposed themselves in the aeronautic field for nearly 50 years. Nevertheless, despite numerous advantages making them an elegant solution to replace metallic alloys, such composites have a huge drawback: a low damage tolerance. Various toughening solutions have been developed, including the addition of thermoplastic (TP) polymers which exhibit a much higher ductility than the TS matrix. The present work relates on a representative matrix of currently considered laminates. It is constituted of an epoxy-amine system leading to a high Tg network, and two TP used as reinforcing agents: a polyethersulfone (PES) initially soluble in the system, and a polyamide (PA) preformed in micro-particles. A literature review about TS/semi-crystalline TP blends and TP reinforcement agents used in laminates is given previously to the experimental results. The study focuses on the behavior of these two TP in regard to the growing epoxy-amine network during its polymerization. The interest is put in the understanding of the phenomena linking all the matrix components together. In a first time the PES behavior in the epoxy-amine system dependence on curing conditions (i.e. the applied cure schedule) is studied. The reaction-induced phase separation (RIPS) phenomenon being competitive with the TS network gelation, and taking into account that both phenomena are temperature dependent, various types of morphologies were obtained. Apprehension of PA behavior is different. In fact, this polymer is initially soluble in the epoxy-amine system and may be compatibilized after chemical coupling with epoxy prepolymers. Moreover, physical affinities between PA and the considered amine hardener impact the PA melting behavior. Consequently, binary epoxy-PA and amine-PA model systems have been studied to uncouple and understand all these interactions. Finally, resulting morphologies and properties of the epoxy-amine system, simultaneously modified with both PES and PA, have been monitored and controlled thanks to a choice of suitable cure schedules. The understanding of the development of such a complicated system, in terms of morphologies and curing mechanisms, was made possible thanks to the preliminary studies on the model systems.

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Face aux défis environnementaux actuels, les industriels ont mis en œuvre de nouveaux matériaux recyclables et permettant une réduction significative de la masse. Le développement de la résine thermoplastique Elium par ARKEMA s’inscrit dans cette problématique. L’utilisation de cette résine pour la fabrication de pièces composites qui peuvent être sujettes à des dommages d’impact, nécessite au préalable des études, dans le but de comprendre leurs mécanismes de ruine sous ce type de sollicitation. Ainsi, la présente thèse propose une contribution à l’analyse multi-échelle de la tenue à l’impact des composites stratifiés à base de la résine Elium. Une étude expérimentale préliminaire a permis de confirmer la meilleure résistance à l’impact des composites à matrice Elium acrylique, comparativement à celles des composites thermodurcissables conventionnels. Ensuite, les performances à l’impact des composites stratifiés ont été améliorées par l’introduction de copolymères à blocs dans la matrice. Ces derniers sont capables de former des micelles de tailles nanométriques et ainsi d’améliorer la ténacité de la matrice acrylique. Les effets de l’énergie d’impact, de la température et de la composition en nanocharges sur la réponse du matériau composite ont été analysés. Afin de proposer un outil d’aide à la prédiction de la réponse à l’impact des matériaux fibres de verre/Acrylique, deux stratégies de modélisation ont été retenues. La première modélisation (macroscopique) considère le pli tissé du stratifié comme un matériau homogène tandis que la seconde (mésoscopique) utilise une description géométrique de l’ondulation et de l’entrecroisement des torons noyés dans la résine Elium. Ces deux modèles considèrent des zones cohésives à l’interface entre les plis adjacents pour simuler le délaminage interlaminaire. Des essais de délaminage (expérimentaux et numériques) ont permis d’alimenter le modèle d’endommagement de l’interface interplis. D’autre part, des essais de caractérisation du comportement mécanique et de l’endommagement du matériau couplés à l’homogénéisation multi-échelle des matériaux par la Mécanique du Génome de Structure ont permis d’identifier les paramètres du modèle macroscopique. A l’échelle mésoscopique, le modèle géométrique a été réalisé grâce au logiciel Texgen. Ce logiciel permet d’obtenir une description approchée mais réaliste de l’ondulation des torons de fibres. La même description a servi à l’homogénéisation numérique multi-échelle des stratifiés étudiés. La simulation numérique de l’impact basse vitesse a été effectuée au moyen du logiciel d’éléments finis ABAQUS/Explicit. Les modèles de comportement du matériau ont été implémentés via la routine utilisateur VUMAT. Les résultats obtenus offrent une bonne corrélation avec les données expérimentales / In the race for light materials able of meeting modern environmental challenges, an acrylic resin (Elium) has been developed. Elium is a thermoplastic resin able to replace thermosetting matrices, which are widespread nowadays in the industrial world. The present study aims to evaluate the impact resistance and to understand the failure mechanisms of composite laminates based on acrylic matrix under impact loading. We provide a contribution to the multiscale analysis of the impact resistance of laminated composite.First, the impact resistance and the damage tolerance of the acrylic resin based composites were compared with those of conventional composites. Then, the impact performance of the laminated composites has been enhanced by adding copolymer blocks to the liquid acrylic resin. These copolymers are able to form micelles of nanometer sizes, which lead to the improvement of both the acrylic matrix fracture toughness and the impact resistance. The effects of the impact energy, temperature, and composition in nano-copolymers have also been investigated.In order to provide a numerical tool for the prediction of the impact response of the glass fiber/Acrylic laminates, two strategies have been analyzed. The first one, performed at the macroscopic scale, considers the woven ply of the laminate as homogeneous material, and the second one (at the mesoscopic scale), deals with a realistic geometrical description of the yarns undulation. Both models use cohesive zones at the interface between the adjacent plies, to simulate the delamination. For this purpose, experimental and numerical delamination tests were performed to feed the inter-ply damage model. Mechanical tests for material characterization were also performed on specimens in order to identify the ply-damage model parameters. The Mechanics of Structure Genome (MSG) and a finite element based micromechanics approaches were then conducted to evaluate the effective thermomechanical properties of the yarns and the plain woven composite laminate. The realistic topological and morphological textures of the composite were accounted through Texgen software. These numerical impact simulations were performed using the finite element software ABAQUS/Explicit. Both models were implemented through a user material subroutine VUMAT. The obtained results appear in a good agreement with the experimental data and confirm the relevance of the proposed approach.

Advances in the design and manufacturing technologies have greatly enhanced the utility of fiber reinforced composite materials in aircraft, helicopter and space- craft structural components. The special characteristics of composites such as high strength and stiffness, light-weight corrosion resistance make them suitable sub- stitute for metals/metallic alloys. However, composites are very sensitive to the anomalies induced during their fabrication and service life. Also, they are suscepti- ble to the impact and high frequency loading conditions because the epoxy matrix is at-least an order of magnitude weaker than the embedded reinforced carbon fibers. On the other hand, the carbon based matrix posses high electrical conductivity which is often undesirable. Subsequently, the metal matrix produces high brittleness. Var- ious forms of damage in composite laminates can be identified as indentation, fiber breakage, matrix cracking, fiber-matrix debonding and interply disbonding (delam- ination). Among all the damage modes mentioned above, delamination has been found to be serious for all cases of loading. They are caused by excessive interlaminar shear and normal stresses. The interlaminar stresses that arise in the case of composite materials due to the mismatch in the elastic constants across the plies. Delamination in composites reduce it’s tensile and compressive strengths by consid- erable margins. Hence the knowledge of these stresses is the most important aspect to be looked into. Basic theories like the Euler-Bernoulli’s theory and Timoshenko beam theory are based on many assumptions which poses limitation to determine these stresses accurately. Hence the determination of these interlaminar stresses accurately requires higher order theories to be considered. Most of the conventional methods of determination of the stresses are through the solutions, involving the trigonometric series, which are available only to small and simple problems. The most common method of solution is by Finite Element (FE) Method. There are only few elements existing in the literature and very few in the commercially available finite element software to determine the interlaminar stresses accurately in the composite laminates. Accuracy of finite element solution depends on the choice of functions to be used as interpolating polynomials for the field variable. In-appropriate choice will manifest in the form of delayed convergence. This delayed convergence and accuracy in predicting these stresses necessiates a formulation of elements with a completely new concept. The delayed convergence is sometimes attributed to the shear locking phenomena, which exist in most finite element formulation based on shear deformation theories. The present work aims in developing finite elements based on higher order theories, that alleviates the slow convergence and achieves the solutions at a faster rate without compromising on the accuracy. The accuracy primarily depends on the theory used to model the problem. Thus the basic theories (such as Elementary Beam theory and Timoshenko Beam theory) does not suffice the condition to accuratley determine the interlaminar stresses through the thickness, which is the primary cause for delamination in composites. Two different elements developed on the principle of super-convergence has been presented in this work. These elements are subjected to several numerical experiments and their performance is assessed by comparing the solutions with those available in literature. Spacecraft and aircraft structures are light in weight and are also lightly damped because of low internal damping of the material of construction. This increased exibility may allow large amplitude vibration, which might cause structural instability. In addition, they are susceptible to impact loads of very short duration, which excites many structural modes. Hence, structural dynamics and wave propagation study becomes a necessity. The wave based techniques have found appreciation in many real world problems such as in Structural Health Monitoring (SHM). Wave propagation problems are characterized by high frequency loads, that sets up stress waves to propagate through the medium. At high frequency, the wave lengths are small and from the finite element point of view, the element sizes should be of the same order as the wave lengths to prevent free edges of the element to act as a free boundary and start reflecting the stress waves. Also longer element size makes the mass distribution approximate. Hence for wave propagation problems, very large finite element mesh is an absolute necessity. However, the finite element problems size can be drastically reduced if we characterize the stiffness of the structure accurately. This can accelerate the convergence of the dynamic solution significantly. This can be acheived by the super-convergent formulation. Numerical results are presented to illustrate the efficiency of the new approach in both the cases of dynamic studies viz., the free vibration study and the wave propagation study. The thesis is organised into five chapters. A brief organization of the thesis is presented below, Chapter-1 gives the introduction on composite material and its constitutive law. The details of shear locking phenomena and the interlaminar stress distribution across the thickness is brought out and the present methods to avoid shear locking has been presented. Chapter-2 presents the different displacement based higher order shear deformation theories existing in the literature their advantages and limitations. Chapter-3 presents the formulation of a super-convergent finite element formulation, where the effect of lateral contraction is neglected. For this element static and free vibration studies are performed and the results are validated with the solution available in the open literature. Chapter-4 presents yet another super-convergent finite element formulation, wherein the higher order effects due to lateral contraction is included in the model. In addition to static and free vibration studies, wave propagation problems are solved to demonstrate its effectiveness. In all numerical examples, the super-convergent property is emphasized. Chapter-5 gives a brief summary of the total research work performed and presents further scope of research based on the current research.

This project had two primary goals: (1) to explore opportunities to further a deep-ocean vehicle’s reach using alternative pressure spheres, and (2) to implement an existing deep-ocean vehicle (lander) in active scientific research. I gained a greater understanding of the limitations and design choices made for existing pressure spheres using Finite Element Analysis (FEA). My simplified FEA model predicted sphere failure for the existing 30% Fiber Glass 70% Nylon injection molded spheres at an external pressure of 3,954psi or 2,690m ocean-depth (only a 7.38% error compared to the tested minimum failure depth), so I determined it a valid model. I also explored alternative designs and materials that could be used for pressure spheres in deep-sea applications. Existing pressure sphere models filled with an incompressible fluid failed at 12,670psi or 8,621m ocean-depth - over three times the depth of the same sphere filled with air. Next, I varied the sphere thickness of existing spheres to determine its impact on depth rating. While the increased thickness did provide an increase in depth rating, there were diminishing returns as the sphere was made thicker. I deemed both of these design options infeasible for our application. To consider the use of laminated composite spheres, the addition of an equatorial ring was required to manufacture O-ring seals safely and reliably. A simple cylindrical equatorial ring model using a stainless-steel ring had a predicted failure at 3,017psi or 2,053m ocean-depth. While this model predicted failure at 637m shallower than the sphere without the ring, it was the only ring material tested to reach the rated depth for the existing pressure spheres (2km), so I concluded stainless-steel is the best ring material. A spherical stainless-steel equatorial ring design was then analyzed which predicted failure at 3,915psi or 2,664m ocean-depth – only 8.3% less than the original sphere with no ring. Because of its successful performance and near identical results to the original model, I determined a stainless-steel spherical equatorial ring is the best option for laminated composite sphere sealing. Finally, I analyzed three different kinds of laminated composite pressure spheres: two carbon fiber and one fiber glass. Each laminate was designed to be quasi-isotropic and as close to 0.8” thick as possible to keep it consistent with the original sphere design. The sphere made of 584 Carbon Fiber with a lay-up of: [[-45/45/0/90]6]s was found to predict failure at 10,000psi or 6,804m ocean-depth, more than 2.5 times that of the original sphere. Next, a model made of 282 Carbon Fiber with a lay-up of: [[-45/45/0/90]11]s predicted failure at 9,242psi or 6,289m ocean-depth – more than 2.3 times as deep as the original pressure spheres. Lastly, a sphere of 7781 Fiber Glass with a lay-up of: [[-45/45/0/90]11]s predicted failure at 6,630psi or 4,511m ocean-depth – about two-thirds the depth of the 584 Carbon Fiber composite, but more than 1.6 times the depth of the original sphere. While real-life applications of these materials would include design modifications and manufacturing imperfections which would lower their maximum depth rating, these results are highly encouraging and show that all three materials could be viable options for future production. Additionally, through partnership with Dr. Crow White and his marine science undergraduate students, I completed numerous deployments for a Before and After Controlled Impact (BACI) study on the area of the proposed windfarm off the coast of Morro Bay, CA. Many modifications were made to the existing lander which enabled it to successfully be implemented in these studies including a new bait containment unit, light color filters, a GPS tracking device, and a large vessel recovery device. A total of 5 pier deployments and 3 boat deployments were conducted by my team over the course of 6-months. Planning for these deployments included accounting for budgeting, weather, permitting, and multi-organizational logistics while working with both NOAA and the Cal Poly marine operations staff.