De nos jours, de nombreuses pièces mécaniques sont fabriquées en polymères. Ces matériaux présentent un comportement complexe très sensible à la vitesse de déformation et à la température. De nombreux modèles de comportement mécanique, tenant compte de cette double sensibilité, ont été développés au cours des dernières années dans le but de décrire le comportement élasto-viscoplastique des polymères en grandes déformations sur de larges plages de vitesses de déformation et de températures. Afin de prévoir la tenue de pièces mécaniques en polymère soumises à un ensemble de sollicitations complexes, l'utilisation de méthodes numériques, telles que la méthode des Éléments Finis (EF), s'avèrent incontournables. Cependant, la qualité de la prévision numérique est fortement dépendante de la loi de comportement utilisée. Ainsi, nous proposons d'étudier deux modèles de comportement qui ont été introduits dans deux codes de calcul par EF : un modèle phénoménologique simple, introduit dans CAST3M, et un modèle micromécanique, introduit dans ABAQUS/Explicit. Le modèle phénoménologique permet de modéliser le comportement mécanique des polymères vitreux en petites déformations sur une plage de vitesses de déformation et de températures réduite. Un essai de compression reproduisant le dispositif des barres d'Hopkinson a été simulé pour plusieurs vitesses de déformation et températures. Une bonne corrélation a été trouvée entre résultats expérimentaux et les prévisions numériques. De plus, de rapides estimations du coefficient de Taylor-Quinney et de la contrainte à l'interface, liée au frottement entre l'échantillon et les barres de compression, ont pu être trouvées. Le modèle micromécanique décrit le comportement des polymères amorphes en grandes déformations sur de larges gammes de vitesses de déformation et de températures. Il a été développé au sein de notre équipe de recherche par Richeton et al. [Int. J. Solids Struct. 44 (2007) 7938] et propose une dépendance à la vitesse de déformation et à la température de différentes propriétés matériau (module élastique, contrainte seuil, durcissement structural). Afin de modéliser le comportement de structures polymères soumises à des chargements dynamiques ou à de la mise en forme, un sous-programme VUMAT est écrit. Après validation de l'intégration numérique du sous-programme sur des essais de compression/traction simple, deux applications ont été simulées. La première application a consisté en la modélisation d'un essai d'impact d'une plaque polymère par un projectile hémisphérique. La seconde application est un essai de forgeage à froid. Dans les deux cas, les prévisions numériques sont en accord avec les résultats expérimentaux issus de la littérature. / Nowadays, numerous structural parts are made in polymeric materials. These materials exhibit a complex behavior strongly sensitive to strain rate and temperature. Numerous constitutive equations have been developed during the last decades in order to describe the elastic-viscoplastic behavior of polymers in finite strain for a wide range of strain rates and temperature. To provide for the holding of mechanical parts polymer subject to a complex set of loads, the use of numerical methods, such as Finite Element (FE) method, is unavoidable. However, the quality of the numerical prediction is strongly dependent to the used constitutive equations. Thus, we proposed to study two models of mechanical behavior implemented in two FE softwares: a simple phenomenological model, introduced in CAST3M, and a micromechanical model, introduced in ABAQUS/Explicit. The phenomenological model allows simulating the mechanical behavior of glassy polymers in small strains over a reduced range of strain rates and temperatures. A compressive test reproducing the Split Hopkinson Pressure Bar device is simulated for several strain rates and temperatures. A good correlation is found between experimental results and numerical predictions. Moreover, an estimation of Taylor-Quinney coefficient and the interfacial stress, due to the friction between the polymer sample and the compressive bars, have been found. The micromechanical model describes the mechanical behavior of amorphous polymers in finite strain over a wide range of strain rates and temperatures. It has been developed in our research team by Richeton et al. [Int. J. Solids Struct. 44 (2007) 7938] and proposes to take into account the strain rate and temperature dependence of various material properties (elastic modulus, yield stress, orientational hardening). In order to simulate the mechanical behaviour of polymeric structures under dynamic loadings or during forming processes, a VUMAT subroutine is written. After validation of the numerical implementation of the VUMAT subroutine for simple compressive/tensile tests, two applications were simulated. The first application is a normal impact test of a polymeric plate by a hemispherical projectile. The second application is a cold forging test. In both cases, numerical predictions are in agreement with the experimental results from the literature.

Dans le cadre des opérations de perçage, les billettes en acier subissent un réchauffage de la température ambiante à une température d’environ 1250°C. Au cours de ce réchauffage, le gradient de température dans les billettes entraîne la détérioration de la santé axiale de celles-ci et est à l’origine de l’apparition de défauts sur le tube formé. Une méthodologie d’analyse des mécanismes à l’origine de ces défauts a été mise en place. Elle se base sur la caractérisation de la santé axiale par essais rhéologiques permettant d’établir des indicateurs de ductilité et par des examens métallurgiques identifiant les défauts internes.L'étude de la sollicitation thermomécanique induite par le réchauffage du produit est analysée à l’aide de simulations numériques par éléments finis et les zones de sollicitations critiques associées au procédé sont identifiées. La caractérisation des anomalies observées sur les billettes est ensuite faite à partir d’essais de fissuration et de simulations numériques X-FeM. L’implémentation d’un critère de rupture en contrainte dans la simulation du cycle de chauffe a permis de définir les valeurs de gradient thermique limite et les courbes de chauffe optimales. Les analyses montrent que les conditions de chauffe en début de cycle thermique ont une forte influence sur la santé axiale des billettes. Les résultats de ces travaux conduisent à des solutions concrètes pour l’amélioration de la productivité. / As part of the piercing operations, billets undergo a reheating process from room temperature to a temperature of about 1250°C. During this heating, the thermal gradient in the billet leads to a deterioration of the axial health and is responsible of the initiation ofdefects on the formed tube.A methodology for the analysis of the mechanisms at the origin of these defects has been established. It is based on first, the characterization of the axial health with hot rheological tests to establish some indicators of ductility and second, on metallurgical analyses to identify the internal defects.Then finite element simulations have been performed to study the thermo-mechanical loadings induced by heating. Critical solicitation zones of the product during the processes have been identified.Finally a characterization of the observed defects into the billets has been led coupling cracks growth tests and X-FeM numerical simulations. The implementation of the experimental stress failure criterion, in the simulation of the heating cycle allows to obtain good values of thermal gradient boundary curves and leads to optimal heating curves.The analysis shows that the conditions at the beginning of the reheating process have a strong influence on the axial health of the billets. The results of these studies lead to friendly industrial solutions for improving productivity.

La justification de la stabilité d’un barrage-poids existant sur une fondation rocheuse nécessite une justification de la stabilité vis-à-vis du glissement à l’interface béton-roche. Le comportement au cisaillement de cette interface dépend de l’effort normal appliqué, des déformabilités de la roche et du béton, de la morphologie de la surface rocheuse et éventuellement de la propreté avant le coulage. Dans la littérature, un effet d’échelle a été mis en évidence : les évaluations de la résistance au cisaillement réalisées expérimentalement sur de petites interfaces en laboratoire donnent des valeurs différentes de celles estimées par rétro-analyse sur barrages existants. Le travail de cette thèse porte sur l'évaluation de cet effet d'échelle en tenant compte des facteurs influents, en particulier la morphologie de la surface rocheuse, l'objectif étant d'améliorer l'évaluation de la résistance au cisaillement à la base d'un barrage-poids.Tout d’abord, des essais de cisaillement directs ont été effectués sur plusieurs éprouvettes d’une même combinaison de différentes dimensions : à petite échelle sur des carottes et à des échelles intermédiaire et métrique sur des éprouvettes parallélépipédiques. Ces essais ont été complétés par des essais de traction directe permettant de caractériser l’adhésion initiale du contact béton-roche. Les résultats ont effectivement permis d'observer une variabilité des mesures de résistance au cisaillement selon l'échelle d'observation. Les essais usuels sur des carottes ont donné les mesures les plus élevées. A l'échelle métrique, les mesures de la résistance au cisaillement de l’interface béton-roche ont indiqué une valeur de cohésion non négligeable. A l'échelle intermédiaire, les valeurs de la résistance se sont réparties en deux groupes correspondant à deux morphologies différentes de la surface rocheuse. Du point de vue de l'effet d'échelle sur la résistance au cisaillement, si on représente les résultats par un critère linéaire, il a été constaté un effet d'échelle positif sur l'angle de frottement et un effet d'échelle négatif sur la cohésion.Un outil de description de la morphologie de la surface rocheuse basé sur une décomposition en fonctions sinusoïdales a été développé. Il a permis de décrire objectivement les caractéristiques de la morphologie de la surface rocheuse propres à chacun des deux groupes identifiés à l'échelle intermédiaire. Le premier groupe de surfaces rocheuses, avec les valeurs de résistance les plus élevées, se caractérise par une longueur d'onde principale de l'ordre de la taille de l'échantillon. Pour le second groupe, où les valeurs de résistance sont plus faibles, la longueur d'onde est comprise entre la moitié et les deux tiers de la taille de l'échantillon. Suite à ces observations expérimentales, les hypothèses suivantes ont été posées pour effectuer l'analyse des résultats : les essais sur carotte à petite échelle permettent de caractériser la résistance d'une interface béton-roche sans effet de morphologie de surface et l'échelle intermédiaire correspond à la surface élémentaire qui permet de caractériser les principaux effets de la géométrie de cette surface rocheuse sur la résistance. Sur cette base, un modèle 2D aux éléments finis de l'essai de cisaillement direct a été développé sous le logiciel Abaqus. Ce modèle a permis de reproduire le comportement au cisaillement des interfaces béton-roche à l’échelle intermédiaire. Ainsi il a pu être identifié que selon la morphologie, différents mécanismes d'initiation et de propagation de la rupture interviennent localement le long de l'interface et contribuent à moduler sa valeur de résistance globale, observée à l'échelle de l'essai. A l'échelle métrique, une décomposition de la surface en surfaces élémentaires et l'analyse de la morphologie de ces surfaces ont permis de retrouver les valeurs de résistance évaluées expérimentalement. / The shear strength of concrete-rock interface is a key factor to justify the stability of an hydraulic structure foundation. The shear behavior of this interface depends on the applied normal force, the deformability of rock and concrete, the rock surface morphology and the cleanliness of the rock surface before concrete casting. A scale effect was highlighted in the literature: the assessments of shear strength in a laboratory by achieving tests on small interfaces give values different from those estimated by back-analysis on the existing dams. This thesis work aims to assess the scale effect on the shear strength of concrete-rock interface taking into account some related factors, especially the rock surface morphology. The objective is to improve the shear strength assessment at the base of a gravity dam.Firstly, direct shear tests were performed on several prepared samples having different sizes: at small scale on cored samples usually used in the engineering field to assess the shear strength and at medium and metric scales on parallelepiped samples. To complete these tests, direct tensile tests were achieved to characterize the bonding of the concrete-rock contact. The results allowed a variability of shear strength measurements to be observed according to the observation scale. The usual tests on cored sample gave the highest values with high standard deviation. At metric scale, in the range of normal stresses to which the gravity dam foundation is mostly subjected, the concrete-rock interface shear strength showed a significant cohesion value. At medium scale, the shear strength values are divided into two groups corresponding to two different morphologies of the rock surface. Regarding the scale effect on the shear strength, if the results are fitted in a linear criterion, it was found a positive effect on the friction angle and negative effect on the cohesion.A descriptive tool based on sinusoidal functions was developed to characterize the rock surface morphology. It allowed to objectively describe the appropriate characteristics of the rock surface morphology for both groups identified at medium scale. The rock surfaces of the first group, which has the highest values of shear strength, are characterized relative to the best fit plane by a geometry having a main wavelength in the order of the sample size. For the second group, which has the lowest values of shear strength, the obtained wavelength is between half and two-thirds of the sample size.After these experimental observations and in order to accomplish the results analysis, the following assumptions were set: the tests on cored samples at small scale allowed the concrete-rock shear strength to be characterized independently of the rock surface morphology effect and the medium scale corresponds to the elementary surface which allows characterizing the main effects of the rock surface geometry on the interface shear behavior. On this basis, a 2D finite elements model was developed for direct shear test on Abaqus. This model reproduced the shear behavior of the concrete-rock interfaces at medium scale and therefore the stress distribution along the interface during the shearing process was studied. Thus it was identified that, according to surface morphology, different initiation and local failure propagation occur along the interface and contribute to adjust the overall shear strength of the interface. At scale 1, a decomposition of the surface by elementary surfaces and the analysis of the morphology of these surfaces allowed to recover the shear strength values assessed experimentally.

[pt] Neste trabalho é realizado um estudo da estabilidade de dutos enterrados submetidos a cargas térmicas. As cargas térmicas são devidas ao aquecimento do fluido com o objetivo de facilitar o transporte dos óleos que são escoados nos dutos. O duto expande devido a estas cargas térmicas. Como o duto está restringido em suas extremidades e devido à expansão são causadas forças axiais de compressão no duto. Para a análise destes dutos submetidos à variação da carga térmica foram utilizados modelos teóricos e numéricos para o problema de flambagem vertical e lateral, considerando o duto perfeito e com imperfeição. Os modelos numéricos foram desenvolvidos utilizando o programa ABAQUS. Para estes modelos numéricos o duto foi considerado como uma viga e a o solo como elementos de interface e elementos de mola. Foi desenvolvido também um modelo de viga-casca onde parte do duto é modelada como uma casca cilíndirca para permitir a análise de enrugamento e da deformação da seção transversal. São realizados estudos paramétricos numéricos para investigar o efeito do recobrimento do duto da forma e amplitude da imperfeição e da rigidez do solo na temperatura crítica de flambagem do duto. / [en] In this work a study of the stability of buried pipelines subjected to thermal loads is developed. The thermal loads are due to the heated fluid that flows through the pipe. Fluid heating is for ease of oil transportation. The pipe expands due to the thermal loading. Axial forces are developed in the pipe due to the expansion since the pipe is restricted on its ends. The analysis of pipes subject to thermal loadas were carried out with use of theoretical and numerical methods for upheaval and snaking buckling problems considering perfect pipes and pipes with imperfection. The numerical models were developed with the support of the ABAQUS software. The pipe was modeled as a beam and the soil is represented by interface elements and alternatively by spring elements. A beam-shell model was also developed where part of the pipe was modeled as a shell to allow a wrinkling analysis. Parametric studies were also carried out to investigate the effects of the soil stiffness, shape and amplitude or the imperfection and internal pressure on the critical temperature of the pipe.

[pt] Simulações numéricas tendem a simplificar o comportamento de problemas reais, na maioria das vezes pela adoção de um modelo 2D para descrição da resposta hidráulico-mecânica de barragens de terra, escavações, fundações, etc., com base na maior facilidade da construção geométrica de malhas, rapidez de processamento, simplicidade na introdução das condições de contorno, menor dificuldade na obtenção dos parâmetros de engenharia, etc. Entretanto, para certos fenômenos como o fluxo através de barragem em vales estreitos ou no rebaixamento do lençol freático para execução de escavações para construção de fundações, os efeitos tridimensionais podem afetar consideravelmente os resultados obtidos com uma solução simplificada, seja em termos de vazão, cargas, gradientes hidráulicos ou fatores de segurança. Esta dissertação tem como objetivo principal analisar problemas de fluxo, na condição transiente e/ou permanente, considerando solos saturados e parcialmente saturados, em simulações 2D e 3D pelo método dos elementos finitos buscando destacar as principais diferenças entre as respostas obtidas, ressaltando as principais vantagens e dificuldades da realização de uma simulação 3D em relação a uma análise simplificada 2D. Os exemplos numéricos abordados neste trabalho se referem à barragem de terra Macusani, no Peru, à escavação realizada para construção das estruturas da Pequena Central Elétrica Canoa Quebrada - MT e ao rebaixamento do lençol freático para construção das fundações do shopping Brooklin na cidade de São Paulo - SP. / [en] Numerical simulations tend to simplify the behavior of real problems, mainly through the choice of 2D models to describe the hydromechanical responses of earth dams, excavations, foundations, etc., partly because it is easier to construct geometrical meshes, it is simpler to impose the required boundary conditions, the computer calculations are done more rapidly and the estimation of the engineering parameters, either through field or laboratory tests, are less difficulty than it would be if the problem was treated as a complete 3D case. However, for certain phenomena such as the flow of water through dams situated in narrow valleys or the water drawdown in excavations for construction of building foundations, 3D effects can considerably affect the results when compared to a simplified 2D solution, either in terms of quantity of flow, hydraulic heads and gradients, security factors, etc. The main goal of this dissertation is the analysis of flow problems, both in transient and permanent conditions, considering fully saturated or partially saturated soils, employing 2D and 3D numerical models based on the finite element method in order to highlight the main differences between the computed answers, emphasizing the advantages and difficulties of both approaches. The numerical examples studied in this work are the earth dam Macusani, situated in Peru, the excavation carried out for the construction of the structures in the small hydroelectric plant Canoa Quebrada - MT, and groundwater drawdown for the execution of the foundations of the Brooklin shopping mall, in the city of São Paulo - SP.

[pt] Efeitos da taxa de deformação nas propriedades mecânicas podem ser significativos na simulação do comportamento dinâmico de estruturas deformadas plasticamente, e o objetivo deste trabalho é avaliá-los através de duas tarefas complementares: (i) desenvolver e qualificar uma metodologia apropriada para a medição de propriedades mecânicas dinâmicas, incluindo os requisitos necessários para medir e ajustar da melhor forma possível os dados experimentais, quantificando a incerteza a eles associada; e (ii) verificar a influência da estratégia de medição das propriedades mecânicas na previsibilidade do comportamento de estruturas sujeitas a impactos.Os modelos que descrevem o comportamento mecânico dinâmico são baseados na taxa de deformação de/dt, mas freqüentemente seus parâmetros são medidos em testes controlados pela velocidade do carregamento. Todavia, a taxa de/dt não permanece constante nos testes feitos sob velocidade fixa, o que aumenta a incerteza das previsões baseadas nos parâmetros assim medidos. Para avaliar quantitativamente a influência das estratégias de controle nas propriedades mecânicas, primeiro foi estabelecido um procedimento estatístico apropriado para determinar o número de corpos de prova necessários para medir propriedades dinâmicas dentro de um nível de confiança desejado. Todos os dados foram medidos em duplicata, controlando as taxas de deformação ou a velocidade de carregamento imposta nos corpos de prova, numa larga faixa, 10(-4) menor ou igual a de/dt menor ou igual a 10/s, em testes particularmente feitos com cuidado. A aquisição e tratamento dos dados foram feitos através de um programa desenvolvido em Labview. Um programa desenvolvido em Mathcad foi usado para otimizar os parâmetros dos diversos modelos estudados ao conjunto de dados medidos via um algoritmo Levenberg–Marquardt. A partir deste estudo é proposto um novo modelo que descreve adequadamente o patamar de escoamento, e minimiza os erros de ajuste na região de transição elastoplástica, de grande importância na análise estrutural. Um pórtico simples foi escolhido para verificar o efeito das propriedades dinâmicas nas simulações numéricas feitas no programa LS-DYNA, tradicionalmente usado para modelar impactos elastoplásticos. Vários destes pórticos foram submetidos a impactos numa máquina de queda livre (dropweight), para induzir deformações plásticas variáveis em função das velocidades de impacto. As deformações medidas foram comparadas com as previstas usando as propriedades obtidas sob as duas estratégias de controle, e ajustadas pelos diversos modelos estudados. Desta forma pode-se finalmente quantificar a influência da metodologia de medição das propriedades mecânicas dinâmicas na previsibilidade do comportamento de estruturas sujeitas a impactos elastoplásticos. / [en] The strain rate effects in the mechanical properties can be significant in the simulation of the dynamic behavior in plastic deformed structures, this work has the objective to evaluate these effects through two complementary tasks: (i) to develop and qualify an appropriate methodology for the measurement of dynamic mechanical properties, including the requirements necessary to measure and to adjust of the best possible way the experimental data, quantifying the uncertainty they associated; and (ii) to verify the influence of the strategy of measurement of the mechanical properties in the prediction of the behavior of structures submitted to impacts.The models that describe the dynamic mechanical behavior are based on the strain rate de/dt, but usually its parameters are measured in controlled tests by the speed of loading. However, the rate de/dt does not remain constant in the tests realized with fixed speed, which it increases the uncertainty of the predictions based on the measured parameters. For a quantitative evaluation of the influence of the control strategies in the mechanical properties, was first established a appropriated statistical procedure to determine the number of specimens necessary to measure dynamic properties with a acceptable level of reliability. All the data were measured twice, controlling the strain rate or the loading speed imposed in the specimens, in a wide range, 10(-4) less than or equal de/dt less than or equal 10/s, in tests particularly realized with care. The acquisition and data processing were made through a program developed in Labview. A program developed in Mathcad was used to optimize the parameters of the diverse models studied to the data set measured by a Levenberg-Marquardt algorithm. From this study is proposed a new model that describes the yieldind adequately, and minimizes the errors of fitting in the region of transition elasto-plastic, that plays a great role in the structural analysis.A simple porch was chosen to verify the effect of the dynamic properties in the numerical simulations made in program LS-DYNA, used traditionally to simulate elasto-plastics impacts. Several of these porches had been submitted to impacts in a machine of free fall (drop-weight), to induce variable plastic strains in function of the impact speeds. The measured strains were compared with the predicted ones using the properties obtained with the two strategies of control, and adjusted by the diverse studied models. In such way the influence of measurement methodology of the dynamic mechanical properties in the prediction of the behavior of structures submitted to elasto-plastics impacts can be quantified.

Le retournement temporel exploite la réversibilité temporelle de l’équation d’onde dans les milieux sans perte. Cela implique qu’une onde émise par une source peut rebrousser chemin et se focaliser sur sa source originale par le biais d’un miroir à retournement temporel. Cette focalisation permet de situer l’emplacement de cette source. Le but de cette thèse est d’exploiter le phénomène de retournement temporel d’ondes électromagnétiques en vue de la localisation et la caractérisation partielle d’objets diffractants enfouis dans un milieu sans perte. Notre étude est menée dans le domaine temporel large bande en se basant sur une modélisation numérique par la technique d’intégration finie.Le domaine temporel est un domaine assez peu exploré dans la littérature contrairement au domaine fréquentiel. La principale problématique est la détermination de l’instant de focalisation qui nous permet de choisir la distribution des champs à partir de laquelle les objets diffractants seront localisés. Nous introduisons dans ce manuscrit un critère de choix d’instant de focalisation qui est comparé tout au long des études entreprises au critère du minimum d’entropie.La démarche empruntée exploite l’analyse de cartographies d’énergie électromagnétique en deux et trois dimensions. Elle est validée dans un premier temps par l’analyse de configurations canoniques exploitant des données synthétiques obtenues par simulation. L’influence de divers paramètres relatifs aux objets diffractants est étudiée de même que l’impact du nombre d’émetteurs récepteurs du miroir à retournement temporel. Dans une seconde étape une expérimentation contrôlée en chambre anéchoïque à SUPELEC est réalisée en utilisant des antennes en régime harmonique et en régime impulsionnel. / Time reversal is, as is now well-known, exploiting the temporal reversibility of the wave equation in assumed lossless media. To summarize, it implies that a wave emitted by a given source may turn back and thereupon focus onto its original source by means of a so-called Time Reversal Mirror (TRM), which operation, properly simulated from field data acquired in a given measurement domain, could enable us to locate the source indeed. The aim of this thesis is to exploit the phenomenon of time reversal for the localization and the partial characterization, whenever possible, of diffracting objects (dielectric and conducting scatterers, in which sources are induced by given antennas, usually dipole-like) that are buried in a lossless medium (it can be a free space or a half-space) within a fully 3-D transient electromagnetic context. Time-domain certainly is a less explored area in the literature than frequency-domain, and this 3-D context (even if some 2-D validation studies are led also in the present work) is particularly demanding, computatinally speaking as well as at the level of real laboratory experiments. In addition, it requires that we be able to accurately compute the vector electromagnetic field in this time domain in an appropriate wideband situation, as well as whatever field is time reversed during the experiments, which are tasks performed via a full-wave Finite Integration Technique (FIT) developed at LGEP as is validated and discussed in some length in the manuscript. The main problem however is the determination of the moment of focus which would enable us determine the location of the scatterers at least to some extent. Here, to that effect, we introduce and discuss in depth a new criterion of choice of the instant of focus, which is in particular compared throughout the studies undertaken to the usually employed minimum entropy criterion. Influences of the various parameters of the scatterers themselves and of the measurement set-ups are thoroughly discussed on the way. Let us emphasize that what matters to us is the behavior of the (time-reversed) electromagnetic energy and not only of the electric field as standard, that is, the approach taken builds and uses the analysis of energy maps obtained by the aforementioned 3-D numerical modeling. Beyond the modeling of pure synthetic field data and discussions thereof, much attention is also given to leading controlled experiments on canonical targets using both transient and frequency-diverse time-harmonic sources within an anechoic chamber which was made available to us in SUPELEC.

Um dos grandes desafios da engenharia atualmente é viabilizar soluções computacionais que reduzam o tempo de processamento e forneçam respostas ainda mais precisas. Frequentemente surgem propostas com as mais diversas abordagens que exploram novas formas de resolver tais problemas ou tentam, ainda, melhorar as soluções existentes. Uma das áreas que se dedica a propor tais melhorias é a computação paralela e de alto desempenho - HPC (High Performance Computing). Técnicas que otimizem o tempo de processamento, algoritmos mais eficientes e computadores mais rápidos abrem novos horizontes possibilitando realizar tarefas que antes eram inviáveis ou levariam muito tempo para serem concluídas. Neste projeto propõe-se a implementação computacional de uma arquitetura de computação paralela com o intuito de resolver, de forma mais eficiente, em comparação com a arquitetura sequencial, problemas de Dinâmica dos Fluidos e Interação Fluido-Estrutura e que também seja possível estender esta arquitetura para a resolução de outros problemas relacionados com o Método dos Elementos Finitos. O objetivo deste trabalho é desenvolver um algoritmo computacional eficiente em linguagem de programação científica C++ e CUDA - de propriedade da NVIDIAr - tendo como base trabalhos anteriores desenvolvidos no LMC (Laboratório de Mecânica Computacional) e, posteriormente, com a arquitetura desenvolvida, executar e investigar problemas de Dinâmica dos Fluidos e Interação Fluido-Estrutura (aplicando o método dos Elementos Finitos com Fronteiras Imersas e a solução direta do sistema de equações lineares com PARDISO) com o auxílio dos computadores do LMC. Uma análise de sensibilidade para cada problema é realizada de forma a encontrar a melhor combinação entre o número de elementos da malha de elementos finitos e o speedup, e posteriormente é feita uma análise comparativa de desempenho entre a arquitetura paralela a sequencial. Com uma única GPU conseguiu-se uma considerável redução no tempo para o assembly das matrizes globais e no tempo total da simulação. / One of the biggest challenges of engineering is enable computational solutions that reduce processing time and provide more accurate numerical solutions. Proposals with several approaches that explore new ways of solving such problems or improve existing solutions emerge. One of the biggest areas dedicated to propose such improvements is the parallel and high performance computing. Techniques that improve the processing time, more efficient algorithms and faster computers open up new horizons allowing to perform tasks that were previously unfeasible or would take too long to complete. We can point out, among several areas of interest, Fluid Dynamics and Interaction Fluid-Structure. In this work it is developed a parallel computing architecture in order to solve numerical problems more efficiently, compared to sequential architecture (e.g. Fluid Dynamics and Fluid-Structure Interaction problems) and it is also possible to extend this architecture to solve different problems (e.g. Structural problems). The objective is to develop an efficient computational algorithm in scientific programming language C ++, based on previous work carried out in Computational Mechanics Laboratory (CML) at Polytechnic School at University of São Paulo, and later with the developed architecture, execute and investigate Fluid Dynamics and Fluid-Structure Interaction problems with the aid of CML computers. A sensitivity analysis is executed for different problems in order to assess the best combination of elements quantity and speedup, and then a perfomance comparison. Using only one GPU, we could get a 10 times speedup compared to a sequential software, using the Finite Element with Immersed Boundary Method and a direct solver (PARDISO).

Este trabalho consiste em analisar os esforços em tabuleiros de pontes por meio de superfícies de influência. Para isto, o método dos elementos finitos (MEF) é utilizado e os resultados são comparados com os das tabelas de Rüsch. Os elementos finitos de barra, representando longarinas e transversinas, e placa, as lajes do tabuleiro, são implementados no código SIPlacas. Estes elementos finitos são formulados pelas teorias de viga Timoshenko e placa Reissner-Mindlin, respectivamente. Estes apresentam problema de travamento de força cortante (Shear Locking), que é contornado por duas propostas: o artifício matemático da integração reduzida e elementos finitos com campo assumido de deformação de força cortante (CADFC). Verifica-se que os elementos com aproximações quadráticas para os deslocamentos e com CADFC são os que melhor se adequam à proposta de análise da presente pesquisa. Tais elementos apresentam convergência de resultados considerando estruturas com baixa discretização. Os resultados analisados foram o deslocamento, momento fletor e força cortante. Posteriormente realiza-se um estudo de caso de uma ponte em viga. O tabuleiro da ponte é calculado utilizando-se as tabelas de Rüsch e o código SIPlacas. O cálculo dos esforços pelo SIPlacas é realizado de três maneiras. Na primeira consideram-se os painéis de lajes do tabuleiro isolados; na segunda o tabuleiro está sobre apoios não deslocáveis; e na terceira, o tabuleiro apresenta-se com vigas acopladas. Foi concluído que a terceira configuração, cuja representação melhor se aproxima da estrutura real de análise, apresentou os menores esforços internos. / This work aims at the analysis of bridge deck stresses through influence surfaces. The finite element method (FEM) is used and the results are compared with those of Rüsch\'s tables. The bar and plate finite elements represent stringers, cross beams and slabs bridge deck. These finite elements are implemented in the SIPlacas code and the theories of Timoshenko beam and Reissner-Mindlin plate are used to theirs formulation. The Shear Locking problem is solved by two proposals: reduced integration and definition of element with transversal shear strain assumed (TSSA). The elements with quadratic approximations for the displacements and TSSA are the best suited to the proposed analysis of this research. Such elements have convergence of results considering structures with low discretization. Displacement, bending moment and shear force were the results analyzed. Subsequently a case study on a beam bridge was carried out. The bridge deck is calculated using Rüsch\'s tables and SIPlacas code. The calculation of the internal forces by SIPlacas is performed in three ways. The first one considers the slabs isolated panels; the second, the slab deck is on a rigid support; and third, the slab deck is on deformable supports. It was concluded that the third configuration showed the lowest internal forces. This configuration is the optimum representation to the structure analysis.

Esta dissertação apresenta uma análise numérica do controle de vibrações estruturais através de cerâmicas piezoelétricas em extensão e em cisalhamento conectadas a circuitos ativo-passivos compostos por resistência, indutância e fonte de tensão. Para tal, um modelo de elementos finitos de vigas sanduíche com três camadas elásticas e/ou piezoelétricas foi desenvolvido. Realizou-se também uma modelagem dos componentes do circuito elétrico e seu acoplamento à estrutura gerando assim uma equação de movimento acoplada para a estrutura com elementos piezoelétricos conectados aos circuitos elétricos. Uma análise harmônica das equações obtidas foi realizada para se obter uma avaliação preliminar dos efeitos causados pelos componentes elétricos do circuito na estrutura. Observou-se que os elementos passivos do circuito, resistência e indutância, tem não somente um efeito de absorvedor dinâmico de vibrações mas, também, promovem uma amplificação da autoridade de controle no caso de se atuar através da fonte de tensão. Usando a metodologia tradicional de projeto de absorvedores dinâmicos de vibrações, derivou-se expressões para os valores de resistência e indutância de modo a maximizar o desempenho passivo do sistema. Uma análise numérica do desempenho na redução das amplitudes de vibração em um viga engastada-livre com uma cerâmica piezoelétrica em extensão ou cisalhamento foi realizada mostrando bons resultados. Em seguida, uma análise da autoridade de controle para estas estruturas foi realizada visando a implementação de um controle híbrido ativo-passivo. A parcela ativa do controle foi obtida usando-se uma estratégia de controle por retroalimentação ótima do tipo linear quadratic regulator para calcular a tensão aplicada ao circuito. Uma comparação entre os resultados mostra que o controle híbrido ativo-passivo é sempre superior aos controles puramente ativos ou passivo para os dois casos estudados, com cerâmicas piezoelétricas em extensão e cisalhamento. / This work presents a numerical analysis of the structural vibration control using piezoelectric materials in extension and shear mode connected to active-passive electric circuits composed of the resistance, inductance and voltage source. For that, a finite element model for sandwich beams with three elastic or piezoelectric layers was developed. A modeling of the electric circuit dynamics and its coupling to the structure with piezoelectric elements was also done. A harmonic analysis of the resulting equations was performed to yield a preliminary evaluation of the effects caused by the electric circuit components on the structure. It was observed that the passive circuit components not only lead to a dynamic vibration absorber effect but also to an amplification of the control authority in case of actuation using the voltage source. Using the standard methodology for the design of dynamic vibration absorbers, expressions were derived for the resistance and inductance values that optimize the passive vibration control performance of the system. A numerical analysis of the passive vibration control was performed for cantilever beams with extension and shear piezoelectric ceramics showing satisfactory results. Then, an analysis of the control authority was carried out for the same structures aiming at an active-passive vibration control. The active control was achieved using a linear quadratic regulator optimal feedback strategy to evaluate the voltage applied to the circuit. A comparison between the obtained results show that hybrid active-passive control is always superior to the purely active or purely passive control for both cases studied, with extension and shear piezoelectric ceramics.