The response of beams resting on viscoelastically damped foundation under moving SDoF oscillators is scrutinized through a novel state-space formulation, in which a number of internal variables is introduced with the aim of representing the frequency-dependent behaviour of the viscoelastic foundation. A suitable single-step scheme is provided for the numerical integration of the equations of motion, and the Dimensional Analysis is applied in order to define the dimensionless combinations of the design parameters that rule the responses of beam and moving oscillator. The effects of boundary conditions, span length and number of modes of the beam, along with those of the mechanical properties of oscillator and foundation, are investigated in a new dimensionless form, and some interesting trends are highlighted. The inaccuracy associated with the use of effective values of stiffness and damping for the viscoelastic foundation, as usual in the present state-of-practice, is also quantified.

O Método dos Elementos Finitos quando aplicado à análise de estruturas, em sua forma usual, conduz a sistemas de equações que, no caso não-linear, exigem algoritmos iterativos que realizam, em essência, uma linearização a cada passo de carga. Por outro lado, o Método da Energia formula o problema de análise estrutural na forma de uma minimização, podendo apresentar restrições sobre a função deslocamento, por exemplo. Nesse caso, os algoritmos de programação matemática proporcionam a maneira mais consistente para a obtenção da solução. O presente trabalho de mestrado trata, essencialmente, da aplicação das técnicas de otimização como ferramenta para a análise do comportamento não-linear de estruturas, que pode ser decorrente de condições de vinculação. Os problemas estruturais são formulados via Método da Energia, que resulta na minimização de funções quadráticas sujeitas a um conjunto de restrições. São discutidos os métodos do tipo Gradiente, Newton e Quase-Newton, com a descrição dos seus algoritmos básicos e apresentação da regra de busca unidimensional adotada (Regra de Armijo ou Exata). Devido ao fato do Método de Newton ter apresentado uma melhor convergência em relação aos demais algoritmos estudados, optou-se por combiná-lo com uma estratégia de conjuntos ativos para o caso de minimização com variáveis canalizadas. / The finite element method when applied to structural analysis, in its usual form, it drives the equations systems that, in the nonlinear case, they demand algorithms repetitive that accomplish, in essence, a linear programming to each load step. However, the Energy Method formulates the problem of structural analysis in the form of the minimizing, could present restrictions on the displacement function, for example. In that case, the algorithms of mathematical programming provide the most consistent way for obtaining of the solution. The present work negotiates, essentially, of the application in mathematical programming as a form to analyze the nonlinear structures behavior, that can be current of boundary conditions. The structural problems are formulated through Energy Method, that results in the mathematical programming of quadratic functions subject to a group of restrictions. The methods of the type Gradient are discussed, of Newton and Quasi-Newton, with the description of its basic algorithms and presentation of the rule of search adopted unidimensional (Rule of Armijo or Exact). Due to the fact of Newton\'s Method to have presented a better convergence in relation to the other studied algorithms, it was opted for combining it with a \"strategy of the active groups\" for the case of mathematical programming with restricted variables.

In this thesis, we present a collection of newly obtained results concerning the existence of vanishing viscosity solutions to the one-dimensional compressible Euler equations of gas dynamics, with and without geometric structure. We demonstrate the existence of such vanishing viscosity solutions, which we show to be entropy solutions, to the transonic nozzle problem and spherically symmetric Euler equations in Chapter 4, in both cases under the simple and natural assumption of relative finite-energy. In Chapter 5, we show that the viscous solutions of the one-dimensional compressible Navier-Stokes equations converge, as the viscosity tends to zero, to an entropy solution of the Euler equations, again under the assumption of relative finite-energy. In so doing, we develop a compactness framework for the solutions and approximate solutions to the Euler equations under the assumption of a physical pressure law. Finally, in Chapter 6, we consider the Euler equations in special relativity, and show the existence of bounded entropy solutions to these equations. In the process, we also construct fundamental solutions to the entropy equations and develop a compactness framework for the solutions and approximate solutions to the relativistic Euler equations.

Carbon fiber-reinforced silicon carbide matrix (C/SiC) composite is a ceramic matrixcomposite (CMC) that has considerable promise for use in high-temperature structuralapplications. In this thesis, systematic numerical studies including the prediction of elasticand thermal properties, analysis and optimization of stresses and simulation ofhigh-temperature oxidations are presented for the investigation of C/SiC composites.A strain energy method is firstly proposed for the prediction of the effective elastic constantsand coefficients of thermal expansion (CTEs) of 3D orthotropic composite materials. Thismethod derives the effective elastic tensors and CTEs by analyzing the relationship betweenthe strain energy of the microstructure and that of the homogenized equivalent model underspecific thermo-elastic boundary conditions. Different kinds of composites are tested tovalidate the model.Geometrical configurations of the representative volume cell (RVC) of 2-D woven and 3-Dbraided C/SiC composites are analyzed in details. The finite element models of 2-D wovenand 3-D braided C/SiC composites are then established and combined with the stain energymethod to evaluate the effective elastic constants and CTEs of these composites. Numericalresults obtained by the proposed model are then compared with the results measuredexperimentally.A global/local analysis strategy is developed for the determination of the detailed stresses inthe 2-D woven C/SiC composite structures. On the basis of the finite element analysis, theprocedure is carried out sequentially from the homogenized composite structure of themacro-scale (global model) to the parameterized detailed fiber tow model of the micro-scale(local model). The bridge between two scales is realized by mapping the global analysisresult as the boundary conditions of the local tow model. The stress results by global/localmethod are finally compared to those by conventional finite element analyses.Optimal design for minimizing thermal residual stress (TRS) in 1-D unidirectional C/SiCcomposites is studied. The finite element models of RVC of 1-D unidirectional C/SiCIIcomposites with multi-layer interfaces are generated and finite element analysis is realized todetermine the TRS distributions. An optimization scheme which combines a modifiedParticle Swarm Optimization (PSO) algorithm and the finite element analysis is used toreduce the TRS in the C/SiC composites by controlling the multi-layer interfaces thicknesses.A numerical model is finally developed to study the microstructure oxidation process and thedegradation of elastic properties of 2-D woven C/SiC composites exposed to air oxidizingenvironments at intermediate temperature (T<900°C). The oxidized RVC microstructure ismodeled based on the oxidation kinetics analysis. The strain energy method is then combinedwith the finite element model of oxidized RVC to predict the elastic properties of composites.The environmental parameters, i.e., temperature and pressure are studied to show theirinfluences upon the oxidation behavior of C/SiC composites.

O Método dos Elementos Finitos quando aplicado à análise de estruturas, em sua forma usual, conduz a sistemas de equações que, no caso não-linear, exigem algoritmos iterativos que realizam, em essência, uma linearização a cada passo de carga. Por outro lado, o Método da Energia formula o problema de análise estrutural na forma de uma minimização, podendo apresentar restrições sobre a função deslocamento, por exemplo. Nesse caso, os algoritmos de programação matemática proporcionam a maneira mais consistente para a obtenção da solução. O presente trabalho de mestrado trata, essencialmente, da aplicação das técnicas de otimização como ferramenta para a análise do comportamento não-linear de estruturas, que pode ser decorrente de condições de vinculação. Os problemas estruturais são formulados via Método da Energia, que resulta na minimização de funções quadráticas sujeitas a um conjunto de restrições. São discutidos os métodos do tipo Gradiente, Newton e Quase-Newton, com a descrição dos seus algoritmos básicos e apresentação da regra de busca unidimensional adotada (Regra de Armijo ou Exata). Devido ao fato do Método de Newton ter apresentado uma melhor convergência em relação aos demais algoritmos estudados, optou-se por combiná-lo com uma estratégia de conjuntos ativos para o caso de minimização com variáveis canalizadas. / The finite element method when applied to structural analysis, in its usual form, it drives the equations systems that, in the nonlinear case, they demand algorithms repetitive that accomplish, in essence, a linear programming to each load step. However, the Energy Method formulates the problem of structural analysis in the form of the minimizing, could present restrictions on the displacement function, for example. In that case, the algorithms of mathematical programming provide the most consistent way for obtaining of the solution. The present work negotiates, essentially, of the application in mathematical programming as a form to analyze the nonlinear structures behavior, that can be current of boundary conditions. The structural problems are formulated through Energy Method, that results in the mathematical programming of quadratic functions subject to a group of restrictions. The methods of the type Gradient are discussed, of Newton and Quasi-Newton, with the description of its basic algorithms and presentation of the rule of search adopted unidimensional (Rule of Armijo or Exact). Due to the fact of Newton\'s Method to have presented a better convergence in relation to the other studied algorithms, it was opted for combining it with a \"strategy of the active groups\" for the case of mathematical programming with restricted variables.

The effects of a composite overwrapped gun barrel with viscoelastic damping layers are investigated. Interlaminar stresses and constrained layer damping effects are described. The Modal Strain Energy method is developed for measuring the extent to which the barrel is damped. The equations of motion used in the finite element analysis are derived. The transient solution process is outlined. Decisions for selected parameters are discussed. The results of the finite element analyses are presented using the program written in FORTRAN. The static solution is solved with a constant internal pressure resulting in a calculated loss factor from the Modal Strain Energy Method. The transient solution is solved using the Newmark-Beta method and a variable internal pressure. The analyses conclude that strategically placed viscoelastic layers dissipate strain energy more effectively than a thick single viscoelastic layer. The optimal angle for maximizing the coefficient of mutual influence in a composite cylinder is not necessarily the optimal angle when viscoelastic layers are introduced between layers.

Transformers emit a characteristic humming noise due to magnetostriction which is the continuous change in dimensions during magnetization. The noise is amplified if the induced frequencies match the core’s natural frequencies, consequently avoiding geometries that create resonance is critical in order to fulfill customer sound level requirements. In this thesis, a high voltage direct current transformer core with two main limbs and two return limbs is studied. Using finite element analysis (FEA), the core can be modeled and analyzed in a computer environment. The main contributors of noise are the first bending and longitudinal resonance modes. Data for how these modes change with geometric alterations is collected and stored through parametric studies. An analytical expression is then constructed through Rayleigh’s energy method with added coefficients that can be correlated to FEA datasets achieving a verified model via data-fitting. A satisfactory model is created for both resonance modes. / Transformatorer avger ett karaktäristiskt surrande ljud. Ljudet uppkommer på grund av magnetostriktion vilket är förändringar i geometri som uppkommer då kärnan kontinuerligt magnetiseras. Ljudet förstärks om induktionsfrekvenserna matchar kärnans naturliga frekvenser, så att undvika kärngeometrier som skapar resonans är viktigt för att klara ljudnivåkrav som kunden har. I denna studie betraktas resonansfenomenet i en högspänningstransformator för likström (HVDC) med två lindade ben och två sidoben. Med avstamp i en finita elementanalys (FEA) kan kärnan modelleras och analyseras i en datormiljö. Data för hur resonansmoderna som bidrar mest till ljud förändras med förändringar av geometriska parametrar samlas genom parametriska studier. I detta fall analyseras de första böj- och longitudinella resonansmoderna. Ett analytiskt uttryck skapas sedan med hjälp av Rayleigh’s energimetod där coefficienter anpassas efter FEA-datan. Detta leder slutligen till en verifierad modell som fungerar väl för uppskattning av de båda relevanta resonansmoderna.

L’identification des efforts vibratoires agissant sur les structures et la détection des défauts à partir des mesures opérationnelles sont des sujets importants dans des projets académiques et industriels. Le choix de l’outil ou de la méthode utilisée dépend de la bande de fréquences d'étude puisqu’il existe des approches appropriées pour chaque domaine fréquentiel. Une méthode énergétique appelée la méthode énergétique simplifiée (MES) est utilisée pour prédire la répartition de la densité d'énergie vibroacoustique en moyennes et hautes fréquences. L'objectif de ce mémoire est d'étendre cette méthode pour résoudre les problèmes vibro-acoustiques inverses pour identifier d'une part les sources de vibration et d'autre part pour détecter les défauts. La formulation MES inverse (IMES) est numériquement validée pour des systèmes continus basés sur le couplage tel que le cas d’un système comportant plusieurs plaques couplées et celui d’un système composé d’une cavité acoustique couplée avec une plaque. En plus, une nouvelle méthodologie numérique est proposée, pour étendre cet outil d'identification IMES pour la détection des défauts. Une analyse paramétrique est effectuée pour le cas d’un modèle présentant des défauts afin de tester la robustesse et l’efficacité de cette approche. Finalement, une étude expérimentale est effectuée pour valider la technique IMES à fin d'identifier et localiser les charges exercées pour plusieurs cas, et détecter les défauts. / The identification of inputs forces acting on structures and the detection of defects from operating measurement have been important topics in both academic and industrial projects. The choice of the used tool or method depends on the frequency band of study since there are appropriate approaches for each frequency domain. An energetic method so called the simplified energy method (MES) is used to predict the distribution of the vibro-acoustic energy density in the medium and high frequency band. The objective of this thesis is to extend this energy method to solve inverse vibro-acoustic problems and to identify the sources of vibrations on one hand and to detect the defects on the other hand. The inverse MES formulation (IMES) is numerically validated for continuous coupling-based systems such as the case of a system composed with several coupled plates and the case of a system composed of an acoustic cavity coupled with a plate. In addition, a new numerical methodology is proposed to extend this IMES identification tool for the detection of defects. A parametric analysis is performed in the case of plate with defects in order to test the robustness and the efficiency of this approach. Finally, an experimental study is carried out to validate the IMES technique to identify and locate the input loads for several scenarios, and detecting the defects.

Submitted by Verena Bastos (verena@uefs.br) on 2015-08-05T21:29:18Z No. of bitstreams: 1 NEVES_JB_2012_R2.pdf: 2142681 bytes, checksum: 2f1f8d4679734685ccd9edf621f7b8c4 (MD5) / Made available in DSpace on 2015-08-05T21:29:18Z (GMT). No. of bitstreams: 1 NEVES_JB_2012_R2.pdf: 2142681 bytes, checksum: 2f1f8d4679734685ccd9edf621f7b8c4 (MD5) Previous issue date: 2013-09-24 / Funda??o de Amparo ? Pesquisa do Estado de S?o Paulo - FAPESP / The prediction of the reinforced concrete beams behavior under bending is essential to design these elements. Usually the models do not incorporate the concrete stress contribution, which may underestimate the structural element strain that use steel fiber reinforced concrete (SFRC) under permanent or temporary loads. This work presents a variational formulation based on the finite difference energy method (EFDM) in predicting the flexural behavior of concrete beams reinforced, that uses SFRC. The proposed model uses the classical lamination theory (CLT) with a damage model (Mazars, 1984) applied to the SFRC. The reinforcement was considered as a layer of a perfect elastic-plastic material. Comparing the load-displacement numerical results with those of the literature to reinforced concrete beams demonstrates the consistency of the proposed model. / A previs?o do comportamento de vigas de concreto armado sob flex?o ? fundamental para o adequado dimensionamento destes elementos. Usualmente, os modelos n?o incorporam a contribui??o do concreto tracionado, o que pode subestimar as deforma??es no elemento estrutural que utilizem o concreto refor?ado com fibras (CRFA) sob cargas de curta e longa dura??o. No presente trabalho ? apresentada uma formula??o variacional com base no m?todo das diferen?as finitas energ?ticas (MDFE) para a previs?o do comportamento ? flex?o de vigas de concreto simples ou armado refor?adas com fibras de a?o. O modelo proposto combina a teoria cl?ssica de laminados (TCL) com um modelo de dano (Mazars, 1984) aplicado ao concreto. O refor?o (armadura longitudinal) foi considerado como uma l?mina de um material elasto-pl?stico perfeito. A compara??o dos resultados num?ricos com resultados encontrados na literatura para vigas de concreto armado, em termos de cargadeslocamento, demonstra a coer?ncia do modelo proposto.

Les matériaux composites à matrice de carbure de silicium renforcée par des fibres decarbone (C/SiC) sont des composites à matrice céramique (CMC), très prometteurs pour desapplications à haute température, comme le secteur aéronautique. Dans cette thèse, sontmenées des études particulières concernant les propriétés de ces matériaux : prédiction despropriétés mécanique (élastiques), analyses thermiques (optimisation des contraintesthermiques), simulation de l’oxydation à haute température.Une méthode basée sur l’énergie de déformation est proposée pour la prédiction desconstantes élastiques et des coefficients de dilatation thermiques de matériaux compositesorthotropes 3D. Dans cette méthode, les constantes élastiques et les coefficients de dilatationthermique sont obtenus en analysant la relation entre l'énergie de déformation de lamicrostructure et celle du modèle homogénéisé équivalent sous certaines conditions auxlimites thermiques et élastiques. Différents types de matériaux composites sont testés pourvalider le modèle.Différentes configurations géométriques du volume élémentaire représentatif des compositesC/SiC (2D tissés et 3D tressés) sont analysées en détail. Pour ce faire, la méthode énergétiquea été couplée à une analyse éléments finis. Des modèles EF des composites C/SiC ont étédéveloppés et liés à cette méthode énergétique pour évaluer les constantes élastiques et lescoefficients de dilatation thermique. Pour valider la modélisation proposée, les résultatsnumériques sont ensuite comparés à des résultats expérimentaux.Pour poursuivre cette analyse, une nouvelle stratégie d'analyse « globale/locale »(multi-échelle) est développée pour la détermination détaillée des contraintes dans lesstructures composites 2D tissés C/SiC. Sur la base de l'analyse par éléments finis, laprocédure effectue un passage de la structure composite homogénéisée (Echelle macro :modèle global) au modèle détaillé de la fibre (Echelle micro : modèle local). Ce passage entreles deux échelles est réalisé à partir des résultats de l'analyse globale et des conditions auxlimites du modèle local. Les contraintes obtenues via cette approche sont ensuite comparées àcelles obtenues à l’aide d’une analyse EF classique.IVLa prise des contraintes résiduelles thermiques (contraintes d’origine thermique dans lesfibres et la matrice) joue un rôle majeur dans le comportement des composites à matricescéramiques. Leurs valeurs influencent fortement la contrainte de microfissuration de lamatrice. Dans cette thèse, on cherche donc à minimiser cette contrainte résiduelle thermique(TRS) par une méthode d’optimisation de type métaheuristique: Particle Swarm Optimization(PSO), Optimisation par essaims particulaires.Des modèles éléments finis du volume élémentaire représentatif de composites 1-Dunidirectionnels C/SiC avec des interfaces multi-couches sont générés et une analyse paréléments finis est réalisée afin de déterminer les contraintes résiduelles thermiques. Unschéma d'optimisation couple l'algorithme PSO avec la MEF pour réduire les contraintesrésiduelles thermiques dans les composites C/SiC en optimisant les épaisseurs des interfacesmulti-couches.Un modèle numérique est développé pour étudier le processus d'oxydation de microstructureet la dégradation des propriétés élastiques de composites 2-D tissés C/SiC oxydant àtempérature intermédiaire (T<900°C). La microstructure du volume élémentaire représentatifde composite oxydé est modélisée sur la base de la cinétique d'oxydation. La méthode del'énergie de déformation est ensuite appliquée au modèle éléments finis de la microstructureoxydé pour prédire les propriétés élastiques des composites. Les paramètres d'environnement,à savoir, la température et la pression, sont étudiées pour voir leurs influences sur lecomportement d'oxydation de composites C/SiC. / Carbon fiber-reinforced silicon carbide matrix (C/SiC) composite is a ceramic matrixcomposite (CMC) that has considerable promise for use in high-temperature structuralapplications. In this thesis, systematic numerical studies including the prediction of elasticand thermal properties, analysis and optimization of stresses and simulation ofhigh-temperature oxidations are presented for the investigation of C/SiC composites.A strain energy method is firstly proposed for the prediction of the effective elastic constantsand coefficients of thermal expansion (CTEs) of 3D orthotropic composite materials. Thismethod derives the effective elastic tensors and CTEs by analyzing the relationship betweenthe strain energy of the microstructure and that of the homogenized equivalent model underspecific thermo-elastic boundary conditions. Different kinds of composites are tested tovalidate the model.Geometrical configurations of the representative volume cell (RVC) of 2-D woven and 3-Dbraided C/SiC composites are analyzed in details. The finite element models of 2-D wovenand 3-D braided C/SiC composites are then established and combined with the stain energymethod to evaluate the effective elastic constants and CTEs of these composites. Numericalresults obtained by the proposed model are then compared with the results measuredexperimentally.A global/local analysis strategy is developed for the determination of the detailed stresses inthe 2-D woven C/SiC composite structures. On the basis of the finite element analysis, theprocedure is carried out sequentially from the homogenized composite structure of themacro-scale (global model) to the parameterized detailed fiber tow model of the micro-scale(local model). The bridge between two scales is realized by mapping the global analysisresult as the boundary conditions of the local tow model. The stress results by global/localmethod are finally compared to those by conventional finite element analyses.Optimal design for minimizing thermal residual stress (TRS) in 1-D unidirectional C/SiCcomposites is studied. The finite element models of RVC of 1-D unidirectional C/SiCIIcomposites with multi-layer interfaces are generated and finite element analysis is realized todetermine the TRS distributions. An optimization scheme which combines a modifiedParticle Swarm Optimization (PSO) algorithm and the finite element analysis is used toreduce the TRS in the C/SiC composites by controlling the multi-layer interfaces thicknesses.A numerical model is finally developed to study the microstructure oxidation process and thedegradation of elastic properties of 2-D woven C/SiC composites exposed to air oxidizingenvironments at intermediate temperature (T<900°C). The oxidized RVC microstructure ismodeled based on the oxidation kinetics analysis. The strain energy method is then combinedwith the finite element model of oxidized RVC to predict the elastic properties of composites.The environmental parameters, i.e., temperature and pressure are studied to show theirinfluences upon the oxidation behavior of C/SiC composites.