Neste trabalho realiza-se um estudo diversificado e integrado do comportamento de estruturas pré-moldadas de concreto, por meio de ensaios experimentais e computacionais, sejam estáticos ou dinâmicos. Diferentes modelos físicos foram construídos, cada um possuindo uma particularidade estrutural (íntegro, com dano localizado, com dano generalizado e com vínculo pilar-viga semi-rígido). Investigou-se a condição real de vínculo e sua influência na alteração dos parâmetros modais (freqüências naturais, modos de vibração e fatores de amortecimento). Destaca-se a metodologia experimental dinâmica que avalia a rigidez da ligação pilar-fundação diretamente pelos sinais medidos, não apenas pela calibração do modelo numérico. As avaliações computacionais apresentadas neste trabalho empregam modelos de elementos finitos fundamentados na Teoria da Elasticidade e na Mecânica do Dano Contínuo, e os seus resultados são confrontados com os experimentais e com os obtidos por modelos analíticos. Demonstra-se uma boa correlação entre os diversos resultados, comprovando-se a viabilidade da utilização dos testes de vibração, não-destrutivos e precisos, para a determinação da rigidez das ligações, estimativa do dano provocado pela fissuração e alteração de condições estruturais diversas. Comprova-se também a eficiência e a generalidade dos modelos constitutivos de concreto de Mazars e La Borderie para a simulação de ações estáticas e dinâmicas, ressaltada a importância da correta definição das condições de contorno. / This is a comprehensive research, with multiple approaches, on the concrete pre-cast structures behavior through experimental tests and computational analysis, considering both static and dynamic cases. Four different physical models were built, each of them with specific characteristics: no damage, localized damage, generalized damage, and semi-rigid beam-column connection models. A study of their real connection condition and its influence on the modal parameters changes (natural frequencies, mode shapes and damping factors) is presented. It is important to note that the dynamic experimental method allows the direct evaluation of the column-foundation connection stiffness using the measured signals and not only by comparing the numerical model results. The computational evaluation presented in this work employs of the finite element models based on the Theory of Elasticity and on the Continuum Damage Mechanics. The results are compared with both experimental and analytical data. The good correlation among these various results proves the viability of vibration tests as a non-destructive and precise tool to determine the connection stiffness, to estimate the damage produced by cracking and to assess the influence of the structural variables changes. It is also proved the efficiency and the generality of Mazars and La Borderie constitutive concrete models to simulate the static and dynamic behavior when considered the correct definitions of the boundary conditions.

Made available in DSpace on 2014-07-29T16:02:19Z (GMT). No. of bitstreams: 1 Dissertacao Kaye O da Silva.pdf: 935849 bytes, checksum: 3342ffadf63161660c1795053815a170 (MD5) Previous issue date: 2012-02-24 / In this work, we employ topological methods in order to study existence and multiplicity of solutions, of nonlinear boundary value problems of the fourth order. More precisely, we make use of results on connected components of fixed points, as well as global bifurcation, to show existence and multiplicity of weak solutions of Partial Differential Equations, involving the Biharmonic operator under Navier boundary conditions. Proofs of the abstract results used, are presented in detail. / Neste trabalho, utilizamos métodos topológicos para estudar existência e multiplicidade de soluções de Problemas de Contorno Elípticos Não Lineares de 4a ordem. Mais precisamente, utilizamos resultados sobre componentes conexas de pontos fixos e tambem bifurcação global, para provar existência e multiplicidade de soluções fracas de Equações Diferenciais Parciais, envolvendo o Operador Binarmônico, sob condições de fronteira de Navier. As demonstrações dos resultados abstratos que utilizamos, são apresentadas em detalhes.

Estudamos o problema de valores de contorno {\'DELTA POT. 2\' u = f em \'OMEGA\', \'BETA\' u = 0 em \'PARTIAL OMEGA\', um aberto limitado \'OMEGA\' \'ESTÁ CONTIDO\' \'R POT. N\' , sob diferentes condições de contorno. As questões de existência e positividade de soluções para este problema são abordadas com condições de contorno de Dirichlet, Navier e Steklov. Deduzimos condições de contorno naturais através do estudo de um modelo para uma placa com carga estática. Estudamos ainda propriedades do primeiro autovalor de \'DELTA POT. 2\' e o problema semilinear {\'DELTA POT. 2\' u = F (u) em \'OMEGA\' u = \'PARTIAL\'u SUP . \'PARTIAL\' v = 0 em \'PARTIUAL\' \'OMEGA\', para não-linearidades do tipo F(t) = \'l t l POT. p-1\', p \' DIFERENTE\' t, p > 0. Para tal problema estudamos existência e não-existência de soluções e positividade / We study the boundary value problem {\'DELTA POT. 2\' u = f in \'OMEGA\', \'BETA\' u = 0 in \'PARTIAL OMEGA\', in a bounded open \'OMEGA\'\'THIS CONTAINED\' \'R POT. N\' , under different boundary conditions. The questions of existence and positivity of solutions for this problem are addressed with Dirichlet, Navier and Steklov boundary conditions. We deduce natural boundary conditions through the study of a model for a plate with static load. We also study properties of the first eigenvalue of \'DELTA POT. 2\' and the semi-linear problem { \'DELTA POT. 2\' e o problema semilinear {\'DELTA POT. 2\' u = F (u) in \'OMEGA\' u = \'PARTIAL\'u SUP . \'PARTIAL\' v = 0 in \'PARTIUAL\' \'OMEGA\', for non-linearities like F(t) = \'l t l POT. p-1\', p \' DIFFERENT\' t, p > 0. For such problem we study existence and non-existence of solutions and its positivity

In this investigation, a single phase fluid is used to study the coupling between natural convection heat transfer within an enclosure and forced convection through computer covering case to cool the electronic chip. Two working fluids are used (water and air) within a rectangular enclosure and the air flow through the computer case is created by an exhaust fan installed at the back of the computer case. The optimum enclosure size configuration that keeps a maximum temperature of the heat source at a safe temperature level (85°C) is determined. The cooling system is tested for varying values of applied power in the range of 15-40W. The study is based on both numerical models and experimental observations. The numerical work was developed using the commercial software (ANSYS-Icepak) to simulate the flow and temperature fields for the desktop computer and the cooling system. The numerical simulation has the same physical geometry as those used in the experimental investigations. The experimental work was aimed to gather the details for temperature field and use them in the validation of the numerical prediction. The results showed that, the cavity size variations influence both the heat transfer process and the maximum temperature. Furthermore, the experimental results ii compared favourably with those obtained numerically, where the maximum deviation in terms of the maximum system temperature, is within 3.5%. Moreover, it is seen that using water as the working fluid within the enclosure is capable of keeping the maximum temperature under 77°C for a heat source of 40W, which is below the recommended electronic chips temperature of not exceeding 85°C. As a result, the noise and vibration level is reduced. In addition, the proposed cooling system saved about 65% of the CPU fan power.

De nombreux phénomènes physiques ne peuvent être compris qu'en s'intéressant à la structure électronique. Cette dernière peut être interprétée en termes de propriétés électromagnétiques, chacune de ces propriétés révélant diverses informations sur le système étudié. Il est donc important d'avoir des outils efficaces afin de calculer de telles propriétés. C'est dans ce contexte que cette thèse a été écrite, notre principal objectif ayant été de développer une méthode générale donnant accès à une vaste gamme de propriétés électromagnétiques. Dans la première partie de cette thèse, nous décrivons le socle théorique au sein duquel nous travaillons, en particulier la théorie de la fonctionnelle de la densité de courant dépendante du temps (TDCDFT), qui est une approche qui permet de décrire la réponse du système à un champ magnétique. La seconde partie est consacrée à la méthode que nous avons mise au point pour calculer diverses propriétés magnétiques en préservant l'invariance de jauge. Nous démontrons en particulier qu'en utilisant une simple règle de somme, il est possible de placer les courants diamagnétique et paramagnétique sur un pied d'égalité, évitant par là même les écueils habituels intrinsèques au calcul de propriétés magnétiques, comme la dépendance en l'origine de la jauge du vecteur potentiel. Nous illustrons notre méthode en l'appliquant notamment au calcul de la magnétisabilité et du dichroïsme circulaire, qui est une propriété possédant d'importantes applications pratiques, notamment en biologie. Dans la dernière partie, plus exploratoire, nous tentons d'étendre notre formalisme aux systèmes périodiques. Nous y discutons plusieurs stratégies afin de calculer l'aimantation dans des systèmes décrits par des conditions aux limites périodiques. / Various phenomena of matter can only be understood by probing its electronic structure. The latter can be interpreted in terms of electromagnetic properties, each property revealing a different piece of information. Having a reliable method to calculate such properties is thus of great importance. This thesis is to be regarded in this context. Our main goal was to develop a general method that gives access to a wide variety of electromagnetic properties. In the first part of this thesis, we describe the theoretical background with which we work, and in particular time-dependent current-density-functional theory (TDCDFT), which is a density-functional approach that can describe the response due to a magnetic field. The second part is dedicated to the method we developed in order to calculate various magnetic properties in a gauge-invariant manner. In particular, we show that by using a simple sum rule, we can put the diamagnetic and paramagnetic currents on equal footing. We thus avoid the usual problems that arise when calculating magnetic properties, such as the dependence on the gauge origin of the vector potential. We illustrate our method by applying it to the calculation of magnetizabilities and circular dichroism, which has important applications, notably in biology. In the last part, which is more explorative, we aim at extending our formalism to periodic systems. We discuss several strategies to calculate magnetization in systems described with periodic boundary conditions.

This thesis presents the results of computer simulation studies of the structure, dynamics, and deformation of cross-linked polymer gels. Obtaining a fundamental understanding of the interrelation between the detailed structure and the properties of polymer gels is a challenge and a key issue towards designing materials for specific purposes. A new off-lattice method for constructing a closed network is presented that is free from defects, such as looping chains and dangling ends. Using these model networks in Brownian dynamics simulations, I show results for the structure and dynamics of bulk gels and describe a novel approach using spherical boundary conditions as an alternative to the periodic boundary conditions commonly used in simulations. This algorithm was also applied for simulating the diffusion of tracer particles within a static and dynamic network, to illustrate the quantitative difference and importance of including network mobility for large particles, as dynamic chains facilitate the escape of particles that become entrapped. I further investigate two technologically relevant properties of polymer gels: their stimuli-responsive behaviour and their mechanical properties. The collapse of core-shell nanogels was studied for a range of parameters, including the cross-linking degree and shell thickness. Two distinct regimes of gel collapse could be observed, with a rapid formation of small clusters followed by a coarsening stage. It is shown that in some cases, a collapsing shell may lead to an inversion of the core-shell particle which exposes the core polymer chains to the environment. This thesis also explores the deformation of bimodal gels consisting of both short and long chains, subject to uniaxial elongation, with the aim to understand the role of both network composition as well as structural heterogeneity on the mechanical response and the reinforcement mechanism of these materials. It is shown that a bimodal molecular weight distribution alone is sufficient to strongly alter the mechanical properties of networks compared to the corresponding unimodal networks with the same number-average chain length. Furthermore, it is shown that heterogeneities in the form of high-density short-chain clusters affect the mechanical properties relative to a homogeneous network, primarily by providing extensibility.

No contexto do método MAC e baseado em esquemas de diferenças finitas, este trabalho apresenta três estudos: i) uma análise de estabilidade, ii) o desenvolvimento de técnicas implícitas e, iii) a construção de métodos de projeção para escoamentos com superfície livre. Na análise de estabilidade, o principal resultado mostra que o método de Crank-Nicolson torna-se condicionalmente estável quando aplicado para uma malha deslocada com a discretiza ção explícita das condições de contorno do tipo Dirichlet. Entretanto, o mesmo método com condições de contorno implícitas é incondicionalmente estável. Para obter métodos mais estáveis, formulações implícitas são desenvolvidas para a equação da pressão na superfície livre, derivada da condição de tensão normal. Esta estratégia resulta no acoplamento dos campos de velocidade e pressão, o que exige a introdução de novos métodos de projeção. Os métodos de projeção assim desenvolvidos resultam em novas metodologias para escoamentos com superfície livre que são apropriados para o tratamento de problemas com baixo número de Reynolds. Além disso, mostra-se que os métodos propostos podem ser aplicados para fluidos viscoelásticos. Novas estratégias são derivadas para obter métodos de projeção de segunda ordem de precisão para escoamentos com superfícies livres. Além dos resultados teóricos sobre a estabilidade de esquemas numéricos, técnicas implícitas e métodos de projeção, testes computacionais são realizados e comparados para consolidação da teoria apresentada. Os resultados numéricos são obtidos no sistema FREEFLOW. A eficiência e robustez das técnicas desenvolvidas neste trabalho são demonstradas na solução de problemas tridimensionais complexos com superfície livre e baixo número de Reynolds, incluindo os problemas do jato oscilante e do inchamento do extrudado / In the context of the MAC method and based on finite difference schemes, this work presents three studies: i) a stability analysis, ii) the development of implicit techniques, and iii) the construction of projection methods for free surface flows. In the stability analysis, the main result shows a precise stability restriction on the Crank-Nicolson method when one uses a staggered grid with Dirichlet explicit boundary conditions. However, the same method with implicit boundary conditions becomes unconditionally stable. In order to obtain more stable methods, implicit formulations are applied for the pressure equation at the free surface, which is derived from the normal stress condition. This approach results in a coupling of the velocity and pressure fields; hence new projection methods for free surface flows need to be developed. The developed projection methods result in new methodologies for low Reynolds number free surface flows. It is also shown that the proposed methods can be applied for viscoelastic fluids. New strategies are derived for obtaining second-order accurate projection methods for free surface flows. In addition to the theoretical results on the stability of numerical schemes, implicit techniques and projection methods, computational tests are carried out and the results compared to consolidate the theory. The numerical results are obtained by the FREEFLOW system. The eficiency and robustness of the techniques in this work are demonstrated by solving complex tridimensional problems involving free surface and low Reynolds numbers, including the jet buckling and the extrudate swell problems

Ce travail est consacré à l’étude numérique de l’interaction entre un fluide compressible et une structure indéformable, en adaptant une famille récente de schémas d’ordre très élevé à la prise en compte de conditions aux bords particulières entre le fluide et la structure. Plus précisément,on évalue l’apport de schémas d’ordre strictement supérieur à 3 par rapport à des stratégies plus classiques dans la littérature restreintes aux ordres 1 et 2. Un résultat important est qu’il est possible de réaliser le couplage à tout ordre et qu’il existe des configurations pour lesquelles on observe un gain important pour les ordres élevés. Une revue bibliographique est faite rappelant les résultats théoriques concernant les systèmes hyperboliques et décrivant les méthodes utilisées dans la littérature pour la simulation de la dynamique des gaz et la prise en compte des conditions aux bords. Un schéma sur grilles cartésiennes décalées et d’ordre très élevé est proposé pour la résolution des équations d’Euler en 1D/2D. Ce schéma est basé sur le formalisme Lagrange-projection et bien que formulé en énergie interne assure conservation et consistance faible grâce à un correctif en énergie interne. Parallèlement, l’étude pour les systèmes hyperboliques linéaires de discrétisation à l’ordre très élevé des conditions aux bords est faite. Elle met en évidence la nécessité pour l’ordre élevé de s’intéresser à la stabilité des schémas ainsi obtenus. À partir de ces travaux, la prise en compte de conditions aux bords en vitesse normale imposée est réalisée pour les équations d’Euler en 1D et 2D. Enfin, une procédure de couplage entre fluide compressible et structure indéformable est proposée. / This work is devoted to the construction of stable and high-order numerical methods in order to simulate fluid - rigid body interactions. In this manuscript, a bibliographic overview is done, which highlights theoretical results about hyperbolic system of conservation laws, as well as the methods available in the literature for the hydrodynamics simulation and the numericalboundary treatment. A high-order accurate scheme is proposed on staggered Cartesian grids to approximate the solution of Euler equations in 1D and 2D. The scheme relies on Lagrange-remap formalism, and although formulated in internal energy, ensures both conservation and weak consistency thanks to an internal energy corrector. In the same time, the study of high-order numerical boundary treatment for linear hyperbolic system is done. It highlights the necessity to focus especially on the linear stability of the effective scheme. Starting from the linear results, the numerical boundary treatment with imposed normal velocity is done for Euler equations in 1D and 2D. Last, the coupling between a compressible fluid and a rigid body is realized, using the designed procedure for numerical boudary treatment.

Masters of Science / The thesis investigates the potential of the Rietfontein and Spitskop aquifer to meet a demand of 1000 m3/d (12 Lis) as an alternative water resource for the Rietfontein and Spitskop Community. Increasing demand for clean and hygienic drinking water puts more pressure on one of our most valuable resources and supplying all communities with surface water is an extremely difficult and costly task in rural areas like Rietfontein and Spitskop in South Africa. Therefore it is necessary that interim water supplies be found from local aquifers and be utilized to address water supply challenges. Groundwater may serve as a short-term and an interim water supply which may be useful during future dry periods. Abstraction of groundwater is sensitive to recharge. Due to semi-arid conditions in Rietfontein and Spitskop area, there is high rainfall variation and disparity each year. During the research, hydrocensus was carried out. Water samples for chemistry analysis were taken. Literature review and pumping test data was utilized from the previous studies done by different consultants (Botha, 2000, Vivier and Pretorius, 2003). A numerical groundwater flow model for the local aquifers in the area and surroundings was constructed focusing on recharge and abstraction scenarios for the water supply from the local aquifers. For Rietfontein and Spitskop area, the mean annual precipitation (MAP) is 617mm/year. To be assured and rational in determining aquifers ability to meet the required demand a recharge with ninety-five (95th ) percentile was recommended, which estimates the MAP of 308mm/year which is 50% lower than the average MAP of 617mm/year. For a period of ninety six (96) years, the data indicates a severe drought occurred four (4) times where the rainfall was even lower than 95th percentile level of assurance of recharge estimated. This gives a comprehensible indication that average mean is not ideal or steadfast stature when building a water supply numerical groundwater flow modelling. These aquifers can only be exploited and managed if a reliable method can be obtained to estimate their long-term sustainable potential, since the sustainable potential of these aquifers to supply the communities is dependent upon the recharge from rainfall. The results from a numerical groundwater flow model indicated that a combined potential from the local aquifer from eighteen (18) boreholes is sufficient to meet the required demand and a total of 2600m3 Id can potentially be abstracted from the aquifer. With ninety-five (95th ) percentile recharge rate of 308mm/year a numerical groundwater flow model shows that the rate of abstraction is 80% far less than recharge, which gives high level of assurance in terms of local aquifer water supply demand. The abstraction of the boreholes confirmed by a numerical groundwater flow model shows the least impact on the surrounding aquifer for an extended period of time. In the event of drought, the boreholes will see a decline in water level after two (2) months of pumping local aquifer. The water level will decline steadily from two (2) months to two (2) years with a change in water levels of up to 40m. The impact of the drought is minimal compared to recharge rate, which verifies less depletion of the aquifer. The local aquifer shows the potential of 3MLld can be supplied to the communities with an assurance level of 95th percentile of rainfall. Reliable quantification of groundwater recharge rate remains the main challenges the hydrologist experienced and further research is essential for improvement of groundwater management for the area concerned.

Epithelial tissues, one of the four primary tissue structures found in our human body, are known to comprise of tiny cells interconnected in a unique continuous pattern. In most cases, they serve a dual purpose of protecting the internal organs from physical damage, and at the same time, enable in facilitating inter-cellular activities and prevent pathogen break ins. While the tissue mechanics and its proliferation have been scrutinized to great detail, it is their geometric uniqueness, that has remained more or less unexplored. With an intent of doing the same, this thesis identifies and explores those geometric properties/parameters that have an influence on the micro structure’s homogenized and localized response. However, it does so by extracting the microstructures profile and representing its cell edges via three dimensional beam elements - hence the name, bio-inspired structures. The analysis is carried out by first developing a staggered Representative Volume Element (RVE)using finite elements, and identifying its appropriate size. The staggered assembly aids in minimizing boundary effects from creeping in, and at the same time, provides the requisite statistical homogeneity. This is followed by the geometry study. A wide range of epithelial geometries are considered for the study, ranging from completely isotropic skin models, to in plane anisotropic cuboidal structures and out of plane anisotropic stratified geometries. The effects of orientation, relative density and edge length are extracted and studied in great detail. It is observed that cell edges initial orientation has a direct dependence on the particle distribution, whereas the change in orientation is largely dependent on the deformation the microstructure is subjected to. Relative density is documented to show a direct correlation to a materials homogenized response i.e. larger the relative density, greater is the microstructures stiffness and homogenized stress response to the same deformation. Edge length, on the other hand is observed to showcase a downward trend on the cell edge’s axial stress. On average, in any kind of distribution and any kind of deformation, smaller cell edges are known to showcase larger stresses, as compared to the larger cell edges.