[pt] Este trabalho apresenta a previsão do desempenho de três acessórios de união (manilha de união, elo Kenter e elo Multifuncional) utilizados em sistemas de ancoragem de unidades offshore, sob carregamentos monotônicos e cíclicos. Cinqüenta e sete modelos foram analisados pelo método de Elementos Finitos utilizando o software Ansys 10. Inicialmente, com o objetivo de quantificar a influência do contato e mensurar a área onde este ocorre, três modelos com contatos entre manilha de união e elos foram analisados com variações no diâmetro (76, 95 e 120 mm) e mantendo-se constante as propriedades mecânicas do material e a carga aplicada. Em seqüência, cinqüenta e quatro outros modelos foram elaborados sem condições de contato, isto é, com as cargas aplicadas diretamente nos componentes de estudo, que sofreram variações de diâmetros (76, 95 e 120 mm), de propriedades mecânicas (limites de escoamento e resistência mecânica) e de carregamento (proof load e minimum break load). Comparativamente, as manilhas de união apresentaram os menores níveis de tensões e as melhores distribuições de tensões dentre os três componentes para todos os casos analisados. Dos cinqüenta e quatro modelos citados acima, três foram selecionados para análise da vida em fadiga com o software FE-Fatigue. Estes representavam um acessório de união de cada tipo com o diâmetro considerado crítico (120 mm) e sem variações nas propriedades mecânicas do material. Os resultados mostraram que a geometria do componente é determinante para os valores das tensões e da vida-fadiga. A manilha apresentou os melhores resultados de resistência e de vida-fadiga, que para o diâmetro e material escolhidos, foi cerca de três vezes maior do que aquela relativa aos elos Kenter e Multifuncional. / [en] This work represents an approach to predict the performance of three joining accessories (shackle, Kenter link and Multifunctional link) for offshore mooring systems under monotonic and cyclic loading. Fifty seven models were analyzed by the Finite Element method using the software Ansys 10. Initially, in order to quantify the influence of the contact conditions and to measure the area where it occurs, three models presenting contacts between the joining shackle and chain links were analyzed varying the diameter (76, 95, 120 mm) and maintaining constant the material’s mechanical properties as well as the applied loads. In sequence, fifty four other models were created without contact conditions, which means that the loads were applied directly on the components in question, with variations in link diameter (76, 95 and 120 mm), in mechanical properties (yield stress and ultimate strength) and in load conditions (proof and minimum break loads). Comparing the joining shackles with the other accessories, the shackles present the lowest stress levels and the best stress distributions with regard to all the cases studied. Three of the fifty four models cited above were selected for predicting their fatigue life making use of the FE-Fatigue software. These represented one of each joining accessory with a diameter considered critical (120 mm), keeping constant the mechanical properties of the material. The results showed that the influence of the component geometry is determinant for the stress values developed during the loading tests as well as its fatigue life. The shackle presented the best results in terms of strength and fatigue life, which was about three times greater than that for the Kenter and Multifunctional links.

Este trabalho avaliou, utilizando o Método dos Elementos Finitos, o comportamento mecânico em seis ensaios, quatro de flexo compressão com variação apenas no comprimento da haste de fixação, um de flexão ântero-posterior e um de flexão lateral, em um modelo tridimensional de fixador externo construído com auxílio do computador. Para a validação desses ensaios os mesmos testes também foram realizados na máquina universal de ensaio e depois comparados com o método dos elementos finitos. A rigidez no ensaio de flexão lateral obtida no método dos elementos finitos apresentou um valor 106% maior do que o obtido na máquina universal de ensaio, possivelmente por ocorrência de afrouxamento entre as partes adjacentes elo fixador externo no ensaio mecânico, e no ensaio de flexo compressão (número 1) a rigidez obtida pelo método dos elementos finitos foi 7,39% menor elo que a obtida na máquina universal de ensaio. No ensaio número 4 (flexo-compressão) os deslocamentos obtidos, correspondentes a aplicação de uma carga de 15,4 N, utilizando tanto o método dos elementos finitos como a máquina universal ele ensaio, divergiram em 8,5%. Já no ensaio número 5 (flexão ântero-posterior) a divergência foi de 0,9%, para os deslocamentos correspondentes a aplicação de uma carga de 14,4 N. O Métodos dos Elementos Finitos é um eficiente método para prever comportamento mecânico de estruturas complexas. / This work evaluates the mechanical behavior of an external device on a CAD (Computer Aided Design) 3D model in six tests, four of them of flexion-compression with a single variation of the external device stick length, one of longitudinal flexion and one of lateral flexion. They all were carried out applying the Method of the Finite Elements (MFE). For the comparison with the MFE the same mechanical testes were made. The stiffness achieved in the MFE showed a value 106% greater than that of the mechanical test. The test number one of flexion-compression showed a value 7,39% smaller in the MFE than that of the mechanical test. In the test number four (flexion-compression) the corresponding displacement after the application of a 15,4 N working stress showed a difference of 8,5%. The variation of the number five test was of 0,9% for the displacement after the application of a 14,4N working stress. The MEF showed efficient to evaluate the behavior of complex mechanical structures.

Os problemas freqüentes de patologias ortopédicas e traumáticas da coluna vertebral envolvem a colocação de fixadores internos (parafusos longos, os quais são inseridos nos pedículos posteriores até os corpos vertebrais e conectados por fios nas hastes longitudinais podendo ser fixados em todas as posições pelas porcas). Estes fixadores foram simulados no computador através da construção de modelos geométricos dos mesmos, utilizando o software ANSYS 5.5, que consiste de várias ferramentas para análise do projeto baseado no método dos elementos finitos. Foi também utilizado um software para a modelagem das peças e do conjunto do fixador já existente chamado SOLID EDGE, e logo em seguida o mesmo foi transferido para o software ANSYS 5.5 e simulado. Esta comparação servirá como complemento para possíveis modificações das montagens, dimensões e aplicações, não necessitando de novos ensaios mecânicos na máquina universal de ensaios e sim realizando simulações computadorizadas / The frequent problems of orthopedic and traumatic pathologies of the spinal column that involves the placement of an internal fixator (long screws, which are inserted in the subsequent pedicle until the vertebral and connected by bodies for wires in the longitudinal stems could be fastened in all the positions by the screw). These fixators were simulate in the computer through the construction of geometric models of the same ones, using the software ANSYS 5.5, that consists of several tools for analysis of the project based on the method of the finite elements. It was also used a software for the modelling of the pieces and of the group of the fixador already called existent SOLID EDGE, and then the same was transferred to the software ANSYS 5.5 and simulated. This comparison will serve a complement for possible modifications of the assemblies, dimensions and applications, not needing new mechanical test in the universal machine test but accomplishing computerized simulations

Este trabalho tem o intuito de fazer uso do processamento paralelo na análise não linear de cascas pelo método dos elementos finitos. O elemento finito de casca é obtido com o acoplamento de um elemento de placa e um de chapa. O elemento de placa utiliza formulação de Kirchhof (DKT) para placas delgadas e o elemento de chapa faz uso da formulação livre (FF), introduzindo um grau de liberdade rotacional nos vértices. A análise não-linear com plasticidade utiliza o modelo de plasticidade associada com algoritmo de integração explícito, modelo de escoamento de von Mises com integração em camadas (modelo estratificado), para materiais isotrópicos. A implementação em paralelo é realizada em um sistema com memória distribuída e biblioteca de troca de mensagens PVM (Parallel Virtual Machine). O procedimento não-linear é completamente paralelizado, excetuando a impressão final de resultados. As etapas que constituem o método dos elementos finitos, matriz de rigidez da estrutura e resolução do sistema de equações lineares são paralelizadas. Para o cálculo da matriz de rigidez utiliza-se um algoritmo com decomposição de domínio explícito. Para resolução do sistema de equações lineares utiliza-se o método dos gradientes conjugados com implementação em paralelo. É apresentada uma breve revisão bibliográfica sobre o paralelismo, com comentários sobre perspectivas em análise estrutural / This work aims at using parallel processing for nonlinear analysis of shells through finite element method. The shell finite element is obtained by coupling a plate element with a membrane one. The plate element uses Kirchhoff’s formulation (DKT) for thin plates and the membrane element makes use of the free formulation (FF), introducing a rotational degree of freedom at the vertexes. Nonlinear plastic analysis uses associated plasticity model with explicit integration algorithm, von Mises yelding model with layer integration (stratified model) for isotropic materials. Parallel implementation is done on a distributed memory system and message exchange library PVM (Parallel Virtual Machine). Nonlinear procedure is completely parallelised, but final printing of results. The finite element method steps, structural stifness matrix and solution of the linear equation system are parallelised. An explicit domain decomposition algorithm is used for the stifness matrix evaluation. To solve the linear equation system, one uses conjugated gradients method, with parallel implementation. A brief bibliography about parallelism is presented, with comments on structural analysis perspectives

This thesis examines the quantification of uncertainty in real-world engineering systems using the multilevel Monte Carlo method. It is often infeasible to use the traditional Monte Carlo method to investigate the impact of uncertainty because computationally it can be prohibitively expensive for complex systems. Therefore, the newer multilevel method is investigated and the cost of this method is analysed in the finite element framework. The Monte Carlo and multilevel Monte Carlo methods are compared for two prototypical examples: structural vibrations and buoyancy driven flows through porous media. In the first example, the impact of random mass density is quantified for structural vibration problems in several dimensions using the multilevel Monte Carlo method. Comparable eigenvalues and energy density approximations are found for the traditional Monte Carlo method and the multilevel Monte Carlo method, but for certain problems the expectation and variance of the quantities of interest can be computed over 100 times faster using the multilevel Monte Carlo method. It is also tractable to use the multilevel method for three dimensional structures, where the traditional Monte Carlo method is often prohibitively expensive. In the second example, the impact of uncertainty in buoyancy driven flows through porous media is quantified using the multilevel Monte Carlo method. Again, comparable results are obtained from the two methods for diffusion dominated flows and the multilevel method is orders of magnitude cheaper. The finite element models for this investigation are formulated carefully to ensure that spurious numerical artefacts are not added to the solution and are compared to an analytical model describing the long term sequestration of CO2 in the presence of a background flow. Additional cost reductions are achieved by solving the individual independent samples in parallel using the new podS library. This library schedules the Monte Carlo and multilevel Monte Carlo methods in parallel across different computer architectures for the two examples considered in this thesis. Nearly linear cost reductions are obtained as the number of processes is increased.

The dissertation is organized into two main parts. The first part considers fractal extension operators. Although extension operators are available for general subsets of Euclidean domains or metric spaces, our extension operator is unique in that it utilizes both the iterative nature of the fractal and finite element approximations to construct the operator. The resulting operator is especially well suited for future numerical work on domains with prefractal boundaries. In the dissertation we prove the existence of a linear extension operator, Π from the space of Hölder continuous functions on a fractal set S to the space of Hölder continuous functions on a larger domain Ω. Moreover this same extension operator maps functions of finite energy on the fractal to H1 functions on the larger domain Ω. In the second part, we consider boundary value problems in domains with fractal boundaries. First we consider the Sierpinski prefractal and how we might apply the technique of singular homogenization to thin layers constructed on the prefractal. We will also discuss numerical approximation in domains with fractal boundaries and introduce a finite element mesh developed for studying problems in domains with prefractal Koch boundaries. This mesh exploits the self-similarity of the Koch curve for arbitrary rational values of α and its construction is crucial for future numerical study of problems in domains with prefractal Koch curve boundaries. We also show a technique for mesh refinement so that singularities in the domain can be handled and present sample numerical results for the transmission problem.

O trabalho tem como objetivo a utilização do método dos elementos finitos para o cálculo da durabilidade de componentes mecânicos. Para isso, foi desenvolvido um estudo de caso que contempla, passo a passo, a metodologia utilizada. Um conjunto knuckle assembly dianteiro de um veículo off-road, fornecido por uma montadora nacional foi utilizado no estudo de caso. A geometria foi discretizada e modelada em software de pré-processamento em elementos finitos, o MSC.Patran®. Em seguida, foi submetida à análise estática no solver MSC.Nastran® para enfim obter-se o cálculo de durabilidade através do solver Fatigue®. Uma extensa revisão teórica foi realizada a fim de que o estudo tivesse embasamento teórico. / The work has as objective the use of the finite elements method for the calculation of the components durability. A case study using the proposal methodology was developed. A front set knuckle assembly of an off-road vehicle, supplied by a national assembly company was used in the case study. Geometry was discretized and shaped in software of pre-processing in finite elements, the MSC.Patran®. After that, it was submitted to the static analysis using the solver MSC.Nastran®, and the durability calculation using the solver Fatigue®. An extensive theoretical revision was carried through so that the study had theoretical basement.

Ces travaux se placent dans le cadre de l'étude des propriétés mécaniques des architectures à renforcement tridimensionnel dans les structures composites. Nous proposons une approche permettant de caractériser les propriétés mécaniques de structures composites Interlock et en particulier de résoudre les problèmes liés à la création de ces géométries complexes et leur discrétisation.Une des difficultés des approches méso-macro réside dans la manière de reproduire de façon fidèle la géométrie de ces architectures aux formes très complexes et d'obtenir en particulier un Volume Elémentaire Représentatif (VER) duquel on peut déduire par calcul éléments finis les propriétés mécaniques par homogénéisation. Cette pluralité des formes engendre des difficultés de mise en œuvre essentiellement géométriques et des difficultés de maillage bien connues : interpénétration et contact des mèches, maillage de fines couches de résines aux interfaces, détermination en tout point de l'orientation des fibres. Nous proposons une approche qui consiste à créer un modèle géométrique des mèches limitant ou contrôlant les intersections et les contacts, à définir un VER périodique et à mailler ce VER en tétraèdres avec des maillages conformes aux interfaces. Une fois le modèle maillé obtenu et les conditions de périodicités définies, les propriétés mécaniques effectives sont obtenues par homogénéisation. Les calculs par éléments finis sont réalisés avec le logiciel ABAQUS. Les tissages complexes ont été traités automatiquement avec cette technique. Les résultats sont confrontés à ceux d’autres modélisations, issus de la littérature et de l’expérience. / The work proposed here is devoted to the prediction and the characterization of the mechanical behavior of interlock woven composite structures. We propose an approach to characterize the mechanical properties of interlock woven composite structures and particularly to solve the problems associated with the creation of these complex geometries and their discretization into a conform mesh. One of the difficulties of this meso-macro approach is to reproduce faithfully the geometry of these architectures with complex shapes and to obtain a Representative Volume Element (RVE). Once this complex step is achieved, the mechanical properties of the composite can be thereafter obtained by homogenization from a finite element analysis. The difficulties to generate a RVE of such structures are well known: interpenetration and contacts between yarns, meshing of thin resin layers at interfaces, determination of the orientation of the fibers at all points of the structure. We propose an approach which consists of creating a geometric model of the yarns limiting or controlling the intersections and the contacts, defining a periodic RVE, meshing this RVE by tetrahedral with compatible meshes at the interfaces. Once the model is meshed and the symmetry conditions are defined, the properties are obtained by homogenization. The finite element calculations are performed on the ABAQUS software. Complex weaves can be automatically processed with this technique. The results are compared whit other modeling from the literature and with experimental data.

La Radio/Hadron-thérapie consiste à déposer une dose létale de rayonnement dans la tumeur tout en réduisant l'impact de cette dose sur les tissus sains. Les mouvements internes, en particulier ceux engendrés par la respiration modifient la forme, la position et la densité des organes, source d'erreur et d'incertitude sur la position du dépôt de dose. Lorsque la tumeur se trouve sur un organe en mouvement, la dificulté majeure est de cibler la tumeur pendant le traitement. Cette incertitude sur la position rend indispensable la mise en place d'une stratégie permettant la prédiction du mouvement tumoral. Ceci permet en eet de guider le faisceau de rayons ionisants de sorte qu'il suive les mouvements tumoraux. De plus, le traitement par hadronthérapie nécessite également l'accès à une description précise de la densité de l'ensemble des organes traversés par le faisceau, car la position du dépôt maximal de l'énergie véhiculée par les ions (le pic de Bragg) en dépend. Malheureusement, le mouvement respiratoire est complexe et sa prédiction n'est pas une tâche simple – en particulier, la respiration est commandée par l'action indépendante des muscles de la cage thoracique et du diaphragme. Les techniques actuelles basées sur l'imagerie, telles que le Cone-Beam ou le recalage dé- formable d'images, tentent de prédire la position des tumeurs pulmonaires. Ces méthodes font l'hypothèse d'un mouvement reproductible de l'appareil respiratoire dans le temps. D'autres techniques basées sur l'emploi de deux caméras à rayons X (cyberknife, tracking mis au point par l'équipe du Centre carbone d'Heildelberg [HIT]) peuvent permettre la pré- diction de la position des tumeurs, quand leur segmentation et leur contourage automatique en temps réel est possible. Cependant, ces méthodes sont, si ce n'est risquées, invasives, et elles ne permettent pas de calculer l'évolution des organes environnants, une information indispensable pour déterminer la position du pic de Bragg. Ainsi déduire le mouvement de la tumeur à partir de seules séries d'images médicales apparaît comme insuffisant. Une solution peut alors résider dans le développement d'un modèle biomécanique patient-spécifique du système respiratoire intégrant la variabilité du mouvement respiratoire. Pour que ce modèle soit précis, il doit comprendre la modélisation de la cage thoracique, du diaphragme et des poumons. Il est tout aussi important que ce modèle puisse être piloté par des paramètres mesurés en externe (capteurs 3D, spiromètre, etc.) an de préserver un caractère non-invasif et de corréler le mouvement externe du thorax et de l'abdomen, ainsi que le ux d'air échangé avec les mouvements internes. Les changements de propriétés mécaniques des milieux traversés par le faisceau doivent également être modélisés an de satisfaire les besoins de l'hadronthérapie. / The 4D computational patient specic of the respiratory system could be potentially used in various medical contexts; for diagnosis, treatment planning, laparoscopic, dose computation or the registration between online imaging systems such as positron emission tomography (PET), computed-tomography (CT) as well as high delity and precise computer-based training simulators. The main novelty of this PhD project lies in the context of radiation therapy; we have developed a patient-specic biomechanical model of the respiratory system enabling the correlation of the internal organs motion with respiratory surrogate signal(s) during the treatment. This permits to take into account the respiratory motion variabilities. The deformation of the dierent structures is controlled and driven by simulated rib cage (mimic the external intercostal muscles) and diaphragm actions. For the diaphragm, we have applied the radial direction of muscle forces, and simple homogeneous dirichlet boundary condition is applied to the lower part of the diaphragm, which is attached to the rib cage. For each rib a rigid transformation is calculated automatically by nite helical axis method (rigid translation and rotation) and used to dene displacement boundary conditions. The resulting widening of the thoracic cavity forces the lungs to expand due to an applied negative pressure in the pleural cavity. Other novelty of the PhD project, that the amplitude of the lung pressure and diaphragm force are patient-specic, and determined at dierent respiratory states by an optimization framework based on inverse FE analysis methodology, by minimizing the volume lungs errors, between the respiratory volume (calculated from CT scan images at each state) and the simulated volume (calculated by biomechanical simulation). All other structures are linked to each other, but feature dierent deformation behavior due to the assigned material properties. Our results are quite realistic compared to the 4D CT scan images and the proposed physically-based FE model is able to predict correctly the respiratory motion

A recently developed crystal-mechanics-based constitutive model for polycrystalline shape-memory alloys (Thamburaja and Anand [1]) is shown to quantitatively predict the in-plane anisotropy of superelastic sheet Ti-Ni to reasonable accord. / Singapore-MIT Alliance (SMA)