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

The aim of the thesis is the understanding of the thermal, mechanical and metallurgical phenomena occurring during friction stir welding of a 6005A aluminum alloy and the determination of the mechanical properties of the welded joints. The forces and the torque needed for welding as well as the thermal cycles were measured in the various zones of the joint. A first model predicts the influence of the welding parameters on the thermal cycles, and especially on the asymmetry of the temperature evolution with respect to the weld centerline. A second model links the local microstructural evolutions, and in particular the precipitation kinetics, to the thermomechanical cycles. A third model relates the local microstructures to the local mechanical properties, based on a novel physics-based strain hardening model. Finally, the link between the mechanical properties of the joint in service, the local mechanical properties and the microstructures is modeled using a multi-scale approach including a micro-mechanics damage constitutive model. The models are calibrated and validated through in-depth microstructure characterization and mechanical tests on the base material, on heat treated samples and on the friction stir welds.

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)

Hollow section members are widely used in industrial applications for the design of many machine and structural components. These components are often fabricated at lower cost by welding rather than by casting or forging. For instance, in agricultural machinery, the hollow tubes are typically connected together through welding to form T-joints. Such T-joint connections are also employed in other engineering applications such as construction machinery, offshore structures, bridges, and vehicle frames. In this dissertation, the behaviour of tubular T-joint connections, in particular square hollow section (SHS)-to-SHS T-joints, subjected to static and cyclic loads is studied both experimentally and numerically. The techniques used for the fabrication of the T-joint connections can affect their strengths to different degrees. With modern advances in manufacturing technologies, there are many alternatives for the fabrication of the T-joint connections. For instance, in recent years, the use of the laser beam has become increasingly common in industrial applications. From a manufacturing point of view, the T-joint connections can be fabricated by using traditional mechanical cutting or laser cutting techniques. Currently, for the fabrication of the T-joint connections, the straight edge of one tube is cut using mechanical tools (e.g., flame cutting) and then welded to the body of the other tube. A major contribution of this research work is investigating the feasibility of using laser cutting to produce welded square hollow-section T-joints with similar or higher fatigue strengths than their conventional mechanical cut counterparts. For this purpose, a total of 21 full-scale T-joint samples, typical of those found in the agricultural machinery, are included for the study. Finite Element (FE) models of the T-joints manufactured with the different cutting techniques are also developed and the FE results are verified with the experiments. The results of the numerical and experimental study on the full-scale T-joint samples show that the fatigue strength of the samples that are manufactured with laser cutting is higher than those fabricated with conventional mechanical cutting. From a structural analysis view point, despite of the wide use of tubular T-joint connections as efficient load carrying members, a practical but yet simple and accurate approach for their design and analysis is not available. For this purpose, engineers must often prepare relatively complicated and time consuming FE models made up of shell or solid elements. This is because unlike solid-section members, when hollow section members are subjected to general loadings, they may experience severe deformations of their cross-sections that results in stress concentrations in the connections vicinity. One of the objectives/contributions of this research work is the better understanding of the behaviour of SHS-to-SHS T-joint connections under in-plane bending (IPB) and out-of-plane bending (OPB) loading conditions. Through a detailed Finite Element Analysis (FEA) using shell and solid elements, the stiffness and stress distribution at the connection of the tubular T-joints are obtained for different loading conditions. It is observed that at a short distance away from the connection of the T-joints, the structure behaves similar to beams when subjected to loadings. The beam like stresses cease to be valid only in the vicinity of the connection. Therefore, several parameters are defined to recognize the joints stress concentrations and the bending stiffness reduction. These parameters permit the accurate modelling of the tubes and the T-connection by simple beam elements with certain modifications. The models consisting of beam elements are significantly easier to prepare and analyze. Through several numerical examples, it is shown that the modified beam models provide accurately all important information of the structural analysis (i.e. the stresses, displacements, reaction forces, and the natural frequencies) at substantially reduced computational effort in comparison with the complicated Finite Element (FE) models built of shell or solid elements. Another contribution of this research work is the FE modelling of the weld geometry and its effect on the stresses at the vicinity of the connection. The results of the FE modelling are verified through a detailed experimental study. For the experimental study, two test fixtures with hydraulic actuators capable of applying both static and cyclic loadings are designed and used. Strain gauges are installed at several locations on full-scale T-joint samples to validate the developed FE models. It is shown that the membrane stresses which occur at the mid-surface of the tubes remain similar regardless of the weld geometry. The weld geometry only affects the bending stresses. It is also shown that this effect on bending stresses is highly localized and disappears at a distance of about half of the weld thickness away from the weld-toe. To reduce the stress concentrations at the T-joint, plate reinforcements are used in a number of different arrangements and dimensions to increase the load carrying capacity of the connection.

Hollow section members are widely used in industrial applications for the design of many machine and structural components. These components are often fabricated at lower cost by welding rather than by casting or forging. For instance, in agricultural machinery, the hollow tubes are typically connected together through welding to form T-joints. Such T-joint connections are also employed in other engineering applications such as construction machinery, offshore structures, bridges, and vehicle frames. In this dissertation, the behaviour of tubular T-joint connections, in particular square hollow section (SHS)-to-SHS T-joints, subjected to static and cyclic loads is studied both experimentally and numerically. The techniques used for the fabrication of the T-joint connections can affect their strengths to different degrees. With modern advances in manufacturing technologies, there are many alternatives for the fabrication of the T-joint connections. For instance, in recent years, the use of the laser beam has become increasingly common in industrial applications. From a manufacturing point of view, the T-joint connections can be fabricated by using traditional mechanical cutting or laser cutting techniques. Currently, for the fabrication of the T-joint connections, the straight edge of one tube is cut using mechanical tools (e.g., flame cutting) and then welded to the body of the other tube. A major contribution of this research work is investigating the feasibility of using laser cutting to produce welded square hollow-section T-joints with similar or higher fatigue strengths than their conventional mechanical cut counterparts. For this purpose, a total of 21 full-scale T-joint samples, typical of those found in the agricultural machinery, are included for the study. Finite Element (FE) models of the T-joints manufactured with the different cutting techniques are also developed and the FE results are verified with the experiments. The results of the numerical and experimental study on the full-scale T-joint samples show that the fatigue strength of the samples that are manufactured with laser cutting is higher than those fabricated with conventional mechanical cutting. From a structural analysis view point, despite of the wide use of tubular T-joint connections as efficient load carrying members, a practical but yet simple and accurate approach for their design and analysis is not available. For this purpose, engineers must often prepare relatively complicated and time consuming FE models made up of shell or solid elements. This is because unlike solid-section members, when hollow section members are subjected to general loadings, they may experience severe deformations of their cross-sections that results in stress concentrations in the connections vicinity. One of the objectives/contributions of this research work is the better understanding of the behaviour of SHS-to-SHS T-joint connections under in-plane bending (IPB) and out-of-plane bending (OPB) loading conditions. Through a detailed Finite Element Analysis (FEA) using shell and solid elements, the stiffness and stress distribution at the connection of the tubular T-joints are obtained for different loading conditions. It is observed that at a short distance away from the connection of the T-joints, the structure behaves similar to beams when subjected to loadings. The beam like stresses cease to be valid only in the vicinity of the connection. Therefore, several parameters are defined to recognize the joints stress concentrations and the bending stiffness reduction. These parameters permit the accurate modelling of the tubes and the T-connection by simple beam elements with certain modifications. The models consisting of beam elements are significantly easier to prepare and analyze. Through several numerical examples, it is shown that the modified beam models provide accurately all important information of the structural analysis (i.e. the stresses, displacements, reaction forces, and the natural frequencies) at substantially reduced computational effort in comparison with the complicated Finite Element (FE) models built of shell or solid elements. Another contribution of this research work is the FE modelling of the weld geometry and its effect on the stresses at the vicinity of the connection. The results of the FE modelling are verified through a detailed experimental study. For the experimental study, two test fixtures with hydraulic actuators capable of applying both static and cyclic loadings are designed and used. Strain gauges are installed at several locations on full-scale T-joint samples to validate the developed FE models. It is shown that the membrane stresses which occur at the mid-surface of the tubes remain similar regardless of the weld geometry. The weld geometry only affects the bending stresses. It is also shown that this effect on bending stresses is highly localized and disappears at a distance of about half of the weld thickness away from the weld-toe. To reduce the stress concentrations at the T-joint, plate reinforcements are used in a number of different arrangements and dimensions to increase the load carrying capacity of the connection.