Multidisciplinary design optimization (MDO) refers to the process of designing systems characterized by the interaction of multiple interconnected disciplines. High-fidelity MDO usually requires large computational resources due to the computational cost of achieving multidisciplinary consistent solutions by coupling high-fidelity physics-based solvers. Gradient-based minimization algorithms are generally applied to find local minima, due to their efficiency in solving problems with a large number of design variables. This represents a limitation to performing global MDO and integrating black-box type analysis tools, usually not providing gradient information. The latter issues generally inhibit a wide use of MDO in complex industrial applications. An architecture named multi-criterion adaptive sampling MDO (MCAS-MDO) is presented in the current research for complex simulation-based applications. This research aims at building a global derivative-free optimization tool able to employ high-fidelity/expensive black-box solvers for the analysis of the disciplines. MCAS-MDO is a surrogate-based architecture featuring a variable level of coupling among the disciplines and is driven by a multi-criterion adaptive sampling (MCAS) assessing coupling and sampling uncertainties. MCAS uses the dynamic radial basis function surrogate model to identify the optimal solution and explore the design space through parallel infill of new solutions. The MCAS-MDO is tested versus a global derivative-free multidisciplinary feasible (MDF) approach, which solves fully-coupled multidisciplinary analyses, for two analytical test problems. Evaluation metrics include number of function evaluations required to achieve the optimal solution and sample distribution. The MCAS-MDO outperforms the MDF showing a faster convergence by clustering refined function evaluations in the optimum region. The architecture is applied to a steady fluid-structure interaction (FSI) problem, namely the design of a tapered three-dimensional carbon fiber-reinforced plastic hydrofoil for minimum drag. The objective is the design of shape and composite material layout subject to hydrodynamic, structural, and geometrical constraints. Experimental data are available for the original configuration of the hydrofoil and allow validating the FSI analysis, which is performed coupling computational fluid dynamics, solving the Reynolds averaged Navier-Stokes equations, and finite elements, solving the structural equation of elastic motion. Hydrofoil forces, tip displacement, and tip twist are evaluated for several materials providing qualitative agreement with the experiments and confirming the need for the two-way versus one-way coupling approach in case of significantly compliant structures. The free-form deformation method is applied to generate shape modifications of the hydrofoil geometry. To reduce the global computational expense of the optimization, a design space assessment and dimensionality reduction based on the Karhunen–Loève expansion (KLE) is performed off-line, i.e. without the need for high-fidelity simulations. It provides with a selection of design variables for the problem at hand through basis rotation and re-parametrization. By using the KLE, an efficient design space is identified for the current problem and the number of design variables is reduced by 92%. A sensitivity analysis is performed prior to the optimization to assess the variability associated with the shape design variables and the composite material design variable, i.e. the fiber orientation. These simulations are used to initialize the surrogate model for the optimization, which is carried out for two models: one in aluminum and one in composite material. The optimized designs are assessed by comparison with the original models through evaluation of the flow field, pressure distribution on the body, and deformation under the hydrodynamic load. The drag of the aluminum and composite material hydrofoils is reduced by 4 and 11%, respectively, increasing the hydrodynamic efficiency by 4 and 7%. The optimized designs are obtained by evaluating approximately 100 designs. The quality of the results indicates that global derivative-free MDO of complex engineering applications using expensive black-box solvers can be achieved at a feasible computational cost by minimizing the design space dimensionality and performing an intelligent sampling to train the surrogate-based optimization.

Ce travail consiste à développer un logiciel métier basé sur la modélisation thermomécanique linéaire de l'échangeur tout en intégrant les techniques d'homogénéisation. Une méthodologie de modélisation de l'échangeur constitué par un empilement de différentes ondes et tôles brasées, est donc adoptée. Cette méthodologie suppose que le comportement global de chaque couche d'ondes et tôles, est encadré par deux comportements limites déterminés par des approches mécanique périodique (HMP) et cinématique périodique (HCP). Ces deux approches sont mises en œuvre pour l’application numérique tout en étudiant le chargement interne global dû à la température et à la pression. Un outil d'homogénéisation (HomPass) est ensuite développé afin de déterminer automatiquement les comportements équivalents à chaque onde et tôle brasées. Cela contribue au développement de l'outil métier final (SiTEME) dédié à l'étude thermomécanique globale de l'échangeur. / This work consists of developing a software tool based on the linear thermomechanical modeling of the heat exchanger using homogenization techniques. A methodology for modeling the heat exchanger constituted by stacking of different brazed fins and sheets is adopted. This methodology assumes that the global behavior of every layer of fins and sheets is found between two behavior limits determined by periodic mechanical approach (HMP) and periodic kinematical approach (HCP). These techniques are implemented for numerical application while studying global loading due to the temperature and pressure internal loads. A homogenization tool (HomPass) is then developed in order to calculate automatically equivalent behaviors to each layer of brazed fins and sheets. That contributes to the development of the final software tool (SiTEME) dedicated to the global thermomechanical study of the heat exchanger.

Der Erfolg einer operativen Behandlung der Lendenwirbelsäule hängt von mehreren oft unbekannten Faktoren ab. Einen möglichen unbekannten Faktor stellen mechanische Größen dar, welche in In-vivo-Studien nur teilweise messbar oder in In-vitro-Versuchen nur eingeschränkt aussagefähig sind. Hier stellt die Finite-Elemente-Methode eine reproduzierbare numerische Möglichkeit dar, den mechanischen Einfluss verschiedener Operationsverfahren a priori zu ermitteln. In dieser Arbeit ist ein Finite-Elemente-Modell der Lendenwirbelsäule erstellt worden, welches mit Hilfe vorhandener Ergebnisse aus In-vivo- und In-vitro-Untersuchungen validiert werden konnte und das die Simulation verschiedener Operationsverfahren ermöglicht. Weiterhin wurde eine Methode zur Abschätzung der Muskelkräfte entwickelt, die eine realistischere Belastung des Modells erlaubt als bisher üblich. Die Anwendung des Modells erstreckte sich in dieser Arbeit auf Dekompressionsverfahren zur Entlastung des Spinalkanals und Fusionsverfahren zur Herstellung der lumbalen Stabilität. Der Einfluss der Variation verschiedener Modell- und Operationsparameter wurde ermittelt. Hierzu zählen insbesondere die Steifigkeiten der Bänder, der Resektionsgrad bei der Dekompression des Spinalkanals und die unterschiedlichen Charakteristika des für die Fusion nötigen Knochenspans. Die Ergebnisse erweitern das biomechanische Verständnis der Wirbelsäule und geben Aufschluss über die Einflüsse wichtiger Operationsparameter. / The success of a surgical treatment at the lumbar spine depends on several, often unknown, factors. Mechanical values are one possible unknown factor. During in vivo studies these values are often not measurable and their relevance during in vitro experiments is limited. The finite element method is a reproducible numerical method which allows to determine the mechanical influence of different surgical techniques a priori. A finite element model of the lumbar spine has been created in this study. It was validated with existing values from in vivo and in vitro investigations and therefore makes the simulation of surgical techniques possible. Additionally, a method to estimate muscle forces was created. This method allows a more realistic loading of the model than usual. In this study, the model was used to simulate decompressional procedures to release the spinal cord and fusional techniques to regain lumbar stability. The influence of variations in model and surgical parameters on the mechanical behaviour was determined. In particular, the effects of ligament stiffness, the degree of decompression and different bone graft characteristics was determined. The results extend biomechanical knowledge about the spine and reveal the influence of important surgical parameters.

[pt] A fundação em estaxa é uma das alternativas mais antigas de suporte de estruturas,mas seu projeto ainda é um desfio para engenharia geotécnica, sendo muito em pricípios empíricos. As estacas são elementos esbeltos de grande comprimento relativo, gerlamente utilizadas quando os solos que compõem as camadas mais superficiais do terreno não são suficientemente resistentes para suportar as cargas da superestrutura. A capacidade de suporte de estacas pode ser estimada através de métodos teóricos, semi-empíricos. Para aplicação de um método teórico é necessário o conhecimento mais detalhado da geometria do problema, das propriedades tensão x defromação x resistência dos solos, das características da interface solo-estaca,etc., enquanto que para os métodos semiempíricos a aplicação é geralmenta feita com base em resultados de ensaios de campo. As formulaçõessemi-empíricas são as mais usuais na prática da engenharia para o cálculo da capacidade de suporte de estacas visto que os métodos teóricos, à exceção de grandes projetos, têm sua aplicação ainda restrita. Na prática brasileira,os projetos de fundações são elaborados frequentemente com base em resultados de ensaio SPT, sendo os dois métodos mais utilizados para a obtenção da capacidade de carga de estacas os métodos propostos por Aoki e Velloso (1975) e Décourt e Quaresma (1978, 1982). O objetivo deste trabalho consiste em comparar algumas das metodologias correntemente utilizadas na previsão da capacidade de suporte de estacas sob carregamento axial com as previsões obtidas em análises teóricaspelo método dos elementos finitos, através da utilização do programa Plaxis v. 8. / [en] Pile is one of the oldest alternatives of support of structures but its designis still considered a challenge for the ground engineering,being based on empirical principles. Piles are slender elements of great relative length, generally used when soils that compose the most superficial layers of the soil profile are not sufficiently resistant to support the loads from superstructure. The bearing capacity of piles can be estimated by empirical and theoretical approaches. For application of a theoretical approach a more detailed knowledge is necessary about the geometry of the problem, the tension x deformation x resistence soil satate, interface soil-pile characteristics and others, while for empirica approaches the application is generally done on the basis of field test results. The empirical formulations are the most usual in the practice of the engineering for the calculation of the bearing capacity of piles since theoretical approaches have iots application restricted. In brazilian engineering practice, the projects of foundations are elaborated frequently on the basis of SPT test results, being the two approachesd more utilized proposed by Aoki and Velloso (1975) and Décourt and Quaresma (1978, 1982). The objective of this work is compare some of the methodologies currently utilized to obtain the bearing capacity of the piles under axial loading with the results obtained in theoretical analysis by finite element approach, using Plaxis verion 8.0 software.

The first ocean general circulation models developed in the late sixties were based on finite differences schemes on structured grids. Many improvements in the fields of engineering have been achieved since three decades with the developments of new numerical methods based on unstructured meshes. Some components of the first models may now seem out of date and new second generation models are therefore under study, with the aim of taking advantage of the potential of modern numerical techniques such as finite elements. In particular, unstructured meshes are believed to be more efficient to resolve the large range of time and space scales present in the ocean. Besides the classical continuous finite element or finite volume methods, another popular new trend in engineering applications is the Discontinuous Galerkin (DG) method, i.e. discontinuous finite elements presenting many interesting numerical properties in terms of dispersion and dissipation, errors convergence rates, advection schemes, mesh adaptation, etc. The method is especially efficient at high polynomial orders. The motivation for this PhD research is therefore to investigate the use of the high-order DG method for geophysical flow modeling. A first part of the thesis is devoted to the mesh adaptation using the DG method. The inter-element jumps of the fields are used as error estimators. New mesh size fields or polynomial orders are then derived and local h- or p-adaptation is performed. The technique is applied to standard benchmarks and computations in more realistic domains as the Gulf of Mexico. A second part deals with the use of the high order DG method with high-order representation of geometrical features. On one hand, a method is proposed to deal with complex representations of the coastlines. Computations are performed using high-order mappings around the Rattray island, located in the Great Barier Reef. Numerical results are then compared to in-situ measurements. On the other hand, a new method is proposed to deal with curved manifolds in order to represents oceanic or atmospheric flows on the sphere. The approach is based on the use of a local high-order non-orthogonal basis, and is equivalent to the use of vectorial shape and test functions to represent the vectorial conservation laws on the manifold's surface. A method is finally proposed to analyze the dispersion and dissipation properties of any numerical scheme on any kind of grid, possibly unstructured. The DG method is then compared to other techniques as the mixed non-conforming linear elements, and the impact of unstructured meshes is studied.

L’adaptation des surfaces pour des fonctions prédéterminées par le choix des matériaux métalliques ou des couches minces ayant des propriétés mécaniques avancées peut potentiellement permettre de réaliser des nouvelles applications à petites échelles. Concevoir de telles applications utilisant des nouveaux matériaux nécessite en premier lieu la connaissance des propriétés mécaniques des matériaux ciblés à l’échelle microscopique et nanoscopique. Une méthode souvent appliquée pour caractériser les matériaux à petites échelles est la nanoindentation, qui peut être vue comme une mesure de dureté à l’échelle nanoscopique. Ce travail présente une contribution relative à l'interprétation des résultats de la nanoindentation, qui fait intervenir un grand nombre de phénomènes physiques couplés à l'aide de simulations numériques. A cette fin une approche interdisciplinaire, adaptée aux phénomènes apparaissant à petites échelles, et située à l’intersection entre la physique, la mécanique et la science des matériaux a été utilisée. Des modèles numériques de la nanoindentation ont été conçus à l'échelle atomique (modèle discret) et à l'échelle des milieux continus (méthode des éléments finis), pour étudier le comportement du nickel pur. Ce matériau a été choisi pour ses propriétés mécaniques avancées, sa résistance à l'usure et sa bio-compatibilité, qui peuvent permettre des applications futures intéressantes à l'échelle nanoscopique, particulièrement dans le domaine biomédical. Des méthodes avancées de mécanique du solide ont été utilisées pour prendre en compte les grandes déformations locales du matériau (par la formulation corotationelle), et pour décrire les conditions de contact qui évoluent au cours de l'analyse dans le modèle à l'échelle des milieux continus (traitement des conditions de contact unilatérales et tangentielles par une forme de Lagrangien augmenté). L’application des modèles numériques a permis de contribuer à l’identification des phénomènes qui gouvernent la nanoindentation du nickel pur. Le comportement viscoplastique du nickel pur pendant nanoindentation a été identifié dans une étude expérimentale-numérique couplée, et l'effet cumulatif de la rugosité et du frottement sur la dispersion des résultats de la nanoindentation a été montré par une étude numérique (dont les résultats sont en accord avec des tendances expérimentales). Par ailleurs, l’utilisation de l’outil numérique pour une autre application à petites échelles, la manipulation des objets par contact, a contribué à la compréhension de la variation de l’adhésion électrostatique pendant micromanipulation. La déformation plastique des aspérités de surface sur le bras de manipulateur (en nickel pur) a été identifiée comme une source potentielle d’augmentation importante de l'adhésion pendant la micromanipulation, qui peut potentiellement causer des problèmes de relâche et de précision de positionnement, observés expérimentalement. Les résultats présentés dans cette thèse montrent que des simulations numériques basées sur la physique du problème traité peuvent expliquer des tendances expérimentales et contribuer à la compréhension et l'interprétation d'essais couramment utilisé pour la caractérisation aux petites échelles. Le travail réalisé dans cette thèse s’inscrit dans un projet de recherche appelé "mini-micro-nano" (mµn), financé par la Communauté Française de Belgique dans le cadre de "l'Action de Recherche Concertée", convention 04/09-310.

Intervertebral disc (IVD) degeneration is primarily involved in back pain, a morbidity that strongly affects the quality of life of individuals nowadays. Lumbar IVDs undergo stressful mechanical loads while being the largest avascular tissues in our body: Mechanical principles alone cannot unravel the intricate phenomena that occur at the cellular scale which are fundamental for the IVD regeneration. The present work aimed at coupling biomechanical and relevant molecular transport processes for disc cells to provide a mechanobiological finite element framework for a deeper understanding of degenerative processes and the planning of regenerative strategies. Given the importance of fluid flow within the IVD, the influence of poroelastic parameters such as permeabilities and solid-phase stiffness of the IVD subtissues was explored. A continuum porohyperelastic material model was then implemented. The angles of collagen fibers embedded in the annulus fibrosus (AF) were calibrated. The osmotic pressure of the central nucleus pulposus (NP) was also taken into account. In a parallel study of the human vertebral bone, microporomechanics was used together with experimental ultrasonic tests to characterize the stiffness of the solid matrix, and to provide estimates of poroelastic coefficients. Fluid dynamics analyses and microtomographic images were combined to understand the fluid exchanges at the bone-IVD interface. The porohyperelastic model of a lumbar IVD with poroelastic vertebral layers was coupled with a IVD transport model of three solutes - oxygen, lactate and glucose - interrelated to reproduce the glycolytic IVD metabolism. With such coupling it was possible to study the effect of deformations, fluid contents, solid-phase stiffness, permeabilities, pH, cell densities of IVD subtissues and NP osmotic pressure on the solute transport. Moreover, cell death governed by glucose deprivation and lactate accumulation was included to explore the mechanical effect on cell viability. Results showed that the stiffness of the AF had the most remarkable role on the poroelastic behavior of the IVD. The permeability of the thin cartilage endplate and the NP stiffness were also relevant. The porohyperelastic model was shown to reproduce the local AF mechanics, provided the fiber angles were calibrated regionally. Such back-calculation led to absolute values of fibers angles and to a global IVD poromechanical behavior in agreement with experiments in literature. The inclusion of osmotic pressure in the NP also led to stress values under confined compression comparable to those measured in healthy and degenerated NP specimens. For the solid bone matrix, axial and transverse stiffness coefficients found experimentally in the present work agreed with universal mass density-elasticity relationships, and combined with continuum microporomechanics provided poroelastic coefficients for undrained and drained cases. The effective permeability of the vertebral bony endplate calculated with fluid dynamics was highly correlated with the porosity measured in microtomographic images. The coupling of transport and porohyperelastic models revealed a mechanical effect acting under large volume changes and high compliance, favored by healthy rather than degenerated IVD properties. Such effect was attributed to strain-dependent diffusivities and diffusion distances and was shown to be beneficial for IVD cells due to the load-dependent increases of glucose levels. Cell density, NP osmotic pressure and porosity were the most important parameters affecting the coupled mechano-transport of metabolites. This novel study highlights the restoration of both cellular and mechanical factors and has a great potential impact for novel designs of treatments focused on tissue regeneration. It also provides methodological features that could be implemented in clinical image-based tools and improve the multiscale understanding of the human spine mechanobiology.

Many important factors affect the spread of childhood infectious disease. To understand better the fundamental drivers of infectious disease spread, several researchers have estimated seasonal transmission coefficients using discrete-time models. This research addresses several shortcomings of the discrete-time approaches, including removing the need for the reporting interval to match the serial interval of the disease using infectious disease data from three major cities: New York City, London, and Bangkok. Using a simultaneous approach for optimization of differential equation systems with a Radau collocation discretization scheme and total variation regularization for the transmission parameter profile, this research demonstrates that seasonal transmission parameters can be effectively estimated using continuous-time models. This research further correlates school holiday schedules with the transmission parameter for New York City and London where previous work has already been done, and demonstrates similar results for a relatively unstudied city in childhood infectious disease research, Bangkok, Thailand.

This study aims to develop a computer program to perform finite elements based fracture mechanics analyses of three dimensional surface cracks in T-welded joints of construction machinery. The geometrical complexity of the finite elements models and the requirement of large computer resources for the analyses necessitate the use of shell elements for general stress distribution optimization. A sub-modeling technique, together with a shell to solid conversion method, enables the user to model a local region and analyze it by defining the weld and crack parameters. It is assumed that the weld material is the same with the sheet metal material and the surface cracks are considered to occur on two weld toes and weld root. The surface cracks are assumed to have a semi elliptical crack front profile. In order to simulate the square-root strain singularity around the crack front, collapsed 20-node three dimensional brick elements are utilized. The rest of the local model is modeled by using 20-node three dimensional brick elements. The main objective of this work is to calculate the mixed mode energy release rates around the crack front for a sub-model of a global shell model by using J-integral method.

In an effort to achieve lighter and more economical space structures, a new patented steel composite member has been suggested and used in the construction of some steel roof structures. This special element has a sandwich construction composed of some strips of steel plates placed longitudinally along a helical wire core. The function of the helical core is to transfer the shear between the flange plates and increase the sectional inertia of the resulting composite member by keeping the flange plates at a desired distance from each other. Because of the lack of research, design engineers usually treat such elements as a solid member as if it has a full shear transfer between the flanges. However, a detailed analysis shows that this is not a valid assumption and leads to very unsafe results. In this context, the purpose of this study is to investigate the behavior of such members under axial compression and determine their effective sectional flexural rigidity by taking into account the shear deformations. This study applies an analytical investigation to a specific form of such elements with four flange plates placed symmetrically around a helical wire core. Five independent parameters of such a member are selected for this purpose. These are the spiral core and core wire diameters, the pitch of the spiral core, and the flange plate dimensions. Elements with varying combinations of the selected parameters are first analyzed in detail by finite element method, and some design charts are generated for the determination of the effective sectional properties to be used in the structural analysis and the buckling loads. For this purpose, an alternative closed-form approximate analytical solution is also suggested.