Dans le contexte industriel actuel, où la simulation numérique joue un rôle majeur, de nombreux outils sont développés afin de rendre les calculs les plus performants et exacts possibles en utilisant les ressources numériques de façon optimale. Parmi ces outils, ceux non-intrusifs, c’est-à-dire ne modifiant pas les codes commerciaux disponibles mais permettant d’utiliser des méthodes de résolution avancées telles que l’analyse isogéométrique ou les couplages multi-échelles, apparaissent parmi les plus attirants pour les industriels. L’objectif de cette thèse est ainsi de coupler l’Analyse IsoGéométrique (AIG) et la Méthode des Éléments Finis (MEF) standard pour l’analyse de détails structuraux par une approche non-intrusive et certifiée. Dans un premier temps, on développe un lien global approché entre les fonctions de Lagrange, classiquement utilisées en éléments finis et les fonctions NURBS bases de l’AIG, ce qui permet d’implémenter des analyses isogéométriques dans un code industriel EF vu comme une boîte noire. Au travers d’exemples linéaires et non-linéaires implémentés dans le code industriel Code_Aster de EDF, nous démontrons l’efficacité de ce pont AIG\MEF et les possibilités d’applications industrielles. Il est aussi démontré que ce lien permet de simplifier l’implémentation du couplage non-intrusif entre un problème global isogéométrique et un problème local éléments finis. Ensuite, le concept de couplage non-intrusif entre les méthodes étant ainsi possible, une stratégie d’adaptation est mise en place afin de certifier ce couplage vis-à-vis d’une quantité d’intérêt. Cette stratégie d’adaptation est basée sur des méthodes d’estimation d’erreur a posteriori. Un estimateur global et des indicateurs d’erreur d’itération, de modèle et de discrétisation permettent de piloter la définition du problème couplé. La méthode des résidus est utilisée pour évaluer ces erreurs dans des cas linéaires, et une extension aux problèmes non-linéaires via le concept d’Erreur en Relation de Comportement (ERC) est proposée. / In the current industrial context where the numerical simulation plays a major role, a large amount of tools are developed in order to perform accurate and effective simulations using as less numerical resources as possible. Among all these tools, the non-intrusive ones which do not modify the existing structure of commercial softwares but allowing the use of advanced solving methods, such as isogeometric analysis or multi-scale coupling, are the more attractive to the industry. The goal of these thesis works is thus the coupling of the Isogeometric Analysis (IGA) with the Finite Element Method (FEM) to analyse structural details with a non-intrusive and certified approach. First, we develop an approximate global link between the Lagrange functions, commonly used in the FEM, and the NURBS functions on which the IGA is based. It’s allowed the implementation of isogeometric analysis in an existing finite element industrial software considering as a black-box. Through linear and nonlinear examples implemented in the industrial software Code_Aster of EDF, we show the efficiency of the IGA\FEM bridge and all the industrial applications that can be made. This link is also a key to simplify the non-intrusive coupling between a global isogeometric problem and a local finite element problem. Then, as the non-intrusive coupling between both methods is possible, an adaptive process is introduced in order to certify this coupling regarding a quantity of interest. This adaptive strategy is based on a posteriori error estimation. A global estimator and indicators of iteration, model and discretization error sources are computed to control the definition of the coupled problem. Residual base methods are performed to estimated errors for linear cases, an extension to the concept of constitutive relation errors is also initiated for non-linear problems.

Es werden Kontaktprobleme im Rahmen der nichtlinearen Elastizitätstheorie mit Mitteln der Variationsrechnung behandelt. Dabei liegt das Hauptaugenmerk auf der Untersuchung des Selbstkontakts eines nichtlinear elastischen Körpers. Unter Verwendung einer geeigneten Lagrangeschen Multiplikatorenregel wird eine notwendige Bedingung für Minimierer hergeleitet. Weiterhin werden Ergebnisse für den Kontakt zweier elastischer Körper formuliert.

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The goal of this project is to develop virtual surgical simulation software in order to simulate the suturing and knot tying processes associated with surgical thread. State equations are formulated using Lagrangian mechanics, which is useful for the conservation of energy. Solver methods are developed with theory based in Differential Algebraic Equations (DAEs) which concern governing Ordinary Differential Equations (ODEs) that are constraint with Algebraic Equations (AE). An implicit integration scheme and Newton's method is used to solve the system in each step. Furthermore, a collision response process based on the Linear Complementarity Problem (LCP) is implemented to handle collisions and measure their forces. Models have been developed to represent the different types of objects. A spline model is used to represent the suture and mass-spring model for the tissue. They were both selected for their efficiency and base on real physical properties. The spline model was also chosen as it is continuous and can be evaluated at any point along the length. Other objects are also defined such as rigid bodies. The Lagrangian multiplier method is used to define the constraints in the model. This allows for the construction of complex models. An important constraint is the suturing constraint, which is created when a sufficient force is applied by the suture tip on to the tissue. This constraint allows only a sliding point along the suture to pass through a specific point on the tissue. This results in a virtual suturing model which can be built on for use in surgical simulations. Further investigations would be interesting to increase performance, accuracy and scope of the simulator. / Det här projektet syftar till att utveckla mjukvara för virtuell simulering av kirurgi som involverar knytande av suturtråd. Lagranges ekvationer används för att härleda energibevarande tillståndsekvationer. Lösningsmetoderna grundar sig i teori från området Differential-Algebraiska Ekvationer (DAEer), som avser att kontrollera Ordinära Differentialekvationer (ODEer) med algebraiska bivillkor. Ett implicit integrationsschema och Newtons metod används för att lösa systemet i varje steg. Utöver det så implementeras en kollisionsrespons-process baserad på det linjära komplementaritetsproblemet (LCP) för att hantera kollisioner och mäta deras krafter. Modeller har utvecklats för att representera olika typer av objekt. En spline-modell används för att representera suturtråden och ett mass-fjäder system för vävnaden. Valet baserades på deras höga prestanda samt starka anknytning till objektens fysiska egenskaper. Spline-modellen valdes också då dess kontinuitet innebär att den går att evaluera för en godtycklig punkt inom dess domän. Andra objekt, såsom stela kroppar, finns också definierade. Lagrangemultiplikator används för att definiera bivillkor i modellen. Detta tillåter konstruktionen av komplexa modeller. Ett viktigt bivillkor är sutur-bivillkoret som uppstår när tillräcklig kraft från spetsen på den kirurgiska nålen appliceras på vävnaden. Detta bivillkor tillåter att endast en glidande punkt längsmed suturen passerar genom en specifik punkt på vävnaden. Detta resulterar i en virtuell modell för stygn som kan byggas vidare på för användning i kirurgiska simulationer. Det vore intressant med ytterligare undersökningar för att förbättra prestandan, precisionen och simulatorns omfattning.

This thesis aims to explore if multibody simulations is a suitable method to investigate vibrations in the steering system of trucks. Vibrations in the steering system and subsequently in the steering wheel is a common issue that automotive manufacturers face. The vibration levels in the steering wheel are in some countries regulated and some vibration phenomena can even cause issues with the handling properties of the whole vehicle. Therefore being able to predict and reduce these with the help of multibody simulations would be of great value. The thesis does this by comparing the simulations to measurements. It investigates what parts can be approximated as rigid, what the effects different numerical solvers have and compares different driving scenarios. This can however be quite challenging, one reason being that the differential equations arising when performing multibody simulations of trucks are very stiff. The numerical challenges of this must be overcome while still keeping the resolution of the accelerations in the solution high enough to still be representative of reality. The thesis also explains how to mathematically model a physical system such that the numerical analysis of it can be efficient. The results show that the success of multibody simulations is very dependent on the test case. However, they also show that together with physical measurements multibody simulations can be a powerful complementary tool. The thesis also presents improvements that could be made to the model as well as certain key areas that need to be studied more in order to align the multibody simulations results with measurements. The multibody simulations software used to perform the calculations and the modelling in the report is Adams developed by Hexagon AB. / Den här rapporten syftar till att ge inblick i om flerkroppssimuleringar kan vara ett användbart verktyg för att undersöka styrsystemsvibrationer i lastbilar. Dessa vibrationer är orsaken till en mängd styrningsproblem samt att rattvibrationer har lagkrav att inte vara för stora. Att kunna förutspå och efterlikna dessa vibrationer med flerkroppssimulering skulle därmed vara till stor fördel. Detta undersöks genom att jämföra simuleringarna med mätdata. Det undersöks vilken påverkan stelkroppsapproximationer av vissa komponenter har, påverkan av olika numeriska integrationmetoder samt steglängder och även olika körningslastfall. Att genomföra flerkroppssimuleringar av lastbilar är dock inte alltid helt enkelt, på grund av differentialekvationernas styva karaktär uppstår ofta konvergensproblem. Ska man sedan använda resultaten för att undersöka styrsystemsvibrationer måste man överkomma dessa konvergensproblem men bibehålla en tillräckligt fin upplösning av resultatet för att resultatet fortfarande ska vara representativt av den fysiska lastbilens dynamiska egenskaper. Rapporten beskriver även hur man kan gå tillväga för att matematiskt modellera ett fysisk system så att det effektivt går att utföra dynamisk analys av det. Resultaten visar att flerkroppssimulering kan vara väldigt beroende på vad körfallet är, med vissa körfall där simuleringar och mätningar stämmer väl överens och andra där detta inte är fallet. På grund av detta kan det vara otillräckligt att endast använda flerkroppssimulering för att utvärdera styrsystemsvibrationer, men resultaten visar att tillsammans med mätdata kan flerkroppssimulering vara ett kraftfullt komplement. I rapporten presenteras även exempel av viktiga komponenter att ta hänsyn till för att bättre kunna simulera styrsystemsvibrationer samt områden där mer forskning har potential att förbättra flerkroppssimuleringar i hänsyn till styrsystemsvibrationer. Mjukvaran som används för att utföra flerkroppssimulering är Adams som utvecklas av Hexagon AB.

Thesis (MEng) -- Stellenbosch University, 2014. / ENGLISH ABSTRACT: See PDF for abstract. / AFRIKKANSE OPSOMMING: Sien PDF vir die opsomming.

L'objectif de la thèse est de contribuer à l'amélioration du modèle des astéroïdes dans l'éphéméride INPOP (Intégration Numérique Planétaire de l'Observatoire de Paris). La prise en compte imparfaite des astéroïdes dans les modèles dynamiques est considérée aujourd'hui comme le facteur limitant de la qualité des éphémérides, que ce soit en terme de précision des paramètres ajustés ou en terme de capacité à extrapoler les éphémérides au-delà des observations disponibles. Le grand nombre d'astéroïdes présents dans le Système Solaire et le peu d'informations disponibles sur leurs masses rendent en effet l'implémentation de ces objets particulièrement difficile. Après la présentation d'un cadre analytique et la recherche numérique des astéroïdes les plus perturbateurs, on propose une approche nouvelle. L'approche consiste à sélectionner un nombre restreint d'individus parmi un ensemble d'environ 25000 astéroïdes de telle sorte que la perturbation induite sur les planètes par l'ensemble, privé de la sélection, soit similaire à la perturbation induite par un anneau solide centré sur le Soleil. L'optimisation de la sélection fait partie des problèmes quadratiques mixtes où on cherche à ajuster simultanément des paramètres réels et entiers. On compile une nouvelle liste de 276 astéroïdes à implémenter avec un anneau dans le modèle dynamique d'une éphéméride planétaire. L'optimisation de la sélection dépend des masses incertaines des astéroïdes, par conséquent les résultats sont obtenus dans le cadre d'expériences Monte-Carlo où les masses des astéroïdes varient de manière aléatoire dans des intervalles raisonnables. On introduit la méthode de régularisation de Tikhonov avec contraintes de boîtes pour l'ajustement efficace du nouveau modèle. Une deuxième partie de la thèse est consacrée à l'étude des effets qui peuvent être induits par les astéroïdes sur une orbite quasi-périodique autour du point de Lagrange L2 du système Terre-Soleil. Ce point accueille depuis 2009 les satellites Herschel et Planck et accueillera dans les prochaines années la mission Gaia. Les satellites Herschel et Planck sont pris comme cas d'étude. Leurs orbites nominales sont déterminées par le calcul de la forme normale du problème circulaire restreint à 3 corps. Les orbites obtenues sont ensuite injectées dans le modèle dynamique de INPOP et stabilisées par la méthode de multiple-shooting. On développe un cadre analytique, basé sur le problème quasi-bicirculaire restreint, permettant de prédire l'effet d'un astéroïde en orbite circulaire sur les sondes. Les perturbations induites par des astéroïdes évoluant sur des orbites réalistes sont ensuite étudiées en intégrant avec INPOP les sondes successivement en présence et en absence d'astéroïdes particuliers. On montre que les effets des astéroïdes sont, de manière générale, négligeables.

Redundantly actuated manipulators have only recently aroused significant scientific interest. Their advantages in terms of enlarged workspace, higher payload ratio and better manipulability with respect to non-redundantly actuated systems explain the appearance of numerous applications in various fields: high-precision machining, fault-tolerant manipulators, transport and outer-space applications, surgical operation assistance, etc. The present Ph.D. research proposes a unified approach for modeling and actuation of redundantly actuated parallel manipulators. The approach takes advantage of the actuator redundancy principles and thus allows for following trajectories that contain parallel (force) singularities, and for eliminating the negative effect of the latter. As a first step of the approach, parallel manipulator kinematic and dynamic models are generated and treated in such a way that they do not suffer from kinematic loop closure numeric problems. Using symbolic models based on the multibody formalism and a Newton-Euler recursive computation scheme, faster-than-real-time computer simulations can thus be achieved. Further, an original piecewise actuation strategy is applied to the manipulators in order to eliminate singularity effects during their motion. Depending on the manipulator and the trajectories to be followed, this strategy results in non-redundant or redundant actuation solutions that satisfy actuator performance limits and additional optimality criteria. Finally, a validation of the theoretical results and the redundant actuation benefits is performed on the basis of well-known control algorithms applied on two parallel manipulators of different complexity. This is done both by means of computer simulations and experimental runs on a prototype designed at the Center for Research in Mechatronics of the UCL. The advantages of the actuator redundancy of parallel manipulators with respect to the elimination of singularity effects during motion and the actuator load optimization are thus confirmed (virtually and experimentally) and highlighted thanks to the proposed approach for modeling, simulation and control.

<p>Both optimal disturbances and optimal control are studied by means of numerical simulations for the case of the flat-plate boundary-layer flow. The optimisation method is the Lagrange multiplier technique where the objective function is the kinetic energy of the flow perturbations and the constraints involve the linearised Navier–Stokes equations. We consider both the optimal initial condition leading to the largest growth at finite times and the optimal time-periodic forcing leading to the largest asymptotic response. The optimal disturbances for spanwise wavelengths of the order of the boundary layer thickness are streamwise vortices exploiting the lift-up mechanism to create streaks. For long spanwise wavelengths it is the Orr mechanism combined with the amplification of oblique wave packets that is responsible for the disturbance growth. Control is applied to the bypass-transition scenario with high levels of free-stream turbulence. In this scenario low frequency perturbations enter the boundary layer and streamwise elongated disturbances emerge due to the non-modal growth. These so-called streaks are growing in amplitude until they reach high enough energy levels and breakdown into turbulent spots via their secondary instability. When control is applied in the form of wall blowing and suction, within the region that it is active, the growth of the streaks is delayed, which implies a delay of the whole transition process. Additionally, a comparison with experimental work is performed demonstrating a remarkable agreement in the disturbance attenuation once the differences between the numerical and experimental setup are reduced.</p><p> </p><p> </p>

Dynamic panel data models are widely used by econometricians to study over time the economics of, for example, people, firms, regions, or countries, by pooling information over the cross-section. Though much of the panel research concerns inference in stationary models, macroeconomic data such as GDP, prices, and interest rates are typically trending over time and require in one way or another a nonstationary analysis. In time series analysis it is well-established how autoregressive unit roots give rise to stochastic trends, implying that random shocks to a dynamic process are persistent rather than transitory. Because the implications of, say, government policy actions are fundamentally different if shocks to the economy are lasting than if they are temporary, there are now a vast number of univariate time series unit root tests available. Similarly, panel unit root tests have been designed to test for the presence of stochastic trends within a panel data set and to what degree they are shared by the panel individuals. Today, growing data certainly offer new possibilities for panel data analysis, but also pose new problems concerning double-indexed limit theory, unobserved heterogeneity, and cross-sectional dependencies. For example, economic shocks, such as technological innovations, are many times global and make national aggregates cross-country dependent and related in international business cycles. Imposing a strong cross-sectional dependence, panel unit root tests often assume that the unobserved panel errors follow a dynamic factor model. The errors will then contain one part which is shared by the panel individuals, a common component, and one part which is individual-specific, an idiosyncratic component. This is appealing from the perspective of economic theory, because unobserved heterogeneity may be driven by global common shocks, which are well captured by dynamic factor models. Yet, only a handful of tests have been derived to test for unit roots in the common and in the idiosyncratic components separately. More importantly, likelihood-based methods, which are commonly used in classical factor analysis, have been ruled out for large dynamic factor models due to the considerable number of parameters. This thesis consists of four papers where we consider the exact factor model, in which the idiosyncratic components are mutually independent, and so any cross-sectional dependence is through the common factors only. Within this framework we derive some likelihood-based tests for common and idiosyncratic unit roots. In doing so we address an important issue for dynamic factor models, because likelihood-based tests, such as the Wald test, the likelihood ratio test, and the Lagrange multiplier test, are well-known to be asymptotically most powerful against local alternatives. Our approach is specific-to-general, meaning that we start with restrictions on the parameter space that allow us to use explicit maximum likelihood estimators. We then proceed with relaxing some of the assumptions, and consider a more general framework requiring numerical maximum likelihood estimation. By simulation we compare size and power of our tests with some established panel unit root tests. The simulations suggest that the likelihood-based tests are locally powerful and in some cases more robust in terms of size. / Solving Macroeconomic Problems Using Non-Stationary Panel Data