[pt] Neste trabalho um estudo de estruturas pneumáticas considerando acoplamento pressão–volume e modelos constitutivos plásticos e viscoplásticos são desenvolvidos. Estruturas pneumáticas são estruturas de membrana sobre as quais atuam pressão de gases estabilizadas por tensões de tração. Essas estruturas são mais leves que estruturas convencionais resultando em soluções mais econômicas. Elas possuem ainda algumas características que contribuem para um desenvolvimento sustentável, como a utilização de luz natural e ventilação e a possibilidade de reutilização. Quando as estruturas pneumáticas são submetidas a cargas externas, essas estruturas apresentam variação da pressão internal e do volume. Este acoplamento é um dos objetos de estudo do presente trabalho. Soluções analíticas são desenvolvidas para descrever este acoplamento. Em programas convencionais de elementos finitos esse acoplamento não é considerado. Uma formulação para o acoplamento pressão–volume para câmaras fechadas é incluído no modelo de elementos finitos com grandes deformações. A variedade de modelos de material implementados tem a finalidade de abranger o comportamento de muitos tipos de materiais de membrana usados em estruturas pneumáticas. Na literatura o estudo dos materiais de membrana para estruturas pneumáticas tem foco na análise experimental. Modelos para material de membrana são incorporados no modelo de elementos finitos para pequenas e grandes deformações. Os modelos constitutivos considerados neste trabalho são hiperelástico, elastoplástico e elastoviscoplástico. A ocorrência de grandes deformações é incluída. Um novo material baseado em superfícies NURBS é proposto e validado com base em resultados experimentais e modelos clássicos de materiais. Neste trabalho ênfase é dada ao material ETFE (Etileno tetrafluoretileno), o qual é amplamente usado em estruturas pneumáticas. Os modelos desenvolvidos aqui, como o acoplamento pressão–volume e os modelos de materiais são implementados em elementos finitos no programa usado na cadeira de estática das construções da TUM (Technische Universitat Munchen), chamado CARAT++ (Computer Aided Research Analysis Tool). / [en] In this work a study of pneumatic structures considering pressure–volume coupling under plastic and viscoplastic material behavior is developed. Pneumatic structures are membrane structures acted on by air or gases stabilized by tension. These structures are lighter than conventional structures resulting in economic structural solutions. They present also some characteristics that contribute to the sustainable development, such as the utilization of natural lighting and ventilation and its possibility of reuse. When pneumatic structures are subjected to external loads these structures present both internal pressure and volume variation. This coupling is one of the objects of the present work. Analytical solutions are developed to describe this coupling. In conventional finite element systems this coupling is not considered. A formulation for pressure–volume coupling by closed chambers is included in the framework of a finite element large strain model. The variety of material models implemented has the purpose to cover the behavior of the many kinds of membrane materials used in pneumatic structures. In the literature the study of the membrane materials for pneumatic structures focuses on experimental analysis. Membrane material models are incorporated in the finite element model for small and large strains. The constitutivematerial models considered in this work are hyperelastic, elastoplastic and elastoviscoplastic. The onset of large strains is enclosed. A new material model based on NURBS surfaces is proposed an validated on hand of experimental results and classic material models. In this work emphasis is given to the material ETFE (Ethylene tetrafluoroethylene), which is widely used in pneumatic structures. The models developed here, such as the pressure-volume coupling and the material models, are implemented in finite elements on the program used in the Static Chair at TUM (Technische Universitat Munchen), which is called CARAT++ (Computer Aided Research Analysis Tool).

Deformable image registration (DIR) is an essential tool in medical image processing. It provides a means to combine image datasets, allowing for intra-subject, inter-subject, multi-modality, and multi-instance analysis, as well as motion detection and compensation. One of the most popular DIR algorithms models the displacement vector field (DVF) as B-splines, a sum of piecewise polynomials with coefficients that enable local shape control. B-splines have many advantageous properties in the context of DIR, but they often struggle to adequately model steep local gradients and discontinuities. This dissertation addresses that limitation by proposing the replacement of conventional B-splines with a generalized formulation known as a Non-Uniform Rational B-Splines (NURBS). Beginning with the 1D fitting, heuristic rules are developed to determine the values of the additional free parameters introduced by NURBS. These rules are subsequently modified and extended to the 2D and 3D fitting of anonymized and publicly available patient DVFs. Based on the lessons learned from these increasingly complex test cases, a 2D DIR scheme is developed and tested on slices from a thoracic computed tomography (CT) scan. Finally, an automatic, non-uniform scheme is presented, and its registration performance is compared to the conventional uniform methods.

O presente trabalho tem por objetivo desenvolver uma formulação numérica baseada em Análise Isogeométrica para o estudo de escoamentos incompressíveis isotérmicos de fluidos newtonianos. Com o emprego desta metodologia, os procedimentos de pré-processamento e análise são unificados, melhorando as condições de continuidade das funções de base empregadas tanto na discretização espacial do problema como na aproximação das variáveis do sistema de equações. O sistema de equações fundamentais do escoamento é formado pelas equações de Navier-Stokes e pela equação de conservação de massa, descrita segundo a hipótese de pseudo-compressibilidade, além de uma equação constitutiva para fluidos viscosos de acordo com a hipótese de Stokes. Para problemas com escoamentos turbulentos emprega-se a Simulação de Grandes Escalas - LES (Large Eddy Simulation), na qual o modelo clássico de Smagorinsky é utilizado para a representação das escalas inferiores à resolução da malha. O esquema explícito de dois passos de Taylor-Galerkin é aplicado no contexto da Análise Isogeométrica para a discretização das equações governantes, sendo que a discretização espacial é realizada empregando-se funções NURBS (Non Uniform Rational Basis B-Splines). Essas funções base apresentam vantagens em relação às tradicionais funções utilizadas no MEF (Método dos Elementos Finitos), principalmente no que diz respeito à facilidade de obtenção de continuidade superior a C0 entre os elementos e representação precisa das geometrias. Propõe-se também o desenvolvimento de ferramentas de pré e pós-processamento baseadas na estrutura de dados da Análise Isogeométrica para a geração de malhas e visualização de resultados. Alguns problemas clássicos da Dinâmica dos Fluidos Computacional são analisados para a validação da metodologia apresentada. Os resultados apresentados demonstram boa aproximação da formulação em relação a dados de referência, além de maior versatilidade quanto à discretização espacial dos problemas em comparação com as tradicionais formulações baseadas em elementos finitos. / This work aims to develop a numerical formulation based on Isogeometric Analysis for the study of incompressible flows of Newtonian fluids under isothermal conditions. By using this methodology, pre-processing and analysis procedures are unified, improving the conditions of continuity of the basis functions utilized in the approximations of the equation variables and spatial discretization of the problem. The system of fundamental equations of the fluid flow is constituted by the Navier-Stokes equations and the mass conservation equation, which is described according to the pseudo-compressibility hypothesis. In addition, a constitutive equation for viscous fluids according to Stokes' hypothesis is also provided. Turbulent flows are analyzed using LES (Large Eddy Simulation), where the Smagorinsky’s model is adopted for sub-grid scales. The explicit two-step Taylor-Galerkin method is applied into the context of Isogeometric Analysis for the discretization of the flow equations, where spatial discretization is carried out taking into account Non Uniform Rational Basis B-Splines (NURBS) basis functions. These basis functions have advantages over traditional functions employed in the FEM (Finite Element Method). Particularly, it is easier to obtain continuity order higher than C0 between adjacent elements and geometry representation is more accurate. Pre and post-processing tools for mesh generation and results visualization are also proposed considering the data structure inherent to Isogeometric Analysis. Some classic problems of Computational Fluid Dynamics are analyzed in order to validate the proposed methodology. Results obtained here show that the present formulation has good approximation when compared with predictions obtained by reference authors. Moreover, Isogeometric Analysis is more versatile than traditional finite element formulations when spatial discretization procedures are considered.

Nous nous intéressons à la création de surfaces à pôles (NURBS essentiellement), largement utilisées dans les systèmes de modélisation géométrique. Un des avantages de cette modélisation est de permettre d'appréhender la forme des surfaces par la position de points de contrôle. L'approche déclarative de la modélisation de surfaces est destinée à la réalisation rapide et facile d'ébauches de formes et de surfaces. Elle est aussi et surtout destinée à accélérer les processus de conception des spécialistes en leur proposant des solutions adaptées répondant à un ensemble de contraintes et de propriétés.<br /><br />Pour y parvenir, le travail réalisé dans la thèse se divise en quatre étapes :<br /><br />* Etude de faisabilité : réalisée en collaboration avec l'Ecole Nationale Supérieure des Arts et Métiers d'Aix-en-Provence, elle s'est focalisée sur la description et la modélisation d'objets de type pièces mécaniques.<br />* Analyse conceptuelle : Cette étape primordiale dans un projet d'une telle envergure nous a permis de mettre au point l'architecture générale de notre processus déclaratif de surfaces. Dans le cadre de la thèse et en vue d'un premier prototype, nous décidons de focaliser notre étude sur la partie résolution qui se scinde en deux : la détermination des classes de solutions et leur construction sous contraintes.<br />* Etude et développement de la "détermination des classes de solutions" : Notre approche repose sur le comportement d'une surface face aux déformations qui lui sont apportées lors de sa construction : deux surfaces appartiennent à la même classe si elles ont le même comportement face à la même succession de déformations.<br />* Etude et développement de la "construction sous contraintes" : Afin d'obtenir une surface solution particulière (ou instance d'une classe de solutions) nous choisissons une construction par l'application successive de déformations. Ces déformations sont soumises à des contraintes plus ou moins fortes. Nous avons donc élaboré une méthode de déformations de surfaces capable de satisfaire des contraintes de passage tout en gardant un fort contrôle sur la forme de chaque zone d'influence.<br /><br />Deux applications mettant en oeuvre ce travail ont été réalisées en C++ et sont disponibles sous les versions 32-bits de MS Windows(R), Linux et MacOS X.

This dissertation describes three aspects of the comprehensive rotorcraft analysis. First, a physics-based methodology for the modeling of hydraulic devices within multibody-based comprehensive models of rotorcraft systems is developed. This newly proposed approach can predict the fully nonlinear behavior of hydraulic devices, and pressure levels in the hydraulic chambers are coupled with the dynamic response of the system. The proposed model evaluates relevant hydraulic quantities such as chamber pressures, orifice flow rates, and pressure relief valve displacements. This model could be used to design lead-lag dampers with desirable force and damping characteristics. The second part of this research is in the area of computational aeroelasticity, in which an interface between computational fluid dynamics (CFD) and computational structural dynamics (CSD) is established. This interface enables data exchange between CFD and CSD with the goal of achieving accurate airloads predictions. In this work, a loose coupling approach based on the delta-airload method is developed in a finite-element method based multibody dynamics formulation, DYMORE. A loose coupling analysis between a CFD code, OVERFLOW-2, and a CSD program, DYMORE, is performed to validate this aerodynamic interface. The ability to accurately capture the wake structure around a helicopter rotor is crucial for rotorcraft performance analysis. In the third part of this thesis, a new representation of the wake vortex structure based on Non-Uniform Rational B-Spline (NURBS) curves and surfaces is proposed to develop an efficient model for prescribed and free wakes. The proposed formulation has the potential to reduce the computational cost associated with the use of the Helmholtz¡¯s law and the Biot-Savart law when calculating the induced flow field around the rotor. An efficient free wake analysis will considerably decrease the computational cost of comprehensive rotorcraft analysis, making the approach more attractive to routine use in industrial settings.

For many years, incompatible computer-aided design (CAD) packages that are based on Non-uniform Rational B-Spline (NURBS) technology carried out the exchange of models and data through either neutral file formats (IGES or STEP) or proprietary formats that have been accepted as quasi industry standards. Although it is the only available solution at the current time, the exchange process most often produces unsatisfactory results. Models that are impeccable in the original modeling system usually end up with gaps or intersections between surfaces on another incompatible system. Issues such as loss of information, change of data accuracy, inconsistent tolerance, and misinterpretation of the original design intent are a few examples of problems associated with migrating models between different CAD systems. While these issues and drawbacks are well known and cost the industry billions of dollars every year, a solution to eradicate problems from their sources has not been developed. Meanwhile, researchers along with the industries concerned with these issues have been trying to resolve such problems by finding means to repair the migrated models either manually or by using specialized software. Designing in recent years is becoming more knowledge intensive and it is essential for NURBS to take its share of the ever increasing use of knowledge. NURBS are very powerful modeling tools and have become the de facto standard in modeling. If we stretch their strength and make them knowledge driven, benefits beyond current expectations can be achieved easily. This dissertation introduces knowledge guided NURBS with theoretical and practical foundations for supporting design intent capturing, retrieval, and exchange among dissimilar CAD systems. It shows that if NURBS entities are tagged with some knowledge, we can achieve seamless data exchange, increase robustness, and have more reliable computations, all of which are ultimate objectives many researchers in the field of CAD have been trying to accomplish for decades. Establishing relationships between a NURBS entity and its origin and destinations can aid with seamless CAD model migration. The type of the NURBS entity and the awareness of any irregularities can lead to more intelligent decisions on how to proceed with many computations to increase robustness and achieve a high level of reliability. As a result, instead of having models that are hardly modifiable because of migrating raw numerical data in isolation, the knowledge driven migration process will produce models that are editable and preserve design intent. We have addressed the issues not only theoretically but also by developing a prototype system that can serve as a test bed. The developed system shows that a click of a button can regenerate a migrated model instead of repairing it, avoiding delay and corrective processes that only limit the effective use of such models.

Hydrocarbon production or injection of fluids in the reservoir can produce changes in the rock stresses and in-situ geomechanics, potentially leading to compaction and subsidence with harmful effects in wells, cap-rock, faults, and the surrounding environment as well. In order to tackle these changes and their impact, accurate simulations are essential. The Mortar Finite Element Method (MFEM) has been demonstrated to be a powerful technique in order to formulate a weak continuity condition at the interface of sub-domains in which different meshes, i.e. non-conforming or hybrid, and / or variational approximations are used. This is particularly suitable when coupling different physics on different domains, such as elasticity and poroelasticity, in the context of coupled flow and geomechanics. In this dissertation, popular Domain Decomposition Methods (DDM) are implemented in order to carry large simulations by taking full advantage of current parallel computer architectures. Different solution schemes can be defined depending upon the way information is exchanged between sub-domain interfaces. Three different schemes, i.e. Dirichlet-Neumann (DN), Neumann-Neumann (NN) and MFEM, are tested and the advantages and disadvantages of each of them are identified. As a first contribution, the MFEM is extended to deal with curve interfaces represented by Non-Uniform Rational B-Splines (NURBS) curves and surfaces. The goal is to have a more robust geometrical representation for mortar spaces, which allows gluing non-conforming interfaces on realistic geometries. The resulting mortar saddle-point problem will be decoupled by means of the DN- and NN-DDM. Additionally, a reservoir geometry reconstruction procedure based on NURBS surfaces is presented as well. The technique builds a robust piecewise continuous geometrical representation that can be exploited by MFEM in order to tackle realistic problems, which is a second contribution. Tensor product meshes are usually propagated from the reservoir in a conforming way into its surroundings, which makes non-matching interfaces highly attractive in this case. In the context of reservoir compaction and subsidence estimation, it is common to deal with serial legacy codes for flow. Indeed, major reservoir simulators such as compositional codes lack parallelism. Another issue is the fact that, generally speaking, flow and mechanics domains are different. To overcome this limitation, a serial-parallel approach is proposed in order to couple serial flow codes with our parallel mechanics code by means of iterative coupling. Concrete results in loosely coupling are presented as a third contribution. As a final contribution, the DN-DDM is applied to couple elasticity and plasticity, which seems very promising in order to speed up computations involving poroplasticity. Several examples of coupling of elasticity, poroelasticity, and plasticity ranging from near-wellbore applications to field level subsidence computations help to show that the proposed methodology can handle problems of practical interest. In order to facilitate the implementation of complex workflows, an advanced Python wrapper interface that allows programming capabilities have been implemented. The proposed serial-parallel approach seems to be appropriate to handle geomechanical problems involving different meshes for flow and mechanics as well as coupling parallel mechanistic codes with legacy flow simulators. / text

The design of curves and surfaces in C.A.D. systems has many applications in car, plane or ship industry. Because they offer more flexibility, rational functions are often preferred to polynomial functions to modelize curves and surfaces. In this work, several methods to generate rational Bezier curves and surfaces which minimize some functionals are proposed. The functionals measure a technical smoothness of the curves and surfaces, and are related to the energy of beams and plates in the sense of the elasticity theory.

L'utilisation des SIG pour la conception de modèles d'écoulements souterrains motive la recherche de méthodes numériques qui ne requièrent pas la discrétisation du domaine de l'écoulement : les SIG sont par nature vectorisés. Les méthodes numériques qui se fient à la discrétisation des frontières plutôt que du domaine offrent l'avantage de garder la description originale de l'information sous forme vecteur, telle que fournie par le SIG, réduisant ainsi les pertes inhérentes à la rastérisation et la vectorisation ultérieure. La méthode des éléments analytiques est particulièrement prometteuse. Cependant,il lui manque la capacité à gérer un type spécifique d'objets, les courbes NURBS. Les fonctions nécessaires à l'inclusion de ces courbes dans le cadre de l'AEM sont dérivées, et des exemples sont fournis. Leur souplesse est présentée, et on montre que les formes courbes exixtantes dans l'AEM peuvent être représentées par des NURBS, permettant ainsi la compatibilité, si elles devaient être supplantées. Une méthode est proposée pour améliorer le temps de réponse des modèles lorque les éléments curvilinéaires sont utilisés, basée sur la méthode des intégrales frontières directes. Les éléments linéaires classiques sont également améliorés pour permettre meilleurs précision et contrôle dans la technique d'accélération.

Neste trabalho buscou-se consolidar aspectos referentes à otimização de problemas envolvidos na mecânica dos meios contínuos, envolvendo diferentes áreas do conhecimento, tais como: otimização matemática, diferenciação automática, análise estrutural, análise aerodinâmica, parametrização de curvas, superfícies e sólidos do tipo B-spline racionais não-uniformes (NURBS, acrônimo do inglês), análise IsoGeométrica (IGA, acrônimo do inglês) e análise por Elementos Finitos (FEA, acrônimo do inglês). Como objetivo final busca-se otimizar formas de cascas estruturais e formas de corpos aerodinâmicos imersos em escoamentos compressíveis. No que concerne à análise estrutural, esta é realizada via análise IsoGeométrica utilizando elementos sólidos para modelar cascas. Uma cinemática co-rotacional abrangente e precisa baseada na exata decomposição polar é desenvolvida, para lidar com problemas estáticos e dinâmicos altamente não lineares. Na análise estática foram implementados o método de Newton-Raphson e controle de deslocamentos generalizado, para problemas dinâmicos foram implementados o método -generalizado (G) e o método energia momento generalizado (GEMM+). A análise aerodinâmica é realizada via análise por Elementos Finitos para modelar escoamentos compressíveis viscosos e não viscosos em regimes transônicos e supersônicos. Um esquema característico baseado na separação da equação de momento (CBS, acrônimo do inglês) é utilizado para obter uma adequada integração temporal. No que concerne à otimização matemática, é utilizado um método baseado em gradientes, conhecido por programação quadrática sequencial (SQP, acrônimo do inglês), onde a avaliação as derivadas de Fréchet são levadas a cabo via diferenciação automática (AD, acrônimo do inglês). No que concerne aos resultados finais é realizada a otimização estrutural de forma de cascas modeladas como sólidos são apresentados, evidenciando um desempenho ótimo com respeito à energia de deformação interna. Os resultados de otimização aerodinâmica bidimensionais apresentam perfis aerodinâmicos ótimos com respeito à relação arrasto/sustentação para uma ampla gama de número de Mach, enquanto um resultado tridimensional é apresentado evidenciando a robustez e eficiência da implementação proposta. Pretendese estabelecer com este trabalho as bases para pesquisas em problemas de otimização aeroelástica. / Consolidation of the link among optimization problems in continuum mechanics, involving different fields, such as mathematical optimization, automatic differentiation, structural analysis, aerodynamic analysis, curves, surfaces and solids parameterization using Non Uniform Rational B-spline (NURBS), IsoGeometric Analysis (IGA), Finite Element Analysis (FEA) is looked for. Structural shape optimization of shell structures and aerodynamic shape optimization of immersed bodies in compressible flows are the main goals of this work. Concerning structural analysis, the so-called IsoGeometric analysis is employed. An accurate and comprehensive corotational kinematic based on the exact polar decomposition is developed in order to study highly nonlinear static and dynamic problems. Static analysis is carried out with Newton-Raphson and Generalized Displacement Control Method, while dynamic analysis is carried out with Generalized- (G) and Generalized Energy-Momentum Method (GEMM+). Aerodynamic analysis is carried out via Finite Element Analysis (FEA) in order to solve compressible flows in transonic and supersonic regimes. A Characteristic Based Split (CBS) method is employed to obtain an accurate time integration, which is based on the splitting of the momentum equation. Concerning mathematical optimization, the so-called Sequential Quadratic Programming (SQP) is employed, which is a gradient-based method, where the Fréchet derivatives are evaluated using Automatic Differentiation (AD). Final results consisting in structural optimization shown an optimal behaviour with respect to internal strain energy. While, results concerning aerodynamic bi-dimensional shape optimization exhibit a optimal behaviour with respect drag/lift ratio, for a large range of Mach number, and a simple result for tri-dimensional case is presented in order to show the efficiency and robustness of the implementation. Bases for future research in aeroelastic optimization problems are established in this work.