Indiana University-Purdue University Indianapolis (IUPUI) / Computer Numerical Control (CNC) is widely used in many industries that needs high speed machining of the parts with high precision, accuracy and good surface finish. In order to avail this the generation of the CNC part program size will be immensely big and leads to an inefficient process, which increases the delivery time and cost of products. This work presents the automation of high-accuracy CNC tool trajectory planning from CAD to G-code generation through optimal NURBs surface approximation. The proposed optimization method finds the minimum number of NURBS control points for a given admissible theoretical cord error between the desired and manufactured surfaces. The result is a compact part program that is less sensitive to data starvation than circular and spline interpolations with potential better surface finish. The proposed approach is demonstrated with the tool path generation of an involute gear profile and a topologically optimized structure is developed using this approach and then finally it is 3D printed.

The dynamic characteristics of a part are highly dependent on geometric and material properties of the part. The identification and tracking of vibrational mode shapes within an iterative design process becomes difficult and time consuming due to the frequently changing part definition. Currently, visual inspection of analysis results is used as the means to identify the shape of each vibrational mode determined by the modal analysis. This thesis investigates the automation of the mode shape identification process through the use of parametric geometry and the Modal Assurance Criterion. Displacement results from finite element modal analysis are used to create parametric geometry templates which can be compared one to another irrespective of part geometry or finite element mesh density. Automation of the mode shape identification process using parametric geometry and the Modal Assurance Criterion allows for the mode shapes from a baseline design to be matched to modified part designs, giving the designer a more complete view of the part's dynamic properties. It also enables the identification process to be completed much more quickly than by visual inspection.

This dissertation discusses the thermomechanical analyses performed on threaded fasteners and curvilinearly stiffened composite panels with internal cutouts. The former problem was analyzed using a global/local approach using the commercial finite element software ANSYS while a fully functional code using isogeometric analysis was developed from scratch for the latter. For the threaded fasteners, a global simplified 3D model is built to evaluate the deformation of the structure. A second local model reproducing accurately the threads of the fasteners is used for the accurate assessment of the stresses in the vicinity of the fasteners. The isogeometric analysis code, capable of performing static, buckling and vibration analysis on stiffened composite plates with cutouts using single patch, multiple patches and level set methods is then discussed. A novel way to achieve displacement compatibility between the panel and stiffeners interfaces is introduced. An easy way of modeling plates with complicated cutouts by using edge curves and generating a ruled NURBS surface between them is described. Influence on the critical thermal buckling load and the fundamental mode of vibration due to the presence of circular, elliptical and complicated cutouts is also investigated. Results of parametric studies are presented which show the influence of ply orientation, size and orientation of the cutout, and the position and profile of the curvilinear stiffener. The numerical examples show high reliability and efficiency when compared with other published solutions and those obtained using ABAQUS, a commercial software. / PHD / Aircraft in flight are subjected to different loads due to maneuvers and gust; there external forces cause internal loads and depend on the location of the panel in the aircraft. The internal loads, may result in the buckling of the panel. Hence, there is a need for studying structural efficiency and develop strong and stiff lightweight structures. Stiffened composite panels is a technology capable of addressing these needs. However, when used in space vehicles moving at hypersonic speeds, such structures experience significant temperature rise in a very short time resulting from the aerodynamic heating due to friction between the vehicle surface and the atmosphere. Such phenomena is more prominent during reentry and launch processes. Hence, it is really important to consider thermal effects while designing and analyzing such structures. Composite stiffened panels have many advantages like small manufacturing cost, high stability, great energy absorption, superior damage tolerance etc. One of the main failure modes for stiffened composite panels is thermal buckling. An extensive literature review on thermal buckling of stiffened composite panels was conducted in this dissertation. Thermal buckling and vibration analysis as well as a parametric study of a stiffened composite panel with internal cutouts was conducted, and verified using ABAQUS, a Finite Element Software.

La Conception Assistée par Ordinateur (C.A.O) qui permet de concevoir des objets physiques à partir de modèles mathématiques est utilisée dans de nombreux secteurs de l’industrie.On constate actuellement une volonté généralisée de tirer parti de deux approches jusqu’à présent plutôt antagonistes : la modélisation géométrique continue qui crée des objets continus représentant par la modélisation à partir de surfaces B-splines ou NURBS) et la modélisation géométrique discrète qui qu’il s’agisse de maillages ou de surfaces de subdivision.Cette dualité d’approche a de nombreuses applications industrielles potentielles et présente donc un intérêt scientifique important. Les surfaces polyédriques et en particulier les surfaces de subdivision offrent intrinsèquement la discrétisation, sont d’une manipulation très simple, mais elles ne remplacent pas les surfaces B-splines ou NURBS. Les travaux présentés dans la thèse et qui ont abouti au passage réciproque d’une surface paramétrique à une surface polyédrique. Nous nous intéressons plus particulière aux surfaces de subdivision considérant comme une liaison entre la surface polyédriquee et la surface paramétrique parce qu’après quelques étapes de subdivision, le polyèdre caractéristique converge à une surface paramétrique correspondant. Nous y proposons des schémas de la subdivision inverse permettent de récréer les surface polyédrique grossier de subdivision précédent. Nous avons donc développé deux méthodes pour la reconstruction d’une courbe/surface paramétrique en utilisant le schéma de subdivision inverse uniforme et le schéma de subdivision inverse non-uniforme. Pour améliorer les résultats de reconstruction par la subdivision inverse, nous associons à ces méthodes une possibilité d’ajustement d’approximation qui permet de diminuer grandement l’erreur de reconstruction. Les résultats obtenus ont été comparés à une méthode bien connu de reconstruction sens au sens des moindres carrés. Nos méthodes sont très prometteuses en termes d’approximation et de compression / Computer Aided Geometric Design (CAGD) which allows us to design the physical objects from mathematical models is used in many sectors of industry. It is currently a general wish to take advantage of the two these approaches rather than the antagonists : The goal that the continuous geometric model creates the continuous objects represented by the modelof the surfaces B-splines or NURBS) and the discreet geometric model made by eitherthe meshes or the subdivision surfaces. This duality of the approach has many potential industrial applications and therefore submits interesting significant science. The polyhedral surfaces and the subdivision surfaces in particular which offer the intrinsically discretization,are a very simple manipulation, but they do not replace the surfaces B-splines or NURBS.The works presented in this thesis aim to the reciprocal passage from a parametric surfaceto a polyhedral surface. We are more specialy interested to subdivisions surfaces considering as a liaison between the polyhedral surface and the parametric surface, because after a few steps of subdivision, the polyhedron characteristic converges to a parametric surface corresponding.We have proposed the schemas of the inverse subdivision allowing recreating the polyhedral surface coarse of subdivision precedent. We thus presented two methods for there construction of a parametric curve/surface : one for using the schema of uniform inverse subdivision and the other for non-uniform inverse subdivision. To improve the results of reconstruction by the inverse subdivision methods, we associate these methods with the process of adjustment the approximation which allows reducing the error of reconstruction.The results obtained have been compared with a well-known least squares method. Our methods are very promising in terms of approximation and compression.

Made available in DSpace on 2015-05-08T14:59:31Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 3097304 bytes, checksum: d5aed81c6383bfcc8edaae1463e53296 (MD5) Previous issue date: 2011-03-31 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nowadays the increasing demand for products with high dimensional accuracy and geometric measures has required increasingly accurate. It is necessary to use inspection systems more accurate and flexible to expect these demands. The Coordinate Measuring Machines (CMMs) are an important tool in the design, fabrication and inspection of products manufactured today. These machines are used by the engineer, whose main purpose is to produce an accurate digital model in a virtual space for later use in CAD / CAE / CAM / CAI. To identify the several shapes and surface features, there are many techniques such as Bezier surfaces, splines, B-Splines and NURBS (Non-Rational B-Splines). The NURBS present many advantages, simplicity and facility of data handling, which tends to minimize the problems of randomness and inaccuracy of the cloud of points obtained by the CMM. Thus, the NURBS are an important tool for modeling free-form, making significant contributions in reverse engineering. It is known however that the accuracy of the modeling process of a piece will be greater the larger the number of points collected or measured on the surface (whether by use of laser or continuous scanning by contact or touch point to point). Simulations results showed the effective of the proposed approach. Additionally, experimental results demonstrated that it is of practical use, non time consuming and an alternative way to apply CMMs that incorporated touch trigger probe in modeling processes. The results obtained both by simulation and experimentally demonstrated the relevance of this methodology. / Hoje em dia, a crescente demanda por produtos com alta exatidão dimensional e geométrica tem exigido tolerâncias cada vez mais estreitas. Adicionalmente, peças de geometrias complexas e formas livres tem sido uma prática comum em indústrias dos setores automotivos, aeronáuticos, bioengenharia dentre outros. Para atender as estas demandas se faz necessário sistemas de inspeção cada vez mais exatos e flexíveis. As Máquinas de Medição por Coordenadas (MMCs) são uma importante ferramenta no processo de concepção, fabricação e inspeção dos produtos manufaturados nos dias de hoje. Para identificar as mais diversas formas e características das superfícies existem várias técnicas, tais como, superfícies Bézier, Splines, B-Splines, e NURBS (Non- Uniform Rational B-splines). As NURBS são uma ferramenta importante e uma grande aliada na modelagem de formas geométricas complexas, dando significativas contribuições na engenharia reversa. Sem dúvida, a exatidão do processo de modelagem de uma peça será tão maior quanto maior for o número de pontos coletados ou medidos sobre a sua superfície (seja por uso de laser ou escaneamento contínuo por contato ou por contato ponto a ponto). Então, o principal objetivo desta tese é desenvolver e implementar uma nova metodologia para modelagem de superfícies de formas livres e geometrias complexas utilizando a técnica NURBS em MMC com apalpador touch trigger. Também, foi desenvolvida uma estratégia de medição para obtenção de pontos sobre a superfície estudada. A metodologia proposta foi aplicada experimentalmente para a obtenção de um perfil evolvental de uma engrenagem cilíndrica de dentes retos, um modelo físico reduzido de um avião e um capacete de ciclista. Os resultados obtidos tanto por simulação quanto experimentalmente mostraram a relevância da metodologia desenvolvida.

Les réservoirs clastiques sont constitués pour la plupart d'un agencement géométrique de plusieurs structures. Le but de ces travaux est de fournir une représentation volumétrique de ces différents objets afin de pouvoir reproduire la grande hétérogénéité des dépôts sédimentaires. Nous proposons une paramétrisation tridimensionnelle compacte des objets sédimentaires qui permet de représenter des géométries variées et qui fournit un espace curvilinéaire pour la modélisation des hétérogénéités internes des structures sédimentaires. Les modèles de corps géologiques sont définis par une représentation par frontières, chacune des frontières étant construite par une surface paramétrique déformable. La formulation mathématique utilisée pour construire les espaces paramétriques sont les B-Splines rationnelles non uniformes dites NURBS (pour Non Uniform Rational B-Splines). Chaque forme élémentaire est contrôlée par des règles de déformations afin de maintenir la géométrie et la cohérence des objets durant l'édition. Les modèles de structures sédimentaires sont appliqués à la simulation de chenaux et des structures qui y sont liées telles que les barres d'accrétion latérale. Ils servent alors de support pour réaliser des simulations de propriétés pétrophysiques qui suivent l'espace paramétrique particulier de chaque objet. Les modèles d'objets sédimentaires sont également appliqués dans le cadre de l'interprétation semi-automatique d'images géologiques en adaptant des méthodes classiques d'extraction de formes. Cette approche est appliquée sur des images satellites de chenaux alluviaux. Des résultats préliminaires sur des données de sismiques 3D sont également présentés / Most clastic deposits consist in geometric arrangements of several structures. The purpose of this work is to provide a volumetric representation of these objects in order to reproduce the high heterogeneity of the sedimentary deposits. These models are constructed to be flexible and compact in order to model the sedimentary formations at different scales. The sedimentary models are defined by a boundary representation ; each boundary is defined by a deformable parametric surface. The proposed parametrization is the Non Uniform Rational B-Spline (NURBS). Each elementary shape is controlled by deformation rules and has connection constraints with associated objects, in order to maintain the geometry and the consistency through editing. Sedimentary structure models are applied to channel simulation and to the construction of the related structures such as point bars. These structures are then used as framework for petrophysical property simulations. The models are also applied to semi-automatically interpret geological images by adapting classical shape extraction methods. This approach is applied on satellite pictures showing alluvial channels and some preliminary results on 3D seismic time slices are also presented

In the first part I discuss ancestors of NURBS curves and surfaces, rather Ferguson, Beziere, Coons and B-spline curves and surfaces and furthermore B-spline functions. In the second part I devote to NURBS curves and surfaces, their description as a linear combination of B-spline functions in the projective space. I specify conical arcs more detailed, their submit in the projective space and NURBS surfasec given as tensor product of NURBS curves. Last part is devote to describtion programs for modeling conicals and NURBS surface.

L’objectif de ce travail de thèse est d’étudier l’interaction des ondes électromagnétiques en bande L avec les vagues côtières déferlantes, en particulier pour un observateur situé à proximité de la surface. Le travail s’attache à effectuer une modélisation électromagnétique précise en lien étroit avec le modèle hydrodynamique. Pour modéliser et calculer les champs électromagnétiques diffusés par les vagues déferlantes, nous utilisons une approche numérique par intégrale de frontière, notamment la Méthode des Moments (MdM). Dans ce cadre, nous focalisons le travail sur la problématique de la fiabilité et la convergence du calcul numérique pour des géométries de forte courbure comme peuvent l’être des surfaces de vagues déferlantes. Après une analyse approfondie de la problématique, nous montrons qu’une solution fondée sur la Méthode des Moments d’Ordre Supérieur (MdM-OS) combinée avec la technique de maillage Non Uniform Rational Basis Splines (NURBS) permet d’améliorer les performances de la méthode MdM-Classique. En parallèle du travail de modélisation électromagnétique, nous nous attachons à introduire un modèle hydrodynamique capable de simuler le plus fidèlement possible le mouvement et la déformation des vagues à proximité de la côte. Nous retenons une modélisation hydrodynamique basée sur la Méthode Désingularisée. Cette approche méthodologique nous permet d’étudier l’évolution des vagues en fonction de la pente du fond, de la hauteur relative et de la cambrure des vagues. La combinaison des résultats issus de la modélisation numérique électromagnétique et de la description hydrodynamique permettent ainsi d’évaluer l’évolution des champs électromagnétiques diffusés par les vagues côtières déferlantes en fonction du temps pour trois types de déferlement standard : glissant, plongeant et gonflant. / The purpose of this thesis work is to study the interaction of electromagnetic waves in L bandwith breaking coastal sea waves, in particular for an observer situated close to the surface. The work attempts to realize a precise electromagnetic modeling in narrow link with hydrodynamic model. To model and calculate electromagnetic fields scattered by breaking sea waves, we use a numerical approach by boundary integral technique, in particular Method of Moments (MoM). In this frame, we focus on the reliability and the convergence problem of numerical computation for strong curvature geometries as the surfaces of breaking sea waves are. After a thorough analysis of the problem, we show that a solution based on Higher-Order Method of Moments (HO-MoM) combined with Non Uniform Rational Basis Splines (NURBS) meshing technique allows the improvement of the performances of Classical-MoM. In parallel of the work on electromagnetic modeling, we attempt to introduce a hydrodynamic model able to precisely simulate the movement and the deformation of waves near the coast. We choose a hydrodynamic modeling based on Desingularized Method. This methodological approach allows the study of the evolution of waves according to the bottom slope, the relative height and the wave steepness. The combination of the results obtained from the numerical electromagnetic modeling and from the hydrodynamic description allows us to estimate the evolution of the electromagnetic fields scattered by breaking coastal sea waves according to time for three types of standard breaking : spilling, plunging and surging.

O presente trabalho consiste no desenvolvimento de uma ferramenta computacional para análises de fratura e fadiga de componentes tridimensionais a partir de modelos geométricos de Desenho Assistido por Computador (CAD, acrônimo do inglês). Modelos de propagação de fissuras associados a leis empíricas de fadiga permitem a determinação da vida útil de peças mecânico-estruturais. Tais análises são de vital importância para garantir a segurança estrutural em diversos projetos de engenharia tais como os de pontes, plataformas off-shore e aeronaves. No entanto, a criação de modelos de análise a partir de modelos geométricos de CAD envolve diversas etapas intermediárias que visam a obtenção de malhas volumétricas adequadas. A grande maioria dos modelos de CAD trabalha com a representação de sólidos a partir de seu contorno utilizando superfícies paramétricas, dentre as quais se destacam as superfícies B-Splines Racionais Não Uniformes (NURBS, acrônimo do inglês). Para gerar malhas volumétricas é necessário que o conjunto de superfícies NURBS que descrevem o objeto seja \"estanque\", ou seja, sem lacunas e/ou superposições nas conexões das superfícies, o que não é possível garantir na grande maioria dos modelos constituídos por NURBS. As contribuições propostas no presente trabalho são aplicáveis a modelos baseados no Método dos Elementos de Contorno dual (MEC dual), os quais exigem apenas a discretização das superfícies do problema, ou seja, contorno mais fissuras. No intuito de criar os modelos de análise de maneira eficiente a partir dos modelos geométricos de CAD, desenvolveu-se uma estratégia de colocação que permite discretizar de maneira independente cada uma das superfícies NURBS que compõem os modelos geométricos sólidos. Com a estratégia proposta evitam-se as dificuldades no tratamento das conexões entre as superfícies sendo possível analisar modelos geométricos \"não estanques\". A implementação abrange superfícies NURBS, aparadas ou não, de ordens polinomiais quaisquer e elementos de contorno triangulares e quadrilaterais de aproximação linear. As equações integrais de deslocamentos e de forças de superfície são regularizadas e as integrais singulares e hipersingulares são tratadas pelo Método de Guiggiani. Fissuras de borda são inseridas nos modelos de análise a partir de um algoritmo de remalhamento simples baseado em tolerâncias dimensionais. O mesmo algoritmo é utilizado para as análises incrementais de propagação. Três técnicas de extração dos Fatores de Intensidade de Tensão (FIT) foram implementadas para os modelos baseados na Mecânica da Fratura Elástica Linear (MFEL), a saber, as técnicas de correlação, de extrapolação e de ajuste de deslocamentos. A extensão dessa última técnica para problemas tridimensionais é outra contribuição do presente trabalho. Os critérios da máxima taxa de liberação de energia e de Schöllmann foram utilizados para determinar o FIT equivalente e o caminho de propagação das fissuras. O ângulo de deflexão é determinado por um algoritmo de otimização e o ângulo de torção, definido para o critério de Schöllmann, é imposto no vetor de propagação a partir de uma formulação variacional unidimensional, definida sobre a linha de frente da fissura. Nos modelos de fadiga adota-se a MFEL e a equação de Paris-Erdogan para determinar a vida útil à propagação de defeitos preexistentes. Um procedimento iterativo foi desenvolvido para evitar a interpenetração da matéria após o contato das faces da fissura, permitindo análises de fadiga com carregamentos alternados. Como proposta para a continuidade da pesquisa propõe-se desenvolver formulações isogeométricas de elementos de contorno para analisar problemas de fratura e fadiga diretamente dos modelos geométricos de CAD, sem a necessidade de gerar as malhas de superfície. Um estudo numérico preliminar envolvendo uma versão isogeométrica do MEC dual baseada em NURBS e a versão convencional utilizando polinômios de Lagrange lineares e quadráticos foi realizado. A partir do estudo foi possível apontar as vantagens e desvantagens de cada formulação e sugerir melhorias para ambas. / The present work consists in the development of a computational tool for fracture and fatigue analysis of three-dimensional components obtained from geometrical models of Computer-Aided Design (CAD). Crack propagation models associated with empirical fatigue laws allow the determination of residual life for structural-mechanical pieces. These analyses are vital to ensure the structural safety in several engineering projects such as in bridges, offshore platforms and aircraft. However, the creation of the analysis models from geometrical CAD models requires several intermediary steps in order to obtain suitable volumetric meshes of the problems. The majority of CAD models represent solids with parametric surfaces to describe its boundaries, which is known as the Boundary representation (B-representation). The most common parametric surfaces are Non-Uniform Rational B-Splines (NURBS). To generate a volumetric mesh it is required that the set of surfaces that describe the object must be watertight, i.e., without gaps or superposition at the surfaces connections, which is not possible to unsure using NURBS. The contributions proposed at the present thesis are applicable to models based on the Dual Boundary Element Method (DBEM), which require only the discretization of the surfaces of the problems, i.e., boundary and cracks. A special collocation strategy was developed in order to create the analysis models efficiently from the geometrical CAD models. The collocation strategy allows discretizing independently each one of the NURBS surfaces that compose the geometrical solid models. Therefore, the difficulties in the treatment of the surface connections are avoided and it becomes possible to create analysis models from non-watertight geometrical models. The implementation covers trimmed and non-trimmed NURBS surfaces of any polynomial orders and also triangular and quadrilateral boundary elements of linear order. The displacement and traction boundary integral equations are regularized and the strong and hypersingular integrals are treated with the Guiggiani\'s method. Edge cracks are inserted in the models by a simple remeshing procedure based on dimensional tolerances. The same remeshing approach is adopted for the incremental crack propagation analysis. Three techniques were adopted to extract the Stress Intensity Factors (SIF) in the context of Linear Elastic Fracture Mechanics (LEFM), i.e., the displacement correlation, extrapolation and fitting techniques. The extension of this last technique to three-dimensional problems is another contribution of the present work. Both the general maximum energy realise rate and the Schöllmann\'s criteria were adopted to determine the equivalent SIF and the crack propagation path. The deflection angle is obtained by an optimization algorithm and the torsion angle, defined for the Schöllmann\'s criterion, is imposed in the propagation vector through a one-dimensional variational formulation defined over the crack front line. The concepts of LEFM are adopted together with the Paris-Erdogan equation in order to determine the fatigue life of pre-existing defects. An iterative procedure was developed to avoid the self-intersection of the crack surfaces allowing fatigue analysis with alternate loadings. Finally, as suggestion for future researches, it was started the study of isogeometric boundary element formulations in order to perform fracture and fatigue analysis directly from CAD geometries, without surface mesh generation. A preliminary numerical study involving an isogeometric version of the DBEM using NURBS and the conventional DBEM using linear and quadratic Lagrange elements was presented. From the study it was possible to point out the advantages and disadvantages of each approach and suggest improvements for both.

This thesis is on the space--time variational multiscale (ST-VMS) computation of wind-turbine rotor and tower aerodynamics. The rotor geometry is that of the NREL 5MW offshore baseline wind turbine. We compute with a given wind speed and a specified rotor speed. The computation is challenging because of the large Reynolds numbers and rotating turbulent flows, and computing the correct torque requires an accurate and meticulous numerical approach. The presence of the tower increases the computational challenge because of the fast, rotational relative motion between the rotor and tower. The ST-VMS method is the residual-based VMS version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method, and is also called ``DSD/SST-VMST'' method (i.e., the version with the VMS turbulence model). In calculating the stabilization parameters embedded in the method, we are using a new element length definition for the diffusion-dominated limit. The DSD/SST method, which was introduced as a general-purpose moving-mesh method for computation of flows with moving interfaces, requires a mesh update method. Mesh update typically consists of moving the mesh for as long as possible and remeshing as needed. In the computations reported here, NURBS basis functions are used for the temporal representation of the rotor motion, enabling us to represent the circular paths associated with that motion exactly and specify a constant angular velocity corresponding to the invariant speeds along those paths. In addition, temporal NURBS basis functions are used in representation of the motion and deformation of the volume meshes computed and also in remeshing. We name this ``ST/NURBS Mesh Update Method (STNMUM).'' The STNMUM increases computational efficiency in terms of computer time and storage, and computational flexibility in terms of being able to change the time-step size of the computation. We use layers of thin elements near the blade surfaces, which undergo rigid-body motion with the rotor. We compare the results from computations with and without tower, and we also compare using NURBS and linear finite element basis functions in temporal representation of the mesh motion.