CAD objects are geometrical descriptions of physical scenes from the real world. Ray tracing is used to project the objects onto a pixel screen. A lit and a shadow zone are formed according to the direction of the incoming field (light) and the orientation of the pixel screen. The arc length along the surface of the object, from the shadow boundary to a point in the lit zone, is computed by means of numerical integration. The arclengths corresponding to two orthogonal directions that are aligned with the pixels on the pixel screen are computed and used for interpolation to obtain the arc length for all directions. A number of simulations for various CAD geometries are made using a ray-tracer implemented in FORTRAN 90.

In Nonlinear Finite Element Analysis (FEA) applied to structures, displacements at which the tangent stiffness matrix KT becomes singular are called critical points, and correspond to instabilities such as buckling or elastoplastic softening (e.g., necking). Prior to the introduction of Arc Length Methods (ALMs), critical points posed severe computational challenges, which was unfortunate since behavior at instabilities is of great interest as a precursor to structural failure. The original ALM was shown to be capable in some circumstances of continued computation at critical points, but limited success and unattractive features of the formulation were noted and addressed in extensive subsequent research. The widely used Crisfield Cylindrical and Spherical ALMs may be viewed as representing the 'state-of-the-art'. The more recent Stiff Arc Length method, which is attractive on fundamental grounds, was introduced in 2004, but without implementation, benchmarking or performance assessment. The present thesis addresses (a) implementation and (b) performance comparisons for the Crisfield and Stiff methods, using simple benchmarks formulated to incorporate elastoplastic softening. It is seen that, in contrast to the Crisfield methods, the Stiff ALM consistently continues accurate computation at, near and beyond critical points.

In this thesis a number of problems in harmonic analysis of a geometric flavour are discussed and, in particular, the Lebesgue space mapping properties of certain averaging and Fourier restriction operators are studied. The first three chapters focus on the perspective afforded by affine-geometrical considerations whilst the remaining chapter considers some discrete variants of these problems. In Chapter 1 there is an overview of the basic affine theory of the aforementioned operators and, in particular, the affine arc-length and surface measures are introduced. Chapter 2 presents work of the author, submitted for publication, concerning an operator which takes averages of functions on Euclidean space over both translates and dilates of a fixed polynomial curve. Moreover, the averages are taken with respect to the affine arc-length; this allows one to prove Lebesgue space estimates with a substantial degree of uniformity in the constants. The sharp range of uniform estimates is obtained in all dimensions except for an endpoint. Chapter 3 presents some work of the author, published in Mathematika, concerning a family of Fourier restriction operators closely related to the averaging operators discussed in Chapter 2. Specifically, a Fourier restriction estimate is obtained for a broad class of conic surfaces by introducing a certain measure which exhibits a special kind of affine invariance. Again, the sharp range of estimates is obtained, but the results are limited to the case of 2-dimensional cones. Finally, Chapter 4 discusses some recent joint work of the author and Jim Wright considering the restriction problem over rings of integers modulo a prime power. The sharp range of estimates is obtained for Fourier restriction to the moment curve in finitely-generated free modules over such rings. This is achieved by lifting the problem to the p-adics and applying a classical argument of Drury in this setting. This work aims to demonstrate that rings of integers offer a simplified model for the Euclidean restriction problem.

Nas últimas décadas, considerável evidência tem sido direcionada no desenvolvimento de métodos computacionais que analisam os comportamentos não lineares das estruturas. O método da corda é considerado o tipo de método de seguimento de trajetórias que possui a técnica mais comum e versátil para analisar tais comportamentos não lineares. No entanto, testes realizados pelos autores concluem que tais métodos ainda apresentam algumas dificuldades quando as estruturas possuem formas complexas e comportamentos fortemente não lineares. Devido a isso, o objetivo do trabalho em questão é acrescentar duas modificações ao método da corda, a fim de desenvolver um modelo mais seguro e estável. A esses métodos, inclui-se (i) uma equação alternativa para o passo previsor, que tornará o método mais estável ao ultrapassar pontos críticos; e (ii) um parâmetro de controle, que através do conceito de soma dos comprimentos de corda, é chamado de método da corda acumulado. Ao final, por consequência destas alterações, um procedimento mais robusto para o método da corda é obtido. Sua validação é apresentada, pelos autores, através de exemplos utilizando estruturas treliçadas (bidimensionais e tridimensionais) em um programa de simulação numérica desenvolvida. / In the last decades, a considerable effort has been directed to develop of computational methods to analyze the nonlinear behavior of structures. The arc-length method is considered the type of path following method which have the most common and versatile techniques for analyzing such nonlinear behaviors. Nevertheless, tests performed by the authors conclude that such methods present some difficulties when the structures possess complex shapes and strongly nonlinear behaviors. Due to this, the purpose of the present work is to add two amendments to the arc-length method, in order to develop a model safer and more stable. In such methods, it is included (i) an alternative equation for the predictor step, that will make the method most stable to overcoming critical points, and (ii) a control parameter, through the concept of sum of the arc length up to now, referred to as accumulated arc-length method. By the end, as a result of these modifications, a more robust procedure for the method of the string is obtained. And its validation is presented by the authors through examples using truss structures in a two-dimensional and three-dimensional numerical simulation program developed.

<p>This master thesis deals with problems in the arc length control in Pulsed MIG/MAG Welding. The main problem is that it is not possible to measure the arc length. In the present solution the voltage over both the electrode and the arc represents the arc length. </p><p>To improve the arc length control a model of the electrode melting has been built. One output from the model is the voltage over the electrode and with this voltage together with the measured voltage it is possible to calculate the voltage over just the arc. Then, having the arc voltage as a value of arc length the arc length control can be improved, which is showed in the end by simulations. Simulations with the present control system are compared with the new one, when the controller is able to control the arc voltage instead of the sum of both the electrode voltage and the arc voltage.</p>

This master thesis deals with problems in the arc length control in Pulsed MIG/MAG Welding. The main problem is that it is not possible to measure the arc length. In the present solution the voltage over both the electrode and the arc represents the arc length. To improve the arc length control a model of the electrode melting has been built. One output from the model is the voltage over the electrode and with this voltage together with the measured voltage it is possible to calculate the voltage over just the arc. Then, having the arc voltage as a value of arc length the arc length control can be improved, which is showed in the end by simulations. Simulations with the present control system are compared with the new one, when the controller is able to control the arc voltage instead of the sum of both the electrode voltage and the arc voltage.

Nas últimas décadas, considerável evidência tem sido direcionada no desenvolvimento de métodos computacionais que analisam os comportamentos não lineares das estruturas. O método da corda é considerado o tipo de método de seguimento de trajetórias que possui a técnica mais comum e versátil para analisar tais comportamentos não lineares. No entanto, testes realizados pelos autores concluem que tais métodos ainda apresentam algumas dificuldades quando as estruturas possuem formas complexas e comportamentos fortemente não lineares. Devido a isso, o objetivo do trabalho em questão é acrescentar duas modificações ao método da corda, a fim de desenvolver um modelo mais seguro e estável. A esses métodos, inclui-se (i) uma equação alternativa para o passo previsor, que tornará o método mais estável ao ultrapassar pontos críticos; e (ii) um parâmetro de controle, que através do conceito de soma dos comprimentos de corda, é chamado de método da corda acumulado. Ao final, por consequência destas alterações, um procedimento mais robusto para o método da corda é obtido. Sua validação é apresentada, pelos autores, através de exemplos utilizando estruturas treliçadas (bidimensionais e tridimensionais) em um programa de simulação numérica desenvolvida. / In the last decades, a considerable effort has been directed to develop of computational methods to analyze the nonlinear behavior of structures. The arc-length method is considered the type of path following method which have the most common and versatile techniques for analyzing such nonlinear behaviors. Nevertheless, tests performed by the authors conclude that such methods present some difficulties when the structures possess complex shapes and strongly nonlinear behaviors. Due to this, the purpose of the present work is to add two amendments to the arc-length method, in order to develop a model safer and more stable. In such methods, it is included (i) an alternative equation for the predictor step, that will make the method most stable to overcoming critical points, and (ii) a control parameter, through the concept of sum of the arc length up to now, referred to as accumulated arc-length method. By the end, as a result of these modifications, a more robust procedure for the method of the string is obtained. And its validation is presented by the authors through examples using truss structures in a two-dimensional and three-dimensional numerical simulation program developed.

FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico / O objetivo deste trabalho foi realizar um estudo sistemÃtico de parÃmetros de soldagem TIG com alimentaÃÃo de arame frio para aplicaÃÃo de revestimento de ligas de nÃquel (UNS N06625, UNS N06686 e UNS N10276) em substratos de aÃo C-Mn considerando a anÃlise das caracterÃsticas geomÃtricas, econÃmicas e operacionais dos depÃsitos, de forma a adequar estes revestimentos para as indÃstrias do Setor de PetrÃleo e GÃs Natural. As soldagens foram realizadas utilizando um robà industrial e um alimentador automÃtico de arame frio. Foi realizado um estudo preliminar para determinar as condiÃÃes iniciais para exploraÃÃo dos parÃmetros, em seguida realizado a soldagem de um fatorial completo. Em uma Ãltima exploraÃÃo dos parÃmetros de soldagem foi aplicado o MÃtodo Taguchi para realizar a anÃlise de diversos fatores de controle com um nÃmero reduzido de experimentos. O perfil geomÃtrico do cordÃo de solda foi levantado na seÃÃo transversal dos corpos de prova. ApÃs obtenÃÃo dos resultados, foram feitos alguns ajustes de modo a realizar soldagens dos revestimentos. Os resultados mostraram que, o correto ajuste da DistÃncia da Ponta do Arame a PeÃa (DPAP) influenciou na geometria e diluiÃÃo do cordÃo de solda e na estabilidade do arco. Foi visto tambÃm que para obter menores nÃveis de diluiÃÃo, a DistÃncia da Ponta do Eletrodo a PeÃa (DPEP) depende do nÃvel de energia utilizado, para menores energias utiliza-se menores DPEPs e, para maiores energias, maiores DPEPs devem ser utilizadas. Os nÃveis de diluiÃÃo e reforÃo foram reduzidos com o uso do tecimento. A tÃcnica da energia influenciou de forma significativa na geometria e diluiÃÃo do cordÃo de solda. Para uma mesma energia de soldagem e, consequentemente velocidade de resfriamento e aporte tÃrmico semelhantes, podem haver nÃveis distintos de diluiÃÃo sem alteraÃÃes metalÃrgicas. O gÃs de proteÃÃo influenciou na diluiÃÃo e no Ãndice de convexidade (R/L) do cordÃo de solda, de uma maneira geral, a mistura de argÃnio e Ãxido nitroso apresentou a melhor condiÃÃo para soldagem dos revestimentos. O ajuste da energia pela corrente de soldagem (Tipo I) apresentou melhor eficiÃncia de deposiÃÃo para baixa energia, jà para alta energia, o melhor ajuste se dà pela velocidade de soldagem (Tipo V). Para baixos nÃveis de diluiÃÃo, o uso do tecimento reduz de maneira significativa os tempos e custos associados a realizaÃÃo dos revestimentos. Com os resultados obtidos foi possÃvel realizar revestimentos de qualidade com baixos nÃveis de diluiÃÃo (<10 %) atravÃs do processo TIG com alimentaÃÃo de arame frio. / The aim of this work was to carry out a systematic study of GTAW welding parameters with feeding of cold wire for covering application of nickel alloys (UNS N06625, UNS N06686 and UNS N10276) in substract of steel C-Mn considering the analysis of geometric, economic and operational characteristics of layers, form to adjust these coverings for the industries of the Sector of Oil and Natural Gas. The weldings were carried out employing an industrial robot and an automatic feeder of cold covered. A preliminary study was carried out to determine the initial conditions to exploration of the parameters, after that it was carried through the welding of a complete factorial. In a last exploration of welding parameters was applied the Taguchi Method to carry out to the analysis of diverse factories of control with a reduced number of experiments. The geometric profile of weld filet was raised in the transversal section of the test specimen. After it obtained the results, some adjustments were made to carry out weldings of coverings. The results showed that the correct adjustments of the Distance of the Tip of the Wire Workpiece (DTWW) influenced in the geometry and diluition weld filet and in the arc stability. It was also seen that to obtain minors levels of dilution, a Distance of the Tip of the Electrode Workpiece (DTEW) depends of the level of energy employed, for lesser energies use lesser DTEWs and, for higher energies, higher DTEWs must be used. The levels of dilution and reinforcement were reduced with the use of the weaving technique. The technique of the energy influenced of significant way in the geometry and dilution of the weld filet. For the same energy welding and, consequently nearly equal cooling rate and heat in the sample, it can have diverse levels of the dilution without metallurgical alterations. The protection gas influenced in the dilution and the convexity index (R/L) of the weld metal, in a general way, the mixture of argon and nitrous oxide presented the best condition for welding of coverings. The adjustment of the energy for current welding (Type I) presented the best efficiency of for low energy, already for high energy, the best adjustment is for welding speed (Type V). For low levels of dilution, the use of weaving technique reduced of significant way the times and associates costs accomplishment of coverings. With the results obtained it was possible to carry out coverings of quality with low levels of dilution (<10 %) trough of GTAW process with feeding of cold wire.

Finite element analysis using Cohesive Zone Method (CZM) is a commonly used method to investigate delamination in laminated composites. In this study, two plane strain, zero-thickness six-node quadratic (6-NQ) and four-node linear (4-NL) interface elements are developed to implement CZM. Two main approaches for CZM formulation are categorized as Unified Mode Approach (UMA) and Separated Mode Approach (SMA), and implemented into 6-NQ interface elements to model a double cantilever beam (DCB) test of a unidirectional laminated composite. The results of the approaches are nearly identical. However, it is theoretically shown that SMA spawns non-symmetric tangent stiffness matrices, which may lower convergence and/or overall performance, for mixed-mode loading cases. Next, a UMA constitutive relationship is rederived. The artificial modifications for improving convergence rates such as lowering penalty stiffness, weakening interfacial strength and using 6-NQ instead of 4-NL interface elements are investigated by using the derived UMA and the DCB test model. The modifications in interfacial strength and penalty stiffness indicate that the convergence may be improved by lowering either parameter. However, over-softening is found to occur if lowering is performed excessively. The morphological differences between the meshes of the models using 6-NQ and 4-NL interface elements are shown. As a consequence, it is highlighted that the impact to convergence performance and overall performance might be in opposite. Additionally, benefits of selecting CZM over other methods are discussed, in particular by theoretical comparisons with the popular Virtual Crack Closure Technique. Finally, the numerical solution scheme and the Arc-Length Method are discussed.

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