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Thèse de doctorat : Sciences : Paris, Faculté des sciences : 1867. / Titre provenant de l'écran-titre.

Thesis (M.S.)--University of Toledo, 2007. / Typescript. "Submitted as partial fulfillments of the requirements for the Master of Science Degree in Mechanical Engineering." "A thesis entitled"--at head of title. Bibliography: leaves 196-205.

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An investigation of the possible performance improvements of thin circular cylindrical shells through the use of the variable stiffness concept is presented. The variable stiffness concept implies that the stiffness parameters change spatially throughout the structure. This situation is achieved mainly through the use of curvilinear fibers within a fiber-reinforced composite laminate, though the possibility of thickness variations and discrete stiffening elements is also allowed. These three mechanisms are incorporated into the constitutive laws for thin shells through the use of Classical Lamination Theory. The existence of stiffness variation within the structure warrants a formulation of the static equilibrium equations from the most basic principles. The governing equations include sufficient detail to correctly model several types of nonlinearity, including the formation of a nonlinear shell boundary layer as well as the Brazier effect due to nonlinear bending of long cylinders. Stress analysis and initial buckling estimates are formulated for a general variable stiffness cylinder. Results and comparisons for several simplifications of these highly complex governing equations are presented so that the ensuing numerical solutions are considered reliable and efficient enough for in-depth optimization studies. Four distinct cases of loading and stiffness variation are chosen to investigate possible areas of improvement that the variable stiffness concept may offer over traditional constant stiffness and/or stiffened structures. The initial investigation deals with the simplest solution for cylindrical shells in which all quantities are constant around the circumference of the cylinder. This axisymmetric case includes a stiffness variation exclusively in the axial direction, and the only pertinent loading scenarios include constant loads of axial compression, pressure, and torsion. The results for these cases indicate that little improvement over traditional laminates exists through the use of curvilinear fibers, mainly due to the presence of a weak link area within the stiffness variation that limits the ultimate load that the structure can withstand. Rigorous optimization studies reveal that even though slight increases in the critical loads can be produced for designs with an arbitrary variation of the fiber orientation angle, the improvements are not significant when compared to traditional design techniques that utilize ring stiffeners and frames. The second problem that is studied involves arbitrary loading of a cylinder with a stiffness variation that changes only in the circumferential direction. The end effects of the cylinder are ignored, so that the problem takes the form of an analysis of a cross-section for a short cylinder segment. Various load cases including axial compression, pressure, torsion, bending, and transverse shear forces are investigated. It is found that the most significant improvements in load-carrying capability exist for cases which involve loads that also vary around the circumference of the shell, namely bending and shear forces. The stiffness variation of the optimal designs contribute to the increased performance in two ways: lowering the stresses in the critical areas through redistribution of the stresses; and providing a relatively stiff region that alters the buckling behavior of the structure. These results led to an in-depth optimization study involving weight optimization of a fuselage structure subjected to typical design constraints. Comparisons of the curvilinear fiber format to traditional stiffened structures constructed of isotropic and composite materials are included. It is found that standard variable stiffness designs are quite comparable in terms of weight and load-carrying capability yet offer the added advantage of tailorability of distinct regions of the structure that experience drastically different loading conditions. The last two problems presented in this work involve the nonlinear phenomenon of long tubes under bending. Though this scenario is not as applicable to fuselage structures as the previous problems, the mechanisms that produce the nonlinear effect are ideally suited to be controlled by the variable stiffness concept. This is due to the fact that the dominating influence for long cylinders under bending is the ovalization of the cross-section, which is governed mainly by the stiffness parameters of the cylindrical shell. Possible improvement of the critical buckling moments for these structures is investigated using either a circumferential or axial stiffness variation. For the circumferential case involving infinite length cylinders, it is found that slight improvements can be observed by designing structures that resist the cross-sectional deformation yet do not detract from the buckling resistance at the critical location. The results also indicate that bucking behavior is extremely dependent on cylinder length. This effect is most easily seen in the solution of finite length cylinders under bending that contain an axial stiffness variation. For these structures, the only mechanism that exhibits improved response are those that effectively shorten the length of the cylinder, thus reducing the cross-sectional deformation due to the forced restraint at the ends. It was found that the use of curvilinear fibers was not able to achieve this effect in sufficient degree to resist the deformation, but that ring stiffeners produced the desired response abmirably. Thus it is shown that the variable stiffness concept is most effective at improving the bending response of long cylinders through the use of a circumferential stiffness variation. / Ph. D.

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Several methods are presented for improving upon the traditional analytic “circular” method for constructing a flux-surface aligned curvilinear coordinate system representation of equilibrium plasma geometry and magnetic fields, and the most accurate Asymmetric Miller method is applied to calculations of poloidal asymmetries in plasma density, velocity, and electric potential. Techniques for developing an orthogonalized coordinate system from a general curvilinear representation of plasma flux surfaces and for representing the poloidal component of the magnetic field in the orthogonalized curvilinear system are developed generally, in order to be applied to four plasma flux-surface models. The formalism for approximating flux surfaces originally presented by Miller is extended to include poloidal asymmetries between the upper and lower plasma hemispheres, and is subsequently shown to be more accurate at fitting the shapes of flux surfaces calculated using EFIT than both the traditional “circular” model and two alternative curvilinear models of comparable complexity based on Fourier expansions of major radius, vertical position, and minor radius. Applying the coordinate system orthogonalization technique to these four models allows for calculations of the poloidal magnetic field which, upon comparison to a calculation of the poloidal field performed in a Cartesian system using the experimentally based EFIT prediction for the Grad-Shafranov equilibrium, demonstrates that the asymmetric “Miller” model is also superior to other methods at representing the poloidal magnetic field. A system of equations developed by representing the poloidal variations of velocity, density, and electric potential using O(1) Fourier expansions in the flux-surface averaged neoclassical plasma continuity and momentum balances is solved using several variations of both the “Miller” and “circular” curvilinear models to set geometric scale factors, illustrating the effects that these improvements in geometric modeling have on tokamak fluid theory calculations.

[pt] No presente trabalho é realizada uma análise do desempenho de três diferentes modelos de turbulência na previsão de escoamentos que apresentam separação e recolamento. Investigou-se o escoamento turbulento através de dutos com obstruções curvilíneas. Os modelos selecionados pertecem a classe de modelos de suas equações diferenciais k-e para baixos números de Reynolds. A análise tem por objetivo verificar se estes modelos são capazes de captar as regiões de recirculação e repercução de pressão após a abstrução, grandezas fundamentais para a avaliação da distribuição de tensões. Os campos de velocidade, energia cinética turbulenta, taxa de dissipação obtidos pelos diferentes modelos são comparados com dados numéricos e experimentais na literatura, visando identificar qual é o modelo mais adequado para esse tipo de escoamento. Para a determinação numérica do escoamento na geometria com a uma obstrução curvilínea, do tipo cossenoidal, utilizou-se o método de volumes com coordenadas curvilíneas não ortogonais que se adaptam à geometria. Os componentes contravariantes da velocidade foram empregadas como variáveis independentes nas esquações de conservação de quantidade de movimento e o acoplamento velocidade pressão foi resolvido pelo algoritmo SIMPLEC. Dentre os modelos testados, nenhum conseguiu reproduzir exatamente todos os dados experimentais, porém concluiu-se que o modelo LSH, proposto por Launder e Sharma (1974) com a modificação proposta por Hanjalic e Launder (1980) apresentou o melhor desempenho, o qual pode ser considerado como satisfatório. / [en] In the present work an analysis of the performance of three different turbulence models in the prediction of flows that present seperation and reattachment. The tuberlent flow was investigated through ducts with curvilenar obstructions. The selected models belong to the class of models with two differential equations k- e for low numbersof Reynolds. The objetive of the analysis is to verify if these models are capable of capturing the recirculation areas and pressure recovery after the obstruction, fundamentals for the evaluation of the distribution of tensions. The fields of velocity, turbulent kinetic energy, dissipation rate obtained by different models are comparared with numeric and experiments data found in the literature, seeking to identify which is the model more adapted for those tyope of flows. The numeric determination of the fluid flows in the geometry with a curvilinear obstruction, described by a sine curve, was accomplished by a finite volume method with non ortthogonal curvilinear coordinates which adapt to the geometry. The countervariants velocity components was empployed as independent variables in the momentum conservation equation and the velocity-pressure coupling was solved by the SIMPLEC algorithm. Among all the tested models, none was able to reproduce exactly the experimental data. However, the LSH model, proposed by Launder and Sharma (1974) with the modification proposal for Hanjalic and Launder (1980) presented the best performance, which can be considered satisfactory.

"Art is contemplation. It is the pleasure of the mind which searches into nature and which there defines the spirit of which nature herself is animated" (Auguste Rodin). My intention as a sculptor is to explore the intersection between nature and industry. I seek to find a balance between the industrial (steel) and the natural (stone). Steel represents societal obligations. Stone (river rock) is specific to place and representative of family. With these juxtaposed elements I strive to create sculptural forms of wonder and contemplation. I attempt to interpret and understand my involvement with the complex world through the process of creating sculpture.

It is possible to create laminae that have spatially varying fiber orientation with a tow placement machine. A laminate which is composed of such plies will have stiffness properties which vary as a function of position. Previous work had modelled such variable-stiffness laminae by taking a reference fiber path and creating subsequent paths by shifting the reference path. This thesis introduces a method where subsequent paths are truly parallel to the reference fiber path. The primary manufacturing constraint considered in the analysis of variable-stiffness laminates was limits on fiber curvature which proved to be more restrictive for parallel fiber laminae than for shifted fiber. The in-plane responses of shifted and parallel fiber variable-stiffness laminates to either an applied uniform end shortening or in-plane shear were determined. Both shifted and parallel fiber variable-stiffness laminates can redistribute the applied load thereby increasing critical buckling loads compared to traditional straight fiber laminates. The primary differences between the two methods is that parallel fiber laminates are not able to redistribute the loading to the degree of the shifted fiber. This significantly reduces the increase in critical buckling load for parallel fiber variable-stiffness laminates over straight fiber laminates. / Master of Science