La presente tesis trata sobre la novedosa aplicación de materiales funcionalmente graduados (-FGM- Functionally Graded Materials) en el diseño de estructuras tipo viga. Como es sabido, los estudios de rigidización dinámica, se llevan a cabo para evitar resonancias y/o reducir tensiones dinámicas. La forma tradicional que se emplea para optimizar la rigidez de la viga, es variando su sección transversal; ya sea reduciéndola de forma discontinua (multi-steps beams tal como se las conoce en inglés), ahusada (tapered beams tal como se las denomina en inglés) o bien empleando combinaciones de ambas. Surge la originalidad, desde el punto vista de la optimización dinámica, de adicionar una nueva solución al problema de la rigidización. La misma consiste en hacer variar las propiedades de estos modernos materiales en la dirección axial de las vigas (-AFGM-Axially Funtionally Graded Materials). El problema de vibraciones libres para las vigas AFG, se estudia implementando las teorías clásicas de Bernoulli-Euler y de Timoshenko, mediante tres enfoques aproximados; el método energético de Rayleigh-Ritz, el método de cuadratura diferencial generalizada (GDQM, por sus siglas en inglés) y el método de elementos finitos (FEM, por sus siglas en inglés). Los resultados obtenidos se comparan con valores disponibles en la literatura. La muy buena correlación de los mismos, permite dar certezas de que el método de Rayleigh-Ritz, GDQM y FEM, son herramientas de gran precisión y eficiencia para la resolución de esta clase de problemas. Los casos de vigas propuestos se modelan con condiciones de bordes clásicas y con extremos elásticamente restringidos. Para la modelación numérica de los problemas, se implementa el software Wolfram Mathematica 9.0. En el estudio se tratan leyes de distribución del tipo axial asimétrica y axial simétrica; para varias composiciones y distintos materiales AFG. En particular, se da especial énfasis al material compuesto por alúmina (Alum) y acero (Ac), ya que desde el punto de vista ingenieril presenta propiedades atractivas para la rigidización dinámica de vigas. Se analiza el efecto dinámico que tiene adosar una o varias masas a la viga. Evidenciando que su presencia disminuye, en todos los casos, a los coeficientes de frecuencias naturales de la viga sin masa adosada. Y además, constituye un factor importante, desde el punto de vista del diseño, en la elección de la composición del material AFG a implementar. Para las vigas AFG cantiléver con características asimétricas del material, la composición a) Ac-Alum rigidiza más que la composición b) Alum-Ac, cuando el exponente n (de las leyes de variación) es menor a 1, exista o no masa adosada en el extremo libre. En cambio, para 1n> la composición b) es quien optimiza la solución. El caso 1n= es particular, ya que la composición a) rigidiza levemente más que b) cuando la viga no tiene masa adosada. Pero, cuando se adosa la masa, se aprecia que el coeficiente de frecuencia fundamental aumenta más para la composición b). Para vigas AFG con características simétricas, se evidencia que la composición c) Ac-Alum- Ac optimiza la rigidización haya o no masa adosada, frente a la composición d) Alum-Ac- Alum. / This thesis deals with the novel application of functionally graduated materials (FGM) in the design of beams. It is known that dynamic stiffening studies are carried out to avoid resonances and/or reduce dynamic stresses. The traditional method to optimize the rigidity of the beam consists in variations of its cross section; either by reducing it in a discontinuous way (multi-steps beams), in a tapered way (tapered beams) or by using a combination of both. In this Thesis, from the point of view of dynamic optimization, an original solution of the problem of stiffening is proposed. This novel solution consists in varying the properties of these modern materials in the axial direction of the beams (AFGM). With this aim, the problem of free vibrations for the AFG beams is studied through the classical theories of Bernoulli-Euler and Timoshenko, using three approximation approaches: the Rayleigh-Ritz energy method, the generalized differential quadrature method (GDQM) and the finite element method (FEM). The obtained results are compared with those available in the related literature. The very good correlation of these, allows to give certainty that the Rayleigh-Ritz method, GDQM and FEM, are tools of great precision and efficiency for the resolution of this class of problems. The cases of proposed beams are modeled with classic edge conditions and with elastically restrained edge supports. For the numerical modeling of the problems, Wolfram Mathematica 9.0 software is implemented. The used distribution laws are the axial asymmetric and axial symmetric and were applied for various compositions and different AFG materials; with a particular emphasis on the material composed of alumina (Alum) and steel (St), since it has attractive properties for the dynamic stiffening of beams from the engineering point of view. The dynamic effect of attaching one or several masses to the beam is analyzed. It is shown that their presence decreases, in all cases, the natural frequency coefficients of the beam that do not have attached mass. In addition, it constitutes an important factor, from the point of view of the design, in the choice of the composition of the AFG material to be implemented. In cantilever AFG beams with asymmetric characteristics of the material, the composition a) St-Alum stiffens more than the composition b) Alum-St, when the exponent n (of the laws of variation) is less than 1, whether or not there is an attached mass at the free end. On the other hand, for the composition b) it is the one that optimizes the solution. The case 1n= is particular, since the composition a) stiffens slightly more than b) when the beam has not attached mass. But, when the mass is attached, the fundamental frequency coefficient increases more for the composition b). In AFG beams with symmetrical characteristics, it is evident that the composition c) St- Alum-St optimizes the stiffening whether or not there is an attached mass, compared to the composition d) Alum-St-Alum.

The aerospace industry is increasingly coming to the conclusion that physics-based high-fidelity models need to be used as early as possible in the design of its products. At the preliminary design stage of wing structures, though highly desirable for its high accuracy, a detailed finite element analysis(FEA) is often not feasible due to the prohibitive preparation time for the FE model data and high computation cost caused by large degrees of freedom. In view of this situation, often equivalent beam models are used for the purpose of obtaining global solutions. However, for wings with low aspect ratio, the use of equivalent beam models is questionable, and using an equivalent plate model would be more promising. An efficient method, Equivalent Plate Analysis or simply EPA, using an equivalent plate model, is developed in the present work for studying the static and free-vibration problems of built-up wing structures composed of skins, spars, and ribs. The model includes the transverse shear effects by treating the built-up wing as a plate following the Reissner-Mindlin theory (FSDT). The Ritz method is used with the Legendre polynomials being employed as the trial functions. Formulations are such that there is no limitation on the wing thickness distribution. This method is evaluated, by comparing the results with those obtained using MSC/NASTRAN, for a set of examples including both static and dynamic problems. The Equivalent Plate Analysis (EPA) as explained above is also used as a basis for generating other efficient methods for the early design stage of wing structures, such that they can be incorporated with optimization tools into the process of searching for an optimal design. In the search for an optimal design, it is essential to assess the structural responses quickly at any design space point. For such purpose, the FEA or even the above EPA, which establishes the stiffness and mass matrices by integrating contributions spar by spar, rib by rib, are not efficient enough. One approach is to use the Artificial Neural Network (ANN), or simply called Neural Network (NN) as a means of simulating the structural responses of wings. Upon an investigation of applications of NN in structural engineering, methods of using NN for the present purpose are explored in two directions, i.e. the direct application and the indirect application. The direct method uses FEA or EPA generated results directly as the output. In the indirect method, the wing inner-structure is combined with the skins to form an "equivalent" material. The constitutive matrix, which relates the stress vector to the strain vector, and the density of the equivalent material are obtained by enforcing mass and stiffness matrix equities with regard to the EPA in a least-square sense. Neural networks for these material properties are trained in terms of the design variables of the wing structure. It is shown that this EPA with indirect application of Neural Networks, or simply called an Equivalent Skin Analysis (ESA) of the wing structure, is more efficient than the EPA and still fairly good results can be obtained. Another approach is to use the sensitivity techniques. Sensitivity techniques are frequently used in structural design practices for searching the optimal solutions near a baseline design. In the present work, the modal response of general trapezoidal wing structures is approximated using shape sensitivities up to the second order, and the use of second order sensitivities proved to be yielding much better results than the case where only first order sensitivities are used. Also different approaches of computing the derivatives are investigated. In a design space with a lot of design points, when sensitivities at each design point are obtained, it is shown that the global variation in the design space can be readily given based on these sensitivities. / Ph. D.

Récemment de nouvelles méthodes de simulation numérique ont fait leur apparition. Ces méthodes basées sur un nuage de noeuds ne font pas intervenir de maillage comme pour la méthode des éléments finis. Malgré leur nombre, leur base théorique est semblable. De plus, de part leur caractère récent, leurs développements sont encore à ce jour qu 'aux prémices. Ce travail récapitule les grandes lignes des procédures indispensables pour une résolution à l'aide d'une méthode sans maillage appelée méthode HP-Clouds. Entre autre, les fondements mathématiques par la création de nouvelles fonctions de forme sans maillage, supportées par des boules, sont présentés dans un premier chapitre. Puis, une procédure de résolution des équations de Maxwell en électromagnétisme à l'aide de la méthode HP-Clouds est présentée en décrivant précisément la méthode de. Ritz-Galerkin dans un cas simple. Nous avons d'autre part mis l'accent sur la structure rie données basée sur les boules, supports des fonctions de forme, permettant, ainsi de faciliter l'insertion de la méthode HP-Clouds dans un logiciel de simulation numérique. Dans toutes ces étapes nous nous sommes astreint à ne pas utiliser de maillage même intermédiaire ou fictif. Enfin, nous avons validé nos résultats sur trois problèmes concrets qui laisse présager un avenir prometteur pour les méthodes sans maillage.

A wide range of dynamic systems can be approximated as linear and time invariant, for which a wealth of tools are available to characterize or modify their dynamic characteristics. Experimental modal analysis (EMA) is a procedure whereby the natural frequencies, damping ratios and mode shapes which parameterize vibratory, linear, time invariant systems are derived from experimentally measured response data. EMA is commonly applied in a multitude of applications, for example, to generate experimental models of dynamic systems, validate finite element models and to characterize dissipation in vibratory systems. Recent EMA has also been used to characterize damage or defects in a variety of systems. The Algorithm of Mode Isolation (AMI), presented by Drexel and Ginsberg in 2001, employs a unique strategy for modal parameter estimation in which modes are sequentially identified and subtracted from a set of FRFs. Their natural frequencies, damping ratios and mode vectors are then refined through an iterative procedure. This contrasts conventional multi-degree-of-freedom (MDOF) identification algorithms, most of which attempt to identify all of the modes of a system simultaneously. This dissertation presents a hybrid multi-input-multi-output (MIMO) implementation of the algorithm of mode isolation that improves the performance of AMI for systems with very close or weakly excited modes. The algorithmic steps are amenable to semi-automatic identification, and many FRFs can be processed efficiently and without concern for ill-conditioning, even when many modes are identified. The performance of the algorithm is demonstrated on noise contaminated analytical response data from two systems having close modes, one of which has localized modes while the other has globally responsive modes. The results are compared with other popular algorithms. MIMO-AMI is also applied to experimentally obtained data from shaker excited tests of the Z24 highway bridge, demonstrating the algorithm's performance on a data set typical of many EMA applications. Considerations for determining the number of modes active in the frequency band of interest are addressed, and the results obtained are compared to those found by other groups of researchers.

In this thesis I propose a new approach to the study of the “childlike” in five works from the first half of the 20th century: Les Enfants terribles (1929) by Jean Cocteau, “Un diamant gros comme le Ritz” (1922) by F. Scott Fitzgerald, La Métamorphose (1915) by Franz Kafka, Le Petit Prince (1943) by Antoine de Saint-Exupéry and L’Arrache-coeur (1953) by Boris Vian. Distinct from both childhood narratives and narratives for children, these texts nevertheless exhibit a childlike quality that can best be described as an in-between state of ambiguity. In the first section of the thesis, I look at the “between” identity of the children. There are children who fly and who are extraterrestrials. There are others who have adult jobs and who even marry. In fact, I call these ambiguous characters, “les enfantins”. In the second section of the thesis, I show that the language is “between”. In 1951, child psychologist Jean Piaget published “La Formation du symbole chez l’enfant”, a work in which he studies the tendency of young children to take one object for another. I show how this type of almost magical thinking that Piaget calls “symbolic thought” appears in the “récit”. In the final section of my thesis, I study areas in the story where the reader finds himself in a “between” position, unable to establish whether what he is reading is occurring or whether it belongs to the imaginary symbolic thought of the child. Here I focus on the readers’ hesitation, contrasting it with the hesitation that Tzvetan Todorov explores in the genre of the fantastic. While this thesis is a close reading of five specific works, it incites several theoretical questions that can be applied more widely to studies concerning the “literary child”: what constitutes a child character in a work, what effect does a child character have on the language of the text, and how does a child character affect the way a text is read? / Thesis (Master, French) -- Queen's University, 2008-02-14 12:16:39.799

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In this thesis three different approaches for solving partial differential equa-tions with neural networks will be explored; namely Physics-Informed NeuralNetworks, Fourier Neural Operators and the Deep Ritz method. Physics-Informed Neural Networks and the Deep Ritz Method are unsupervised machine learning methods, while the Fourier Neural Operator is a supervised method. The Physics-Informed Neural Network is implemented on Burger’s equation,while the Fourier Neural Operator is implemented on Poisson’s equation and Darcy’s law and the Deep Ritz method is applied to several variational problems. The Physics-Informed Neural Network is also used for the inverse problem; given some data on a solution, the neural network is trained to determine what the underlying partial differential equation is whose solution is given by the data. Apart from this, importance sampling is also implemented to accelerate the training of physics-informed neural networks. The contributions of this thesis are to implement a slightly different form of importance sampling on the physics-informed neural network, to show that the Deep Ritz method can be used for a larger class of variational problems than the original publication suggests and to apply the Fourier Neural Operator on an application in geophyiscs involving Darcy’s law where the coefficient factor is given by exponentiated two-dimensional pink noise.

The lowest natural frequencies of thin-walled noncircular fiber-reinforced composite cylinders, specifically cylinders with elliptical cross sections, are investigated. Of interest is the variation of the lowest natural frequency, the so-called fundamental frequency, as a function of wall laminate properties, cross-sectional eccentricity and other cylinder geometric parameters. Both simple and clamped support boundary conditions are investigated. Laminate properties that are uniform with circumferential location and laminate properties that vary with circumferential location, by way of varying laminate fiber angle with circumferential location, are considered. As the radius of curvature of a noncircular cylinder varies with circumferential location, it is logical to consider the influence of circumferentially varying fiber orientation on the fundamental frequency. The analysis for predicting the fundamental frequency is based on Donnell shell theory, linear elastic properties, and the use of Hamilton's Principle in conjunction with the Rayleigh-Ritz technique. By use of a so-called shape factor, the magnitude of cylinder normal displacements are modulated to be larger in the regions of the cross section with the largest radius of curvatures and smaller in the regions with the smallest radius of curvature. The final equations for predicting the fundamental frequency are quite complex, but a series of approximations results in a hierarchy of simpler equations, the simplest being referred to as Lo's approximation. The prediction of the fundamental frequencies is spot checked by comparing the results as predicted by the various levels of approximation with predictions of a shell-based finite element model. Considering uniform laminate properties, comparisons between the developed analysis and the finite element model are good for all levels of simpler equations, and excellent in some cases. The developed analysis is subsequently used for parameter studies. It is found that compared to a circular cylinder of the same circumference and with uniform laminate properties, the fundamental frequency of an elliptical cylinder is always less. Surprisingly, based on the results obtained, it appears that for a given cylinder geometry the fundamental frequency is not particularly sensitive to wall lamination sequence, though the wave number in the circumferential direction of the mode shape associated with the fundamental frequency is sensitive to lamination sequence. Considering cylinders with circumferentially varying fiber orientation, comparisons between the developed analysis and the finite element model for most of the cases studied are good. However, the developed equations are limited since it is difficult to find a set of known functions to describe the deformation of an arbitrary lamination sequence when applying the Rayleigh-Ritz technique. In general, in can be concluded that the effect of varying fiber orientation on the fundamental frequency is much less than the influence of cylinder aspect ratio. It can also be concluded that the developed analysis would be an excellent tool for design purposes, as the calculation of the fundamental frequency is done quickly, and design trade-offs studies would be easy. / Ph. D.

We present a unified and self-contained treatment of rational Krylov methods for approximating the product of a function of a linear operator with a vector. With the help of general rational Krylov decompositions we reveal the connections between seemingly different approximation methods, such as the Rayleigh–Ritz or shift-and-invert method, and derive new methods, for example a restarted rational Krylov method and a related method based on rational interpolation in prescribed nodes. Various theorems known for polynomial Krylov spaces are generalized to the rational Krylov case. Computational issues, such as the computation of so-called matrix Rayleigh quotients or parallel variants of rational Arnoldi algorithms, are discussed. We also present novel estimates for the error arising from inexact linear system solves and the approximation error of the Rayleigh–Ritz method. Rational Krylov methods involve several parameters and we discuss their optimal choice by considering the underlying rational approximation problems. In particular, we present different classes of optimal parameters and collect formulas for the associated convergence rates. Often the parameters leading to best convergence rates are not optimal in terms of computation time required by the resulting rational Krylov method. We explain this observation and present new approaches for computing parameters that are preferable for computations. We give a heuristic explanation of superlinear convergence effects observed with the Rayleigh–Ritz method, utilizing a new theory of the convergence of rational Ritz values. All theoretical results are tested and illustrated by numerical examples. Numerous links to the historical and recent literature are included.

Detta examensarbete är indelat i tre delar. Examensarbetet består av en översättning av tre kapitel ur Etta James självbiografi Rage to survive: the Etta James story skriven av James och spökförfattaren David Ritz, samt ett kapitel om vilka textspecifika översättningsproblem som uppstod vid översättningen. Den tredje delen består av en djupanalys av hur varieteten African-American English (AAE) översatts i två andra verk, nämligen I know why the caged bird sings av Maya Angelou och The bluest eye av Toni Morrison där översättningarna av dessa verk jämförs med min översättning av Rage to survive: the Etta James story. Djupanalysens syfte är att undersöka hur många talspråksmarkörer som finns i de ovannämnda verken, samt hur många av dessa markörer är specifika för AAE. Dessutom används Englund Dimitrovas varietetsskala (2001). Detta för att undersöka huruvida måltexterna ligger på skalan i relation till källtexterna genom mängden talspråksmarkörer. Översättningen genomfördes med målet att ligga så nära källtextens stil som var möjligt med hänsyn till målspråkets grammatiska regler och förutsättningar. Detta för att kunna erbjuda den målspråklige läsaren en likvärdig effekt som läsaren av källtexten. För att uppfylla detta mål fick en del kompromisser göras. / This thesis is divided into three main parts. It consists of a translation of three chapters from Etta James’ autobiography named Rage to survive: the Etta James story, written by James herself and ghost writer David Ritz. The thesis also features a part involving the issues that arose when I translated Rage to survive: the Etta James story and how I solved these issues. The third and final part consists of an analysis of how African-American English (AAE) has been translated in two other novels in the past, namely I know why the caged bird sings by Maya Angelou and Toni Morrison’s The bluest eye. I compare the translations of these two novels with my own translation of Rage to survive: the Etta James story in the analysis where I strive to gain insight into the norms for translating spoken varieties. The translation was carried out with the purpose of maintaining the stylistic and informal markers as intact as possible while at the same time adhering to the grammatical prerequisites of the target language (Swedish). / <p>Översättningen är borttagen ur den publicerade versionen i fulltext i DiVA (denna version) på grund av upphovsrätten.</p><p>The translation has been removed from the published version of the essay in DiVA due to copyright.</p>