This work focuses mainly on the resistance of members to flexural buckling according to Eurocode 3. The work provides the mathematical backgrounds to the equations and buckling curves presented in Eurocode 3. The work also, attempts to reveal how different imperfections influence the flexural buckling resistance which is demonstrated through Finite Element (FE) simulations. The work presents modeling and analysis on a steel column in ABAQUS 6.14. Linear and non-linear buckling analyses of the steel column, with the influence of imperfections, are implemented in this work. Specifically, the imperfections considered in this study are material plasticity, initial bow and residual stress. The influence of initial bow imperfection of 0.1% of the length of the column considering flexural buckling was found to be 45.28% of the Euler buckling load. The influence of residual stresses, with a magnitude of maximum about 13% in the flange and 35% in the web, of the yielding strength, on flexural buckling is about 31.9% of the design Euler buckling load. The combined effect of residual stress and initial bow imperfection on flexural buckling is about 45.34% of the design Euler buckling load.

A general eigen-value buckling solution is developed for the buckling of long thick pipes subjected to internal and external hydrostatic pressure. The principle of stationary potential energy is used to formulate the conditions of equilibrium, neutral stability conditions, and associated boundary conditions using polar coordinates. The formulation accounts for shear deformation effects and is suited for composite pipe systems with thick cores. It involves destabilizing terms: one is due to the external hydrostatic pressure and incorporates the follower effects, and the other, is due to the pre-bucking stresses undergoing the nonlinear components of strains. The formulation adopts a work conjugate triplet consisting the Cauchy stress tensor, the Green Lagrange strain tensor, and constant constitutive relations. A Fourier series expansion of the displacement fields is adopted to transform the 2D problem into a series of independent 1D problems, thus keeping the computational effort to a minimum while preserving the accuracy of the solution. Two numerical solutions were developed and implemented under MATLAB; the first one is based on the finite difference technique and the second one is based on the finite element solution. Both solutions were shown to converge to the same solution, the finite difference from below, while the finite element converges from above. The finite element solution is then applied to predict the buckling capacity of sandwich pipes consisting of two steel pipes with a soft core. A comprehensive verification study is conducted and the validity of the formulation was established through comparison with other solutions. A parametric study is then conducted to investigate the effect of hydrostatic internal pressure, core material, core thickness, and internal and external pipe thicknesses, on the external buckling pressure of sandwich pipes.

[pt] A modelagem de fenômenos climatológicos constitui um dos maiores desafios enfrentados pela humanidade, impactando toda a vida do planeta. Muitos modelos têm sido propostos e muitas ferramentas têm sido construídas na tentativa de explicar a dinâmica destes processos e sua evolução espacial e temporal. Este trabalho visa oferecer uma contribuição para a modelagem, análise e compreensão dos fenômenos climatológicos com base no conceito da Inovação. Ao invés de procurar, como os modelos clássicos, a representação de comportamentos e relações com base em técnicas estatísticas, esta pesquisa apóiase em um novo conceito: a Inovação, que busca o novo, e não o padrão, identificando a diferença e modelando o fenômeno a ela associado O conceito da Inovação é capaz de caracterizar o fenômeno climatológico, reconhecendo seu surgimento, localização, intensidade e duração. A aplicação do Conceito da Inovação leva à identificação das conexões globais, definindo propagações espaciais e temporais, além de delinear caminhos que explicam as teleconexões entre regiões e sua variação ao longo do tempo. Os resultados obtidos são bastante promissores, uma vez que conseguem caracterizar os processos e sua evolução com uma precisão e eficiência até agora não obtidas pelos métodos disponíveis. Além disso, a descoberta e a individualização dos caminhos que explicam as teleconexões globais iniciam uma nova classe de ferramentas para um conhecimento mais profundo e abrangente de todo o processo climatológico. / [en] Modeling climatological phenomena is one of the most intriguing challenges faced by mankind; the results impact on the whole planet life. Most existing models and tools search for the explanation of these process dynamics and associated spatial and temporal evolution. This work targets a contribution to the modeling, analysis and understanding of climatological phenomena based on the Innovation concept. Instead of following the classical search for statistical behaviors, the aim is searching for the transient and the associated impacts. The Innovation concept is initially applied to the climatological phenomena, identifying its birth, location, duration and intensity. Next, global connections are identified, defining spatial and temporal propagations. Finally, global paths and corresponding variations in time are highlighted and used to explain global teleconnections between regions. The obtained results are promising, characterizing processes and corresponding evolution within a precision and efficiency not offered by existing models. Furthermore, uncovering the roots of global teleconnections permits a new class of tools for a more complete and deep understanding of the whole climatological environment.

[pt] Desenvolve-se uma técnica para a extração de auto-pares relacionados com a solução de problemas de Elementos Finitos. O algoritmo consiste no uso dos métodos da Iteração Inversa e Gradiente Conjugado para a obtenção do vetor solução associado ao menor auto-valor. As soluções do auto-sistema são calculadas sequencialmente pela modificação da matriz dos coeficientes das equações de equilíbrio do problema através do uso de uma técnica de Deflação. O uso extensivo desta técnica introduz auto-valores múltiplos na matriz dos coeficientes, tornando necessário proceder-se a uma combinação dos dois métodos. É efetuado também um estudo para encontrar vetores iniciais apropriados a serem utilizados pelos métodos. O algoritmo foi implementado e alguns resultados de resolução de exemplos são apresentados, para ilustrar o seu desempenho. / [en] A vector iterative technique is developed for the extraction of eigenpairs related to the solution of finite element problems. The algorithm consists of using inverse iteration and conjugate gradient methods so as to obtain the solution vector associated to the smallest eigenvalue. Eigensolutions are sequentially calculated by replacing the coefficient matrix in the problem equilibrium equation using a deflation technique. The extensive usage of this technique, introduces multiple eigenvalue in the coefficient matrix, requiring a procedure to combine both methods. Also, a study is performed to find the appropriate starting vector to be used with methods. The algorithm has been implemented and the results of some example solutions are given that yield insight into its predictive capabilities.

[pt] As informações sobre a sensibilidade da solução de um dado escoamento mediante a perturbações infinitesimais é importante para o seu completo entendimento. A análise de estabilidade de escoamentos pode ser utilizada na otimização de processos industriais. Na indústria de revestimento o controle da estabilidade é fundamental, uma vez que o escoamento na região de aplicação da camada de líquido sobre o substrato, de um modo geral, tem que ser laminar, bidimensional e em regime permanente. O objetive é determinar, dentro do espaço de parâmetros de operação, a região onde o escoamento é estável e conseqüêntemente a camada a ser revestida uniforme. Porém, por ser uma análise complexa, só é usada na indústria em estudos mais apurados. O sistema linear que descreve a estabilidade vai ser discretizado com o método de Galerkin / elementos finitos, dando origem a um problema de autovalor generalizado.Tanto para escoamentos com líquidos newtonianos como para escoamentos com líquidos viscoelásticos, uma das matrizes do problema de autovalor generalizado é singular e alguns autovalores se encontram no infinito. No escoamento com líquidos viscoelásticos parte do espectro é contínuo, aumentando o grau de dificuldade da análise numérica para encontrá-lo. Nesse trabalho, vamos apresentar um método baseado em transformações lineares tirando vantagem das estruturas matriciais e transformando-as em um problema de autovalor clássico com dimens são, pelo menos, três vezes menor que o original. O método elimina os autovalores infinitos do problema com um baixo custo computacional. A estabilidade de um escoamento de Couette unidimensional de líquido newtoniano é analisada como um primeiro exemplo. Depois, o início do estudo da estabilidade em um escoamento de Couette bidimensional e também um escoamento pistonado com o mesmo líquido. Generaliza-se o método para o escoamento de Couette de um líquido viscoelástico, os resultados para o escoamento de um líquido cujo comportamento mecânico é descrito pelo modelo de Maxwell são apresentados e comparados com a solução analítica de Gorodtsov & Leonov, 1967. A relação entre os autovetores do problema transformado e do original é apresentada. / [en] Steady state,two-dimensional flows may become unstable under two and three-dimensional disturbances, if the flow parameters exceed some critical values. In many practical situations, determining the parameters at which the flow becomes unstable is essential. The complete understanding of viscous and viscoelastic flows requires not only the steady state solution of the governing equations, but also its sensitivity to small perturbations. Linear stability analysis leads to a generalized eigenvalue problem, GEVP. Solving the GEVP is challenging, even for Newtonian liquids, because the incompressibility constraint creates singularities that lead to nonphysical eigenvalues at infinity. For viscoelastic flows, the difficulties are even higher because of the continuous spectrum of eigenmodes associated with differential constitutive equations. The complexity and high computational cost of solving the GEVP have probably discouraged the use of linear stability analysis of incompressible flows as a general engineering tool for design and optimization. The Couette flow of UCM liquids has been used as a classical problem to address some of the important issues related to stability analysis of viscoelastic flows. The spectrum consists of two discrete eigenvalues and a continuous segment of eigenvalues with real part equal to -1/We (We is the Weissenberg number). Most of the numerical approximation of the spectrum of viscoelastic Couette flow presented in the literature were obtained using spectral expansions. The eigenvalues close to the continuous part of the spectrum show very slow convergence. In this work, the linear stability of Couette flow of a Newtonian and UCM liquids were studied using finite element method, which makes it easier to extend the analysis to complex flows. A new procedure to eliminate the eigenvalues at infinity from the GEVP that come from differential equations is also proposed. The procedure takes advantage of the structure of the matrices involved and avoids the computational effort of common mapping techniques. With the proposed procedure, the GEVP is transformed into a smaller simple EVP, making the computations more effcient. Reducing the computational memory and time. The relation between the eigenvector from the original problem and the reduced one is also presented.

Les contributions de cette thèse consistent en trois principaux résultats. Le premier résultat concerne la théorie des perturbations analytique pour les modèles de type Kohn-Sham. Nous montrons, sous certaines conditions techniques, l'existence, l'unicité et l'analyticité de la matrice densité de l'état fondamental du modèle de Hartree-Fock réduit pour des perturbations régulières provenant d'un potentiel extérieur. Notre analyse englobe le cas où le niveau de Fermi de l'état fondamental non-perturbé est une valeur propre dégénérée de l'opérateur de champ moyen et où les orbitales frontières sont partiellement occupées. Le deuxième résultat concerne la construction mathématique de pseudos potentiels pour les modèles Kohn-Sham. Nous définissons l'ensemble des pseudos potentiels semi-locaux à normes conservées de régularité de Sobolev donnée, et nous prouvons que cet ensemble est non-vide et fermé pour une topologie appropriée. Cela nous permet de proposer une nouvelle façon de construire des pseudos potentiels, qui consiste à optimiser sur cet ensemble un critère tenant compte des impératifs de régularité et de transférabilité. Le troisième résultat est une étude numérique du modèle de Hartree-Fock réduit pour les atomes. Nous proposons une méthode de discrétisation et un algorithme de résolution numérique des équations de Kohn-Sham pour un atome soumis à un potentiel extérieur à symétrie cylindrique. Nous calculons les niveaux d'énergie occupés et les nombres d'occupations pour tous les éléments des quatre premières rangées du tableau périodique et considérons le cas d'un atome soumis à un champ électrique uniforme / The contributions of this thesis consist of three main results. The first result is concerned with analytic perturbation theory for Kohn-Sham type models. We prove, under some technical conditions, the existence, uniqueness and analyticity of the perturbed reduced Hartree-Fock ground state density matrix for regular perturbations arising from an external potential. Our analysis encompasses the case when the Fermi level of the unperturbed ground state is a degenerate eigenvalue of the mean-field operator and the frontier orbitals are partially occupied. The second result is concerned with the mathematical construction of pseudo potentials for Kohn-Sham models. We define a set of admissible semi local norm-conserving pseudo potentials of given local Sobolev regularity and prove that this set is non-empty and closed for an appropriate topology. This allows us to propose a new way to construct pseudo potentials, which consists in optimizing on the latter set some criterion taking into account both smoothness and transferability requirements. The third result is a numerical study of the reduced Hartree-Fock model of atoms. We propose a discretization method and an algorithm to solve numerically the Kohn-Sham equations for an atom subjected to a cylindrically-symmetric external potential. We report the computed occupied energy levels and the occupation numbers for all the atoms of the four first rows of the periodic table and consider the case of an atom subjected to a uniform electric-field