Solid rocket motors consist of a thin metallic or composite shell filled with a soft rubbery propellant. Such motors are vulnerable and prone to buckling due to sudden external pressures produced by nearby detonation. The stability conditions of rocket motors subjected toaxisymmetric, external pressure loading are examined. The outer cases of motors are considered as isotropic (metallic) or anisotropic (composite), thin and high-strength shells, which are the main structures of interest in the stability analyses. The inner, low-strength elastic cores are modeled as linear and nonlinear elastic foundations. A general, refined, Sanders' nonlinear shell theory, which accounts for geometric nonlinearity in the form of von Karman type of nonlinear strain-displacement relations, is used to model thin-walled, laminated,composite cylindrical shells. The first order shear deformable concept is adopted in the analyses to include the transverse shear flexibility of composites. A winkler-type of linear and nonlinear elastic foundation is applied to model the internal foundations. Pasternak-foundation constants are also chosen tomodify the proposed elastic foundation model for the purpose of shear interactions. A set of displacement-based finite element codes have been formulated to determine critical buckling loads and mode shapes. The effect of initial imperfections on the structural responses are also incorporated in the formulations. A variety of numerical examples are investigated to demonstrate the validity and efficiency of the purposed theory under various boundary condiitions and loading cases. First, linear eigenvalue analysis is used to examine approximate buckling loads and buckling modes as well as symmetric conditions. An iterative solution procedure, either Newton-Raphson or Riks-Wempner method is employed to trace the nonlinear equilibrium paths for the cases of stress, buckling and post-buckling analyses. Both ring and shell-type models are applied for the structural analyses with different internal elastic foundations and initial imperfections. / Ph. D.

Neste trabalho desenvolve-se uma formulação teórica consistente para a análise não-linear, física e geométrica, de pórticos planos de aço, através do Método dos Elementos Finitos (MEF), considerando barras com imperfeições iniciais e tensões residuais nas suas seções transversais, visando analisar os critérios de resistência adotados para projeto das colunas de aço, baseados no conceito de resistência-última, e estudar o comportamento não-linear dos pórticos de aço considerando estes dois fatores. São feitas considerações qualitativas sobre a influência das imperfeições iniciais e das tensões residuais no cálculo da resistência das colunas. e é dada uma visão geral sobre a evolução dos critérios usados na prática para dimensionamento das colunas de aço. Apresenta-se o desenvolvimento da teoria geral, que leva em conta a presença das tensões residuais auto-equilibradas nas equações de equilíbrio do elemento. Este desenvolvimento é feito dentro de uma formulação Lagrangiana utilizando a técnica corrotacional para a dedução consistente da matriz de rigidez tangente do elemento de pórtico plano com imperfeição inicial. Para implementação desta formulação é desenvolvido um programa em linguagem FORTRAN para micro-computador capaz de fazer a análise não-linear elasto-plástica de pórticos planos, baseado num processo incremental-iterativo. Utiliza-se o modelo de fatias para avaliar os coeficientes de rigidez do elemento, modelo este que se mostrou bastante adequado, permitindo o acompanhamento da plastificação ao longo da altura da seção e a consideração de qualquer modelo de distribuição das tensões residuais. Finalmente, os exemplos apresentados mostram a grande potencialidade da formulação desenvolvida. São analisados vários casos cujos resultados são comparados com os obtidos por outros autores, demonstrando a precisão e correção da teoria proposta. A aplicação na análise de pórticos de andares múltiplos confirma a validade da formulação e demonstra a sua aplicabilidade nos casos práticos. / A consistent finite element formulation to consider material and geometric nonlinearities of steel plane frames is presented. Residual stresses and initial imperfections are considered to evaluate steel columns failure criteria based on the ultimate strength and also to investigate the nonlinear behavior of steel plane frames. Some qualitative considerations are made on the initial imperfections and residual stresses influence on the practical steel columns design. A general theory considering self equilibrated residual stresses is developed based on the Lagrangian formulation. Corotacional technique is used to obtain the tangent stiffness matrix of plane frame taking the initial imperfection into account. A stand alone code has been written in FORTRAN and implemented on a microcomputer platform to perform incremental-iterative analysis of nonlinear elastoplastic plane frame problems. The frame element is made up of layers such that the plastic region can be readily identified and any kind of residual stresses through the cross section area can be taken into account in the analysis. Some examples are presented and their results compared to others in the literature. The multistory building analyses using the plane frame element presented in this research has shown to be very effective and useful to practical applications.

Neste trabalho desenvolve-se uma formulação teórica consistente para a análise não-linear, física e geométrica, de pórticos planos de aço, através do Método dos Elementos Finitos (MEF), considerando barras com imperfeições iniciais e tensões residuais nas suas seções transversais, visando analisar os critérios de resistência adotados para projeto das colunas de aço, baseados no conceito de resistência-última, e estudar o comportamento não-linear dos pórticos de aço considerando estes dois fatores. São feitas considerações qualitativas sobre a influência das imperfeições iniciais e das tensões residuais no cálculo da resistência das colunas. e é dada uma visão geral sobre a evolução dos critérios usados na prática para dimensionamento das colunas de aço. Apresenta-se o desenvolvimento da teoria geral, que leva em conta a presença das tensões residuais auto-equilibradas nas equações de equilíbrio do elemento. Este desenvolvimento é feito dentro de uma formulação Lagrangiana utilizando a técnica corrotacional para a dedução consistente da matriz de rigidez tangente do elemento de pórtico plano com imperfeição inicial. Para implementação desta formulação é desenvolvido um programa em linguagem FORTRAN para micro-computador capaz de fazer a análise não-linear elasto-plástica de pórticos planos, baseado num processo incremental-iterativo. Utiliza-se o modelo de fatias para avaliar os coeficientes de rigidez do elemento, modelo este que se mostrou bastante adequado, permitindo o acompanhamento da plastificação ao longo da altura da seção e a consideração de qualquer modelo de distribuição das tensões residuais. Finalmente, os exemplos apresentados mostram a grande potencialidade da formulação desenvolvida. São analisados vários casos cujos resultados são comparados com os obtidos por outros autores, demonstrando a precisão e correção da teoria proposta. A aplicação na análise de pórticos de andares múltiplos confirma a validade da formulação e demonstra a sua aplicabilidade nos casos práticos. / A consistent finite element formulation to consider material and geometric nonlinearities of steel plane frames is presented. Residual stresses and initial imperfections are considered to evaluate steel columns failure criteria based on the ultimate strength and also to investigate the nonlinear behavior of steel plane frames. Some qualitative considerations are made on the initial imperfections and residual stresses influence on the practical steel columns design. A general theory considering self equilibrated residual stresses is developed based on the Lagrangian formulation. Corotacional technique is used to obtain the tangent stiffness matrix of plane frame taking the initial imperfection into account. A stand alone code has been written in FORTRAN and implemented on a microcomputer platform to perform incremental-iterative analysis of nonlinear elastoplastic plane frame problems. The frame element is made up of layers such that the plastic region can be readily identified and any kind of residual stresses through the cross section area can be taken into account in the analysis. Some examples are presented and their results compared to others in the literature. The multistory building analyses using the plane frame element presented in this research has shown to be very effective and useful to practical applications.

Cette thèse s’inscrit dans une démarche d’amélioration des connaissances des instabilités des éléments comprimés et fléchis sensibles aux effets du second ordre. Il s’agit de traiter la prise en compte des imperfections initiales dans l’analyse de la structure et d’adapter les critères actuels de vérification pour les structures tubulaires de type échafaudage. Les formulations existantes, proposées dans la littérature et les codes de calculs, sont souvent issues d’hypothèses, et conduisent à des incohérences entre les critères de vérification en section, et les critères de vérification en instabilité. L’approche développée traite l’interaction entre la résistance en section et les phénomènes d’instabilités, et inclut l’influence des imperfections initiales. Ces effets seront, dans la mesure du possible, découplés. À ce titre, une méthode a été conçue pour permettre la définition des imperfections initiales d’une structure, de manière à être la plus précise possible. Cette méthode, basée sur la définition d’une imperfection unique, d’allure identique à la déformée critique du mode de flambement prépondérant, est une méthode précise, entièrement définie permettant de tenir compte des caractéristiques géométriques, des caractéristiques mécaniques intrinsèques, des conditions aux limites et de la forme du chargement, dans la définition de l’imperfection initiale unique d’une structure. Une campagne d’essai a été réalisée en collaboration avec le SFECE, visant à analyser le comportement expérimental au flambement de sections tubulaires formées à froid. Des essais de flambement sur des échelles d’échafaudage, provenant de divers fournisseurs européens, ont été effectués. Une étude statistique des résultats expérimentaux a permis de mettre en évidence que le facteur d’imperfection actuellement défini pour les sections tubulaires formées à froid est bien trop pénalisant à l’égard des sections usitées dans le domaine des échafaudages. Afin de répondre à la problématique, de nouveaux critères de vérification en instabilité ont également été établis en utilisant une approche similaire à celle d’Ayrton-Perry. Ces nouveaux critères permettent de s’affranchir de la modélisation des imperfections initiales tout en offrant une estimation sûre et précise du facteur de sollicitation d’une structure. Des études comparatives ont été menées de manière à s’assurer de la sécurité des formulations proposées par rapport aux critères de vérification en section de la norme actuelle. / This thesis is part of an effort to improve knowledge of the instabilities of beam-columns sensitive to second-order effects. The works deal with the means to take into account the initial imperfections in the structural analysis and to adapt the current verification criteria for tubular section structures, such as scaffold structures. The existing formulations, proposed in the literature and calculation codes, are often based on hypotheses, and thus lead to inconsistencies between, on the one hand, the verification criteria in section, and on the other hand, the verification criteria in instability. The developed approach takes into account the interaction between section resistance and instability phenomena, and includes the influence of initial imperfections (initial defect of aplomb, lack of straightness, residual stresses). As far as possible, these effects will be decoupled. As such, a method has been developed to allow the definition of initial imperfections of a structure, to be as accurate as possible. This method, based on the definition of a single imperfection, identical in appearance to the shape of the predominant critical buckling mode, is a precise, fully defined method to take into account the geometric characteristics, intrinsic mechanical characteristics, limits and the form of loading, in the definition of the initial imperfections of a structure. A test campaign was carried out in collaboration with the French Syndicate of Scaffolding, Formwork and Shoring (SFECE), aiming to analyze the experimental behavior of buckling of cold-formed tubular sections. Nine buckling tests on scaffold ladders, from various European suppliers, have been carried out. A statistical study of the experimental results has made it possible to highlight that the imperfection factor currently defined for the cold-formed tubular sections is far too penalizing for the sections used in the field of scaffolds. In order to respond to the problem, new instability criteria have also been established using a similar approach to that of Ayrton-Perry. These new criteria make it possible to free ourselves from the modeling of initial imperfections while offering a safe and accurate estimate of the stress factor of a structure. A comparative study was conducted in order to ensure the safety of the proposed formulations as regards the section verification criteria of the NF EN 1993-1-1 current standard.