The total wind power capacity installed in the world has substantially grown during the last few years, mainly due to the increasing number of horizontal axis wind turbines (HAWT). Consequently, a big effort was employed to increase HAWT\'s power capacity, which is directly associated to the size of blades. Then, novel designs of blades may lead to very fexible structures, susceptive to large deformation, not only during extreme events, but also for operational conditions. In this context, this thesis aims to compare two geometrically nonlinear structural modeling approaches that handle large deformation of blade structures: 3D geometrically-exact beam and shell finite element models. Regarding the beam model, due to geometric complexity of typical cross-sections of wind turbine blades it is adopted a theory that allows creation of arbitrary multicellular cross-sections. Two typical blade geometries are tested, and comparisons between the models are done in statics and dynamics, always inducing large deformation and exploring the accuracy limits of beam models, when compared to shells. Results showed that the beam and shell models present very similar behavior, except when violations occur on the beam formulation hypothesis, such as when shell local buckling phenomena takes place. / A capacidade total de energia eólica instalada no mundo cresceu substancialmente nos últimos anos, principalmente devido ao número crescente de turbinas eólicas de eixo horizontal. Consequentemente, um grande esforço foi empregado com o intuito de aumentar a capacidade de produção das turbinas eólicas, que está diretamente associada ao tamanho das pás. Assim, surgiram projetos inovadores quanto à concepção de pás de turbinas eólicas levando a estruturas bastante flexíveis, susceptíveis a grandes deslocamentos, não apenas em eventos extremos, mas também em condições normais de operação. Nesse contexto, a presente dissertação tem por objetivo comparar duas abordagens de modelos estruturais geometricamente não-lineares capazes de lidar com grandes deslocamentos de pás de turbinas eólicas: elementos finitos geometricamente exatos 3D de vigas e cascas. Em relação ao modelo de viga, devido à complexidade geométrica das seções transversais típicas de pás de turbinas eólicas, adota-se uma teoria que permite a criação de seções transversais arbitrárias multicelulares. Duas geometrias de pás s~ao testadas e comparações entre os modelos s~ao feitas em análises estáticas e dinâmicas, sempre induzindo grandes deslocamentos e explorando os limites de precisão do modelo de viga, quando comparado ao modelo de cascas. Os resultados indicam que os modelos de viga e casca apresentam comportamento muito similar, exceto quando ocorrem violações em hipóteses do modelo de viga, tal como quando ocorre flambagem local do modelo de casca.

The total wind power capacity installed in the world has substantially grown during the last few years, mainly due to the increasing number of horizontal axis wind turbines (HAWT). Consequently, a big effort was employed to increase HAWT\'s power capacity, which is directly associated to the size of blades. Then, novel designs of blades may lead to very fexible structures, susceptive to large deformation, not only during extreme events, but also for operational conditions. In this context, this thesis aims to compare two geometrically nonlinear structural modeling approaches that handle large deformation of blade structures: 3D geometrically-exact beam and shell finite element models. Regarding the beam model, due to geometric complexity of typical cross-sections of wind turbine blades it is adopted a theory that allows creation of arbitrary multicellular cross-sections. Two typical blade geometries are tested, and comparisons between the models are done in statics and dynamics, always inducing large deformation and exploring the accuracy limits of beam models, when compared to shells. Results showed that the beam and shell models present very similar behavior, except when violations occur on the beam formulation hypothesis, such as when shell local buckling phenomena takes place. / A capacidade total de energia eólica instalada no mundo cresceu substancialmente nos últimos anos, principalmente devido ao número crescente de turbinas eólicas de eixo horizontal. Consequentemente, um grande esforço foi empregado com o intuito de aumentar a capacidade de produção das turbinas eólicas, que está diretamente associada ao tamanho das pás. Assim, surgiram projetos inovadores quanto à concepção de pás de turbinas eólicas levando a estruturas bastante flexíveis, susceptíveis a grandes deslocamentos, não apenas em eventos extremos, mas também em condições normais de operação. Nesse contexto, a presente dissertação tem por objetivo comparar duas abordagens de modelos estruturais geometricamente não-lineares capazes de lidar com grandes deslocamentos de pás de turbinas eólicas: elementos finitos geometricamente exatos 3D de vigas e cascas. Em relação ao modelo de viga, devido à complexidade geométrica das seções transversais típicas de pás de turbinas eólicas, adota-se uma teoria que permite a criação de seções transversais arbitrárias multicelulares. Duas geometrias de pás s~ao testadas e comparações entre os modelos s~ao feitas em análises estáticas e dinâmicas, sempre induzindo grandes deslocamentos e explorando os limites de precisão do modelo de viga, quando comparado ao modelo de cascas. Os resultados indicam que os modelos de viga e casca apresentam comportamento muito similar, exceto quando ocorrem violações em hipóteses do modelo de viga, tal como quando ocorre flambagem local do modelo de casca.

This thesis presents a geometrically exact curved beam theory, with the assumption that the cross-section remains rigid, and its finite element formulation/implementation. The theory provides a theoretical view and an exact and efficient means to handle a large range of nonlinear beam problems. A geometrically exact curved/twisted beam theory, which assumes that the beam cross-section remains rigid, is re-examined and extended using orthonormal reference frames starting from a 3-D beam theory. The relevant engineering strain measures at any material point on the current beam cross-section with an initial curvature correction term, which are conjugate to the first Piola-Kirchhoff stresses, are obtained through the deformation gradient tensor of the current beam configuration relative to the initially curved beam configuration. The Green strains and Eulerian strains are explicitly represented in terms of the engineering strain measures while other stresses, such as the Cauchy stresses and second Piola-Kirchhoff stresses, are explicitly represented in terms of the first Piola-Kirchhoff stresses and engineering strains. The stress resultant and couple are defined in the classical sense and the reduced strains are obtained from the three-dimensional beam model, which are the same as obtained from the reduced differential equations of motion. The reduced differential equations of motion are also re-examined for the initially curved/twisted beams. The corresponding equations of motion include additional inertia terms as compared to previous studies. The linear and linearized nonlinear constitutive relations with couplings are considered for the engineering strain and stress conjugate pair at the three-dimensional beam level. The cross-section elasticity constants corresponding to the reduced constitutive relations are obtained with the initial curvature correction term. For the finite element formulation and implementation of the curved beam theory, some basic concepts associated with finite rotations and their parametrizations are first summarized. In terms of a generalized vector-like parametrization of finite rotations under spatial descriptions (i.e., in spatial forms), a unified formulation is given for the virtual work equations that leads to the load residual and tangent stiffness operators. With a proper explanation, the case of the non-vectorial parametrization can be recovered if the incremental rotation is parametrized using the incremental rotation vector. As an example for static problems, taking advantage of the simplicity in formulation and clear classical meanings of rotations and moments, the non-vectorial parametrization is applied to implement a four-noded 3-D curved beam element, in which the compound rotation is represented by the unit quaternion and the incremental rotation is parametrized using the incremental rotation vector. Conventional Lagrangian interpolation functions are adopted to approximate both the reference curve and incremental rotation of the deformed beam. Reduced integration is used to overcome locking problems. The finite element equations are developed for static structural analyses, including deformations, stress resultants/couples, and linearized/nonlinear bifurcation buckling, as well as post-buckling analyses of arches subjected to conservative and non-conservative loads. Several examples are used to test the formulation and the Fortran implementation of the element. / Master of Science

Design optimization is a method that can be used to automate the design process to obtain better results. When applied to aeroelastic structures, design optimization often leads to the creation of highly flexible aeroelastic structures. There are, however, a number of conventional design procedures that must be modified when dealing with highly flexible aeroelastic structures. First, the deformed geometry must be the baseline for weight, structural, and stability analyses. Second, potential couplings between aeroelasticity and rigid-body dynamics must be considered. Third, dynamic analyses must be modified to handle large nonlinear displacements. These modifications to the conventional design process significantly increase the difficulty of developing an optimization framework appropriate for highly flexible aeroelastic structures. As a result, when designing these structures, often either gradient-free optimization is performed (which limits the optimization to relatively few design variables) or optimization is simply omitted from the design process. Both options significantly decrease the design exploration capabilities of a designer compared to a scenario in which gradient-based optimization is used. This dissertation therefore presents various contributions that allow gradient-based optimization to be more easily used to optimize highly flexible aeroelastic structures. One of our primary motivations for developing these capabilities is to accurately capture the design constraints of solar-regenerative high-altitude long-endurance (SR-HALE) aircraft. In this dissertation, we therefore present a SR-HALE aircraft optimization framework which accounts for the peculiarities of structurally flexible aircraft while remaining suitable for use with gradient-based optimization. These aircraft tend to be extremely large and light, which often leads to significant amounts of structural flexibility. Using this optimization framework, we design an aircraft that is capable of flying year-round at \SI{35}{\degree} latitude at \SI{18}{\kilo\meter} above sea level. We subject this aircraft to a number of constraints including energy capture, energy storage, material failure, local buckling, stall, static stability, and dynamic stability constraints. Critically, these constraints were designed to accurately model the actual design requirements of SR-HALE aircraft, rather than to provide a rough approximation of them. To demonstrate the design exploration capabilities of this framework, we also performed several parameters sweeps to determine optimal design sensitivities to altitude, latitude, battery specific energy, solar efficiency, avionics and payload power requirements, and minimum design velocity. Through this optimization framework, we demonstrate both the potential of gradient-based optimization applied to highly flexible aeroelastic structures and the challenges associated with it. One challenge associated with the gradient-based optimization of highly flexible aeroelastic structures, is the ability to accurately, efficiently, and reliably model the large deflections of these structures in gradient-based optimization frameworks. To enable large-scale optimization involving structural models with large deflections to be performed more easily, we present a finite-element implementation of geometrically exact beam theory which is designed specifically for gradient-based optimization. A key feature of this implementation of geometrically exact beam theory is its compatibility with forward and reverse-mode automatic differentiation, which allows accurate design sensitivities to be obtained with minimal development effort. Another key feature is its native support for unsteady adjoint sensitivity analysis, which allows design sensitivities to be obtained efficiently from time-marching simulations. Other features are also presented that build upon previous implementations of geometrically exact beam theory, including a singularity-free rotation parameterization based on Wiener-Milenkovi\'c parameters, an implementation of stiffness-proportional structural damping using a discretized form of the compatibility equations, and a reformulation of the equations of motion for geometrically exact beam theory from a fully implicit index-1 differential algebraic equation to a semi-explicit index-1 differential algebraic equation. Several examples are presented which verify the utility and validity of each of these features. Another challenge associated with the gradient-based optimization of highly flexible aeroelastic structures is the ability to reliably track and constrain individual dynamic stability modes across the design iterations of an optimization framework. To facilitate the development of mode-specific dynamic stability constraints in gradient-based optimization frameworks we develop a mode tracking method that uses an adaptive step size in order to maintain an arbitrarily high degree of confidence in mode correlations. This mode tracking method is then applied to track the modes of a linear two-dimensional aeroelastic system and a nonlinear three-dimensional aeroelastic system as velocity is increased. When used in a gradient-based optimization framework, this mode tracking method has the potential to allow continuous dynamic stability constraints to be constructed without constraint aggregation. It also has the potential to allow the stability and shape of specific modes to be constrained independently. Finally, to facilitate the development and use of highly flexible aeroelastic systems for use in gradient-based optimization frameworks, we introduce a general methodology for coupling aerodynamic and structural models together to form modular monolithic aeroelastic systems. We also propose efficient methods for computing the Jacobians of these coupled systems without significantly increasing the amount of time necessary to construct these systems. For completeness we also discuss how to ensure that the resulting system of equations constitutes a set of first-order index-1 differential algebraic equations. We then derive direct and adjoint sensitivities for these systems which are compatible with automatic differentiation so that derivatives for gradient-based optimization can be obtained with minimal development effort.

A análise das estruturas de aço sujeitas a ações verticais e horizontais, em termos de esforços solicitantes, deslocamentos e rotações, muitas vezes requer a consideração dos efeitos da não linearidade geométrica. Em outras palavras, a interação entre os deslocamentos e os esforços externos pode provocar uma alteração na intensidade dos esforços internos que solicitam a estrutura que, caso não seja adequadamente avaliada, pode conduzir a uma redução significativa dos níveis de segurança. Nesse contexto, destacam-se duas metodologias de avaliação desses efeitos: aquelas baseadas em análises aproximadas e aquelas baseadas em análises geometricamente exatas. As análises aproximadas podem ser caracterizadas em sua grande maioria por desenvolver um estudo baseado no equilíbrio da estrutura na configuração inicial ou indeformada (análise sob linearidade geométrica) e, em seguida, estimar os esforços solicitantes atuantes na configuração final ou deformada por meio de coeficientes majoradores. Por outro lado, a característica principal da análise geometricamente exata é verificar as condições de equilíbrio estrutural na configuração deformada e sem fazer nenhuma restrição quanto à magnitude dos deslocamentos e rotações ou, em outras palavras, observar o comportamento geometricamente exato (não linear) de maneira direta na configuração final de equilíbrio. Este trabalho propõe realizar um estudo comparativo entre um dos métodos de análise aproximada aquele baseado nos coeficientes B1 e B2, que é recomendado pela norma brasileira ABNT NBR 8800:2008 e um método baseado em análise geometricamente exata, de maneira a verificar as semelhanças e as diferenças entre os resultados. O aço é admitido como elástico. As ferramentas computacionais utilizadas são os programas FTOOL e PEFSYS, formulados segundo teorias de barras lineares e não lineares, respectivamente. / The analysis of steel structures subjected to vertical and horizontal loads, regarding internal forces, displacements and rotations, often requires the consideration of geometrically nonlinear effects. In other words, the interaction between displacements and external loads may cause a changing in the intensity of internal forces acting on the structure which, if not correctly evaluated, lead to significant reducing of structural safety. In this context, there exist two main methodologies to evaluate these effects: one based on approximated analysis and another based on geometrically exact analysis. The approximated analysis can be usually characterized by a study based on the equilibrium of the structure at its initial or undeformed configuration (geometrically linear analysis) and, further, by estimating the internal forces acting at the final or deformed configuration by means of amplifier coefficients. On the other hand, the main characteristic of the geometrically exact analysis is to verify the equilibrium conditions directly at the deformed configuration, without any restrictions regarding the magnitude of displacements and rotations or, in other words, observe the geometrically exact (nonlinear) behaviour directly at the final equilibrium configuration. This work purposes to develop a comparative study between one of the approximated methods the one based on the so called B1 and B2 coefficients, recommended by the Brazilian code ABNT NBR 8800:2008 and a method based on geometrically exact analysis, to verify the similarities and differences of results. The computational tools employed are the softwares FTOOL and PEFSYS, based on linear and nonlinear rod theories, respectively.

Este trabalho apresenta uma formulação tensorial genérica para parametrização das rotações do tipo vetorial destinada ao estudo de grandes rotações no espaço tridimensional. Esta formulação é compatível com as parametrizações de Euler e de Rodrigues. É dada ênfase aos que aqui se denominou parâmetros generalizados de Rodrigues, que fornecem expressões simples, computacionalmente mais eficientes que a parametrização clássica de Euler. A formulação apresentada é adequada para uso em métodos numéricos baseados nas projeções de Galerkin, como o método dos elementos finitos, podendo ser implementada com facilidade em programas já existentes de elementos finitos. Apresentam-se aqui expressões para o tensor das rotações e suas derivadas, bem como os tensores necessários à análise incremental. As formas fracas são construídas tanto com projeção ortogonal como não-ortogonal, correspondentes à aplicação do Teorema dos Trabalhos Virtuais e Teorema das Potências Virtuais, respectivamente. Os modelos propostos foram aplicados em um programa de elementos finitos utilizando formulações cinemáticas Lagrangiana total e Lagrangiana atualizada e foram resolvidos vários exemplos, dentre eles alguns clássicos da literatura, de forma a avaliar sua validade e aplicação. / This work presents a generic formulation of vector-type for the parameterization of large rotations in three-dimensional space. This formulation adapts to the Euler and the Rodrigues parameterization. Special distinction is made to the here named generalized Rodrigues parameters which result in very simple and computationally efficient expressions. The attained formulation is convenient for numerical procedures employing Galerkin projection like the finite element method and can be readily implemented in a FE code. The expressions of rotation tensor and its derivatives, which lead to a consistent linearization, are herein derived. The necessary tensor quantities employed in the derivation of the tangent bilinear weak form of incremental analysis are obtained too. The weak forms are constructed here with both orthogonal and non-orthogonal projections, corresponding to the application of the virtual work theorem or virtual power theorem respectively. The formulation is implemented within a finite element code in total Lagrangian and updated Lagrangian framework and assessment of the scheme is made by means of several numerical simulations.

Este trabalho apresenta uma formulação tensorial genérica para parametrização das rotações do tipo vetorial destinada ao estudo de grandes rotações no espaço tridimensional. Esta formulação é compatível com as parametrizações de Euler e de Rodrigues. É dada ênfase aos que aqui se denominou parâmetros generalizados de Rodrigues, que fornecem expressões simples, computacionalmente mais eficientes que a parametrização clássica de Euler. A formulação apresentada é adequada para uso em métodos numéricos baseados nas projeções de Galerkin, como o método dos elementos finitos, podendo ser implementada com facilidade em programas já existentes de elementos finitos. Apresentam-se aqui expressões para o tensor das rotações e suas derivadas, bem como os tensores necessários à análise incremental. As formas fracas são construídas tanto com projeção ortogonal como não-ortogonal, correspondentes à aplicação do Teorema dos Trabalhos Virtuais e Teorema das Potências Virtuais, respectivamente. Os modelos propostos foram aplicados em um programa de elementos finitos utilizando formulações cinemáticas Lagrangiana total e Lagrangiana atualizada e foram resolvidos vários exemplos, dentre eles alguns clássicos da literatura, de forma a avaliar sua validade e aplicação. / This work presents a generic formulation of vector-type for the parameterization of large rotations in three-dimensional space. This formulation adapts to the Euler and the Rodrigues parameterization. Special distinction is made to the here named generalized Rodrigues parameters which result in very simple and computationally efficient expressions. The attained formulation is convenient for numerical procedures employing Galerkin projection like the finite element method and can be readily implemented in a FE code. The expressions of rotation tensor and its derivatives, which lead to a consistent linearization, are herein derived. The necessary tensor quantities employed in the derivation of the tangent bilinear weak form of incremental analysis are obtained too. The weak forms are constructed here with both orthogonal and non-orthogonal projections, corresponding to the application of the virtual work theorem or virtual power theorem respectively. The formulation is implemented within a finite element code in total Lagrangian and updated Lagrangian framework and assessment of the scheme is made by means of several numerical simulations.

A análise das estruturas de aço sujeitas a ações verticais e horizontais, em termos de esforços solicitantes, deslocamentos e rotações, muitas vezes requer a consideração dos efeitos da não linearidade geométrica. Em outras palavras, a interação entre os deslocamentos e os esforços externos pode provocar uma alteração na intensidade dos esforços internos que solicitam a estrutura que, caso não seja adequadamente avaliada, pode conduzir a uma redução significativa dos níveis de segurança. Nesse contexto, destacam-se duas metodologias de avaliação desses efeitos: aquelas baseadas em análises aproximadas e aquelas baseadas em análises geometricamente exatas. As análises aproximadas podem ser caracterizadas em sua grande maioria por desenvolver um estudo baseado no equilíbrio da estrutura na configuração inicial ou indeformada (análise sob linearidade geométrica) e, em seguida, estimar os esforços solicitantes atuantes na configuração final ou deformada por meio de coeficientes majoradores. Por outro lado, a característica principal da análise geometricamente exata é verificar as condições de equilíbrio estrutural na configuração deformada e sem fazer nenhuma restrição quanto à magnitude dos deslocamentos e rotações ou, em outras palavras, observar o comportamento geometricamente exato (não linear) de maneira direta na configuração final de equilíbrio. Este trabalho propõe realizar um estudo comparativo entre um dos métodos de análise aproximada aquele baseado nos coeficientes B1 e B2, que é recomendado pela norma brasileira ABNT NBR 8800:2008 e um método baseado em análise geometricamente exata, de maneira a verificar as semelhanças e as diferenças entre os resultados. O aço é admitido como elástico. As ferramentas computacionais utilizadas são os programas FTOOL e PEFSYS, formulados segundo teorias de barras lineares e não lineares, respectivamente. / The analysis of steel structures subjected to vertical and horizontal loads, regarding internal forces, displacements and rotations, often requires the consideration of geometrically nonlinear effects. In other words, the interaction between displacements and external loads may cause a changing in the intensity of internal forces acting on the structure which, if not correctly evaluated, lead to significant reducing of structural safety. In this context, there exist two main methodologies to evaluate these effects: one based on approximated analysis and another based on geometrically exact analysis. The approximated analysis can be usually characterized by a study based on the equilibrium of the structure at its initial or undeformed configuration (geometrically linear analysis) and, further, by estimating the internal forces acting at the final or deformed configuration by means of amplifier coefficients. On the other hand, the main characteristic of the geometrically exact analysis is to verify the equilibrium conditions directly at the deformed configuration, without any restrictions regarding the magnitude of displacements and rotations or, in other words, observe the geometrically exact (nonlinear) behaviour directly at the final equilibrium configuration. This work purposes to develop a comparative study between one of the approximated methods the one based on the so called B1 and B2 coefficients, recommended by the Brazilian code ABNT NBR 8800:2008 and a method based on geometrically exact analysis, to verify the similarities and differences of results. The computational tools employed are the softwares FTOOL and PEFSYS, based on linear and nonlinear rod theories, respectively.

Cette thèse traite de l'analyse limite des structures de châssis en acier, qui s'utilise souvent comme la structure principale de support des bâtiments. La structure du cadre en acier est caractérisée par une réponse très ductile et un grand potentiel pour dissiper l'énergie, ce qui est crucial pour la résistance par rapport aux tremblements de terre. La ductilité dans la réponse de la structure est la cause du comportement du matériau lui-même et du comportement des connexions entre les éléments de la structure. Les connexions entre les poutres et les poteaux peuvent influencer de manière significative la réponse de la structure du cadre en acier, parfois jusqu'à 30%. L'idée est de intégrer le comportement des connexions par les éléments de poutres qui seront situés dans les coins du cadre et la modélisation du reste serra fait avec des éléments de poutres non-linéaires qui décrirons le comportement des poutres en acier. Cette recherche est composée de deux parties. La première partie est consacrée au comportement des connexions structurelles, la deuxième partie présente le développement de l'élément fini du faisceau non linéaire capable de représenter le comportement ductile d'un élément de la structure en acier. Dans la première partie de la thèse, nous définissons la procédure d'identification des paramètres constitutifs pour le modèle couplé de plasticité-dégâts avec dix-huit inconnus. Ce modèle constitutif est très robuste et capable de représenter une large gamme de problèmes. La procédure définie a été utilisée dans la préparation de tests expérimentaux pour trois types de connexions en acier structuré. Les tests expérimentaux ont été effectués pour deux cas de charge. Pour la première, la charge a été appliquée dans un sens avec les cycles de chargement et de déchargement. À partir des mesures expérimentales, nous avons conclu que le modèle de plasticité peut bien représentée le comportement de la connexion structurale. Paramètres constitutifs ont été déterminés à partir des résultats de l'expérimentation, on a utilisé une poutre géométriquement exacte avec la loi bilinéaires renforcement du matériel et la loi linéaire pour le ramollissement. Également, on a effectué des essais expérimentaux de deux types de raccords en acier en cas de chargement cyclique. Les données mesurées montrent que le modèle de la plasticité n'est pas assez bon pour décrire le comportement de connexion pour ce type de charge. A savoir, en raison de changements du sens de l'application du chargement, les connexions montrent moins de rigidité, qui peut être décrite avec un modèle constitutif de dommages. Pour cette raison, nous avons développé un nouveau modèle plasticité-dommages qui est capable d'inclure le phénomène mentionné ci-dessus. A la fin de cette section est faite l'identification des paramètres constitutifs. La deuxième partie de la thèse de doctorat est composé de formulations théoriques et la mise en œuvre numérique des faisceaux géométriquement exacte. La réponse de durcissement de la poutre comprend l'interaction entre les forces de la section résultant du stress (N, T et M), et la réponse de ramollissement est définit par la loi non linéaire. Ce type d'élément fini de poutre est capable de décrire le comportement ductile des structures en acier et inclure les effets du second ordre, qui sont très importantes pour l'analyse ultime des structures de cadre en acier. L'élément fini développé de poutre géométriquement exacte et les lois définies de liaison de comportement dans la construction en acier, offrant la possibilité d'une analyse de haute qualité des structures en acier. En utilisant les modèles de poutre proposé et la méthodologie de modélisation des structures de châssis en acier, il est possible de déterminer une distribution réaliste des forces de section transversale , y compris la redistribution due à la formation de rotules plastiques. / This thesis deals with the ultimate load limit analysis of steel frame structures. The steel frame structure has a very ductile response and a large potential to dissipate energy, which is crucial in the case of earthquakes. The ductility in the response of the structure comes from the behavior of the material itself and the behavior of the semi-rigid structural connections. The semi-rigid connections between beams and columns can significantly influence the response of the structure, sometimes up to 30%. In this thesis, we propose a methodology for modeling steel frame structures with included connection behavior. The idea is to model the behavior of the structural connections by the beam elements positioned in the corners of the steel frame structure. Other members of the steel frame structure, steel beams, and columns, will be modeled with nonlinear beam elements. This research consists of two parts. The first part deals with the behavior of the structural steel connections. In the second part, we present the development of the nonlinear beam element capable of representing the ductile behavior of steel structural elements, beams and columns. In the first part of the thesis, we define constitutive parameters identification procedure for the coupled plasticity-damage model with eighteen unknowns. This constitutive model is very robust and capable of representing a wide range of problems. The identification procedure was used in the preparation of experimental tests for three different types of structural steel connections. The experimental tests have been performed for two load cases. In the first, the load was applied in one direction with both the loading and unloading cycles. From the experimental measurements, we have concluded that the response of the experimental structure can be represented by the plasticity model only because no significant change in the elastic response throughout the loading program was observed. Therefore, we have chosen an elastoplastic geometrically exact beam to describe connection behavior. The hardening response of the beam is governed by bilinear law, and the softening response is governed by nonlinear exponential law. The identification of the parameters has been successfully done with fifteen unknown parameters identified. The two types of the experimental structures were also exposed to the cyclic loading. Measured experimental data shows complex connection behavior that cannot be described by the plasticity model alone. Namely, after changing load direction stiffness of the connection decreases. This suggests that the damage model should be incorporated in the constitutive law for the connections behavior as well. Therefore, we propose a new coupled plasticity-damage model capable of representing the loss in the stiffness of the connection with the changing of the load direction. At the end of this part, we also give the constitutive parameters identification for the proposed model. The second part of the thesis deals with the theoretical formulation and numerical implementation of the elastoplastic geometrically exact beam. The hardening response of the beam includes interaction between stress resultant section forces (N, T and M), and the softening response of the beam, which is governed by the nonlinear law. This type of the beam element is capable of representing the ductile behavior of a steel frame structure, and it takes into account second order theory effects. Performed numerical simulations show that the proposed geometrically nonlinear beam element is very robust and is able to provide a more precise limit load analysis of steel frame structures. By using proposed methodology for modeling steel structures, we are able to obtain the real distribution of section forces, including their redistribution caused by forming of the hinges and the connections behavior.

Dans la première partie de la thèse, les schémas d’intégration conservatifs sont appliqués aux poutres co-rotationnelles 2D. Les cinématiques d'Euler-Bernoulli et de Timoshenko sont abordées. Ces formulations produisent des expressions de l'énergie interne et l'énergie cinétique complexe et fortement non-linéaires. L’idée centrale de l’algorithme consiste à définir, par intégration, le champ des déformations en fin de pas à partir du champ de vitesses de déformations et non à partir du champ des déplacements au travers de la relation déplacement-déformation. La même technique est appliquée aux termes d’inerties. Ensuite, une poutre co-rotationnelle plane avec rotules généralisées élasto-(visco)-plastiques aux extrémités est développée et comparée au modèle fibre avec le même comportement pour des problèmes d'impact. Des exemples numériques montrent que les effets de la vitesse de déformation influencent sensiblement la réponse de la structure. Dans la seconde partie de cette thèse, une théorie de poutre spatiale d’Euler-Bernoulli géométriquement exacte est développée. Le principal défi dans la construction d’une telle théorie réside dans le fait qu’il n’existe aucun moyen naturel de définir un trièdre orthonormé dans la configuration déformée. Une nouvelle méthodologie permettant de définir ce trièdre et par conséquent de développer une théorie de poutre spatiale en incorporant l'hypothèse d'Euler- Bernoulli est fournie. Cette approche utilise le processus d'orthogonalisation de Gram-Schmidt couplé avec un paramètre rotation qui complète la description cinématique et décrit la rotation associée à la torsion. Ce processus permet de surmonter le caractère non-unique de la procédure de Gram-Schmidt. La formulation est étendue au cas dynamique et un schéma intégration temporelle conservant l'énergie est également développé. De nombreux exemples démontrent l’efficacité de cette formulation. / In the first part of the thesis, energymomentum conserving algorithms are designed for planar co-rotational beams. Both Euler-Bernoulli and Timoshenko kinematics are addressed. These formulations provide us with highly complex nonlinear expressions for the internal energy as well as for the kinetic energy which involve second derivatives of the displacement field. The main idea of the algorithm is to circumvent the complexities of the geometric non-linearities by resorting to strain velocities to provide, by means of integration, the expressions for the strain measures themselves. Similarly, the same strategy is applied to the highly nonlinear inertia terms. Next, 2D elasto-(visco)-plastic fiber co-rotational beams element and a planar co-rotational beam with generalized elasto-(visco)-plastic hinges at beam ends have been developed and compared against each other for impact problems. In the second part of this thesis, a geometrically exact 3D Euler-Bernoulli beam theory is developed.The main challenge in defining a three-dimensional Euler-Bernoulli beam theory lies in the fact that there is no natural way of defining a base system at the deformed configuration. A novel methodology to do so leading to the development of a spatial rod formulation which incorporates the Euler-Bernoulli assumption is provided. The approach makes use of Gram-Schmidt orthogonalisation process coupled to a one-parametric rotation to complete the description of the torsional cross sectional rotation and overcomes the non-uniqueness of the Gram-Schmidt procedure. Furthermore, the formulation is extended to the dynamical case and a stable, energy conserving time-stepping algorithm is developed as well. Many examples confirm the power of the formulation and the integration method presented.