[pt] As estruturas ajustáveis ou dobráveis (deployable structures) consistem em um grupo de estruturas capazes de modificar sua forma e volume para atender a uma variedade de aplicações. Geralmente, são estruturas pré-fabricadas compostas por barras retas ou curvas unidas por meio de articulações que permitem que se movimentem para formar um arranjo compacto e se desdobrem em formas estruturais de grande porte. Essas estruturas atuam como mecanismos durante sua implantação e se tornam estruturas capazes de suportar cargas externas durante a fase de serviço. Além disso, elas devem ser leves e compactas a fim de serem facilmente transportadas e simples e rápidas de montar. Todas essas restrições dificultam a escolha dos melhores parâmetros que levem ao menor peso, maior rigidez e que permitam à estrutura desempenhar suas duas funcionalidades e garantir sua reutilização. Entre os tipos de estruturas dobráveis, os elementos pantográficos (tesouras) têm despertado grande interesse de engenheiros e arquitetos nos últimos anos. Este estudo avalia o comportamento não linear geométrico de arcos planos constituídos por dois tipos clássicos de elementos pantográficos: polar e translacional. Para isso, uma análise geométrica não linear detalhada é conduzida por meio de software de elemento finito elaborado com formulação corrotacional, a fim de avaliar a influência dos parâmetros geométricos da estrutura, como o tipo de elemento patográfico, o tipo de apoio e número de elementos no comportamento não linear e na estabilidade da estrutura. Os resultados obtidos por nossas análises revelam, na maioria dos casos, um comportamento eminentemente não linear característico de arcos esbeltos, com o caminho de equilíbrio exibindo vários pontos limites de carga e deslocamento, onde podem ocorrer saltos para configurações remotas e indesejáveis. Com base nestes resultadods, a influência dos parâmetros do sistema na capacidade de carga do arco é quantificada. / [en] Deployable structures consist of a group of structures capable of modifying their shape and volume in order to meet a range of conditions and needs. They are usually prefabricated structures consisting of straight or curved bars linked together in a compact bundle, which can then be unfolded into large-span, load bearing structural shapes. These structures have dual functionality since they act as mechanisms during its deployment and become immovable structures capable of supporting external loads during the service phase. In addition, they should be lightweight and compact to be easily transported and simple and quick to deploy. All these restrictions make it difficult to choose the best parameters regarding the shape and material of the structure, since many analyzes must be performed in order to find parameters that give lowest weight, highest stiffness, and that allow the structure to perform its two functions and ensure its reuse. Among the types of folding structure, those made of pantographic elements (scissors) have attracted great interest from engineers and architects in recent years. This study evaluates the geometric nonlinear behavior of plane arches constituted by two classic type of pantographic element, namely: polar and translational. For this, a detailed nonlinear geometrical analysis is conducted through tailored corotational finite element software in order to evaluate the influence of the structure s geometrical parameters, type of scissor units and supports on the nonlinear behavior and stability of the structure. The results obtained by our analyzes reveal, in most cases, a characteristic non-linear behavior of these structures with the nonlinear equilibrium path exhibiting several load and displacement limit points where jumps to remote and undesirable configurations may occur. Based on them, the influence of system parameters on the load carrying capacity of the arch is quantified.

This thesis presents the results of basically two separate studies. The first study involved identifying structural and earthquake parameters that influenced seismic structural collapse. The parameter study involved nonlinear dynamic analyses using single-degree-of-freedom (SDOF) bilinear models. Four parameters were associated with the SDOF models — the lateral stiffness, the post-yield stiffness ratio, the yield strength, and the stability ratio (P-Delta effects). Then, three parameters were associated with the ground motions — the records themselves, the lateral ground motion scales, and the vertical ground motion scales. From the parameter study, it was found that the post-yield stiffness ratio augmented by P-Delta effects (rp) in conjunction with the ductility demand was the best predictor of collapse. These two quantities include all four structural parameters and the seismic displacement demands. It was also discovered in the parameter study that vertical accelerations did not significantly influence lateral displacements unless a given combination of model and earthquake parameters was altered such that the model was on the verge of collapsing. The second study involved Incremental Dynamic Analysis (IDA) using bilinear SDOF models representative of low rise buildings in both the Western United States (WUS) and the Central and Eastern United States (CEUS). Models were created that represented three, five, seven, and nine story buildings. Five sites from both the WUS and CEUS were used. Four different damage measures were used to assess the performance of the buildings. The IDA study was primarily interested in the response of the structures between the earthquake intensities that have a 10 percent probability of occurring in 50 years (10/50) and 2 percent probability of occurring in 50 years (2/50). The results showed that all structures could be in danger of severe damage and possible collapse, depending on which damage measure and which earthquake was used. It is important to note, though, that the aforementioned is based on a damage-based collapse rule. The damage-based rule results were highly variable. Using an intensity-based collapse rule, proved to be more consistent. Due to the nature of the bilinear models, only those structures with negative rp values ever collapsed using an intensity-based collapse rule. Most of the WUS models had positive rp values and many of the CEUS models had negative rp values. While many of the CEUS structures had negative rp values, which made them prone to collapse, most of the CEUS structures analyzed did not collapse at the 2/50 intensity. The reason was that the periods of the CEUS models were much longer than the approximate periods that were required to determine the strengths. Consequently, the strength capacity of most of the CEUS models was much greater than the seismic strength demands. While many of the CEUS models did have sudden collapses due to the large negative rp values, the collapses happened at intensities that were generally much higher than the 2/50 event. In the IDA, it was also shown that vertical accelerations can significantly affect the ductility demands of a model with a negative rp post-yield stiffness ratio as the earthquake intensity approaches the collapse intensity. Since IDA is concerned with establishing collapse limit states, it seems that the most accurate collapse assessments would include vertical accelerations. / Master of Science

This study investigates the tensile behavior of anchor pull-out tests from super early age concrete(less than 12h) by finite element(FE) software ANSYS Workbench. In previous experiment, several series of pull-out tests were finished and analyzed. In each per hour, different speeds(1mm/s, 0.2mm/s, 0.1mm/s and 0.833mm/s) were evaluated, getting the results about correlation of pull-out force and displacement(F-D curve). It is difficult to evaluate the specific development of tensile strength in super young concrete, due to the super plasticity that makes itself soft and unstable. The first step of this study is to collect relevant empirical formula, theoretical varying material properties with time and pull-out force of experimental applied anchors. Comparison of simulation analysis results and empirical formulas determines whether the establishment of the finite element model and adapted constitutive model of known natural hardened concrete(NHC) are valid or not. The second procedure is that the material properties of NHC are replaced by different age values and modified until getting the same simulation results as experiment outcome. The propose of this paper is to investigate a more accurate modified formula to describe the development of tensile behavior in super early age concrete:1. Introduction 2. Background 2.1 Modes of failure 2.2 A new failure mode 2.3 Finite Element Numerical Simulation 3. Research Questions 4. Aims/Objectives of the Research 5. Proposed Research Method 5.1 Previous Empirical theory 5.1.1 Cubic Compressive strength of Early Age Concrete 5.1.2 Tensile Strength of Early Age Concrete 5.1.3 Modulus of Elasticity in Early Age Concrete 5.1.4 Prediction of pull-out maximum force to headed studs from concrete 5.2 Pervious Experiment 5.3 Numerical Simulation 6. Significance/Contribution to the Discipline 7. Experiment Program 7.1 Experiment Setup 7.2 Experiment Result 8. Numerical simulation and analysis 8.1 Material Properties 8.2 Modelling Setup 8.3 The first pull-out test 8.4 Comparison Results at different stages 9. Discussion and Results 10. Summary and Conclusion 11. Recommendation for future studies 12. References 13. Appendix

[pt] Gridshells são estruturas leves que combinam eficiência e arquiteturas atraentes. Devido ao fato de a transmissão de esforços ocorrer majoritariamente por compressão, esse tipo de estrutura é suscetível a flambagem. Este estudo buscou avaliar como determinados fatores influenciam na instabilidade desse tipo de estruturas e, assim, estabelecer pontos de referência para o desenvolvimento de projetos. Foi realizado um estudo paramétrico de gridshells de malha quadrangular reforçados por cabos a partir de simulação numérica, em que foi investigado o efeito da presença de cabos, o efeito do nível de protensão e efeito de imperfeições iniciais. Os resultados mostraram um benefício geral com o reforço de cabos, aumentando de maneira considerável a carga de flambagem da estrutura, além de proporcionar um aumento nas frequências naturais do sistema. Contudo, os resultados mostraram uma redução significativa na resistência a flambagem, bem como uma alteração nas frequências naturais com a presença de imperfeições. Desse modo foi possível concluir que gridshells são estruturas altamente não lineares e sensíveis a imperfeições, tanto no aspecto dinâmico como estático. / [en] Gridshells are lightweight structures that combine efficiency and attractive architecture. Due to the fact that the load is mainly carried by compression, this type of structure is susceptible to buckling, thus the stability check is essential. This study investigated how certain factors influence the stability of this type of structure and targeted reference points for the designers. A parametric study was conducted through numerical simulations, in which it was investigated the effect of the presence of a cable net, the level of prestress on the cables and the effect of initial imperfections. The results showed a benefit from the adoption of the cable net as a reinforcement, increasing considerably the buckling load, as well as the natural frequencies of the system. However, a significant reduction of the buckling load and a change in the natural frequencies with the presence of the imperfection were observed. Thus, it was concluded that gridshells are highly nonlinear structures and sensitive to imperfections, so much in the static aspect as dynamically.

The use of fully grouted reinforced masonry shear walls (RMSWs) has been growing in several areas around the world owing to their relative ease of construction and their in-plane ductile behavior. However, RMSWs possess low out-of-plane ductility which amplifies the vulnerability of such components under blast loading. Furthermore, the long time and high costs of recovery following devastating (deliberate or accidental) explosions have created a need for resilience-based design for risk mitigation, especially considering the different sources of associated uncertainty. As such, this study aims to lay out the foundations of a probabilistic resilience–based blast analysis and design framework. The framework should have the capability of quantifying the overall building post-blast functionality in order to estimate its recovery cost and time, and thus the building resilience following such a demand. The proposed framework will be specifically applied for RMSW buildings incurring blast loads through a profound investigation for the behavior of rectangular RMSWs as being a primary structural element in reinforced masonry buildings. The investigation will subsume an experimental and analytical evaluation for the performance of load-bearing RMSWs with different in-plane ductility levels subjected to out-of-plane quasi-static loading. This will be followed by a numerical investigation of RMSWs to conclude the blast probabilistic performance of RMSWs that can be applied within the proposed probabilistic resilience-based blast framework. The work in this dissertation presents a key step towards adopting resilience based analysis and design in future editions of blast-resistant construction standards and provides the decisionmakers with a complete insight into post-blast building functionality and its recovery. / Thesis / Doctor of Philosophy (PhD)

Une nouvelle notion d'enlacement pour les paires d'ensembles $A\subset B$, $P\subset Q$ dans un espace de Hilbert de type $X=Y\oplus Y^{\perp}$ avec $Y$ séparable, appellée $\tau$-enlacement, est définie. Le modèle pour cette définition est la généralisation de l'enlacement homotopique et de l'enlacement au sens de Benci-Rabinowitz faite par Frigon. En utilisant la théorie du degré développée dans un article de Kryszewski et Szulkin, plusieurs exemples de paires $\tau$-enlacées sont donnés. Un lemme de déformation est établi et utilisé conjointement à la notion de $\tau$-enlacement pour prouver un théorème d'existence de point critique pour une certaine classe de fonctionnelles sur $X$. De plus, une caractérisation de type minimax de la valeur critique correspondante est donnée. Comme corollaire de ce théorème, des conditions sont énoncées sous lesquelles l'existence de deux points critiques distincts est garantie. Deux autres théorèmes de point critiques sont démontrés dont l'un généralise le théorème principal de l'article de Kryszewski et Szulkin mentionné ci-haut. / A new notion of linking for pairs of sets $A\subset B$, $P\subset Q$ in a Hilbert space of the form $X=Y\oplus Y^{\perp}$ with $Y$ separable, called $\tau$-linking, is defined. The model for this definition is the generalization of homotopical linking and linking in the sense of Benci-Rabinowitz made by Frigon. Using the degree theory developped in an article of Kryszewski and Szulkin, many examples of $\tau$-linking pairs are given. A deformation lemma is established and used jointly with the notion of $\tau$-linking to prove an existence theorem for critical points of a certain class of functionals defined on $X$. Moreover, a characterization of a minimax nature for the corresponding critical value is given. As a corollary of this theorem, conditions are stated under which the existence of two distinct critical points is guaranteed. Two other critical point theorems are demonstrated, one of which generalizes the main theorem of the article of A new notion of linking for pairs of sets $A\subset B$, $P\subset Q$ in a Hilbert space of the form $X=Y\oplus Y^{\perp}$ with $Y$ separable, called $\tau$-linking, is defined. The model for this definition is the generalization of homotopical linking and linking in the sense of Benci-Rabinowitz made by Frigon~\cite{frigon:1}. Using the degree theory developped in~\cite{szulkin:1}, many examples of $\tau$-linking pairs are given. A deformation lemma is established and used jointly with the notion of $\tau$-linking to prove an existence theorem for critical points of a certain class of functionals defined on $X$. Moreover, a characterization of a minimax nature for the corresponding critical value is given. As a corollary of this theorem, conditions are stated under which the existence of two distinct critical points is guaranteed. Two other critical point theorems are demonstrated, one of which generalizes the main theorem of the article by Kryszewski and Szulkin cited above.

Mais recentemente a exploração offshore de petróleo e gás tem se intensificado na costa brasileira. Uma das características da exploração offshore no Brasil está ligada ao fato de os hidrocarbonetos se situarem a grandes profundidades no mar, frequentemente abaixo de uma espessa camada de sal, exigindo o desenvolvimento de novas tecnologias para vencer os desafios para sua prospecção e extração. A profundidade dos poços pode variar entre dois mil e sete mil metros abaixo da superfície do mar. Um dos grandes desafios é garantir uma boa conexão dos equipamentos de extração com a unidade de produção na superfície, o que se faz com risers. Há distintas configurações de risers, entre as quais os verticais, em catenária, lazy waves ou steep waves, sendo que o riser em catenária e o vertical, em particular, serão estudados aqui. Este trabalho visa a estudar os efeitos dinâmicos não lineares no riser, que, por ser extremamente esbelto, exige a consideração da não linearidade geométrica. Entre eles, destaca-se a possibilidade de ocorrência da ressonância paramétrica. Os carregamentos dinâmicos podem ser provenientes da movimentação da unidade flutuante, correntezas ou escoamento interno. Neste trabalho serão elaborados modelos em elementos finitos, utilizando o software Abaqus, que possui mais recursos que a maioria dos softwares comerciais para as análises que se pretende realizar. Esses modelos simularão inicialmente a configuração de equilíbrio estático do riser e posteriormente serão adicionados os carregamentos dinâmicos. Na representação do encontro do riser com o solo no fundo do mar, serão utilizados elementos de contato elásticos. Pretende-se discutir a viabilidade e as limitações no uso de programas generalistas de análise estrutural pelo método dos elementos finitos, no confronto com programas dedicados, e ainda comparando os resultados obtidos com aqueles que decorrem de soluções analíticas, ou experimentais, quando disponíveis. / More recently the offshore oil and gas exploitation has being intensified on the Brazilian coast. One of the characteristics of offshore exploitation in Brazil is linked to the fact that hydrocarbons are located at great depths under the sea bed, often below a thick layer of salt, requiring the development of new technologies to meet these challenges. The depth of the wells can vary between 2,000 and 7,000 meters below the sea surface. A major challenge is to ensure a good connection between the extraction system and the production unit at the sea surface, which is provided by risers. There are different configurations of risers, including the vertical, catenary, lazy-wave or steep-wave; the catenary and vertical risers will be studied in this work. This work aims at studying the nonlinear dynamic effects on the riser, which, being extremely slender, requires consideration of the geometric nonlinearity. Among them, there is the possibility of occurrence of parametric resonance. The dynamic loads may come from the motion of the floating unit and external or internal fluid flow. This work will be developed using finite-element models in Abaqus, which has more resources than most commercial softwares to carry out the type of analyses of interest. Initially these models simulate the static equilibrium configuration of the catenary riser, which will be later disturbed by dynamic loads. The modeling of the so called touch-down zone (TDZ) will use elastic contact elements. It is intended to discuss the feasibility and limitations when using generalist codes for structural analysis by the finite-element method, in comparison with dedicated codes, and also to correlate these results with those from analytical and experimental studies, whenever available.

Nesta tese discute-se a necessidade de se desenvolver novas ferramentas para auxiliar o projeto e análise de estruturas de cabos e membranas. Esse tipo de estrutura, essencialmente não linear, é geralmente analisada por meio do Método dos Elementos Finitos, combinado com o Método de Newton-Raphson, para a resolução do sistema de equações não lineares resultante. Porém, a ausência de um campo de tensão de tração sobre toda estrutura composta por elementos finitos de cabos e membranas pode gerar uma matriz de rigidez tangente indeterminada, levando à divergência da solução pelo Método de Newton-Raphson. O Método da Relaxação Dinâmica é uma alternativa interessante para resolver problemas não lineares complicados de equilíbrio estático, na qual o problema do equilíbrio estático é resolvido por uma análise dinâmica, com integração no tempo. A resposta transiente é fictícia e não tem significado físico, entretanto a parte estacionária é a solução do problema de equilíbrio estático. Nesta tese, apresenta-se uma contextualização histórica sobre o Método da Relaxação Dinâmica, apontando as contribuições mais relevantes já desenvolvidas por outros autores. Propõe-se um procedimento de sintonia da massa dos elementos, capaz de uniformizar as condições impostas ao incremento de tempo, para se obter estabilidade do processo de integração numérica. Implementam-se as formulações dos elementos finitos adotados, bem como um algoritmo de enrugamento para os elementos de membrana e diversas rotinas de pós-processamento, no programa de elementos finitos SATS (A System for the Analysis of Taut Structures), desenvolvido pelo autor desta tese, em colaboração com seu orientador. A implementação desenvolvida é aplicada a uma série de exemplos relativos ao projeto e análise de estruturas de cabos e membranas, permitindo verificar a eficiência dos procedimentos de amortecimento e cinético e de sintonia de massa propostos. / This thesis discusses the need to develop new tools to assist the design and analysis of cables and membrane structures. This type of structures, essentially non-linear is generally analyzed using the Finite Element Method, where in most cases the solution is obtained by the Newton-Raphson Method. However, the absence of a tension stress field over the entire structure composed only with cable and membrane finite element can generate a non-positive definite tangent stiffness matrix, leading to the divergence of Newton-Raphson iterations. The Method of Dynamic Relaxation is an interesting alternative to solve complicated nonlinear problems of static equilibrium, replaced by an equivalent dynamic analysis. The transient solution is fictitious and without physical meaning, and the stationary phase provides the static equilibrium solution. This thesis presents a historical contextualization of the Dynamic Relaxation Method, highlighting the most relevant contributions already developed by other authors. A procedure for the tuning of the element masses is proposed, which is capable of making uniform the restrictions imposed to the time steps in order to preserve the stability of the numerical integration. Some adopted finite element formulations are implemented, as well as an algorithm for representing the wrinkling of membrane elements and several post-processing routines, in the SATS (A System for the Analysis of Taut Structures) finite element program, developed by the author of this thesis, in collaboration with his advisor. The developed implementation is applied to a series of examples on the design and analysis of cables and membrane structures, allowing verification of the efficiency of the procedures proposed for kinetic damping and mass tuning.

O trabalho trata da formulação e implementação numérica de modelos matemáticos do comportamento de estruturas considerando-se as não-linearidades física e geométrica. O equilíbrio na posição deslocada é formulado via Princípio dos Trabalhos Virtuais, empregando-se o método dos elementos finitos para a discretização espacial das estruturas e busca de soluções aproximadas. Inicialmente destaca-se com base no caso de treliças planas o emprego de medidas de deformação e tensão conjugadas energeticamente. Particularizando-se a formulação geral do equilíbrio para os pórticos planos apresenta-se uma análise crítica das formulações lagrangiana total e atualizada. Em seguida, tendo-se em vista aplicações às estruturas em concreto armado, aborda-se o comportamento não-linear físico pela mecânica do dano em meios contínuos, empregando-se os modelos de dano para o concreto propostos por Mazars e La Borderie. Estendem-se os estudos do comportamento estrutural não-linear físico (dano) e geométrico incorporando-se a análise dinâmica. Utiliza-se para integração no domínio do tempo o método implícito de Newmark combinado com o procedimento incremental e iterativo de Newton-Raphson. O amortecimento é levado em conta por meio da regra de Rayleigh. Exemplos consistindo de análises não lineares estática e dinâmica de estruturas reticulares planas compõem numéricas. Os resultados obtidos ilustram o desempenho e as potencialidades das formulações empregadas. / The formulation and numerical implementation of mathematical models of the structural behavior of plane frames considering material and geometrical nonlinearities are treated in this work. The Principle of Virtual Work is presented in order to characterize the equilibrium in the displaced position. The structure is discretized by the finite element method. Plane trusses analysis is performed in order to show how important it is to take into account the strain and stress tensors energetically conjugated. Being particularized, the general equilibrium formulation for the plane frames a critical analysis of the total and updated lagrangian formulations is presented. The material nonlinear behavior is modeled by continuum damage mechanics by using both Mazars and La Boderie\'s damage models. The nonlinear analysis is extended including the dynamic response of the reinforced concrete plane frames. The usual iterative Newton-Raphson technique is used combined with implicit Newmark method in order to carry out the integration at time. The damping is introduced by means of the Rayleigh\'s rule. Numerical analysis by a suitable computer program show the theoretical results considering static and dynamic response of plane frames.

Este trabalho apresenta uma contribuição ao emprego do Método dos Elementos Finitos Generalizados (MEFG) na análise tridimensional não-linear de sólidos. A análise numérica em campo não-linear, com modelos de dano e plasticidade, é original. O MEFG é uma formulação não-convencional do Método dos Elementos Finitos (MEF), que resulta da incorporação a este último de conceitos e técnicas dos denominados métodos sem malha, especialmente o enriquecimento da aproximação inicial (partição de unidade) por funções convenientes. Apresenta-se uma breve revisão bibliográfica dos métodos sem malha e do método dos elementos finitos generalizados, bem como suas principais características. Apresenta-se, com base no MEFG, a formulação de elementos tetraédricos e hexaédricos. Três modelos constitutivos são considerados visando análises não-lineares: o de plasticidade (perfeita ou com encruamento isótropo linear) com critério de plastificação de von Mises; o de dano frágil em concreto sob carregamento monótono crescente (modelo de Mazars) e o de dano e plasticidade acoplados (modelo de Lemaitre), próprio para materiais metálicos. São apresentados detalhes do código computacional, baseado no MEFG e nos modelos constitutivos acima mencionados, bem como resultados de análises numéricas. Esses resultados ressaltam algumas das vantagens do MEFG aplicado à análise não-linear, tais como: o enriquecimento da aproximação inicial limitado a regiões de interesse no domínio, como por exemplo, as que exibem elevados gradientes de deformação e tensão; uma definição mais precisa da distribuição de grandezas como a variável de dano e a tensão equivalente de von Mises, evitando a necessidade de alterações na malha; e a superação do travamento volumétrico associado a modelos de plasticidade / This work presents a contribution to the generalized finite element method (GFEM) employment in three-dimensional nonlinear analysis of solids. The nonlinear numerical analysis conduced with damage and plasticity models is original. GFEM is a nonconventional formulation of finite element method (FEM) which results from the addition to the latter of concepts and techniques of the so called Meshless methods, specially the enrichment of the initial approximations (partition of unity) by customized functions. A brief review of Meshless methods and generalized finite element method bibliography is presented, as well as their main features. Based on GFEM, the formulation of tetrahedral and hexahedral elements is shown. Three material laws are considered aiming nonlinear analysis: plasticity (perfectly plastic or linear isotropic hardening), with von Mises yield criterion; brittle damage on concrete under monotonic increasing loading (Mazars model) and damage coupled with plasticity (Lemaitre model), a suitable model for metals. Details of the computational code, based on GFEM and material laws mentioned above, are presented, as well as results of numerical analysis. These results emphasize some of the advantages of GFEM applied to nonlinear analysis, such as: enrichment of the basic approximations limited to some regions of interest in the domain, for instance, those exhibiting high strain and stress gradients; an accurated definition of the distributions of quantities like damage variable and von Mises equivalent stress, avoiding remeshing; and overcoming of volumetric locking associated to plasticity models