<p> Traditionally, Molecular Dynamics combined with pair potential functions or the Embedded Atom Method (EAM) is applied to simulate the motion of atoms. When a defect is generated in the crystalline lattice, the equilibrium of atoms around it is destroyed. The atoms move to find a new place where the potential energy in the system is minimum, which could result in a change of the local atomic structure. This thesis introduces a new Dynamic Relaxation algorithm, which is based on explicit Finite Element Analysis, and pair or EAM potential function, to find equilibrium positions of the block of atoms containing different structural defects.</p> <p> The internal force and stiffness at the atoms (nodes) are obtained by the first and second derivatives of the potential energy functions. The convergence criterion is based on the Euclidean norm of internal force being close to zero when the potential energy is minimum. The damping ratio affects the solution path so that different damping ratios could lead to different minimum potential energy and equilibrium shapes. The choice of scaled mass of atoms, proper time step, boundary conditions and damping appropriate for the efficient and stable simulation is studied.</p> <p> A small block of atoms is used to obtain the numerical responses from a hybrid algorithm of potential energy functions and Dynamic Relaxation techniques such as repulsion and attraction in pair potential, minimum configuration, damping effects and different boundary conditions.</p> <p> The simulation using modified Dynamic Relaxation techniques is performed to the real material model with dislocation defect. The results after relaxation are in agreement with the prediction and current Molecular Dynamics simulation. Therefore, Dynamic Relaxation could be an alternative tool for atomistic simulation.</p> / Thesis / Master of Applied Science (MASc)

Les structures de type gridshell élastique permettent de réaliser des enveloppes courbes par la déformation réversible d’une grille structurelle régulière initialement plane. Cette capacité à “former la forme” de façon efficiente prend tout son sens dans le contexte actuel où, d’une part la forme s’impose comme une composante prédominante de l’architecture moderne, et d’autre partl’enveloppe s’affirme comme le lieu névralgique de la performance des bâtiments. Fruit des recherches de l’architecte et ingénieur allemand Frei Otto dans les années 1960, elles ont été rendues populaires par la construction de la Multihalle de Mannheim en 1975. Cependant, en dépit de leur potentiel, très peu de projets de ce type ont vu le jour suite à cette réalisation emblématique qui en a pourtant démontré la faisabilité à grande échelle. Et pour cause, les moyens engagés à l’époque ne sauraient assurer la reproductibilité de cette expérience dans un contexte plus classique de projet, notamment sur le plan économique. Par ailleurs, les techniques et les méthodes développées alors sont pour la plus part tombées en désuétude ou reposent sur des disciplines scientifiques qui ont considérablement évoluées. Des matériaux nouveaux, composites, ont vu le jour. Ils repoussent les limitations intrinsèques des matériaux usuels tel que le bois et offrent des performances techniques bien plus intéressantes pour ce type d’application. Enfin, notons que le cadre réglementaire a lui aussi profondément muté, apportant une certaine rigidité vis-à-vis de la pénétration des innovations. Ainsi la conception des gridshells se pose-t-elle en des termes nouveaux aux architectes et ingénieurs actuels et se heurte à l’inadéquation des outils et méthodes existant. Dans cette thèse, qui marque une étape importante dans une aventure de recherche personnelle initiée en 2010, nous tentons d’embrasser la question de la conception des gridshells élastiques dans toute sa complexité, en abordant aussi bien les aspects théoriques que techniques et constructifs. Dans une première partie, nous livrons une revue approfondie de cette thématique et nous présentons de façon détaillée l’une de nos principales réalisation, la cathédrale éphémère de Créteil, construite en 2013 et toujours en service. Dans une seconde partie, nous développons un élément de poutre discret original avec un nombre minimal de degrés de liberté adapté à la modélisation de la flexion et de la torsion dans les gridshells constitués de poutres de section anisotrope. Enrichi d’un noeud fantôme, il permet de modéliser plus finement les phénomènes physiques au niveau des connexions et des appuis. Son implémentation numérique est présentée et validée sur quelques cas tests. Bien que cet élément ait été développé spécifiquement pour l’étude des gridshells élastiques, il pourra avantageusement être utilisé dans tout type de problème où la nécessité d’un calcul interactif avec des tiges élastiques prenant en compte les couplages flexion-torsion s’avère nécessaire / An elastic gridshell is a freeform structure, generally doubly curved, but formed out through the reversible deformation of a regular an initially flat structural grid. Building curved shapes that way seems to offer the best of both worlds : shell structures are amongst the most performant mechanically speaking while planar and orthogonal constructions are much more efficient and economic to produce than curved ones. This ability to “form a form” efficiently is of peculiar importance in the current context where morphology is a predominant component of modern architecture, and envelopes appear to be the neuralgic point for building performances. The concept was invented by Frei Otto, a German architect and structural engineer who devoted many years of research to gridshells. In 1975 he designed the Multihalle of Mannheim, a 7500 m2 wooden shell which demonstrated the feasibility of this technology and made it famous to a wide audience. However, despite their potential, very few projects of this kind were built after this major realization. And for good reason, the ressources committed at that time cannot guarantee the replicability of this experiment for more standard projects, especially on the economic level. Moreover, the technics and methods developed by Otto’s team in the 1960s have mostly fall into disuse or are based on disciplines that have considerably evolved. New materials, such as composite materials, have recently emerged. They go beyond the limitations of conventional materials such as timber and offer at all levels much better technical performances for this kind of application. Finally, it should be noted that the regulatory framework has also deeply changed, bringing a certain rigidity to the penetration of innovations in the building industry. Therefore, the design of gridshells arises in new terms for current architects and engineers and comes up against the inadequacy of existing tools and methods. In this thesis, which marks an important step in a personal research adventure initiated in 2010, we try to embrace the issue of the design of elastic gridshells in all its complexity, addressing both theoretical, technical and constructive aspects. In a first part, we deliver a thorough review of this topic and we present in detail one of our main achievements, the ephemeral cathedral of Créteil, built in 2013 and still in service. In a second part, we develop an original discrete beam element with a minimal number of degrees of freedom adapted to the modeling of bending and torsion inside gridshell members with anisotropic cross-section. Enriched with a ghost node, it allows to model more accurately physical phenomena that occur at connections or at supports. Its numerical implementation is presented and validated through several test cases. Although this element has been developed specifically for the study of elastic gridshells, it can advantageously be used in any type of problem where the need for an interactive computation with elastic rods taking into account flexion-torsion couplings is required

Les structures constructives de type Gridshells sont réalisées à partir d'une grille régulière plane que l'on déforme élastiquement, puis que l'on rigidifie dans la position souhaitée. Les Gridshells en matériaux composites ont été développés et étudiés depuis plusieurs années au laboratoire Navier. La thèse propose, à travers un historique des réalisations Navier, un retour d'expérience. Elle identifie également les aspects à mieux maîtriser, d'un point de vue simulation numérique ou d'un point de vue matériau et technologie. La thèse détaille alors des développements numériques nouveaux permettant l'analyse ultime de la structure, prise en compte des ruptures de barres (robustesse), et permettant la prise en compte de la torsion dans des poutres anisotropes, c'est-à-dire à section quelconque. Dans le premier chapitre on traite ainsi du contexte dans lequel s'inscrivent les travaux sur les gridshells. La conception des gridshells au laboratoire Navier y est détaillée. En particulier, la méthode numérique historiquement utilisée, à savoir la méthode de relaxation dynamique, est présentée. Le second chapitre présente les réalisations du laboratoire Navier. Plusieurs prototypes ont été réalisés durant les dix dernières années. Les deux dernières structures, le gridshell de Solidays et la Cathédrale Ephémère de Créteil, ont été conçues et fabriquées pour accueillir du public. Les choix importants de conception et de fabrication de ces gridshells sont détaillés, avec un accent sur les avancées technologiques et sur les retours d'expérience. Le troisième chapitre traite du comportement des gridshells en matériaux composites. La démarche a été d'investiguer le comportement du gridshell pour comprendre les processus d'endommagement des gridshells. On montre que le flambement conditionne la robustesse des gridshells. En effet, les résultats de l'étude montrent que lorsque le gridshell a été bien dimensionné et que les risques de flambement de la structure sont écartés, la structure se comporte de manière robuste, du fait de sa forte redondance. Finalement, le dernier chapitre traite d'un nouveau modèle de poutre permettant de prendre en compte la torsion dans les poutres de section quelconque. Dans les précédents chapitres, il est souligné que la non prise en compte de la torsion peut-être préjudiciable pour diverses raisons, sous-estimation des contraintes, méconnaissance des efforts de jonctions, erreur sur la géométrie. Dans ce chapitre, le modèle de poutre est un modèle à quatre degrés de liberté, à la manière des travaux de Basile Audoly et Ethan Grinspun. La simulation numérique, à nouveau réalisée à l'aide d'un algorithme de relaxation dynamique, permet d'obtenir les configurations d'équilibre de structures fortement réticulées telles que les gridshells. Une des particularités de ce travail est que le modèle de poutre est développé en continu jusqu'à l'obtention des efforts intérieurs. Le modèle est ensuite discrétisé et implémenté de manière à pouvoir être utilisé. Une sous-étape permet d'ajouter des forces et des moments extérieurs. Pour des poutres de section rectangulaire, les résultats du modèle sont comparés à un logiciel élément fini et donnent de bons résultats en termes de précision et de temps de calcul. Finalement la méthode numérique est appliquée à des structures composées de poutres connectées. La transmission des efforts au niveau des connexions est implémentée. L'excentricité des connexions est également modélisée ce qui permet d'obtenir de précieuses informations sur les efforts transitant au sein des connexions. Grâce à ces travaux, il devient possible d'utiliser la richesse de forme que peuvent offrir les poutres élancées présentant deux inerties en flexion différentes / The structures like gridshells are structures made of a plane regular grid which is elastically deformed and then stiffened in the wished configuration. The composite materials gridshells have been developed and studied for several years at Navier laboratory. The thesis offer a feedback, through a history of Navier realisations. It also precise the points to improve, in numerical simulation or about materials or technological aspects. Then, the thesis explains the new numerical developments that make possible the ultimate analysis of the structure, taking account the ruptures of beams (robustness), and that makes possible the consideration of the torsion in anisotropic beams, that is to say beams with any cross-section. In the first chapter the context of the work is presented. This chapter explains how the Navier laboratory designs and builds gridshells. In particular, the numerical method historically used - the dynamic relaxation method - is presented. The second chapter presents the gridshell realisations of the Navier laboratory. Several prototypes have been built during the past ten years. The two last ones, the Solidays gridshell and the Ephemeral Cathedral of Creteil, have been designed to shelter public. The important choices during design and fabrication are detailed with an accent on technological progresses and feedbacks. The third chapter deals with the behaviour of composite materials gridhsells. The approach was to investigate the behaviour of the gridshell to understand the processes of damage. It is shown that buckling is particularly dangerous for the gridshell. The results of the study shows that when the gridshell has been well designed and in particular if buckling is avoided, the gridshell behave in a robust manner, thanks to its redundancy. Finally the last chapter deals with a new beam model, able to take into account torsion, for beams with any section. In the previous chapters it was underlined that the consideration of torsion aspects was lacking and has various consequences – incorrect estimation of stress, ignorance of forces and moments in connections, imprecision in geometry. In this chapter, the model of beams used is a four degrees of freedom model, similar to the ones presented by Basile Audoly and Ethan Grinspun. The numerical simulation, performed once again thanks to a dynamic relaxation algorithm, is able to provide equilibrium configurations of highly reticulated structures as gridshells. One of the particularity of this work is the fact that the model is a continuous model, only discretized for numerical simulations. The external forces and moments can be implemented. For beams with rectangular cross-section, the results of the model are compared to finite element modelling simulations. The results are satisfying in term of accuracy and computational time. Finally the numerical method is applied to structures made of interconnected beams. The connections are modelled and the efforts through them are provided by the model. This provides important information about how to design the connections. Thanks to these work it become possible to use the large possibility of shapes offered by slender beams whose flexural inertias are different

Les structures constructives de type Gridshells sont réalisées à partir d'une grille régulière plane que l'on déforme élastiquement, puis que l'on rigidifie dans la position souhaitée. Les Gridshells en matériaux composites ont été développés et étudiés depuis plusieurs années au laboratoire Navier. La thèse propose, à travers un historique des réalisations Navier, un retour d'expérience. Elle identifie également les aspects à mieux maîtriser, d'un point de vue simulation numérique ou d'un point de vue matériau et technologie. La thèse détaille alors des développements numériques nouveaux permettant l'analyse ultime de la structure, prise en compte des ruptures de barres (robustesse), et permettant la prise en compte de la torsion dans des poutres anisotropes, c'est-à-dire à section quelconque. Dans le premier chapitre on traite ainsi du contexte dans lequel s'inscrivent les travaux sur les gridshells. La conception des gridshells au laboratoire Navier y est détaillée. En particulier, la méthode numérique historiquement utilisée, à savoir la méthode de relaxation dynamique, est présentée. Le second chapitre présente les réalisations du laboratoire Navier. Plusieurs prototypes ont été réalisés durant les dix dernières années. Les deux dernières structures, le gridshell de Solidays et la Cathédrale Ephémère de Créteil, ont été conçues et fabriquées pour accueillir du public. Les choix importants de conception et de fabrication de ces gridshells sont détaillés, avec un accent sur les avancées technologiques et sur les retours d'expérience. Le troisième chapitre traite du comportement des gridshells en matériaux composites. La démarche a été d'investiguer le comportement du gridshell pour comprendre les processus d'endommagement des gridshells. On montre que le flambement conditionne la robustesse des gridshells. En effet, les résultats de l'étude montrent que lorsque le gridshell a été bien dimensionné et que les risques de flambement de la structure sont écartés, la structure se comporte de manière robuste, du fait de sa forte redondance. Finalement, le dernier chapitre traite d'un nouveau modèle de poutre permettant de prendre en compte la torsion dans les poutres de section quelconque. Dans les précédents chapitres, il est souligné que la non prise en compte de la torsion peut-être préjudiciable pour diverses raisons, sous-estimation des contraintes, méconnaissance des efforts de jonctions, erreur sur la géométrie. Dans ce chapitre, le modèle de poutre est un modèle à quatre degrés de liberté, à la manière des travaux de Basile Audoly et Ethan Grinspun. La simulation numérique, à nouveau réalisée à l'aide d'un algorithme de relaxation dynamique, permet d'obtenir les configurations d'équilibre de structures fortement réticulées telles que les gridshells. Une des particularités de ce travail est que le modèle de poutre est développé en continu jusqu'à l'obtention des efforts intérieurs. Le modèle est ensuite discrétisé et implémenté de manière à pouvoir être utilisé. Une sous-étape permet d'ajouter des forces et des moments extérieurs. Pour des poutres de section rectangulaire, les résultats du modèle sont comparés à un logiciel élément fini et donnent de bons résultats en termes de précision et de temps de calcul. Finalement la méthode numérique est appliquée à des structures composées de poutres connectées. La transmission des efforts au niveau des connexions est implémentée. L'excentricité des connexions est également modélisée ce qui permet d'obtenir de précieuses informations sur les efforts transitant au sein des connexions. Grâce à ces travaux, il devient possible d'utiliser la richesse de forme que peuvent offrir les poutres élancées présentant deux inerties en flexion différentes / The structures like gridshells are structures made of a plane regular grid which is elastically deformed and then stiffened in the wished configuration. The composite materials gridshells have been developed and studied for several years at Navier laboratory. The thesis offer a feedback, through a history of Navier realisations. It also precise the points to improve, in numerical simulation or about materials or technological aspects. Then, the thesis explains the new numerical developments that make possible the ultimate analysis of the structure, taking account the ruptures of beams (robustness), and that makes possible the consideration of the torsion in anisotropic beams, that is to say beams with any cross-section. In the first chapter the context of the work is presented. This chapter explains how the Navier laboratory designs and builds gridshells. In particular, the numerical method historically used - the dynamic relaxation method - is presented. The second chapter presents the gridshell realisations of the Navier laboratory. Several prototypes have been built during the past ten years. The two last ones, the Solidays gridshell and the Ephemeral Cathedral of Creteil, have been designed to shelter public. The important choices during design and fabrication are detailed with an accent on technological progresses and feedbacks. The third chapter deals with the behaviour of composite materials gridhsells. The approach was to investigate the behaviour of the gridshell to understand the processes of damage. It is shown that buckling is particularly dangerous for the gridshell. The results of the study shows that when the gridshell has been well designed and in particular if buckling is avoided, the gridshell behave in a robust manner, thanks to its redundancy. Finally the last chapter deals with a new beam model, able to take into account torsion, for beams with any section. In the previous chapters it was underlined that the consideration of torsion aspects was lacking and has various consequences – incorrect estimation of stress, ignorance of forces and moments in connections, imprecision in geometry. In this chapter, the model of beams used is a four degrees of freedom model, similar to the ones presented by Basile Audoly and Ethan Grinspun. The numerical simulation, performed once again thanks to a dynamic relaxation algorithm, is able to provide equilibrium configurations of highly reticulated structures as gridshells. One of the particularity of this work is the fact that the model is a continuous model, only discretized for numerical simulations. The external forces and moments can be implemented. For beams with rectangular cross-section, the results of the model are compared to finite element modelling simulations. The results are satisfying in term of accuracy and computational time. Finally the numerical method is applied to structures made of interconnected beams. The connections are modelled and the efforts through them are provided by the model. This provides important information about how to design the connections. Thanks to these work it become possible to use the large possibility of shapes offered by slender beams whose flexural inertias are different

Diverse construction work of engineering involves the execution of excavation and embankments, such as the construction of foundations, dams and urban infrastructure. In general, geomechanical problems have a high degree of complexity due to the difficulty on the parameters quantification, the definition of representative models of the soil and the interaction soil-structure. Many models are based on the final arrangement of the system, not considering the intermediate analyses that are important steps in the study of those problems. In this study was developed a methodology for modeling problems that need redefinitions of analysis domain in function of the consideration of excavations and embankments, using an alternative technique for solution of the balance equations, the Dynamic Relaxation, combined with the Finite Element Methods for the development of the model. / Fundação de Amparo a Pesquisa do Estado de Alagoas / Diversas obras de engenharia envolvem a execução de escavações e aterros, a exemplo da construção de fundações, barragens e infra-estrutura urbana. De um modo geral, a modelagem desses tipos de problemas possui um grau de complexidade alto devido à dificuldade da quantificação de parâmetros, de definição dos modelos representativos do solo e da interação solo-estrutura. Muitas modelagens baseiam-se no arranjo final do sistema, dispensando as análises intermediárias que correspondem a passos importantes no estudo desses problemas. Neste trabalho desenvolve-se uma metodologia para modelagem de problemas que necessitam de redefinições de domínios de análise em função da consideração de escavações e aterros, utilizando-se uma técnica alternativa para solução das equações de equilíbrio, a Relaxação Dinâmica, em conjunto com o Método dos Elementos Finitos para discretização do modelo.

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.

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.

The aim of the thesis is to create an analytical model of frame construction. Determining load at which individual plastic hinges are formed until the collapse of the structure. The analysis is going to be performed by RFEM with an additional module RFDYNAM. Subsequently, the parameters of dynamic relaxation is going to be optimized to specify and speed up the calculations. Finally, the optimized parameters is going to be used to analyze the storeyed frame construction formed Ing. Jan Vales including a comparison of findings.

This diploma thesis deals with methods for design of membrane structure shape. Main purpose is to analyze topology designs by Formfinder and Rhinoceros in RFEM and compare results. Test a possibility of designing shape by software RFEM.

The aim of the thesis is to create an analytical 2D model of a multi-storey building and its consequent loading until the point of collapse which occures due to formation of plastic hinges. The first part is going to present a linear analysis of the problem; it focuses on location and level of load when the plastic hinges are formed. Then a nonlinaer analysis is going to be performed by RFEM programme using postcritical analysis and dynamic relaxation. Differences between the results of mentioned types and methods of analysis are going to be compared and an impact of variables is going to be evaluated .