No description available.

This thesis describes a novel new method, termed the Tangent-Line-Chord (TLC) method, that can be used to more efficiently model creep deformation dominated by the tertiary regime. Creep deformation is a widespread mechanical mode of failure found in high-stress and temperature mechanical systems. To accurately simulate creep and its effect on structures, researchers utilize finite element analysis (FEA). General purpose FEA packages require extensive amounts of time and computer resources to simulate creep softening in components because of the large deformation rates that continuously evolve. The goal of this research is to employ multi-regime creep models, such as the Kachanov-Rabotnov model, to determine a set of equations that will allow creep to be simulated using as few iterations as possible. The key outcome is the freeing up of computational resources and the saving of time. Because both the number of equations and the value of material constants within the model change depending on the approach used, programming software will be utilized to automate this analytical process. The materials being considered in this research are mainly generic Ni-based superalloys, as they exhibit creep responses that are dominated by secondary and tertiary creep.

[pt] Uma análise não linear geométrica de estruturas, utilizando o Método dos Elementos Finitos (MEF), depende de cinco aspectos: a teoria de flexão, da descrição cinemática, das relações entre deformações e deslocamentos, da metodologia de análise não linear e das funções de interpolação de deslocamentos. Como o MEF é uma solução numérica, a discretização da estrutura fornece grande influência na resposta dessa análise. Contudo, ao se empregar funções de interpolação correspondentes à solução homogênea da equação diferencial do problema, obtêm-se o comportamento exato da estrutura para uma discretização mínima, como ocorre em uma análise linear. Assim, este trabalho visa a integrar as soluções para o problema da não linearidade geométrica, de maneira a tentar reduzir essa influência e permitir uma discretização mínima da estrutura, considerando ainda grandes deslocamentos e rotações. Então, utilizando-se a formulação Lagrangeana atualizada, os termos de ordem elevada no tensor deformação, as teorias de flexão de Euler-Bernoulli e Timoshenko, os algoritmos para solução de problemas não lineares e funções de interpolação, que consideram a influência da carga axial, obtidas da solução da equação diferencial do equilíbrio de um elemento infinitesimal na condição deformada, desenvolve-se um elemento de pórtico espacial com uma formulação completa. O elemento é implementado no Framoop e sua resposta, utilizando-se uma discretização mínima da estrutura, é comparada com formulações usuais, soluções analíticas e com o programa Mastan2 v3.5. Os resultados evidenciam a eficiência da formulação desenvolvida para prever a carga crítica de estruturas planas e espaciais utilizando uma discretização mínima. / [en] A structural geometric nonlinear analysis, using the finite element method (FEM), depends on the consideration of five aspects: the bending theory, the kinematic description, the strain-displacement relations, the nonlinear solution scheme and the interpolation (shape) functions. As MEF is a numerical solution, the structure discretization provides great influence on the analysis response. However, applying shape functions calculated from the homogenous solution of the differential equation of the problem, the exact behavior of the structure is obtained for a minimum discretization, as for a linear analysis. Thus, this work aims to integrate the solutions for the formulations of the geometric nonlinearity problem, in order to reduce this influence and allow a minimum discretization of the structure, also considering, large displacements and rotations. Then, using an updated Lagrangian kinematic description, considering a higher-order Green strain tensor, The Euler-Bernoulli and Timoshenko beam theories, the nonlinear solutions schemes and the interpolation functions, that includes the influence of axial force, obtained directly from the solution of the equilibrium differential equation of an deformed infinitesimal element, a spatial bar frame element is developed using a complete formulation. The element was implemented in the Framoop, and their results, for a minimum discretization, were compared with conventional formulations, analytical solutions and with the software Mastan2 v3.5. Results clearly show the efficiency of the developed formulation to predict the critical load of plane and spatial structures using a minimum discretization.

Ce travail comprends deux parties indépendantes, mais intimement liées. La première partie concerne le calcul et l'évaluation numérique des invariants holomorphes des difféomorphismes tangents à l'identité, dans le cas-type. On y expose notamment trois méthodes de calculs numériques, dont l'une est basée sur une formule explicite des invariants. Celle-ci résulte de l'évaluation de l'application de cornes 7[+, dont les ingrédients de base sont des rationnels, des coefficients de Taylor du difféomorphisme étudié et des multitangentes. La seconde partie concerne l'étude des multitangentes et des relations les liant entre elles. Il s'agit de fonctions I-périodiques, généralisant les séries d'Eisenstein, et définissant un moule symétr~l. D'autres relations existent, tels la réduction en monotangentes qui indique un lien profond entre les multitangentes et les multizêtas. Des propriétés et conjectures de nature purement algébrique, arithmétique ou analytique sont ensuite exposées. / This work contains two independant parts, witch are deeply very closed. The first part deals with the calculation and the numerical evaluation of the holomor¬phic invariants of tangent to identity diffeomorphisms, in the type-case. ln particular, we display here three methods of numerical computation whose the last is based on an ex¬plicit formula of invariants. These result of calculation of the horn map 7[+, whose basics components are sorne rationnaIs, sorne Taylor coefficients of the diffeomorphism which is studied and multitangents. The second part deals with a général study of multitangents and relations between them. They are I-periodic functions, generalizing Eisenstein series and defining a symetr~l mould. There are others relations, like the reduction into monotangents which point out to us a profound link between multitangents and multiz~tas values. Properties and conjec¬tures of purely algebraic, arithmetical or analytical kirig are then explain

Nous étudions les propriétés métriques locales des ensembles de niveau des applicationshorizontalement différentiables entre des groupes de Carnot, c'est-à-dire différentiable par rapport à la structure sous-riemannienne intrinsèque.Nous considérons des applications dont la différentielle horizontale est surjective,et notre étude peut être vue comme une généralisation du théorème des fonctions implicites pour les groupes de Carnot.Tout d'abord, nous présentons deux notions de tangence dans les groupes de Carnot:la première basée sur la condition de platitude au sens de Reifenberg et la deuxième issue de l'analyse convexe classique.Nous montrons que dans les deux cas, l'espace tangent à un ensemble de niveau coïncide avec le noyau de la différentielle horizontale.Nous montrons que cette condition de tangence caractérise en fait les ensembles de niveaudits ‘co-abéliens', c'est-à-dire ceux pour lesquels l'espace d'arrivée est abélien, et qu'une telle caractérisation n'est pas vraie en général.Ce résultat sur les espaces tangents a plusieurs conséquences remarquables.La plus importante est que la dimension de Hausdorff des ensembles de niveau est celle à laquelle l'on s'attend.Nous montrons également la connectivité locale des ensembles de niveau, et le fait que les ensembles de niveau de dimension 1 sont topologiquement des arcs simples.Pour les ensembles de niveau de dimension 1 nous trouvons une formule de l'aire qui permet d'exprimer la mesure de Hausdorff en termes d'intégrales de Stieltjes généralisées.Ensuite, nous menons une étude approfondie du cas particulier des ensembles de niveau dans les groupes d'Heisenberg.Nous montrons que les ensembles de niveau sont topologiquement équivalents à leurs espaces tangents.Il s'avère que la mesure de Hausdorff des ensembles de niveau de codimension élevée est souvent irrégulière, étant, par exemple, localement nulle ou infinie.Nous présentons une condition simple de régularité supplémentaire pour une application pour assurer la régularité au sens d'Ahlfors des ses ensembles de niveau.Parmi d'autres résultats, nous obtenons une nouvelle caractérisation généraledes graphes Lipschitziens associés à une décomposition en produit semi-direct d'un groupe de Carnot.Nous traitons, en particulier, le cas des groupes de Carnot dont le nombre de stratesest plus grand que $2$.Cette caractérisation nous permet de déduire une nouvelle caractérisation des ensemblesde niveau co-abéliens qui admettent une représentation en tant que graphe. / Metric properties of level sets of differentiable maps on Carnot groupsAbstract.We investigate the local metric properties of level sets of mappings defined between Carnot groups that are horizontally differentiable, i.e.with respect to the intrinsic sub-Riemannian structure. We focus on level sets of mapping having a surjective differential,thus, our study can be seen as an extension of implicit function theorem for Carnot groups.First, we present two notions of tangency in Carnot groups: one based on Reifenberg's flatness condition and another coming from classical convex analysis.We show that for both notions, the tangents to level sets coincide with the kernels of horizontal differentials.Furthermore, we show that this kind of tangency characterizes the level sets called ``co-abelian'', i.e.for which the target space is abelian andthat such a characterization may fail in general.This tangency result has several remarkable consequences.The most important one is that the Hausdorff dimension of the level sets is the expected one. We also show the local connectivity of level sets and, the fact that level sets of dimension one are topologically simple arcs.Again for dimension one level set, we find an area formula that enables us to compute the Hausdorff measurein terms of generalized Stieltjes integrals.Next, we study deeply a particular case of level sets in Heisenberg groups. We show that the level sets in this case are topologically equivalent to their tangents.It turns out that the Hausdorff measure of high-codimensional level sets behaves wildly, for instance, it may be zero or infinite.We provide a simple sufficient extra regularity condition on mappings that insures Ahlfors regularity of level sets.Among other results, we obtain a new general characterization of Lipschitz graphs associated witha semi-direct splitting of a Carnot group of arbitrary step.We use this characterization to derive a new characterization of co-ablian level sets that can be represented as graphs.

Made available in DSpace on 2014-12-17T14:55:19Z (GMT). No. of bitstreams: 1 GustavoAC_TESE.pdf: 3178455 bytes, checksum: bdea1ce583a318f3a35fb4f3221877a8 (MD5) Previous issue date: 2014-04-28 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / The use of flexible materials for the development of planar circuits is one of the most desired and studied characteristics, lately, by researchers. This happens because the flexibility of the substrate can provide previously impracticable applications, due to the rigidity of the substrates normally used that makes it difficult to fit into the circuits in irregular surfaces. The constant interest in recent years for more lighter devices, increasingly more compacts, flexible and with low cost, led to a new line of research of great interest from both academic and technological views, that is the study and development of textile substrates that can be applied in the development of planar circuits, for applications in the areas of security, biomedical and telecommunications. This paper proposes the development of planar circuits, such as antennas , frequency selective surfaces (FSS) and planar filters, using textile (cotton ticking, jeans and brim santista) as the dielectric substrate and the Pure Copper Polyester Taffeta Fabric, a textile of pure copper, highly conductive, lightweight and flexible, commercially sold as a conductive material. The electrical characteristics of textiles (electric permittivity and loss tangent) were characterized using the transmission line method (rectangular waveguide) and compared with those found in the literature. The structures were analyzed using commercial software Ansoft Designer and Ansoft HFSS, both from the company Ansys and for comparison we used the Iterative Method of Waves (WCIP). For the purpose of validation were built and measured several prototypes of antennas, planar filters and FSS, being possible to confirm an excellent agreement between simulated and measured results / A utiliza??o de materiais flex?veis para o desenvolvimento de circuitos planares ? uma das caracter?sticas mais desejadas e estudadas, ultimamente, pelos pesquisadores, pois essa maleabilidade do substrato proporciona aplica??es antes imposs?veis, devido ? rigidez dos substratos normalmente utilizados o que dificultava a adequa??o dos circuitos em superf?cies irregulares. O constante interesse nos ?ltimos anos por dispositivos mais leves, cada vez mais compactos, flex?veis e com custo reduzido, levou a uma nova linha de pesquisa de grande interesse tanto do ponto de vista acad?mico quanto tecnol?gico que ? o estudo e desenvolvimento de substratos t?xteis que possam ser aplicados no desenvolvimento de circuitos planares, para aplica??es nas ?reas de seguran?a, biom?dica e telecomunica??es. Este trabalho prop?e o desenvolvimento de circuitos planares, tais como antenas, superf?cies seletivas de frequ?ncia (FSS) e filtros planares, utilizando tecidos (lona, jeans e brim santista) como substrato diel?trico e o tecido Pure Copper Polyester Taffeta Fabric, um tecido de cobre puro, altamente condutivo, leve e flex?vel, comercialmente vendido como material condutivo. As caracter?sticas el?tricas dos tecidos (permissividade el?trica e tangente de perda) foram determinadas utilizando o m?todo de linha de transmiss?o e comparadas com os encontrados na literatura. As estruturas foram analisadas utilizando os softwares comerciais Ansoft Designer, Ansoft HFSS ambos da empresa Ansys e para efeito de compara??o foi utilizado o M?todo Iterativo das Ondas (WCIP). Para efeito de valida??o foram constru?dos e medidos v?rios prot?tipos de antenas, FSS e filtros planares sendo poss?vel constatar uma excelente concord?ncia entre os resultados simulados e medidos

Cette thèse est divisée en trois parties. Dans la première partie, nous commençons par décrire les théories de Ziglin, Yoshida et Morales-Ramis et les motiver. Dans la deuxième partie, on étudie l’intégrabilité des équations différentielles de Newton à trois degrés de liberté dont les forces sont des polynômes homogènes de degrés trois. En utilisant une analyse du groupe de Galois différentiel des équations aux variations d’ordre supérieur, nous faisons une classification (presque) complète des forces génériques et intégrables. Dans une dernière partie, nous intéressons à l’intégrabilité d’un système d’équations différentielles homogènes d’ordre un (système A). L’application directe de la théorie de Morales-Ramis ne donne des obstructions à l’intégrabilité. En dérivant le système A par rapport au temps, nous obtenons un système différentiel de Newton homogène d’ordre 2 (système B). L’avantage est que ce dernier possède des solutions particulières algébriquement non triviales et le critère classique de Morales-Ramis nous permet d’établir des conditions nécessaires d’intégrabilité. Nous prouvons qu’il existe des relations explicites entre les intégrales premières des deux systèmes et nous introduisons une nouvelle méthode de recherche d’intégrales premières que l’on appelle « Extension tangente double ». Nous appliquons cette méthode à des systèmes planaires homogènes quadratiques. Comme deuxième application, nous montrons que, sous certaines conditions, les racines newtoniennes d’un système différentiel de Newton avec force centrale sont intégrables par quadratures. Nous présentons plusieurs systèmes intégrables avec deux, trois et quatre degrés de liberté. / This thesis is divided into three parts. In the first part we begin by describing the theories of Ziglin, Yoshida and Morales-Ramis and motivating them. In the second part we study the integrability of three-dimensional differential Newton equations with homogeneous polynomial forces of degree three. Using an analysis of differential Galois group of higher order variational equations, we give an almost complete classification of integrable generic forces. The last part is devoted to a study of the integrability of a system of first order homogeneous differential equations (system A ). The direct application of the Morales-Ramis theory does not lead to obstructions to the integrability. If we differentiate the differential system A with respect to time, we obtain a homogeneous Newtonian system (system B). The advantage is that the system B has a non-trivial particular solution and the classical criterion of Morales-Ramis allows us to establish necessary conditions for integrability. We prove that there are explicit relationships between first integrals of the both systems and we introduce a new method for finding first integrals called ``Double tangent extension method''. We apply the obtained results for a detailed analysis of homogeneous planar differential system. Using the double tangent extension method, we formulate some conditions under which the Newtonian roots of Newton's system with central force are integrable by quadratures. Some new cases of integrability with two, three and four degrees of freedom are found.

L’objectif de ce mémoire est d’introduire une nouvelle méthode smoothed particle hydrodynamics (SPH) implicite purement lagrangienne, pour la résolution des équations de Navier- Stokes incompressibles bidimensionnelles en présence d’une surface libre. Notre schéma de discrétisation est basé sur celui de Kéou Noutcheuwa et Owens [19]. Nous avons traité la surface libre en combinant la méthode multiple boundary tangent (MBT) de Yildiz et al. [43] et les conditions aux limites sur les champs auxiliaires de Yang et Prosperetti [42]. Ce faisant, nous obtenons un schéma de discrétisation d’ordre $\mathcal{O}(\Delta t ^2)$ et $\mathcal{O}(\Delta x ^2)$, selon certaines contraintes sur la longueur de lissage $h$. Dans un premier temps, nous avons testé notre schéma avec un écoulement de Poiseuille bidimensionnel à l’aide duquel nous analysons l’erreur de discrétisation de la méthode SPH. Ensuite, nous avons tenté de simuler un problème d’extrusion newtonien bidimensionnel. Malheureusement, bien que le comportement de la surface libre soit satisfaisant, nous avons rencontré des problèmes numériques sur la singularité à la sortie du moule. / The objective of this thesis is to introduce a new implicit purely lagrangian smoothed particle hydrodynamics (SPH) method, for the resolution of the two-dimensional incompressible Navier-Stokes equations in the presence of a free surface. Our discretization scheme is based on that of Kéou Noutcheuwa et Owens [19]. We have treated the free surface by combining Yildiz et al. [43] multiple boundary tangent (MBT) method and boundary conditions on the auxiliary fields of Yang et Prosperetti [42]. In this way, we obtain a discretization scheme of order $\mathcal{O}(\Delta t ^2)$ and $\mathcal{O}(\Delta x ^2)$, according to certain constraints on the smoothing length $h$. First, we tested our scheme with a two-dimensional Poiseuille flow by means of which we analyze the discretization error of the SPH method. Then, we tried to simulate a two-dimensional Newtonian extrusion problem. Unfortunately, although the behavior of the free surface is satisfactory, we have encountered numerical problems on the singularity at the output of the die.

La combinatoire a permis de résoudre certains problèmes en Mathématiques, en Physique et en Informatique, en retour celles-ci inspirent des questions nouvelles à la combinatoire. Ce mémoire de thèse intitulé "Combinatoire et algorithme des factorisations tangentes à l'identité" regroupe plusieurs travaux sur la combinatoire des déformations du produit de Shuffle. L'objectif de cette thèse est d'écrire des factorisations dont le terme principal est l'identité à travers l'utilisation d'outils portant principalement sur la combinatoire des mots (ordres, graduation etc.). Dans le cas classique, soit F une algèbre libre. En raison du fait que F est une algèbre enveloppante, on a une factorisation exacte de l'identité de End(F) = F*⨶F comme un produit infini d'exponentielles (End(F) étant muni du produit de Shuffle sur la gauche et de la concaténation sur la droite, une représentation fidèle du produit de convolution). La procédure est la suivante : premièrement on commence avec une base de Poincaré-Birkhoff-Witt, deuxièmement on calcule la famille des formes coordonnées et alors les propriétés (combinatoires) non triviales de ces familles en dualité donne la factorisation. Si on part de l'autre côté, l'écriture pour le même produit ne donne exactement l'identité que sous des conditions très restrictives que nous précisons ici. Dans de nombreux autres cas (déformés), la construction explicite des paires de bases en dualité nécessite une étude combinatoire et algorithmique que nous fournissons dans ce mémoire. / Combinatorics has solved many problems in Mathematics, Physics and Computer Science, in return these domains inspire new questions to combinatorics. This memoir entitled "Combinatorics and algorithmics of factorization tangent to indentity includes several works on the combinatorial deformations of the shuffle product. The aim of this thesis is to write factorizations wich principal term is the identity through the use of tools relating mainly to combinatorics on the words (orderings, grading etc). In the classical case, let F be the free algebra. Due to the fact that F is an enveloping algebra, one has an exact factorization of the identity of End(F) = F⨶F as an infinite product of exponentials (End(F) being endowed with the shuffle product on the left and the concatenation on the right, a faithful representation of the convolution product) as follows : first on begins with a PBW basis, second one computes the family of coordinate forms and then non-trivial (combinatorial) properties of theses families in duality gives the factorization. Starting from the other side and writing the same product does give exactly identity only under very restrictive conditions that we clarify here. In many other (deformed) cases, the explicit construction of pairs of bases in duality requires combinatorial and algorithmic studies that we provide in this memoir.

<p>The research topic of this PhD thesis is a comparative analysis of classical specic&nbsp;geometric frameworks and of their anisotropic extensions; the construction of three different&nbsp;types of Finsler frameworks, which are suitable for the analysis of the cancer cells population&nbsp;dynamical system; the development of the anisotropic Beltrami framework theory with the&nbsp;derivation of the evolution&nbsp;ow equations corresponding to different classes of anisotropic&nbsp;metrics, and tentative applications in image processing.</p> / <p>Predmet istraživanja doktorske disertacije je uporedna analiza klasičnih i specifičnih&nbsp;geometrijskih radnih okruženja i njihovih anizotropnih pro&scaron;irenja; konstrukcija &nbsp;tri Finslerova&nbsp;radna okruženja različitog tipa koja su pogodna za analizu dinamičkog &nbsp;sistema populacije&nbsp;kanceroznih ćelija; razvoj teorije anizotropnog Beltramijevog radnog okruženja i formiranje&nbsp;jednačina evolutivnog toka za različite klase anizotropnih metrika, kao i mogućnost primene&nbsp;dobijenih teorijskih rezultata u digitalnoj obradi slika.</p>