Made available in DSpace on 2015-03-04T18:51:18Z (GMT). No. of bitstreams: 1 Apresentacao.pdf: 121883 bytes, checksum: da58d642d3c4e264571ed24d208c16d7 (MD5) Previous issue date: 2006-03-15 / Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior / In this dissertation, we study the stationary heat equation in a heterogeneous tridimensional plate, using a "dimension reduction" techinique called hierarchical modelling and we generate model the original problem in a two-dimensional domain. To estimate the error modelling, we develop an asymptotic expansion for the original problem solution and for the aproximate solution. Comparing both solutions with their own asymptotic expansions, we obtain an estimative of the error modelling. We perform some computational experiments, using the Residual Free Bubbles (RFB) Method and the Multiscale Finite Element Method for the diffusion problem and for the diffusion-reaction problem in a two-dimensional domain, with small parameters. Finally, we extend the numeric solutions found the original tridimensional problem. / Neste trabalho, estudamos a equação do calor estacionária em uma placa heterogênea tridimensional. Para a modelagem deste problema, utilizamos uma técnica de redução de dimensão conhecida por Modelagem Hierárquica. Desta forma, geramos um modelo para o problema original em um domínio bidimensional. Com o objetivo de estimar o erro de modelagem, desenvolvemos a expansão assintótica da solução do problema original e da solução aproximada. Comparando as soluções com suas respectivas expansões assintóticas, obtemos uma estimativa para o erro de modelagem. Realizamos alguns experimentos computacionais, desenvolvendo o método Residual Free Bubbles (RFB) e o método de Elementos Finitos Multiescala (MEFM) para o problema de difusão e para o problema de difusão-reação em um domínio bidimensional, com parâmetros pequenos. Com base nestes experimentos, encontramos algumas soluções numéricas para o problema da placa tridimensional.

No presente trabalho, uma combinação do método dos elementos de contorno (MEC) com o método dos elementos finitos (MEF) é apresentada para a análise da interação entre estacas e o solo, considerado como um meio infinito tridimensional e homogêneo. O meio contínuo tridimensional de domínio infinito é modelado pelo MEC, enquanto as estacas consideradas como elementos reticulares são tratadas pelo MEF. As equações das estacas oriundas do método dos elementos finitos são combinadas com as do meio contínuo obtidas a partir do método dos elementos de contorno, resultando em um sistema completo de equações, que convenientemente tratadas, proporcionam a formulação de coeficientes de rigidez do conjunto solo-estacas. Finalmente, uma formulação para a análise do comportamento não-linear do solo na interface com a estaca é desenvolvida, tornando o modelo mais abrangente. / In the present work a combination of the Boundary Element Method (BEM) and the Finite Element Method (FEM) is used for pile-soil interaction analyses, considering the soil as a homogeneous, three-dimensional and infinite medium. The three-dimensional infinite continuous medium is modeled by the BEM, and the piles are, considered as beam elements, modeled by the FEM. This combination also is used for studying the interaction of plates sitting on a continuous medium. The pile equations generated from the FEM are combined with the medium equations generated from the BEM, resulting a complete equation system. Manipulating properly this equation system, a set of stiffness coefficients for the system soil-pile is obtained. Finally, to make the model more comprehensive, it presented a formulation to take into account the soil nonlinear behavior at the pile interface.

Cette thèse est consacrée à l’étude de méthodes de domaines fictifs pour les éléments finis. Ces méthodes, initialement conçues pour l’approximation de problèmes d’interactions fluide/structure, consistent à prolonger un domaine réel par un domaine de géométrie simple appelé domaine fictif. On applique ces méthodes à un problème de contact unilatéral sans frottement en petite déformation entre deux corps élastiques séparés par une distance initiale non nulle et possédant par ailleurs des conditions aux bords de type Dirichlet et Neumann. Les deux premiers chapitres sont consacrés à l’introduction des méthodes de domaines fictifs et du problème unilatéral de contact de deux corps élastiques. Le chapitre 3 est consacré à l’analyse a priori et à l’étude numérique de ce problème de contact en domaine fictif avec les conditions aux bords de Dirichlet et de contact qui sont prises en compte à l’aide d’une méthode de type Nitsche. Des résultats théoriques de consistance de la méthode discrète, d’existence et d’unicité sont présentés. Afin d’obtenir une estimation d’erreur a priori optimale, une stabilisation de la méthode de domaine fictif est nécessaire. Ces résultats sont validés numériquement sur des cas tests en dimensions deux et trois. Le chapitre 4 est consacré à l’étude d’un estimateur d’erreur de type résidu d’un problème de contact sans domaine fictif entre un corps élastique et un corps rigide. Les résultats théoriques sont également validés sur deux cas tests numériques : un domaine rectangulaire avec seulement une partie de la zone de contact en contact effectif ainsi qu’un contact de type Hertz en dimensions deux et trois. Le chapitre 5 est une généralisation du chapitre 4 à l’approche domaine fictif et au cas de deux corps élastiques. / This thesis is dedicated to the study of the fictitious domain methods for the finite element methods. These methods, initially designed for the fluid-structure interaction, consist in immersing the real domain in a simply-shaped and a geometrically bigger domain called the fictitious domain. We apply these methods to a unilateral frictionless contact problem in small deformation of two deformable elastics bodies separated by an initial gap and satisfying boundary Dirichlet and Neumann conditions. The first two chapters are devoted to the introduction of these methods and to the unilateral contact problem. The chapter 3 is dedicated to a theoretical study for Dirichlet and contact boundary conditions taken into account with a Nitsche type method. Some theoretical results are presented: the consistency of the discrete method, existence and uniqueness results. To obtain an optimal a priori error estimate, a stabilized fictitious domain method is necessary. These results are numerically validated using Hertz contact in two and three dimensions. The chapter 4 is devoted to the study of a residual-based a posteriori error estimator, without the fictitious domain approach, between an elastic body and rigid obstacle. The numerical study of two tests cases will be performed: a rectangular domain with only a part of the potential zone of contact in effective contact as well as a Hertz contact in two and three dimensions. The chapter 5 is a generalization of the chapter 4 to the fictitious domain approach and the care of to two elastics bodies.

Dans un contexte d'adaptabilité ciblée, l'erreur commise sur une quantité d'intérêt peut être représentée grâce aux erreurs globales des problèmes direct et adjoint. Cette représentation de l'erreur est majorée par la somme des indicateurs d'erreurs élémentaires. Ces derniers sont alors utilisés pour produire des raffinements de maillage optimaux. Dans ces travaux, nous proposons de représenter l’erreur du problème adjoint via un opérateur alternatif. L’avantage principal de notre approche est que lorsque l'on choisit correctement l'opérateur alternatif, la majoration correspondante de l'erreur à la quantité d'intérêt devient plus précise, pour autant l'adaptabilité issue de l'utilisation de ces nouveaux indicateurs s'en trouve améliorée. Ces représentations peuvent être employées pour concevoir des algorithmes adaptatifs en espace (h), en ordre d’approximation (p) ou les deux (hp), basés sur la norme d’énergie ou bien ciblés sur une quantité d'intérêt. Bien que la méthode puisse être appliquée à une large gamme de problèmes, nous nous concentrons tout d’abord sur des problèmes unidimensionnels (1D), comme le problème d’Helmholtz et le problème de convection-diffusion stationnaire à convection dominante. Les résultats numériques en 1D montrent que, pour les problèmes de propagation d'ondes, les avantages de notre méthode sont notoires lorsque l'on considère l'opérateur de Laplace pour la représentation de l'erreur. Plus précisément, les majorations issues de la nouvelle représentation sont plus précises que celles provenant de la méthode classique et ce si l'on considère l'énergie globale ou bien une quantité d'intérêt particulière. Le phénomène est d’autant plus notable lorsque l'erreur de dispersion (pollution) est significative. Le problème 1D de convection-diffusion stationnaire à convection dominante avec des conditions limites de Dirichlet homogènes présente une couche limite qui produit une perte de stabilité numérique. La nouvelle représentation d'erreur délivre des majorations plus précises. Lorsqu’appliquée à une p-adaptabilité ciblée, la représentation d'erreur alternative permet une capture plus efficace la couche limite, malgré les oscillations numériques parasites existantes. Devant ces résultats encourageants, nous nous penchons sur l'équation d'Helmholtz à deux et trois dimensions (2D et 3D). Nous montrons, au travers de multiples simulations numériques, que les majorations fournies par les représentations d'erreur alternatives sont plus précises que celle de la représentation classique. Lorsque l'on utilise les indicateurs d'erreur alternatifs, un processus naïf de p-adaptabilité ciblée converge, tandis que dans les mêmes conditions, la méthode classique échoue et requiert l'utilisation d'un opérateur de projection ou d'autre techniques pour récupérer la convergence. Dans ce travail, nous fournissons également des directives pour déterminer les opérateurs qui fournissent des représentations d’erreur induisant de majorations précises. Des résultats similaires sont aussi établis tant pour un problème 2D de convection-diffusion stationnaire à convection dominante que pour des problèmes 2D ayant des coefficients de matériaux discontinus. Nous considérons un problème de diagraphie ultra-sonique en cours de forage pour illustrer l'applicabilité de la méthode proposée. / In Goal-Oriented Adaptivity (GOA), the error in a Quantity of Interest (QoI) is represented using global error functions of the direct and adjoint problems. This error representation is subsequently bounded above by element-wise error indicators that are used to drive optimal refinements. In this work, we propose to replace, in the error representation, the adjoint problem by an alternative operator. The main advantage of the proposed approach is that, when judiciously selecting such alternative operator, the corresponding upper bound of the error representation becomes sharper, leading to a more efficient GOA. These representations can be employed to design novel h, p, and hp energy-norm and goal-oriented adaptive algorithms. While the method can be applied to a variety of problems, in this Dissertation we first focus on one-dimensional (1D) problems, including Helmholtz and steady state convection-dominated diffusion problems. Numerical results in 1D show that for the Helmholtz problem, it is advantageous to select the Laplace operator for the alternative error representation. Specifically, the upper bounds of the new error representation are sharper than the classical ones used in both energy-norm and goal-oriented adaptive methods, especially when the dispersion (pollution) error is significant. The 1D steady state convection-dominated diffusion problem with homogeneous Dirichlet boundary conditions exhibits a boundary layer that produces a loss of numerical stability. The new error representation based on the Laplace operator delivers sharper error upper bounds. When applied to a p-GOA, the alternative error representation captures earlier the boundary layer, despite the existing spurious numerical oscillations. We then focus on the two- and three-dimensional (2D and 3D) Helmholtz equation. We show via extensive numerical experimentation that the upper bounds provided by the alternative error representations are sharper than the classical ones. When using the alternative error indicators, a naive p-adaptive process converges, whereas under the same conditions, the classical method fails and requires the use of the so-called Projection Based Interpolation (PBI) operator or some other technique to regain convergence. We also provide guidelines for finding operators delivering sharp error representation upper bounds. / En un contexto de adaptatividad orientada a un objetivo, el error en una cantidad de interés está representado a través de los errores globales de los problemas directo y adjunto. Esta representación del error se acota superiormente por una suma de indicadores de error de cada elemento. Estos se utilizan para producir refinamientos óptimos. En este trabajo, proponemos representar el error del problema adjunto utilizando un operador alternativo. La principal ventaja de nuestro enfoque es que cuando se elige correctamente dicho operador alternativo, la correspondiente cota superior se vuelve más cercana al error en la cantidad de interés, lo que permite una adaptatividad más eficiente. Estas representaciones pueden ser utilizadas para diseñar algoritmos adaptativos en h, p o hp, basados en la norma de la energía o para aproximar una cantidad de interés específica. Aunque el método propuesto se puede aplicar a una amplia gama de problemas, en esta tesis doctoral nos centramos primero en problemas unidimensionales (1D), tales como el problema de Helmholtz y el problema estacionario de convección-difusión con convección dominante. Los resultados numéricos en 1D muestran que, para los problemas de propagación de ondas, las ventajas de este método son notorias cuando se considera el operador de Laplace para la representación del error. Específicamente, las cotas superiores derivadas de la nueva representación son más cercanas a la cantidad de interés que las del método convencional. Esto es cierto tanto para la norma de la energía global como para una cantidad de interés particular, especialmente cuando el error de dispersión es significativo. El problema estacionario 1D de convección-difusión con convección dominante y con condiciones de Dirichlet homogéneas tiene una capa límite que produce una pérdida de estabilidad numérica. La nueva representación del error proporciona cotas superiores más cercanas a la cantidad de interés. Cuando se aplica a un algoritmo adaptativo en p orientado a un objetivo, la representación alternativa del error captura antes la capa límite, a pesar de las existentes oscilaciones numéricas no físicas. En esta tesis doctoral, también nos centramos en la ecuación de Helmholtz en dos y tres dimensiones (2D y 3D). Mostramos a través de múltiples experimentos numéricos que las cotas superiores proporcionadas por las representaciones alternativas del error son más cercanas a la cantidad de interés que cuando uno considera la representación clásica. Al utilizar los indicadores alternativos del error, un algoritmo adaptativo en p sencillo converge, mientras que en las mismas condiciones, el método convencional falla y requiere el uso de operadores de proyección o de otras técnicas para recuperar la convergencia. En este trabajo, también determinamos operadores que proporcionan representaciones del error que inducen cotas superiores más ajustadas. Establecemos resultados similares tanto para el problema estacionario de convección-difusión con convección dominante en 2D como para problemas 2D con materiales discontinuos. Finalmente, se considera un problema sónico en pozos petrolíferos para ilustrar la aplicabilidad del método propuesto.

Wind energy technologies are considered to be among the most promising types of renewable energy sources, which have since attracted broad considerations through recent years due to the soaring oil prices and the growing concerns over climate change and energy security. In Kuwait, rapid industrialisation, population growth and increasing water desalination are resulting in high energy demand growth, increasing the concern of oil diminishing as a main source of energy and the climate change caused by CO2 emissions from fossil fuel based energy. These demands and challenges compelled governments to embark on a diversification strategy to meet growing energy demand and support continued economic growth. Kuwait looked for alternative forms of energy by assessing potential renewable energy resources, including wind and sun. Kuwait is attempting to use and invest in renewable energy due to the fluctuating price of oil, diminishing reserves, the rapid increase in population, the high consumption of electricity and the environment protection. In this research, wind energy will be investigated as an attractive source of energy in Kuwait.

Este trabalho descreve um modelo matemático para simulação da laringe humana durante a fonação. O objetivo foi produzir uma técnica computacional de grande escala de processamento para capturar os fenômenos fisiológicos que ocorrem na laringe durante a vocalização e servir de base para estudos mais aprofundados sobre esta importante estrutura do corpo humano. Usando o método dos elementos finitos como base para discretizar as equações dos tecidos musculares da laringe e das equações de Navier-Stokes, e um modelo de descrição da colisão entre as pregas vocais, o sinal glotal foi obtido a partir de diferentes geometrias de laringes com diferentes propriedades viscoelásticas. Os resultados confirmaram a teoria mioelástica-aerodinâmica que descreve a dinâmica da fonação, reproduzindo inclusive fenômenos fisiológicos que os modelos existentes são incapazes de simular. Estudos adicionais foram feitos para verificar a viabilidade do modelo para simular algumas doenças que danificam a laringe. / This work describes a mathematical model to simulate the human larynx during a phonation. The objective was to produce a large-scale computational technique to capture several physiological phenomena that take place on the larynx during the vocalization and to assist further studies about this important structure of the human body. Using the finite element methods as the way to discretize the muscle tissue equations of the larynx and the Navier-Stokes equations and a model to describe the collision between both vocal folds, the glottal signal for different larynx geometries with different viscoelastic properties was obtained. The results confirmed the myoelastic-aerodynamic theory which describes the dynamic of the phonation, also reproducing physiologic phenomena that current models are unable to simulate. Additional studies were conducted to confirm the feasibility of the model to simulate some diseases that affect the larynx.

In our age in which the use of electronic devices is expanding all over the world, their reliability and miniaturization have become very crucial. The thesis is based on the study of one of the most frequent failure mechanisms in semiconductor packages, the delamination of interface or the separation of two bonded materials, in order to improve their adhesion and a fortiori the reliability of microelectronic devices. It focuses on the metal (-oxide) / polymer interfaces because they cover 95% of all existing interfaces. Since several years, research activities at mesoscopic scale (1-10µm) have proved that the more roughened the surface of the interface, i.e., presenting sharp asperities, the better the adhesion between these two materials. Because roughness exhibits extremely complex shapes, it is difficult to find a description that can be used for reliability analysis of interfaces. In order to investigate quantitatively the effect of roughness variation on adhesion properties, studies have been carried out involving analytical fracture mechanics; then numerical studies were conducted with Finite Element Analysis. Both were done in a deterministic way by assuming an ideal profile which is repeated periodically. With the development of statistical and stochastic roughness representation on the one hand, and with the emergence of probabilistic fracture mechanics on the other, the present work adds a stochastic framework to the previous studies. In fact, one of the Stochastic Finite Element Methods, the Perturbation method is chosen for implementation, because it can investigate the effect of the geometric variations on the mechanical response such as displacement field. In addition, it can carry out at once what traditional Finite Element Analysis does with numerous simulations which require changing geometric parameters each time. This method is developed analytically, then numerically by implementing a module in a Finite Element package MSc. Marc/Mentat. In order to get acquainted and to validate the implementation, the Perturbation method is applied analytically and numerically to the 3 point bending test on a beam problem, because the input of the Perturbation method in terms of roughness parameters is still being studied. The capabilities and limitations of the implementation are outlined. Finally, recommendations for using the implementation and for furture work on roughness representation are discussed.

The continuously increasing demand for clean renewable energy has rekindled interest in multi-terminal high voltage direct current (HVDC) grids. Although such grids have several advantages and a great potential, their materialization has been thwarted due to the absence of HVDC breakers. In comparison with traditional alternating current (AC) breakers, they should operate and interrupt fault currents in a time frame of a few milliseconds. The aim of this thesis is focused on the design of ultra-fast electro-mechanical actuator systems suitable for such HVDC breakers.Initially, holistic multi-physics and hybrid models with different levels of complexity and computation time were developed to simulate the entire switch. These models were validated by laboratory experiments. Following a generalized analysis, in depth investigations involving simulations complemented with experiments were carried out on two of the sub-components of the switch: the ultra-fast actuator and the damper. The actuator efficiency, final speed, peak current, and maximum force were explored for different design data.The results show that models with different levels of complexity should be used to model the entire switch based on the magnitude of the impulsive forces. Deformations in the form of bending or elongation may deteriorate the efficiency of the actuator losing as much as 35%. If that cannot be avoided, then the developed first order hybrid model should be used since it can simulate the behavior of the mechanical switch with a very good accuracy. Otherwise, a model comprising of an electric circuit coupled to an electromagnetic FEM model with a simple mechanics model, is sufficient.It has been shown that using a housing made of magnetic material such as Permedyn, can boost the efficiency of an actuator by as much as 80%. In light of further optimizing the ultra-fast actuator, a robust optimization algorithm was developed and parallelized. In total, 20520 FEM models were computed successfully for a total simulation time of 7 weeks. One output from this optimization was that a capacitance of 2 mF, a charging voltage of 1100 V and 40 turns yields the highest efficiency (15%) if the desired velocity is between 10 m/s and 12 m/s.The performed studies on the passive magnetic damper showed that the Halbach arrangement gives a damping force that is two and a half times larger than oppositely oriented axially magnetized magnets. Furthermore, the 2D optimization model showed that a copper thickness of 1.5 mm and an iron tube that is 2 mm thick is the optimum damper configuration. / <p>QC 20150422</p>

Le mouvement de Séchilienne est situé à une trentaine de kilomètre au sud-est de l'agglomération grenobloise sur la bordure Sud du Massif de Belledonne. Il affecte le versant rocheux en rive droite de la vallée alpine de la Romanche façonné par les nombreux cycles de glaciation et déglaciation et qui lors de la dernière phase glaciaire a été complètement recouvert par le glacier. Le raidissement des pentes et l'approfondissement du pied du versant associés au phénomène de décompression affectant le versant et correspondant au relâchement des contraintes liées à la disparition progressive du glacier seraient donc les facteurs prédominants dans l'initiation et l'évolution du mouvement de Séchilienne. Les récentes contraintes temporelles obtenues sur l'escarpement sommital ont cependant montré une initiation différée du mouvement par rapport à la déglaciation et suggèrent une initiation lors de l'Optimum climatique de l'Holocène suite à une modification brusque du climat. L'initiation et l'évolution de grands mouvements de versants rocheux en domaine montagneux peuvent être le résultat de la contribution de différents facteurs géologiques (la fracturation, la lithologie ou le régime tectonique), géomorphologiques (relief, pente) mais également de facteurs de forçage externe tels que les séismes, le pergélisol, les variations hydrologiques, le retrait du glacier ou encore les effets climatiques. Ces facteurs étant tous potentiellement actifs sur le mouvement de Séchilienne, l'identification des facteurs contrôlant l'initiation et l'évolution du mouvement et pouvant expliquer le délai observé entre la déglaciation et l'initiation du mouvement est donc délicate.Nous avons donc pour cela mené une étude multidisciplinaire permettant à partir (1) des données géophysiques et d'essais en laboratoire de déterminer en profondeur les limites du mouvement et d'évaluer le volume déstabilisé ainsi que son état de déstructuration, (2) d'une analyse de la structure détaillée du versant en surface et en profondeur de préciser l'origine des fractures observées mais également leur rôle de contrôle sur le mouvement (3) d'une analyse géomorphologique des objets présents à la surface du versant, d'identifier de discrétiser et de sélectionner les structures glaciaires et gravitaires sur lesquels nous avons par la suite appliqué la méthode de datation permettant ainsi d'obtenir le modèle cinématique du retrait du glacier de la Romanche le long du versant de Séchilienne et de l'initiation et de l'évolution du mouvement (4) d'une modélisation thermique du versant basée sur la courbe d'évolution des températures reconstruite depuis la dernière phase glaciaire quaternaire de caractériser la géométrie et la persistance du pergélisol depuis la dernière phase glaciaire jusqu'à la période actuelle.La confrontation de l'ensemble de ces résultats et leur replacement dans le contexte climatique régnant depuis la dernière phase glaciaire il ya 21000ans jusqu'à l'actuelle permet ainsi de proposer un modèle conceptuel de l'initiation et de l'évolution du mouvement de Séchilienne et du rôle des différents facteurs étudiés. Le mouvement se serait donc initié suite à la décompression du versant en réponse au retrait du glacier. La mise en place et le développement du pergélisol au sein du versant aurait cependant limité la propagation du mouvement en renforçant mécaniquement le versant. Son action ne c'est cependant pas limitée à renforcer le versant mais aurait également sur une échelle de temps plus importante favoriser l'endommagement et l'affaiblissement mécanique de la zone affecté imposant ainsi au mouvement sa géométrie actuelle. / The Sechilienne landslide is located thirty kilometers at the Southeast of Grenoble on the Southern edge of the massif of Belledonne. It affects the rock slope on the right bank of the Romanche alpine valley shaped by many cycles of glaciation and deglaciation and which was completely covered by the glacier during the last glacial phase. The oversteepening of the slopes and the deepening of the foot of the slope associated with the phenomenon of debutressing affecting the slope and corresponding to the lateral stress release resulting from ice melting would be so predominant factors in the initiation and development of the Sechilienne landslide. However the recent temporal constraints obtained on the scarp showed a delayed motion relative to the initiation and deglaciation suggest initiation during the Holocene climatic Optimum after a sudden climate change. The initiation and evolution of large movements of rock slopes in mountainous area may be the result of the contribution of different geological factors (fracturing , lithology or tectonic regime) , geomorphology (relief, slope) but also external forcing factors such as earthquakes , permafrost , hydrological changes , the glacier disappearance or climatic effects. These factors are all potentially active in the Sechilienne landslide, so the identification of factors controlling the initiation and development of the movement and which can explain the delay observed between deglaciation and the initiation of movement is tricky.Therefore, we conducted a multidisciplinary study from (1) geophysical data and laboratory tests to determine the depth limits of the mass movement and to assess the volume and the breakdown state, (2) an analysis of the detailed structures of the slope at the surface and in depth to identify the origin of the observed fractures and also their role in the control of the movement (3) a geomorphological analysis of objects on the surface of the slope to discretize , to identify and to select the glacial and gravitational structures on which then we applied the datation method to obtain the kinematic model of the Romanche glacier retreat along the slope of Séchilienne and of the initiation and the evolution of the movement (4) a thermal modeling of the slope based on the temperature curve proposed since the last quaternary glacial stage to characterize the geometry and the persistence of permafrost since the last glacial phase to the current period.The comparison of all these results and their replacement in the climatic conditions prevailing since the last glacial stage 21000 years ago to the present, allows to propose a conceptual model for the initiation and the evolution of Séchilienne landslide and the role of the various studied factors. So, the landslide would be initiated by slope debutressing in response to the glacier retreat. However the establishment and the development of the permafrost within the slope would limit the propagation of the movement by reinforcing mechanically the slope.

Este trabalho descreve um modelo matemático para simulação da laringe humana durante a fonação. O objetivo foi produzir uma técnica computacional de grande escala de processamento para capturar os fenômenos fisiológicos que ocorrem na laringe durante a vocalização e servir de base para estudos mais aprofundados sobre esta importante estrutura do corpo humano. Usando o método dos elementos finitos como base para discretizar as equações dos tecidos musculares da laringe e das equações de Navier-Stokes, e um modelo de descrição da colisão entre as pregas vocais, o sinal glotal foi obtido a partir de diferentes geometrias de laringes com diferentes propriedades viscoelásticas. Os resultados confirmaram a teoria mioelástica-aerodinâmica que descreve a dinâmica da fonação, reproduzindo inclusive fenômenos fisiológicos que os modelos existentes são incapazes de simular. Estudos adicionais foram feitos para verificar a viabilidade do modelo para simular algumas doenças que danificam a laringe. / This work describes a mathematical model to simulate the human larynx during a phonation. The objective was to produce a large-scale computational technique to capture several physiological phenomena that take place on the larynx during the vocalization and to assist further studies about this important structure of the human body. Using the finite element methods as the way to discretize the muscle tissue equations of the larynx and the Navier-Stokes equations and a model to describe the collision between both vocal folds, the glottal signal for different larynx geometries with different viscoelastic properties was obtained. The results confirmed the myoelastic-aerodynamic theory which describes the dynamic of the phonation, also reproducing physiologic phenomena that current models are unable to simulate. Additional studies were conducted to confirm the feasibility of the model to simulate some diseases that affect the larynx.