[pt] Em problemas geotécnicos podem ocorrer grandes deformações devido a chuvas prolongadas, sismos, deslizamentos de encostas, etc. Material point method (MPM) é um método de solução baseado no Método dos Elementos Finitos (MEF) que oferece vantagens para o cálculo estático e dinâmico que envolve deformações desse tipo. O objetivo desta dissertação é utilizar o MPM em problemas geotécnicos em condições estáticas e dinâmicas. Esta pesquisa mostra o procedimento de analises do MPM para a condição não acoplada (só solido sem presença de água) e depois acoplada. Para a revisão matemática de MPM se faz antes um resumo da teoria do MEF na metodologia de conservação de quantidade de movimento. Nestas duas formas de resolver os problemas geotécnicos foram expostos três exemplos simples. O primeiro é uma coluna de solo simulado sob os fundamentos da elasticidade, com o objetivo de verificar o deslocamento vertical pelo peso próprio. Isto foi resolvido mediante quatro diferentes métodos: analítica, MEF por resíduos ponderados, MEF por conservação de quantidade de movimento, e MPM. Todos eles consideram somente a fase solida. No segundo exemplo, tem-se solo na geometria de quadrado de lado 1 metro, onde busca-se obter as poropressões quando atingir a condição permanente enquanto os deslocamentos ocorrem ao longo do tempo; ou seja, a análise é acoplada e é resolvida pelo método MPM. Para uma aplicação mais realista, foi feita a análise (não acoplada) da barragem Palo Redondo, pertencente ao projeto Chavimochic, localizada na região de La Libertad, Perú. Nesta análise dinâmica considerou-se dois modelos constitutivos: Elástico e Mohr Coulomb, além de um sismo. / [en] In geotechnical problems can happen large strains because of prolonged rains, earthquake, slide slope, etc. Material point method is a solution method based on the finite element method (FEM) which offers advantages for static and dynamic calculation that involve that kind of strains. The objective in this dissertation is to use the MPM in geotechnical problems in statics and dynamics conditions. This research shows the analysis procedure of MPM for uncoupled condition (only solids, without water) and then coupled. Before the mathematical theory of MPM, a review of the theory of FEM in the conservation of quantidade de movimento is done. In this two methodology were raised three examples. The first one is a soil column that was modeled elastically, in which the main objective in to analyze the vertical displacement because of own weight. This was solved by four different methods: analytically, FEM weighted residual, FEM conservation of momentum, and MPM. All of them consider only the solid phase. The second example is a square of soil with side 1 meter, where the objective is to know the pore-pressure in the permanent condition and at the same time the vertical displacement were generated, it means that the analysis is coupled and were solved by MPM. In order to make a more realistic application, Palo Redondo dam is analyzed (uncoupled condition), which belongs to the Chavimochic project located in La Libertad, region of Perú. This dynamic analysis was done considering two constitutive models: Elastic and Mohr Coulomb, additionally seismic forces.

O presente trabalho consiste no uso do Método dos Elementos Finitos (MEF) para a análise de interação fluido-estruturas de barras com foco em problemas transientes envolvendo explosões ou outras ações com propagação de ondas de choque. Para isso é necessário o estudo de três diferentes aspectos: a dinâmica das estruturas computacional, a dinâmica dos fluidos computacional e o problema do acoplamento. No caso da dinâmica das estruturas computacional deve-se identificar em função da cinemática de deformações, quais são os requisitos para que um elemento seja adequado para analisar tais problemas, tendo em vista que a formulação deve admitir grandes deslocamentos. Para evitar problemas relacionados com aproximações de rotações finitas, opta-se por empregar uma formulação descrita em termos de posições e que leva em consideração os efeitos de empenamento da seção transversal. No caso da dinâmica dos fluidos computacional, busca-se uma formulação para escoamentos compressíveis que seja estável e ao mesmo tempo sensível ao movimento da estrutura, sendo empregado um algoritmo de integração temporal explícito baseado em características com as equações governantes descritas na forma Lagrangeana-Euleriana Arbitrária (ALE). No que se refere ao acoplamento, busca-se modularidade e versatilidade, empregando-se um modelo particionado fraco (explícito) de acoplamento e técnicas de transferência das condições de contorno (Dirichlet-Neummann), sendo estudados os efeitos de utilizar transferência bidirecional ou unidirecional dessas condições de contorno. / This work consists in the use of the Finite Element Method (FEM) for numerical analysis of fluid-bar structures, focusing on transient problems involving explosions or other actions with shock waves propagation. For this purpose, one needs to study three different aspects: the computational structural dynamics, the computational fluid dynamics and the coupling problem. Regarding computational structural dynamics, one need firstly to identify the requirements for an element to be adequate to analyze such problems, taking into account the fact that such element should admit large displacements. In order to avoid problems related to finite rotation approximations and to give a realist representation of a 3D bar structure, we chose a formulation defined in terms of positions and that considers the cross-section warping effects. Regarding computational fluid dynamics, we seek for a stable formulation for compressible flows, and at same time, sensitive to the movement of the structure, leading to an explicit time integration algorithm based on characteristics with governing equations described in the Arbitrary Lagrangian-Eulerian (ALE) form. Regarding to coupling, we chose to use a weak (explicit) partitioning coupling model in order to ensure modularity and versatility. The developed coupling scheme is bases on boundary conditions transfer techniques (Dirichlet-Neummann), and we study the effects of using bidirectional or unidirectional boundary conditions transfers.

We present three new stabilized finite element (FE) based Petrov-Galerkin methods for the convection-diffusionreaction (CDR), the Helmholtz and the Stokes problems, respectively. The work embarks upon a priori analysis of a consistency recovery procedure for some stabilization methods belonging to the Petrov- Galerkin framework. It was ound that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not appropriate when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov-Galerkin (HRPG) method for the CDR problem. The structure of the method in 1 D is identical to the consistent approximate upwind (CAU) Petrov-Galerkin method [doi: 10.1016/0045-7825(88)90108-9] except for the definitions of he stabilization parameters. Such a structure may also be attained via the Finite Calculus (FIC) procedure [doi: 10.1 016/S0045-7825(97)00119-9] by an appropriate definition of the characteristic length. The prefix high-resolution is used here in the sense popularized by Harten, i.e. second order accuracy for smooth/regular regimes and good shock-capturing in non-regular re9jmes. The design procedure in 1 D embarks on the problem of circumventing the Gibbs phenomenon observed in L projections. Next, we study the conditions on the stabilization parameters to ircumvent the global oscillations due to the convective term. A conjuncture of the two results is made to deal with the problem at hand that is usually plagued by Gibbs, global and dispersive oscillations in the numerical solution. A multi dimensional extension of the HRPG method using multi-linear block finite elements is also presented. Next, we propose a higher-order compact scheme (involving two parameters) on structured meshes for the Helmholtz equation. Making the parameters equal, we recover the alpha-interpolation of the Galerkin finite element method (FEM) and the classical central finite difference method. In 1 D this scheme is identical to the alpha-interpolation method [doi: 10.1 016/0771 -050X(82)90002-X] and in 2D choosing the value 0.5 for both the parameters, we recover he generalized fourth-order compact Pade approximation [doi: 10.1 006/jcph.1995.1134, doi: 10.1016/S0045- 7825(98)00023-1] (therein using the parameter V = 2). We follow [doi: 10.1 016/0045-7825(95)00890-X] for the analysis of this scheme and its performance on square meshes is compared with that of the quasi-stabilized FEM [doi: 10.1016/0045-7825(95)00890-X]. Generic expressions for the parameters are given that guarantees a dispersion accuracy of sixth-order should the parameters be distinct and fourth-order should they be equal. In the later case, an expression for the parameter is given that minimizes the maximum relative phase error in 2D. A Petrov-Galerkin ormulation that yields the aforesaid scheme on structured meshes is also presented. Convergence studies of the error in the L2 norm, the H1 semi-norm and the I ~ Euclidean norm is done and the pollution effect is found to be small. / Presentamos tres nuevos metodos estabilizados de tipo Petrov- Galerkin basado en elementos finitos (FE) para los problemas de convecci6n-difusi6n- reacci6n (CDR), de Helmholtz y de Stokes, respectivamente. El trabajo comienza con un analisis a priori de un metodo de recuperaci6n de la consistencia de algunos metodos de estabilizaci6n que pertenecen al marco de Petrov-Galerkin. Hallamos que el uso de algunas de las practicas estandar (por ejemplo, la eoria de Matriz-M) para el diserio de metodos numericos esencialmente no oscilatorios no es apropiado cuando utilizamos los metodos de recu eraci6n de la consistencia. Por 10 tanto, con res ecto a la estabilizaci6n de conveccion, no preferimos tales metodos de recuperacion . A continuacion, presentamos el diser'io de un metodo de Petrov-Galerkin de alta-resolucion (HRPG) para el problema CDR. La estructura del metodo en 10 es identico al metodo CAU [doi: 10.1016/0045-7825(88)90108-9] excepto en la definicion de los parametros de estabilizacion. Esta estructura tambien se puede obtener a traves de la formulacion del calculo finito (FIC) [doi: 10.1 016/S0045- 7825(97)00119-9] usando una definicion adecuada de la longitud caracteristica. El prefijo de "alta-resolucion" se utiliza aqui en el sentido popularizado por Harten, es decir, tener una solucion con una precision de segundo orden en los regimenes suaves y ser esencialmente no oscilatoria en los regimenes no regulares. El diser'io en 10 se embarca en el problema de eludir el fenomeno de Gibbs observado en las proyecciones de tipo L2. A continuacion, estudiamos las condiciones de los parametros de estabilizacion para evitar las oscilaciones globales debido al ermino convectivo. Combinamos los dos resultados (una conjetura) para tratar el problema COR, cuya solucion numerica sufre de oscilaciones numericas del tipo global, Gibbs y dispersiva. Tambien presentamos una extension multidimensional del metodo HRPG utilizando los elementos finitos multi-lineales. fa. continuacion, proponemos un esquema compacto de orden superior (que incluye dos parametros) en mallas estructuradas para la ecuacion de Helmholtz. Haciendo igual ambos parametros, se recupera la interpolacion lineal del metodo de elementos finitos (FEM) de tipo Galerkin y el clasico metodo de diferencias finitas centradas. En 10 este esquema es identico al metodo AIM [doi: 10.1 016/0771 -050X(82)90002-X] y en 20 eligiendo el valor de 0,5 para ambos parametros, se recupera el esquema compacto de cuarto orden de Pade generalizada en [doi: 10.1 006/jcph.1 995.1134, doi: 10.1 016/S0045-7825(98)00023-1] (con el parametro V = 2). Seguimos [doi: 10.1 016/0045-7825(95)00890-X] para el analisis de este esquema y comparamos su rendimiento en las mallas uniformes con el de "FEM cuasi-estabilizado" (QSFEM) [doi: 10.1016/0045-7825 (95) 00890-X]. Presentamos expresiones genericas de los para metros que garantiza una precision dispersiva de sexto orden si ambos parametros son distintos y de cuarto orden en caso de ser iguales. En este ultimo caso, presentamos la expresion del parametro que minimiza el error maxima de fase relativa en 20. Tambien proponemos una formulacion de tipo Petrov-Galerkin ~ue recupera los esquemas antes mencionados en mallas estructuradas. Presentamos estudios de convergencia del error en la norma de tipo L2, la semi-norma de tipo H1 y la norma Euclidiana tipo I~ y mostramos que la perdida de estabilidad del operador de Helmholtz ("pollution effect") es incluso pequer'ia para grandes numeros de onda. Por ultimo, presentamos una coleccion de metodos FE estabilizado para el problema de Stokes desarrollados a raves del metodo FIC de primer orden y de segundo orden. Mostramos que varios metodos FE de estabilizacion existentes y conocidos como el metodo de penalizacion, el metodo de Galerkin de minimos cuadrados (GLS) [doi: 10.1016/0045-7825(86)90025-3], el metodo PGP (estabilizado a traves de la proyeccion del gradiente de presion) [doi: 10.1 016/S0045-7825(96)01154-1] Y el metodo OSS (estabilizado a traves de las sub-escalas ortogonales) [doi: 10.1016/S0045-7825(00)00254-1] se recuperan del marco general de FIC. Oesarrollamos una nueva familia de metodos FE, en adelante denominado como PLS (estabilizado a traves del Laplaciano de presion) con las formas no lineales y consistentes de los parametros de estabilizacion. Una caracteristica distintiva de la familia de los metodos PLS es que son no lineales y basados en el residuo, es decir, los terminos de estabilizacion dependera de los residuos discretos del momento y/o las ecuaciones de incompresibilidad. Oiscutimos las ventajas y desventajas de estas tecnicas de estabilizaci6n y presentamos varios ejemplos de aplicacion

Ce travail s'inscrit dans la compréhension du comportement de la sous-surface d'une pièce présentant des hétérogénéités contrôlées, soumise à un chargement de type hertzien sans affecter l'intégrité de sa surface initiale. Le but est de qualifier le champ de contraintes en sous couche. Pratiquement, des défauts de forme cylindrique sont positionnés là où le champ de contraintes est maximal. Le contact est dimensionné pour pouvoir observer, par photoélasticimétrie, les évolutions du champ de contraintes et développer une modélisation numérique pour étudier le comportement statique puis dynamique. Il ressort que la présence d'un trou sur l'axe de symétrie z (x = 0) est le facteur prépondérant. Les caractéristiques qui permettent de diminuer la contrainte de cisaillement sur l'axe de symétrie sont celles qui conduisent à un renforcement de la contrainte de cisaillement maximale dans le massif. Cette dualité nous conduit à proposer un indicateur qui prend en compte, à la fois, la contrainte de cisaillement, l'aplomb du contact et l"évolution de la contrainte maximale dans le massif. La méthodologie de travail a été mise en oeuvre et validée. Les approches analytiques et expérimentales ont permis de valider les modélisations numériques qui sont seules à même de permettre l'étude de nombreux cas. Les perspectives sont nombreuses, avec des incursions possibles en structuration de sous-surfaces, perçage simple, frittage sélectif par laser. Ce doctorat a permis de traiter le cas des défauts circulaires. Dans un autre domaine, le soudage est également un cas d'intérêt pour l'étude du comportement des cordons de soudure présentant des défauts de type porosités ou inclusions.

Les phénomènes de couplage électromagnétique entre les lignes aériennes de transmission d'énergie et des structures voisines sont inévitables, surtout dans les zones densément peuplées. Les effets indésirables découlants de cette proximité sont variés, allant de l'établissement des tensions dangereuses à l'apparition de phénomènes de corrosion dus au courant alternatif. L'étude de cette classe de problèmes est nécessaire pour assurer la sécurité dans les alentours de la zone d'interaction et aussi pour préserver l'intégrité des équipements et des dispositifs présents. Cependant, la modélisation complète de ce type d'application implique la représentation tridimensionnelle de la région d'intérêt et nécessite des méthodes numériques de calcul de champs spécifiques. Dans ces travaux, des problèmes liés à la circulation de courants électriques dans le sol (ou de couplage dit conductif) seront abordés avec la méthode des éléments finis. D'autres problèmes résultants de la variation temporelle des champs électromagnétiques (ou de couplage dit inductif) seront aussi considérés et traités avec la méthode PEEC (Partial Element Equivalent Circuit) généralisée. Plus précisément, une condition limite particulière sur le potentiel électrique est proposée pour tronquer le domaine de calcul dans l'analyse par éléments finis des problèmes de couplage conductif et une formulation PEEC complète pour la modélisation de problèmes de couplage inductif est présentée. Des configurations tests de complexités croissantes sont considérées pour valider les approches précédentes. Ces travaux visent ainsi à apporter une contribution à la modélisation de cette classe de problèmes, qui tendent à devenir communs avec l'expansion des réseaux électriques. / Electromagnetic coupling phenomena between overhead power transmission lines and other nearby structures are inevitable, especially in densely populated areas. The undesired effects resulting from this proximity are manifold and range from the establishment of hazardous potentials to the outbreak of alternate current corrosion phenomena. The study of this class of problems is necessary for ensuring security in the vicinities of the interaction zone and also to preserve the integrity of equipment and devices there present. However, the complete modeling of this type of application requires the three-dimensional representation of the region of interest and needs specific numerical methods for field computation. In this work, the modeling of problems arising from the flow of electrical currents in the ground (the so-called conductive coupling) will be addressed with the finite element method. Those resulting from the time variation of the electromagnetic fields (the so-called inductive coupling) will be considered as well, and they will be treated with the generalized PEEC (Partial Element Equivalent Circuit) method. More specifically, a special boundary condition on the electric potential is proposed for truncating the computational domain in the finite element analysis of conductive coupling problems, and a complete PEEC formulation for modeling inductive coupling problems is presented. Test configurations of increasing complexities are considered for validating the foregoing approaches. These works aim to provide a contribution to the modeling of this class of problems, which tend to become common with the expansion of power grids. / Fenômenos de acoplamento eletromagnético entre linhas aéreas de transmissão de energia e outras estruturas vizinhas são inevitáveis, sobretudo emáreas densamente povoadas. Os efeitos indesejados decorrentes desta proximidadesão variados, indo desde o estabelecimento de potenciais perigosos até o surgimento de processos de corrosão por corrente alternada. O estudo desta classe de problemas é necessária para a garantia da segurança nas imediações da zona de interação e também para se preservar a integridade de equipamentos e dispositivos ali presentes. Entretanto, a modelagem completa deste tipo de aplicação requer a representação tridimensional da região de interesse e necessita de métodos numéricos de cálculo de campos específicos. Neste trabalho, serão abordadas as modelagens de problemas decorrentes da circulação de correntes elétricas no solo (ditos de acoplamentocondutivo) com o método dos elementos finitos. Também serão considerados problemas produzidos pela variação temporal dos campos eletromagnéticos (ditos de acoplamento indutivo), que serão tratados com o método PEEC(Partial Element Equivalent Circuit) generalizado. Mais especificamente, uma condição de contorno particular sobre o potencial elétrico é proposta para o truncamento do domínio de cálculo na análise de problemas de acoplamento condutivo com o método dos elementos finitos, e uma formulação completa tipo PEEC para a modelagem de problemas de acoplamento indutivo é apresentada. Problemas teste de complexidades crescentes são considerados para a validação das abordagens precedentes. Estes trabalhos visam fornecer desta forma uma contribuição à modelagem desta classe de problemas, que tendem a se tornar comuns com a expansão das redes elétricas.

Made available in DSpace on 2014-12-17T14:57:46Z (GMT). No. of bitstreams: 1 JohnENV.pdf: 2614116 bytes, checksum: 0c3230c680d60ac346167f3aa79669e3 (MD5) Previous issue date: 2004-06-04 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / The investigation of viability to use containers for Natural Gas Vehicle (NGV) storage, with different geometries of commercial standards, come from necessity to join the ambient, financial and technological benefits offered by the gas combustion, to the convenience of not modify the original proposal of the automobile. The use of these current cylindrical models for storage in the converted vehicles is justified by the excellent behavior that this geometry presents about the imposed tensions for the high pressure that the related reservoirs are submitted. However, recent research directed toward application of adsorbent materials in the natural gas reservoirs had proven a substantial redusction of pressure and, consequently, a relief of the tensions in the reservoirs. However, this study considers alternative geometries for NGV reservoirs, searching the minimization of dimensions and weight, remaining capacity to resist the tensions imposed by the new pressure situation. The proposed reservoirs parameters are calculated through a mathematical study of the internal pressure according to Brazilian standards (NBR) for pressure vessels. Finally simulations of the new geometries behavior are carried through using a commercially avaible Finite Element Method (FEM) software package ALGOR? to verify of the reservoirs efficincy under the gas pressure load / A investiga??o da viabilidade de se utilizar recipientes para armazenamento de g?s natural veicular (GNV), com geometrias diferentes dos padr?es comerciais, parte da necessidade de se aliar os benef?cios ambientais, financeiros e tecnol?gicos oferecidos pela combust?o do g?s, ? conveni?ncia de n?o se alterar a proposta original do autom?vel. O uso dos atuais modelos cil?ndricos para estocagem nos ve?culos convertidos justifica-se pelo excelente comportamento que essa geometria apresenta diante das tens?es provocadas pela alta press?o a que os referidos reservat?rios est?o submetidos. Entretanto, recentes pesquisas, voltadas para aplica??o de materiais adsorventes nos reservat?rios de g?s natural, comprovaram uma substancial redu??o de press?o e, consequentemente, um al?vio das tens?es nos reservat?rios. Diante desse contexto, este estudo prop?e geometrias alternativas para os reservat?rios de GNV buscando a minimiza??o das dimens?es e do peso, mantendo-se, por?m, a capacidade de resistir ?s tens?es impostas pela nova situa??o de press?o. Todos os par?metros geom?tricos dos reservat?rios propostos s?o calculados realizando o estudo matem?tico das tens?es internas de trabalho tomando como base ? norma brasileira (NBR). Por ?ltimo s?o realizadas simula??es do comportamento das novas geometrias fazendo uso do software comercial ALGOR? o qual se baseia no M?todo dos Elementos Finitos (MEF), para realizar a comprova??o da efici?ncia dos reservat?rios sob a press?o imposta pelo g?s

O presente trabalho consiste no uso do Método dos Elementos Finitos (MEF) para a análise de interação fluido-estruturas de barras com foco em problemas transientes envolvendo explosões ou outras ações com propagação de ondas de choque. Para isso é necessário o estudo de três diferentes aspectos: a dinâmica das estruturas computacional, a dinâmica dos fluidos computacional e o problema do acoplamento. No caso da dinâmica das estruturas computacional deve-se identificar em função da cinemática de deformações, quais são os requisitos para que um elemento seja adequado para analisar tais problemas, tendo em vista que a formulação deve admitir grandes deslocamentos. Para evitar problemas relacionados com aproximações de rotações finitas, opta-se por empregar uma formulação descrita em termos de posições e que leva em consideração os efeitos de empenamento da seção transversal. No caso da dinâmica dos fluidos computacional, busca-se uma formulação para escoamentos compressíveis que seja estável e ao mesmo tempo sensível ao movimento da estrutura, sendo empregado um algoritmo de integração temporal explícito baseado em características com as equações governantes descritas na forma Lagrangeana-Euleriana Arbitrária (ALE). No que se refere ao acoplamento, busca-se modularidade e versatilidade, empregando-se um modelo particionado fraco (explícito) de acoplamento e técnicas de transferência das condições de contorno (Dirichlet-Neummann), sendo estudados os efeitos de utilizar transferência bidirecional ou unidirecional dessas condições de contorno. / This work consists in the use of the Finite Element Method (FEM) for numerical analysis of fluid-bar structures, focusing on transient problems involving explosions or other actions with shock waves propagation. For this purpose, one needs to study three different aspects: the computational structural dynamics, the computational fluid dynamics and the coupling problem. Regarding computational structural dynamics, one need firstly to identify the requirements for an element to be adequate to analyze such problems, taking into account the fact that such element should admit large displacements. In order to avoid problems related to finite rotation approximations and to give a realist representation of a 3D bar structure, we chose a formulation defined in terms of positions and that considers the cross-section warping effects. Regarding computational fluid dynamics, we seek for a stable formulation for compressible flows, and at same time, sensitive to the movement of the structure, leading to an explicit time integration algorithm based on characteristics with governing equations described in the Arbitrary Lagrangian-Eulerian (ALE) form. Regarding to coupling, we chose to use a weak (explicit) partitioning coupling model in order to ensure modularity and versatility. The developed coupling scheme is bases on boundary conditions transfer techniques (Dirichlet-Neummann), and we study the effects of using bidirectional or unidirectional boundary conditions transfers.

Actuellement, les technologies sont de plus en plus performantes. Elles progressent de jour en jour et la miniaturisation des composants est de plus en plus présente. Dans ce contexte, les structures innovantes dites intelligentes sont de plus en plus utilisées et leurs dimensions diminuent très vite. Les matériaux piézo-électriques ou électro-magnéto-élastiques ont la capacité de changer de forme lorsqu'ils sont soumis à un champ électrique ou magnétique. Ces matériaux diélectriques peuvent servir comme corps actif dans les capteurs, les transducteurs, les oscillateurs ou encore d'autres éléments actifs. D'un côté, ces matériaux actifs de très petites tailles sont utilisés dans les petits appareils et d'un autre côté, ils utilisent une forte tension électrique afin de provoquer un déplacement maximal et/ou une force d'arrêt. Les structures actives intelligentes sont exposées à différents défauts, tels que le décollement ou le délaminage. Ces défauts peuvent apparaître lors de la fabrication du matériau ou lors de sa mise en service. Les risques de rupture sont alors accrus et la durée de vie utile de la structure est par conséquent fortement diminuée. La rupture par délaminage peut être de plusieurs types : l'apparition d'une fissure dans la couche adhésive ou dans la résine, une fissure provoquée par un décollement à l'interface entre la résine et le renfort. La défaillance qu'elle soit de nature électrique ou mécanique, provoquée par un claquage électrique ou une fissure qui se propage est un problème primordial qui a une influence importante sur la performance et la fiabilité de ces matériaux. Ce travail vise à développer un modèle de fissuration en considérant des conditions aux limites physiques et des chargements externes combinés, à la fois électriques et mécaniques. Si on se réfère au cours de mécanique de la rupture linéaire, la présence d'une fissure provoque des singularités en termes de contraintes en pointe de fissure. Egalement, il est connu que le champ électrique au niveau du front de la fissure est plus grand que sa valeur critique et ceci peut être une cause de rupture diélectrique pour les matériaux céramiques piézoélectriques. La première étape de ce travail concerne la modélisation des zones de pré-fracture dans un matériel piézoélectrique dans le but de formuler un modèle sans les singularités évoquées précédemment. Les zones de chargement mécanique limite et de saturation électrique ont été introduites en pointe de fissure et les conditions des perméabilités limitées ont été introduites à la surface de la fissure. Le modèle de fissuration présenté avec deux zones de pré-fracture permet d'éliminer toutes les singularités au voisinage de la fissure. Dans les zones de pré-fracture, une distribution non homogène des déplacements électriques saturés est considérée. Les résultats contiennent les solutions analytiques et numériques de ce problème. Dans la solution numérique, le code ABAQUS a été utilisé. Dans un deuxième temps, le problème d’une série périodique de fissures est considéré pour un matériau magnéto-électro-élastique. Comme un cas limite, une seule fissure avec la condition de la perméabilité limitée est aussi étudiée. Le problème est résolu de manière exacte et des calculs numériques illustrant l'influence de différentes caractéristiques sur les paramètres de fissuration sont présentés sous forme graphique ou dans des tableaux. Egalement, l'influence de la fraction volumique piézo-électrique dans les matériaux magnéto-électro-élastiques sur les paramètres électro-magnétiques dans la région fissurée est étudiée. Enfin, l'attention est focalisée sur l'application de la zone de pré-fracture en pointe de fissure dans les matériaux magnéto-électro-élastiques. La même façon que précédemment, les zones de chargement mécanique limite et de saturation électrique ont été adoptées. Aussi, une zone analogue à une zone de saturation électrique pour le champ magnétique a été introduite. (...) / Nowadays, technologies are improving day by day and at the same high speed smart structures decrease in size. Piezoelectric or magneto-electro-elastic materials have the ability to change its shape under electric or magnetic field. These dielectrics can serve as working bodies at various sensors, transducers, oscillators, modulators and other active elements. On the one hand these active materials are used in small devices and have very small dimensions; on the other hand they use high electrical voltage in order to receive a maximal displacement and/or blocking force. The active smart structure is predisposed to different defects, like debonding and delamination. These situations may take a place during the manufacture (imperfect bounding) and service life of the active smart structure. Delamination failure can be of several types, such as: fracture within the adhesive or resin, fracture within the reinforcement and debonding of the resinfrom the reinforcement. Electric or mechanical failure, such as electrical breakdown or destruction of cracks is an important problem in performance and reliability of these materials. This work aims to develop the model of crack with physical boundary conditions under combined external loads. Consideration of any crack in the course of linear fracture mechanics initiates (creates) singularities in stresses at the crack tips. As known, the electric field, ahead of crack tip, is bigger than its critical value and this can be a cause of dielectric breakdown in piezoceramics. The first task of the work concerns the modelling of pre-fracture zones in piezoelectric material in order to formulate the model without the mentioned singularities. The mechanical yielding and electric saturation zones have been introduced ahead of crack tips and the limited permeable conditions on crack surfaces have been used. The present model of crack with two pre-fracture zones eliminates all singularities on crack continuation. In pre-fracture zones, a non homogeneous distribution of saturated electric displacement is considered. Results contain analytical and numerical solutions of the problem. In the numerical solution ABAQUS code was used. As the second task the problem for a periodic set of the limited electrically and magnetically permeable cracks is considered for magneto-electro-elastic material. As a limiting case, a single limited permeable crack is studied as well. The problem is solved exactly and some numerical calculations which illustrate the influence of various characteristics on fracture parameters are presented in graphical and tabular form. The influence of the piezoelectric volume fraction in magneto-electro-elastic material on electro-magnetic parameters in the crack regions is studied. As the third task, the attention is focused on application of pre-fracture zone ahead of crack in magneto-electro-elastic materials. Similarly to the previous problem, the mechanical yielding and electric saturation zones have been adopted. Also, analogue of electric saturation zone for magnetic field was considered. The present model of crack with three pre-fracture zones eliminates singularities in mechanical, electric and magnetic fields on crack continuation. The problem is solved exactly. Some numerical calculations which illustrate the influence of various characteristics on fracture parameters are presented in graphical and tabular form.

Depuis plusieurs décennies, l’évaluation des armes à létalité réduite (ALR) et des gilets pare-balles suscite l’intérêt majeur des forces de l’ordre autour du globe. En effet, ces armes présumées à létalité réduite ou non létales sont tenues d’occasionner uniquement une douleur suffisamment importante à un individu afin d’assurer sa neutralisation. Les gilets pare-balles, quant à eux, doivent garantir un certain niveau de protection pour réduire le risque de traumatismes lié à leur déformation dynamique. Le Centre de Recherche, d’Expertise et d’appui Logistique (CREL) du Ministère de l’Intérieur français a ainsi pour objectif le développement d’un outil de prédiction du risque lésionnel thoracique lors d’impacts balistiques non pénétrants. Cela permettrait alors d’évaluer les performances des ALR et des gilets pare-balles avant leur déploiement en théâtre d’opérations. Plus précisément, cette méthode doit uniquement être fondée sur la mesure directe du processus dynamique de déformation d’un bloc de gel synthétique soumis à un impact balistique. Pour répondre à ce besoin, l’approche numérique est considérée dans ces travaux de thèse par l’emploi du mannequin numérique du thorax humain HUByx comme un outil intermédiaire permettant la détermination de fonctions de transfert entre les mesures expérimentales sur un bloc de gel et le risque lésionnel. La reproduction de conditions d’impact réelles sur HUByx nécessite la caractérisation et la modélisation de projectiles ALR ainsi que de projectiles d’armes à feu et de gilets pare-balles. Elles reposent sur une procédure d’identification par méthode inverse appliquée à l’essai de Taylor pour la modélisation des ALR et à l’essai du cône dynamique d’enfoncement sur le bloc de gel pour celle du couple projectile/gilet pare-balles. Des travaux sont dédiés à la caractérisation mécanique et à la modélisation du gel synthétique sous sollicitations dynamiques. Enfin, une approche statistique basée sur des analyses de corrélation est introduite exploitant à la fois les mesures expérimentales, les données numériques ainsi que les rapports de cas de la littérature. Une cartographie du thorax associée au risque de fractures costales est établie et est uniquement fonction d’une mesure expérimentale. / For decades, the assessment of less-lethal weapons (LLW) and bulletproof vests has generated major interest from law enforcement agencies around the world. Indeed, these presumed less-lethal or non-lethal weapons are required to cause only significant pain to an individual to ensure their neutralization. Bulletproof vests, in turn, must provide a certain level of protection to reduce the risk of trauma related to their dynamic deformation. The Center for Research, Expertise and Logistics Support (CREL) of the French Ministry of the Interior aims to develop a tool to predict thoracic injury risk during non-penetrating ballistic impacts. It would therefore be possible to evaluate the performance of LLW and bulletproof vests before their deployment in operations. More precisely, this method must only be based on the direct measurement of the dynamic process of deformation of a synthetic gel block subjected to a ballistic impact. To address that issue, the numerical approach is considered in this thesis by the use of the human thorax dummy HUByx as an intermediate tool for the determination of transfer functions between experimental metrics on a gel block and the risk of injury. The reproduction of real impact conditions on HUByx thus requires the characterization and modeling of less-lethal projectiles as well as projectiles of firearms and bulletproof vests. They rely on an inverse method identification procedure applied to the Taylor test for modeling LLW and on the analysis of blunt impacts on the gel block for projectiles/bulletproof vests. Work is then dedicated to the mechanical characterization and modeling of the synthetic gel under dynamic loadings. Finally, a statistical approach based on correlation analyses is introduced using both experimental measurements, numerical data as well as case reports from the literature. A thorax mapping associated with the risk of rib fractures is established and only depends on an experimental metric.

[ES] La contaminación acústica se ha convertido en una causa de importantes problemas de salud, como alteraciones del sueño, cardiovasculares o cognitivas. En áreas urbanas, los altos valores del ruido debido al transporte y a otras actividades humanas pueden ser especialmente dañinos. Se trata de un tema de estudio abierto, debido a la amplia naturaleza del ruido y su gama de posibles fuentes (y, por lo tanto, las posibles soluciones para paliar cada una de ellas). Esta tesis se centra en la minimización del (i) ruido del sistema de escape, que puede abordarse mediante el uso de silenciadores (que a su vez tienen otras aplicaciones, como en los sistemas HVAC, es decir, calefacción, ventilación y aire acondicionado), así como del (ii) ruido y las vibraciones generales causados por el transporte, como por ejemplo el ruido de rodadura de los ferrocarriles, y el uso de barreras acústicas para mitigarlo. Por un lado, los silenciadores (que se pueden dividir en configuraciones reactivas, disipativas e híbridas) fueron adoptados hace tiempo en la línea de escape, pero también se ha extendido el uso de convertidores catalíticos y filtros de partículas diésel, los cuales, si bien su uso responde a razones medioambientales más que de reducción del ruido, tienen un impacto en el rendimiento acústico del sistema de escape. En este punto, se revisan diversas técnicas para la simulación numérica de la propagación del sonido dentro de conductos y demás dispositivos mencionados, y se proponen varios esquemas de optimización para la minimización de la transmisión del ruido. Esto incluye (i) la optimización dimensional de los silenciadores (incluidas las cámaras reactivas y disipativas), (ii) la optimización topológica del material disipativo (su distribución de densidad) dentro de la cámara disipativa y (iii) la optimización dimensional de los dispositivos de postratamiento de escape (convertidores catalíticos y filtros de partículas diésel). Por otro lado, el apantallamiento acústico tiene una amplia gama de aplicaciones, como las barreras acústicas de tráfico, carenados de ruedas de trenes o incluso revestimientos de conductos HVAC. En este punto, se requiere acoplar los problemas acústico y elástico en el contorno aire-estructura para obtener el problema vibroacústico. Aquí se plantea una formulación híbrida en desplazamiento-presión y se aplica a varios casos prácticos, con el fin de obtener diseños elásticos acústicamente optimizados. / [CA] La contaminació acústica s'ha convertit en una causa d'importants problemes de salut, com ara alteracions del son, cardiovasculars o cognitives. En àrees urbanes, els alts valors del soroll degut al transport i a altres activitats humanes poden ser especialment nocius. Es tracta d'un tema d'estudi obert, a causa de l'àmplia naturalesa del soroll i la gamma de possibles fonts (i, per tant, les possibles solucions per pal·liar cadascuna). Aquesta tesi se centra en la minimització del (i) soroll del sistema d'escapament, que es pot abordar mitjançant l'ús de silenciadors (que alhora tenen altres aplicacions, com en els sistemes HVAC, és a dir, calefacció, ventilació i aire condicionat), així com del (ii) soroll i les vibracions generals causats pel transport, com ara el soroll de rodament dels ferrocarrils, i l'ús de barreres acústiques per mitigar-lo. D'una banda, els silenciadors (que es poden dividir en configuracions reactives, dissipatives i híbrides) van ser adoptats fa temps a la línia d'escapament, però també s'ha estès l'ús de convertidors catalítics i filtres de partícules dièsel, els quals, si bé el seu ús respon a raons mediambientals més que de reducció del soroll, tenen un impacte en el rendiment acústic del sistema d'escapament. En aquest punt, es revisen diverses tècniques per a la simulació numèrica de la propagació del so dins de conductes i altres dispositius esmentats, i es proposen diversos esquemes d'optimització per minimitzar la transmissió del soroll. Això inclou (i) l'optimització dimensional dels silenciadors (incloses les càmeres reactives i dissipatives), (ii) l'optimització topològica del material disipatiu (la distribució de densitat) dins de la càmera disipativa i (iii) l'optimització dimensional dels dispositius de posttractament d'escapament (convertidors catalítics i filtres de partícules dièsel). D'altra banda, l'apantallament acústic té una àmplia gamma d'aplicacions, com ara les barreres acústiques de trànsit, carenats de rodes de trens o fins i tot revestiments de conductes HVAC. En aquest punt, cal acoblar els problemes acústic i elàstic al contorn aire-estructura per obtenir el problema vibroacústic. Aquí es planteja una formulació híbrida en desplaçament-pressió i s'aplica a diversos casos pràctics per obtenir dissenys elàstics acústicament optimitzats. / [EN] Noise pollution has become a cause of major health problems, such as sleep, cardiovascular or cognitive alterations. In urban areas, the high values of transport and other human-activity-related noise can be especially harmful. This issue is a large subject of study, due to the broad nature of noise and its range of possible sources (and therefore the potential solutions to alleviate each of them). This Thesis focuses on the minimization of (i) exhaust system noise, which can be addressed by the use of mufflers (which in turn have other applications, such as in HVAC systems, i.e., heating, ventilation, and air conditioning), and (ii) general noise and vibration caused by transport, such as railway rolling noise, and the use of sound barriers to alleviate it. On the one hand, mufflers (which can be divided into reactive, dissipative, and hybrid configurations) were long ago adopted in the exhaust line, but also the use of catalytic converters and diesel particulate filters has become spread, and, while their use responds to environmental rather than noise reduction reasons, they have an impact in the acoustic performance of the exhaust system. Diverse techniques for the modelling of sound propagation within ducts and the other aforementioned devices are reviewed, and several optimization schemes are proposed for the minimization of noise transmission. This includes (i) the sizing optimization of mufflers (including reactive and dissipative chambers), (ii) the topology optimization of the dissipative material (its density layout) within the dissipative chamber, and (iii) the sizing optimization of exhaust aftertreatment devices (catalytic converters and diesel particulate filters). On the other hand, sound barriers have a wide range of applications, such as traffic noise barriers, train wheel fairings or even HVAC duct coatings. At this point, it is required to pair the acoustic and the elastic problems at the air-structure boundary to obtain the vibroacoustic problem. A hybrid displacement-pressure formulation is recalled here and applied to several case studies, in order to obtain acoustically-optimized elastic designs. / Ferrándiz Catalá, B. (2023). Development of topology optimization techniques for noise pollution minimization in acoustic and fluid-structure problems [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/197985