A method for solving the inverse geometrical problem is presented by reconstructing the unknown subsurface cavity geometry using boundary element methods, a genetic algorithm, and Nelder-Mead non-linear simplex optimization. The heat conduction problem is solved utilizing the boundary element method, which calculates the difference between the measured temperature at the exposed surface and the computed temperature under the current update of the unknown subsurface flaws and cavities. In a first step, clusters of singularities are utilized to solve the inverse problem and to identify the location of the centroid(s) of the subsurface cavity(ies)/flaw(s). In a second step, the reconstruction of the estimated cavity(ies)/flaw(s) geometry(ies) is accomplished by utilizing an anchored grid pattern upon which cubic spline knots are restricted to move in the search for unknown geometry. Solution of the inverse problem is achieved using a genetic algorithm accelerated with the Nelder-Mead non-linear simplex. To optimize the cubic spline interpolated geometry, the flux (Neumann) boundary conditions are minimized using a least squares functional. The automated algorithm successfully reconstructs single and multiple subsurface cavities within two dimensional mediums. The solver is also shown to accurately predict cavity geometries with random noise in the boundary condition measurements. Subsurface cavities can be difficult to detect based on their location. By applying different boundary conditions to the same geometry, more information is supplied at the boundary, and the subsurface cavity is easily detected despite its low heat signature effect at the boundaries. Extensions to three-dimensional applications are outlined

[pt] Este trabalho apresenta um estudo do cálculo de sensibilidades necessário para a análise de problemas inversos e de otimização, usando o método híbrido dos elementos de contorno. Com esta finalidade, é desenvolvida uma formulação que permite obter as sensibilidades à mudança de forma, por diferenciação implícita das integrais de contorno, de uma estrutura já discretizada. Demonstra-se que as sensibilidades das matrizes obtidas desta formulação apresentam propriedades espectrais definidas, que são derivadas da formulação básica do método híbrido dos elementos de contorno. Todo o desenvolvimento é feito para um problema da elastostática tridimensional, embora sejam apresentadas apenas aplicações de problemas bidimensionais e de potencial, como casos particulares. As singularidades que surgem na integração no cálculo das sensibilidades são facilmente solucionáveis a partir das integrais da formulação básica do método híbrido dos elementos de contorno. As implementações numéricas são feitas utilizando a linguagem de programação Maple V release 3. Para ambos os casos, de potencial e elasticidade bidimensional, são usados elementos lineares para a representação do contorno. São apresentadas comparações entre os resultados analíticos obtidos através desta formulação com os resultados obtidos usando a técnica de diferenças finitas (centradas), com o objetivo de demonstrar a eficiência e precisão da metodologia aqui desenvolvida. / [en] The present work describes a formulation for computing design sensitivities required in inverse problems and shape optimization of solid objects, in the frame of the hybrid boundary element method. The so-called direct differentiation method is applied in order to calculate the gradients, i.e. the implicit diferentiation of the discretized boundary is performed, resulting in a general and efficient analysis technique for shape design sensitivity analysis of all structural quantities. It is demonstrated that the resulting sensitivities matrices present some useful spectral properties, which are related to the matrix spectral properties of the basic hybrid formulation. This formulation is valid for tridimensional solids, although only potential and bidimensional applications are considered as particular cases. The singularities that appear in the resulting boundary integrals are exactly the same which have already been dealt with in the basic formulation. The analytical and numerical procedures were performed by using the mathematical package Maple V release 3. Linear boundary elements were used for both potential and elasticity problems. Numerical results obtained by the present procedure are compared to finite differences results to demonstrate the effectiveness of the present formulation. / [es] Este trabajo presenta un estudio del cálculo de sensibilidades, que tiene gran importancia en el análisis de problemas inversos y de optimización, usando el método híbrido de los elementos de contorno. Con esta finalidad, se desarrolla una formulación que permite obtener las sensibilidades al cambio de forma de una extructura ya discretizada, por diferenciación implícita de las integrales de contorno. Se demuestra que las sensibilidades de las matrices obtenidas por esta formulación presentan propriedades espectrales definidas, que son derivadas de la formulación básica del método híbrido de los elementos de contorno. El desarrollo de la formulación se realiza para un problema de elastostática tridimensional, aunque se presentan apenas las aplicaciones de problemas bidimensionales y de potencial, como casos particulares. Las singularidades que surgen en la integración en el cálculo de las sensibilidades pueden ser fácilmente resueltas a partir de las integrales de la formulación básica del método híbrido de los elementos de contorno. La implementación numérica utiliza el lenguaje de programación Maple V release 3. Para los casos de potencial y elasticidad bidimensional, se utilizan elementos lineales para la representación del contorno. Se comparan los resultados analíticos obtenidos a través de esta formulación con los resultados obtenidos usando la técnica de diferencias finitas (centradas), con el objetivo de demostrar la eficiencia y precisión de la metodología aqui desarrollada.

Ultrasound directed self-assembly (DSA) utilizes the acoustic radiation force associated with a standing ultrasound wave field to organize particles dispersed in a fluid medium into specific patterns. The ability to tailor the organization and packing density of spherical particles using ultrasound DSA in a viscous fluid medium is crucial in the context of (additive) manufacturing of engineered materials with tailored properties. However, the fundamental physics of the ultrasound DSA process in a viscous fluid medium, and the relationship between the ultrasound DSA process parameters and the specific patterns of particles that result from it, are not well-understood. Researchers have theoretically described the acoustic radiation force and the acoustic interaction force that act on spherical particles in a standing ultrasound wave field in both inviscid and viscous media. In addition, they have solved the forward and inverse ultrasound DSA problem in an inviscid medium, in which they relate the patterns of particles and the ultrasound DSA operating parameters. However, no theoretical model exists that allows simulating the steady-state and transient local particle packing density in a viscous medium during ultrasound DSA. Thus, in this dissertation, we (i) theoretically derive and experimentally validate a model to determine the steady-state locations where spherical particles assemble during ultrasound DSA as a function of medium viscosity and particle volume fraction. (ii) We also theoretically derive and experimentally validate a model to quantify the steady-state and transient local packing density of spherical particles within the pattern features that result from ultrasound DSA. Using these models, we quantify and predict the locations where spherical particles assemble during ultrasound DSA in a viscous medium, considering the effects of medium viscosity and particle volume fraction. We demonstrate that the deviation between locations where particles assemble in viscous and inviscid media first increases and then decreases with increasing particle volume fraction and medium viscosity, which we explain by means of the sound propagation velocity of the mixture. In addition, we quantify and predict the steady-state and transient local packing density of spherical particles within the pattern features, using ultrasound DSA in combination with vat photopolymerization (VP). We show that the steady-state local particle packing density increases with increasing particle volume fraction and increases with decreasing particle size. We also show that the transient local particle packing density increases with increasing particle volume fraction, decreasing particle size, and decreasing fluid medium viscosity. Increasing particle size and decreasing fluid medium viscosity decreases the time to reach steady-state. Finally, we implement single and multiple scattering in the calculation of the acoustic radiation force for spherical particles in a viscous medium and quantify their relative contributions to the calculation of the acoustic radiation force as a function of ultrasound DSA operating parameters and material properties. We demonstrate that the deviation between considering single and multiple scattering may reach up to 100%, depending on the ultrasound DSA process parameters and material properties. Also, increasing the particle volume fraction increases the need to account for multiple scattering. Quantifying and predicting the local packing density of spherical particles during ultrasound DSA in a viscous medium, as a function of ultrasound DSA process parameters is crucial towards using ultrasound DSA in engineering applications, in particular (additive) manufacturing of engineered polymer matrix composite materials with tailored properties whose properties depend on the spatial organization and packing density of particles in the matrix material. / Doctor of Philosophy / Ultrasound directed self-assembly (DSA) is a technique that uses ultrasound waves to arrange small particles submerged in a fluid into specific patterns. When combined with other manufacturing techniques, ultrasound DSA can be used to fabricate composite materials that derive their properties from the spatial organization of particles in a matrix material. However, ultrasound DSA in viscous fluids is not well-understood. Researchers have studied the forces associated with ultrasound waves that move small spherical particles in an inviscid fluid medium (fluids that experience little to no internal resistance to flow), and they have demonstrated intricate control of the patterns of particles that form using ultrasound DSA. However, that knowledge is not currently available for ultrasound DSA in viscous media. In this dissertation, we develop and evaluate theoretical models to understand ultrasound DSA of small spherical particles in a viscous fluid medium. We simulate where particles organize and how densely they pack together. We also determine the difference of the time-dependent motion of particles in a viscous fluid compared to that in an inviscid fluid medium and relate the difference to the number of particles submerged in the fluid and the viscosity of the fluid. Additionally, we examine the effect of particle size and fluid viscosity on the speed by which the particles reach their final location. We also study how ultrasound waves interact with multiple small particles in a viscous fluid, focusing on the forces that move these particles. We explore two models that account for single and multiple ultrasound wave scattering. Scattering is the process by which ultrasound waves deflect in different directions when they encounter a particle. The results show that the difference between single and multiple scattering models can be significant, depending on the ultrasound DSA process parameters and the properties of the fluid and particles. In general, the importance of accounting for multiple scattering increases with the number of particles submerged in the fluid. Understanding particle packing density when using ultrasound DSA in a viscous fluid is essential in many engineering applications, in particular manufacturing of composite materials that derive their properties from the spatial arrangement of particles in a matrix material.

Ce travail de recherche se situe dans le cadre du développement de la méthode des éléments de frontière (BEM) pour les milieux poreux multiphasiques. À l'heure actuelle, l'application de la BEM aux pr oblèmes des milieux poreux non-saturés est encore limitée, car l'expression analytique exacte de la solution fondamentale n'a pas été obtenue, ni dans le domaine transformé ni dans le domaine réel. Ceci provient de la complexité du système d'équations régissant le comportement des milieux poreux non-saturés. Les développements de la BEM pour les sols non-saturés effectués au cours de cette thèse sont basés sur les modèles thermo-hydro-mécanique (THHM) et hydro-mécanique (HHM) présentés dans la première partie de ce mémoire. Ces modèles phénoménologiques basés sur la théorie de la poromécanique et les acquis expérimentaux sont obtenus dans le cadre du modèle mathématique présenté par Gatmiri (1997) et Gatmiri et al. (1998). Après avoir présenté les modèles THHM et HHM, on établit pour la première fois les équations intégrales de frontière et les solutions fondamentales associées pour un milieu poreux non-saturé sous chargement quasi-statique pour les deux cas isotherme (2D dans le domaine de Laplace) et non-isotherme (2D et 3D dans les domaines de Laplace et temporel). Aussi, les équations intégrales de frontière ainsi que les solutions fondamentales 2D et 3D (dans le domaine de Laplace) pour le modèle dynamique couplé des sols non-saturés sont obtenues. Ensuite, les formulations d'éléments de frontière (BEM) basées sur la méthode quadrature de convolution (MQC) concernant les milieux poreux saturé et non-saturé sous chargement quasi-statique isotherme et dynamique sont implémentées dans le code de calcul « HYBRID ». Ayant intégrées les formulations de BEM pour les problèmes de propagation d'ondes ainsi que pour les problèmes de consolidation dans les milieux poreux saturés et non-saturés, il semble que nous ayons fourni à l'heure actuelle le premier code de calcul aux éléments de frontière (BEM) qui modélise les différents problèmes dans les sols secs, saturés et non-saturés. Une fois le code vérifié et validé, des études paramétriques portant sur des effets de site sismiques sont effectuées. Le but recherché est d'aboutir à un critère simple, directement exploitable par les ingénieurs, combinant les caractéristiques géométriques et les caractéristiques du sol, permettant de prédire l'amplification du spectre de réponse en accélération dans des vallées sédimentaires aussi bien que vides / The purpose of this dissertation is to develop a boundary element method (BEM) for multiphase porous media. Nowadays, the application of the BEM for solving problems of unsaturated porous media is still limited, because no fundamental solution exists in the published literature, neither in the frequency nor time domain. This fact rises from the complexity of the coupled partial differential equations governing the behaviour of such media. The developments of the BEM for the unsaturated soils carried out during this thesis are based on the thermo-hydro-mechanical (THHM) and hydro-mechanical (HHM) models presented in the first part of this dissertation. These phenomenological models are presented based on the experimental observations and with respect to the poromechanics theory within the framework of the suction-based mathematical model presented by Gatmiri (1997) and Gatmiri et al. (1998). After having presented the THHM and HHM models, for the first time, one establishes the boundary integral equations (BIE) and the associated fundamental solutions for the unsaturated porous media subjected to quasi-static loading for both isothermal (2D in the Laplace transform domain) and non-isothermal (2D and 3D in Laplace transform and time domains) cases. Also, the boundary integral equations as well as the fundamental solutions (2D and 3D in the Laplace transform domain) are obtained for the fully coupled dynamic model of unsaturated soils.In the next step, the boundary element formulations (BEM) based on the convolution quadrature method (CQM) regarding the saturated and unsaturated porous media subjected to isothermal quasi-static and dynamic loadings are implemented via the computer code HYBRID. Having integrated the BEM formulations for the wave propagation, as well as the consolidation problems in the saturated and unsaturated porous media, it seems that now the first boundary element code is obtained that can model the various problems in dry, saturated and unsaturated soils. Once the code is verified and validated, parametric studies on seismic site effects are carried out. The aim is to achieve a simple criterion directly usable by engineers, combining the topographical and geological characteristics of the soil, to predict the amplification of acceleration response spectra in sedimentary as well as hollow valleys

La simulation numérique de la propagation d'ondes sismiques est un besoin actuel, par exemple pour modéliser les vibrations induites dans les sols par le trafic ferroviaire ou pour analyser la propagation d'ondes sismiques ou l'interaction sol-structure. La modélisation de ce type de problèmes est complexe et nécessite l'utilisation de méthodes numériques avancées. La méthode des éléments de frontière (boundary element method, BEM) est une méthode très efficace pour la solution de problèmes de dynamique dans des régions étendues (idéalisées comme non-bornées), en particulier après le développement des méthodes BEM accélérées par multipôle rapide (Fast Multipole Method, FMM), la méthode utilisée dans ce travail de thèse. La BEM est basée sur une formulation intégrale qui nécessite de discrétiser uniquement la frontière du domaine (i.e. une surface en 3-D) et prend implicitement en compte les conditions de radiation à l'infini. En revanche, la BEM nécessite la résolution d'un système linéaire dont la matrice est pleine et (pour la formulation par collocation de la BEM) non-symétrique. Cette méthode est donc trop onéreuse pour des problèmes de grandes dimensions (par exemple O(106) DDLs). L'application à la BEM de la méthode multipôle rapide multi-niveaux (multi-level fast multipole method, ou ML-FMM diminue considérablement la complexité et les besoins de mémoire affectant les formulations BEM classiques, rendant la BEM très compétitive pour modéliser la propagation des ondes élastiques. La version élastodynamique de la ML-FMBEM, dans une forme étendue aux domaines homogènes par morceaux, a par exemple été appliquée avec succès dans un travail précédent (thèse S. Chaillat, ENPC, 2008) pour résoudre les problèmes de propagation des ondes sismiques. Cette thèse vise a développer les capacités de la version élastodynamique fréquentielle de la ML-FMBEM dans deux directions. Premièrement, la formulation de la ML-FMBEM a été étendue au cas de matériaux viscoélastiques linéaires faiblement dissipatifs. Deuxièmement, la ML-FMBEM et la méthode des éléments finis (finite element method, FEM) ont été couplées afin de permettre la résolution de problèmes plus compliqués. En effet, le couplage FEM/FMBEM permet de profiter d'un côté de la flexibilité de la FEM pour la modélisation de structures de géométrie complexe ou présentant des non-linéarités de comportement, de l'autre côté de la prise en compte naturelle par la ML-FMBEM des ondes se propageant dans un milieu étendu et rayonnant à l'infini. De nouvelles perspectives d'application (par exemple prise en compte d'hétérogénéités, non-linéarités de comportement) sont ainsi ouvertes. Dans cette thèse, nous avons considéré deux stratégies pour coupler la FMBEM et la FEM avec l'objectif de résoudre les problèmes tridimensionnels de propagation des ondes harmoniques dans le temps et dans des domaines non-bornés. L'idée principale consiste à séparer une ou plusieurs sous-régions pouvant contenir des structures complexes, de fortes hétérogénéités ou des non-linéarités (modélisées au moyen de la FEM) du milieu propagatif complémentaire semi-infini et (visco-) élastique (modélisé au moyen de la FMBEM). Cette séparation est effectuée au moyen d'une décomposition de domaines sans recouvrement. Le deux approches proposées ont été mises en oeuvre, et une série d'expérimentations numériques a été effectuée pour les évaluer et les comparer / The numerical simulation of elastic wave propagation in unbounded media is a topical issue. This need arises in a variety of real life engineering problems, from the modelling of railway- or machinery-induced vibrations to the analysis of seismic wave propagation and soil-structure interaction problems. Due to the complexity of the involved geometries and materials behavior, modelling such situations requires sophisticated numerical methods. The Boundary Element method (BEM) is a very effective approach for dynamical problems in spatially-extended regions (idealized as unbounded), especially since the advent of fast BEMs such as the Fast Multipole Method (FMM) used in this work. The BEM is based on a boundary integral formulation which requires the discretization of the only domain boundary (i.e. a surface in 3-D) and accounts implicitly for the radiation conditions at infinity. As a main disadvantage, the BEM leads a priori to a fully-populated and (using the collocation approach) non-symmetrical coefficient matrix, which make the traditional implementation of this method prohibitive for large problems (say O(106) boundary DoFs). Applied to the BEM, the Multi-Level Fast Multipole Method (ML-FMM) strongly lowers the complexity in computational work and memory that hinder the classical formulation, making the ML-FMBEM very competitive in modelling elastic wave propagation. The elastodynamic version of the Fast Multipole BEM (FMBEM), in a form enabling piecewise-homogeneous media, has for instance been successfully used to solve seismic wave propagation problems in a previous work (thesis dissertation of S. Chaillat, ENPC, 2008). This thesis aims at extending the capabilities of the existing frequency-domain elastodynamic FMBEM in two directions. Firstly, the time-harmonic elastodynamic ML-FMBEM formulation has been extended to the case of weakly dissipative viscoelastic media. Secondly, the FMBEM and the Finite Element Method (FEM) have been coupled to take advantage of the versatility of the FEM to model complex geometries and non-linearities while the FM-BEM accounts for wave propagation in the surrounding unbounded medium. In this thesis, we consider two strategies for coupling the FMBEM and the FEM to solve three-dimensional time-harmonic wave propagation problems in unbounded domains. The main idea is to separate one or more bounded subdomains (modelled by the FEM) from the complementary semi-infinite viscoelastic propagation medium (modelled by the FMBEM) through a non-overlapping domain decomposition. Two coupling strategies have been implemented and their performances assessed and compared on several examples

Contexte : Le tissu biologique mou présente une organisation structurelle extrêmement complexe et est le siège de nombreux phénomènes d'échanges. De nombreuses applications s'étendant du diagnostic clinique à l'ingénierie tissulaire nécessitent la connaissance du comportement mécanique du tissu. A cette fin, de nombreuses approches plus ou moins satisfaisantes sont développées. Elles s'efforcent toutes de tenir compte de manière plus ou moins systématique de la microstructure du milieu. La considération du tissu biologique comme un milieu micromorphe donne des résultats probants dans sa particularisation au milieu micropolaire appliquée au tissu osseux. Il est donc fort probable que des résultats du genre soient obtenus pour d'autres tissus. Notre travail était orienté vers le tissu cardiaque et la problématique de l'infarctus ischémique. Dans ce contexte, il nous a semblé que la particularisation de comportement la mieux adaptée est celle d'un milieu à microdilatation. Travail réalisé : Le travail réalisé dans le cadre de cette thèse est essentiellement numérique. Il a pour objectif de mettre en lumière les particularités de la réponse à une sollicitation extérieure d'un échantillon de milieu à microdilatation. Cette étape est essentielle pour l'analyse future des résultats d'expériences qui seront menées. Il a également pour objectif d'étudier les potentialités du modèle vis-à-vis du tissu cardiaque en considérant l'infarctus ischémique et la perte associée de la capacité d'éjection de volume sanguin. Les outils numériques d'analyse de tels milieux sont en plein développement. Il nous a fallu développer notre propre outil basé sur la LPI-BEM (Local Point Interpolation - Boundary Element Method). Du fait de la similitude des équations de champs associées, la validité de la stratégie numérique mise en oeuvre est testée sur le cas d'un matériau piézoélectrique. Ce choix n'est pas innocent car, dans l'avenir la considération du milieu piézoélectrique à microdilatation permettra d'analyser le cas d'une sollicitation électrique du tissu. Les détails de cette stratégie numérique originale sont consignés dans le chapitre 2 du mémoire. Le chapitre 3 est consacré à l'analyse de la robustesse de la méthode et aux particularités de la réponse d'un milieu à microdilatation. Le quatrième chapitre est consacré à l'application au tissu cardiaque. En se limitant au cas de petites déformations, on montre que le modèle est bien adapté à la représentation du comportement du tissu cardiaque. En effet, assimilant le ventricule gauche à une structure tubulaire, la fraction d'éjection du ventricule gauche (critère clinique d'insuffisance cardiaque) est fortement diminuée en présence d'une zone infarcie. Cette dernière est modélisée comme une région à frontière diffuse où les points matériels ont perdu leur capacité de « respirer ». Ces résultats sont prometteurs. Ils encouragent à poursuivre dans cette voie en prenant en compte le caractère anisotrope du tissu et en se plaçant dans le cadre des grandes déformations / Background: A soft biological tissue is subjected to numerous exchange phenomena and has an extremely complex structural organization. The knowledge of its mechanical behavior is required in many applications ranging from clinical diagnostic to tissue engineering. To achieve this goal, more or less satisfactory approaches are developed. They all seek to take into account in a more or less systematic manner the microstructure of the medium. Assuming that the biological tissue is a particular micromorphic medium (micropolar medium) leads to good results in the case bone tissue. It is therefore likely that the results of this kind will be obtained for other tissues. Our interest is on the heart tissue and the problem of ischemic heart attack. In this context, it seemed that the most appropriate behavior particularization is that of a microdilatation medium. Work done: The work presented in this thesis is essentially numerical. It aims to highlight the features of the response of microdilatation medium to an external mechanical load. This step is essential for the analysis of the experimental results to be conducted in the future. The work also aims to investigate the potentialities of the model with respect to the heart tissue regarding heart attack and the associated loss of the ability to eject sufficient blood volume. The numerical tools for the analysis of such media are in increasing development. We had to develop our own tool based on the LPI-BEM (Local Point Interpolation - Boundary Element Method). Because of the similarity of the associated field equations, the validity of the numerical strategy is assessed in the case of a piezoelectric material. This choice is not innocent because the piezoelectric medium with microdilatation will allow analyzing the case of an electrical solicitation of the tissue. The details of this original numerical approach are given in Chapter 2 of the thesis. Chapter 3 is devoted to the analysis of the robustness of the method and to the peculiarities of the response of a microdilatation medium. The fourth chapter is devoted to the application to the cardiac tissue. By limiting the study to the case of small strains, it is shown that the model is well suited to the representation of the behavior of cardiac tissue. Indeed, considering the left ventricle as a tubular structure, the left ventricle ejection fraction (clinical criterion of the heart failure) is greatly reduced in the presence of an infarcted area. The latter is modeled as a zone with diffuse boundary where the material points have lost their ability to "breath". These results are promising and encourage further investigations in this direction by taking into account the anisotropic nature of the tissue in a geometrically nonlinear context

Este trabalho trata da análise da propagação de fissuras, independente do tempo, em domínios bidimensionais utilizando uma formulação alternativa do método dos elementos de contorno (MEC). O MEC vem sendo utilizado com sucesso na análise de diversos problemas de engenharia. Considerando problemas de mecânica da fratura, o MEC é especialmente eficiente devido à redução da dimensionalidade de sua malha, o que permite a simulação do crescimento das fissuras sem as dificuldades do processo de remalhamento. Nesta pesquisa, desenvolvem-se formulações não lineares do MEC para a análise da propagação de fissuras em materiais quase frágeis. Nesses materiais, a zona de processo à frente da ponta da fissura introduz efeitos fisicamente não lineares no comportamento estrutural. Assim, para a simulação da presença da zona de processo, modelos não lineares são necessários. Classicamente a formulação dual do MEC é utilizada para modelar propagação de fissuras na quais equações singulares e hipersingulares são escritas para elementos definidos ao longo das faces das fissuras. O presente trabalho propõe uma segunda formulação utilizando um campo de tensões iniciais para a representação da zona coesiva. Nesta formulação, o termo de domínio da equação integral clássica do MEC é degenerado, de forma a atuar somente ao longo do caminho de crescimento das fissuras, sendo que esse procedimento dá origem a uma nova variável denominada dipolo, responsável por garantir o atendimento das condições de contorno. Em conjunto com essa nova formulação, se propõe o uso do operador tangente (OT), que é deduzido no trabalho, a fim de acelerar o processo de convergência da solução. Os resultados obtidos, por meio da formulação alternativa, são comparados tanto com dados experimentais quanto com o MEC dual, ambos disponíveis na literatura. As respostas encontradas foram satisfatórias no sentido de conseguir reproduzir o comportamento real da estrutura explorando as vantagens computacionais proporcionadas pelo OT. / This work presents a time-independent crack propagation analysis, in two-dimensional domains, using an alternative boundary element method (BEM) formulation. BEM has been used successfully to analyze several engineering problems. Considering fracture mechanics problems, BEM is especially efficient due to its mesh reduction aspects, which allows the simulation of crack growth without remeshing difficulties. In this research, nonlinear BEM formulations are develop in order to analyze crack propagation in quasi-brittle materials. Considering these materials, the process zone ahead of the crack tip leads to nonlinear effects related to structural behavior. Thus, nonlinear models are required for simulating the presence of the process zone. Classically, the dual BEM is used for modeling the crack propagation, in which singular and hyper-singular equations are written for elements defined along the crack faces. This work proposes an alternative formulation using the initial stress field to represent the cohesive zone. In this formulation, the classic domain integral term is degenerated in order to be non-null only at the crack growth path. This procedure leads the creation of new variable called dipole, which is responsible for ensuring the compliance of the boundary conditions. In addition to this new formulation, it is proposed the use of the tangent operator (TO), which is derived in this work, in order to accelerate the convergence. The results obtained using the new formulation, are compared with experimental data and dual BEM results available in the literature. The responses were found satisfactory in reproducing the behavior of real structures exploiting the computational advantages provided by the TO.

O estudo do comportamento mecânico do complexo sistema advindo da interação entre solo/subestrutura/superestrutura é o tema do trabalho. Neste contexto, a representação do maciço é feita usando-se o método dos elementos de contorno (MEC) em abordagem 3D, de maneira que se possa simular o maciço com características mecânicas não-homogêneas, além de se considerar uma camada de apoio indeslocável a distâncias prescritas a priori e condição de aderência perfeita. A subestrutura também é representada via MEC tridimensional, a qual está imersa dentro deste meio heterogêneo. A infra e a superestrutura são modeladas empregando o método dos elementos finitos (MEF), com o uso de elementos estruturais reticulares e elementos laminares. São apresentados alguns exemplos em que se valida a formulação e outros que demonstram a potencialidade e a necessidade de se empregar a formulação para a melhor análise do complexo fenômeno em estudo. Por fim, demonstra-se a obrigatoriedade de se otimizar a formulação, empregando-se duas grandes ferramentas numéricas: o paralelismo e o emprego de um adequado método de resolução de sistemas esparsos. / The analysis of the soil-structure system interaction is a vast field of interest in the area of civil engineering. A realistic representation of its behaviour. Thus, in the present research, the soil is considered a non-homogeneous continuum supported by a rigid and adhesive interface and modelled by boundary element method via Kelvin solution in 3D space. The foundation is also modelled by this above-mentioned modelling technique. The raft foundation and the superstructure are represented by finite shell and 3D frame elements. In order to estimate the accuracy and the potentiality of the proposed numerical formulation, some examples are validated when compared to similar approaches, and others simulations are presented to stress the necessity of coupling the non-homogeneous soil-foundation-radier-superstructure system as a whole. Finally, to acquire numerical time efficiency, it is shown that it is imperative to apply parallel processing and sparse techniques for the solution of the final system.

A identificação de parâmetros físicos e geométricos utilizando medições experimentais é um procedimento comum no tratamento de muitos problemas da ciência e engenharia. Neste contexto, a análise inversa apresenta-se como uma importante ferramenta no tratamento desses problemas. Este trabalho apresenta formulações que acoplam o uso do método dos elementos de contorno (MEC) e a técnica de correlação de imagens digitais (CID) (para obtenção dos campos de deslocamentos) na resolução de alguns problemas inversos de interesse para engenharia de estruturas. Implementou-se um código computacional baseado no MEC, em técnicas de regularização e em algoritmo genético, para análise inversa em problemas de identificação das propriedades dos materiais, recuperação das condições de contorno e identificação de parâmetros do modelo coesivo de fraturamento. Exemplos com dados oriundos de uma prévia análise direta (simulando dados experimentais) são apresentados para demonstrar a eficiência das formulações propostas. Ensaios de vigas em flexão em três pontos com entalhe foram realizados com aquisição de imagens para obtenção dos campos de deslocamentos da região de propagação da fissura, via CID. Estes campos foram utilizados para alimentar o modelo inverso proposto. A técnica de CID originou dados em quantidade e precisão suficientes para os fins almejados neste trabalho. A utilização do MEC mostrou-se simples e de grande eficiência para a solução dos problemas inversos tratados. / The identification of physical and geometrical parameters utilizing experimental measurements is a common procedure in treating many problems of science and engineering. In this context, the inverse analysis is an important tool in treating these problems. This work presents formulations that associate the use of boundary element method (BEM) and the technique of digital image correlation (DIC) (for obtaining the displacement fields) in solving some inverse problems of interest to Structure Engineering. A computer code based on the BEM, on regularization techniques and genetic algorithm has been implemented for the treatment of problems such as Identification of material properties, recovery of boundary conditions and identification of cohesive model parameters. Examples with data from a previous direct analysis (simulating experimental data) are presented to demonstrate the effectiveness of the proposed formulations. Three point flexural tests with notch were performed and images were acquired to obtain the displacement fields on one lateral surface of the samples, via DIC. These displacement fields were used to feed the inverse model proposed. The DIC technique resulted in quantitative and accurate data for the purposes of this study. The use of the BEM proved to be simple and efficient in solving the inverse problems treated.

O objetivo do presente trabalho é o desenvolvimento de um código computacional que possibilite a análise dinâmica de estruturas tridimensionais em regime elástico-linear acopladas ao solo, tratado como meio infinito elastoplástico. As superestruturas são tratadas por elementos finitos simples de casca e de barra geral, as estruturas de fundações são tratadas por elementos de casca que simulam o contato com o solo, modelando radiers, túneis e reservatórios enterrados. Blocos são modelados por elementos de contorno tridimensionais. O solo é modelado de duas maneiras distintas: na região plastificada emprega-se a solução fundamental de Kelvin (estática) e na região não plastificada (elástica) adota-se a solução fundamental do problema de Stokes. O acoplamento entre os meios é feito aplicando-se a técnica de subregiões. Deve ficar claro que todo procedimento estático equivalente foi implementado. Vários exemplos numéricos são apresentados, onde se percebe a eficiência do código computacional desenvolvido / The objective of the present work is the development of a computational code that makes possible dynamic analyses of three-dimensional structures in elastic-linear behavior coupled to the soil, modeled as elastoplastic infinite medium. Simple finite elements, shell and general bars, are used to model elastic structures. The structures of foundations are modeled by shell’s elements which simulate the contact with the soil, modeling radiers, tunnels and buried reservoirs. Blocks are modeled by three-dimensional boundary elements. The soil is modeled in two different ways: in the plastic region Kelvin’s fundamental solution (static) is used and in the elastic region the fundamental solution of the Stoke’s problem is adopted. The coupling among the media is done applying the sub-region technique. It is important to note that the equivalent static procedure has been implemented. Several numerical examples are presented, demonstrating the efficiency of the developed computational code