Kinetic energy extraction devices for ocean and river flows are often located in the vicinity of the fluid free surface. This differs from wind turbines where the atmosphere may be considered to extend to infinity for the purposes of numerical modelling. As most kinetic energy extraction devices are based on lifting surfaces, a numerical model is sought which can model both lifting and free surface flows. One such model is the boundary element method which has been successfully applied to free surface problems and to lifting flows as well as the combined problem. This study seeks to develop a high order boundary element method that is capable of modelling unsteady lifting and free surface flows in three dimensions. Although high order formulations of boundary element methods are common for free surface problems, providing improved accuracy and computational time, their usage for lifting flows is less frequent. This may be due to the hypersingular boundary integral equation (HBIE) which must be solved in order to find the velocity of the vortex wakes behind lifting surfaces. In previous lifting flow studies using high order boundary element methods the wake velocities have been determined at the element centres and then interpolated to the collocation points. Not until the paper of Gray et al. (2004b) has a method been available for the direct solution of the HBIEs at the edges of three dimensional high order elements with C0 continuous interfaces. The solution employs a technique known as the Galerkin boundary element method. This study shows, for the first time, that the Galerkin boundary element method is applicable to the solution of the HBIE on the vortex wake of a lifting body. The application of the technique is then demonstrated as part of the numerical model developed herein. The model is based on the high order boundary element method developed by Xu (1992) for non-linear free surface flows. This formulation is extended to include steady uniform flow throughout the computational domain as well as the presence of lifting and non-lifting bodies. Several verification cases are implemented to test the accuracy of the model.

Motility of flagellated bacteria has been a topic of increasing scientific interest over the past decades, attracting the attention of mathematicians, physicists, biologists and engineers alike. Bacteria and other micro-organisms cause substantial damage through biofilm growth on submerged interfaces in water cooling systems, ship hulls and medical implants. This gives social and economic motivations for learning about how micro-organisms swim and behave in different environments. Fluid flows on such small scales are dominated by viscosity and therefore behave differently from the inertia-dominated flows that we are more familiar with, making bacterial motility a physically intriguing phenomenon to study as well. We use the boundary element method (BEM) to simulate the motion of singly flagellated bacteria in a viscous, Newtonian fluid. One of our main objectives is to investigate the influence of external surfaces on swimming behaviour. We show that the precise shape of the cell body and flagellum can be important for determining boundary behaviour, in particular, whether bacteria are attracted or repelled from surfaces. Furthermore, we investigate the types of motion that may arise between two parallel plates and in rectangular channels of fluid and show how these relate to the plane boundary interactions. As an extension to original models of flagellar propulsion in bacteria that assume a rotation of the rigid helical flagellum about an axis fixed relative to the cell body, we consider flexibility of the bacterial hook connecting the aforementioned parts of the swimmer. This is motivated by evidence that the hook is much more flexible than the rest of the flagellum, which we therefore treat as a rigid structure. Elastic dynamics of the hook are modelled using the equations for a Kirchhoff rod. In some regimes, the dynamics are well described by a rigid hook model but we find the possibility of additional modes of behaviour.

In this work two inverse methodologies are developed based on the Green element method for the recovery of contaminant release histories and reconstruction of the historical concentration plume distribution in groundwater. Unlike direct groundwater contaminant transport simulations which generally produce stable and well-behaved solutions, the solutions of inverse groundwater contaminant transport problems may exhibit non-uniqueness, non-existence and instability, with escalation in computational challenges due to paucity of data. Methods that can tackle inverse problems are of major interest to researchers, and this is the goal of this work. Basically, the advection dispersion equation which governs the transport of contaminants can be handled by analytical or numerical methods like the Finite element method, the Finite difference method, the Boundary element method and their many variants and hybrids. However, if a numerical method is used to solve an inverse problem the resulting matrix is ill-conditioned requiring special techniques to be employed in order to obtain meaningful solutions. In view of this we explore the Green element method, which is a hybrid technique, based on the boundary element theory but is implemented in an element by element manner. This method is attractive to inverse modelling because of the fewer degrees of freedom that are generated at each node. We develop two approaches, in the first approach inverse Green element formulations are developed, the ill-conditioned matrix that results is decomposed with the aid of the singular value decomposition method and solved using the Tikhonov regularized least square method. The second approach utilizes the direct Green element method and the Shuffled complex evolutionary (SCE) optimization method. Finally, the proposed approaches are implemented to solve typical problems in contaminant transport with analytical solutions besides those that have appeared in various research papers. An investigation on the capability of these approaches for the simultaneous recovery of the source strength and the contaminant concentration distribution is carried out for three types of sources and they include boundary iv sources, instantaneous point sources and continuous point sources. The assessment accounts for different transport modes, time discretization, spatial discretization, location of observation points, and the quality of observation data. The numerical results demonstrate the applicability and limitations of the proposed methodologies. It is found in most cases that the solutions with inverse GEM and the least squares approach are of comparable accuracy to those with direct GEM and the SCE approach. However, the latter approach is found to be computationally intensive.

Neste trabalho, estudam-se problemas bidimensionais de propagação de ondas acústicas e elásticas, no domínio da freqüência, formulados através do Método dos Elementos de Contorno. A formulação é baseada nas representações integrais das equações diferenciais que governam os fenômenos de propagação de ondas acústicas num meio fluido e de ondas elásticas numa estrutura elástica. Analisa-se também a interação entre o fluido e a estrutura com o uso de sistemas de equações acoplados. As soluções fundamentais utilizadas são expressões exatas e não há necessidade de subdivisão dos domínios em células de integração. São aplicadas técnicas de integração alternativas na escolha das equações algébricas no domínio do fluido, visando a melhora das respostas globais do conjunto. Apresentam-se ainda exemplos numéricos, com o objetivo de possibilitar a modelagem numérica de problemas de acoplamento fluido-estrutura e de radiação e difusão acústica. / In this work, acoustic and elastic wave propagation problems in 2D, in frequency domain, are studied and formulated with the Boundary Element Methods. The formulation is based on the integral representations derived from the differential equations that govern the phenomena of acoustic wave propagation in a fluid medium and elastic wave propagation inside an elastic domain. The fluid-structure interaction is also formulated by coupling appropriately the corresponding systems of equations. The fundamental solutions adopted in this work are conveniently chosen to avoid the mass integral terms in the elastic wave integral representation and the equivalent terms in the acoustic integral equation. Thus, the algebraic representations of both problems are written only in terms of boundary values. Subdivisions of the domain to perform integrals over cells are not required. In an attempt to improve the global answers of the fluid problem, several integration techniques have been experimented to build alternative algebraic matrix equations. Numerical examples are presented in order to shown the accuracy of the studied acoustic radiation and scattering problems and also to verify the proposed fluid-structure coupling.

Este trabalho trata da análise de problemas planos de chapa compostos por materiais anisotrópicos, definidas em uma região ou no domínio por completo, utilizando-se o método dos elementos de contorno. As soluções fundamentais para problemas anisotrópicos, embora existentes, mostram-se difíceis de serem utilizadas devido à complexidade de sua formulação matemática ou da necessidade de se encontrar partes da solução numericamente. Nesse sentido, a formulação alternativa mostrada nesse trabalho permite o estudo de meios anisotrópicos utilizando-se as soluções fundamentais para meios isotrópicos nas representações integrais de problemas planos com campo de tensões iniciais. A região do domínio com propriedades anisotrópicas ou diferentes das propriedades elásticas de um meio isotrópico usado como referência é discretizada em células triangulares, enquanto que o contorno do problema é discretizado em elementos lineares. As componentes do tensor de tensões iniciais da região anisotrópica são definidas como uma correção das tensões elásticas do material isotrópico de referência através de uma matriz de penalização. Essa matriz, por sua vez, é obtida através de relações envolvendo as constantes elásticas de rigidez do meio desejado e os coeficientes elásticos de flexibilidade do meio isotrópico de referência. Essa técnica é particularmente adequada para a análise de inclusões anisotrópicas onde há a necessidade de discretizar apenas uma parte pequena do domínio, aumentando, portanto, pouco o número de graus de liberdade do sistema. Os resultados obtidos com a formulação proposta são comparados com os resultados numéricos existentes na literatura. / This work deals with elastic 2D problems characterized by the presence of zones with different materials and anisotropic inclusions using the boundary element method. The anisotropy can be assumed either over the whole domain or defined only over some particular inclusions, which is the most usual case. Fundamental solutions for anisotropic domains, although well-known, lead to more complex formulations and may introduce difficulties when the analysis requires more complex material models as for instance plastic behavior, finite deformations, etc. The alternative formulation proposed in this work can be applied to anisotropic bodies using the classical fundamental solutions for 2D elastic isotropic domains plus correction given by an initial stress field. The domain region with anisotropic properties or only with different isotropic elastic parameters has to be discretized into cells to allow the required corrections, while the complementary part of the body requires only boundary discretization. The initial stress tensor to be applied to the anisiotropic region is defined as the isotropic material elastic stress tensor correction by introducing a local penalty matrix. This matrix is obtained by the difference between the elastic parameters between the reference values and the anisotropic material. This technique is particularly appropriate for anisotropic inclusion analysis, in which the domain discretization is required only over a small region, therefore increasing very little the number of degrees of freedom of the final algebraic system. The numerical results obtained by using the proposed formulation have demonstrated to be very accurate in comparison with either analytical solutions or the other numerical values.

Neste trabalho, foi desenvolvida uma formulação do método dos elementos de contorno (MEC) isoparamétrico com aproximação de ordem qualquer para análise de domínios bidimensionais enrijecidos, particularmente túneis. Tal formulação simula os enrijecedores a partir de correções da rigidez local, que são introduzidas utilizando-se um termo adicional escrito em tensões iniciais sobre a área estreita do enrijecedor. Além das equações integrais usuais para pontos do contorno foram também necessárias as equações integrais da força normal e do momento fletor escritas para pontos do eixo do enrijecedor. Através do polinômio de Lagrange foi feita a generalização da ordem das funções polinomiais responsáveis pela aproximação tanto das variáveis quanto da representação geométrica do problema. A partir daí, a formulação apresentada simulou com êxito a inclusão de enrijecedores em tais meios, como por exemplo, na análise de estacas, ou de enrijecedores na escavação de túneis. Foi desenvolvida também neste trabalho uma formulação para considerar o atraso na instalação do suporte de túneis. Com o desenvolvimento do elemento de contorno curvo de ordem qualquer, pôde-se obter resultados ainda melhores com discretizações reduzidas. / In this work, an isoparametric boundary element method (BEM) formulation with approximation of any order was developed to the analysis of stiffened two-based on local stiffness corrections, which are made using an additional integral written in terms of initial stresses, applied over the areas close to stiffeners. Besides the usual displacement integral equations the presented formulation also requires integral equations of the normal forces and the bending moments written for points defined along the stiffener axis. By using Lagrange polynomials, the generalization of the shape function order used to approximate the boundary values and the geometry was made. Excavations in infinite media or large domains are engineering applications in which the BEM is efficient due to its accuracy, reliable results and also to require coarser discretizations, always leading to smaller algebraic systems when compared to other methods. Thereafter, the presented formulation can simulate successfully the inclusion of stiffeners into two-dimensional domains, such as the analysis of piles embedded in a 2-D solids or lined tunnels. It was also developed a formulation to consider the delay to install tunnel linings.

Este trabalho trata da formulação do método dos elementos de contorno para a análise não linear de pavimentos de concreto armado. A teoria utilizada é a de Reissner, que mostrou-se eficiente tanto para placas esbeltas quanto para as moderadamente espessas. Considera-se a ocorrência de cargas concentradas, distribuídas em sub-regiões da placa e em linha. Admite-se também a possibilidade de um campo de momentos iniciais, que viabiliza o estudo da não linearidade física nos problemas. Foram utilizados campos de momentos iniciais aplicados apenas em pontos internos ao domínio. As integrais que envolvem as células de domínio foram modificadas, eliminando-se os núcleos complexos e as aproximações através de séries. Foi desenvolvida uma formulação para a análise de placas vinculadas a estruturas quaisquer em seu domínio, com o uso de cargas aplicadas incógnitas atuando como enrijecedores. O acoplamento MEC/MEF foi empregado utilizando-se modelos simples, porém robustos. O sistema de equações algébricas foi otimizado com a utilização da técnica dos mínimos quadrados. O concreto foi modelado adotando-se o modelo de dano de Mazars; para as armaduras um modelo elastoplástico uniaxial com endurecimento isótropo. A análise não linear do problema é efetuada utilizando-se procedimento incremental-iterativo. São apresentados alguns exemplos simples que mostram a precisão da técnica usada. / This work refers to the formulation of the boundary element method for non-linear analysis of building floor structures. The plate bending theory adopted to develop the work wad due to Reissner, which has demonstrated to be efficient for thick, moderated thick and thin plates. The kinds of load applied on the plate medium surface have been taken into account: concentrated loading, distributed over sub-domains; distributed along internal lines. The presence of initial moment fields convenient to model temperature effects and to be used to build up non-linear solutions has also been considered in the formulation. The domain integrals containing complex kernels to take into account the initial moment field influences were modified by introducing their primitive functions, avoiding therefore using series expansions. To integrate the initial moments fields only approximations based on internal nodal points were used. The resulting cell integrals have been transformed to the cell boundary which results into regular integral only. A boundary element formulation to treat structural system defined by combining plates with other structural element was developed, using interface force as unknowns. The BEM/FEM coupling developed to treat this case is simple but robust; only displacements have been coupled avoiding important singularities that may happen when coupling rotations. The resulting system of algebraic equations has been regularized by using the least square method. The concrete material was modeled by using the Mazar\'s damage model, while the steel reinforcement was assumed to behave as elastoplastic material with isotropic hardening. Finally, some examples are shown to illustrate the accuracy of the presented formulation and the numerical schemes proposed in this work.

Neste trabalho a formulação direta do Método dos Elementos de Contorno é utilizada para o estudo da interação de placas com o meio contínuo. O solo, considerado como um meio contínuo, tem a sua reação representada pelo acréscimo de uma integral de domínio nas equações integrais usuais de placas. Essa integral de domínio é tratada utilizando-se células internas, o processo da reciprocidade dual e uma formulação alternativa. Inicialmente a reação do solo é aproximada utilizando-se a teoria de Winkler. Em seguida, o solo é considerado como sendo um sólido tridimensional elástico de domínio semi-infinito, e analisado pelo Método dos Elementos de Contorno utilizando-se as soluções fundamentais de Boussinesq-Cerruti e Mindlin, neste caso a interação entre a placa e o solo, é feita impondo-se o equilíbrio dos esforços e a compatibilidade de deslocamentos transversais, em todos os pontos da interface. Adotando-se um critério de plastificação simples e bilinear, é considerada a não-Iinearidade da reação do solo. Em cada caso, são apresentadas aplicações numéricas utilizando-se as três formulações, cujos resultados são comparados entre si e com valores teóricos, mostrando a eficiência das mesmas. / In this work the direct formulation of Boundary Element Method is adopted to study interaction of plates in bending with the continuum medium. The soil material, assumed as a continuum medium, applies on the plate surface what is represented in the usual integral equations by a domain integral. That domain integral is treated by approaching the subgrade reaction using cells, the dual reciprocity method or an alternative procedure. Initially, the reaction of soil is given by assuming the Winkler\'s theory. Then, the soil is assumed as a semi-infinite three-dimensional elastic solid for which the Boundary Element Method is applied using the Boussineq-Cerruti and Mindlin\'s fundamental solutions. In this case, the interaction of the plate with the soil is made by enforcing displacement compatibility and equilibrium at all interface points define by the plate surface discretization. Non-linear behaviour is also assumed to govern the interaction reaction between plate and the soil medium. For that, a simple non symmetric stress-strain curve is taken to represent the elastoplastic responses. In each case, numerical examples, using the three subgrade reaction approximations discussed here, are shown to illustrate the accuracy and efficiency of the proposed models.

This thesis presents new boundary element formulations for solution of bending problems in plates and shells. Also presented are the dual boundary element formulations for analysis of crack problems in plates and shells. Reissner plate theory is adopted to represent the bending and shear, and two dimensional (2-D) plane stress is used to model the membrane behaviour of the plate. New set of boundary element formulations to solve bending problems of shear deformable shallow shells having quadratic mid-surface is derived based on the modified Reissner plate and two dimensional plane stress governing equations which are now coupled due to the curvature of the shell. Dual Boundary Element Methods (DBEM) for plates and shells are developed for fracture mechanics analysis of structures loaded in combine bending and tension. Five stress intensity factors, that is, two for membrane and three for bending and shear are computed. The JIntegral technique and Crack Surface Displacements Extrapolation (CSDE) technique are used to compute the stress intensity factors. Special shape functions for crack tip elements are implemented to represent mom accurately displacement fields close to the crack tip. Crack growth processes are simulated with an incremental crack extension analysis. During the simulation, crack growth direction is determined using the maximum principal stress criterion. The crack extension is modelled by adding new boundary elements to the previous crack boundaries. As a consequence remeshing of existing boundaries is not required, and using this method the simulation can be effectively performed. Finally, a multi-region boundary element formulation is presented for modelling assembled plate-structures. The formulation enforces the compatibility of translations and rotations as well as equilibrium of membrane, bending and shear tractions. Examples are presented for plate and shell structures with different geometry, loading and boundar-y conditions to demonstrate the accuracy of the proposed formulations. The results obtained are shown to be in good agreement with analytical and other numerical results. Also presented are crack growth simulations of flat and curved panels loaded in combine bending and tension. The DBEM results are in good agreement with existing numerical and experimental results. Assembled plate-structure and a non-shallow shell bending problems are also analysed using a multi-region formulation developed in this thesis.

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