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.

No description available.

The implicit-solvent model uses continuum electrostatic theory to represent the salt solution around dissolved biomolecules, leading to a coupled system of the Poisson-Boltzmann and Poisson equations. This thesis uses the implicit-solvent model to study solvation, binding and adsorption of proteins. We developed an implicit-solvent model solver that uses the boundary element method (BEM), called PyGBe. BEM numerically solves integral equations along the biomolecule-solvent interface only, therefore, it does not need to discretize the entire domain. PyGBe accelerates the BEM with a treecode algorithm and runs on graphic processing units. We performed extensive verification and validation of the code, comparing it with experimental observations, analytical solutions, and other numerical tools. Our results suggest that a BEM approach is more appropriate than volumetric based methods, like finite-difference or finite-element, for high accuracy calculations. We also discussed the effect of features like solvent-filled cavities and Stern layers in the implicit-solvent model, and realized that they become relevant in binding energy calculations. The application that drove this work was nano-scale biosensors-- devices designed to detect biomolecules. Biosensors are built with a functionalized layer of ligand molecules, to which the target molecule binds when it is detected. With our code, we performed a study of the orientation of proteins near charged surfaces, and investigated the ideal conditions for ligand molecule adsorption. Using immunoglobulin G as a test case, we found out that low salt concentration in the solvent and high positive surface charge density leads to favorable orientations of the ligand molecule for biosensing applications. We also studied the plasmonic response of localized surface plasmon resonance (LSPR) biosensors. LSPR biosensors monitor the plasmon resonance frequency of metallic nanoparticles, which shifts when a target molecule binds to a ligand molecule. Electrostatics is a valid approximation to the LSPR biosensor optical phenomenon in the long-wavelength limit, and BEM was able to reproduce the shift in the plasmon resonance frequency as proteins approach the nanoparticle.

No description available.

In this research project, the Boundary Element Method (BEM) is developed and formulated for the solution of two-dimensional convection-diffusion-reaction problems. A combined approach with the dual reciprocity boundary element method (DRBEM) has been applied to solve steady-state problems with variable velocity and transient problems with constant and variable velocity fields. Further, the radial integration boundary element method (RIBEM) is utilised to handle non-homogeneous problems with variable source term. For all cases, a boundary-only formulation is produced. Initially, the steady-state case with constant velocity is considered, by employing constant boundary elements and a fundamental solution of the adjoint equation. This fundamental solution leads to a singular integral equation. The conservation laws, usually applied to avoid this integration, do not hold when a chemical reaction is taking place. Then, the integrals are successfully computed using Telles' technique. The application of the BEM for this particular equation is discussed in detail in this work. Next, the steady-state problem for variable velocity fields is presented and investigated. The velocity field is divided into an average value plus a perturbation. The perturbation is taken to the right-hand-side of the equation generating a non-homogeneous term. This nonhomogeneous equation is treated by utilising the DRM approach resulting in a boundary-only equation. Then, an integral equation formulation for the transient problem with constant velocity is derived, based on the DRM approach utilising the fundamental solution of the steady-state case. Therefore, the convective terms will be encompassed by the fundamental solution and lie within the boundary integral after application of Greens's second identity, leaving on the right-hand-side of the equation a domain integral involving the time-derivative only. The proposed DRM method needs the time-derivative to be expanded as a series of functions that will allow the domain integral to be moved to the boundary. The expansion required by the DRM uses functions which take into account the geometry and physics of the problem, if velocity-dependent terms are used. After that, a novel DRBEM model for transient convection-diffusion-reaction problems with variable velocity field is investigated and validated. The fundamental solution for the corresponding steady-state problem is adopted in this formulation. The variable velocity is decomposed into an average which is included into the fundamental solution of the corresponding equation with constant coefficients, and a perturbation which is treated using the DRM approximation. The mathematical formulation permits the numerical solution to be represented in terms of boundary-only integrals. Finally, a new formulation for non-homogeneous convection-diffusion-reaction problems with variable source term is achieved using RIBEM. The RIM is adopted to convert the domain integrals into boundary-only integrals. The proposed technique shows very good solution behaviour and accuracy in all cases studied. The convergence of the methods has been examined by implementing different error norm indicators and increasing the number of boundary elements in all cases. Numerical test cases are presented throughout this research work. Their results are sufficiently encouraging to recommend the use of the techniques developed for solution of general convection-diffusion-reaction problems. All the simulated solutions for several examples showed very good agreement with available analytical solutions, with no numerical problems of oscillation and damping of sharp fronts.