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.

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.

Desenvolvem-se a formulação do Método dos Elementos de Contorno e correspondente algoritmo (para implementação em microcomputador) para a análise de propagação de fraturas em domínios bidimensionais. São utilizados elementos lineares isoparamétricos, tanto para discretizar o contorno quanto para simular a fratura. Os elementos de fratura são descontínuos. A formulação é baseada em equações integrais de tensões e de deslocamentos, onde o termo que considera tensões iniciais concentradas na linha de fratura é formulado a partir da definição de dipolos. O critério adotado é o modelo de fratura coesiva. Os termos singulares e hiper-singulares da formulação são tratados analiticamente e os termos quase-singulares são calculados através de um esquema numérico baseado na utilização de sub-elementos. Os valores dos dipolos são estimados ponto a ponto. Ao longo das fraturas, o valor máximo da tensão normal de tração permite definir novos elementos. As tensões de cisalhamento são removidas para manter a direção principal durante o processo. / The Boundary Element Method formulation and corresponding algorithrn (for microcomputer implementation) are developed for crack growth analysis in two-dimensional domains. Linear isoparametric elements are used to discretize both boundary and crack path. Fracture elements are assumed to be discontinuous. The formulation is based on stress and displacement integral equations, where the term that takes into account initial stresses concentrated along fracture line is formulated from dipoles definition. The coesive fracture rnodel is the criterium adopted. Singular and hipersingular formulation terms are anallitically treated and quasi-singular terms are computed by a numerical scheme based on element subdivision. Dipole values are estirnated point by point. Along fractures, the maximum normal tensile strenght is used to define new elements. Shear stresses are also removed to maintain the principal direction during the process.

O objetivo deste trabalho é apresentar uma nova formulação direta do Método dos Elementos de Contorno (M.E.C.) para análise de placas, utilizando a teoria de Kirchhoff, admitindo três parâmetros nodais de deslocamentos para sua representação integral: deslocamento transversal e suas derivadas nas direções normal e tangencial ao contorno. Dois valores nodais são usados para os esforços, momento fletor normal mn e força cortante equivalente Vn. Desta forma são escritas três equações integrais de contorno por nó, obtidas a partir da discretização da placa, segundo a forma usual do método. A vantagem mais perceptível desta formulação é a possibilidade de se fazer a ligação da placa analisada pelo M.E.C. com elementos lineares, representados por três valores nodais de deslocamentos que passam a ser compatibilizados diretamente, para a análise de edifícios. São apresentados exemplos numéricos da formulação e das ligações para comprovação da formulação. / The aim of this work is to present an alternative formulation for plate bending analysis, using Kirchhoff\'s theory, in wich the boundary equation for displacements and its derivative in tangential and normal directions to the boundary for each boundary node are used. The efforts, according to Kirchhoff\'s theory, are the normal bending mn and the equivalent shear force Vn. This formulation is adequate for the analysis of plates coupled with flexible colunms and beams because these structural elements have three nodal displacement values at its nodes. Many examples of single plates and buildings slab are presented using the formulation proposed in this work.

Large silencers used in the power generation industry usually have a very large cross section at the inlet and outlet. Higher-order modes will populate the inlet and outlet even at very low frequencies. Although the silencer itself is often modeled by a three-dimensional analysis tool such as the boundary element method (BEM) or finite element method (FEM), a direct computation of the transmission loss (TL) from the BEM or FEM model can be challenging without incorporating certain forms of modal expansion. A so-called “impedance-to-scattering matrix method” is proposed to extract the modes at the inlet and outlet from the BEM impedance matrix based on the point collocation method. The BEM impedance matrix relates the sound pressures at the inlet and outlet to the corresponding particle velocities, while the scattering matrix relates the modes at the inlet and outlet. Normally there are more boundary elements than the total number of modes at the inlet and outlet, and a least-squares procedure is used to condense the element-based impedance matrix to the mode-based scattering matrix. The TL computation will follow if a certain form of the incident wave is assumed and the outlet is non-reflective. Several commonly used inlet/outlet configurations are considered in this dissertation, which include axisymmetric, non-axisymmetric circular, and rectangular inlet/outlet shapes. In addition to the single inlet and outlet silencers, large multi-inlet and multi-outlet silencers are also investigated. Besides the collocation-based impedance-to-scattering matrix method, an integral-based impedance-to-scattering matrix method based on the reciprocal identity is also proposed for large silencer analysis. Although it may be more time-consuming to perform the additional numerical integration, an integral-based method is free of any uncertainties associated with collocation points. The computational efficiency, accuracy and stability are compared between two proposed methods. One bonus effect of producing the scattering matrix is that it can also be used to combine subsystems in series connection. The Redheffer’s star product is introduced to combine scattering matrices of subsystems. In the design stage, rapid assessment of the silencer performance is always preferred. However, the existing analytical approaches are only suitable for simple dissipative silencers such as straight lined ducts. A two-dimensional first-mode semi-analytical solution is developed to quickly evaluate the performance of tuned dissipative silencers below the cut-off frequency. The semi-analytical solution can also serve as a validation tool for the BEM.

No description available.

In this dissertation, we introduce and analyse a scheme for the fast evaluation of integrals stemming from boundary element methods including discretisations of the classical single and double layer potential operators. Our method is based on the parametrisation of boundary elements in terms of a d-dimensional parameter tuple. We interpret the integral as a real-valued function f depending on d parameters and show that f is smooth in a d-dimensional box. A standard interpolation of f by polynomials leads to a d-dimensional tensor which is given by the values of f at the interpolation points. This tensor may be approximated in a low rank tensor format like the canonical format or the hierarchical format. The tensor approximation has to be done only once and allows us to evaluate interpolants in O(dr(m+1)) operations in the canonical format, or O(dk³ + dk(m + 1)) operations in the hierarchical format, where m denotes the interpolation order and the ranks r, k are small integers. In particular, we apply an efficient black box scheme in the hierarchical tensor format in order to adaptively approximate tensors even in high dimensions d with a prescribed (but heuristic) target accuracy. By means of detailed numerical experiments, we demonstrate that highly accurate integral values can be obtained at very moderate costs.

Efficiency is one of the key issues in numerical simulation of large-scale problems with complex 3-D geometry. Traditional domain based methods, such as finite element methods, may not be suitable for these problems due to, for example, the complexity of mesh generation. The Boundary Element Method (BEM), based on boundary integral formulations (BIE), offers one possible solution to this issue by discretizing only the surface of the domain. However, to date, successful applications of the BEM are mostly limited to linear and continuum problems. The challenges in the extension of the BEM to nonlinear problems or problems with non-continuum boundary conditions (BC) include, but are not limited to, the lack of appropriate BIE and the difficulties in the treatment of the volume integrals that result from the nonlinear terms. In this thesis work, new approaches and techniques based on the BEM have been developed for 3-D nonlinear problems and Stokes problems with slip BC. For nonlinear problems, a major difficulty in applying the BEM is the treatment of the volume integrals in the BIE. An efficient approach, based on the precorrected-FFT technique, is developed to evaluate the volume integrals. In this approach, the 3-D uniform grid constructed initially to accelerate surface integration is used as the baseline mesh to evaluate volume integrals. The cubes enclosing part of the boundary are partitioned using surface panels. No volume discretization of the interior cubes is necessary. This grid is also used to accelerate volume integration. Based on this approach, accelerated BEM solvers for non-homogeneous and nonlinear problems are developed and tested. Good agreement is achieved between simulation results and analytical results. Qualitative comparison is made with current approaches. Stokes problems with slip BC are of particular importance in micro gas flows such as those encountered in MEMS devices. An efficient approach based on the BEM combined with the precorrected-FFT technique has been proposed and various techniques have been developed to solve these problems. As the applications of the developed method, drag forces on oscillating objects immersed in an unbounded slip flow are calculated and validated with either analytic solutions or experimental results.