[Truncated abstract] The scaled boundary finite element method is a novel computational method developed by Wolf and Song which reduces partial differential equations to a set of ordinary linear differential equations. The method, which is semi-analytical, is suitable for solving linear elliptic, parabolic and hyperbolic partial differential equations. The method has proved to be very efficient in solving various types of problems, including problems of potential flow and diffusion. The method out performs the finite element method when solving unbounded domain problems and problems involving stress singularities and discontinuities. The scaled boundary finite element method involves solution of a quadratic eigenproblem, the computational expense of which increases rapidly as the number of degrees of freedom increases. Consequently, to a greater extent than the finite element method, it is desirable to obtain solutions at a specified level of accuracy while using the minimum number of degrees of freedom necessary. In previous work, no systematic study had been performed so far into the use of elements of higher order, and no consideration made of p adaptivity. . . The primal problem is solved normally using the basic scaled boundary finite element method. The dual problem is solved by the new technique using the fundamental solution. A guaranteed upper error bound based on the Cauchy-Schwarz inequality is derived. A iv goal-oriented p-hierarchical adaptive procedure is proposed and implemented efficiently in the scaled boundary finite element method.

Thesis (Ph. D.)--State University of New York at Binghamton, Department of Geological Sciences and Environmental Studies, 2007. / Includes bibliographical references (leaves 308-314).

Uma implementação computacional baseada nos conceitos da mecânica do contato e no Método dos Elementos de Contorno é desenvolvida para simular a interação entre discos de corte e maciço rochosos. Simula-se o contato considerando-se inicialmente uma superfície potencial de contato que é atualizada durante um processo de carregamento incremental, podendo conter elementos separados, em contato sem deslizamento ou com deslizamento parcial. A cada passo do carregamento incremental estima-se a configuração do modelo e os dados obtidos neste passo serão utilizados como parâmetros no passo seguinte até que todo o carregamento esteja aplicado. O modelo em estudo consiste em dois discos de corte paralelos atuando sobre uma base sólida com característica elástica linear. São feitas duas simulações com os discos de corte. Na primeira delas, compara-se a penetração dos discos utilizando-se como parâmetro os valores calculados em uma análise por elementos finitos. No segundo caso, estuda-se a distribuição de tensões no maciço quando se altera o espaçamento entre os discos para um mesmo carregamento. Além desta análise, duas outras comparações são feitas utilizando como parâmetros soluções analíticas e numéricas de modelos clássicos da mecânica do contato. São estes: cilindro e pilar em base elástica. / A computational implementation based on contact mechanics and on the Boundary Element Method is developed in order to simulate the interaction between disc cutters and rock mass. The contact simulation considers initially a potential contact area which is updated during an incremental load process, in such way the surface can include elements in separation, stick or partial slip. At each incremental load step the configuration of the model shall be evaluated and the values computed at such step are used as parameter to the next load step until the end of the loading process. The investigated model consists in two parallel cutter discs on a flat elastic foundation. In the first simulation the penetration of the discs are studied and the results are compared against a finite element simulation. In the second simulation, the stress distribution in the rock mass is evaluated considering different spacing between the disc cutters by keeping the same load. In addition, two benchmark problems of contact mechanics, such as the cylinder and the flat punch on a elastic foundation, were modeled in order to validate the proposed algorithm. The obtained results were compared against analytical and numerical solutions.

Orientadores: Eder Lima de Albuquerque, Paulo Sollero / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-15T04:21:12Z (GMT). No. of bitstreams: 1 Sousa_KerllesRafaelPereira_M.pdf: 1489778 bytes, checksum: 08fe8a77e9ca4ba0d1272c061013bac7 (MD5) Previous issue date: 2009 / Resumo: Este trabalho apresenta uma formulação dinâmica do método dos elementos de contorno para o cálculo de tensões e critério de falhas de placas finas anisotrópicas. As formulações utilizam soluções fundamentais da elasto-estática e os termos de inércia são tratados como forças de corpo. As integrais de domínio provenientes de forcas de corpo são transformadas em integrais de contorno usando o método da integração radial (RIM). No RIM, a função de aproximação "thin plate spline"de placas finas e usada na aproximação das forças de corpo. São implementados formulações para análise transiente de placas finas. A integração no tempo é realizada usando o método de Houbolt. Uma equação integral para a segunda derivada de deslocamento é desenvolvida e todas as derivadas da solução fundamental são calculadas analiticamente. Apenas o contorno é discretizado. Os resultados numéricos apresentaram boa concordância com os resultados disponíveis na literatura e também com resultados do método dos elementos finitos / Abstract: This work presents a dynamic formulation of the boundary element method for stress and failure criterion analyses of anisotropic thin plates. Formulations use elastostatic fundamental solutions and inertia terms are treated as body forces. Domain integrals that come from body forces are transformed into boundary integrals using the radial integration method (RIM). In the RIM, the augmented thin plate spline is used as the aproximation function. A formulation for transient analysis is implemented. The time integration is carried out using the Houbolt method. Integral equations for the second derivatives of deflection are developed and all derivatives of fundamental solutions are computed analitically. Only the boundary is discretized in the formulation. Numerical results show good agreement with results available in literature as well as finite element results / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

Orientadores: Paulo Sollero, Eder Lima de Albuquerque / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-11T04:07:05Z (GMT). No. of bitstreams: 1 UsecheVivero_JairoFrancisco_D.pdf: 4442457 bytes, checksum: 707a93966692d7daf8a71f104b9a1bb5 (MD5) Previous issue date: 2007 / Resumo: O objetivo deste projeto é o desenvolvimento de uma ferramenta computacional para 'a an'alise e projeto de estruturas aeronáuticas trincadas e reparadas por placas de materiais compósitos laminadas coladas. As placas metálicas isotrópicas da estrutura aeronáutica serão modeladas pelo método dos elementos de contorno considerando a presença de tensões de cisalhamento nos planos normais á superfície das placas (formulação de Reissner-Mindlin). No modelamento do reparo será usada uma formula¸c¿ao por elementos de contorno para placas anisotrópicas sem considerar a presençaa de tensões de cisalhamento nos planos normais à superfície da placa (formulação do Kirchhoff-Love). A análise será validada com resultados analíticos, numéricos e experimentais disponíveis na literatura e com modelos desenvolvidos pelo método dos elementos finitos / Abstract: The objective of this project is the development of a computational tool for the analysis and design of cracked aeronautical structures repaired by adhesively bonded laminated composites. The isotropic metallic plates of the aeronautical structure will be modeled by the boundary element method considering the presence of shear stresses in planes that are normal to the surface of the plates (formulation of Reisner-Mindlin). In order to model the repair, a boundary element formulation for anisotropic plates will be used neglecting the presence of shear stresses in planes that are normal to the surface of the plate (formulation of Kirchhoff-Love). The analysis will be validated with analytical, numerical and experimental results avalilable in the literature and with finite element models / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

Orientadores: Eder Lima de Albuquerque, Paulo Sollero / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-11T17:16:52Z (GMT). No. of bitstreams: 1 Torsani_FernandoLuiz_M.pdf: 2116426 bytes, checksum: 8a045e9dbe79f3db053d6de885ade97e (MD5) Previous issue date: 2007 / Resumo: O presente trabalho tem por objetivo o cálculo de tensões em pontos no interior do domínio de placas finas anisotrópicas usando o método dos elementos de contorno. As equações integrais de contorno para deslocamentos e rotações em placas anisotrópicas são apresentadas. as derivadas de segunda ordem da equação integral de deslocamento são de senvol vidas. A partir destas equações, são calculadas as deformações e, em seguida, as tensões. Por fim são desenvolvidos procedimentos para o cálculo de critérios de falha para materiais anisotrópicos, analisando a falha em cada uma das lâminas. Exemplos são apresentados usando as rotinas desenvolvidas, cujos resultados são comparados com soluções encontradas na literatura. Os resultados obtidos pelas análises numéricas apresentam boa concordância com os resultados da literatura indicando a sua aplicabilidade em problemas reais de engenharia / Abstract: The objective of the present work is the calculation of stresses in domain internal points af anisotropic thin plates using the boundary element method. Boundary integral equations for displacements and rotations in anisotropic plates are presented. Second order derivatives af the integral equation of displacement are developed. From these equations, strains and stresses are calculated. Finally procedures for the calculation of failure criteria for anisotropic matei-ials are developed, analyzing the failure in each laminae of the laminate. Examples are presented using the developed routines, wh.ose results are compared with solutions found in literature. Results for the numerical analysis present good agreement with results from the literature, indicating its applicability in real engineering problems / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

This paper presents three new coupling methods for interior penalty discontinuous Galerkin finite element methods and boundary element methods. The new methods allow one to use discontinuous basis functions on the interface between the subdomains represented by the finite element and boundary element methods. This feature is particularly important when discontinuous Galerkin finite element methods are used. Error and stability analysis is presented for some of the methods. Numerical examples suggest that all three methods exhibit very similar convergence properties, consistent with available theoretical results.:1. Introduction 2. Model Problem and Background 3. New Coupling Methods 4. Stability and Error Analysis 5. Numerical Examples 6. Summary A. Appendix

<p>Droplet dispersions with adsorbed exotic surface active species (proteins, fatty alcohol, fatty acids, solid particulates, lipids, or polymers) find an immense number of applications in the field of engineering and bioscience. Interfacial rheology plays an essential role in the dynamics of many of these systems, yet little is understood about how these effects alter droplet dynamics. Most surfactants studied historically have been simple enough that the droplet dynamics can be described by Marangoni effects (surfactant concentration gradients), surface dilution, and adsorption/desorption kinetics without including the intrinsic surface rheology. One of the challenges in examining droplet systems with complex interfaces is that the intrinsic rheological effects are strongly coupled with surfactant transport effects (surface convection, diffusion, dilution and adsorption/desorption). The surface rheology can impact the ability of surfactant to transport along the surface, while surfactant transport can alter the surface rheology by changing the surface concentration. In this work, we develop axisymmetric boundary-integral simulations that allow us to quantitatively explore the combined effect of intrinsic surface rheology and surfactant transport on droplet dynamics in the Stokes flow limit. We assume that the droplet interface is predominantly viscous and that the Boussinesq Scriven constitutive relationship describes the properties of the viscous membrane. The key questions that we address in this work are:</p> <p><br></p> <ul> <li>How do viscous membranes impact droplet deformation, breakup and relaxation?      </li> </ul> <p>     When a droplet is placed under external flow, it can either attain a stable shape under flow or stretch indefinitely above a critical flow rate and break apart. In this topic, we first discuss the breakup conditions for a droplet suspended in an unbounded immiscible fluid under a general linear flow field using perturbation theories for surface viscosity in the limit of small droplet deformation. We neglect the inhomogeneity in surfactant concentration and surface tension for this part. We find that the surface shear/dilational viscosity increases/decreases the critical capillary number for droplet breakup compared to a clean droplet at the same capillary number and droplet viscosity ratio value. In the second part of this topic, we solve the problem using boundary integral simulations for the case of axisymmetric extensional flow. Numerically solving this problem allows us to examine the effect of Marangoni stresses, pressure thickening/thinning surface viscosities, and stronger flows. We compare the droplet breakup results from our simulations to results from second-order perturbation theories. We present the physical mechanism behind our observations using traction arguments from interfacial viscosities. We conclude this topic by examining the combined role of surface viscosity and surfactant transport on the relaxation of an initially extended droplet in a quiescent external fluid.</p> <p><br></p> <ul> <li>How do viscous membranes alter droplet sedimentation?</li> </ul> <p>      When an initially deformed droplet sediment under gravity, it can either revert to a spherical shape or undergo instability where the droplet develops a long tail or cavity at its rear end. Here, we use numerical simulations to discuss how interfacial viscosity alters the breakup criterion and the formation of threads/cavities under gravity. We examine the combined influence of intrinsic surface viscosity and surfactant transport on droplet stability by assuming a linear dependence of surface tension on surfactant concentration and an exponential dependence of interfacial viscosities on surface pressure. We find that surface shear viscosity inhibits the tail/cavity growth at the droplet’s rear end and increases the critical capillary number compared to a clean droplet. In contrast, surface dilational viscosity promotes tail/cavity growth and lowers the critical capillary number compared to a clean droplet.</p> <p><br></p> <ul> <li>How do viscous membranes affect droplet coalescence?</li> </ul> <p>      When two droplets approach under external flow, a thin film is formed between the two droplets. Here, we develop numerical simulations to model the full coalescence process from the collision of two droplets under uniaxial compressional flow to the point where the film approaches rupture. We investigate the role of interfacial viscosity on the film profiles and drainage time. We observe that both surface shear and dilational viscosity significantly delay the film drainage time relative to a clean droplet. Interestingly, we find that the film drainage behaviour of a droplet with surface viscosity is not altered by the relative ratio of shear to dilational viscosity but rather depends on the sum of shear and dilational Boussinesq numbers. This is in contrast to the effect of surface viscosity observed in the previous processes (droplet breakup and sedimentation), where surface shear viscosity increases the critical capillary number compared to a clean droplet, while surface dilatational viscosity has the opposite effect.</p>

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No presente trabalho, uma combinação do método dos elementos de contorno (MEC) com o método dos elementos finitos (MEF) é apresentada para a análise da interação entre estacas e o solo, considerado como um meio infinito tridimensional e homogêneo. O meio contínuo tridimensional de domínio infinito é modelado pelo MEC, enquanto as estacas consideradas como elementos reticulares são tratadas pelo MEF. As equações das estacas oriundas do método dos elementos finitos são combinadas com as do meio contínuo obtidas a partir do método dos elementos de contorno, resultando em um sistema completo de equações, que convenientemente tratadas, proporcionam a formulação de coeficientes de rigidez do conjunto solo-estacas. Finalmente, uma formulação para a análise do comportamento não-linear do solo na interface com a estaca é desenvolvida, tornando o modelo mais abrangente. / In the present work a combination of the Boundary Element Method (BEM) and the Finite Element Method (FEM) is used for pile-soil interaction analyses, considering the soil as a homogeneous, three-dimensional and infinite medium. The three-dimensional infinite continuous medium is modeled by the BEM, and the piles are, considered as beam elements, modeled by the FEM. This combination also is used for studying the interaction of plates sitting on a continuous medium. The pile equations generated from the FEM are combined with the medium equations generated from the BEM, resulting a complete equation system. Manipulating properly this equation system, a set of stiffness coefficients for the system soil-pile is obtained. Finally, to make the model more comprehensive, it presented a formulation to take into account the soil nonlinear behavior at the pile interface.