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[pt] DESENVOLVIMENTO DE PROCEDIMENTOS NUMÉRICOS PARA ANÁLISE DE INFILTRAÇÃO E ESTABILIDADE DE TALUDES EM BACIAS DE DRENAGEM / [en] DEVELOPEMENT OF NUMERICAL PROCEDURES FOR THE ANALYSIS OF INFILTRATION AND SLOPE STABILITY IN CATCHMENT BASINSMARCELO MIQUELETTO 02 April 2008 (has links)
[pt] Este trabalho tem por objetivo o desenvolvimento de uma
ferramenta numérica para avaliação do fluxo saturado-não
saturado em encostas de grandes dimensões, com aplicação na
análise de estabilidade dessas áreas. Emprega-se o método
dos elementos finitos na solução da equação de Richards,
considerando a carga de pressão como variável primária e
utilizando formulação adequada para minimização dos
problemas de conservação de massa, freqüentemente,
associados a esse fato. O modelo constitutivo utilizado
para a curva característica e função de condutividade
hidráulica é o proposto por Van Genuchten (1980). Para
solução da não-linearidade, emprega-se um método quasi-
Newton (BFGS). Com o objetivo de minimizar os requisitos de
memória computacional, utiliza-se esquema de armazenamento
de matriz esparsa, associado ao método de gradiente
biconjugado, na solução do sistema de equações.
Paralelamente, é apresentado algoritmo de geração de malha
tridimensional de elementos finitos, a partir de uma malha
superficial de triângulos, representativa da topografia.
Análises numéricas são executadas com a finalidade de
validação do código gerado, comparando-se os resultados
obtidos com aqueles gerados por outros programas já
consagrados na literatura técnica. É proposta metodologia
para geração de mapas de susceptibilidade a escorregamentos
translacionais rasos, empregando-se o método do talude
infinito, associado à estrutura da malha de elementos
finitos e aos resultados do problema de fluxo, incorporando-
se, assim, o efeito do estado de não saturação na
resistência do material. / [en] The aim of this work is to develop a numerical tool for the
analysis of saturated-unsaturated flow in large scale
natural slopes, applied to the study of the stability of
these areas. The finite element method is applied to solve
the Richard`s equation, taking into account the pressure
head as the primary variable and using an adequate
formulation to minimize the mass conservation issues. The
constitutive model used to the characteristic curve and
hydraulic constitutive function is the one presented by van
Genuchten (1980). A quasi-Newton method (BFGS) is applied
for the solution of the non-linearity. A sparse matrix
storage scheme, with the objective of reducing the
computational memory requirements, is associated to the bi-
conjugated gradient method for the solution of the system
of equations. An algorithm of finite elements mesh is
presented, which generates the 3D mesh from a triangle
superficial mesh representing the relief. Numerical
analyses are performed in order to validate the code, by
comparing the results with those generated by others widely
known codes presented in the technical literature. A
methodology for the generation of susceptibility maps to
shallow translational landslides is delineated, which
employs the infinite slope method to the finite elements
mesh structure and the flow problem results, considering
the effect of the unsaturated state in the material
strength.
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[pt] ANÁLISE DA ESTABILIDADE DE TALUDES SOLAPADOS POR VOÇOROCAMENTO / [en] STABILITY ANALYSIS OF SOIL SLOPES UNDERMINED BY VOÇOROCASCARLOS ATALIBA BORGES SILVEIRA 01 November 2001 (has links)
[pt] Neste trabalho o método dos elementos finitos é empregado
para analisar a estabilidade de taludes em solo solapados
por voçorocas. Muitos dos deslizamentos de solo que ocorrem
em taludes e encostas têm sido causados pelo fenômeno de
voçorocas, o resultado de um processo de erosão de solos
muito complexo. Uma breve revisão sobre a formação e o
crescimento de voçorocas, bem como sobre os seus efeitos na
estabilidade de taludes em solo, é feita neste trabalho.
Exemplos ilustrativos da aplicação desta técnica para
alguns casos de taludes e encostas erodidos por voçorocas
são apresentados, incluindo-se duas análises numéricas da
estabilidade de encostas situadas na cidade de Goiânia -
GO. Dificuldades numéricas devido à baixa taxa de
convergência da solução nas proximidades do colapso do
talude são também discutidas. / [en] In this work the finite element method is employed to
analyze the stability of soil slopes undermined by voçorocas
(gulling). Many of the shear slides occurred in both
natural slopes and embankments have been caused by the
phenomenon of voçorocas, the outcome of a very complex soil
erosion mechanism. A brief review about the formation and
growing of voçorocas, as well as an overview of their
effects on soil slope stability, are made in this work.
In the numerical simulation by the finite element method,
the potential slip surface is identified through the
progressive formation of a region of yielded soil as the
erosion process advances. A simple model, consisting of
incremental excavations of soil near the foot of the slope,
is used in this work to represent the undermining mechanism.
Illustrative examples of this technique are presented for
some cases of natural soil slopes eroded by voçorocas in
the city of Goiania - GO. Numerical difficulties due to the
poor convergence of the solution near the soil collapse are
also discussed.
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Formation of wrinkles on a coated substrateNebel, Lisa Julia 18 December 2023 (has links)
The dissertation “Formation of wrinkles on a coated substate“ treats the finite element simulations of controlled wrinkle formation experiments conducted at the Leibniz Institute for Polymer Research. The systems used for the experiments consist of a soft polydimethylsiloxane (PDMS) layer with a thin, stiff layer on top. The wrinkling process is triggered by a stress mismatch between the bulk and the thin layer. To create the stress mismatch, the bulk material is first uni-axially stretched and then the thin layer is created by a low-pressure plasma treatment of the stretched bulk in a vacuum chamber. Under subsequent relaxation, wrinkles form. Their wavelength depends on the choice of the process gas and the duration of the treatment.
The use of thin silicon masks placed directly on the PDMS allows to sharply restrict the plasma-exposed area. Sequential exposures of the same sample to multiple treatment processes with and without a mask allow to locally modify the layer thickness and stiffness. With this, we can locally control the wavelength of the resulting wrinkles and trigger the formation of branches and line defects at the boundary between areas of different wavelengths.
The dissertation first covers the mathematical model for the coated substrate, a combination of a hyperelastic material model from three-dimensional elasticity for the bulk (an almost incompressible Mooney–Rivlin material model) and a Cosserat shell model for the film on top. A nonlinear and nonconvex minimization problem is deduced and transferred to a suitable finite element space. Existence of minimizers is proven in the continuous and the discrete case before the discrete problem is solved numerically. The numerical simulations show a good agreement with corresponding physical experiments.
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Beltrami FlowsMargetis, Alexander 11 May 2018 (has links)
No description available.
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Error Analysis for Geometric Finite Element Discretizations of a Cosserat Rod Optimization ProblemBauer, Robert 08 April 2024 (has links)
In summary, this thesis focuses on developing an a priori theory for geometric finite element discretizations of a Cosserat rod model, which is derived from incompatible elasticity. This theory will be supported by corresponding numerical experiments to validate the convergence behavior of the proposed method.
The main result describes the qualitative behavior of intrinsic H1-errors and L2-errors in terms of the mesh diameter 0 < h ≪ 1 of the approximation scheme.
Geometric Finite Element functions uh with its subclasses Geodesic Finite Elements and Projection- based Finite Elements as conforming path-independent and objective discretizations of Cosserat rod configurations were used. Existence, regularity, variational bounds and vector field transport estimates of the Cosserat rod model were derived to ob- tain an intrinsic a-priori theory.
In the second part, this thesis concerns the derivation of the Cosserat rod from 3D elasticity featuring prestress together with numerical experiments for microheteroge- neous prestressed materials.
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[pt] AVALIAÇÃO DO COMPORTAMENTO DE ESCAVAÇÃO GRAMPEADA INSTRUMENTADA EM SOLO DE PEDREGULHO / [en] EVALUATION OF THE BEHAVIOR OF AN INSTRUMENTED SOIL NAILED EXCAVATION IN GRAVEL SOILFERNANDO CHAVEZ CARMEN 01 February 2022 (has links)
[pt] Nos últimos anos na cidade de Lima as escavações profundas alcançaram
uma presença maior, devido à recente demanda pela construção de edifícios altos e
centros comerciais com vários níveis de subsolos, onde utilizam-se
preferencialmente as cortinas atirantadas para a contenção dos solos. No entanto, a
técnica de solo grampeado mostra-se como uma alternativa interessante, dado que
também permite fornecer suporte lateral e limitar os movimentos do solo. A técnica
consiste em reforçar o bloco do solo atrás da parede através das inclusões passivas,
criando uma estrutura de gravidade consistente que permite aumentar a resistência
geral ao cisalhamento e restringir os deslocamentos. Este estudo de caso procura
avaliar os deslocamentos horizontais em uma escavação de 15m de altura em um
entorno urbano, onde o solo é predominantemente de pedregulho denso mal
graduado, parte do depósito aluvial do Conglomerado de Lima. A estimativa dos
parâmetros de resistência baseou-se em ensaios de cisalhamento direto in situ em
grande escala e ensaios de arrancamento encontrados na literatura. O
acompanhamento dos deslocamentos ao longo do processo construtivo, foi
realizado a través de inclinômetros instalados no perímetro, em locais estratégicos
para avaliar os deslocamentos mais críticos na escavação. A avaliação de erros
sistemáticos em inclinômetros é também abordada no estudo. Complementarmente,
realizaram-se análises numéricas com programas de equilíbrio limite e elementos
finitos, que permitiram avaliar os fatores de segurança e os deslocamentos com o
objetivo de comparar os dados de campo com os resultados calculados. Através de
análise paramétrica e calibração do modelo foi possível conhecer a influência dos
parâmetros geotécnicos e geométricos de escavações profundas grampeadas. / [en] In recent years in the city of Lima, the execution of deep excavations growth,
due to the recent demand for the construction of high-rise buildings and shopping
malls having various levels of basements, where anchorage walls systems are
preferably used to soil retention. However, the soil nailing technique is an
interesting alternative, by reason to provide lateral support and limit movements.
The soil nailing technique consists of reinforcing the soil block behind the wall
through passive inclusions, producing a consistent gravity structure that allows the
increas of the shear strength and restricting displacements. This case study aims to
evaluate the horizontal displacements generated in a 15m high deep excavation in
an urban environment, where the existing soil is predominantly of poorly graded
dense gravel, component of the alluvial deposit of the Lima Conglomerate. The
estimate of strength parameters for this type of soil was based on large-scale in situ
direct shear tests and pullout tests found in the literature. The monitoring of
displacements throughout the construction process was carried out using vertical
inclinometers installed on the perimeter, in strategic locations to assess the most
critical displacements that the excavation could experience. The evaluation of
systematic errors in inclinometers is also approached in the study. In addition,
numerical analyzes were carried out with limit equilibrium and finite element
programs, which allowed evaluating the safety factors and displacements in order
to compare the field data with the calculated results. Through parametric analysis
and model calibration, it was possible to know the influence of geotechnical and
geometric parameters of nailed deep excavations.
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[pt] ANÁLISE NUMÉRICA E COMPORTAMENTO MECÂNICO EXPERIMENTAL DE VIGAS DE UHPC COM SEÇÃO TRANSVERSAL OTIMIZADA / [en] NUMERICAL ANALYSIS AND EXPERIMENTAL MECHANICAL BEHAVIOR OF UHPC BEAMS WITH OPTIMIZED CROSS-SECTIONPAULO HENRIQUE MARANGONI FEGHALI 11 November 2024 (has links)
[pt] O concreto de ultra alto desempenho (UHPC) reforçado com fibras é um material que foi
desenvolvido nas últimas décadas para atender à necessidade de estruturas modernas por
um material mais resistente e durável. Suas características altamente não lineares tanto
na tração quanto na compressão levam a um comportamento complexo. Além disso, a
distribuição não homogênea das fibras e a alta resistência à tração, quando comparada ao
concreto convencional, resultam em menor ductilidade para vigas de UHPC. A análise de
elementos finitos mostra ser uma ferramenta adequada para representar a resposta de
elementos estruturais de UHPC, mas a calibragem do modelo deve ser aplicada
corretamente e técnicas de modelagem coerentes devem ser usadas para representar
corretamente os tramos pós-pico de curvas força-deslocamento para vigas de UHPC
submetidas a testes de flexão de quatro pontos. Foi realizada uma extensa caracterização
do material tanto em tração quanto em compressão. Testes axiais monotônicos foram
conduzidos para obter curvas tensão-deformação na compressão e tensão-abertura de
fissura na tração. Testes cíclicos foram realizados para determinar a evolução do dano
experimental em compressão e na tração. Esses dados serviram como referência para
calibrar modelos uniaxiais e modelos de evolução de dano de acordo com expressões
analíticas disponíveis na literatura. Modelos heterogêneos simulando a dispersão do
material nas propriedades mecânicas do UHPC ao longo do volume das vigas foram
utilizados para obter uma seção transversal que apresentasse resistência otimizada,
mantendo a ductilidade desejada. Finalmente, cinco vigas foram testadas, com diferentes
formas e porcentagens de reforço, e estratégias de modelagem foram comparadas aos
dados experimentais das vigas. / [en] Ultra-high performance concrete is a material which has been developed in the last
decades to fulfill modern structures need for a more resistant and durable material. Its
highly nonlinear characteristics in both tension and compression leads to a complex
behavior. In addition to that, the inhomogeneous distribution of the fibers and the high
tensile strength when compared to conventional concrete result in reduced ductility for
UHPC beams. Finite element analysis is shown to be an adequate tool to represent UHPC
structural element s response but the model calibration must be correctly applied and
coherent modeling techniques must be used to correctly model the post-peak branches of
load-displacement curves for UHPC beams subjected to four-point load bending tests. An
extensive material characterization in both tension and compression was conducted.
Monotonic axial tests were conducted to obtain stress-strain curves in compression and
stress-crack opening in tension and cyclic tests were made to determine the experimental
damage evolution in compression and in tension. These data served as input to calibrate
uniaxial models and damage evolution models according to analytical expressions
available in the literature. Heterogeneous models simulating the material dispersion of
the mechanical properties of the UHPC over structural beams were used to obtain a cross-section that presented optimized resistance while maintaining target ductility. Finally,
five beams were tested, with different shapes and reinforcement ratios and the modeling
strategies were benchmarked to the beams experimental data.
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A Finite-Element Coarse-GridProjection Method for Incompressible FlowsKashefi, Ali 23 May 2017 (has links)
Coarse grid projection (CGP) methodology is a novel multigrid method for systems involving decoupled nonlinear evolution equations and linear elliptic Poisson equations. The nonlinear equations are solved on a fine grid and the linear equations are solved on a corresponding coarsened grid. Mapping operators execute data transfer between the grids. The CGP framework is constructed upon spatial and temporal discretization schemes. This framework has been established for finite volume/difference discretizations as well as explicit time integration methods. In this article we present for the first time a version of CGP for finite element discretizations, which uses a semi-implicit time integration scheme. The mapping functions correspond to the finite-element shape functions. With the novel data structure introduced, the mapping computational cost becomes insignificant. We apply CGP to pressure correction schemes used for the incompressible Navier Stokes flow computations. This version is validated on standard test cases with realistic boundary conditions using unstructured triangular meshes. We also pioneer investigations of the effects of CGP on the accuracy of the pressure field. It is found that although CGP reduces the pressure field accuracy, it preserves the accuracy of the pressure gradient and thus the velocity field, while achieving speedup factors ranging from approximately 2 to 30. Exploring the influence of boundary conditions on CGP, the minimum speedup occurs for velocity Dirichlet boundary conditions, while the maximum speedup occurs for open boundary conditions. We discuss the CGP method as a guide for partial mesh refinement of incompressible flow computations and show its application for simulations of flow over a backward facing step and flow past a cylinder. / Master of Science / Coarse Grid Projection (CGP) methodology is a new multigrid technique applicable to pressure projection methods for solving the incompressible Navier-Stokes equations. In the CGP approach, the nonlinear momentum equation is evolved on a fine grid, and the linear pressure Poisson equation is solved on a corresponding coarsened grid. Mapping operators transfer the data between the grids. Hence, one can save a considerable amount of CPU time due to reducing the resolution of the pressure filed while maintaining excellent to reasonable accuracy, depending on the level of coarsening.
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Modélisation et Simulation des Ecoulements Compressibles par la Méthode des Eléments Finis Galerkin Discontinus / Modeling and Simulation of Compressible Flows with Galerkin Finite Elements MethodsGokpi, Kossivi 28 February 2013 (has links)
L’objectif de ce travail de thèse est de proposer la Méthodes des éléments finis de Galerkin discontinus (DGFEM) à la discrétisation des équations compressibles de Navier-Stokes. Plusieurs challenges font l’objet de ce travail. Le premier aspect a consisté à montrer l’ordre de convergence optimal de la méthode DGFEM en utilisant les polynômes d’interpolation d’ordre élevé. Le deuxième aspect concerne l’implémentation de méthodes de ‘‘shock-catpuring’’ comme les limiteurs de pentes et les méthodes de viscosité artificielle pour supprimer les oscillations numériques engendrées par l’ordre élevé (lorsque des polynômes d’interpolation de degré p>0 sont utilisés) dans les écoulements transsoniques et supersoniques. Ensuite nous avons implémenté des estimateurs d’erreur a posteriori et des procédures d ’adaptation de maillages qui permettent d’augmenter la précision de la solution et la vitesse de convergence afin d’obtenir un gain de temps considérable. Finalement, nous avons montré la capacité de la méthode DG à donner des résultats corrects à faibles nombres de Mach. Lorsque le nombre de Mach est petit pour les écoulements compressibles à la limite de l’incompressible, la solution souffre généralement de convergence et de précision. Pour pallier ce problème généralement on procède au préconditionnement qui modifie les équations d’Euler. Dans notre cas, les équations ne sont pas modifiées. Dans ce travail, nous montrons la précision et la robustesse de méthode DG proposée avec un schéma en temps implicite de second ordre et des conditions de bords adéquats. / The aim of this thesis is to deal with compressible Navier-Stokes flows discretized by Discontinuous Galerkin Finite Elements Methods. Several aspects has been considered. One is to show the optimal convergence of the DGFEM method when using high order polynomial. Second is to design shock-capturing methods such as slope limiters and artificial viscosity to suppress numerical oscillation occurring when p>0 schemes are used. Third aspect is to design an a posteriori error estimator for adaptive mesh refinement in order to optimize the mesh in the computational domain. And finally, we want to show the accuracy and the robustness of the DG method implemented when we reach very low mach numbers. Usually when simulating compressible flows at very low mach numbers at the limit of incompressible flows, there occurs many kind of problems such as accuracy and convergence of the solution. To be able to run low Mach number problems, there exists solution like preconditioning. This method usually modifies the Euler. Here the Euler equations are not modified and with a robust time scheme and good boundary conditions imposed one can have efficient and accurate results.
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A fictitious domain approach for hybrid simulations of eukaryotic chemotaxisSeguis, Jean-Charles January 2013 (has links)
Chemotaxis, the phenomenon through which cells respond to external chemical signals, is one of the most important and universally observable in nature. It has been the object of considerable modelling effort in the last decades. The models for chemotaxis available in the literature cannot reconcile the dynamics of external chemical signals and the intracellular signalling pathways leading to the response of the cells. The reason is that models used for cells do not contain the distinction between the extracellular and intracellular domains. The work presented in this dissertation intends to resolve this issue. We set up a numerical hybrid simulation framework containing such description and enabling the coupling of models for phenomena occurring at extracellular and intracellular levels. Mathematically, this is achieved by the use of the fictitious domain method for finite elements, allowing the simulation of partial differential equations on evolving domains. In order to make the modelling of the membrane binding of chemical signals possible, we derive a suitable fictitious domain method for Robin boundary elliptic problems. We also display ways to minimise the computational cost of such simulation by deriving a suitable preconditioner for the linear systems resulting from the Robin fictitious domain method, as well as an efficient algorithm to compute fictitious domain specific linear operators. Lastly, we discuss the use of a simpler cell model from the literature and match it with our own model. Our numerical experiments show the relevance of the matching, as well as the stability and accuracy of the numerical scheme presented in the thesis.
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