Neste trabalho, o escoamento incompressível ao redor de um cilindro fixo é estudado numericamente através do método de elementos finitos. Foram realizadas simulações bidimensionais no domínio do tempo, com números de Reynolds variando entre 100 e 600, utilizando-se, para tanto, malhas não-estruturadas com elementos triangulares. Pretende-se aqui analisar a eficácia da solução das equações de Navier-Stokes utilizando o método das penalidades, meio pelo qual o acoplamento pressão-velocidade foi tratado. Avalia-se a convergência da solução para diferentes valores do fator de penalidade e sugere-se um método para estimá-lo. Analisa-se, ainda, a sensibilidade da resposta à utilização da matriz de inércia nos formatos consistente e concentrada. Por fim, é realizada a comparação dos coeficientes de arrasto médio, flutuação do coeficiente de sustentação e número de Strouhal obtidos neste trabalho com resultados de outras publicações. / In this work, the incompressible flow around a stationary cylinder is investigated by using the Finite Element Method. Two-dimensional simulations in time domain have been carried out, with Reynolds number varying from 100 to 600, using non-structured meshes with triangular elements. The aim of this work is to analyze the efficiency of Penalty Methods, which is the way that the velocity-pressure coupling problem is treated here, in Navier-Stokes equations solution. The solution convergence from different values of penalty parameter is evaluated and it is suggested a method to estimate it. In addition, it is studied the sensibilty of response when using the mass matrix in consistent or lumped format. At last, a comparison between average drag coefficient, fluctuating lift and Strouhal number obtained here and those found in other publications is shown.

FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico / Among the new-found data about the availability of fossil fuels, which affirms that oil and natural gas sources will be almost depleted in the next century and the coal in the following two centuries. There is a global pursuit about new ways to produce energy. Another important fact that ratify this quest, lies at rise of the environment imbalance arouse from the burn of fossil fuels which, through the greenhouse effect, leads, for instance, to melting glaciers and increasing the temperature in the earth. The wind power, already used to move ships since antiquity is a relevant alternative way to produce energy, since it dispose of, at least, two great advantages, namely, it is endless and produce low negative consequences to environment. A place is considered to be good to receive the wind power engines called wind turbines, which convert the wind kinetic energy in electricity, if it is a ground plane with little amount of barriers. The sea, especially the regions far from the coast, satisfy the two latter requirement, and, furthermore, it is a place in which there are less obstructions about the noise pollution from the offshore wind turbines and there is not concern about deceases arouse in people who leave near of wind farms. In order to install the wind turbines in those spots away from the seashore, is required that its towers must be attached at the sea floor or must be develop a system that allow the turbine to float. Therefore the objective of the present work is to develop a structural modelling of the Monopile, TLP (Tension Leg Platform) and Spar type wind turbines subject using Finite Element Methods with the coupling method accomplished by Localized Lagrange Multipliers, jointly with the software SolidWorks and Autocad (drawing creation), ANSYS (mesh development) and Matlab (solver). The obtained results are relevant since such models are those which are most commonly used in offshore wind power plants. Lastly, due to the use of the latter coupling method, there is not the requisition to develop the study using meshes that agree each other. On the contrary, the analysis can be performed with non match meshes adjusting them with the Zero Moment Rule described in this present study. / Diante dos mais recentes dados com respeito a quantidade de combustÃveis fÃsseis ainda disponÃveis na natureza, os quais atestam que nÃo hà mais nem um sÃculo sequer para que o petrÃleo e o gÃs natural sejam praticamente extintos e que as reservas de carvÃo mineral suprirÃo somente mais 2 sÃculos de consumo, levando em conta o gasto atual. A preocupaÃÃo quanto a novas formas de extraÃÃo de energia se tornam necessÃrias e urgentes. Outro importante fator que ratifica o imediatismo de se buscar diferentes fontes de energia em detrimento de combustÃvel fÃssil, à o fato de que as emissÃes intrÃnsecas à sua queima estÃo gerando desequilÃbrio no clima global pela intensificaÃÃo do efeito estufa, apontado como um dos principais contribuidores do derretimento de geleiras e aquecimento da temperatura da terra. A energia eÃlica, jà utilizada desde a antiguidade para auxÃlio de locomoÃÃo de embarcaÃÃes e em moinhos de vento, se mostra uma alternativa de extrema relevÃncia, jà que, ela nÃo à portadora dos dois problemas crÃticos citados anteriormente. A saber, ela à infindÃvel e tem baixa consequÃncia negativa ao meio ambiente. Quanto aos locais que oferecem maior rendimento e produÃÃo para instalaÃÃo dos aerogeradores, responsÃveis pela conversÃo da energia cinÃtica do vento em energia elÃtrica, sÃo os que dispÃem de terreno mais plano e ausente de barreiras que impeÃam a continuidade do fluxo de vento. O mar, sobretudo as regiÃes mais distantes da costa, satisfazem Ãs duas necessidades citadas anteriormente, e, ainda se tratam de um local no qual nÃo hà a preocupaÃÃo quanto a poluiÃÃo sonora gerada pelos aerogeradores e nem com distÃrbios e doenÃas que possam ser desencadeadas em pessoas que residam pertos de grandes parques Ãolicos. A utilizaÃÃo de aerogeradores no mar (offshore) distantes da costa, e por conseguinte, em grandes profundidades, requer torres de sustentaÃÃo fixadas ao solo ou um sistema que proporcione que a turbina flutue. Diante do exposto, o trabalho em questÃo tem por objetivo realizar a modelagem estrutural do aerogerador flutuante (Spar), do portador de torre de tripà e do modelo monopile, sujeitos a carregamentos decorrentes de situaÃÃes normais e extremas, utilizando os mÃtodos dos Elementos Finitos juntamente com o MÃtodo de Acoplamento por Multiplicadores de Lagrange Localizados, atrelados aos softwares SolidWorks e Autocad (criaÃÃo do desenho), ANSYS (malha) e Matlab (solver). E, em decorrÃncia do fato da utilizaÃÃo do mÃtodo de acoplamento, nÃo hà necessidade de que as malhas dos subdomÃnios envolvidos sejam coincidentes. Pelo contrÃrio, pode-se utilizar malhas nÃo encaixantes para discretizar o sistema e, nas regiÃes onde hà contato entre malhas que nÃo coicidem, aplica-se a Regra do Momento Zero, descrita no presente trabalho. Nesse tipo de abordagem, pode haver uma separaÃÃo dos cÃdigos computacionais utilizados para o fluido e para a estrutura, os quais sÃo inicialmente tratados como entidades individuais e sà apÃs terem sido discretizados à que a informaÃÃo sobre suas malhas à recebida pela parte do cÃdigo responsÃvel por realizar o acoplamento dos subdomÃnios. Problemas de malhas que nÃo se encaixam podem surgir por diversos motivos, dentre eles, o fato de um subdomÃnio requerer uma malha mais refinada do que outros para que dele resultem resultados acurados. Pesquisadores de diferentes Ãreas podem gerar malhas separadas de distintos subdomÃnios e desejarem unÃ-los pelo mÃtodo abordado nesse trabalho em uma simulaÃÃo, ou a conformidade das malhas pode requerer muito tempo dispendido devido ao grande esforÃo computacional para a geraÃÃo de malhas conformes. Por fim, a aplicaÃÃo do mÃtodo produz resultados de grande relevÃncia, visto que, os modelos a que dizem respeito sÃo os mais comumente utilizados em projetos de aproveitamento de energia eÃlica offshore.

Orientador: Jose Luiz Antunes de Oliveira e Sousa / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-08T23:02:14Z (GMT). No. of bitstreams: 1 Rosa_AlaorLeandro_M.pdf: 2119051 bytes, checksum: 8f5c501220a7f5599ce9888da3461e86 (MD5) Previous issue date: 2005 / Resumo: Este trabalho enfoca o estudo de processos de fratura em vigas de concreto, concreto reforçado com fibras de aço, concreto armado e concreto armado reforçado com fibras de aço, através da simulação numérica com o código de elementos finitos DIANA. O estudo envolve a área de pesquisa em materiais compósitos à base de cimento, resultantes da adição de fibras de aço descontínuas orientadas aleatoriamente, e a análise numérica de sólidos contendo fissuras. Foram realizadas simulações numéricas de processos de fratura em vigas, sob carregamento monotônico, de acordo com os modelos de fissura discreta (¿discrete crack model¿) e de fissura distribuída (¿smeread crack model¿). As curvas tensão-abertura de fissura (s ¿ ?w), que caracterizam o comportamento do concreto e do concreto reforçado com fibras de aço, após a tensão de tração ser atingida, foram obtidas por retroanálise de vigas entalhadas submetidas ao ensaio de flexão em três pontos. As simulações foram realizadas para comparar resultados numéricos e experimentais de vigas entalhadas carregadas em três pontos e vigas armadas projetadas para ruptura à flexão e ao esforço cortante. Em todos os casos, foram considerados espécimes sem e com adição de fibras de aço / Abstract: This work addresses the study of fracture processes in concrete beams with conventional and steel fiber reinforcements, through numerical simulation with DIANA Finite Element Analysis code. The study include the research area of cementitious material composites, obtained from the addition of discrete and randomly oriented steel fibers to the concrete, and the area of numerical analysis of solids containing cracks. Numerical simulations of fracture processes in beams, subject to flexure and shear under monotonic load, were performed according to the smeared crack model and to the discrete crack model. The stress-crack opening curves (s ¿ ?w), used to characterize the material constitutive behavior of the concrete after tensile stress is reached, were obtained by inverse analysis of notched prismatic specimens subject to three-point-bending tests. The simulations were performed to compare numerical and experimental results from notched three-point-bending specimens and from reinforced beams designed for diagonal shear or flexural failure. Specimens with and without steel fibers were analyzed in all the cases / Mestrado / Estruturas / Mestre em Engenharia Civil

In this paper we present two hierarchically preconditioned methods for the fast solution of mesh equations that approximate 2D-elliptic boundary value problems on unstructured quasi uniform triangulations. Based on the fictitious space approach the original problem can be embedded into an auxiliary one, where both the hierarchical grid information and the preconditioner by decomposing functions on it are well defined. We implemented the corresponding Yserentant preconditioned conjugate gradient method as well as the BPX-preconditioned cg-iteration having optimal computational costs. Several numerical examples demonstrate the efficiency of the artificially constructed hierarchical methods which can be of importance in the industrial engineering, where often only the nodal coordinates and the element connectivity of the underlying (fine) discretization are available.

This paper is concerned with mesh refinement techniques for treating elliptic boundary value problems in domains with re- entrant edges and corners, and focuses on numerical experiments. After a section about the model problem and discretization strategies, their realization in the experimental code FEMPS3D is described. For two representative examples the numerically determined error norms are recorded, and various mesh refinement strategies are compared.

Une grande part des muqueuses à l’intérieur du corps humain sont recouvertes de cils qui, par leurs mouvements coordonnés, conduisent à une circulation de la couche de fluide nappant la muqueuse. Dans le cas de la paroi interne des bronches, ce processus permet l’évacuation des impuretés inspirées à l’extérieur de l’appareil respiratoire.Dans cette thèse, nous nous intéressons aux effets du ou des cils sur le fluide, en nous plaçant à l’échelle du cil, et on considère pour cela les équations de Stokes incompressible. Due à la finesse du cil, une simulation directe demanderait un raffinement important du maillage au voisinage du cil, pour un maillage qui évoluerait à chaque pas de temps. Cette approche étant trop onéreuse en terme de coûts de calculs, nous avons considéré l’asymptotique d’un diamètre du cil tendant vers 0 et d’une vitesse qui tend vers l’infini : le cil est modélisé par un Dirac linéique de forces en terme source. Nous avons montré qu’il était possible de remplacer ce Dirac linéique par une somme de Dirac ponctuels distribués le long du cil. Ainsi, nous nous sommes ramenés, par linéarité, à étudier le problème de Stokes avec en terme source une force ponctuelle. Si les calculs sont ainsi simplifiés (et leurs coûts réduits), le problème final est lui plus singulier, ce qui motive une analyse numérique fine et l’élaboration d’une nouvelle méthode de résolution.Nous avons d’abord étudié une version scalaire de ce problème : le problème de Poisson avec une masse de Dirac en second membre. La solution exacte étant singulière, la solution éléments finis est à définir avec précaution. La convergence de la méthode étant dégradée dans ce cas-là, par rapport à celle dans le cas régulier, nous nous sommes intéressés à des estimations locales. Nous avons démontré une convergence quasi-optimale en norme Hs (s ě 1) sur un sous-domaine qui exclut la singularité. Des résultats analogues ont été obtenus dans le cas du problème de Stokes.Pour palier les problèmes liés à une mauvais convergence sur l’ensemble du domaine, nous avons élaboré une méthode pour résoudre des problème elliptiques avec une masse de Dirac ou une force ponctuelle en terme source. Basée sur celle des éléments finis standard, elle s’appuie sur la connaissance explicite de la singularité de la solution exacte. Une fois données la position de chacun des cils et leur paramétrisation, notre méthode rend possible la simulation directe en 3d d’un très grand nombre de cils. Nous l’avons donc appliquée au cas du transport mucociliaire dans les poumons. Cet outil numérique nous donne accès à des informations que l’on ne peut avoir par l’expérience, et permet de simuler des cas pathologiques comme par exemple une distribution éparse des cils. / Numerous mucous membranes inside the human body are covered with cilia which, by their coordinated movements, lead to a circulation of the layer of fluid coating the mucous membrane, which allows, for example, in the case of the internal wall of the bronchi, the evacuation of the impurities inspired outside the respiratory system.In this thesis, we integrate the effects of the cilia on the fluid, at the scale of the cilium. For this, we consider the incompressible Stokes equations. Due to the very small thickness of the cilia, the direct computation would request a time-varying mesh grading around the cilia. To avoid too prohibitive computational costs, we consider the asymptotic of a zero diameter cilium with an infinite velocity: the cilium is modelled by a lineic Dirac of force in source term. In order to ease the computations, the lineic Dirac of forces can be approached by a sum of punctual Dirac masses distributed along the cilium. Thus, by linearity, we have switched our initial problem with the Stokes problem with a punctual force in source term. Thus, we simplify the computations, but the final problem is more singular than the initial problem. The loss of regularity involves a deeper numerical analysis and the development of a new method to solve the problem.We have first studied a scalar version of this problem: Poisson problem with a Dirac right-hand side. The exact solution is singular, therefore the finite element solution has to be defined with caution. In this case, the convergence is not as good as in the regular case, and thus we focused on local error estimates. We have proved a quasi-optimal convergence in H1-norm (s ď 1) on a sub-domain which does not contain the singularity. Similar results have been shown for the Stokes problem too.In order to recover an optimal convergence on the whole domain, we have developped a numerical method to solve elliptic problems with a Dirac mass or a punctual force in source term. It is based on the standard finite element method and the explicit knowl- edge of the singularity of the exact solution. Given the positions of the cilia and their parametrisations, this method permits to compute in 3d a very high number of cilia. We have applied this to the study of the mucociliary transport in the lung. This numerical tool gives us information we do not have with the experimentations and pathologies can be computed and studied by this way, like for example a small number of cilia.

The numerical solution of the convection-diffusion-reaction problem is considered in two and three dimensions. A stabilized finite element method of Galerkin/Least squares type accomodates diffusion-dominated as well as convection- and/or reaction- dominated situations. The resolution of boundary layers occuring in the singularly perturbed case is accomplished using anisotropic mesh refinement in boundary layer regions. In this paper, the standard analysis of the stabilized Galerkin method on isotropic meshes is extended to more general meshes with boundary layer refinement. Simplicial Lagrangian elements of arbitrary order are used.

The experimental program ¨SPC-PM Po 3D¨ is part of the ongoing research of the Chemnitz research group Scientific Parallel Computing (SPC) into finite element methods for problems over three dimensional domains. The package in its version 2.0 is documented in two manuals. The User's Manual provides an overview over the program, its capabilities, its installation, and handling. Moreover, test examples are explained. The aim of the Programmer's Manual is to provide a description of the algorithms and their realization. It is written for those who are interested in a deeper insight into the code, for example for improving and extending. In Version 2.0 the program can solve the Poisson equation and the Lam'e system of linear elasticity with in general mixed boundary conditions of Dirichlet and Neumann type. The domain $\Omega\subset\R^3$ can be an arbitrarily bounded polyhedron. The input is a coarse mesh, a description of the data and some control parameters. The program distributes the elements of the coarse mesh to the processors, refines the elements, generates the system of equations using linear or quadratic shape functions, solves this system and offers graphical tools to display the solution. Further, the behavior of the algorithms can be monitored: arithmetic and communication time is measured, the discretization error is measured, different preconditioners can be compared. We plan to extend the program in the next future by including a multigrid solver, an error estimator and adaptive mesh refinement, as well as the treatment of coupled thermo-elastic problems. The program has been developed for MIMD computers; it has been tested on Parsytec machines (GCPowerPlus-128 with Motorola Power PC601 processors and GCel-192 on transputer basis) and on workstation clusters using PVM. The special case of only one processor is included, that means the package can be compiled for single processor machines without any change in the source files.

The paper is concerned with the finite element resolution of layers appearing in singularly perturbed problems. A special anisotropic grid of Shishkin type is constructed for reaction diffusion problems. Estimates of the finite element error in the energy norm are derived for two methods, namely the standard Galerkin method and a stabilized Galerkin method. The estimates are uniformly valid with respect to the (small) diffusion parameter. One ingredient is a pointwise description of derivatives of the continuous solution. A numerical example supports the result. Another key ingredient for the error analysis is a refined estimate for (higher) derivatives of the interpolation error. The assumptions on admissible anisotropic finite elements are formulated in terms of geometrical conditions for triangles and tetrahedra. The application of these estimates is not restricted to the special problem considered in this paper.

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