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Dissertations / Theses on the topic 'Monolithic finite element formulation'

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Published: 6 September 2023

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1

Chiang, Chen-Yu. "Transport in biological systems. Monolithic method for fluid-structure interaction." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS477.

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Le travail de cette thèse a pour objectif de développer un solveur dédié aux problèmes d'interaction fluide-structure (IFS), en particulier ceux rencontré en biologie, tels que la dynamique d'un écoulement sanguin à travers des tronçons veineux munis de valves. La circulation du sang est étudiée à l'aide de modèles pertinents sur les plans anatomique et physique. Le premier aspect des problèmes d'IFS concerne la gestion de la stabilité. Une formulation monolithique eulérienne basée sur la méthode des caractéristiques assure la stabilité inconditionnelle et introduit une approximation du premier ordre en temps avec deux modèles distincts de matériaux hyper élastiques. Le second aspect est relatif au contact entre deux parties du domaine solide, tel celui apparaissant entre deux valvules au cours de la fermeture de la valve et à l'état fermé sur un surface valvulaire relativement importante. Un algorithme de contact est proposé et validé à l'aide de tests de référence. L'étude computationnelle de l'écoulement sanguin à travers des tronçons veineux munis de valves est mené, une fois le solveur IFS vérifié et validé. Le domaine computationnel bidimensionnel est soit constitué d'une simple unité de base, soit du modèle de circuit veineux en forme d'échelle avec une veine superficielle et une profonde, communicant par une série de veines perforantes. Un maillage tridimensionnel de l'unité de base a été construit. Les simulations dans ce domaine tridimensionnel nécessite le recours au calcul haute performance. La dynamique de l'écoulement sanguin est fortement couplée à la mécanique de la paroi vasculaire. La paroi déformable des veines et artères de gros calibre est composée de trois couches principales (l'intima, la media, et l'adventitia) constituées de matériaux composites ayant une composition spécifique dans chaque couche. Dans ce travail, la rhéologie de la paroi est supposée être représentée par un matériau du type Mooney-Rivlin
The present work aims at developing a numerical solver for fluid-structure interaction (FSI) problems, especially those encountered in biology such as blood circulation in valved veins. Blood flow is investigated using anatomically and physically relevant models. The first aspect of FSI problems is related to management of algorithm stability. An Eulerian monolithic formulation based on the characteristic method unconditionally achieves stability and introduce a first order in time approximation with two distinct hyperelastic material models. The second aspect deals with between-solid domain contact such as that between valve leaflets during closure and in the closed state over a finite surface, which avoid vcusp tilting and back flow. A contact algorithm is proposed and validated using benchmarks. Computational study of blood flow in valved veins is investigated, once the solver was verified and validated. The 2D computational domain comprises a single basic unit or the ladder-like model of a deep and superficial veins communicating by a set of perforating veins. A 3D mesh of the basic unit was also built. Three-dimensional computation relies on high performance computing. Blood flow dynamics is strongly coupled to vessel wall mechanics. Deformable vascular walls of large veins and arteries are composed of three main layers (intima, media, and adventitia) that consist of composite material with a composition specific to each layer. In the present work, the wall rheology is assumed to be a Mooney-Rivlin material
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2

El, Feghali Stéphanie. "Nouvelle formulation monolithique en élément finis stabilisés pour l'interaction fluide-structure." Phd thesis, Ecole Nationale Supérieure des Mines de Paris, 2012. http://pastel.archives-ouvertes.fr/pastel-00743488.

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L'Interaction Fluide-Structure (IFS) décrit une classe très générale de problème physique, ce qui explique la nécessité de développer une méthode numérique capable de simuler le problème FSI. Pour cette raison, un solveur IFS est développé qui peut traiter un écoulement de fluide incompressible en interaction avec des structures différente: élastique ou rigide. Dans cet aspect, le solveur peut couvrir une large gamme d'applications.La méthode proposée est développée dans le cadre d'une formulation monolithique dans un contexte Eulérien. Cette méthode consiste à considérer un seul maillage et résoudre un seul système d'équations avec des propriétés matérielles différentes. La fonction distance permet de définir la position et l'interface de tous les objets à l'intérieur du domaine et de fournir les propriétés physiques pour chaque sous-domaine. L'adaptation de maillage anisotrope basé sur la variation de la fonction distance est ensuite appliquée pour assurer une capture précise des discontinuités à l'interface fluide-solide.La formulation monolithique est assurée par l'ajout d'un tenseur supplémentaire dans les équations de Navier-Stokes. Ce tenseur provient de la présence de la structure dans le fluide. Le système est résolu en utilisant une méthode élément fini et stabilisé suivant la formulation variationnelle multiéchelle. Cette formulation consiste à décomposer les champs de vitesse et pression en grande et petite échelles. La particularité de l'approche proposée réside dans l'enrichissement du tenseur de l'extra contraint.La première application est la simulation IFS avec un corps rigide. Le corps rigide est décrit en imposant une valeur nul du tenseur des déformations, et le mouvement est obtenu par la résolution du mouvement de corps rigide. Nous évaluons le comportement et la précision de la formulation proposée dans la simulation des exemples 2D et 3D. Les résultats sont comparés avec la littérature et montrent que la méthode développée est stable et précise.La seconde application est la simulation IFS avec un corps élastique. Dans ce cas, une équation supplémentaire est ajoutée au système précédent qui permet de résoudre le champ de déplacement. Et la contrainte de rigidité est remplacée par la loi de comportement du corps élastique. La déformation et le mouvement du corps élastique sont réalisés en résolvant l'équation de convection de la Level-Set. Nous illustrons la flexibilité de la formulation proposée par des exemples 2D.
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3

Sivess, Andrew Gregory. "Chebyshev polynomial based finite element stiffness matrix formulation." Diss., Connect to online resource, 2005. http://wwwlib.umi.com/cr/colorado/fullcit?p1427762.

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4

Liu, Guanhui, and 刘冠辉. "Formulation of multifield finite element models for Helmholtzproblems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44204875.

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5

PASTOR, JORGE AURELIO SANTA CRUZ. "RESERVOIR MODELING THROUGH A COUPLED FINITE ELEMENT FORMULATION." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2001. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=2082@1.

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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
A produção de hidrocarbonetos resulta na redução da pressão do reservatório( depletação ). À medida que a pressão do reservatório diminui, as tensôes efetivas aplicadas na matriz rochosa aumentam, provocando reduções na porosidade e na permeabilidade da rocha assim como redução de volume, esta última conhecida como compactação.A compactação do reservatório pode provocar subsidência da superfície com conseqüentes impactos ambientais e problemas em equipamentos localizados no poço, tais como revestimentos, e outros problemas associados, tais como produção de sólidos. No entanto, compactação não é sempre prejudicial porque ajuda a manter a pressão do reservatório e, conseqüentemente, a produtividade. O acoplamento fluxo-deformação é fundamental na análise deste problema. Este trabalho tem com objetivo discutir a teoria e as equações que modelam este processo acoplado, suas limitações e sua capacidade de representar corretamente os fenômenos físicos envolvidos.Além disto, foi desenvolvido um simulador numérico baseado no método dos elementos finitos, para a modelagem transiente de um fluxo monofásico através de um meio poroso, considerando-se o acoplamento fluxo do fluido,deformações e temperatura.O material rochoso é modelado segundo um modelo poroelástico. O simulador foi testado comparando resultados com resultados obtidos através de soluções analíticas.Além disto, uma simulção de fluxo em reservatório foi efetuada para avaliar a capacidade do simulador, tendo-se comparado os resultados com resultados encontrados na literatura. A análise foi feita considerando o overburden e o sideburden.Foi verificada uma ótima concordância entre os resultados.O simulador mostrou-se capaz de representar as variações de pressão não apenas decorrentes da difusão do fluido, mas também aquelas provocadas por variações de tensões totais. Em alguns casos, a variação de tensões totais no topo do reservatório é significativa,demonstrando que simuladores convencionais podem induzir erros significativos em termos de variações das pressões no fluido.
Prodution ofhydrocarbon often to a reduction in reservoir pressure. Depending upon the rock compressibility, this reduction in reservoir pressure causes substancial strains and eventual shear collapse. While reservoir pressure decreases the effective stress increases, induting porosity and permeability reduction changes and an overall volume decrease known as compaction. Compaction of reservoir may eventually be transmitted to the surface and cause vertical movements, known as subsidence. Compaction may have serious consequences upon well casing,and other associated problems, such as solid production. However, compaction is not always detrimental because it helps maitaining reservoir pressure and consequently, reservoir productivity. Hydromechaninical coupling is essential to analyze this problem.The aim of this work is to discuss the theory and develop the equations that governthis coupled process. The limitations and possibilities in representing the associated phenomena are highlighted. A numerical, finite element based, simulator was developed to model the single-phase flow through porous media taking into accout the hydrothermo-mechanical coupling. The rock material is assumed to behave as a poroelastic material.The results obtained by the computer simulator were compared with theorical solutions for the classical problem of uniaxial deformation test and for the stress concentration aroun inclined welbores in porous media. The results showed excellent agreement. A idealized reservoir simulation was carrierd out using the computer model and the results of pore pressure, total stresses and displacement changes were compared with results published in the literature, obtained by similar approaches. The comparisons showed very good agreement. In the simulations the presences of overburden, sideburden and underburden were recognized. The simulator represented well the changes in fluid pressure associated with both the diffusion process and the changes in total stresses. In some cases, the changes in total stresses at the top of the reservoir are significant which demonstrates the partial flaw of the conventional flow simulators that are not able to take this effect into account.
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Liu, Guanhui. "Formulation of multifield finite element models for Helmholtz problems." Click to view the E-thesis via HKUTO, 2010. http://sunzi.lib.hku.hk/hkuto/record/B44204875.

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7

FREY, SERGIO LUIZ. "A FINITE ELEMENT FORMULATION FOR THE NAVIER-STOKES PROBLEM." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1991. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=19805@1.

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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
Métodos estabilizados de elementos finitos são propostos e analisados para problemas de fluidos, com particular ênfase nas equações de Navier-Stokes incomprenssível. Após a apresentação da mecânica dos escoamentos dos fluidos, introduzimos no Capítulo 3, no contexto de problema de Stokes, as dificuldadas numéricas associadas ao método de Galerkin em problemas de fluidos e simulamos em sucesso alguns escoamentos lentos através de formulações finitos para estabilizadas. No capítulo 4, propomos uma nova formulação de elementos finitos para a equação da energia, mais precisamente para o modelo da advecção-difusão do calor. Graças a um novo desenho do parâmetro de estabilidade T, o qual permite adicionar difusão às regiões advectivas e difusivas-dominadas do escoamento de maneira diferemciada, obtivemos um bom desempenho novo método mesmo em situações de altíssimo número de Péclet (10(2) menor que Pe menor que 10 e (6)), conforme ilustram os testes numéricos realizados. Coletando as experiências adquiridas com modelos lineares de Stokes e da advencção-difusão, nos foi possível propor, analisar o erro e testar dois novos métodos estabilizados para o problema de Navier-Stokes transiente. Construídos de maneira a herdar as boas características de estabilidade dos métodos propostos apresentam bom desempenho em escoamentos fortemente advectivos, bem como não necessitam atender a priori à condição de Baduska-Brezzi. Através de um algoritmo preditor/ multi-corretor de integração do termo inercial da equação de movimento, estes ,métodos foram capazes de de simular de maneira precisa escoamentos de interesse em Mecânica(400 menor que Re< menor que 500), captando escoamentos secundários, tais como recirculações de fluido.
Stabilized methods for fluid problems are proposed and analysed with particular emphasis to the incompressible Navier-Stokes equations. We Begin in Chapter 2 introducing the balance equations of fluid Mechanics. Next. In Chapter 3, we discuss the numerical difficulties of the Galerkin method in fluids(in the contexto f the Stokes problem) and performance some succeful simulations of creeping flows, employing stabilized formulations. In Chapter 4, we propose a new finite element formulation for the energy equation, or more preciselly for the advective-diffusive model. Taking advantage of new design of the stability parameter T, which permits to add diffusion to advective and diffusive regions of the flow in a different way, we success to obtain a good performance of the new method in flows with very high Péclet numbers (10(2) lass than Pe lessa than 10(6)), as illustred at numerical testes performed. By collecting the Stokes and advective-diffusive experiences,it was possible to propose, analyse and test two new stabilized methods for the transient Navier-Stokes problem. These methods were built in a way to heritage the good characteristics showed by the stabilized methods introduced for the Stokes and adventive-diffusive models. The new methods propoposed have a good performance in high advective flows, besides there is no need to satisfy the Babuska-Brezzi condition. Employing a predictor/multi-corretor algorithm, we were able to simulate accruratly some useful flows(400 less than Re less than 500), such as fluid recirculations.
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Pratap, Rudra 1964. "A NEW RESIDUAL FINITE-ELEMENT FORMULATION FOR ELASTODYNAMIC PROBLEMS." Thesis, The University of Arizona, 1987. http://hdl.handle.net/10150/276552.

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In the research undertaken a finite element formulation has been developed for an elastodynamic problem using a least squares approach. The special requirements of the problem demanded a study of suitability of various elements. The emergence of the final element is a result of both theoretical and numerical study of three different elements. The approximation function is assumed on the basis of the order of the governing differential equations. Then the square of the error resulting from the approximate solution is minimized over the entire domain as well as the boundaries in the same functional. The element equation emerging from the formulation does not yield a singular stiffness matrix, since the boundary conditions are already taken into account in the element equation. The formulation presented in this thesis is only for the normal propagation of phi-wave. A finite element code has been developed based on the new formulation.
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9

Wang, Haitao, and 王海濤. "Formulation of finite element methods for determining singular stress fields." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B31243708.

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10

PORTO, ANA CRISTINA DOS SANTOS DA SILVA. "CAVITY BACKED SLOT ANTENNAS: A FINITE ELEMENT-BOUNDARY INTEGRAL FORMULATION." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2004. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=5270@1.

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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
Devido às propriedades de banda larga e polarização circular, as antenas espirais tornaram-se bastante atrativas para diversos serviços de telecomunicações modernos e móveis. Neste trabalho uma antena espiral tipo fenda apoiada em uma cavidade cilíndrica metálica foi analisada. Por causa de sua geometria complexa, optou-se por um método numérico híbrido, realizado através de uma implementação de elementos mistos do método dos elementos finitos - integral de fronteira. Baseado nesta formulação, um programa computacional foi desenvolvido. Um grande esforço foi realizado a fim de escrever o programa de maneira que o armazenamento e as necessidades computacionais fossem mínimos, boa parte conseguida pela aplicação das condições de contorno na superfície metálica. Com o objetivo de melhor explorar a geometria do problema, definiu-se uma malha de elementos finitos onde a parte que cabia a abertura foi dividida em quadriláteros enquanto que no restante da superfície, elementos triangulares foram utilizados. Repetiu-se então esta malha ao longo da altura da cavidade, de maneira que hexaedros e prismas formaram a malha final. Para cada espécie de elemento, funções de base vetoriais específicas foram aplicadas. A fim de verificar a precisão do algoritmo, o mesmo programa computacional foi utilizado na análise de uma antena tipo fenda retangular, também apoiada em uma cavidade cilíndrica metálica.
Known for the properties of broadband and circular polarization, spiral antennas have become sufficiently attractive for services of modern and mobile telecommunications. In this work a cavity-backed slot spiral antenna was analyzed. Because of its complex geometry, it was chosen a hybrid numerical method, carried through an implementation of mixing elements of the finite elements - boundary integral method. Based in this formulation, a computer program was developed. A great effort was carried out in order to write the program thus the computational storage and necessities were minimum, good part obtained by application of the boundary conditions on the metallic surface. With the goal of better exploring the geometry of the problem, a mesh of finite elements was defined where the part that fit the aperture was divided into quadrilaterals, while that in the rest of the surface, triangular elements were used. By repeating this mesh along the height of the cavity, hexahedrals and prisms formed the final mesh. For each kind of element, specific vector base functions were applied. In order to verify the accuracy of the algorithm, the same computational program was used in the analysis of a cavity-backed slot rectangular antenna.
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Wang, Haitao. "Formulation of finite element methods for determining singular stress fields /." Hong Kong : University of Hong Kong, 2002. http://sunzi.lib.hku.hk/hkuto/record.jsp?B25151502.

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12

Druma, Calin. "Formulation of steady-state and transient potential problems using boundary elements." Ohio : Ohio University, 1999. http://www.ohiolink.edu/etd/view.cgi?ohiou1175886094.

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13

Li, Jing. "A Geometrically nonlinear curved beam theory and its finite element formulation." Thesis, Virginia Tech, 2000. http://hdl.handle.net/10919/31071.

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This thesis presents a geometrically exact curved beam theory, with the assumption that the cross-section remains rigid, and its finite element formulation/implementation. The theory provides a theoretical view and an exact and efficient means to handle a large range of nonlinear beam problems. A geometrically exact curved/twisted beam theory, which assumes that the beam cross-section remains rigid, is re-examined and extended using orthonormal reference frames starting from a 3-D beam theory. The relevant engineering strain measures at any material point on the current beam cross-section with an initial curvature correction term, which are conjugate to the first Piola-Kirchhoff stresses, are obtained through the deformation gradient tensor of the current beam configuration relative to the initially curved beam configuration. The Green strains and Eulerian strains are explicitly represented in terms of the engineering strain measures while other stresses, such as the Cauchy stresses and second Piola-Kirchhoff stresses, are explicitly represented in terms of the first Piola-Kirchhoff stresses and engineering strains. The stress resultant and couple are defined in the classical sense and the reduced strains are obtained from the three-dimensional beam model, which are the same as obtained from the reduced differential equations of motion. The reduced differential equations of motion are also re-examined for the initially curved/twisted beams. The corresponding equations of motion include additional inertia terms as compared to previous studies. The linear and linearized nonlinear constitutive relations with couplings are considered for the engineering strain and stress conjugate pair at the three-dimensional beam level. The cross-section elasticity constants corresponding to the reduced constitutive relations are obtained with the initial curvature correction term. For the finite element formulation and implementation of the curved beam theory, some basic concepts associated with finite rotations and their parametrizations are first summarized. In terms of a generalized vector-like parametrization of finite rotations under spatial descriptions (i.e., in spatial forms), a unified formulation is given for the virtual work equations that leads to the load residual and tangent stiffness operators. With a proper explanation, the case of the non-vectorial parametrization can be recovered if the incremental rotation is parametrized using the incremental rotation vector. As an example for static problems, taking advantage of the simplicity in formulation and clear classical meanings of rotations and moments, the non-vectorial parametrization is applied to implement a four-noded 3-D curved beam element, in which the compound rotation is represented by the unit quaternion and the incremental rotation is parametrized using the incremental rotation vector. Conventional Lagrangian interpolation functions are adopted to approximate both the reference curve and incremental rotation of the deformed beam. Reduced integration is used to overcome locking problems. The finite element equations are developed for static structural analyses, including deformations, stress resultants/couples, and linearized/nonlinear bifurcation buckling, as well as post-buckling analyses of arches subjected to conservative and non-conservative loads. Several examples are used to test the formulation and the Fortran implementation of the element.
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(UPC), Universidad Peruana de Ciencias Aplicadas, J. Yarasca, J. L. Mantari, and R. A. Arciniega. "Hermite–Lagrangian finite element formulation to study functionally graded sandwich beams." Elsevier B.V, 2016. http://hdl.handle.net/10757/607194.

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This paper presents a static analysis of functionally graded single and sandwich beams by using an efficient 7DOFs quasi-3D hybrid type theory. The governing equations are derived by employing the principle of virtual works in a weak form and solved by means of the Finite Element Method (FEM). A C1 cubic Hermite interpolation is used for the vertical deflection variables while C0 linear interpolation is employed for the other kinematics variables. Convergence rates are studied in order to validate the finite element technique. Numerical results of the present formulation are compared with analytical and FEM solutions available in the literature.
Revisión por pares
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Kehl, Richard Eugene. "Application of unified constitutive relations to hybrid stress finite element formulation." Thesis, Massachusetts Institute of Technology, 1989. http://hdl.handle.net/1721.1/39022.

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House, Robert C. (Robert Clayton) Carleton University Dissertation Engineering Mechanical. "A finite element formulation for heat transfer incorporating latent heat effects." Ottawa, 1986.

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17

Weicker, Kevin. "Finite element formulation for analysis of pipes based on thin shell theory." Thesis, University of Ottawa (Canada), 2008. http://hdl.handle.net/10393/28035.

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A general solution for the stress-deformation analysis of pipes subjected to general loading conditions is developed. The solution is based on the assumptions of thin-walled shell theory and is limited to straight pipes of prismatic cross-section made of linearly elastic isotropic material subjected to general loading. The principle of stationary potential energy is used in conjunction with general Fourier series expansion for the displacement fields to formulate the equilibrium conditions and boundary conditions. The equilibrium equations for each Fourier mode are observed to be uncoupled from other modes, a feature that is exploited in formulating a general closed form solution for the displacement fields. The analytical solution developed is then successfully adopted to solve two pipe problems. Comparisons with established finite element solutions demonstrate the ability of the model to accurately capture complex shell behaviour with a remarkably small number of degrees of freedoms. However, the algebraic manipulations in the analytical solution are found quite tedious for hand calculations, even for simple problems. In order to remedy this limitation and to make the solution scheme amenable to more complex problems, a finite element solution is formulated based on the analytical solution developed. The expressions for the displacement fields obtained are used to formulate a series of exact shape functions which relate the intermediate displacements within a finite element to the nodal displacements. Using the exact shape functions, the principle of stationary potential energy is adopted to formulate the stiffness matrices and associated energy equivalent load vectors for pipe finite elements. The new finite element is tested for a variety of practical loading conditions including point loads, gravity loads, internal and external pressure, twisting deformation, axial deformation, transverse deformations, and combinations thereof. Results are found in excellent agreement with those based on shell finite elements in ABAQUS. The pipe element developed is shown to be free of discretization errors and is thus computationally efficient. The element can very accurately predict the displacements and stresses of a pipe with only a very few elements and a few Fourier modes.
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18

Wu, Dan, and 吴丹. "Advanced transition finite element formulation for adaptive refinementanalysis of solids and structures." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44769271.

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GUIMARAES, GUILHERME PINTO. "AN AXISYMMETRIC FINITE ELEMENT FORMULATION FOR THE ANALYSIS OF LAMINATED COMPOSITE TUBES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2006. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=9239@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
O emprego de materiais compósitos em estruturas tem ganhado importância na prática da engenharia devido às suas características de alta resistência mecânica, baixa densidade e boa estabilidade a efeitos térmicos. Uma das classes de compósitos, a de laminados fibrosos, pode ser utilizada em tubulações sujeitas às diversas formas de carregamentos, como pressão interna e/ou externa, tração longitudinal, torção, temperatura, etc. O presente Trabalho tem por objetivo propor, implementar e testar a formulação de um modelo de elemento finito axissimétrico, para a representação do comportamento de um tubo laminado por camadas de materiais compósitos fibrosos. A modelagem consiste em representar a seção geratriz de um tubo cilíndrico por um elemento quadrilateral de quatro nós, com três graus de liberdade por nó, com os deslocamentos nodais tomados em relação aos eixos de um sistema cilíndrico de coordenadas. Considera-se a perfeita adesão das camadas, garantindo a continuidade do campo de deslocamentos. Modelos constitutivos de materiais com o comportamento ortotrópico e/ou o transversalmente isotrópico foram implementados, obtendo-se respostas para os campos de deslocamentos, de deformações e de tensões atuantes. Na validação do modelo numérico, considerou-se a comparação de seus resultados com os de soluções analíticas, disponíveis na literatura, e aqueles fornecidos por um programa comercial de elementos finitos, empregando o modelo com elementos sólidos. Foram propostos, para os testes em ambos os casos, exemplos de laminados com uma a quatro camadas, com fibras orientadas em diferentes ângulos. Destas comparações, verifica-se uma boa convergência das soluções numéricas obtidas com o presente modelo, representativo das principais características cinemáticas da classe de problemas representada.
The use of composite materials in structures has grown in the engineering practice due to its characteristics, of high strength, low density and a good stability to thermal effects. A class of composites, the fibrous laminates, is generally used in tubes subjected to many types of loadings as internal and/or external pressure, traction, torsion, temperatures, etc. This work has the objectives to propose, implement and test an axisymmetric finite element model formulation that represents the mechanical behavior of a fibrous laminated composite tube. Modeling consists in representing the cylindrical tube generating section by a quadrilateral element with four nodes and three degrees-of-freedom per node, with three nodal displacements defined in a cylindrical coordinate system. Layers are considered perfectly bonded together, assuring continuity between elements on the displacement fields. Orthotropic and/or transverse isotropic constitutive material models were implemented, allowing solutions for displacement, strain and stress fields. In the element numerical model validation, result comparisons with those from analytical solutions available on literature and those from the use of layered solid elements in a commercial finite element program were considered. Some examples, considering one to four layers, with different fiber angles, were proposed for model testing. It is noted a good numerical convergence for the presenting model solutions which represent the main kinematic characteristics for this class of problems.
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Chyou, Hui-Huang Abel. "Variational formulation and finite element implementation of Pagano's theory of laminated plates /." The Ohio State University, 1989. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487671108308444.

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21

Börner, Eiris F. I. "A finite element formulation based on the theory of a Cosserat point." Hannover Inst. für Kontinuumsmechanik, 2008. http://d-nb.info/994805179/04.

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Tremblay, Frédéric. "Introduction of a second-moment closure turbulence model in a finite element formulation." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ29632.pdf.

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23

Domkin, Konstantin. "Constitutive models based on dislocation density : formulation and implementation into finite element codes." Doctoral thesis, Luleå, 2005. http://epubl.luth.se/1402-1544/2005/35.

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Arslan, Haydar. "Localization analysis of granular materials in Cosserat elastoplasticity: Formulation and finite element implementation." Diss., Connect to online resource, 2006. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3239421.

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25

Tremblay, Frédéric 1970. "Introduction of a second-moment closure turbulence model in a finite element formulation." Thesis, McGill University, 1997. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=27258.

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The present thesis deals with the successful introduction of a second-moment closure turbulence model into a computer program using the Finite Element Method to solve the Navier-Stokes equations. The implementation presented has the advantage of using an equal interpolation for all the variables. It is also very economical in terms of the amount of memory required from the computer, since a fully decoupled formulation has been adopted, along with an iterative solver which permits to store in memory only the non-zero coefficients of the linear system of equations to be solved. Specialized elements are used to avoid resolving the near-wall region of the flow. The apparent viscosity concept is derived for the finite element formulation, along with a correction factor which permits a better representation of the Reynolds stresses. The RSM is compared to the older $k - epsilon$ model in two test cases where experimental data was available. The conclusion drawn from this work is that the RSM is able to reproduce more phenomenon occurring in turbulent flows than the $k - epsilon$ model. It is thought that the $k - epsilon$ model will gradually be supplanted by more complex models, as more computing power become available.
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Ganu, Shreerang. "Implementation of coupled magnetoelastic finite element formulation in machinery application, including magnetostriction effects." FIU Digital Commons, 2007. https://digitalcommons.fiu.edu/etd/3622.

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A high frequency physical phase variable electric machine model was developed using FE analysis. The model was implemented in a machine drive environment with hardware-in-the-loop. The novelty of the proposed model is that it is derived based on the actual geometrical and other physical information of the motor, considering each individual turn in the winding. This is the first attempt to develop such a model to obtain high frequency machine parameters without resorting to expensive experimental procedures currently in use. The model was used in a dynamic simulation environment to predict inverter-motor interaction. This includes motor terminal overvoltage, current spikes, as well as switching effects. In addition, a complete drive model was developed for electromagnetic interference (EMI) analysis and evaluation. This consists of the lumped parameter models of different system components, such as cable, inverter, and motor. The lumped parameter models enable faster simulations. The results obtained were verified by experimental measurements and excellent agreements were obtained. A change in the winding arrangement and its influence on the motor high frequency behavior has also been investigated. This was shown to have a little effect on the parameter values and in the motor high frequency behavior for equal number of turns. An accurate prediction of overvoltage and EMI in the design stages of the drive system would reduce the time required for the design modifications as well as for the evaluation of EMC compliance issues. The model can be utilized in the design optimization and insulation selection for motors. Use of this procedure could prove economical, as it would help designers develop and test new motor designs for the evaluation of operational impacts in various motor drive applications.
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27

高學常 and Hok-sheung Go. "Lateral and torsional analysis of shear cores by semi-analytical formulation." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1991. http://hub.hku.hk/bib/B31209725.

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Go, Hok-sheung. "Lateral and torsional analysis of shear cores by semi-analytical formulation /." [Hong Kong] : University of Hong Kong, 1991. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13009564.

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29

Wahlberg, James S. "The formulation and implementation of a plane stress element into the mixed Lagrangian approach to finite element analysis." Connect to online resource, 2008. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:1460196.

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30

Vitali, Efrem. "An extended finite element formulation for contact in multi-material arbitrary Lagrangian-Eulerian calculations." Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2007. http://wwwlib.umi.com/cr/ucsd/fullcit?p3274505.

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Thesis (Ph. D.)--University of California, San Diego, 2007.
Title from first page of PDF file (viewed October 4, 2007). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 111-113).
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31

Ghose, Dhrubajyoti. "Finite element formulation of a thin-walled beam with improved response to warping restraint." Thesis, This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-12052009-020042/.

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32

Siethoff, Eric Ten. "A Formulation for Updating Finite Element Models Through Consistent Use of Laser Vibrometer Data." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/36704.

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This thesis suggests a formulation for updating physically meaningful parameters in analytical finite element(FE) models using scanning laser Doppler vibrometer(SLDV) dynamic response data. The update formulation is demonstrated in several computer simulations. The formulation is the result of incorporating an analytical FE model into an experimental model. The experimental model efficiently utilizes SLDV data to fully exploit the instrument's capability to automatically make measurements at many locations. The data in the experimental model is posed in a manner consistent with an analytical FE model's representation for harmonic response, simplifying comparison between the two. The experimental model, which uses finite element shape functions as a basis for a least squares fit to the data, can be solved to give a velocity field based only on that data. The function resulting from inserting the analytical model into the experimental model is an expression of the prediction error of the FE model as compared to the test data. This function is minimized using a quasi-Newton optimization routine, reducing the error and resulting in an updated model. Computer simulations of the update algorithm indicate that: 1. Analytically supplied derivatives and variable scaling are required by the optimization routine to consistently converge, 2. The percentage error of updated parameters falls within two standard deviations of the data's percentage error, 3. Error in the position of the laser results in the update algorithm's failure, and, 4. Error in the parameters not included in the update will appear as error in the updated parameters' solution.
Master of Science
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33

Liu, Hon Ho. "A finite element formulation and analysis for advection-diffusion and incompressible Navier-Stokes equations." Case Western Reserve University School of Graduate Studies / OhioLINK, 1993. http://rave.ohiolink.edu/etdc/view?acc_num=case1057156956.

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TANOV, ROMIL R. "A CONTRIBUTION TO THE FINITE ELEMENT FORMULATION FOR THE ANALYSIS OF COMPOSITE SANDWICH SHELLS." University of Cincinnati / OhioLINK, 2000. http://rave.ohiolink.edu/etdc/view?acc_num=ucin962134920.

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35

Kida, Naoki. "Finite element formulation and analysis for an arterial wall with residual and active stresses." Kyoto University, 2014. http://hdl.handle.net/2433/189352.

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Lee, Seung-Cheol. "A Finite Element Boundary Element Method for Infinite Periodic Structures on Non-Periodic Meshes Using an Interior Penalty Formulation." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1331098281.

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37

Ugail, Hassan. "Parametric surface meshing for design optimisation using a PDE formulation." ISSG, Mississippi State University, 2002. http://hdl.handle.net/10454/2688.

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yes
The problem of parametric surface meshing for the purpose of design optimisation using finite element analysis is considered. Here the surface mesh is generated as a solution of a suitably posed boundary value problem implemented on a 2D parameter space. A robust meshing scheme is presented where an initial mesh is manipulated, with the aid of the 2D parameter space, so as to obtain a suitable surface triangulation. This meshing scheme can then be used to create suitable finite element meshes with which accurate design optimisations can be carried out.
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Szumski, Ricard Gerard. "A finite element formulation for the time domain vibration analysis of an elastic-viscoelastic structure." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/17053.

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39

Bucur, Constantin 1967. "Finite element computations of transonic viscous flows with the streamline upwind Petrov-Galerkin (SUPG) formulation." Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=98947.

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Computations of transonic viscous flows are very challenging. The major difficulty comes from the discontinuity in the solution across a shock wave, causing undesired oscillations in the solution. In this work we focus on minimizing the oscillations by the use of a limiter to control the amount of diffusivity. This limiter provides the right amount of viscosity to capture a sharp shock and an accurate solution in high gradient regions. The limiter employs changes in pressure and entropy and has been implemented into the Streamline Upwind Finite Element Method. A mesh adaptation strategy has been employed to further enhance the accuracy of the solution. Results of simulations over RAE 2822 airfoil and ONERA M6 wing indicate significant improvements to the solution with this implementation.
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40

Pontaza, Juan Pablo 1976. "Formulation and evaluation of finite element discretization schemes for high Reynolds number incompressible fluid flows." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/89319.

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41

Jara-Almonte, J. "Extraction of eigen-pairs from beam structures using an exact element based on a continuum formulation and the finite element method." Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/54300.

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Studies of numerical methods to decouple structure and fluid interaction have reported the need for more precise approximations of higher structure eigenvalues and eigenvectors than are currently available from standard finite elements. The purpose of this study is to investigate hybrid finite element models composed of standard finite elements and exact-elements for the prediction of higher structure eigenvalues and eigenvectors. An exact beam-element dynamic-stiffness formulation is presented for a plane Timoshenko beam with rotatory inertia. This formulation is based on a converted continuum transfer matrix and is incorporated into a typical finite element program for eigenvalue/vector problems. Hybrid models using the exact-beam element generate transcendental, nonlinear eigenvalue problems. An eigenvalue extraction technique for this problem is also implemented. Also presented is a post-processing capability to reconstruct the mode shape each of exact element at as many discrete locations along the element as desired. The resulting code has advantages over both the standard transfer matrix method and the standard finite element method. The advantage over the transfer matrix method is that complicated structures may be modeled with the converted continuum transfer matrix without having to use branching techniques. The advantage over the finite element method is that fewer degrees of freedom are necessary to obtain good approximations for the higher eigenvalues. The reduction is achieved because the incorporation of an exact-beam-element is tantamount to the dynamic condensation of an infinity of degrees of freedom. Numerical examples are used to illustrate the advantages of this method. First, the eigenvalues of a fixed-fixed beam are found with purely finite element models, purely exact-element models, and a closed-form solution. Comparisons show that purely exact-element models give, for all practical purposes, the same eigenvalues as a closed-form solution. Next, a Portal Arch and a Verdeel Truss structure are modeled with hybrid models, purely finite element, and purely exact-element models. The hybrid models do provide precise higher eigenvalues with fewer degrees of freedom than the purely finite element models. The purely exact-element models were the most economical for obtaining higher structure eigenvalues. The hybrid models were more costly than the purely exact-element models, but not as costly as the purely finite element models.
Ph. D.
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42

Ben, Souda Karima. "Finite element formulation of the bone adaptation process following arthroplasty and application to the distal femur." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ29890.pdf.

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43

Ben, Souda Karima. "Finite element formulation of the bone adaptation process following arthroplasty and application to the distal femur." Thesis, McGill University, 1996. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=41982.

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This thesis presents the formulation of a general finite element program for the computation of the bone adaptation process after total joint arthroplasty. This program is applied to study this phenomenon in the distal femur resurfaced with a prosthetic component whose fixation is achieved by bone ingrowth. The motivation for this formulation and application stems from the fact that evidence of adverse bone adaptation after total joint arthroplasty is being increasingly reported in the literature.
The stability of the bone adaptation model is investigated in terms of the exponents of some of its constitutive equations. These exponents are determined based on previous experimental studies and based on the constraint of the stability criterion. The iterative procedure that models the bone adaptation process is evaluated by comparing the computed results with analytical solutions for the density in a beam. The finite element model of the resurfaced bone takes into account the frictional properties of the contact between bone and the prosthetic component. The general contact formulation is evaluated by comparing the computed results with analytical solutions for the contact pressures in test situations for which these solutions are available.
The application of the general program to the resurfaced distal femur clarifies the role of the model variables in terms of their influence on the computed bone adaptation. The computed results compare favourably with the available clinical observations of bone adaptation in the distal femur following total knee arthroplasty. Furthermore, the present application allows the investigation of the possible beneficial effects of some of the prosthesis design parameters.
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44

Lam, Siu-Shu Eddie. "Linear and geometrically nonlinear analysis of shell structures by a shear flexible finite element shell formulation." Thesis, University of Southampton, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328340.

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45

Patel, Bhavin Ramesh. "State space formulation of TFEA & uncharted islands of instability in milling." Diss., Columbia, Mo. : University of Missouri-Columbia, 2007. http://hdl.handle.net/10355/4898.

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Thesis (M.S.)--University of Missouri-Columbia, 2007.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on January 7, 2008) Includes bibliographical references.
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46

Honkala, Keith A. "An analysis of Stokes fluid flow in a converging channel using a penalty function finite element formulation /." Online version of thesis, 1985. http://hdl.handle.net/1850/10283.

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47

Eve, Robin Andrew. "Formulation and implementation of conforming finite element approximations to static and eigenvalue problems for thin elastic shells." Master's thesis, University of Cape Town, 1987. http://hdl.handle.net/11427/22509.

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Bibliography: pages 132-135.
In deriving asymptotic error estimates for a conforming finite element analyses of static thin elastic shell problems, the French mathematician Ciarlet (1976) proposed an approach to the formulation of such problems. The formulation he uses is based on classical shell theory making use of Kirchhoff-Koiter assumptions. The shell problem is posed in two-dimensional space to which the real problem, in three-dimensional space, is related by a mapping of the domain of the problem to the shell mid-surface. The finite element approximation is formulated in terms of the covariant components of the shell mid-surface displacement field. In this study, Ciarlet's formulation is extended to include the eigenvalue problem for the shell. In addition to this, the aim of the study is to obtain some indication of how well this approach might be expected to work in practice. The conforming finite element approximation of both the static and eigenvalue problems are implemented. Particular attention is paid to allowing generality of the shell surface geometry through the use of an approximate mapping. The use of different integration rules, in-plane displacement component interpolation schemes and approximate geometry schemes are investigated. Results are presented for shells of different geometries for both static and eigenvalue analyses; these are compared with independently obtained results.
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48

Moreno, Navarro Pablo. "Multiphysics formulation and multiscale finite element discretizations of thermo-electro-magneto-mechanic coupling for smart materials design." Thesis, Compiègne, 2019. http://www.theses.fr/2019COMP2525.

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Les algorithmes numériques basés sur la méthode des éléments finis seront spécialisés dans l’analyse, la conception et l’optimisation de capteurs et d’actionneurs (S-A), ainsi que dans leur application aux structures intelligentes. Les S-A basés sur des actifs tangibles peuvent coupler plusieurs domaines, tels que les domaines mécanique, électrique, magnétique et thermique. Ils sont utilisés dans de nombreuses applications, notamment dans les structures intelligentes, la surveillance des dommages ou l’aérodynamique. Malgré l’expérience considérable de ces études, les étapes abordées consistent d’abord à développer une formulation thermodynamiquement cohérente à l’échelle macro pour introduire des modèles de plasticité; deuxièmement, fournir les outils permettant de prendre en compte les hétérogénéités des modèles multi-échelles pour les matériaux intelligents. L’objectif principal est la mise au point d’un code informatique de recherche permettant de simuler et d’étudier les performances, non seulement des S-A eux-mêmes, mais également des structures intelligentes dans lesquelles ces S-A seront montés
Numerical algorithms based on the Finite Element Method will be specialized for Analysis, Design, and Optimization of Sensors and Actuators (S-A) and their Application to Smart Structures. The S-A based on tangible assets can couple several fields, such as mechanical, electrical, magnetic, and thermal. They are used in many applications, particularly in smart structures, damage monitoring, or aerodynamics. Despite the considerable experience in these studies, the steps addressed are first to develop a thermodynamically consistent formulation for macro-scale to introduce plasticity models; second, to provide the tools to take into account the heterogeneities of multi-scale models for smart materials. The main objective is the development of a research computer code to simulate and study the performance, not only of the S-A themselves but also of the smart structures in which these S-A will be mounted
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Forner, Escrig Josep. "Numerical formulation of physical phenomena in nanoparticles for their application to nanofluids." Doctoral thesis, Universitat Jaume I, 2021. http://hdl.handle.net/10803/672111.

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This thesis presents a numerical formulation grounded on continuum physics to study different coupled phenomena, such as thermomechanics and high-frequency thermoelectricity, in nanoparticles for their use in nanofluids for both thermal energy storage and direct solar absorption applications. The main difficulties tackled in the present work are the analysis of the mechanical failure of the shell of nanoencapsulated phase change materials and the influence of the shell thickness on the mechanical strength of nanoparticles, determining the probability of failure of the shell of nanoencapsulated phase change materials by incorporating the measurement uncertainty into the numerical analysis and the relation between shell failure and enthalpy losses of nano-capsules and finally, the prediction of temperature increments around nanoparticles when optically excited.
Aquesta tesi presenta una formulació numèrica basada en física de medis continus per a estudiar diferents fenòmens acoblats com, per exemple, termomecànica i termoelectricitat a altes freqüències en nanopartícules per al seu ús en nanofluids per a aplicacions d'emmagatzemament d'energia tèrmica i d'absorció solar directa. Les problemàtiques abordades en el present treball són l'anàlisi de la fallada mecànica de l'escorça de materials de canvi de fase nanoencapsulats i la influència del seu gruix en la resistència de les nanopartícules, la determinació de la probabilitat de fallada de l'escorça dels nanoencapsulats incorporant les incerteses de mesura en l'anàlisi numèrica i la relació entre la fallada mecànica i les pèrdues d'entalpia de les nanocàpsules i, per últim, la predicció d'increments de temperatura al voltant de nanopartícules excitades òpticament.
Programa de Doctorat en Tecnologies Industrials i Materials
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50

Larsson, Karl. "Finite element methods for threads and plates with real-time applications." Licentiate thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-38198.

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Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while using a minimal amount of material. Computer modeling and analysis of thin and slender structures has its own set of problems stemming from assumptions made when deriving the equations modeling their behavior from the theory of continuum mechanics. In this thesis we consider two kinds of thin elastic structures; threads and plates. Real-time simulation of threads are of interest in various types of virtual simulations such as surgery simulation for instance. In the first paper of this thesis we develop a thread model for use in interactive applications. By viewing the thread as a continuum rather than a truly one dimensional object existing in three dimensional space we derive a thread model that naturally handles both bending, torsion and inertial effects. We apply a corotational framework to simulate large deformation in real-time. On the fly adaptive resolution is used to minimize corotational artifacts. Plates are flat elastic structures only allowing deflection in the normal direction. In the second paper in this thesis we propose a family of finite elements for approximating solutions to the Kirchhoff-Love plate equation using a continuous piecewise linear deflection field. We reconstruct a discontinuous piecewise quadratic deflection field which is applied in a discontinuous Galerkin method. Given a criterion on the reconstruction operator we prove a priori estimates in energy and L2 norms. Numerical results for the method using three possible reconstructions are presented.
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