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Fernàndez, Méndez Sònia. ""Mesh-free methods and finite elements: friend or foe?"." Doctoral thesis, Universitat Politècnica de Catalunya, 2001. http://hdl.handle.net/10803/6705.
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This thesis is devoted to the numerical analysis of mesh-free methods and, in particular, to the study of the possible advantages of the EFG (Element Free Galerkin) mesh-free method against the well-known FE (Finite Element) method. More precisely, the EFG method and the FE method behavior are compared in two particular interesting problems: (1) analysis of volumetric locking in mechanical problems and (2) accurate resolution of transient convection dominated problems. In both cases the good properties and possibilities of mesh-free methods become apparent. However, in several situations the FE method is still more competitive: for instance, the computation of the FE shape functions and its integrals are less costly, and essential boundary conditions can be easily imposed. Thus, in order to take advantage of the good properties of both methods, a mixed interpolation combining FE and EFG is proposed. This formulation can be applied in two useful situations: (i) enrichment of finite elements with EFG, and (ii) coupling of FE and EFG. An a priori error estimate for the first one is presented and proved. Several examples show the applicability of the mixed interpolation in adaptive computations.
Aquesta tesi està dedicada a l'anàlisi numèrica dels mètodes sense malla i, en particular, a l'estudi dels possibles avantatges del mètode EFG (Element Free Galerkin) davant del ben conegut MEF (Mètode dels Elements Finits). Concretament, es comparen el mètode EFG i el MEF en dos problemes concrets d'interès: (1) l'anàlisi del bloqueig volumètric en problemes mecànics i (2) la resolució precisa de problemes transitoris amb convecció dominant. Les bones propietats i possibilitats dels mètodes sense malla es fan evidents en tots dos casos.
Tot i així, en varis aspectes el MEF resulta més competitiu: per exemple, el càlcul de les funcions de forma i de les seves integrals es menys costós, i les condicions de contorn essencials es poden imposar fàcilment. Amb l'objectiu d'aprofitar les bones qualitats dels dos mètodes, es proposa una interpolació mixta combinant elements finits y EFG, aplicable en dues situacions: (i) enriquiment d'elements finits amb EFG i (ii) acoblament d'elements finits i EFG. Per al primer cas, es presenta i demostra una cota a priori de l'error. L'aplicabilitat d'aquesta interpolació mixta en processos adaptatius es mostra amb varis exemples.
Esta tesis está dedicada al análisis numérico de los métodos sin malla y, en particular, al estudio de las posibles ventajas del método EFG (Element Free Galerkin) frente al bien conocido MEF (Método de los Elementos Finitos). Concretamente, se comparan el método EFG y el MEF en dos problemas concretos de interés: (1) el análisis del bloqueo volumétrico en problemas mecánicos y (2) la resolución precisa de problemas transitorios con convección dominante. Las buenas propiedades y posibilidades de los métodos sin malla se hacen evidentes en ambos casos.
Sin embargo, en varios aspectos el MEF resulta más competitivo: por ejemplo, el cálculo de las funciones de forma y sus integrales es menos costoso, y las condiciones de contorno esenciales se pueden imponer fácilmente. Con el objetivo de aprovechar las buenas cualidades de ambos métodos, se propone una interpolación mixta combinando elementos finitos y EFG, aplicable en dos situaciones: (i) enriquecimiento de elementos finitos con EFG, y (ii) acoplamiento de elementos finitos y EFG. Para el primer caso, se presenta y demuestra una cota a priori del error. La aplicabilidad de esta interpolación mixta en procesos adaptativos se muestra con varios ejemplos.
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Dietzsch, Julian. "Implementierung gemischter Finite-Element-Formulierungen für polykonvexe Verzerrungsenergiefunktionen elastischer Kontinua." Master's thesis, Universitätsbibliothek Chemnitz, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-217381.
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In der vorliegenden Arbeit wird ein gemischtes Element gegen Locking-Effekte untersucht. Dazu wird ein Fünf-Feld-Hu-Washizu-Funktional (CoFEM-Element) für lineare und quadratische Hexaeder-Elemente unter einer hyperelastischen, isotropen, polykonvexen sowie einer transversal-isotropen Materialformulierung implementiert. Die resultierenden nichtlinearen Gleichungen werden mithilfe eines Mehrebenen-NEWTON-RAPHSON-Verfahren unter Beachtung einer konsistenten Linearisierung gelöst. Als repräsentatives Beispiel der numerischen Untersuchungen dient der einseitig eingespannte Cook-Balken mit einer quadratischen Druckverteilung am Rand. Zur Beurteilung des CoFEM-Elements wird das räumliche Konvergenzverhalten für unterschiedliche Polynomgrade und für verschiedene Netze unter Beachtung der algorithmischen Effizienz untersuchtThis paper presents a mixed finite element formulation of Hu-Washizu type (CoFEM) designed to reduce locking effects with respect to a linear and quadratic approximation in space. We consider a hyperelastic, isotropic, polyconvex material formulation as well as transverse isotropy. The resulting nonlinear algebraic equations are solved with a multilevel NEWTON-RAPHSON method. As a numerical example serves a cook-like cantilever beam with a quadratic distribution of in-plane load on the Neumann boundary. We analyze the spatial convergence with respect to the polynomial degree of the underlying Lagrange polynomials and with respect to the level of mesh refinement in terms of algorithmic efficiency
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Kobelansky, Allan John. "Divergence-free fields in the solution of waveguide problems by finite elements." Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=61936.
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Tchakoutio, Paul. "The numerical approximation of minimal surfaces with free boundaries by finite elements." [S.l. : s.n.], 2003. http://www.freidok.uni-freiburg.de/volltexte/765.
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Asdal, Bent. "Static and free vibration analysis of advanced composites using shear-deformable rectangular plate finite elements." Thesis, Virginia Polytechnic Institute and State University, 1988. http://hdl.handle.net/10919/80092.
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A comparison of rectangular finite elements based on a first order shear deformation plate theory and a refined higher order plate theory is presented. Special attention is given to the representation of transverse shear strain, the phenomenon of "shear locking", and the selection of the interpolating polynomial. Both C⁰ and C¹ continuity elements are represented; the elements range from: 3 or 5 DOF per node, and 12 - 27 DOF per element. Static and free vibration analysis of isotropic and laminated plates with thicknesses ranging from extremely thin to very thick are presented, along with a convergence study. The finite element results are compared with the exact plate theory solutions. Of the elements investigated, the modified refined higher order theory element exhibits the best overall behavior.Master of Science
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Scheichl, Robert. "Iterative solution of saddle point problems using divergence-free finite elements with applications to groundwater flow." Thesis, University of Bath, 2000. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341106.
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Junior, Alex Neves. "Sobre a modelagem de estruturas delgadas usando elementos finitos tridimensionais." Universidade de São Paulo, 2006. http://www.teses.usp.br/teses/disponiveis/3/3144/tde-08122006-152205/.
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O propósito principal do presente trabalho é estabelecer diretrizes para o uso de elementos finitos sólidos na modelagem de estruturas delgadas submetidas à flexão. Por meio de um conjunto de problemas estudou-se o travamento de elementos finitos da elasticidade bi e tridimensionais, quando usados para modelar estruturas delgadas submetidas à flexão. Foram usados elementos planos de 4, 8 e 9 nós e elementos tridimensionais de 4, 10, 11, 8, 20 e 27 nós, considerando elementos não distorcidos e distorcidos. A análise dos resultados nesses modelos permitiram entender melhor o comportamento e o uso de elementos sólidos em estruturas delgadas.The main objective of the present work is to establish guidelines for the use of solid finite elements in the modeling of thin structures submitted to bending. By means of a set of problems the locking of elements three-dimensional and two-dimensional elasticity was studied, when used to model problems thin structures subjected to bending. We use 2-D displacements-based elements of 4, 8 and 9 nodes and 3-D displacement based of 4, 10, 11, 8, 20 and 27 nodes, considering undistorted and distorted elements. The analysis of the results of these models lead to the understanding of the behavior and the use of solid elements in thin structures.
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Wang, Peng. "Solid–shell finite elements for quasi-static and dynamic analysis of 3D thin structures : application to sheet metal forming processes." Thesis, Paris, ENSAM, 2017. http://www.theses.fr/2017ENAM0010/document.
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La simulation numérique par la méthode des éléments finis (MEF) fournit de nos jours une grande aide pour les ingénieurs dans les processus de conception d’optimisation des produits. Malgré le développement croissant des ressources de calcul, la fiabilité et l’efficacité des simulations numériques par la MEF restent à améliorer. Ce travail de thèse consiste à développer une famille d’éléments solide-coque (SHB) pour la modélisation tridimensionnelle des structures minces. Cette famille d’éléments SHB est basée sur une formulation tridimensionnelle en grands déplacements et rotations. La technique dite “d’intégration réduite dans le plan”, en utilisant un nombre arbitraire de points d’intégration dans la direction de l’épaisseur, permet la modélisation des structures minces avec une seule couche d'éléments. Dans ce travail de thèse, deux éléments linéaires SHB prismatique et hexaédrique, ainsi que leurs contreparties quadratiques, ont été implantés dans le code par éléments finis ABAQUS pour l’analyse quasi-statique et dynamique des structures minces. La performance de ces éléments a été validée à travers une série de cas tests académiques, ainsi que sur des problèmes complexes de type impact/crash et des procédés de mise en forme de tôles minces. L'ensemble des résultats numériques obtenus révèle que les éléments SHB représentent une alternative intéressante aux éléments coques et solides traditionnels pour la modélisation tridimensionnelle des structures mincesNowadays, the finite element (FE) simulation provides great assistance to engineers in the design of products and optimization of manufacturing processes. Despite the growing development of computational resources, reliability and efficiency of the FE simulations remain the most important features. The current work contributes to the development of a family of assumed strain based solid-shell elements (SHB), for the modeling of 3D thin structures. Based on reduced integration and special treatments to eliminate locking effects and to control spurious zero-energy modes, the SHB solid‒shell elements are capable of modeling most thin 3D structural problems with only a single element layer, while describing accurately the various through-thickness phenomena. In the current contribution, a family of prismatic and hexahedral SHB elements with their linear and quadratic versions have been implemented into ABAQUS using both standard/quasi-static and explicit/dynamic solvers. The performance of the SHB elements is evaluated via a series of popular benchmarks as well as with impact/crash and sheet metal forming processes. All numerical results reveal that the SHB elements represent an interesting alternative to traditional shell and solid elements for the 3D modeling of thin structural problems
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Albuquerque, Arthur Álax de Araújo. "Implementação de elementos finitos de barra e placa para a análise de esforços em tabuleiros de pontes por meio de superfícies de influência." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-28072014-093844/.
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Este trabalho consiste em analisar os esforços em tabuleiros de pontes por meio de superfícies de influência. Para isto, o método dos elementos finitos (MEF) é utilizado e os resultados são comparados com os das tabelas de Rüsch. Os elementos finitos de barra, representando longarinas e transversinas, e placa, as lajes do tabuleiro, são implementados no código SIPlacas. Estes elementos finitos são formulados pelas teorias de viga Timoshenko e placa Reissner-Mindlin, respectivamente. Estes apresentam problema de travamento de força cortante (Shear Locking), que é contornado por duas propostas: o artifício matemático da integração reduzida e elementos finitos com campo assumido de deformação de força cortante (CADFC). Verifica-se que os elementos com aproximações quadráticas para os deslocamentos e com CADFC são os que melhor se adequam à proposta de análise da presente pesquisa. Tais elementos apresentam convergência de resultados considerando estruturas com baixa discretização. Os resultados analisados foram o deslocamento, momento fletor e força cortante. Posteriormente realiza-se um estudo de caso de uma ponte em viga. O tabuleiro da ponte é calculado utilizando-se as tabelas de Rüsch e o código SIPlacas. O cálculo dos esforços pelo SIPlacas é realizado de três maneiras. Na primeira consideram-se os painéis de lajes do tabuleiro isolados; na segunda o tabuleiro está sobre apoios não deslocáveis; e na terceira, o tabuleiro apresenta-se com vigas acopladas. Foi concluído que a terceira configuração, cuja representação melhor se aproxima da estrutura real de análise, apresentou os menores esforços internos.This work aims at the analysis of bridge deck stresses through influence surfaces. The finite element method (FEM) is used and the results are compared with those of Rüsch\'s tables. The bar and plate finite elements represent stringers, cross beams and slabs bridge deck. These finite elements are implemented in the SIPlacas code and the theories of Timoshenko beam and Reissner-Mindlin plate are used to theirs formulation. The Shear Locking problem is solved by two proposals: reduced integration and definition of element with transversal shear strain assumed (TSSA). The elements with quadratic approximations for the displacements and TSSA are the best suited to the proposed analysis of this research. Such elements have convergence of results considering structures with low discretization. Displacement, bending moment and shear force were the results analyzed. Subsequently a case study on a beam bridge was carried out. The bridge deck is calculated using Rüsch\'s tables and SIPlacas code. The calculation of the internal forces by SIPlacas is performed in three ways. The first one considers the slabs isolated panels; the second, the slab deck is on a rigid support; and third, the slab deck is on deformable supports. It was concluded that the third configuration showed the lowest internal forces. This configuration is the optimum representation to the structure analysis.
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Le, Thi Huyen Cham. "Robust variable kinematics plate finite elements for composite structures." Thesis, Paris 10, 2019. http://faraway.parisnanterre.fr/login?url=http://bdr.parisnanterre.fr/theses/intranet/2019/2019PA100053/2019PA100053.pdf.
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Le but de ce travail est de développer deux nouveaux éléments finis quadrilatéraux à quatre et à huit nœuds implantés dans le code commercial de calcul par Eléments Finis (EF) Abaqus pour plaques composites. Les modèles plaques à cinématique variable sont formulés dans le cadre de la formulation unifiée de Carrera (CUF), qui regroupent des descriptions de type: couche équivalente (ESL) et couches discrètes (LW), avec les variables définies par des polynômes jusqu’au 4ème ordre suivant épaisseur z. Les deux formulations variationnelles sont utilisées pour dériver les matrices des éléments finis: le Principe des Déplacements Virtuels (PVD) et le Théorème Variationnel Mixte de Reissner (RMVT). Grâce à la technique de condensation statique, une formulation hybride basée sur le RMVT est introduite. Afin d’éliminer la pathologie de verrouillage en cisaillement transverse, deux approximations compatibles pour le champ de déformations de cisaillement transverse indépendantes en z, notée QC4 et CL8, sont étendues aux éléments plaques à cinématique variable basés sur CUF. De plus, les QC4S et CL8S interpolations sont également introduites pour les contraintes de cisaillement transverse dans les éléments mixtes et les éléments hybrides. Les résultats numériques comparés à ceux disponibles dans la littérature montrent que les FE proposés sont efficaces pour modéliser des éléments finis robustesThe aim of this work is the development of two classes of new four-node and eightnode quadrilateral finite elements implemented into the commercial finite element (FE) code Abaqus for composite plates. Variable kinematics plate models are formulated in the framework of Carrera’s Unified Formulation (CUF), which encompasses Equivalent Single Layer (ESL) as well as Layer-Wise (LW) models, with the variables that are defined by polynomials up to 4th order along the thickness direction z. The two classes refer to two variational formulations that are employed to derive the finite elements matrices, namely the Principle of Virtual Displacement (PVD) and Reissner’s Mixed Variational Theorem (RMVT). Thanks to the static condensation technique, a Hybrid formulation based on the RMVT is derived. For the purpose of eliminating the shear locking pathology, two field compatible approximations for only the z−constant transverse shear strain terms, referred to as QC4 and CL8 interpolations, are extended to all variable kinematics CUF plate elements. Moreover, the QC4S and CL8S interpolations, are also introduced for the transverse shear stress field within RMVT-based and Hybrid mixed-based elements. Numerical results in comparison with those available in literature show that the proposed FEs are efficient for modeling a robust finite elements
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Jordam, Alice. "Implementação do método das características na modelagem de problemas de convecção natural em cavidades cilíndricas /." Bauru : [s.n.], 2010. http://hdl.handle.net/11449/91714.
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Orientador: Vicente Luiz ScalonBanca: Helio Aparecido Navarro
Banca: Sergio Rodrigues Fontes
Resumo: A fluidodinâmica computacinal (CFD) tem sido utilizada, estudadda e implementada ao longa das duas últimas décadas na solução dos mais diversos problemas de engenharia. O princípio básico desta ciência é a aplicação de métodos numéricos em problemas que envolvam mecânica dos fluidos. Nesse contexto, este trabalho utiliza essa técnica para analisar o comportamento de um fluido incompreensível, que se encontra numa cavidade cilíndrica fechada onde as faces inferior e superior são adiabáticas e as superfícies laterais se encontram em diferentes temperaturas. Os perfis de velocidade e temperatura resultantes - ocasionados pela convecção natural - serão avaliados em todo o domínio do problema. Existe uma série de técnicas para a solução de problemas envolvendo escoamentos, sendo as mais comuns as que se utilizam do "Esquema de Passo Fracionado" proposto por Chorin no final da década de 60. Dentre as diversas soluções que se utilizam desta técnica, este trabalho optou pelo uso do método das características e do algoritmo CBS de solução proposto por Zienkiewicz e Codina (1995). Para a implementação do algoritmo de solução do problema proposto foi realizada uma discretização geral através do método dos elementos finitos usando-se de uma malha formada por elementos bilineares. A solução foi obtida a partir de um ambiente matemático adequado, a GNU-Octave (2008). Os resultados foram analisados para diferentes razões de curvatura, números de Rayleigh e métodos de solução, sendo plotados para as suas diversas variáveis buscando descrever o comportamento do fenônemo
Abstract: The Computational Fluid Dynamics (CFD) has been used, studied and performed through the last two decades to solve the series of problems in Engineering. The most basic aim of this science is the appliance of numerical methods in cases that envolve fluid mechanics. In this context, this work uses this technic to analyze the behaviour of an incompressible fluid, which is found in a closed cylindrical cavity, a place where the inferior and superior surfaces are adiabatic and the lateral surfaces are shown in different temperatures. The resultant profiles of speed and temperature - induced by the free convection - are going to be appraised in all the dominion of the problem. There is a set of technics to solve the problems which involve the drainage, but the most usual are those which use the techic "Fractional Step Method" offered by Chorin in the final of 60s. Among the several solutions that are solved through this technic, this research used the characteristics method and of the CBS algorthm, offered by Zienkiewicz e Codina (1995). For the implementation of the algorithm, it was realized a general discretization through the finite elements method, making use of a loop formed by bilinear elements. The resolution was obtained from an adequated mathematical ambient, the GNU-Octave (2008). The results were analysed for different curvature ratios, Rayleigh numbers and methods of solution, being plotted for its different variables searching to describe the behavior of the phenomenon
Mestre
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Jordam, Alice [UNESP]. "Implementação do método das características na modelagem de problemas de convecção natural em cavidades cilíndricas." Universidade Estadual Paulista (UNESP), 2010. http://hdl.handle.net/11449/91714.
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A fluidodinâmica computacinal (CFD) tem sido utilizada, estudadda e implementada ao longa das duas últimas décadas na solução dos mais diversos problemas de engenharia. O princípio básico desta ciência é a aplicação de métodos numéricos em problemas que envolvam mecânica dos fluidos. Nesse contexto, este trabalho utiliza essa técnica para analisar o comportamento de um fluido incompreensível, que se encontra numa cavidade cilíndrica fechada onde as faces inferior e superior são adiabáticas e as superfícies laterais se encontram em diferentes temperaturas. Os perfis de velocidade e temperatura resultantes - ocasionados pela convecção natural - serão avaliados em todo o domínio do problema. Existe uma série de técnicas para a solução de problemas envolvendo escoamentos, sendo as mais comuns as que se utilizam do Esquema de Passo Fracionado proposto por Chorin no final da década de 60. Dentre as diversas soluções que se utilizam desta técnica, este trabalho optou pelo uso do método das características e do algoritmo CBS de solução proposto por Zienkiewicz e Codina (1995). Para a implementação do algoritmo de solução do problema proposto foi realizada uma discretização geral através do método dos elementos finitos usando-se de uma malha formada por elementos bilineares. A solução foi obtida a partir de um ambiente matemático adequado, a GNU-Octave (2008). Os resultados foram analisados para diferentes razões de curvatura, números de Rayleigh e métodos de solução, sendo plotados para as suas diversas variáveis buscando descrever o comportamento do fenônemo
The Computational Fluid Dynamics (CFD) has been used, studied and performed through the last two decades to solve the series of problems in Engineering. The most basic aim of this science is the appliance of numerical methods in cases that envolve fluid mechanics. In this context, this work uses this technic to analyze the behaviour of an incompressible fluid, which is found in a closed cylindrical cavity, a place where the inferior and superior surfaces are adiabatic and the lateral surfaces are shown in different temperatures. The resultant profiles of speed and temperature - induced by the free convection - are going to be appraised in all the dominion of the problem. There is a set of technics to solve the problems which involve the drainage, but the most usual are those which use the techic Fractional Step Method offered by Chorin in the final of 60s. Among the several solutions that are solved through this technic, this research used the characteristics method and of the CBS algorthm, offered by Zienkiewicz e Codina (1995). For the implementation of the algorithm, it was realized a general discretization through the finite elements method, making use of a loop formed by bilinear elements. The resolution was obtained from an adequated mathematical ambient, the GNU-Octave (2008). The results were analysed for different curvature ratios, Rayleigh numbers and methods of solution, being plotted for its different variables searching to describe the behavior of the phenomenon
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Gao, Sasa. "Development of a new 3D beam finite element with deformable section." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEI026/document.
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Le nouvel élément de poutre est une évolution d'un élément de Timoshenko poutre avec un nœud supplémentaire situé à mi-longueur. Ce nœud supplémentaire permet l'introduction de trois composantes supplémentaires de contrainte afin que la loi constitutionnelle 3D complète puisse être utilisée directement. L'élément proposé a été introduit dans un code d'éléments finis dans Matlab et une série d'exemples de linéaires/petites contraintes ont été réalisées et les résultats sont systématiquement comparés avec les valeurs correspondantes des simulations ABAQUS/Standard 3D. Ensuite, la deuxième étape consiste à introduire le comportement orthotrope et à effectuer la validation de déplacements larges / petites contraintes basés sur la formulation Lagrangienne mise à jour. Une série d'analyses numériques est réalisée qui montre que l'élément 3D amélioré fournit une excellente performance numérique. En effet, l'objectif final est d'utiliser les nouveaux éléments de poutre 3D pour modéliser des fils dans une préforme composite textile. A cet effet, la troisième étape consiste à introduire un comportement de contact et à effectuer la validation pour un nouveau contact entre 3D poutres à section rectangulaire. La formulation de contact est dérivée sur la base de formulation de pénalité et de formulation Lagrangian mise à jour utilisant des fonctions de forme physique avec l'effet de cisaillement inclus. Un algorithme de recherche de contact efficace, qui est nécessaire pour déterminer un ensemble actif pour le traitement de contribution de contact, est élaboré. Et une linéarisation constante de la contribution de contact est dérivée et exprimée sous forme de matrice appropriée, qui est facile à utiliser dans l'approximation FEM. Enfin, on présente quelques exemples numériques qui ne sont que des analyses qualitatives du contact et de la vérification de l'exactitude et de l'efficacité de l'élément de 3D poutre proposéThe new beam element is an evolution of a two nodes Timoshenko beam element with an extra node located at mid-length. That extra node allows the introduction of three extra strain components so that full 3D stress/strain constitutive relations can be used directly. The second step is to introduce the orthotropic behavior and carry out validation for large displacements/small strains based on Updated Lagrangian Formulation. A series of numerical analyses are carried out which shows that the enhanced 3D element provides an excellent numerical performance. Indeed, the final goal is to use the new 3D beam elements to model yarns in a textile composite preform. For this purpose, the third step is introducing contact behavior and carrying out validation for new 3D beam to beam contact with rectangular cross section. The contact formulation is derived on the basis of Penalty Formulation and Updated Lagrangian formulation using physical shape functions with shear effect included. An effective contact search algorithm is elaborated. And a consistent linearization of contact contribution is derived and expressed in suitable matrix form, which is easy to use in FEM approximation. Finally, some numerical examples are presented which are only qualitative analysis of contact and checking the correctness and the effectiveness of the proposed 3D beam element
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Zidane, Ali. "Risk of subsidence and aquifer contamination due to evaporite dissolution : modelization of flow and mass transport in porous and free flow domains." Phd thesis, Université de Strasbourg, 2012. http://tel.archives-ouvertes.fr/tel-00867207.
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The groundwater flow in aquifers contain evaporite rocks can cause problems such as geo-mechanical subsidence or collapse. In this work, we focus on the development of numerical models to simulate the flow in porous and non-porous domains in order to study the dissolution phenomenon and fractures evolution over time. The first part of this thesis is devoted to developing new solutions for the validation of numerical models to simulate density driven flow in porous media. The new procedure consist of solving simultaneously the flow and the transport equations using the Levenberg-Marquardt algorithm. The use of this technique allowed us to develop, for the first time, semi-analytical solutions of saltwater intrusion in the case of small diffusion and in the case of a large density contrast. In the second part of this work, we studied the flow in evaporitic rocks. A numerical code was developed to solve the nonlinear system using advanced numerical methods. To validate this new model, we have developed a semi-analytical solution for the density Stokes flow. The third part of this work is devoted to transport with dissolution of rock salt. As a first step, we studied the influence of various parameters on the dissolution of salt in Adlertunnel located at a depth of 160 m in the region of Basel in Switzerland. In a second step, we are interested in the simulation of the fracture's evolution as a result of the dissolution. The numerical model takes into account the Stokes flow and mass transport effects and dissolution of the fracture walls.
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Chen, Youbin. "Modélisation de la rupture ductile par approche locale : simulation robuste de la déchirure." Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLEM038/document.
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Cette étude a pour objectif principal d’établir une stratégie de modélisation robuste, fiable et performante pour décrire des propagations de fissures d’échelle centimétrique en régime ductile dans des composants industriels. Le modèle d’endommagement de GTN écrit en grandes déformations est utilisé pour modéliser l’endommagement ductile. Ce modèle conduit généralement à une localisation de la déformation, conformément à l’expérience. L’échelle caractéristique de ce phénomène est introduite dans les équations de comportement via l’adoption d’une formulation non locale.Sur le plan numérique, ce modèle non local rend bien compte de la localisation dans une bande d’épaisseur donnée lorsqu’on raffine suffisamment le maillage. Par ailleurs, le problème de verrouillage numérique associé au caractère initialement isochore de la déformation plastique est limité en utilisant une formulation à base d’éléments finis mixtes. Enfin, la distorsion des éléments totalement cassés (i.e. sans rigidité apparente), qui pourrait nuire à la bonne convergence des simulations numériques, est traitée par une régularisation viscoélastique.L’ensemble de ces ingrédients sont appliqués pour simuler la propagation de fissure dans un milieu infini plasticité confinée), de sorte à établir un lien avec les approches globales en J-Δa. L’émoussement, l’amorçage et la (grande) propagation de fissure sont bien prédits. Le modèle est également appliqué à une tuyauterie métallique testée en grandeur réelle dans le cadre du projet européen Atlas+. Après une phase d’identification des paramètres sur éprouvette, les réponses globales et locales d’autres éprouvettes et du tube sont confrontés aux résultats expérimentaux. Ces résultats illustrent le degré de robustesse, de fiabilité et de performance qu’on peut attendre du modèleThe major goal of this work is to establish a robust, reliable and efficient modeling technique so as to describe ductile tearing over a distance of several centimeters in industrial cases. The GTN damage model expressed in the context of finite strains is chosen to model ductile damage. Generally, the model leads to strain localization in agreement with experimental observations. The characteristic length scale of this phenomenon is introduced into the constitutive equations through the use of a nonlocal formulation.On a numerical ground, the nonlocal model controls the width of the localization band as soon as the mesh is sufficiently refined. Besides, the issue of volumetric-locking associated with plastic incompressibility is handled using a mixed finite element formulation. Finally, the distortion of broken elements (i.e. without any stiffness), which may affect the computational convergence of numerical simulations, is treated using a viscoelastic regularization.The improved GTN model is applied to simulate crack propagation under small-scale yielding conditions, so as to establish a relation with the global (J-Δa) approach. Crack tip blunting, crack initiation and (large) crack propagation are well captured. The model is also applied to a full-scale metallic pipe in the framework of the UE project Atlas+. After a phase of parameter calibration based on the experimental results on some small specimens, the global and local responses of other small specimens and of the full-scale pre-cracked pipe are compared with the experimental results. The results illustrates the robustness, the reliability and the efficiency of the current model
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Mazzochi, Rudimar. "Elementos finitos quadrilaterais Hermitianos de alta regularidade gerados pela partição de unidade aplicados na solução de problemas de elasticidade e elastodinâmica." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2014. http://hdl.handle.net/10183/96314.
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Neste trabalho foram desenvolvidas as funções de interpolação com regularidades C1 e C2, utilizando o Método da Partição de Unidade, referentes ao elemento quadrilateral de quatro nós. Estes elementos quadrilaterais Hermitianos de regularidade C1 e C2 foram implementados em uma plataforma própria de elementos finitos, considerando uma estratégia do tipo sub-paramétrica. De forma comparativa com os elementos Lagrangeanos de regularidade C0 e diferentes ordens polinomiais, os elementos de regularidade C1 e C2 foram aplicados na solução de: problemas clássicos de elasticidade plana infinitesimal isotrópica; aproximação das frequências naturais de vibração livre de barras e viga; pro- pagação de onda elástica em barra devido à aplicação de força impulsiva. Os resultados obtidos mostraram que foi possível se obter um maior percentual de frequências naturais aproximadas do espectro discreto, dado um certo nível de erro máximo, com os elementos de regularidade C1 e C2 em comparação com os elementos Lagrangeanos de regularidade C0 de quatro, oito, dezesseis e vinte e cinco nós. Quanto ao problema de propagação de onda elástica devido à aplicação de força impulsiva, as soluções obtidas com os elementos de regularidade C1 e C2 também apresentaram-se satisfatórias em relação à solução ana- lítica e às soluções aproximadas obtidas com os elementos Lagrangeanos de regularidade C0 de quatro e oito nós. Por outro lado, nas simulações dos problemas de elasticidade plana infinitesimal isotrópica, os elementos de regularidade C1 e C2 não apresentaram um comportamento satisfatório. Os erros relativos em normas L2 e de energia da solução aproximada foram maiores do que aqueles obtidos com o elemento Lagrangeano de regularidade C0 de oito nós, por exemplo, e as taxas de convergência em norma de energia obtidas com tais elementos foram inferiores às preditas pelo estimador de erro a priori.In this work the shape functions with regularity C1 e C2 were developed, by means of the Partition of Unity Method, concerning to the four-node quadrilateral element. These Hermitian quadrilateral elements with regularity C1 e C2 were implemented in an own platform of finite elements, considering the subparametric strategy. Comparatively with the C 0 regularity Lagrangian elements of different polynomial order, C1 and C2 regularity elements were applied in simulations of: classical isotropic infinitesimal plane elasticity problems; approximation of natural frequencies of free vibration for bars and beam; elastic wave propagation in bar caused by forced vibration with impulsive loading applied. The results obtained showed that was possible to get a major number of natural frequencies of free vibration for the discrete spectrum, given a certain level of error, for C1 and C2 regularity elements in comparison with C 0 regularity Lagrangian elements of four, eight, sixteen and twenty-five nodes. Regarding to the elastic wave propagation problem in bar due to the application of impulsive loading, the solution obtained with C1 and C2 regularity elements also presented satisfactory results with relation to the analytical solution and those obtained with C 0 regularity Lagrangian elements with four and eight nodes. On the other hand, for isotropic infinitesimal plane elasticity problems, C1 and C2 regularity elements did not present satisfactory results. Relative errors in L2 and energy norms of approximate solution were greater than those computed for the C 0 Lagrangian element of eight nodes, for example, and convergence rates obtained with the C1 and C2 regularity elements were lower than those predicted by the a priori error estimator.
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Ben, henni Mohamed. "Contribution à l'étude de la vibration des plaques en matériaux composites sous chargements mécanique et thermomécanique." Thesis, Reims, 2019. http://www.theses.fr/2019REIMS020.
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Ce travail a pour objectif d’analyser le comportement en vibrations libres de composites stratifiés à fibres hybrides en utilisant d’une part, une théorie d’ordre élevé à quatre variables qui prend en considération l’effet de cisaillement transverse lors du calcul des déformations ; et d’autre part une analyse par la méthode des éléments finis. L’équation du mouvement de la plaque stratifiée est obtenue en utilisant de principe d'Hamilton. Les expressions mathématiques sont obtenues en utilisant la solution de Navier pour différentes conditions aux limites. Afin de valider les modèles proposés nous avons d’abord comparé nos résultats avec des modèles existants dans la littérature pour les matériaux non hybrides. Les modules élastiques de la plaque hybride sont calculés en utilisant la loi des mélanges. Ensuite, nous avons étudié les effets des dimensions de la plaque, de la fraction volumique et du type de fibres, de la position des couches (pour le cas de l’hybridation intercouche) ainsi que les conditions aux limites sur les fréquences fondamentales des plaques composites hybrides. Comme il n’y a aucune donnée disponible dans la littérature pourles plaques composites hybrides, la solution en éléments finis a été utilisée pour valider les résultats obtenus par la théorie d’ordre élevé. Les résultats montrent la bonne précision de la solution analytique proposée pour la prévision des fréquences fondamentales des plaques stratifiées hybrides. Comme les conditions hygrothermiques généralement dégradent la rigidité des structures, nous avons étudié les effets de température et de l’humidité sur la stabilité des plaques composites hybrides et non hybrides. Les résultats obtenus pour les fréquences fondamentales montrent que les conditions hygrothermiques affectent le comportement des plaques composites mais à moindre échelleThe aim of this work is to analyze the vibration behavior of hybrid fiber composite laminates by using, on the one hand, the fourvariable high order theory taking into account the transverse shear effect for strain calculation; and on the other hand by the finite element method analysis. The equation of motion of the laminated plate is obtained using Hamilton's principle. The mathematical expressions are obtained using the Navier solution for different boundary conditions. In order to validate the proposed models, we compared our results with existing models in the literature for non-hybrid composites. The elastic moduli of the hybrid plate were calculated using the law of mixtures. Then, we studied the effects of the plate dimensions, the volume fraction, the type of fiber, the position of layers (in the case of interlayer hybridization) on the fundamental frequencies of hybrid composite plates.Since, there is no data available in the literature for hybrid composite plates, the finite element solution is used to validate the results obtained by the high order theory. The results show good accuracy of the proposed analytical solution for the prediction of the fundamental frequencies of hybrid stratified plates. Hygrothermal conditions generally degrade the rigidity of structures, we studied the effects of temperature and humidity on the stability of hybrid and non-hybrid composite plates. The results obtained for the fundamental frequencies show that the hygrothermal conditions can affect the behavior of composite plates but with a lesser effect
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Ricchiuto, Mario. "Contributions to the development of residual discretizations for hyperbolic conservation laws with application to shallow water flows." Habilitation à diriger des recherches, Université Sciences et Technologies - Bordeaux I, 2011. http://tel.archives-ouvertes.fr/tel-00651688.
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In this work we review 12 years of developments in the field of residual based discretizations for hyperbolic problems and their application to the solution of the shallow water equations. Fundamental concepts related to the topic are recalled and he construction of second and higher order schemes for steady problems is presented. The generalization to time dependent problems by means of multi-step implicit time integration, space-time, and genuinely explicit techniques is thoroughly discussed. Finally, the issues of C-property, super consistency, and wetting/drying are analyzed in this framework showing the power of the residual based approach.
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Valdés, Vázquez Jesús Gerardo. "Nonlinear Analysis of Orthotropic Membrane and Shell Structures Including Fluid-Structure Interaction." Doctoral thesis, Universitat Politècnica de Catalunya, 2007. http://hdl.handle.net/10803/6866.
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Problemas de interacciónn fluido-estructura representan hoy en día un gran desafío en diferentes áreas de ingeniería y ciencias aplicadas. Dentro de las aplicaciones en ingeniería civil, el flujo del viento y los movimientos estructurales pueden ocasionar inestabilidades aeroelásticas en construcciones tales como puentes de gran luz, rascacielos y cubiertas estructurales ligeras. Por otro lado, aplicaciones en biomecánica están interesadas en el estudio de hemodinámica, por ejemplo: flujo sanguíneo en arterias, donde grandes deformaciones de las venas interactúan con fluidos.En la parte estructural de este trabajo, una nueva metodología para el análisis geométricamente no-lineal ortótropo de membranas y láminas sin grados de libertad de rotación es desarrollada basándose en la orientación de la fibra principal del material. Una consecuencia directa de la estrategia de orientación de fibras es la posibilidad de analizar membranas y láminas pretensadas cuya configuración inicial está fuera del plano. Por otra parte, ya que la teoría convencional de membranas permite que existan tensiones de compresión, un modelo de arrugado basado en la modificación de la ecuación constitutiva se presenta. El desarrollo estructural es modelado con elementos finitos provenientes de las ecuaciones de la elastodinámica.La parte de fluidos de este trabajo está gobernada por las ecuaciones de Navier-
Stokes para flujos incompresibles, las cuales son modeladas por interpolaciones estabilizadas de elementos finitos. Ya que la solución monolítica de dichas ecuaciones tiene la desventaja que consumen mucho tiempo en la solución de grandes sistemas de ecuaciones, el método de pasos fraccionados se usa para aprovechar las ventajas computacionales que brinda gracias al desacoplamiento de la presión del campo de las velocidades. Además, el esquema α-generalizado para integración en el tiempo para fluidos es adaptado para que se use con la t´ecnica de los pasos fraccionados.
El problema de interacción fluido-estructura es formulado como un sistema de tres campos: la estructura, el fluido y el movimiento de la malla. El movimiento del dominio del fluido es tomado en cuenta mediante la formulación arbitraria Lagrangiana-Euleriana, para la cual se usan dos estrategias de movimiento de malla.
Para el acoplamiento entre el fluido y la estructura se usa un acoplamiento fuerte por bloques usando la técnica de Gauss-Seidel. Debido a que la interacción entre el fluido y la estructura es altamente no-lineal, se implementa el método de relajación basado en la técnica de Aitken, la cual acelera la convergencia del problema.
Finalmente varios problemas se presentan en los diferentes campos, los cuales verifican la eficiencia de los algoritmos implementados.
Nowadays, fluid-structure interaction problems are a great challenge of different fields in engineering and applied sciences. In civil engineering applications, wind flow and structural motion may lead to aeroelastic instabilities on constructions such as long-span bridges, high-rise buildings and light-weight roof structures. On the other hand, biomechanical applications are interested in the study of hemodynamics, i.e. blood flow through large arteries, where large structural membrane deformations interact with incompressible fluids.
In the structural part of this work, a new methodology for the analysis of geometrically nonlinear orthotropic membrane and rotation-free shell elements is developed based on the principal fiber orientation of the material. A direct consequence of the fiber orientation strategy is the possibility to analyze initially out-ofplane prestressed membrane and shell structures. Additionally, since conventional membrane theory allows compression stresses, a wrinkling algorithm based on modifying the constitutive equation is presented. The structure is modeled with finite elements emerging from the governing equations of elastodynamics.
The fluid portion of this work is governed by the incompressible Navier-Stokes equations, which are modeled by stabilized equal-order interpolation finite elements.
Since the monolithic solution for these equations has the disadvantage that take great computer effort to solve large algebraic system of equations, the fractional step methodology is used to take advantage of the computational efficiency given by the uncoupling of the pressure from the velocity field. In addition, the generalized-α time integration scheme for fluids is adapted to be used with the fractional step technique.
The fluid-structure interaction problem is formulated as a three-field system: the structure, the fluid and the moving fluid mesh solver. Motion of the fluid domain is accounted for with the arbitrary Lagrangian-Eulerian formulation with two different mesh update strategies. The coupling between the fluid and the structure is performed with the strong coupling block Gauss-Seidel partitioned technique.
Since the fluid-structure interaction problem is highly nonlinear, a relaxation technique based on Aitken's method is implemented in the strong coupling formulation to accelerate the convergence.
Finally several example problems are presented in each field to verify the robustness and efficiency of the overall algorithm, many of them validated with reference solutions.
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Dietzsch, Julian. "Implementierung gemischter Finite-Element-Formulierungen für polykonvexe Verzerrungsenergiefunktionen elastischer Kontinua." Master's thesis, 2016. https://monarch.qucosa.de/id/qucosa%3A20633.
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In der vorliegenden Arbeit wird ein gemischtes Element gegen Locking-Effekte untersucht. Dazu wird ein Fünf-Feld-Hu-Washizu-Funktional (CoFEM-Element) für lineare und quadratische Hexaeder-Elemente unter einer hyperelastischen, isotropen, polykonvexen sowie einer
transversal-isotropen Materialformulierung implementiert. Die resultierenden nichtlinearen Gleichungen werden mithilfe eines Mehrebenen-NEWTON-RAPHSON-Verfahren unter Beachtung
einer konsistenten Linearisierung gelöst. Als repräsentatives Beispiel der numerischen Untersuchungen dient der einseitig eingespannte Cook-Balken mit einer quadratischen Druckverteilung am Rand. Zur Beurteilung des CoFEM-Elements wird das räumliche Konvergenzverhalten für unterschiedliche Polynomgrade und für verschiedene Netze unter Beachtung der algorithmischen Effizienz untersucht.This paper presents a mixed finite element formulation of Hu-Washizu type (CoFEM) designed to reduce locking effects with respect to a linear and quadratic approximation in space. We consider a hyperelastic, isotropic, polyconvex material formulation as well as transverse isotropy. The resulting nonlinear algebraic equations are solved with a multilevel NEWTON-RAPHSON method. As a numerical example serves a cook-like cantilever beam with a quadratic distribution of in-plane load on the Neumann boundary. We analyze the spatial convergence with respect to the polynomial degree of the underlying Lagrange polynomials and with respect to the level of mesh refinement in terms of algorithmic efficiency.
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Quaglino, Alessio. "Membrane locking in discrete shell theories." Doctoral thesis, 2012. http://hdl.handle.net/11858/00-1735-0000-000D-F063-B.
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Chuang, Ting-Yu, and 莊庭語. "Improvements of Distal Locking Plate by Finite Elements Analysis and Biomechanical Test." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/u24qnp.
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碩士國立臺灣科技大學
機械工程系
107
Femurs are the thickest bones in human bodies. When people stand and move, our femurs suffer not only axial load but also the bending load because of their anatomical shapes and the muscles that pulling around. Nowadays locking plates are the most popular treatments for the destruction of a femur. After the occurrence of the bone fracture, the main support of the body weight when the patients stand and walk all relies on the plate at the early stage of recovery. However if there is any shortcoming of the plate design or any lack knowledge of the usage of the plates, the plates will be broken under a fatigue load after frequently walking or excessively using. This may result in failure of the treatment and another operation will be needed once again. There are two parts in this study. The first one is about the weak point of a plate. We use finite element analysis to infer the weakest part of a plate and then we validate the result by biomechanical tests. In the second part, we investigate the effect of the different screw working length only by biomechanical tests. From the result of finite element analysis, the stress concentration is on the screw-hole edges and most of the maximum stress are near the fracture gap. It finds out that the weak point of the plate is the screw-hole edges at the thinnest part of the plate. In mechanical tests, although there is a great stress at the thinnest part of the plate, the maximum stress is at the screw-hole near the middle diaphysis. This is a result of a larger lever arm and the inferior bending of the bone. In aspect of the working length, an longer working length has a good effect at the low fracture model, but goes worse at a higher fracture. This comes to a result of a transform of loading.
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""Mesh-free methods and finite elements: friend or foe?"." Universitat Politècnica de Catalunya, 2001. http://www.tesisenxarxa.net/TDX-0919102-145705/.
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Linke, Alexander [Verfasser]. "Divergence-free mixed finite elements for the incompressible Navier-Stokes equation / vorgelegt von Alexander Linke." 2008. http://d-nb.info/991225457/34.
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Tchakoutio, Paul [Verfasser]. "The numerical approximation of minimal surfaces with free boundaries by finite elements / vorgelegt von Paul Tchakoutio." 2003. http://d-nb.info/968491901/34.
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Lin, Yu-Yuan, and 林鈺淵. "Studies of Free Vibration of Rotating Rectangular Cross-Section Composite Rings Using Straight Beam Finite Elements." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/49563705030931630550.
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碩士國立中興大學
機械工程學系所
105
The objective of this thesis is to develop a finite element model of a rotating ring with rectangular cross-section using one-dimensional three-node straight beam element with twenty-three degrees of freedom. The straight beam element has included structural effects such as transverse shear deformation, twisting, warping, chordwise curvature, and sidewise bending. In the elements, the mixed Lagrangian-Hermite type of interpolation functions are used to represent the twisting deformation, while Lagrangian interpolation functions are used for other displacement variables. As a result, the finite element model developed here is able to predict more truly the deformation of vibrational behaviors of rotating composite rings than those using simple beam model. To develop the finite element model of the rotating ring, first, the straight beam finite elements are used to approximate the deformation of the ring. The displacement field of beam in Ref. [10] is adopted. The kinetic energy and the strain energy of the straight beam element at a typical location on the ring are found. Then, by employing Hamilton’s principle together with the finite element method, the equations of motion of straight beam element at such a typical ring’s location are derived. Next, the displacement transform matrix between elements similar to that of Ref. [13] is derived. With the displacement matrix and beam element’s matrices, the finite element equations of motion of rotating composite rings are obtained. Based on the above ring finite element model, the natural frequencies and mode shapes of rotating rings are studied. The influence of the width to thickness ratios, rotating speeds, material types: isotropic material, single-layered and laminated composite material, as well as the fiber angles are investigated.
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Lin, Ben-Fu, and 林本富. "Studies of Free Vibration of Rotating Composite Rings of Rectangular or Circular Cross-Section Using Curved Beam Finite Elements." Thesis, 2019. http://ndltd.ncl.edu.tw/cgi-bin/gs32/gsweb.cgi/login?o=dnclcdr&s=id=%22107NCHU5311041%22.&searchmode=basic.
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碩士國立中興大學
機械工程學系所
107
The objective of this thesis is to develop plane curved beam elements of rectangular cross-section and of circular cross-section, and apply these plane curved beam elements to the analysis of the vibration characteristics of composite rotating rings. In the derivation of the rectangular cross-section plane curved beam element, both the √g for the differential volume of the plane curved beam and the relations between physical and tensor strain components are both taken into account. Furthermore, a warping degree of freedom is also added which would improve the accuracy of obtaining the natural frequencies of rings having the rectangular cross section. Based on the derived plane curved beam elements, MATLAB programs are written to analyze the circular rings made of isotropic as well as composite materials. The vibration characteristics of the free circular rings at rest or spinning with a constant velocity are studied. The influences of the geometric and material properties of circular rings, and for rings of rectangular cross-section in particular, the effects of different aspect ratios of cross-section are analyzed. To verify the present curved finite element beam models and the developed programs, the results obtained from the present theory are compared with those in literatures and from ANSYS. They are found in good agreement.
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Chen, Hung-Chin, and 陳宏晉. "Studies of Free Vibration of Fiber-Reinforced Composite Helical Springs with Circular Cross Sections Using Circularly Curved Beam Finite Elements." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/80223243921081227798.
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碩士國立中興大學
機械工程學系所
103
In this thesis, a three-node, 6 degree of freedom per node, curved beam element including the effect of initial curvature and torsion of beam is proposed. In this curved beam element, the lateral and axial displacements, as well as the deformation due to both twisting and shearing of beam are also considered. The curved beam element is employed to analyze circular helical springs with circular cross section, where the springs are made of unidirectional fiber-reinforced composite layers having a preselected set of lamination angles. To study the initial torsion and initial curvature effects in the above curved beam element, the current element is further simplified into other two types of element, a curved beam element without initial torsion and a straight beam element. Using these three types of elements, the effectiveness of curved and straight beam elements to simulate both static and dynamic characteristics of springs then can be evaluated. To ensure the elements being derived and the computer program being developed are correct, first, springs made of an isotropic material are analyzed and the results expressed as the spring constants are compared with the analytical solution derived using the virtual work method. It is found that for the problem being analyzed all three types of elements yield a little bit smaller spring constant values than the analytical one, and the difference of the results between analytical method and any of three types of element is at its largest not exceeding 8%. Next, the vibration characteristics of springs made of an isotropic material are analyzed using these three types of element. The results are compared with those of ANSYS and they are found in good agreement. To study the effect of lamination angle η on the static and dynamic characteristic of springs made of unidirectional fiber-reinforced composite material, composite solid springs with a single lamination angle (or composite solid springs) and laminated composite hollow springs with a particular set of lamination angles (or laminated composite hollow springs) are analyzed. Static analyses of composite solid springs indicate that discrepancies among the three types of elements are more conspicuous when η=〖15〗^o~〖45〗^o, and the values of spring constant seem attain their largest values as η approaches 〖45〗^o. This could be attributed by the bending and twisting deformation coupling of the off-axis composite layer as the coupling effect is strongest when 〖η=45〗^o and one knows that the spring deformed accompanied by both bending and twisting. From dynamic analysis, one finds that all three types of element yield similar trend of natural frequency to η relation. There are a few modes don’t match exactly (like the modes swing directions are different), or have a little bit greater natural frequency discrepancies at certain η values. Finally, the analyses of laminated composite hollow springs show almost the same trends of results as the composite solid springs. But the discrepancies among the mode shapes and natural frequencies become smaller. This might be due to the deformation coupling of layers of the different lamination angles, as well as more layers with 〖η=0〗^o.
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Huang, Yi Shang, and 黃衣聖. "Comparisons of Curved and Straight Beam Finite Elements on Free Vibration Analysis of Rectangular Cross-Section Helical Springs made of Fiber-Reinforced Composite Materials." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/00385617958224759536.
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碩士國立中興大學
機械工程學系所
105
In this thesis the free vibration of rectangular cross-section helical springs is studied using two types of beam element. The first type element is the 3 node, 18 degree-of-freedom, curved beam element and the second, the 3 node, 23 degree-of-freedom, straight beam finite element. The springs are assumed to be made of isotropic materials or fiber-reinforced composite materials. In both elements, the axial and lateral displacement, as well as the deformation due to both shearing and twisting of beam are considered, while in straight beam element, additional flexural deformations of beam’s flexibility in its width direction and the warping of cross section are included. The curved beam element of rectangular cross section is adapted from Ref. [14] where springs of circular cross section are treated. The straight beam element are derived based on displacement field of Ref. [18] and by following the same procedure of obtaining the displacement transformation matrix considered by Ref. [4]. The circular cylindrical spring deformation is described in terms of Frenet-Serret local coordinates. The Hamilton’s principle together with finite element method is used to derive the element’s mass and stiffness matrices for both curved and straight beam elements. For the case of curved beam element matrices, they can be directly assembled to obtain the corresponding global mass and stiffness matrices. In contrast, the straight beam element matrices must be transformed first using the displacement transform matrix before being assembled to obtain the global ones. In the numerical examples, natural frequencies and mode shapes of isotropic helical springs of 3 turns and the width to thickness ratio b/h=1, 3, 5 are studied and compared with those of ANSYS for the free-free and fix-free boundary conditions. It is found that the present curved beam element performs well when b/h = 1 or close to one, while the straight beam element although doesn’t work well when b/h = 1, do obtain much better results than curved beam element comparing with those of ANSYS for the studied cases b/h = 3, 5. Also studied in the numerical examples are the effects of Poisson’s ratio, fiber angles of composite laminate.