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1
Dag, Idris. "Studies of B-spline finite elements." Thesis, Bangor University, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358041.
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Waters, Timothy Paul. "Finite element model updating using frequency response functions." Thesis, University of Bristol, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.294617.
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Ramsay, Tim. "A bivariate finite element smoothing spline applied to image registration." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ54429.pdf.
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Wang, Hongrui. "Error and stability analysis for B-spline finite element methods." Thesis, University of Strathclyde, 2015. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=26570.
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The thesis studies the approximation properties of splines with maximum smoothness. We are interested in the behaviour of the approximation as the degree of the spline increases (so does its smoothness). By studying B-spline interpolation, we obtain error estimates measured in the semi-norm that are explicit in terms of mesh size, degree and smoothness. This new result also gives a higher approximation order than existing estimations. With the results, we investigate the B-spline finite element approximation with k-refinement, which is a strategy of improving the accuracy by increasing the degree and smoothness. The problem is studied in the setting of heat equations and wave equations. We give B-spline FEM schemes for the problems, and obtain error estimates. Moreover, by proving a Markov-type inequality for splines, where an exact constant is derived, we deduce how the stability of the scheme behaves with the k-refinements. We also improve the efficiency of the schemes for problems with periodic boundary conditions by applying the fast Fourier transform. The thesis also focuses on developing algorithms for efficiently evaluating the element system matrices in finite element methods with Berstein-Bâezier splines as shape functions, where the splines are of arbitrary order and defined on quadrilaterals and hexahedrons. The algorithms achieve the optimal complexity by making use of the sum factorial procedure. We test the algorithms in C++ implementation, and the numerical results illustrate that the optimal cost and expected accuracy are achieved.
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Zarad, Abdallah. "Developing an advanced spline fatigue prediction method." Thesis, Blekinge Tekniska Högskola, Institutionen för maskinteknik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-18927.
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Fatigue failure is one of the most critical issues in industry nowadays as 60 to 90 percent of failures in metals are due to fatigue. Therefore, different methods and approaches are developed to estimate the fatigue life of metallic parts. In this research, a case-hardened steel splined shaft is studied to estimate the fatigue life that the shaft will withstand before failure. The purpose of the research is to develop an advanced fatigue prediction method for splines.A static experimental test was performed on the splined shaft for analyzing the load-strain behavior of the shaft and determining the suitable load cases of the study. A dynamic test of pure torsional load was carried out to collect experimental results for validating the generated fatigue methods and investigating the failure behavior of the shaft. Stress analysis was performed on the part for investigating critical areas and the effect of the different spline teeth designs on the resulting stress. Two finite element models were analyzed using two software, MSC Marc software with a geometry of straight spline teeth and Spline LDP with an involute spline teeth model. DIN 5466-1 spline standard’s analytical solution was used for verification purposes. Stress and strain-based approaches were used to estimate fatigue life. The most suitable method was evaluated against experimental test results.The research findings show that the most critical stress areas on the shaft are the spline root fillet and relief. When the part fails due to fatigue the crack initiates at the root fillet and propagates to the relief. It is also shown that involute teeth spline gives higher stress than straight teeth for the same load due to less contact area.The conclusion of the research could be summarized in: the stress-based method (Wöhler curve) is giving good accuracy and proved a reliable method. While among six different approaches used of strain-based methods, four-point correlation method is giving the best correlation to test results. Hence, it is recommended to use four-point correlation method for fatigue analysis for its accuracy and for considering both elastic and plastic behavior of the material.
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Musuva, Mutinda. "The multiscale wavelet finite element method for structural dynamics." Thesis, Brunel University, 2015. http://bura.brunel.ac.uk/handle/2438/12468.
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The Wavelet Finite Element Method (WFEM) involves combining the versatile wavelet analysis with the classical Finite Element Method (FEM) by utilizing the wavelet scaling functions as interpolating functions; providing an alternative to the conventional polynomial interpolation functions used in classical FEM. Wavelet analysis as a tool applied in WFEM has grown in popularity over the past decade and a half and the WFEM has demonstrated potential prowess to overcome some difficulties and limitations of FEM. This is particular for problems with regions of the solution domain where the gradient of the field variables are expected to vary fast or suddenly, leading to higher computational costs and/or inaccurate results. The properties of some of the various wavelet families such as compact support, multiresolution analysis (MRA), vanishing moments and the “two-scale” relations, make the use of wavelets in WFEM advantageous, particularly in the analysis of problems with strong nonlinearities, singularities and material property variations present. The wavelet based finite elements (WFEs) presented in this study, conceptually based on previous works, are constructed using the Daubechies and B-spline wavelet on the interval (BSWI) wavelet families. These two wavelet families possess the desired properties of multiresolution, compact support, the “two scale” relations and vanishing moments. The rod, beam and planar bar WFEs are used to study structural static and dynamic problems (moving load) via numerical examples. The dynamic analysis of functionally graded materials (FGMs) is further carried out through a new modified wavelet based finite element formulation using the Daubechies and BSWI wavelets, tailored for such classes of composite materials that have their properties varying spatially. Consequently, a modified algorithm of the multiscale Daubechies connection coefficients used in the formulation of the FGM elemental matrices and load vectors in wavelet space is presented and implemented in the formulation of the WFEs. The approach allows for the computation of the integral of the products of the Daubechies functions, and/or their derivatives, for different Daubechies function orders. The effects of varying the material distribution of a functionally graded (FG) beam on the natural frequency and dynamic response when subjected to a moving load for different velocity profiles are analysed. The dynamic responses of a FG beam resting on a viscoelastic foundation are also analysed for different material distributions, velocity and viscous damping profiles. The approximate solutions of the WFEM converge to the exact solution when the order and/or multiresolution scale of the WFE are increased. The results demonstrate that the Daubechies and B-spline based WFE solutions are highly accurate and require less number of elements than FEM due to the multiresolution property of WFEM. Furthermore, the applied moving load velocities and viscous damping influence the effects of varying the material distribution of FG beams on the dynamic response. Additional aspects of WFEM such as, the effect of altering the layout of the WFE and selection of the order of wavelet families to analyse static problems, are also presented in this study.
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Malheiro, Ana Paula Resende. "Construção de separadores globalmente suaves para conjuntos de pontos no R2 e geração de base mínima." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/275758.
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Orientador: Jorge Stolfi<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Computação<br>Made available in DSpace on 2018-08-18T02:35:56Z (GMT). No. of bitstreams: 1
Malheiro_AnaPaulaResende_D.pdf: 11382454 bytes, checksum: 9ea58ac7af766674dc90224444666560 (MD5)
Previous issue date: 2011<br>Resumo: Esta tese tem duas partes relativamente independentes. A primeira estuda o problema de construir uma curva suave (C1) que separa dois conjuntos de pontos do plano. Especificamente, a curva é definida por uma equação implícita F(x, y) = 0 onde F é uma spline polinomial de grau 2 com continuidade adequada. O objetivo é determinar uma única cônica se possível, senão uma curva que minimiza uma função quadrática de "energia". O problema é reduzido a um problema de minimização quadrática com restrições, que é resolvido por uma biblioteca existente (CGAL). A segunda parte descreve um algoritmo geral para determinar uma base de elementos finitos em um espaço de splines arbitrário, definido por exemplo por restrições lineares homogêneas de continuidade ou contorno. Neste caso o problema é caracterizado como o problema de encontrar uma base de peso máximo em um matróide e, portanto, pode ser resolvido pelo algoritmo guloso de Edmonds. Esse algoritmo tem custo exponencial no número n de células da malha. Entretanto, esta tese mostra que para casos de interesse - onde existe uma base de elementos finitos com suporte de k células, no máximo - o algoritmo pode ser melhorado de modo a terminar em tempo O(n km3), onde m é a dimensão do espaço (que é geralmente O(n))<br>Abstract: This thesis has two relatively independent parts. The first part considers the problem of constructing a smooth (C1) curve separating two sets of points of the plane. Specifically, the curve is defined by an implicit equation F(x, y) = 0, where F is a polynomial spline of degree 2 with appropriate continuity. The goal is to determine a unique conic wherever possible, or a piecewise-defined curve that minimizes a quadratic "energy" function. The problem is reduced to a quadratic minimization problem with constraints, which is solved by an existing library (CGAL). The second part describes a general algorithm to determine a finite-element basis on an arbitrary space of splines; for example, a space defined by homogeneous linear boundary or continuity constraints. In this case the problem is defined as the problem of finding a maximum weight basis in a matroid, and therefore can be solved by the greedy algorithm of Edmonds. This algorithm has exponential cost in the number n of mesh cells. However, we show that for cases of interest - wherever there is a finite-element basis with maximum support of ? cells - the algorithm can be improved so as to finish in time O(n km3), where m is the dimension of the space (which is usually O(n))<br>Doutorado<br>Ciência da Computação<br>Doutor em Ciência da Computação
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Mahar, Akshay Mangal. "Buckling and post-buckling behaviour of cold-formed steel built-up columns." Thesis, Queensland University of Technology, 2022. https://eprints.qut.edu.au/232829/1/Akshay%20Mangal_Mahar_Thesis.pdf.
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This research investigated the stability and strength behaviour of cold-formed steel built-up columns. The stability behaviour was investigated by developing a compound spline finite strip based computational tool, while experiments and finite element studies were performed to investigate the strength behaviour. The results highlighted the shortcomings of the current design standards, including North American and Australian/New Zealand Standards, and led to simplified design procedures and strength equations for cold-formed steel built-up columns. Overall, this research has significantly improved the knowledge of cold-formed steel built-up columns, enabling structurally efficient and safer designs.
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Occelli, Matthieu. "Explicit dynamics isogeometric analysis : lr b-splines implementation in the radioss solver." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSEI102/document.
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L'analyse isométrique s'est révélée être un outil très prometteur pour la conception et l'analyse. Une tâche difficile consiste toujours à faire passer l'IGA de concept à un outil de conception pratique pour l'industrie et ce travail contribue à cet effort. Ce travail porte sur l'implémentation de l'IGA dans le solveur explicite Altair Radioss afin de répondre aux applications de simulation de crash et d'emboutissage. Pour cela, les ingrédients nécessaires à une intégration native de l'IGA dans un code éléments finis traditionnel ont été identifiés et adaptés à l'architecture de code existante. Un élément solide B-Spline et NURBS a été développé dans Altair Radioss. Les estimations heuristiques des pas de temps élémentaires ou nodaux sont explorées pour améliorer l'efficacité des simulations et garantir leur stabilité. Une interface de contact existante a été étendue afin de fonctionner de manière transparente avec les éléments finis NURBS et de Lagrange. Un raffinement local est souvent nécessaire pour la bonne représentation de champs non linéaires tels que les champs de déformations plastiques. Une analyse est faite en termes de compatibilité pour l'analyse et de mise en oeuvre pour plusieurs bases de fonctions Spline telles que les Hierarchical B-Splines, les Truncated Hierarchical B-Splines, les T-Splines et les Locally Refined B-Splines (LR B-Splines). Les LR B-Splines sont implémentés. Un schéma de raffinement est proposé et définit un sous-ensemble de raffinements adapté à leur utilisation au sein de Radioss. Le processus de raffinement d’un maillage initialement grossier et régulier est développé au sein du solveur. Il permet à l’utilisateur d’établir du raffinement local par un ensemble d’instructions à fournir dans le jeu de donnée de la simulation. La solution globale est validée sur des cas tests industriels, pour des cas de validation classiquement utilisés pour les codes industriels comme l'emboutissage et les tests de chute<br>IsoGeometric Analysis has shown to be a very promising tool for an integrated design and analysis process. A challenging task is still to move IGA from a proof of concept to a convenient design tool for industry and this work contributes to this endeavor. This work deals with the implementation of the IGA into Altair Radioss explicit finite element solver in order to address crash and stamping simulation applications. To this end, the necessary ingredients to a smooth integration of IGA in a traditional finite element code have been identified and adapted to the existing code architecture. A solid B-Spline element has been developed in Altair Radioss. The estimations of heuristic element and nodal stable time increment are explored to improve the accuracy of simulations and guarantee their stability. An existing contact interface has been extended in order to work seamlessly with both NURBS and Lagrange finite elements. As local refinement is needed for solution approximation, an analysis is made in terms of analysis suitability and implementation aspects for several Spline basis functions as Hierarchical B-Splines (HB-Splines), Truncated Hierarchical B-Splines (THB-Splines), T-Splines and Locally Refined B-Splines (LR B-Splines). The LR B-Spline basis is implemented. An improved refinement scheme is introduced and defines a set of analysis-suitable refinements to be used in Radioss. The refinement process of a regular coarse mesh is developed inside the solver. It allows the user to define a local refinement giving a set of instructions in the input file. The global solution is validated on industrial benchmarks, for validation cases conventionally used for industrial codes like stamping and drop test
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Kempthorne, Daryl Matthew. "The development of virtual leaf surface models for interactive agrichemical spray applications." Thesis, Queensland University of Technology, 2015. https://eprints.qut.edu.au/84525/12/84525%28thesis%29.pdf.
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This project constructed virtual plant leaf surfaces from digitised data sets for use in droplet spray models. Digitisation techniques for obtaining data sets for cotton, chenopodium and wheat leaves are discussed and novel algorithms for the reconstruction of the leaves from these three plant species are developed. The reconstructed leaf surfaces are included into agricultural droplet spray models to investigate the effect of the nozzle and spray formulation combination on the proportion of spray retained by the plant. A numerical study of the post-impaction motion of large droplets that have formed on the leaf surface is also considered.
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Boattin, Boisdon Madeleine. "Approximation en coordonnées barycentriques généralisées." Toulouse 3, 1988. http://www.theses.fr/1988TOU30005.
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Les coordonnées barycentriques généralisées permettent la construction d'une nouvelle catégorie d'approximants et d'espaces fonctionnels associes parmi lesquels les fonctions éléments finis, les fonctions splines d'interpolation, Les approximants fractals sont des cas particuliers. Les courbes fractales ont alors une écriture globale, voire algorithmique et pour un paramétrage intrinsèque appartiennent à des espaces de Sobolev d'ordre non entier
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Mößner, Bernhard. "B-splines als Finite Elemente /." Aachen : Shaker, 2006. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=015210875&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
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Ribeiro, Carlos Fernando Morgado. "Development of computational tools for Isogeometric Analysis (IGA)." Master's thesis, Universidade de Aveiro, 2014. http://hdl.handle.net/10773/14421.
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Mestrado em Engenharia Mecânica<br>A few years ago drawings were made in the drawing boards and using pencils
on vellum. There were no computers helping the designers in the parts
modeling. After designing the object, the design was passed to the analysts.
The designers and analysts were in constant communication. Nowadays, the
designers used Computer Aided Design (CAD) tools in the parts modeling.
For application the analysis at the geometries, initially a mesh to approximate
the geometries is generated. After this, on the mesh the Finite Element
Method (FEM) was applied. In complex engineering design, the generation
and manipulation of meshes in FEA was estimated to take over 80% of the
overall analysis time. The form to break down the barriers between engineering
design and the analysis is with reconstruction the entire process, but
at the same time maintaining compatibility with existing practices. Create
only one geometric model is the focus of reconstruction process. This geometric
model is used in the representation of the geometry, as well as in the
analysis, and this concept is designated by Isogeometric Analysis (IGA).
In this present work the development of the tools for generate the CAD and
calculate the basis function for representation the object are proposed. Initially,
the mathematical formulations for Bézier, B-Spline and NURBS, for
curves and surfaces are presented. The algorithms developed to generate
the curves and surfaces are demonstrated.
The IGA and FEM formulation for tridimensional and bidimensional spaces
are introduced. In this work, a development of a tools for application this
method are proposed. The convergence of the results for FEM and IGA
programs are studied and compared to the theoretical values and Abaqus
comercial program. The results obtained with IGA formulation converge to
the reference values.<br>Há alguns anos atrás, os objectos eram feitos pelos designers e a criação
do desenho era feita com lápis e papel vegetal. Não existiam computadores
nos gabinetes de desenho para ajudar na modelação dos objectos. Após
o desenho estar concluído este era entregue aos analistas para calcularem
a resistência do mesmos quando solicitados por cargas externas. Assim,
o gabinete de design e o gabinete de análise estavam em constante comunicação. Nos tempos de hoje os designers utilizam as ferramentas de
Computer-Aided Design (CAD) para gerar os objectos, representando assim
a geometria original. Por outro lado, os analistas fazem a análise baseada
no Método dos Elementos Finitos (MEF). Neste método, inicialmente, gera-se
uma malha para fazer a aproximação do objecto e utiliza-se esta malha
gerada na análise. A forma de combater esta barreira é a construção de um
novo processo de análise, mas ao mesmo tempo manter a compatibilidade
com a análise do Método de Elementos Finitos. Este novo método foca-se
na geração de um modelo geométrico, sendo este modelo utilizado tanto
para a representação da geometria como para a análise. A principal sustentação deste novo método é a utilização das funções de base da criação e
representação dos objectos, posteriormente, utilizadas na análise dos mesmos.
Este novo conceito é designado por Análise Isogeométrica.
Neste trabalho é exposto o desenvolvimento de ferramentas para gerar curvas
e superfícies utilizando as formulações de Bézier, B-spline e NURBS.
Assim, desenvolveram-se sub-rotinas para calcular as funções de base. Inicialmente
apresentaram-se as formulações matemáticas e posteriormente os
algoritmos desenvolvidos para a representação das curvas e superfícies.
O desenvolvimento de ferramentas de análise para problemas no espaço bidimensional
e tridimensional utilizando o Método de Elementos Finitos e a
Análise Isogeométrica também é abordado neste trabalho. Para ser mais
fácil a sua aplicação, foi desenvolvida um interface. Por fim utilizaram-se
problemas e estudaram-se as curvas de convergência dos resultados e
compararando-os com as referência analíticas e com o programa Abaqus.
Em termos de conclusão, os resultados obtidos com a Análise Isogeométrica
convergem mais rapidamente para os valores de referência do que o Abaqus
e o programa desenvolvido com base no método de elementos finitos.
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Li, Jingang. "Isogeometric Finite Element Analysis Using T-Splines." Diss., CLICK HERE for online access, 2009. http://contentdm.lib.byu.edu/ETD/image/etd3159.pdf.
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Benhida, Soufia. "De l'optimisation pour l'aide à la décision : applications au problème du voyageur de commerce probabiliste et à l'approximation de données." Thesis, Normandie, 2018. http://www.theses.fr/2018NORMIR27.
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La 1ere partie de ce travail traite l'optimisation des tournées sous forme d'un problème d'optimisation nommé Le problème de Voyageur de Commerce. Dans cette partie nous nous intéressons à faire une riche présentation du problème de Voyageur de Commerce, ses variantes, puis nous proposons une stratégie de génération de contrainte pour la résolution du TSP. Ensuite on traite sa version stochastique : le problème de Voyageur de commerce Probabiliste. Nous proposons une formulation mathématique du PTSP et nous présentons des résultats numériques obtenus par résolution exacte pour une série d'instances de petite taille. Dans la seconde partie, nous proposons une méthode d'approximation générale permettant d'approcher différents type de données, d'abord nous traitons l'approximation d'un signal de vent (cas simple, ID), ensuite l'approximation d'un champ de vecteurs avec prise en compte de la topographie qui constitue la principale contribution de cette partie<br>The first part of this work deals with route optimization in the form of an optimization problem named The Traveler's Business Problem. In this part we are interested to make a rich presentation of the problem of Traveler Commerce, its variants, then we propose a strategy of constraint generation for the resolution of the TSP. Then we treat its stochastic version : the probabilistic business traveler problem. We propose a mathematical formulation of the PTSP and we present numerical results obtained by exact resolution for a series of small instances. In the second part, we propose a method of general approximation to approximate different type of data, first we treat the approximation of a wind signal (simple case, 1D), then the approximation of a vector field taking into account the topography which is the main contribution of this part
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Aggarwal, Bhavya. "B-spline finite elements for plane elasticity problems." Texas A&M University, 2006. http://hdl.handle.net/1969.1/4849.
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The finite element method since its development in the 1950âÂÂs has been used
extensively in solving complex problems involving partial differential equations. The
conventional finite element methods use piecewise Lagrange interpolation functions for
approximating displacements. The aim of this research is to explore finite element
analysis using B-spline interpolation. B-splines are piecewise defined polynomial curves
which provide higher continuity of derivatives than piecewise Lagrange interpolation
functions. This work focuses on the implementation and comparison of the B-spline
finite elements in contrast with the conventional finite elements. This thesis observes
that the use of B-spline interpolation functions can reduce the computational cost
significantly. It is an efficient technique and can be conveniently implemented into the
existing finite element programs.
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Mössner, Bernhard [Verfasser]. "B-Splines als Finite Elemente / Bernhard Mössner." Aachen : Shaker, 2006. http://d-nb.info/1186582669/34.
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Wipper, Joachim [Verfasser]. "Finite-Elemente-Approximation mit WEB-Splines / Joachim Wipper." Aachen : Shaker, 2005. http://d-nb.info/1186577789/34.
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Streit, Anja. "Finite Elemente Approximation der Plattengleichung mit web-Splines." [S.l. : s.n.], 2002. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10424234.
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INCH, OSCAR FABRICIO ZULETA. "FINITE ELEMENTS WITH SPLINE FUNCTIONS APPLIED TO STRUCTURAL DYNAMICS AND INSTABILITY." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2008. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=12139@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>No presente trabalho se estuda um elemento finito
subparamétrico que aproxima o campo de deslocamentos com
funções spline, implementando um programa que pode ser
utilizado para calculo estático, dinâmico e de
instabilidade de estruturas compostas de placas, vigas de
paredes finas, vigas caixão e em geral em elementos
alongados (pontes e perfis metálicos). O grau de liberdade
de rotação perpendicular ao plano do elemento é introduzido
na formulação para possibilitar uma análise tridimensional.
Apresenta-se um método que serve como base para determinar a
constante de rigidez correspondente. Nos exemplos
apresentados avalia-se a precisão obtida utilizando pouco
número de divisões longitudinais do continuo, vantagem que
justifica o uso desses elementos em estudos de pré-projeto
ou otimização de estruturas. Comparam-se os resultados com
soluções teóricas ou resultados de outros programas
estruturais, permitindo apreciar as possibilidades e
limitações da modelagem usando elementos finitos com funções
spline. As diferenças observadas, que surgem
principalmente em placas espessas, são explicadas
pela aproximação da deformação de cisalhamento encontrada na
literatura para os elementos utilizados na comparação.
Mostra-se também exemplos de instabilidade analisados em
três dimensões que permitem considerar diferentes
condições de apoio e discutir os resultados de fórmulas
conhecidas.<br>The present work presents a subparametric finite element
model with spline displacement functions, implemented for
static, dynamic and instability analysis of folded plates,
thin-walled beams, box girders, and elongated structures
such as bridges and structural shapes. A drilling degree of
freedom (rotation about an axis perpendicular to the plane
of the element) is introduced in the formulation to
allow for three-dimensional analysis. A method for
determining the corresponding contribution to the stiffness
matrix is presented. The examples presented evaluate the
accuracy obtained using a small number of longitudinal
subdivisions of the continuum, convenient in the case of
analyses for preliminary design and optimization. The
results obtained are compared to theoretical solutions or
results of standard structural analysis programs, allowing
for an appraisal of the advantages and limitations of
modeling with use of spline functions. The
differences in the results, observed specially in the case
of thick plates, are explained by the approximations for the
shear strain in the elements used for comparison. From the
examples it is possible to comment results of
threedimensional modeling of instability problems with
different boundary conditions.
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Boßle, Marco. "R-Funktionen für Finite-Elemente-Approximationen mit web-Splines." [S.l. : s.n.], 2002. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10277660.
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Geis, Winfried. "FEM mit web-Spline-Basis analytische und numerische Behandlung geeigneter Gewichtsfunktionen /." [S.l. : s.n.], 2001. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB9716178.
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Gdhami, Asma. "Méthodes isogéométriques pour les équations aux dérivées partielles hyperboliques." Thesis, Université Côte d'Azur (ComUE), 2018. http://www.theses.fr/2018AZUR4210/document.
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L’Analyse isogéométrique (AIG) est une méthode innovante de résolution numérique des équations différentielles, proposée à l’origine par Thomas Hughes, Austin Cottrell et Yuri Bazilevs en 2005. Cette technique de discrétisation est une généralisation de l’analyse par éléments finis classiques (AEF), conçue pour intégrer la conception assistée par ordinateur (CAO), afin de combler l’écart entre la description géométrique et l’analyse des problèmes d’ingénierie. Ceci est réalisé en utilisant des B-splines ou des B-splines rationnelles non uniformes (NURBS), pour la description des géométries ainsi que pour la représentation de champs de solutions inconnus.L’objet de cette thèse est d’étudier la méthode isogéométrique dans le contexte des problèmes hyperboliques en utilisant les fonctions B-splines comme fonctions de base. Nous proposons également une méthode combinant l’AIG avec la méthode de Galerkin discontinue (GD) pour résoudre les problèmes hyperboliques. Plus précisément, la méthodologie de GD est adoptée à travers les interfaces de patches, tandis que l’AIG traditionnelle est utilisée dans chaque patch. Notre méthode tire parti de la méthode de l’AIG et la méthode de GD.Les résultats numériques sont présentés jusqu’à l’ordre polynomial p= 4 à la fois pour une méthode deGalerkin continue et discontinue. Ces résultats numériques sont comparés pour un ensemble de problèmes de complexité croissante en 1D et 2D<br>Isogeometric Analysis (IGA) is a modern strategy for numerical solution of partial differential equations, originally proposed by Thomas Hughes, Austin Cottrell and Yuri Bazilevs in 2005. This discretization technique is a generalization of classical finite element analysis (FEA), designed to integrate Computer Aided Design (CAD) and FEA, to close the gap between the geometrical description and the analysis of engineering problems. This is achieved by using B-splines or non-uniform rational B-splines (NURBS), for the description of geometries as well as for the representation of unknown solution fields.The purpose of this thesis is to study isogeometric methods in the context of hyperbolic problems usingB-splines as basis functions. We also propose a method that combines IGA with the discontinuous Galerkin(DG)method for solving hyperbolic problems. More precisely, DG methodology is adopted across the patchinterfaces, while the traditional IGA is employed within each patch. The proposed method takes advantageof both IGA and the DG method.Numerical results are presented up to polynomial order p= 4 both for a continuous and discontinuousGalerkin method. These numerical results are compared for a range of problems of increasing complexity,in 1D and 2D
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Kopf, Andreas. "Finite Elemente Approximation mit web-Splines in der ebenen linearen Elastizität." [S.l. : s.n.], 2002. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB11293371.
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Sevilla, Cárdenas Rubén. "NURBS-Enhanced Finite Element Method (NEFEM)." Doctoral thesis, Universitat Politècnica de Catalunya, 2009. http://hdl.handle.net/10803/5857.
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Aquesta tesi proposa una millora del clàssic mètode dels elements finits (finite element method, FEM) per a un tractament eficient de dominis amb contorns corbs: el denominat NURBS-enhanced finite element method (NEFEM). Aquesta millora permet descriure de manera exacta la geometría mitjançant la seva representació del contorn CAD amb non-uniform rational B-splines (NURBS), mentre que la solució s'aproxima amb la interpolació polinòmica estàndard. Per tant, en la major part del domini, la interpolació i la integració numèrica són estàndard, retenint les propietats de convergència clàssiques del FEM i facilitant l'acoblament amb els elements interiors. Només es requereixen estratègies específiques per realitzar la interpolació i la integració numèrica en elements afectats per la descripció del contorn mitjançant NURBS.<br/><br/>La implementació i aplicació de NEFEM a problemes que requereixen una descripció acurada del contorn són, també, objectius prioritaris d'aquesta tesi. Per exemple, la solució numèrica de les equacions de Maxwell és molt sensible a la descripció geomètrica. Es presenta l'aplicació de NEFEM a problemes d'scattering d'ones electromagnètiques amb una formulació de Galerkin discontinu. S'investiga l'habilitat de NEFEM per obtenir solucions precises amb malles grolleres i aproximacions d'alt ordre, i s'exploren les possibilitats de les anomenades malles NEFEM, amb elements que contenen singularitats dintre d'una cara o aresta d'un element. Utilitzant NEFEM, la mida de la malla no està controlada per la complexitat de la geometria. Això implica una dràstica diferència en la mida dels elements i, per tant, suposa un gran estalvi tant des del punt de vista de requeriments de memòria com de cost computacional. Per tant, NEFEM és una eina poderosa per la simulació de problemes tridimensionals a gran escala amb geometries complexes. D'altra banda, la simulació de problemes d'scattering d'ones electromagnètiques requereix mecanismes per aconseguir una absorció eficient de les ones scattered. En aquesta tesi es discuteixen, optimitzen i comparen dues tècniques en el context de mètodes de Galerkin discontinu amb aproximacions d'alt ordre.<br/><br/>La resolució numèrica de les equacions d'Euler de la dinàmica de gasos és també molt sensible a la representació geomètrica. Quan es considera una formulació de Galerkin discontinu i elements isoparamètrics lineals, una producció espúria d'entropia pot evitar la convergència cap a la solució correcta. Amb NEFEM, l'acurada imposició de la condició de contorn en contorns impenetrables proporciona resultats precisos inclús amb una aproximació lineal de la solució. A més, la representació exacta del contorn permet una imposició adequada de les condicions de contorn amb malles grolleres i graus d'interpolació alts. Una propietat atractiva de la implementació proposada és que moltes de les rutines usuals en un codi d'elements finits poden ser aprofitades, per exemple rutines per realitzar el càlcul de les matrius elementals, assemblatge, etc. Només és necessari implementar noves rutines per calcular les quadratures numèriques en elements corbs i emmagatzemar el valor de les funciones de forma en els punts d'integració. S'han proposat vàries tècniques d'elements finits corbs a la literatura. En aquesta tesi, es compara NEFEM amb altres tècniques populars d'elements finits corbs (isoparamètics, cartesians i p-FEM), des de tres punts de vista diferents: aspectes teòrics, implementació i eficiència numèrica. En els exemples numèrics, NEFEM és, com a mínim, un ordre de magnitud més precís comparat amb altres tècniques. A més, per una precisió desitjada NEFEM és també més eficient: necessita un 50% dels graus de llibertat que fan servir els elements isoparamètrics o p-FEM per aconseguir la mateixa precisió. Per tant, l'ús de NEFEM és altament recomanable en presència de contorns corbs i/o quan el contorn té detalls geomètrics complexes.<br>This thesis proposes an improvement of the classical finite element method (FEM) for an efficient treatment of curved boundaries: the NURBSenhanced FEM (NEFEM). It is able to exactly represent the geometry by means of the usual CAD boundary representation with non-uniform rational Bsplines (NURBS), while the solution is approximated with a standard piecewise polynomial interpolation. Therefore, in the vast majority of the domain, interpolation and numerical integration are standard, preserving the classical finite element (FE) convergence properties, and allowing a seamless coupling with standard FEs on the domain interior. Specifically designed polynomial interpolation and numerical integration are designed only for those elements affected by the NURBS boundary representation.<br/><br/>The implementation and application of NEFEM to problems demanding an accurate boundary representation are also primary goals of this thesis. For instance, the numerical solution of Maxwell's equations is highly sensitive to geometry description. The application of NEFEM to electromagnetic scattering problems using a discontinuous Galerkin formulation is presented. The ability of NEFEM to compute an accurate solution with coarse meshes and high-order approximations is investigated, and the possibilities of NEFEM meshes, with elements containing edge or corner singularities, are explored. With NEFEM, the mesh size is no longer subsidiary to geometry complexity, and depends only on the accuracy requirements on the solution, whereas standard FEs require mesh refinement to properly capture the geometry. This implies a drastic difference in mesh size that results in drastic memory savings, and also important savings in computational cost. Thus, NEFEM is a powerful tool for large-scale scattering simulations with complex geometries in three dimensions. Another key issue in the numerical solution of electromagnetic scattering problems is using a mechanism to perform the absorption of outgoing waves. Two perfectly matched layers are discussed, optimized and compared in a high-order discontinuous Galerkin framework.<br/><br/>The numerical solution of Euler equations of gas dynamics is also very sensitive to geometry description. Using a discontinuous Galerkin formulation and linear isoparametric elements, a spurious entropy production may prevent convergence to the correct solution. With NEFEM, the exact imposition of the solid wall boundary condition provides accurate results even with a linear approximation of the solution. Furthermore, the exact boundary representation allows using coarse meshes, but ensuring the proper implementation of the solid wall boundary condition. An attractive feature of the proposed implementation is that the usual routines of a standard FE code can be directly used, namely routines for the computation of elemental matrices and vectors, assembly, etc. It is only necessary to implement new routines for the computation of numerical quadratures in curved elements and to store the value of shape functions at integration points. <br/><br/>Several curved FE techniques have been proposed in the literature. In this thesis, NEFEM is compared with some popular curved FE techniques (namely isoparametric FEs, cartesian FEs and p-FEM), from three different perspectives: theoretical aspects, implementation and performance. In every example shown, NEFEM is at least one order of magnitude more accurate compared to other techniques. Moreover, for a desired accuracy NEFEM is also computationally more efficient. In some examples, NEFEM needs only 50% of the number of degrees of freedom required by isoparametric FEs or p-FEM. Thus, the use of NEFEM is strongly recommended in the presence of curved boundaries and/or when the boundary of the domain has complex geometric details.
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Fredheim, Ole Jørgen. "Isogeometric Finite Element Analysis based on Bézier Extraction of NURBS and T-splines." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for konstruksjonsteknikk, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-15890.
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This thesis will give a theoretical overview of B-splines, as well as NURBS and T-splines which are based on B-splines, and also the concept of Bézier decomposition of these spline functions. Bézier decomposition will decompose the splines into Bernstein polynomials which are defined over the domain of one quadrature element. This theoretical background will then be used to implement a Matlab isogeometric finite element analysis program. Two different choices for implementation are explored, a isogeometric finite element solver built from scratch for use of NURBS, and the use of Bézier extraction to implement isogeometric analysis with NURBS and T-splines in an already existing finite element solver. The main focus will be on use of Bézier extraction, which will signicantly ease the implementation. Numerical studies are performed with problems of linear elasticity and heat conduction, to study the convergence of an isogeometric analysis.The accuracy of isogeometric analysis will prove to be better than for a traditional FEA for the analyzed problems
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Nguyen, Thanh Ngan. "Isogeometric Finite Element Analysis based on Bézier Extraction of NURBS and T-Splines." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for konstruksjonsteknikk, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-15917.
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Data transmission between finite element analysis (FEA) and computer-aided design (CAD) is ahuge bottle-neck today. Therefore, isogeometric analysis has been introduced with aim to merge these fields. While FEA utilizes Lagrange polynomials to approximate both the geometry and the solution field, isogeometric analysis employs non-uniform rational B-splines (NURBS) from CAD technology to this objective. Isogeometric analysis will therefore have the advantage in nogeometric error in the sense that the model is exact. T-splines are a recently introduced generalization of NURBS which allow local refinement, handling complex geometry in a subtle way with fewer degrees of freedom. Increasing the order of the elements in isogeometric analysis is easy and gives higher continuous basis functions than FEA, while also maintaining few degrees of freedom. In conventional isogeometric analysis the basis functions are not confined to one single element, but span a global domain, complicating implementation. The Bézier extraction operator decomposes a set of NURBS or T-spline basis functions to linear combinations of Bernstein polynomials. These polynomials bear a close resemblance to the Lagrange polynomials as they allow for generation of C0 continuous Bézier elements. A local data structure for isogeometric analysis close to traditional FEA is provided. Codes are developed to illustrate conventional isogeometric data structures as well as structures based on Bézier extraction of NURBS. Modifications are made to the latter to be able to run analysis of T-splines modelled in the CAD system Rhino, and numerical studies are performed.Generally, NURBS elements display the same convergence rate as Lagrange elements of equal order, but higher accuracy. The reasons are a smooth solution field and exact geometrical representation.
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Sherar, P. A. "Variational based analysis and modelling using B-splines." Thesis, Cranfield University, 2004. http://hdl.handle.net/1826/125.
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The use of energy methods and variational principles is widespread in many fields of engineering of which structural mechanics and curve and surface design are two prominent examples. In principle many different types of function can be used as possible trial solutions to a given variational problem but where piecewise polynomial behaviour and user controlled cross segment continuity is either required or desirable, B-splines serve as a natural choice. Although there are many examples of the use of B-splines in such situations there is no common thread running through existing formulations that generalises from the one dimensional case through to two and three dimensions.
We develop a unified approach to the representation of the minimisation equations for B-spline based functionals in tensor product form and apply these results to solving specific problems in geometric smoothing and finite element analysis using the Rayleigh-Ritz method. We focus on the development of algorithms for the exact computation of the minimisation matrices generated by finding stationary values of functionals involving integrals of squares and products of derivatives, and then use these to seek new variational based solutions to problems in the above fields. By using tensor notation we are able to generalise the methods and the algorithms from curves through to surfaces and volumes.
The algorithms developed can be applied to other fields where a variational form of the
problem exists and where such tensor product B-spline functions can be specified as potential
solutions.
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FEI, Baowei. "Image Registration for the Prostate." Case Western Reserve University School of Graduate Studies / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=case1224274091.
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Baker, Donald Alexander. "A Finite Element Study of Stresses in Stepped Splined Shafts, and Partially Splined Shafts Under Bending, Torsion, and Combined Loadings." Thesis, Virginia Tech, 1999. http://hdl.handle.net/10919/35637.
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<p>The maximum von Mises stress is calculated for solid finite element models of splined shafts with straight-sided teeth. One spline shaft is stepped with larger diameter section containing spline teeth and the smaller diameter section circular and cylindrical with no spline teeth. A second shaft is not stepped, but contains incomplete spline teeth.</p>
<p>Finite element analyses are performed for the cases of a stepped shaft of three different step size ratios (d/D). The second set of models consists of a solid cylindrical shaft with incomplete spline teeth. The incomplete regions of the spline teeth are modeled in three radii (R). Bending, torsion, and combined loads are applied to each model, including several combinations of bending and torsion between pure bending and pure torsion. Finite element stress results are converged to within 2% for verification.</p>
<p>The stresses in the stepped splined shafts are up to 50% greater than nominal stresses in the non-splined section and up to 88% greater than nominal stresses splined section. Stresses in the partially splined shaft showed little or no correlation between the hob radius and the magnitude of the peak von Mises stress, but show a strong correlation between the peak stress and the proportion of bending to torsion. The peak von Mises stress occurs when the applied load consists of greater proportions of torsion as opposed to bending. Stresses in the partially splined shaft are up to 42% greater than the well-developed nominal stress in the non-splined section of the shaft, and up to 7% greater than the nominal stresses in the splined section.</p><br>Master of Science
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Pechmann, Patrick R. "Penalized Least Squares Methoden mit stückweise polynomialen Funktionen zur Lösung von partiellen Differentialgleichungen." kostenfrei, 2008. http://www.opus-bayern.de/uni-wuerzburg/volltexte/2008/2813/.
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Gonzalez, Csaszar Eduardo. "Analysis of optical propagation in isotropic nonlinear devices by the finite element method." Thesis, University College London (University of London), 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244741.
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Engstrand, Klas E. "Improvements to the weak-post W-beam guardrail." Link to electronic version, 2000. http://www.wpi.edu/Pubs/ETD/Available/etd-0623100-160344.
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Adkins, Keith A. "A Model for Prediction of Fracture Initiation in Finite Element Analyses of Welded Steel Connections." University of Cincinnati / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1399624062.
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Tasneem, Nazia. "Study of wave shaping techniques of split Hopkinson pressure bar using finite element analysis." Thesis, Wichita State University, 2005. http://hdl.handle.net/10057/2341.
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The split Hopkinson pressure bar (SHPB) continues to be one of the most common methods of testing materials at high rates of strain. Elevated rates of strain, such as those found in impact and explosive applications, have been shown to induce phenomena such as strain hardening and phase transitions that can significantly affect the strength of most materials. Due to its relative simplicity and robustness, the SHPB remains one of the preferred platforms for evaluating mechanical properties of materials at rates of strain approaching 10 4 in/in-s (s -1 ). At the National Institute for Aviation Research (NIAR), research has been conducted to study the wave shaping techniques of SHPB using finite element analysis. The SHPB consists of two long, slender cylindrical bars, denoted input and output bars that "sandwich" a cylindrical test specimen. Utilizing a high-pressure gas gun, a third cylindrical steel bar, known as the striker bar, is fired at the input bar, causing a compressive stress wave to travel through the input bar to the input bar - test specimen interface. At this interface, a portion of the stress wave propagates through the test specimen while the remainder of the pulse reflects back through the input bar as a tensile stress wave.<br>Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Mechanical Engineering.<br>Includes bibliographic references (leaves 78-81).
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Gomide, Anamaria 1949. "Splines polinomiais não homogeneos na esfera." [s.n.], 1999. http://repositorio.unicamp.br/jspui/handle/REPOSIP/260855.
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Orientador: Jorge Stolfi, Marcio Luiz de Andrade<br>Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação<br>Made available in DSpace on 2018-07-25T14:59:38Z (GMT). No. of bitstreams: 1
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Previous issue date: 1999<br>Resumo: Estudamos neste trabalho o método de elementos finitos para aproximação de funções, e integração de equações diferenciais parciais sobre a esfera S2. Tais problemas ocorrem em várias aplicações práticas, incluindo modelagem global do tempo, geofísica, iluminação, etc. Definimos um polinômio esférico como sendo a restrição à esfera sn-l de um polinômio nas coordenadas cartesianas (Xl, x2,.", xn) de Rn. Denotamos por pd,n /sn-l o espaço de todos os polinômios esféricos de grau total :s:d, e por 1ld,n/sn-l o espaço dos polinômios esféricos homogêneos de grau total d. As funções que investigamos são as funções esféricas Cr polinomiais por partes, ou splines esféricos Cr, definidos em relação a uma triangulação esférica T de sn-l. Seja p~,n[T]/sn-l o espaço de todas as funções f de sn-l em R tais que (1) a restrição de f a cada triângulo de T coincide com uma função de pd,n/sn-l; e (2) a função f tem continuidade de ordem-r através das fronteiras de T. Analogamente, seja 1l~,n[TJlsn-l o sub-espaço de p~,n[T]/sn-l dos splines esféricos homogêneos, que consiste das funções que são 1ld,n/sn-l em cada triângulo de T. Neste trabalho mostramos que pd,n/sn-l = 1ld-l,n /sn-l EB1ld,n/sn-l, e estendemos esse resultado aos splines esféricos, mostrando que p~,n[TJlsn-l = 1l~-l,n[TJlsn-l EB1l~,n[T]jsn-l. Alfeld, Neamtu e Schumaker propuseram recentemente o espaço 1l~[TJlS2 para aproximação na esfera S2, e obtiveram uma construção explícita de uma base para o espaço 1l~[T]/S2, quando d 2: 3r + 2. Combinando .esta construção com o nosso resultado, acima descrito, nós obtemos uma base local explícita para o espaço P~[T]jS2 quando d 2:3r + 3. Nossa tese é que o P~[T]jS2 é um espaço de aproximação mais natural e eficaz do que 1l~[T]/S2. Analisamos, em particular, o uso dos espaços Pg[T]jS2 e Pf[T]jS2 para aproximar funções restritas a esfera S2, pelo critério dos mínimos quadrados. Analisamos também o uso do espaço Pf[TJlS2 para resolução numérica de equações diferenciais parciais na esfera, pelo método dos elementos finitos, e descrevemos uma
técnica multi-escala para acelerar a convergência em malhas finas<br>Abstract: We study in this work the finite element method for function approximation and integration of partial differential equation on the sphere S2. These problems occur in many pratical applications, including global weather modeling, geophysics, illumination,
etc.. A spherical polynomial is the restriction to the sphere sn-l of a polynomial in the coordinates Xl, X2,. . . , Xn of Rn. We denote by pd,n/sn-l the space of spherical polynomials with total degree :::; d, and by 1íd,n/sn-l the space of homogeneous
spherical polynomials with total degree d. The functions we investigate are the Cr piecewise polynomial functions on sn-l, or Cr spherical splines, defined relative to a spherical triangulation T on the sphere sn-l. Let p~,n[T]jsn-l be the space of all functions f from sn-l to R such that (1) the restriction of f to each triangle of T matches some function in pd,n /sn-l; and (2) the function f has order-r continuity across the boundaries of T. Analogously, let 1í~,n[T]jsn-1 denote the subspace ofP~,n[T]/sn-l, the homogeneous spherical splines, which consists of the functions that are 1íd,n/sn-l within each triangle of T. We show that pd,n/sn-l = 1íd,n/sn-l EB1íd-l,n /sn-l, and generalize this result to spherical splines, showing that p~,n[T]jsn-1 = 1í~,n[T]jsn-1 EB1í~-I,n[T]jsn-l. Alfeld, Neamtu and Shumaker proposed recently the space 1í~[T]jS2 for approximation on the sphere S2, and they obtained explicit bases for that space, when d 2 3r + 2. Combining their construction with our result above, we obtain explicit local bases for the spaces p~[T]jS2, when d 2 3r + q. We argue that the space P~[T]jS2 is a more natural and effective tool than 1í~[T]jS2 for approximation on the sphere. We analyze, in particular, the use of spaces Pg[T]jS2 and Pf[T]jS2 for least squares function approximation on the sphere S2. We analyze also the use of the space Pf[T]jS2 in the numerical integration of partial differential equations; and we describe a multi-scale technique for accelerating the convergence on large grids<br>Doutorado<br>Doutor em Engenharia Elétrica
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Shepherd, Kendrick Monroe. "Modeling Stokes Flow Using Hierarchical Structure-Preserving B-Splines." BYU ScholarsArchive, 2015. https://scholarsarchive.byu.edu/etd/5581.
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A new spline space, the hierarchical structure-preserving B-spline space, is introduced and implemented in the analysis of Stokes flow. The space, when properly constrained, is shown to be stable and to have at least optimal convergence rates in the velocity field and suboptimal convergence rates in the pressure field. However, results show that superoptimal convergence can often be expected in the pressure field, likely due to error reduction in the velocity field. Like other hierarchical spline spaces, these splines are shown to greatly increase accuracy and to drastically lower computation times for analyses on domains whose solution fields have singularities or could otherwise benefit from local refinement. With the advent of this adaptive, locally-refineable, high-fidelity technology, isogeometric methods can become more feasible for use in fluid analyses.
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Lins, Sidney de Oliveira. "Otimiza??o de forma aplicando B-splines sob crit?rio integral de tens?es." Universidade Federal do Rio Grande do Norte, 2009. http://repositorio.ufrn.br:8080/jspui/handle/123456789/15574.
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Previous issue date: 2009-02-09<br>Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior<br>This work proposes a computational methodology to solve problems of optimization in structural design. The application develops, implements and integrates methods for structural
analysis, geometric modeling, design sensitivity analysis and optimization. So, the optimum design problem is particularized for plane stress case, with the objective to minimize the structural mass subject to a stress criterion. Notice that, these constraints must be evaluated at a series of discrete points, whose distribution should be dense enough in order to minimize the chance of any significant constraint violation between specified points. Therefore, the local stress constraints are transformed into a global stress measure reducing the computational cost in deriving the optimal shape design. The problem is approximated by Finite Element Method
using Lagrangian triangular elements with six nodes, and use a automatic mesh generation with a mesh quality criterion of geometric element. The geometric modeling, i.e., the contour is defined by parametric curves of type B-splines, these curves hold suitable characteristics to implement the Shape Optimization Method, that uses the key points like design variables to determine the solution of minimum problem.
A reliable tool for design sensitivity analysis is a prerequisite for performing interactive structural design, synthesis and optimization. General expressions for design sensitivity analysis
are derived with respect to key points of B-splines. The method of design sensitivity analysis used is the adjoin approach and the analytical method. The formulation of the optimization problem applies the Augmented Lagrangian Method, which convert an optimization problem constrained problem in an unconstrained. The solution of the Augmented Lagrangian function is achieved by determining the analysis of sensitivity. Therefore, the optimization problem reduces to the solution of a sequence of problems with lateral limits constraints, which is solved by the Memoryless Quasi-Newton Method It is demonstrated by several examples that this new approach of analytical design sensitivity analysis of integrated shape design optimization with a global stress criterion purpose is computationally efficient<br>Neste trabalho prop?e-se uma metodologia computacional para resolver problemas de Otimiza??o de Forma para projeto estrutural. A aplica??o ? particularizada para problemas bidimensionais em estado plano de tens?es, de modo a minimizar a massa atendendo um crit?rio de tens?o. Para atender ao crit?rio param?trico de tens?es ? proposto um crit?rio global de tens?o de von Mises, dessa maneira, amplia-se o crit?rio local de tens?es sobre o dom?nio, visando ?
obten??o de programas mais seguros. O problema ? aproximado pelo M?todo dos Elementos Finitos utilizando elementos triangulares da base Lagrangiana padr?o com seis n?s, tendo uma estrat?gia de gera??o autom?tica de malhas baseada em um crit?rio geom?trico do elemento. O modelo geom?trico do contorno material ? definido por curvas param?tricas B-splines. Estas curvas possuem caracter?sticas vantajosas para implementa??o do processo de otimiza??o
de forma, que se utiliza dos pontos-chave para determinar o m?nimo do problema. A formula??o do problema de otimiza??o faz uso do M?todo Lagrangiano Aumentado, que transforma o problema de otimiza??o com restri??o, em problema irrestrito. A solu??o da fun??o Lagrangiana Aumentada ? alcan?ada pela determina??o da an?lise das sensibilidades anal?ticas em rela??o aos pontos-chave da curva B-spline. Como conseq??ncia, o problema de otimiza??o reduz-se ? solu??o de uma seq??ncia de problemas de limites laterais do tipo
caixa, o qual ? resolvido por um m?todo de proje??o de segunda ordem que usa o m?todo de Quase-Newton projetado sem mem?ria. S?o demonstrados v?rios exemplos para o M?todo de Otimiza??o de Forma integrado a
An?lise da Sensibilidade Anal?tica sob o crit?rio global de tens?o de von Mises
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Yilmaz, Oguz. "Detailed Fem Analysis Of Two Different Splice Steel Connections." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12609895/index.pdf.
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Beam splices are typically located at moment contraflexure points (where M=0). Most design specifications require these splices to develop a strength either to meet design forces or a minimum value set by specifications. The design forces are typically determined through elastic analysis, which does not include flexibility of splice connections. In this research, two types of splice connections, an extended end plate splice connection and a flange and web plate bolted splice connection, were tested and analyzed to investigate the effect of the partial strength splice connections on structural response. The splices were designed to resist 40% and 34% of connecting section capacities using current steel design codes, respectively. It has been observed from the experiments and FEM analysis results that splice connections designed under capacities of connecting steel members can result in changes in design moment diagrams obtained from analyses without splice connection simulation and can also significantly decrease the rigidity of the structure endangering serviceability. The differences in design moment diagrams can go up to 50 % of elastic analysis without connection flexibility. The vertical displacements can increase to 155% of values obtained from elastic analysis with no splice connection simulation. Therefore, connection flexibility becomes very important to define in analysis.
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Daryusi, Ali. "Beitrag zur Ermittlung der Kerbwirkung an Zahnwellen mit freiem und gebundenem Auslauf." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2009. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1240915811153-56748.
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Durch die zunehmende technologische Entwicklung des Getriebe-, Gelenkwellen-, Werkzeugmaschinen-, Kraftfahrzeug-, sowie Landmaschinenbaus steigen die zu übertragenden Leistungen und Drehmomente enorm. Dies führt zu einem wachsenden Bedarf an formschlüssigen Profilwellenverbindungen und deren erhöhter Lebensdauer und Genauigkeit. Hierbei bilden die Zahnwellenverbindungen (ZWVen) mit Evolventenflanken nach DIN 5480 /N1/ den Regelfall für eine Vielzahl der Anwendung. Abhängig von Festigkeitsüberlegungen, Herstellungsverfahren und Platzbedarf treten in der Praxis nahezu ausschließlich die folgenden zwei Grundtypen auf. Es handelt sich dabei zum Ersten um die Zahnwelle (ZW) mit freiem Auslauf.Die zweite Geometrievariante ist die Zahnwelle mit gebundenem Auslauf, die eine nach DIN 471 /N2/ genormte Sicherungsringnut (SRN) enthalten kann. Zahnwellenverbindungen dienen zur Übertragung großer, wechselnder und stoßartiger Drehmomente ohne zusätzliches Verbindungselement durch die Profilierung der Welle und Nabe. Axiale Verschiebbarkeit unter Last, Profilverschiebungsmöglichkeit, einfache Montage und Demontage sowie die Herstellung mit hochleistungsfähigen umformenden und spanenden Massenfertigungsverfahren, die die Herstellungskosten verhältnismäßig niedrig halten, sind technisch bedeutsame Eigenschaften, die zum ansteigenden Einsatz von ZWVen führen (z.B. /N1/, /Vil84/, /Koh86/ und /Wes96/). Starke Kerbwirkung und erhebliche Überdimensionierung benachbarter Gestaltungszonen sind die wesentlichen Schwachpunkte der Profilverbindungen. Eine große Anzahl (ca. 80 %) von Ausfällen im Maschinenbau ist auf Schäden an Achsen und Wellen infolge konstruktiv bedingter Kerben zurückzuführen (z.B. /N3/ und /Hai89/). Speziell im Bereich der hochbeanspruchten Profilwellen-Verbindungen kommt es auf Grund der starken Querschnittsveränderungen und der häufig angewandten Ausläufe und Formelemente, z. B. Zahn- und Keilwellen zu Kerbwirkungen, die erhebliche örtliche Spannungskonzentrationen sowohl im Zahnfußbereich und Zahnlückenauslauf als auch im Bereich der Verbindung selbst verursachen. Diese Beanspruchungskonzentrationen sind fast in der Hälfte aller Zahnwellenbrüche die häufigste Ursache für Dauerbrüche (Ermüdungs- bzw. Schwingungsbrüche) und für Schäden (bleibende Verformung, Anriss, Gewaltbruch) infolge Maximalbelastung. Hier trifft die Lastüberhöhung am Welle-Nabe-Verbindungsrand mit dem Steifigkeitssprung des Verzahnungsendes auf der Welle zusammen /Die93/. Die erwähnten Schadensfälle belegen, dass der heutige Kenntnisstand über eine beanspruchungsgerechte Auslegung von Zahnwellen noch recht lückenhaft ist. Deshalb sind neue Erkenntnisse über Form- bzw. Kerbwirkungszahlen bei Einzel- und Mehrfachkerben von scharf und weniger scharf gekerbten Zahnwellen mit Auslauf für eine treffsichere Festigkeitsberechnung erforderlich und stellen damit die Hauptschwerpunkte dieser Arbeit dar. Das vorliegende Forschungsprojekt, welches sich erstmals mit der Ermittlung der Beanspruchungen in torsions-, und biegebelasteten Zahnwellen mit freiem und gebundenem Auslauf befasst, wurde im Rahmen der Forschungsvereinigung für Antriebstechnik e.V. (FVA) unter der Nummer T 467 und dem Forschungsthema „ Ermittlung der Kerbwirkung bei Profilwellen für die praktische Getriebeberechnung von Zahnwellen“ initiiert und untersucht.
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Nicolai, Mike [Verfasser]. "Shape Optimization for Fluids Using T-Splines for Shape Representation and Stabilized Finite Elements for the Fluid Flow Simulations / Mike Nicolai." München : Verlag Dr. Hut, 2012. http://d-nb.info/1026652200/34.
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Bouclier, Robin. "Éléments finis isogéométriques massifs coque sans verrouillage pour des simulations en mécanique non linéaire des solides." Thesis, Lyon, INSA, 2014. http://www.theses.fr/2014ISAL0090/document.
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Avec l’arrivée de l’Analyse IsoGéométrique (IGA), le calcul de coque est devenu possible en utilisant la géométrie exacte pour des maillages grossiers. Pour cela, les polynômes de Lagrange sont remplacés pour l’interpolation par des fonctions NURBS (technologie la plus courante en conception assistée par ordinateur). De plus, ces fonctions possèdent une continuité supérieure ce qui offre une meilleure précision qu’un calcul éléments finis à nombre de degrés de liberté égal. L’IGA a déjà été développée pour les formulations coques. Elle n’a été cependant que très peu étudiée pour les modèles massifs coque. Pourtant, cette deuxième approche est très utilisée par l’ingénieur car elle permet de calculer des structures minces à l’aide d’éléments continus 3D, c’est-à-dire en faisant intervenir uniquement des inconnues en déplacements. La difficulté en calcul de coque est de faire face au verrouillage qui conduit à une forte dégradation de la convergence de la solution. Le cadre NURBS ne permet pas lui-même de résoudre ce problème. La meilleure efficacité de l’approximation NURBS ne peut donc être atteinte sans le développement de techniques particulières pour supprimer le verrouillage. C’est le but de cette thèse dans le cadre des éléments massifs coque. Le premier travail a consisté, sur un problème de poutre courbe, à étendre les méthodes sans verrouillage habituelles au contexte NURBS. Deux nouvelles stratégies ont alors été développées pour les NURBS : la première est basée sur une technique d’intégration réduite tandis que la seconde fait appel à une projection B-bar. Le formalisme général des méthodes B-bar semblant plus adapté, c’est celui-ci que nous avons développé ensuite pour les éléments massifs coque. Plus précisément, nous avons mis en place une formulation mixte de laquelle nous avons pu dériver la projection B-bar équivalente. Cette démarche constitue d’un point de vue théorique le résultat principal du travail : une méthode systématique pour construire une projection B-bar consistante est de passer par une formulation mixte. D’un point de vue mise en œuvre, l’idée principale pour traiter le verrouillage des éléments massifs coque a été de modifier l’interpolation de la moyenne dans l’épaisseur de la coque des composantes du tenseur des contraintes. Un contrôle de hourglass a aussi été ajouté pour stabiliser l’élément dans certaines situations. L’élément obtenu est de bonne qualité pour une interpolation de bas degrés et des maillages grossiers : la version quadratique semble plus précise que des éléments standards NURBS de degré 4. La méthode proposée conduit à une matrice de rigidité globale de petite taille mais pleine. Ce problème est inhérent aux NURBS. Il a pu être limité ici en utilisant une procédure de type moindres carrés locaux pour approcher la projection B-bar. Finalement, l’élément mixte a été étendu avec succès en non linéaire géométrique ce qui témoigne du potentiel de la méthode pour mener des simulations complexes<br>With the introduction of IsoGeometric Analysis (IGA), the calculation of shell has become possible using the exact geometry for coarse meshes. In order to that, Lagrange polynomials are replaced by NURBS functions, the most commonly used technology in Computer-Aided Design, to perform the analysis. In addition, NURBS functions have a higher order of continuity, which leads to higher per-degree-of-freedom accuracy of the shell solution than with classical Finite Elements Analysis (FEA). IGA has now been widely applied in shell formulations. Nevertheless, it has still rarely been studied in the context of solid-shell models. This second shell approach is, however, very useful for engineers, since it enables to calculate thin structures using 3D solid elements, i.e. involving only displacements as degrees of freedom. The difficulty in shell analysis is to deal with locking which highly deteriorates the convergence of the solution. The NURBS framework does not enable to solve the problem directly. Then, to really benefit from NURBS in shells, specific strategies need to be implemented to answer the locking issue. This is the goal of the thesis in the context of solid-shell elements. The first work has consisted, on a curved beam problem, in extending the locking-free methods usually encountered in FEA to the NURBS context. The study resulted in the development of two new strategies for NURBS: the first one is based on a selective reduced integration technique and the second one makes use of a B-bar projection. The global formalism offered by the B-bar method appearing more suitable for NURBS, it has then been investigated for solid-shell elements. More precisely, a mixed formulation has first been elaborated from which, it has been possible to derive the equivalent B-bar projection. From a theoretical point of view, this strategy constitutes the most important result of this work: a systematic method to construct a consistent B-bar projection is to write a mixed formulation. With regards to the implementation, the main idea to treat locking of the solid-shell elements has been to modify the average of the strain and stress components across the thickness of the shell. Hourglass control has also been added to stabilize the element in particular situations. The resulting element is of good quality for low order approximations and coarse meshes: the quadratic version seems to be more accurate than basic NURBS elements of order 4. The proposed method leads to a global stiffness matrix of small size but full. This problem is inherent to NURBS functions. It has been limited here by using a local least squares procedure to approach the B-bar projection. Finally, the mixed element has been successfully extended to geometric non-linearity which reflects the ability of the methodology to be used in complex simulations
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Perdão, Junior Paschoal. "Sobre a utilização de 'beta'-splines no metodo dos elementos finitos para a solução de barras, vigas e placas finas." [s.n.], 1999. http://repositorio.unicamp.br/jspui/handle/REPOSIP/264170.
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Orientador: Fernando Iguti<br>Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica<br>Made available in DSpace on 2018-07-31T15:21:15Z (GMT). No. of bitstreams: 1
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Previous issue date: 1999<br>Resumo: Este trabalho trata de expor detalhadamente, passo a passo, todos os requisitos necessários à utilização de B-splines como funções de forma, dentro do método dos elementos finitos, para aproximar a solução de estruturas de Barras, Vigas e Placas Finas. Característica à própria essência das B-splines, a suavidade, proporcionada pela continuidade 'C IND. 2¿ desses polinômios cúbicos, fornece todo um conceito de "robustez" a essas funções de aproximação, aumentando a precisão e a rapidez de convergência dos resultados obtidos. Uma etapa importante do presente trabalho é a introdução de nós auxiliares adicionais na definição das B-Splines próximas ao contorno das estruturas. Na formulação utilizada, o emprego de nós auxiliares, e a inclusão do quarto trecho polinomial de uma Spline cúbica nos elementos de extremidade vem a garantir a completude do espaço de aproximação. Estes nós auxiliares proporcionaram mais um grau de liberdade aos nós posicionados junto ao contorno da discretização. Este grau de liberdade adicional permite através de uma operação matricial a transformação das incógnitas do problema, de coeficientes das B-Splines para grandezas físicas, viabilizando a inclusão das condições de contorno físicas na formulação. Este procedimento é um avanço em relação às formulações reportadas na literatura, onde um "ajuste" nas B-Splines próximas ao contorno é realizado. Diversos exemplos numéricos, tanto em estruturas unidimensionais como em placas finas mostram a eficiência da formulação apresentada<br>Abstract: The present Thesis is a step by step formulation for the use of B-splines Functions in the Finite Element Method to approximate de solution of Bars, Beams and Thin Plates structures. The smooth character of the B-Splines given by the 'C IND. 2¿ continuity of these cubic polynomials provides a robust frame to the trial functions, increasing thus convergence and precision of the solutions. One important contribution of this work is the addition of auxiliary nodes in the definition of the B-Splines in the vicinity of the structure boundaries. These auxiliary nodes allow the inclusion of a fourth polynomial term in the interpolation of Spline elements close to the boundaries, which garantees the completness of the approximation spaces. The auxiliary spline nodes also permits the introduction of an extra physical degree of freedom at the boundaries of the structures. This additional degree of freedom, together with a coordinate transformation, allow the system equation to be written in terms of the physical boundary quantities. This procedure is an improvement, when compared to other formulations, which require a modification in the Spline functions near the boundaries, to account for the correct boundary conditions. Numerical examples for one- and two-dimensional structures show the efficiency and accuracy of the proposed methodologies<br>Doutorado<br>Mecanica dos Sólidos e Projeto Mecanico<br>Doutor em Engenharia Mecânica
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Engel, Dirk. "Hartree-Fock-Roothaan-Rechnungen für Vielelektronen-Atome in Neutronenstern-Magnetfeldern." [S.l. : s.n.], 2007. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-33864.
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Aquino, João José Redondo de. "Structural numerical simulation code development with isogeometric anakysis (IGA)." Master's thesis, Universidade de Aveiro, 2017. http://hdl.handle.net/10773/22375.
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Mestrado em Engenharia Mecânica<br>In the present day most product development industries uses the Finite Element Method (FEM) for structural analysis. Designers model the product geometries using Computer-Aided Design (CAD) software, the geometries are then fitted for analysis, by the analysts, with a mesh approximation that inevitably results in loss of accuracy. Achieving the best geometry description for complex components can be a complex task and it can take a lot of time. Considering this drawback, a new method was developed which takes advantages of curve representation tools and uses them as bases for analysis. Aiming for no loss of geometrical precision, this new method has been called "Isogeometric Analysis" (IGA).
The smoothness of Spline representations used in Isogeometric Analysis can be useful for a particular branch of structural analysis which is the analysis of plates and shells. The classic thin plate theory developed by Gustav Kirchhoff requires a geometry description with C1 continuity between elements which is normally defined by high order polynomial functions, which typically represents a problem with the piecewise Lagrangian shape functions used in conventional FEM. The present work explores parametric descriptions used as basis for Isogeometric
Analysis, such as Bézier curves, B-splines and NURBS, taking advantage of its smoothness to develop formulations for thin plate elements. The 4-node rectangular derived by Melosh, O. Zienkiewicz and Y. Chung called MCZ thin plate element based on Kirchhoff assumptions, was the starting point to build up to a NURBS-based thin plate element.
MCZ thin plate elements, NURBS-based thin plate elements (with different order geometries) and Abaqus commercial software shell elements are evaluated by means of classical plate benchmarks comparing the elements convergences and overall performance. It can be shown that the proposed NURBS-based formulation is reliable for the analysis of thin structures.<br>Nos dias de hoje a maioria da indústria de desenvolvimento do produto utiliza o Método dos Elementos Finitos (MEF) na análise estrutural. Os desenhistas modelam o produto através de ferramentas de Computer-Aided Design (CAD). As geometrias são depois ajustadas para a análise pelos analistas que constroem uma aproximação através de uma malha de elementos
finitos, o que inevitavelmente resulta numa perda de precisão geométrica. Para conseguir a melhor aproximação à geometria original para componentes complexos o processo pode ser complicado e pode consumir muito tempo. Considerando esta desvantagem foi desenvolvido um novo método que tira partido da descrição geométrica das ferramentas de desenho e utiliza as funções base das curvas para analise, com o objectivo de não haver perda de precisão geométrica, este novo método tem o nome de “Análise Isogeométrica” (IGA).
A suavidade das geometrias Splines usadas na análise isogeometrica pode ser muito útil num ramo particular da análise estrutural, no estudo das placas e cascas. A teoria clássica de análise de placas finas de Kirchhoff requer uma descrição geométrica que tenha continuidade C1 entre elementos, que é normalmente definida por polinómios de ordem elevada, que são
tipicamente um problema para as funções de forma Lagrangeanas usadas em MEF. O presente trabalho explora as descrições geométricas utilizadas como funções
de forma para a análise isogeométrica como as curvas de Bézier, as B-splines e as NURBS, tirando vantagem da facilidade de estas conseguirem a requerida continuidade entre elementos para criar elementos de placas finas com as funções de base NURBS como funções de forma. É utilizado o elemento de placa fina MCZ desenvolvido por Melosh, O. Zienkiewicz e
Y. Chung com base nas premissas de Kirchhoff como ponto de partida para desenvolver o elemento com base em NURBS. No fim os elementos de placas finas MCZ, os elementos com funções de base NURBS (com geometrias de diferentes ordens) e elementos do tipo casca do software comercial Abaqus são avaliados através de uma série de diferentes problemas clássicos de placas, comparando a convergência e o desempenho global. É possivel ver que a formulação proposta é fidedigna na análise de estruturas de placa fina.
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Santos, Daniel Barbedo Vasconcelos. "Modelagem numérica em elementos finitos de problemas de contato com atrito para material hiperelástico utilizando o método da superfície b-spline para a suavização da superfície de contato." Escola Politécnica, 2018. http://repositorio.ufba.br/ri/handle/ri/25294.
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Dissertacao Daniel Barbedo versao final corrigida.pdf: 1964343 bytes, checksum: 65c0f4da238b8e1285dc35e992eb7432 (MD5)<br>CAPES<br>Esta dissertação tem como objetivo apresentar um embasamento teórico sobre a formulação de problemas de contato mecânico com atrito para sólidos tridimensionais utilizando o método da superfície B-Spline para a suavização de superfície. Este é baseado na mecânica do contínuo.
Inicialmente é apresentada uma breve descrição dos tensores da mecânica do contínuo necessários à formulação, bem como as suas relações entre si. Parte-se então para a definição da formulação da mecânica dos sólidos utilizando a forma fraca, conhecida como o Princípio dos Trabalhos Virtuais, onde a equação de equilíbrio é obtida pela equação do balanço dos momentos, utilizando-se do modelo de equação de energia de um material Neo-Hookiano, com propriedades hiperelásticas. Descreve-se o processo de linearização das funções, necessário para a obtenção da matriz de rigidez em elementos finitos, e prossegue-se para a discretização em elementos finitos utilizando os elementos hexaédricos de oito nós.
Para a solução numérica do problema de contato (com e sem atrito) é apresentado o método do Lagrangiano Aumentado. Em seguida é apresentada a formulação para contato nó-superfície.
É importante mencionar que nas formulações padrões do contato mecânico, as superfícies de contato são discretizadas por elementos planos, o que resulta na descontinuidade do vetor normal entre as superfícies adjacentes. Neste tipo de abordagem, para que seja possível o deslizamento do nó escravo entre uma superfície mestre e outra adjacente, existe a necessidade de utilizar três tipos de formulações para o contato mecânico, i.e., contato nó-superfície, nó-seguimento e nó-nó. O objetivo desta dissertação é utilizar uma superfície curva e suave, criada a partir da superfície mestre original, que represente as superfícies de contato. Com isto, a direção da normal passa a ser contínua, sendo necessária apenas a formulação do contato com atrito nó-superfície. As superfícies de contato são suavizadas pela superfície B-Spline. Por este motivo, é apresentada a descrição do método da construção da superfície B-Spline para tornar a superfície de contato uma superfície única e suave, eliminando assim, a necessidade da formulação do contato nó-aresta e nó-nó.
Ao final do trabalho, são apresentados exemplos numéricos para evidenciar a eficiência e o desempenho da formulação proposta.<br>This dissertation has as objective to show theoretical background about contact mechanical problems with friction for tridimensional solids, using the B-Spline surface algorithm for surface smoothing. This is based on continuum mechanics.
At first, a short descrition of continuum mechanics is presented, as it is the basis for the posterior solid element and contact B-Spline formulation. In a second moment, the virtual work principle in its weak form is shown, where the equilibrium equation is obtained through the balance of momentum, utilizing the energy density equation of a Neo-Hookean hyperelastic material. Afterwards, the linearization process is presented, which is necessary for obtaining the finite element stiffness matrix and, finally, the finite element discretization for the 8 node hexaedrical element is shown.
At first a short description of continuum mechanics tensors necessary to the formulation is shown, as well as their relations between themselves. Then the definition for the weak form of solid mechanics, the virtual work principle is shown, where the equilibrium equation is obtained through the balance of momentum, utilizing the energy equation of a Neo-hookean material, with hiperelastic properties. The linearization process is presented, which is necessary for obtaining the finite element stiffness matrix, and then the finite element discretization for the 8 node hexaedrical element is shown.
Regarding the numerical solution for the contact problem (with and without friction), the Augmented Lagrangean method is presented. Afterwards, the formulation for node-surface contact is shown.
In the standard mechanical contact formulations, the contact surfaces are discretized by adjacent planes, resulting in discontinuity of the normal vector between adjacent surfaces. In the classical approach, to allow the sliding of a slave node over multiple master surfaces, three different contact mechanical formulations are needed, i.e., node-surfarce, node-segment and node-node contact. This work’s objective is to compose a curve and smooth surface to represent the master surface, utilizing the B-Spline surface algorithm. Achieving that, the normal vector direction is continuous, with only the node-surface contact formulation being necessary. The contact surfaces are discretized with a B-Spline surface, and for that reason, the B-Spline curve construction method is shown.
At the end of the work, numerical examples are shown to evidence the efficiency and performance of the proposed solution.
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Grover, Benjamin Todd. "Surfacing Splicing: A Method of Quadrilateral Mesh Generation and Modification for Surfaces by Dual Creation and Manipulation." BYU ScholarsArchive, 2002. https://scholarsarchive.byu.edu/etd/3457.
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The effective generation high quality quadrilateral surface meshes is an area of important research and development for the finite element community. Quadrilateral elements generally lead to more efficient and accurate finite results. In addition, some all hexahedral volume meshing algorithms are based on an initial quadrilateral mesh surface mesh that has specific connectivity requirements. This thesis presents a new and unique procedure named "Surfaced Splicing". Surface Splicing allows for the generation of all quadrilateral surface meshes as well as the ability to edit these meshes via the dual. The dual contains the same data as the mesh but, unlike the mesh, the dual directly allows the visualization of how surface and volume elements interrelate and connect with one another. The dual also provides mesh connectivity information that is crucial in forming an all-quadrilateral surface mesh that can form the basis of an all-hexahedral volume mesh.
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Ermer, Thomas. "Mappingstrategien für Kommunikatoren." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501073.
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Es werden Fragen der effektiven Kommunikation in parallelen FEM-Systemen behandelt. Durch geschickte Partitionierung des betrachteten Gebietes und Verteilung auf die vorhandenen Prozessoren kann man versuchen, die Kommunikationslast zu minimieren, z. B. mit dem Programmsystem chaco. Ein möglichst paralleler Datenaustausch wird durch Anordnung der Kommunikationsschritte in so genannten Linkleveln versucht. In der vorliegenden Arbeit wird ausgehend von der MPI-basierten Koppelrandkommunikation ein Split-Algorithmus vorgestellt, der versucht, die Koppelranddaten großer Kommunikatoren auf die kleinerer Sub-Kommunikatoren abzubilden und damit die Anzahl der zu übertragenden Datenpakete zu minimieren.
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Nguyen-Thanh, Nhon [Verfasser], Timon [Akademischer Betreuer] Rabczuk, Stephan [Gutachter] Bordas, and Klaus [Gutachter] Güerlebeck. "Isogeometric analysis based on rational splines over hierarchical T-mesh and alpha finite element method for structural analysis / Nhon Nguyen-Thanh ; Gutachter: Stephan Bordas, Klaus Güerlebeck ; Betreuer: Timon Rabczuk." Weimar : Professur Baustatik und Bauteilfestigkeit, 2013. http://d-nb.info/1117031594/34.
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Yang, Peiyu. "Experimental Techniques and Mechanical Behavior of T800/F3900 at Various Strain Rates." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1480601677646997.
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