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Least squares finite element methods for the Stokes and Navier-Stokes equations /Bochev, Pavel B. January 1994 (has links)
Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1994. / Vita. Abstract. Includes bibliographical references (leaves 155-158). Also available via the Internet.
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Higher order hierarchal curvilinear triangular vector elements for the finite element method in computational electromagneticsMarais, Neilen 03 1900 (has links)
Thesis (MScEng)--Stellenbosch University, 2003. / ENGLISH ABSTRACT: The Finite Element Method (FEM) as applied to Computational Electromagnetics
(CEM), can be used to solve a large class of Electromagnetics
problems with high accuracy, and good computational efficiency. Computational
efficiency can be improved by using element basis functions of higher
order. If, however, the chosen element type is not able to accurately discretise
the computational domain, the converse might be true. This paper
investigates the application of elements with curved sides, and higher order
basis functions, to computational domains with curved boundaries. It
is shown that these elements greatly improve the computational efficiency
of the FEM applied to such domains, as compared to using elements with
straight sides, and/or low order bases. / AFRIKAANSE OPSOMMING: Die Eindige Element Metode (EEM) kan breedvoerig op Numeriese Elektromagnetika
toegepas word, met uitstekende akkuraatheid en 'n hoë doeltreffendheids
vlak. Numeriese doeltreffendheid kan verbeter word deur van
hoër orde element basisfunksies gebruik te maak. Indien die element egter
nie die numeriese domein effektief kan diskretiseer nie, mag die omgekeerde
geld. Hierdie tesis ondersoek die toepassing van elemente met geboë sye,
en hoër orde basisfunksies, op numeriese domeine met geboë grense. Daar
word getoon dat sulke elemente 'n noemenswaardinge verbetering in die numeriese
doeltreffendheid van die EEM meebring, vergeleke met reguit- en/of
laer-orde elemente.
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Simulação numérica de escoamentos incompressíveis pelo método de elementos finitos com esquema de Separação Baseado na Característica (CBS)Octaviani, Cristiane Vitório [UNESP] 01 April 2013 (has links) (PDF)
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octaviani_cv_me_ilha.pdf: 1966568 bytes, checksum: f883f82b46613da6228b8b28a1809cfd (MD5) / A simulação computacional de escoamentos de fluidos ou dinâmica de fluidos computacional (CFD) tem se constituído cada vez mais em uma ferramenta muito útil no projeto de equipamentos nos quais este tipo de processo está presente. Diversas técnicas computacionais têm sido desenvolvidas para este fim. Entre estas técnicas, o método de elementos finitos (FEM) tem ganhado espaço na solução de problemas, principalmente em domínios complexos. O método clássico de elementos finitos também denominado de método de elementos finitos de Galerkin (GFEM) é ótimo para solução de problemas difusivos, entretanto, para o caso de problemas com convecção dominante como ocorre em muitos problemas de escoamentos de fluidos, o GFEM produz soluções oscilantes para altos números de Reynolds. Diversas técnicas têm sido associadas à discretização dos termos convectivos nas equações de Navier-Stokes para remediar a deficiência do GFEM. Uma destas técnicas é denominada na literatura de Chracteristic Based Split (CBS) e tem sido aplicada com sucesso para estabilização das soluções de problemas convectivos usando o GFEM. Neste trabalho, o GFEM associado ao esquema CBS será aplicado para simulação de casos de escoamentos bidimensionais / The computer simulation of fluid flow or computational fluid dynamics (CFD) has been constituted in an increasingly useful tool in the design of equipment where this type of process is present. Several computational techniques have been developed for this purpose. Among those techniques, the finite element method (FEM) has gained importance in solving problems, especially in complex domains. The classic method of finite elements also called Galerkin finite element method (GFEM) is optimal for solving diffusion problems, however, in case of problems with dominant convection as in many problems of fluid flow, the GFEM produces oscillating solutions for high Reynolds numbers. Several techniques have been associated with the discretization of the convective terms in the Navier-Stokes equations to remedy the deficiency of GFEM. One of those techniques is known in the literature as Chracteristic Based Split (CBS) and has been applied successfully to stabilize the GFEM when it is used to solve convective problems. In this work, the GFEM associated with CBS scheme is applied to simulation of two-dimensional flows
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Análise numérica e experimental de flambagem em cilindros de paredes finas / Numerical and experimental analysis of buckling in cylindrical shellsCampos, Eduardo Felipe de 15 August 2017 (has links)
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Previous issue date: 2017-08-15 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Estruturas de paredes finas são muito utilizadas na engenharia moderna devido sua boa relação entre peso e resistência. Sua aplicação vai desde obras civis, como cúpulas em edifícios e pontes, até estruturas aeronáuticas e equipamentos industriais. Uma geometria que é muito comum de ser encontrada nas estruturas de paredes finas são os cilindros, como pode ser observado no corpo dos aviões, tubulações e vasos de pressão. Submetidas a esforços compressivos, essas estruturas ficam suscetíveis ao fenômeno de instabilidade ou flambagem, podendo entrar em colapso repentinamente, mesmo antes de apresentar altas tensões. Assim, compreender o comportamento da instabilidade se torna crucial em um projeto de estruturas de paredes finas. Um dos fatores que influenciam no comportamento da instabilidade é a imperfeição geométrica da estrutura, e qualquer processo de fabricação possui erros associados ao processo. Para iniciar o estudo foi necessário medir os defeitos devido ao processo de fabricação do cilindro. Duas alternativas para realizar as medidas foram propostas, a primeira utilizando LVDTs, que medem a variação do raio do cilindro ao longo de toda sua extensão, e a segunda o fotoprocessamento. Ambos os métodos nos deram uma nuvem de pontos que foram processadas para obter a estrutura 3D CAD, possibilitando sua análise pelo método de elementos finitos e obtenção das respectivas cargas de flambagem numéricas. Além do método numérico foi realizado um ensaio experimental visando validar a análise numérica. O cilindro foi fechado com duas tampas e montado em uma bancada experimental, instrumentado com LVDTs, manômetro e por fim, uma bomba de vácuo foi ligada a uma das tampas. A bomba criou vácuo dentro do cilindro até o mesmo sofrer colapso. As cargas de flambagem numéricas foram superiores a encontrada experimentalmente em 14,48% a geometria foto, 11,72% da geometria LVDT e 39,98% a do cilindro referência. Os resultados mostram que as imperfeições geométricas são de grande relevância na resistência a instabilidade de uma estrutura, e também que grandes imperfeições geométricas tendem a ser o local onde ocorrem as ondas de flambagem. Em relação ao método de medição por fotoprocessamento os resultados mostram que é interessante estudar a técnica para aplicações na área de instabilidade. / Thin-walled structures are widely used in modern engineering because of their good weight-to-strength ratio. Its application ranges from civil works, such as domes in buildings and bridges, to aeronautical structures and industrial equipment. One geometry that is very common to be found in thin-walled structures is the cylinder, as can be seen in the body of airplanes, pipes and pressure vessels. Under compressive stresses, these structures are susceptible to the buckling phenomenon, which can suddenly collapse, even before presenting high stresses. Therefore, understanding the behavior of instability becomes crucial in designing thin-walled structures. One of the factors influencing the behavior of instability is the geometric imperfection of the structure, and any manufacturing process has errors associated with the process. To begin the study it was necessary to measure the defects due to the cylinder manufacturing process. Two alternatives to carry out the measurements were proposed, the first using LVDTs, which measure the variation of the cylinder radius along its length, and the second the photoprocessing. Both methods gave us a point cloud that were processed to obtain the 3D CAD structure, allowing its analysis by the finite element method and obtaining the respective numerical buckling loads. In addition to the numerical method, an experimental test was carried out to validate the numerical analysis. The cylinder was closed with two flat heads and mounted on an experimental bench, instrumented with LVDTs, manometer and finally, a vacuum pump was attached to one of the flat heads. The pump has created a vacuum inside the cylinder until it collapses. Numerical buckling loads were greater than that found experimentally at 14.48 % photo geometry, 11.72 % LVDT geometry and 39.98 % a reference cylinder. The results show that the geometric imperfections are of great relevance in the resistance to buckling of a structure, and also that great geometric imperfections tend to be the place where the buckling waves occur. Regarding the method of measurement by photoprocessing the results show that it is interesting to study the technique for applications in the area of instability. / CAPES: 1544963
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A mathematical explanation of the transition between laminar and turbulent flow in Newtonian fluids, using the Lie groups and finite element methodsGoufo, Emile Franc Doungmo 31 August 2007 (has links)
In this scientific work, we use two effective methods : Lie groups theory and the finite
element method, to explain why the transition from laminar flow to turbulence flow
depends on the variation of the Reynolds number. We restrict ourselves to the case
of incompressible viscous Newtonian fluid flows. Their governing equations, i.e. the
continuity and Navier-Stokes equations are established and investigated. Their solutions
are expressed explicitly thanks to Lie's theory. The stability theory, which leads to an
eigenvalue problem is used together with the finite element method, showing a way to
compute the critical Reynolds number, for which the transition to turbulence occurs.
The stationary flow is also studied and a finite element method, the Newton method, is
used to prove the stability of its convergence, which is guaranteed for small variations of
the Reynolds number. / Mathematical Sciences / M.Sc. (Applied Mathematics)
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Design Analysis and Optimization of Front Underrun Protection DeviceSharma, Anil January 2018 (has links)
Under-running of passenger vehicle is one of the major parameters to be considered during the design and development of truck chassis. Front Under-run Protection Device (FUPD) plays an important role in avoiding under-running of vehicles from front side of a truck. This thesis is used to develop additional device which stops the impact from frontal area, which will not allow the passenger car inside the truck. The complete thesis was started from an idea of adding FUPD to truck chassis. Design of FUPD is done using 3D CAD software CATIA V5R20, then complete FUPD assembly is imported and done pre-processing using Altair Hyper Mesh, for visualizing the results. Crash analysis is done using Altair Radioss & results interpretation is done using HyperView and Hypergraph. FUPD is designed based on ECE R93 which satisfies the failure criteria (Standard) of displacement less than 400 mm. An Initial Design is generated along with Holding Brackets as an assembly using CATIA V5 as a tool. Base design is further optimized for getting light weight structure that meets structural performance criteria. By assuming all the loading conditions as per the standards, an amount of 27% mass reduction is obtained in FUPD Assembly along with holding bracket.
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Avaliação das propriedades nanomecânicas e do comportamento micromecânico da interface dentina/adesivo antes e após a degradação hidrolítica: análises através de nanoindentação e método dos elementos finitos tridimensionalAnchieta, Rodolfo Bruniera [UNESP] 13 September 2013 (has links) (PDF)
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000749616.pdf: 1874201 bytes, checksum: f55031c6690632c4ddc7fb5d5819e1ac (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / OBJETIVO: Avaliar a morfologia, a nanoinfiltração, o módulo de elasticidade e o comportamento micromecânico da interface dentina-adesivo (d-a) de espécimes submetidos à degradação, 24 horas após os procedimentos restauradores (T0), e 12 meses após armazenamento em solução de Hanks (T1). MATERIAL E MÉTODO: Cinco sistemas adesivos foram utilizados: SBMU – ScotchBond Multi-Uso; CSEB – Clearfil SE Bond; OUB – One-Up-Bond F; AEO – Adper Easy One; P90 – Adesivo autocondicionante P90. Cinquenta e dois terceiros molares humanos hígidos foram utilizados, 10 para cada grupo (n=10). Dois dentes foram utilizados para a análise da dentina. A espessura da CH e do adesivo, e o comprimentos dos tags foram mensurados no microscópio eletrônico de varredura (MEV). A nanoinfiltração na interface d-a foi avaliada em T0 e T1 através do MEV. Quinze indentações foram feitas em cada estrutura da interface d-a para cada tempo de análise, para se obter o módulo de elasticidade. Cinco modelos de um espécime em dentina, restaurado com resina composta (41x41x82 ?m), com dimensões e módulo de elasticidade baseados nos testes laboratorais, foram elaborados utilizando o programa SolidWorks 2010, representando os grupos em uma situação de união ideal, e para os 2 tempos de análise (T0 e T1). Utilizou-se o programa de elementos finitos foi utilizado (AnsysWorkbench 14.0) para obtenção da tensão máxima principal. O teste Anova e post-hoc Teste-T, empregando-se modelos lineares mistos foram usados para verificar a diferença estatística no teste de nanoinfiltração e nanoindentação. O teste de Anova e HolmSidak foi utilizado para análise das dimensões. RESULTADOS: A CH mais espessa e os tags mais longos ocorreram para o SBMU (p<0,05). Houve redução... / OBJECTIVE: To evaluate the morphology, nanoleakage, elastic modulus and micromechanical behavior of dentin-adhesive (d-a) interface of specimens subjected to degradation, 24 hours after restorative procedures (T0) and 12 months after storage in Hanks' solution (T1). MATERIAL AND METHODS: Five adhesive systems were used (5 groups): SBMP – Scotchbond Multi-Purpose; CSEB – Clearfil SE Bond; OUB – One-Up Bond F-; AEO – Adper Easy One; P90 – Self-etching adhesive P90. Fifty two human sound third molars were used, 10 teeth for each group (n=10). The other two teeth were used to analysis the dentin morphology. At least 4 fragments of d-a interface (specimens) were obtained in mesio-distal direction from each tooth. Fifteen indentations were done for each structure in each time of analysis. Five models of dentin restored with composite resin (41x41x82 mm) were built using the software SolidWorks 2010, representing the groups analyzed in the laboratory tests in an ideal scenario. Other two models per group were built simulating the two times of analysis (T0 and T1). The dimensions and mechanical properties of the models followed the data obtained in the laboratory tests. The numerical analysis was performed using the finite element (AnsysWorkbench 14.0) to obtain the maximum principal stress. Two-way Anova linear mixed models and post-hoc T-test were used to determine the statistical significance from nanoindentation and nanoleakage tests. The test One-way ANOVA and HolmSidak (p <0.05) were used for analysis of the SEM measurements. RESULTS: The thickest hybrid layer and bigger tags were found for SBMU (p<0.05). There were decrease in elastic modulus for HL and dentin for all groups (p<0.05). There were no decrease in elastic modulus on adhesive layer for SBMU and P90 (p>0.05). There increase of nanoleakage between T0... / FAPESP: 10/12926-7 / FAPESP: 12/07012-17
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Application of the discrete element method for concrete fracturingTang, Lingwei January 2013 (has links)
This project focuses on discrete element modelling of fracturing of concrete material at meso-scale, and particularly on calibration of the particle assembly parameters to reproduce phenomenological properties of concrete, and on applying the discrete element method to analyze the failure mechanisms in a three-point bending test and debonding between the FRP sheet and the concrete. The particle flow code PFC2D and PFC3D are employed to carry out the parametric study but only PFC2D is used in the case studies. The calibration of properties of the numerical samples is conducted to determine the effects of the particle level input parameters on the elastic constants, the uniaxial compressive strengths and failure mode of particle assembly. The input parameters are divided into two groups, model constitutive parameters (e.g., particle and bond stiffness, bond shear and normal strengths and friction coefficient) and geometric and physical parameters (e.g., particle and specimen size, particle distribution and loading velocity.). The analysis is constructed using dimensional analysis and numerical uniaxial tests. A random aggregate generation algorithm is incorporated in the DEM code to reproduce the aggregate structure in real concrete material. The aggregate generation algorithm utilizes polygon and polyhedron as the basic shapes of aggregate and is capable of producing multi-graded concrete specimens with aggregate content up to 80% and 60% for two-dimensional and three-dimensional samples respectively. The mode I fracture behavior of three-phased concrete is then simulated by performing a virtual three-point bending test. The mortar matrix phase is simulated with the linear elastic-pure-brittle and softening bond model to ensure a fair comparison. The dynamic debonding process between the FRP sheet and the concrete is simulated with a particle assembly by a regular hexagonal packing arrangement where the heterogeneity of concrete is taken into account by incorporating the Weibull distribution. Based on the analysis of the modelling results, it is conclude that the fracture behavior of concrete can be satisfactorily captured by meso-scale DEM model and comprehensive parameter study allows more confidently implementation of particle flow code.
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Numerical modelling and optimization of new RHS column-to-I beam connectionsWu, Jian January 2013 (has links)
No description available.
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Parallelisation of micromagnetic simulationsNagy, Lesleis January 2016 (has links)
The field of paleomagnetism attempts to understand in detail the the processes of the Earth by studying naturally occurring magnetic samples. These samples are quite unlike those fabricated in the laboratory. They have irregular shapes; they have been squeezed and stretched, heated and cooled and subjected to oxidation. However micromagnetic modelling allows us to simulate such samples and gain some understanding of how a paleomagnetic signal is acquired and how it is retained. Micromagnetics provides a theory for understanding how the domain structure of a magnetic sample alters subject to what it is made from and the environment that it is in. It furnishes the mathematics that describe the energy of a given domain structure and how that domain structure evolves in time. Combining micromagnetics and ever increasing computer power, it has been possible to produce simulations of small to medium size grains within the so-called single to pseudo single domain state range. However processors are no longer built with increasing speed but with increasing parallelism and it is this that must be exploited to model larger and larger paleomagnetic samples. The purpose of the work presented here is twofold. Firstly a micromagnetics code that is parallel and scalable is presented. This code is based on FEniCS, an existing finite element framework, and is shown to run on ARCHER the UK’s national supercomputing service. The strategy of using existing libraries and frameworks allow future extension and inclusion of new science in the code base. In order to achieve scalability, a spatial mapping technique is used to calculate the demagnetising field - the most computationally intensive part of micromagnetic calculations. This allows grain geometries to be partitioned in such a way that no global communication is required between parallel processes - the source of favourable scaling behaviour. The second part of the theses presents an exploration of domain state evolution in increasing sizes of magnetite grains. This simulation, whilst a first approximation that excludes magneto-elastic effects, is the first attempt to map out the transition from pseudo-single domain states to multi domain states using a full micromagnetic simulation.
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