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Dissertations / Theses on the topic 'Quadrilateral'
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Mitchell, Robert Daniel. "The Wesleyan Quadrilateral relocating the conversation /." 24-page ProQuest preview, 2007. http://proquest.umi.com/pqdweb?index=0&did=1367834161&SrchMode=1&sid=5&Fmt=14&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1220041911&clientId=10355.
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Dewey, Mark William. "Automated Quadrilateral Coarsening by Ring Collapse." Diss., CLICK HERE for online access, 2008. http://contentdm.lib.byu.edu/ETD/image/etd2332.pdf.
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Iannaccone, Andrew. "The Conformal Center of a Triangle or Quadrilateral." Scholarship @ Claremont, 2003. https://scholarship.claremont.edu/hmc_theses/149.
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Every triangle has a unique point, called the conformal center, from which a random (Brownian motion) path is equally likely to first exit the triangle through each of its three sides. We use concepts from complex analysis, including harmonic measure and the Schwarz-Christoffel map, to locate this point. We could not obtain an elementary closed form expression for the conformal center, but we show some series expressions for its coordinates. These expressions yield some new hypergeometric series identities. Using Maple in conjunction with a homemade Java program, we numerically evaluated these series expressions and compared the conformal center to the known geometric triangle centers. Although the conformal center does not exactly coincide with any of these other centers, it appears to always lie very close to the Second Morley point. We empirically quantify the distance between these points in two different ways. In addition to triangles, certain other special polygons and circles also have conformal centers. We discuss how to determine whether such a center exists, and where it will be found.
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Saliba, H. T. "Free vibration analysis of non-rectangular quadrilateral plates." Thesis, University of Ottawa (Canada), 1986. http://hdl.handle.net/10393/5264.
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Chung, Hing-yip Ronald, and 鍾興業. "A quadrilateral-based method for object segmentation and tracking." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B31244129.
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Anderson, Bret Dallas. "Automated all-quadrilateral mesh adaptation through refinement and coarsening /." Diss., CLICK HERE for online access, 2009. http://contentdm.lib.byu.edu/ETD/image/etd2948.pdf.
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Anderson, Bret D. "Automated All-Quadrilateral Mesh Adaptation through Refinement and Coarsening." BYU ScholarsArchive, 2009. https://scholarsarchive.byu.edu/etd/1735.
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This thesis presents a new approach to conformal all-quadrilateral mesh adaptation. In finite element modeling applications, it is often desirable to modify the node density of the mesh; increasing the density in some parts of the mesh to provide more accurate results, while decreasing the density in other parts to reduce computation time. The desired node density is typically determined by a sizing function based on either the geometry of the model or the results of a finite element solution. Although there are numerous mesh adaptation methods currently in use, including initial adaptive mesh generation, node redistribution, and adaptive mesh refinement, there are relatively few methods that modify the mesh density by adding and removing mesh elements, and none of these guarantee a conformal, all-quadrilateral mesh while allowing general coarsening. This work introduces a new method that incorporates both conformal refinement and coarsening strategies on an existing mesh of any density or configuration. Given a sizing function, this method modifies the mesh by combining existing template based quadrilateral refinement methods with recent developments in localized quadrilateral coarsening and quality improvement into an automated mesh adaptation routine.
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FIGUEIREDO, ALICE HERRERA DE. "DIRECTIONALITY FIELDS IN GENERATION AND EVALUATION OF QUADRILATERAL MESHES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=32302@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE EXCELENCIA ACADEMICA
Um dos principais desafios para a geração de malhas de quadriláteros é garantir o alinhamento dos elementos em relação às restrições do domínio. Malhas não alinhadas introduzem problemas numéricos em simulações que usam essas malhas como subdivisão do domínio. No entanto, não existe uma métrica de alinhamento para a avaliação de qualidade de malhas de quadriláteros. Um campo de direcionalidade representa a difusão das orientações das restrições no interior do domínio. Kowalski et al. usam um campo de direcionalidade para particionar o domínio em regiões quadrilaterais. Neste trabalho, reproduzimos o método de particionamento proposto por Kowalski et al. com algumas alterações, visando reduzir o número final de partições. Em seguida, propomos uma métrica para avaliar a qualidade de malhas de quadriláteros em relação ao alinhamento com as restrições do domínio.
One of the main challenges in quadrilateral mesh generation is to ensure the alignment of the elements with respect to domain constraints. Unaligned meshes insert numerical problems in simulations that use these meshes as a domain discretization. However, there is no alignment metric for evaluating the quality of quadrilateral meshes. A directionality field represents the diffusion of the constraints orientation to the interior of the domain. Kowalski et al. use a directionality field for domain partitioning into quadrilateral regions. In this work, we reproduce their partitioning method with some modifications, aiming to reduce the final number of partitions. We also propose a metric to evaluate the quality of a quadrilateral mesh with respect to the alignment with domain constraints.
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Huyton, Paul. "Stability of quadrilateral plates and panels for aerospace design." Thesis, University of Edinburgh, 2002. http://hdl.handle.net/1842/14136.
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This thesis presents new knowledge in the area of plate buckling, which has use in practical applications in the design of aircraft structures, such as wing or fuselage panels and thin-walled civil engineering structures. The focus of the research is on plates that are skew (parallelogram) in planform and the buckling strength gains that arise because of a stiffening effect caused by the acute angle of the plate and the fixity along the plate edges that continuity of adjacent skew plates imposes. A finite element code, ABAQUS, is adopted to compare the buckling strength of plates that are continuous over an infinite number of bays with isolated (non-continuous) plates that have varying magnitudes of rotational restraint applied along the edges. The continuous results, obtained from VICONOPT, are available in the open literature. The results are presented in the form of unique and comprehensive buckling curves. The continuous VICONOPT solutions are verified using a finite element model and the validity of the assumptions used to obtain the VICONOPT results is assessed. The work on skew plates is extended to assemblies of plates that form skew panels of the type typically used in aerospace applications. Buckling calculations are presented for varying magnitudes of orthotropy and skew angles. Analysis of the panel is compared with a plate having the equivalent orthotropic properties and the results compared to closed-form solutions for equivalent rectangular plates. Because modern aircraft wing are generally ‘swept-back’ and tapered along their length, the resulting plates that make up the panels are not only skew but also tapered in planform. The effect of this taper together with skew is considered and the buckling strength changes that arise because of the stiffening effect of the planform taper assessed. Finally, panels taken from an optimised benchmark wing, are assessed for buckling to ascertain the effect of making simplifying assumptions about the planform geometry of the panels and the consequences of these assumptions on the panel buckling strength.
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Gheralde, André Luiz Junqueira. "Aplicação de relés adaptativos na proteção digital à distância." Universidade de São Paulo, 1996. http://www.teses.usp.br/teses/disponiveis/18/18133/tde-25012018-121313/.
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O objetivo deste trabalho é o desenvolvimento de \"software\" para proteção digital das linhas de transmissão. Com esse propósito são implementados relés de distância com características quadrilaterais e adaptativas. Um \"software\" básico para este fim consiste de várias etapas como: detecção da falta, filtragem digital, classificação da falta, cálculo da impedância aparente e verificação das zonas de proteção. Na etapa de filtragem digital das ondas, é utilizada a Transformada Discreta de Fourier (TDF) para a extração dos componentes fundamentais de tensão e corrente. A característica quadrilateral mostra-se eficiente para determinadas condições de operação fixas do sistema, mas seu desempenho é comprometido quando ocorrem mudanças das mesmas. Para solucionar este problema, é introduzida a teoria de relés adaptativos onde a característica de abertura do relé digital muda com as alterações nas condições de operação do sistema, mantendo-se assim a eficiência da proteção.The objective of this work is the development of a software for digital protection of transmission lines. For this purpose relays of distance with Quadrilateral and Adaptive characteristics are implemented. A basic software with this aim consists of several steps such as: detection of the fault, digital filtering of the faulted waves, classification of the fault, impedance calculation and verification of the protection zones. For the digital filtering purpose, the Fourier Discret Transform, is used in order to extract the fundamental phasors of voltages and currents. Quadrilateral characteristcs are shown to be effective under certain operation conditions of the system, but its performance is not so efficient when those conditions are changed. In order to solve these problems, the theory of adaptive relays was introduced whereby the characteristic of digital relay changes according to the alterations in the conditions of the system operation, and by these means the protection is kept efficient.
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Bommes, David [Verfasser]. "Quadrilateral surface mesh generation for animation and simulation / David Bommes." Aachen : Shaker, 2013. http://d-nb.info/1030248672/34.
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Chen, Zhuo. "A split-and-merge approach for quadrilateral-based image segmentation." Click to view the E-thesis via HKUTO, 2006. http://sunzi.lib.hku.hk/hkuto/record/B38749440.
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Chen, Zhuo, and 陳卓. "A split-and-merge approach for quadrilateral-based image segmentation." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B38749440.
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Cass, Roger. "A General Three Dimensional All Quadrilateral Surface Mesh Generation Algorithm." BYU ScholarsArchive, 1992. https://scholarsarchive.byu.edu/etd/3459.
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Among the available all-quadrilateral mesh generation algorithms progressive-front offers the best quality and robustness. The paving algorithm is a progressive-front technique that generates a two dimensional mesh of all quadrilaterals on planar surfaces. The technique is particularly suited to meshing irregular boundaries with interior holes. This thesis presents an extension of the paving algorithm to generalized three dimensional surfaces. The major problems in three-dimensional surface mesh generation are projection of nodes, calculation of interior angles, and connection of mesh fronts. The solutions to these problems are presented. This work is part of the ongoing CUBIT project at Sandia Labs. The application is written in object oriented style in C++. A description of object oriented programming is given, with the relative merits and drawbacks for engineering applications.
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Lindquist, Dana Rae. "A comparison of numerical schemes on triangular and quadrilateral meshes." Thesis, Massachusetts Institute of Technology, 1988. http://hdl.handle.net/1721.1/14571.
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Hendriana, Dena. "A parabolic quadrilateral finite element for compressible and incompressible flows." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/50060.
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Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1998.Includes bibliographical references (leaves 156-161).
A unified finite element solution scheme for incompressible and compressible flows would be most attractive in engineering practice. The objective in this thesis was to work toward this goal. A 9-node finite element for compressible and incompressible 2-D flow solutions is presented. In the compressible flow formulation, a new high-order derivative artificial diffusion and a new shock capturing term are employed to stabilize the formulation. The new upwinding term is shown numerically to stabilize the formulation and an inf-sup test is performed assuming idealized 1-D conditions. The new shock capturing term performed well in the solutions of various judiciously selected numerical examples. Various flow problems in which the Mach numbers range from about 0.0005 to 6 are considered. The numerical results indicate that the element is applicable to a wide range of analysis problems. For incompressible flows, the element must satisfy the relevant inf-sup condition, and an element is used with parabolic velocity and linear pressure interpolations (the 9/4c-element). An upwinding term in a similar form as for the compressible flow solution is introduced to stabilize the formulation. A convergence study with the formulation to estimate the order of convergence is performed. In addition, a new low order element is presented. The new solution schemes for compressible and incompressible flows provide effective solution techniques and the study provides insight into the difficulties encountered in the development of a unified scheme for incompressible and compressible flows.
by Dena Hendriana.
Sc.D.
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Butzu, David Alan. "Sources for theological exploration a quadrilateral approach to elementary biblical education /." Online full text .pdf document, available to Fuller patrons only, 2000. http://www.tren.com.
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Sobrinho, Antonio da Silva Castro. "On the generation of quadrilateral element meshes for general CAD surfaces." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/38177.
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Kowalski, Nicolas. "Domain partitioning using frame fields : applications to quadrilateral and hexahedral meshing." Paris 6, 2013. http://www.theses.fr/2013PA066689.
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In this work, we describe a method to partition domains adapted to the generation of quadrilateral and hexahedral meshes. Given a domain D, the proposed approach proceeds in two steps: first, a frame field is defined on a background simplicial mesh of D. Then, singular elements of this field are extracted to create a skeleton that partitions D. The key element of this approach is the use of frames: at a point P of D, a frame allows to orient the quadrilateral or the hexahedral. Thus, we propose a complete study of frames and frame fields. We describe the proposed method both in dimension two and three. The main difference between the two is in the way frame fields are generated. In dimension 2, we solve a non-linear PDE, while in 2D, a heuristic is applied that uses initiallu an advancing front algorithm that takes the stability of the field into account, before using a smoothing algorithm. In both cases, a skeleton is extracted from the frame field. In dimension two, this skeleton always leads to a partition of D into quadrilateral-shaped blocks, and singularities are all of degree three and five. In dimension three, the obtained frame field leads to a partition allowing for hexahedral meshing in numerous cases. Many examples are showcased and compared to results obtained by existing methodsDans ce travail, nous décrivons une méthode de partitionnement de domaines 2D et 3D adaptée à la génération de maillages quadrangulaires et héxahédriques. Etant donné un domaine D, l'approche proposée se décompose en deux étapes: tout d'abord, un champ d'orientations est défini sur un maillage simplicial approximant D. Puis, les éléments singuliers de ce champs sont extraits pour former un squelette qui partitionne D. L'élément clé de cette approche est l'utilisation d'orientations : en un point P de D, une orientation permet d'orienter le quadrilatère ou l'héxahèdre. De ce fait, nous proposons une étude complète des orientations et des champs d'orientations. Nous décrivons ensuite la méthode proposée aussi bien en dimension deux que trois. La différence majeure entre ces deux versions réside dans la génération du champ d'orientations. En dimension 2, nous nous basons sur la résolution d'une EDP non linéaire. En dimension 3, une heuristique est appliquée en utilisant un algorithme par avancée de front tenant compte de la stabilité du champ généré suivi d'un algorithme de lissage. Dans les deux cas, un squelette est extrait du champ d'orientations. En dimension deux, ce squelette fournit toujours un partitionnement de D en blocs quadrangulaires et les singularités obtenues sont de valence trois et cinq uniquement. En dimension trois, le champ d'orientations obtenu permet un partitionnement adéquat pour de nombreuses configurations. De nombreux exemples sont présentés et comparés aux résultats obtenus par des méthodes existantes
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Campen, Marcel [Verfasser]. "Quad Layouts : Generation and Optimization of Conforming Quadrilateral Surface Partitions / Marcel Campen." Aachen : Shaker, 2015. http://d-nb.info/1067735380/34.
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Chen, Pu. "The quadrilateral relation and line tension measurements in liquid-liquid-fluid systems." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0004/NQ41415.pdf.
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Apel, Th. "A note on anisotropic interpolation error estimates for isoparametric quadrilateral finite elements." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801071.
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Anisotropic local interpolation error estimates are derived for quadrilateral and hexahedral Lagrangian finite elements with straight edges. These elements are allowed to have diameters with different asymptotic behaviour in different space directions.
The case of affine elements (parallelepipeds) with arbitrarily high degree of the shape functions is considered first. Then, a careful examination of the multi-linear map leads to estimates for certain classes of more general, isoparametric elements.
As an application, the Galerkin finite element method for a reaction diffusion problem in a polygonal domain is considered. The boundary layers are resolved using anisotropic trapezoidal elements.
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POCHET, AXELLE DANY JULIETTE. "MODELING OF GEOBODIES: AI FOR SEISMIC FAULT DETECTION AND ALL-QUADRILATERAL MESH GENERATION." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2018. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=35861@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE EXCELENCIA ACADEMICA
A exploração segura de reservatórios de petróleo necessita uma boa modelagem numérica dos objetos geológicos da sub superfície, que inclui entre outras etapas: interpretação sísmica e geração de malha. Esta tese apresenta um estudo nessas duas áreas. O primeiro estudo é uma contribuição para interpretação de dados sísmicos, que se baseia na detecção automática de falhas sísmicas usando redes neurais profundas. Em particular, usamos Redes Neurais Convolucionais (RNCs) diretamente sobre mapas de amplitude sísmica, com a particularidade de usar dados sintéticos para treinar a rede com o objetivo final de classificar dados reais. Num segundo estudo, propomos um novo algoritmo para geração de malhas bidimensionais de quadrilaterais para estudos geomecânicos, baseado numa abordagem inovadora do método de quadtree: definimos novos padrões de subdivisão para adaptar a malha de maneira eficiente a qualquer geometria de entrada. As malhas obtidas podem ser usadas para simulações com o Método de Elementos Finitos (MEF).
Safe oil exploration requires good numerical modeling of the subsurface geobodies, which includes among other steps: seismic interpretation and mesh generation. This thesis presents a study in these two areas. The first study is a contribution to data interpretation, examining the possibilities of automatic seismic fault detection using deep learning methods. In particular, we use Convolutional Neural Networks (CNNs) on seismic amplitude maps, with the particularity to use synthetic data for training with the goal to classify real data. In the second study, we propose a new two-dimensional all-quadrilateral meshing algorithm for geomechanical domains, based on an innovative quadtree approach: we define new subdivision patterns to efficiently adapt the mesh to any input geometry. The resulting mesh is suited for Finite Element Method (FEM) simulations.
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Wang, Sili. "An ABAQUS Implementation of the Cell-based Smoothed Finite Element Method Using Quadrilateral Elements." University of Cincinnati / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1416233762.
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Campen, Marcel Verfasser], Leif [Akademischer Betreuer] [Kobbelt, and Denis [Akademischer Betreuer] Zorin. "Quad Layouts – Generation and Optimization of Conforming Quadrilateral Surface Partitions / Marcel Campen ; Leif Kobbelt, Denis Zorin." Aachen : Universitätsbibliothek der RWTH Aachen, 2015. http://d-nb.info/1127739719/34.
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Okamoto, Yuki. "Comparison of the pressure distribution at the stump-socket interface of ischial containment & quadrilateral sockets." Thesis, University of Strathclyde, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.502336.
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The quadrilateral (Quad) socket has been the socket of choice for the transfemoral since the 1950s. It was developed as a result of extensive research work undertaken at the University of California, Berkely and San Francisco at the request of the veterans administration (VA) in USA following the 2nd world war. However, these sockets were mainly designed for maimed but otherwise young and fit amputees, and there arose a doubt regarding whether they are also appropriate to be provided to the aged geriatric amputees which consists most of the today's amputee population. Since the 1970s researchers started to point out the weaknesses of the Quad socket and advocated a newer type of socket which has a bone-locking system by containing the amputee's ischial ramas inside to socket when being worn. This type of socket is called Ischial-ramal containing (IC) socket and there have been many comments heard from researchers and amputees in favour of this newer type of socket This project was designed to provide back up to the possible explanation for these voices to introduce this new type of socket to be more widely available. We looked at the interface pressure distributed of Quad and IC socket for comparison as an index for the comfort level of the amputees wearing those two sockets.
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Hall, Michael G. "Biomechanical and energy analysis of the ischial containment and quadrilateral sockets for the trans femoral amputee." Thesis, University of Strathclyde, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.248527.
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Fonseka, Merrenege Chinthaka Manoranjan. "Combined ring element/quadrilateral element method for the analysis of shells of revolution with geometric imperfections." Thesis, University of Southampton, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.256264.
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Miyagi, Takashi. "The Changing Security Dynamics in the Indo-Pacific: The Re-Emergence of the Quadrilateral Security Dialogue." Thesis, Malmö universitet, Fakulteten för kultur och samhälle (KS), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-23738.
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The recent development of the Indo-Pacific region is characterised by the changing balance of power and the emergences of new forms of security cooperation. The Quadrilateral Security Dialogue (QSD) between Japan, the United States (U.S.), Australia and India came back into existence in 2017 after their failed attempt in 2007-2008. This thesis attempts to investigate what factors explain the re-emergence of the QSD by synthesising several alignment/alliance theories in International Relations (IR). Given the previous research on the QSD and theoretical discussions, this thesis points out the two key factors that contributed to the re-emergence of the QSD: the shared threat perception towards China and the shared objectives in the Indo-Pacific region. The content analysis of a number of official policy documents and press statements revealed that Japan, the U.S., Australia and India have increasingly perceived China as a threat and coordinated their policy objectives in the Indo-Pacific region under the concept of the Free and Open-Indo Pacific.
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Campen, Marcel [Verfasser], Leif [Akademischer Betreuer] Kobbelt, and Denis [Akademischer Betreuer] Zorin. "Quad Layouts – Generation and Optimization of Conforming Quadrilateral Surface Partitions / Marcel Campen ; Leif Kobbelt, Denis Zorin." Aachen : Universitätsbibliothek der RWTH Aachen, 2015. http://nbn-resolving.de/urn:nbn:de:hbz:82-rwth-2015-014538.
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Aziz, Omer Carleton University Dissertation Engineering Civil. "A mechanism free plane quadrilateral element with rotational degrees of freedom and the associated facet shell element." Ottawa, 1988.
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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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Paschoalini, Amarildo Tabone. "Um elemento finito quadrilateral quadratico com refinamento hierarquico para analise estatica e dinamica de placas e cascas." [s.n.], 2001. http://repositorio.unicamp.br/jspui/handle/REPOSIP/263310.
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Orientador : Loir Afonso MoreiraTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica
Made available in DSpace on 2018-08-01T21:31:25Z (GMT). No. of bitstreams: 1 Paschoalini_AmarildoTabone_D.pdf: 8353999 bytes, checksum: bfeebd1be75d31e7d86303a81f912b57 (MD5) Previous issue date: 2001
Resumo: Este trabalho apresenta um elemento subparamétrico hierárquico baseado na versão p do método dos elementos finitos para a análise de placas e cascas. O primeiro nível de aproximação da solução é obtido através do elemento finito quadrilateral quadrático de nove nós da família Lagrangeana, baseado na degeneração de um elemento sólido tridimensional e na formulação de Reissner-Mindlin, com integração numérica consistente. Para outros níveis de aproximação, sucessivos refinamentos hierárquicos são usados, objetivando remover a caracteristica de rigidez excessiva do elemento na análise de placas e cascas finas. Tal formulação é aplicada na análise estática e dinâmica de placas e cascas (finas e moderadamente grossas). Exemplos numéricos são apresentados para mostrar a precisão, eficiência e vantagens da presente formulação. Os resultados numéricos obtidos nos exemplos de aplicação são comparados com soluções analíticas e outras técnicas numéricas, disponíveis na literatura
Abstract: This research presents a subparametric hierarchical finite element based on the p-version concept for the analysis of plates and shells. The first level of approximation for the solution is obtained through the isoparametric quadrilateral quadratic nine-no de Lagrangean shell finite element, based on the degeneration of three-dimensional solid element and the Reissner-Mindlin's formulation, with consistent numerical integration. For other approximation levels, successive hierarchical refinements are used, aiming to remove the characteristic of excessive rigidity of the isoparametric element in the analysis ofthin plates and shells. Such formulation is applied to static and dynamic analysis of plates and shells (thin and moderately thick). Numerical examples are presented to show the accuracy, efficiency and advantages of present formulation. Numerical results obtained for the application examples are compared with analytical solutions and other numerical techniques, available in the open literature
Doutorado
Mecanica dos Sólidos e Projeto Mecanico
Doutor em Engenharia Mecânica
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Juhlin, Eva. "Traces of Mathematical Facts and Students’ Understanding of the Concept `Quadrilateral´ : An enquiry into young students’ communication." Licentiate thesis, Luleå tekniska universitet, Pedagogik, språk och Ämnesdidaktik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-25817.
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Mathematics could be described as a special kind of language, a discourse in which participants communicate abstract concepts. Communication and language are known to be important factors in teaching and learning but little is known about neither communication between students in relation to geometrical concepts, nor what traces of mathematical facts and understanding is incorporated into their communication. Such knowledge would contribute to teachers´ understanding of students’ knowledge of this aspect of mathematical thinking. The purpose of this study is to investigate young students’ communication in the Discourse of geometry. To accomplish this, Swedish students aged between ten and eleven were video-recorded while working with two assignments, one involving describing quadrilaterals to each other and the other sorting quadrilaterals. An analysis of the students’ communication has identified a number of issues that teachers could benefit from being aware of in their teaching of the concept of `geometrical figure´. Examples of issues identified being that conceptual characteristic remain too much in the background of what in the study has been called the visual shape. For example, a long and narrow shape of a geometrical figure seems to draw students’ attention. Students also seem to be having difficulty in understanding that naming a figure is a way of merging the figures´ definitions into one word, and there were problems with words that anchor in daily life.Matematik kan beskrivas som en speciell typ av språk, en diskurs i vilken deltagarna producerar berättelser för att kommunicera abstrakta begrepp. Kommunikation och språk är viktiga faktorer i lärande och undervisning men lite är känt om hur berättelser skapade av elever i relation till geometriska begrepp bidrar till deras kunskap om denna aspekt av matematiskt tänkande. Syftet med denna studie är att undersöka berättelser producerade av unga elever i diskursen geometri. För att genomföra detta videofilmades svenska elever i åldern 10 till 11 år under arbetet med två uppgifter, en där uppgiften var att beskriva fyrhörningar för varandra och en där uppgiften var att sortera fyrhörningar. En analys av de berättelser eleverna producerade identifierade ett antal problem som lärare behöver vara medvetna om och hantera i undervisningen av begreppet `geometrisk figur´. Exempel på identifierade problem är att konceptuella kännetecken alltför mycket hamnar i bakgrunden av vad som i studien kallats för "Den visuella formen", till exempel så verkar en lång och smal form dra till sig elevernas uppmärksamhet. Eleverna verkar också ha problem med att förstå att namnet på en geometrisk figur innebär att man fogat samman figurens konceptuella kännetecken i ett enda ord. Studien visar också på problem med användningen av vardagsord.
Godkänd; 2015; 20150915 (evju)
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Bas, Onur. "Development Of An Incompressible Navier-stokes Solver With Alternating Cell Direction Implicit Method On Structured And Unstructured Quadrilateral Grids." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608775/index.pdf.
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In this research, the Alternating Cell Direction Implicit method is used in temporal discretisation of the incompressible Navier-Stokes equations and compared with the well known and widely used Point Gauss Seidel scheme on structured and quadrilateral unstructured meshes. A two dimensional, laminar and incompressible Navier-Stokes solver is developed for this purpose using the artificial compressibility formulation. The developed solver is used to obtain steady-state solutions with implicit time stepping methods and a third order data reconstruction scheme (U-MUSCL) is added to obtain high order spatial accuracy. The Alternating Cell Directions Implicit method and Point Gauss Seidel scheme is compared in terms of convergence iteration number and total computation time using test cases with growing complexity, including laminar flat plate, single and multi-element airfoil calculations. Both structured and quadrilateral unstructured grids are used in single element airfoil calculations. In these test cases, it is seen that a reduction between 13% and 20% is obtained in total computation time by usage of Alternating Cell Directions Implicit method when compared with the Point Gauss Seidel method.
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Gamble, Stanley Thomas Robert. "The Wesleyan Quadrilateral in Irish Ecumenism : an examination of theological method in Irish Anglican and Methodist conversations since 1965." Thesis, Queen's University Belfast, 2014. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.676472.
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This thesis examines the different methodologies at work within the Irish Anglican-Methodist dialogue from 1965 to 2002 by using the Wesleyan Quadrilateral as a heuristic tool. Through the lens of Scripture, tradition, reason, and experience, it illustrates the similarities and differences between Irish Anglicans and Irish Methodists on the nature and role of the sources by critically examining the key texts of the ecumenical dialogue. It reveals new insights into how the ecumenical process developed and how participants both used and understood the sources in particular ways in their methodologies. Through the lens of the Wesleyan Quadrilateral the research examines the primary source material of the three phases of the dialogue: 1. The Bipartite Conversations 1965-1968, 2. The Tripartite Consultation 1968-1988, and, 3. The Joint Theological Working Party 1989-2002. It finds that when individual Irish Anglicans and Irish Methodists write theology to present the doctrinal position of their respective church, they use the sources in denominational. ways. Their understanding and employment of the sources reflects that of the wider denominational tradition in which they reside. It shows that convergence took place during each phase of the dialogue as Irish Anglicans and Irish Methodists worked together to develop shared and agreed positions. It also charts the location of Irish Anglicans and Irish Methodists on the spectrum of theological opinion at various points in the dialogue. It highlights the potential that existed for the development of a common theological method incorporating the four sources, and the failure to formally realise this. And it suggests that the Wesleyan Quadrilateral could provide Irish Anglicans and Irish Methodists with what they need for the ecumenical future
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Dunlap, Aron Monroe. "Counting to Four: Assessing the Quaternity of C.G. Jung in the Light of Lacan and Sophiology." Diss., Temple University Libraries, 2008. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/9685.
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ReligionPh.D.
This thesis is a critical examination of the question of the fourfold, or quaternities, in the thought of C.G. Jung, as well as an in-depth comparison with the four-fold structures of Jacques Lacan and Sergius Bulgakov. I define quaternities as visual or structural formations conceived in four parts, and I center this study on Jung because I see him as the first thinker to seriously examine the place of quaternity in psychology and modern thought. Part of the work of this thesis will be to give a clear view of Jung's quaternal theories, distinguishing the novelty and authenticity of his work from what has been made of it by subsequent New Age and Jungian thinkers. Jacques Lacan, who uses the term "quadrilateral" to describe his formations, will be contrasted with Jung on several counts. First of all, whereas the Jungian quaternity aims to perfectly integrate its various elements, especially when viewed from the perspective of the fourth element of the quaternity, the Lacanian fourth works in the opposite direction, putting into question any reading of the structure which demands resolution and integration. Lacan's quadrilaterals also avoid the complementarity which is always an important aspect of Jungian quaternity, instead opting for a supplementary logic. Sergius Bulgakov avoids, at least in his later work, referring to quaternities, but, in his reading of Sophia (Wisdom), she clearly functions as something of a fourth within the Christian Trinity. Bulgakov's primary contribution is to provide an answer to Jung's complaint that the Christian Trinity has suppressed its fourth and become unbalanced. The fourth that Bulgakov articulates in the form of Sophia is very different from what Jung had argued for. That is, instead of changing the Trinity into a Quaternity Bulgakov maintains that Sophia underlines the "tri-unity" of the Trinity, and functions not a fourth amidst its members, but as a necessary element in order to both bring out the distinctiveness of each person of the Trinity as well as communicate their common identity.
Temple University--Theses
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Nogueira, Junior Alberto Costa. "Desenvolvimento de um elemento finito do tipo hierarquico para analise estatica de placas e cascas a partir do elemento superparametrico quadrilateral linear." [s.n.], 1998. http://repositorio.unicamp.br/jspui/handle/REPOSIP/263321.
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Orientador: Loir Afonso MoreiraDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica
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Resumo: Este trabalho apresenta uma formulação hierárquica baseada no conceito de aproximação p, de um elemento finito aplicado ao estudo de problemas de valor de contorno envolvendo placas e cascas. Partindo-se de um elemento superparamétrico quadrilateral linear com integração numérica consistente, obtém-se, através do refinamento hierárquico sucessivo, um elemento que se demonstra suficientemente confiável e eficaz dentro de uma ampla variedade de casos. A natureza hierárquica da formulação proposta resulta num modelo bastante eficiente do ponto de vista computacional, sobretudo ao se considerar a possibilidade de implementação do refinamento adaptativo, uma vez que se permite empregar expansões polinomiais diferentes ao longo de lados e elementos distintos, criando-se novos graus de liberdade hierárquicos somente quando a magnitude do erro envolvido na análise o exige. Efetua-se ainda, através de um conjunto de exemplos, uma discussão sobre a aproximação hierárquica quando da utilização de elementos distorcidos, na qual sugere-se o emprego do elemento de 9 nós da família Lagrangiana para a descrição da geometria de problemas abrangendo a análise estática de cascas
Abstract: This investigation presents a hierarchical plate and shell finite element formulation based on the p-approximation concept. Starting with the superparametric quadrilateral linear element with consistent numerical integration, it is achieved, after successive hierarchical refinements, a finite element which is sufficiently accurate and effective in a large variety of cases. The hierarchical nature of this formulation yields a computationally efficient model specially when considering the adaptative refinements since it can use different polynomial expansions at distinct sides and elements generating new hierarchical degrees of freedom just when required by the errors involved in the analysis. It is made at last, through a set of examples, a discussion about hierarchical approximation when employing distorted elements, in which it is suggested the use of the 9-node Lagrangian family element to describe the geometry of boundary value problems concerning shell analysis
Mestrado
Mecanica dos Sólidos e Projeto Mecanico
Mestre em Engenharia Mecânica
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Fields, Lisa Ann. "Use of Web-Based Technology to Enhance Instruction of Virginia's Seventh and Eighth Grade Geometry Standards of Learning." Digital Commons @ East Tennessee State University, 2007. https://dc.etsu.edu/etd/2087.
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The purpose of this thesis is to develop web-based modules for enhancing instruction of the geometry sections of the Virginia Standards of Learning in the seventh and eighth grades. While all of Virginia's seventh and eighth grade Standards of Learning strands are certainly worthy of these types of modules, geometry appeals to me most because of the vast amount of web-based resources that will be valuable when organized into modules. It is my hope that teachers of these grades will find this useful in their instruction of geometry.
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Gauss, Florian [Verfasser], Klaus [Akademischer Betreuer] Rückert, Klaus [Gutachter] Rückert, and Chris [Gutachter] Williams. "The development of computing tools to approximate doubly curved surfaces with quadrilateral planar facets / Florian Gauss ; Gutachter: Klaus Rückert, Chris Williams ; Betreuer: Klaus Rückert." Berlin : Technische Universität Berlin, 2020. http://d-nb.info/1219962775/34.
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Paudel, Gaurab. "Hexahedral Mesh Refinement Using an Error Sizing Function." BYU ScholarsArchive, 2011. https://scholarsarchive.byu.edu/etd/3447.
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The ability to effectively adapt a mesh is a very important feature of high fidelity finite element modeling. In a finite element analysis, a relatively high node density is desired in areas of the model where there are high error estimates from an initial analysis. Providing a higher node density in such areas improves the accuracy of the model and reduces the computational time compared to having a high node density over the entire model. Node densities can be determined for any model using the sizing functions based on the geometry of the model or the error estimates from the finite element analysis. Robust methods for mesh adaptation using sizing functions are available for refining triangular, tetrahedral, and quadrilateral elements. However, little work has been published for adaptively refining all hexahedral meshes using sizing functions. This thesis describes a new approach to drive hexahedral refinement based upon an error sizing function and a mechanism to compare the sizes of the node after refinement.
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Yu, Paul W. Presmeg Norma C. Barrett Jeffrey Edward. "Prototype development and discourse among middle school students in a dynamic geometric environment." Normal, Ill. Illinois State University, 2004. http://wwwlib.umi.com/cr/ilstu/fullcit?p3172886.
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Thesis (Ph. D.)--Illinois State University, 2004.Title from title page screen, viewed November 22, 2005. Dissertation Committee: Norma C. Presmeg, Jeffrey E. Barrett (co-chairs), Sherry L. Meier. Includes bibliographical references (leaves 186-194) and abstract. Also available in print.
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Mansan, Janaína Molon. "Potencialidades e desafios da Rede de Atenção à Saúde do município de Farroupilha." Universidade do Vale do Rio dos Sinos, 2017. http://www.repositorio.jesuita.org.br/handle/UNISINOS/6859.
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As Redes de Atenção à Saúde constituem um método de articulação entre os serviços, que por meio de apoio técnico, logístico e de gestão, buscam a integralidade no cuidado prestado aos usuários. Esta pesquisa buscou verificar como se articula as Redes de Atenção à Saúde no município de Farroupilha, localizado na região nordeste do Rio Grande do Sul. Objetivo: elaborar a proposta de um Programa de Educação Permanente em Saúde para o município de Farroupilha com vistas ao fortalecimento e ativação das Redes de Atenção à Saúde. Método: os componentes da pesquisa estavam de acordo com o Quadrilátero da Formação, abrangendo os eixos Controle Social – Atenção – Gestão. O eixo Formação não foi contemplado, visto que não existe instituição formadora no município. Foram realizadas entrevistas semiestruturadas primeiramente com os usuários (Controle Social) e após análise destes dados, desenvolvido um novo instrumento de coleta a ser aplicado aos profissionais e gestores (Atenção/Gestão). A pesquisa contou com a participação de nove usuários, três profissionais e dois gestores, totalizando quatorze participantes. Para análise dos resultados foi utilizada a análise temática, da qual emergiram duas categorias. Resultado e discussão: a primeira categoria fala sobre as potencialidades e desafios da rede de atenção à saúde do município, tendo como subcategorias a participação do Controle Social e o atendimento na RAS. A segunda categoria analisou a comunicação na Rede de Atenção à Saúde, com suas respectivas subcategorias: potencialidades e desafios do sistema de referência e contrarreferência, comunicação entre a Atenção/Gestão/Controle Social; orientações de alta e prontuário eletrônico. Considerações finais: os resultados revelam falta de conhecimento dos usuários sobre o funcionamento da Rede de Atenção à Saúde do município e uma falta de comunicação entre os profissionais e serviços. Proposta de intervenção: com base nos achados foi elaborada a proposta do estudo, que contou com a elaboração de um Programa de Educação Permanente para os profissionais e a confecção de uma cartilha educativa ilustrada para auxiliar na orientação aos usuários e novos profissionais.
The Health Care Networks consist in an articulation method among the services, which through technical, logistical and management support aim the integrality in the care provided to the users. This research seeks to verify how the Health Care Networks articulate in the city of Farroupilha, located in the northeast region of the State of Rio Grande do Sul. Objective: present a proposal of a Permanent Educational Program in Health for the city of Farroupilha aiming the strengthening and activation of the Health Care Networks. Method: the components of the research agreed to the Formation Quadrilateral, comprehending the thematic axes of Social Control - Attention - Management. The axis Formation was not contemplated, once there is no educational/training institution in the city. Semi-structured interviews were realized firstly with the users (in Social Control) and, past the analysis of the mentioned data, a new instrument for information gathering was developed to be applied among the professionals and managers (Attention/Management). The research counted with the participation of nine users, three professionals and two managers, totalizing fourteen participants. The thematic analysis was deployed for the results’ analysis, from which two categories emerged. Result and discussion: the first category concerns to the potentialities and challenges of the network related to the attention to health in the city, having as subcategories the participation of the Social Control and the attendance at the Health Care Networks. The second category analysed the communication within the Health Care Networks with their respective subcategories: potentialities and challenges in the system of reference and counter-reference; communication among the Attention/Management/Social Control; discharge orientation and electronic prompt-book. Final Considerations: the results display a lack of knowledge from the users about the functioning of the city’s network and an absence of communication between the professionals and services. Intervention Proposal: under these circumstances, the proposal of this study was elaborated, which comprehended the development of a Permanent Educational Program for the professionals and the production of an illustrated educational primer to assist in the orientation of the users and new professionals.
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Mazzochi, Rudimar. "Elementos finitos quadrilaterais Hermitianos de alta regularidade gerados pela partição de unidade aplicados na solução de problemas de elasticidade e elastodinâmica." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2014. http://hdl.handle.net/10183/96314.
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Neste trabalho foram desenvolvidas as funções de interpolação com regularidades C1 e C2, utilizando o Método da Partição de Unidade, referentes ao elemento quadrilateral de quatro nós. Estes elementos quadrilaterais Hermitianos de regularidade C1 e C2 foram implementados em uma plataforma própria de elementos finitos, considerando uma estratégia do tipo sub-paramétrica. De forma comparativa com os elementos Lagrangeanos de regularidade C0 e diferentes ordens polinomiais, os elementos de regularidade C1 e C2 foram aplicados na solução de: problemas clássicos de elasticidade plana infinitesimal isotrópica; aproximação das frequências naturais de vibração livre de barras e viga; pro- pagação de onda elástica em barra devido à aplicação de força impulsiva. Os resultados obtidos mostraram que foi possível se obter um maior percentual de frequências naturais aproximadas do espectro discreto, dado um certo nível de erro máximo, com os elementos de regularidade C1 e C2 em comparação com os elementos Lagrangeanos de regularidade C0 de quatro, oito, dezesseis e vinte e cinco nós. Quanto ao problema de propagação de onda elástica devido à aplicação de força impulsiva, as soluções obtidas com os elementos de regularidade C1 e C2 também apresentaram-se satisfatórias em relação à solução ana- lítica e às soluções aproximadas obtidas com os elementos Lagrangeanos de regularidade C0 de quatro e oito nós. Por outro lado, nas simulações dos problemas de elasticidade plana infinitesimal isotrópica, os elementos de regularidade C1 e C2 não apresentaram um comportamento satisfatório. Os erros relativos em normas L2 e de energia da solução aproximada foram maiores do que aqueles obtidos com o elemento Lagrangeano de regularidade C0 de oito nós, por exemplo, e as taxas de convergência em norma de energia obtidas com tais elementos foram inferiores às preditas pelo estimador de erro a priori.In this work the shape functions with regularity C1 e C2 were developed, by means of the Partition of Unity Method, concerning to the four-node quadrilateral element. These Hermitian quadrilateral elements with regularity C1 e C2 were implemented in an own platform of finite elements, considering the subparametric strategy. Comparatively with the C 0 regularity Lagrangian elements of different polynomial order, C1 and C2 regularity elements were applied in simulations of: classical isotropic infinitesimal plane elasticity problems; approximation of natural frequencies of free vibration for bars and beam; elastic wave propagation in bar caused by forced vibration with impulsive loading applied. The results obtained showed that was possible to get a major number of natural frequencies of free vibration for the discrete spectrum, given a certain level of error, for C1 and C2 regularity elements in comparison with C 0 regularity Lagrangian elements of four, eight, sixteen and twenty-five nodes. Regarding to the elastic wave propagation problem in bar due to the application of impulsive loading, the solution obtained with C1 and C2 regularity elements also presented satisfactory results with relation to the analytical solution and those obtained with C 0 regularity Lagrangian elements with four and eight nodes. On the other hand, for isotropic infinitesimal plane elasticity problems, C1 and C2 regularity elements did not present satisfactory results. Relative errors in L2 and energy norms of approximate solution were greater than those computed for the C 0 Lagrangian element of eight nodes, for example, and convergence rates obtained with the C1 and C2 regularity elements were lower than those predicted by the a priori error estimator.
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Banerjee, Nirjhar. "Random obtuse triangles and convex quadrilaterals." Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/54212.
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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student submitted PDF version of thesis.
Includes bibliographical references (p. 83-85).
We intend to discuss in detail two well known geometrical probability problems. The first one deals with finding the probability that a random triangle is obtuse in nature. We initially discuss the various ways of choosing a random triangle. The problem is at first analyzed based on random angles (adding to 180 degrees) and random sides (obeying the triangle inequality) which is a direct modification of the Broken Stick Problem. We then study the effect of shape on the probability that when three random points are chosen inside a figure of that shape they will form an obtuse triangle. Literature survey reveals the existence of the analytical formulae only in the cases of square, circle and rectangle. We used Monte Carlo simulation to solve this problem in various shapes. We intend to show by means of simulation that the given probabilatity will reach its minimum value when the random points are taken inside a circle. We then introduce the concept of Random Walk in Triangles and show that the probability that a triangle formed during the process is obtuse is itself random. We also propose the idea of Differential Equation in Triangle Space and study the variation of angles during this dynamic process. We then propose to extend this to the problem of calculating the probability of the quadrilateral formed by four random points is convex. The effects of shape are distinctly different than those obtained in the random triangle problem. The effort of true random numbers and normally generated pseudorandom numbers are also compared for both the problems considered.
by Nirjhar Banerjee.
S.M.
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Darch, Melissa. "Characterizing Classes of Quadrilaterals and Hexagons." Thesis, Southern Illinois University at Edwardsville, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10793876.
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The purpose of this thesis is to investigate possibly interesting classes of polygons within quadrilaterals and hexagons. We utilize zero sets of polynomials using the vertices of these polygons to find characteristics of two new quadrilateral classes and four hexagon classes. We will refer to the polynomials as “forms”. These forms are invariant under translation and rotation and scaled by a factor under dilation. We define three functions: X- a reflection across the x-axis, ф- a relabeling of vertices across the AC diagonal (or in a hexagon, across a long diagonal AD), and ρ- a relabeling of the vertices by rotating them clockwise.
We find forms that characterize our classes of polynomials based on how they interact with these functions. For these particular classes, there is one form (up to constant multiples) of order 1 that interacts with the functions in the manner that characterizes the class of polygon. A form of order one is scaled by r2 if the polygon is scaled by r. For each class then, we found several forms that are all equivalent, because they all interact with the functions in the same way.
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Lynch, Keith. "On triangles and quadrilaterals of groups." Diss., Virginia Tech, 1995. http://hdl.handle.net/10919/38574.
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This dissertation demonstrates the existence of a pair of algebraic and geometric structures on triangles of groups and on quadrilaterals of groups. These structures are an automatic and biautomatic structure. In addition, this paper also discusses the growth function for the quadrilaterals.
We show that these groups have these desired structures and discuss what they are. We also give an extraordinary example of a pair of quadrilaterals of groups that are defined nearly identically but do not behave alike.Ph. D.
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StClair, Jessica Lindsey. "Geometry of Spaces of Planar Quadrilaterals." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/26887.
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The purpose of this dissertation is to investigate the geometry of spaces of planar quadrilaterals.
The topology of moduli spaces of planar quadrilaterals (the set of all distinct planar
quadrilaterals with fixed side lengths) has been well-studied [5], [8], [10]. The symplectic
geometry of these spaces has been studied by Kapovich and Millson [6], but the Riemannian
geometry of these spaces has not been thoroughly examined. We study paths in the moduli
space and the pre-moduli space. We compare intraplanar paths between points in the moduli
space to extraplanar paths between those same points. We give conditions on side lengths
to guarantee that intraplanar motion is shorter between some points. Direct applications of
this result could be applied to motion-planning of a robot arm. We show that horizontal lifts
to the pre-moduli space of paths in the moduli space can exhibit holonomy. We determine
exactly which collections of side lengths allow holonomy.Ph. D.
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Park, Yee-han. "Primary mathematics teachers' pedagogical content knowledge of the teaching of quadrilaterals." Click to view the E-thesis via HKUTO, 2003. http://sunzi.lib.hku.hk/hkuto/record/B31963481.
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Souza, Maria Estela Conceição de Oliveira de. "A questão da argumentação e prova na matemática escolar: o caso da medida da soma dos ângulos internos de um quadrilátero qualquer." Pontifícia Universidade Católica de São Paulo, 2009. https://tede2.pucsp.br/handle/handle/11429.
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Maria Estela Conceicao de Oliveira de Souza.pdf: 931053 bytes, checksum: 4ad98d3ccc65b5c15b54131a8deb0af2 (MD5)
Previous issue date: 2009-12-02This study is placed in the context of teaching and learning of mathematical proofs and arguments by students of middle school, developed under the Project Reasoning and Proof in School Mathematics (AProvaME). The aim of the work refers to map the concepts of argumentation and proofs of adolescent students aged between 14 and 16 years of public and private schools of the State of Sao Paulo. For this survey was drawn up a questionnaire in two books, five questions of Algebra and five of Geometry, applied to 1.998 students. More specifically, this work focused on reviewing a matter of Geometry (G3), which called for the truth or falsity of a statement and presenting a justification for the answer. The preparation and discussion of the responses were based largely on research Balacheff (1988) and Healy & Hoyles (1998), on empirical and formal arguments and the complex shift from production of evidence for conceptual pragmatic. After tabulating the information gathered, seeking a more detailed analysis of those 1.998 protocols, drew to a smaller sample of 50 of them. In the next stage, the students were grouped according to types of the presented responses for being submitted to a few individual interviews, in order to obtain additional information about their answers. The work was finished with a conclusive and reflective picture based on the results of previous tests, in which more than 50% of the surveyed students rated the statement of the issue (G3) as true, and for reasons, the preference for empirical arguments (checks for some cases) stood out, but they also had a considerable amount of don t know" and others left empty, with few to justify their answers with the use of properties, for example, the addition of internal angles of any triangle
Este estudo está inserido no contexto do ensino e aprendizagem de provas e argumentos matemáticos de alunos da escola de educação básica, desenvolvido no âmbito do Projeto Argumentação e Prova na Matemática Escolar (AProvaME). O objetivo do trabalho refere-se ao mapeamento das concepções sobre argumentação e provas de alunos adolescentes na faixa etária entre 14 e 16 anos de escolas públicas e particulares do Estado de São Paulo. Para esse levantamento foi elaborado um questionário contendo, em dois cadernos, cinco questões de Álgebra e cinco de Geometria, aplicadas a 1.998 alunos. Mais especificamente, este trabalho centrou-se na análise de uma questão de Geometria (G3) que solicitava a veracidade ou falsidade de uma afirmação e a apresentação de uma justificativa para a resposta. A elaboração e discussão das respostas foram baseadas principalmente nas pesquisas de Balacheff (1988) e Healy & Hoyles (1998) sobre argumentos empíricos e formais e sobre a complexa passagem da produção de provas pragmáticas para conceituais. Após a tabulação das informações coletadas, visando a uma análise mais detalhada desses 1.998 protocolos, extraiu-se uma amostra menor com 50 deles. Na etapa seguinte, esses alunos foram agrupados de acordo com os tipos de resposta apresentados para a realização de algumas entrevistas individuais, visando à obtenção de esclarecimentos adicionais sobre suas respostas. Encerrou-se o trabalho com um panorama conclusivo e reflexivo baseado no resultado das análises anteriores em que mais de 50% dos alunos pesquisados classificaram a afirmação da questão (G3) como verdadeira, e em relação às justificativas, a preferência por argumentos empíricos (verificações para alguns casos) se destacou, mas também houve uma considerável quantidade de respostas não sei e outras deixadas em branco, sendo poucos os que justificaram suas respostas com o uso de propriedades, por exemplo, a soma dos ângulos internos de um triângulo qualquer