Relevant bibliographies by topics / Quadrilateral

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Quadrilateral'

Author: Grafiati
Published: 4 June 2021
Last updated: 2 February 2022

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Journal articles on the topic "Quadrilateral"

1

Josefsson, Martin. "Properties of bisect-diagonal quadrilaterals." Mathematical Gazette 101, no. 551 (June 15, 2017): 214–26. http://dx.doi.org/10.1017/mag.2017.61.

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The general class of quadrilaterals where one diagonal is bisected by the other diagonal has appeared very rarely in the geometrical literature, but they have been named several times in connection with quadrilateral classifications. Günter Graumann strangely gave these objects two different names in [1, pp. 192, 194]: sloping-kite and sliding-kite. A. Ramachandran called them slant kites in [2, p. 54] and Michael de Villiers called them bisecting quadrilaterals in [3, pp. 19, 206]. The latter is a pretty good name, although a bit confusing: what exactly is bisected?We have found no papers and only two books where any theorems on such quadrilaterals are studied. In each of the books, one necessary and sufficient condition for such quadrilaterals is proved (see Theorem 1 and 2 in the next section). The purpose of this paper is to investigate basic properties ofconvexbisecting quadrilaterals, but we have chosen to give them a slightly different name. Let us first remind the reader that a quadrilateral whose diagonals have equal lengths is called an equidiagonal quadrilateral and one whose diagonals are perpendicular is called an orthodiagonal quadrilateral.
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Choudhry, Ajai. "Brahmagupta quadrilaterals with equal perimeters and equal areas." International Journal of Number Theory 16, no. 03 (October 2, 2019): 523–35. http://dx.doi.org/10.1142/s1793042120500268.

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A cyclic quadrilateral is called a Brahmagupta quadrilateral if the lengths of its four sides and two diagonals, and the area are all given by integers. In this paper, we consider the hitherto unsolved problem of finding two Brahmagupta quadrilaterals with equal perimeters and equal areas. We obtain two parametric solutions of the problem — the first solution generates examples in which each quadrilateral has two equal sides while the second solution gives quadrilaterals all of whose sides are unequal. We also show how more parametric solutions of the problem may be obtained.
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Mammana, Maria Flavia, and Biagio Micale. "Quadrilaterals of triangle centres." Mathematical Gazette 92, no. 525 (November 2008): 466–75. http://dx.doi.org/10.1017/s0025557200183664.

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Let Q be a convex quadrilateral ABCD. We denote by TA, TB, Tc, TD, the four triangles BCD, CDA, DAB, ABC, respectivelyThe barycentres (or centroids), orthocentres, incentres and circumcentres of such triangles determine other quadrilaterals in their turn that we call the quadrilateral of the barycentres, of the orthocentres, of the incentres and of the circumcentres, respectively. We denote these quadrilaterals by Qb, Q0, Qi, Qc, respectively.
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RAMASWAMI, SUNEETA, MARCELO SIQUEIRA, TESSA SUNDARAM, JEAN GALLIER, and JAMES GEE. "CONSTRAINED QUADRILATERAL MESHES OF BOUNDED SIZE." International Journal of Computational Geometry & Applications 15, no. 01 (February 2005): 55–98. http://dx.doi.org/10.1142/s0218195905001609.

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We introduce a new algorithm to convert triangular meshes of polygonal regions, with or without holes, into strictly convex quadrilateral meshes of small bounded size. Our algorithm includes all vertices of the triangular mesh in the quadrilateral mesh, but may add extra vertices (called Steiner points). We show that if the input triangular mesh has t triangles, our algorithm produces a mesh with at most [Formula: see text] quadrilaterals by adding at most t+2 Steiner points, one of which may be placed outside the triangular mesh domain. We also describe an extension of our algorithm to convert constrained triangular meshes into constrained quadrilateral ones. We show that if the input constrained triangular mesh has t triangles and its dual graph has h connected components, the resulting constrained quadrilateral mesh has at most [Formula: see text] quadrilaterals and at most t+3h Steiner points, one of which may be placed outside the triangular mesh domain. Examples of meshes generated by our algorithm, and an evaluation of the quality of these meshes with respect to a quadrilateral shape quality criterion are presented as well.
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GROSSMAN, PINHAS, and MASAKI IZUMI. "CLASSIFICATION OF NONCOMMUTING QUADRILATERALS OF FACTORS." International Journal of Mathematics 19, no. 05 (May 2008): 557–643. http://dx.doi.org/10.1142/s0129167x08004807.

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A quadrilateral of factors is an irreducible inclusion of factors N ⊂ M with intermediate subfactors P and Q such that P and Q generate M and the intersection of P and Q is N. We investigate the structure of a noncommuting quadrilateral of factors with all the elementary inclusions P ⊂ M, Q ⊂ M, N ⊂ P, and N ⊂ Q 2-supertransitive. In particular, we classify noncommuting quadrilaterals with the indices of the elementary subfactors less than or equal to 4. We also compute the angles between P and Q for quadrilaterals coming from α-induction and asymptotic inclusions.
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Josefsson, Martin. "Further characterisations of tangential quadrilaterals." Mathematical Gazette 101, no. 552 (October 16, 2017): 401–11. http://dx.doi.org/10.1017/mag.2017.122.

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Tangential quadrilaterals are defined to be quadrilaterals in which a circle can be inscribed that is tangent to all four sides. It is well known and easy to prove that a convex quadrilateral is tangential if, and only if, the angle bisectors of all four vertex angles are concurrent at a point, which is the centre of the inscribed circle (incircle). The most well-known and in problem solving useful characterisation of tangential quadrilaterals is Pitot's theorem, which states that a convex quadrilateral is tangential if and only if its consecutive sides a, b, c, d satisfy the relation a + c = b + d [1, pp. 64-67]. If you want to have more background information about characterisations of tangential quadrilaterals, then we recommend you to check out the lovely papers [2, 3, 4], as well as our previous contributions on the subject [5, 6, 7]. These six papers together include about 30 characterisations that are either proved or reviewed there with references.
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Fraivert, David. "Pascal-points quadrilaterals inscribed in a cyclic quadrilateral." Mathematical Gazette 103, no. 557 (June 6, 2019): 233–39. http://dx.doi.org/10.1017/mag.2019.54.

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This paper presents some new theorems about the Pascal points of a quadrilateral. We shall begin by explaining what these are.Let ABCD be a convex quadrilateral, with AC and BD intersecting at E and DA and CB intersecting at F. Let ω be a circle through E and F which meets CB internally at M and DA internally at N. Let CA meet ω again at L and let DB meet ω again at K. By using Pascal’s theorem for the crossed hexagons EKNFML and EKMFNL and which are circumscribed by ω, the following results can be proved [1]:– (a)NK, ML and AB are concurrent (at a point P internal to AB)(b)NL, KM and CD are concurrent (at a point Q internal to CD)
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IZADI, FARZALI, FOAD KHOSHNAM, DUSTIN MOODY, and ARMAN SHAMSI ZARGAR. "ELLIPTIC CURVES ARISING FROM BRAHMAGUPTA QUADRILATERALS." Bulletin of the Australian Mathematical Society 90, no. 1 (April 10, 2014): 47–56. http://dx.doi.org/10.1017/s0004972713001172.

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AbstractA Brahmagupta quadrilateral is a cyclic quadrilateral whose sides, diagonals and area are all integer values. In this article, we characterise the notions of Brahmagupta, introduced by K. R. S. Sastry [‘Brahmagupta quadrilaterals’, Forum Geom. 2 (2002), 167–173], by means of elliptic curves. Motivated by these characterisations, we use Brahmagupta quadrilaterals to construct infinite families of elliptic curves with torsion group $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z}$ having ranks (at least) four, five and six. Furthermore, by specialising we give examples from these families of specific curves with rank nine.
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Bao, Yuan, Zhaoliang Meng, and Zhongxuan Luo. "AC0-nonconforming quadrilateral finite element for the fourth-order elliptic singular perturbation problem." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 5 (September 2018): 1981–2001. http://dx.doi.org/10.1051/m2an/2018033.

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In this paper, aC0nonconforming quadrilateral element is proposed to solve the fourth-order elliptic singular perturbation problem. For each convex quadrilateralQ, the shape function space is the union ofS21(Q*) and a bubble space. The degrees of freedom are defined by the values at vertices and midpoints on the edges, and the mean values of integrals of normal derivatives over edges. The local basis functions of our element can be expressed explicitly by a new reference quadrilateral rather than by solving a linear system. It is shown that the method converges uniformly in the perturbation parameter. Lastly, numerical tests verify the convergence analysis.
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Bao, Hui, and Xingdi Chen. "A New Hyperbolic Area Formula of a Hyperbolic Triangle and Its Applications." Journal of Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/838497.

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We study some characterizations of hyperbolic geometry in the Poincaré disk. We first obtain the hyperbolic area and length formula of Euclidean disk and a circle represented by its Euclidean center and radius. Replacing interior angles with vertices coordinates, we also obtain a new hyperbolic area formula of a hyperbolic triangle. As its application, we give the hyperbolic area of a Lambert quadrilateral and some geometric characterizations of Lambert quadrilaterals and Saccheri quadrilaterals.
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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 JANEIRO
COORDENAÇÃO 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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Books on the topic "Quadrilateral"

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Urabe, Tohsuke. Dynkin graphs and quadrilateral singularities. Berlin: Springer-Verlag, 1993.

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Blaisdell, Molly. If you were a quadrilateral. Mankato, MN: Picture Window Books, 2010.

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Urabe, Tohsuke. Dynkin Graphs and Quadrilateral Singularities. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/bfb0084369.

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Bercovier, Michel, and Tanya Matskewich. Smooth Bézier Surfaces over Unstructured Quadrilateral Meshes. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-63841-6.

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Dawes, Stephen. The primacy of scripture and the Methodist Quadrilateral. [U.K.]: The Methodist Sacramental Fellowship, 1998.

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Tomlinson, Jim. The iron quadrilateral: Political obstacles to economic reform under the Attlee government. Uxbridge: Brunel University, Department of Economics, 1992.

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The Wesleyan quadrilateral: Scripture, tradition, reason & experience as a model of evangelical theology. Grand Rapids, Mich: Zondervan Pub. House, 1990.

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Thorsen, Donald A. D. The Wesleyan quadrilateral: Scripture, tradition, reason & experience as a model of evangelical theology. Lexington, KY: Emeth Press, 1990.

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Smoothey, Marion. Quadrilaterals. New York: Marshall Cavendish, 1993.

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Leech, Bonnie Coulter. Quadrilaterals. New York: PowerKids Press, 2007.

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Book chapters on the topic "Quadrilateral"

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Wachspress, Eugene. "The Quadrilateral." In Rational Bases and Generalized Barycentrics, 23–36. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-21614-0_2.

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Whiteley, Jonathan. "Quadrilateral Elements." In Mathematical Engineering, 161–73. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49971-0_9.

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Dasgupta, Gautam. "Taig’s Quadrilateral Elements." In Finite Element Concepts, 103–20. New York, NY: Springer New York, 2017. http://dx.doi.org/10.1007/978-1-4939-7423-8_5.

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Goddijn, Aad, Martin Kindt, and Wolfgang Reuter. "A special quadrilateral." In Geometry with Applications and Proofs, 93–105. Rotterdam: SensePublishers, 2014. http://dx.doi.org/10.1007/978-94-6209-860-2_7.

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Jayaraj, Arjun, and Peter Gloviczki. "Quadrilateral Space Syndrome." In Thoracic Outlet Syndrome, 761–69. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-55073-8_88.

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Kattan, Peter I. "The Bilinear Quadrilateral Element." In MATLAB Guide to Finite Elements, 267–302. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05209-9_13.

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Kattan, Peter I. "The Quadratic Quadrilateral Element." In MATLAB Guide to Finite Elements, 303–28. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05209-9_14.

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Kattan, Peter I. "The Bilinear Quadrilateral Element." In MATLAB Guide to Finite Elements, 275–310. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-70698-4_13.

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Kattan, Peter I. "The Quadratic Quadrilateral Element." In MATLAB Guide to Finite Elements, 311–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-70698-4_14.

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Liu, Li, CaiMing Zhang, and Frank Cheng. "Parameterization of Quadrilateral Meshes." In Computational Science – ICCS 2007, 17–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-72586-2_3.

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Conference papers on the topic "Quadrilateral"

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Daniels, Joel, Cláudio T. Silva, Jason Shepherd, and Elaine Cohen. "Quadrilateral mesh simplification." In ACM SIGGRAPH Asia 2008 papers. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1457515.1409101.

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Hormann, Kai, and Marco Tarini. "A quadrilateral rendering primitive." In the ACM SIGGRAPH/EUROGRAPHICS conference. New York, New York, USA: ACM Press, 2004. http://dx.doi.org/10.1145/1058129.1058131.

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Suzuki, Hirotaka. "Skew quadrilateral membrane folding for lampshade design." In The 13th International Conference on Engineering and Computer Graphics BALTGRAF-13. Vilnius Gediminas Technical University, 2015. http://dx.doi.org/10.3846/baltgraf.2015.016.

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Historically, Japanese traditional lampstand 'Andon', was manufactured from paper. And paper folding method was adopted into some Andon or western lampshade design. For example, Yoshimura/Diamond pattern, known as a structure of crashed cylinder, or a structure of building roof, that has been of beneficial use in commercial lampshade products. Yoshimura pattern structure includes a set of skew quadrilaterals which are not on a plane surface and each quadrilateral is constructed with 2 planar triangles. Development of Yoshimura pattern is constructed by one set of horizontal parallel lines at even intervals for valley fold and two sets of oblique parallel lines at even intervals for mountain fold. The author found that similar shape can be constructed from development which includes only mountain fold lines of Yoshimura pattern and this method has various applications. With proposed paper folding method, each skew quadrilateral is constructed by single curved surface. In this paper, the author first defined the principle of the proposed paper folding method, second, explained the. features of the shape made by the proposed method and the luminance distribution on the shape, third, indicated examples of applications of the proposed method. Finally, examples of application of the shape made by SQMF in the field of education are explained.
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Keaton, Jeffrey R., and Richard W. Gailing. "Monitoring Slope Deformation With Quadrilaterals for Pipeline Risk Management." In 2004 International Pipeline Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/ipc2004-0197.

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Ground displacements, strains, and tilts can be calculated by repeated measurements of the lengths of six chords and relative elevations of an array of four points, known as a quadrilateral. Quadrilateral measurements allow ground-surface deformation and strain to be calculated. Typically, soil-pipeline interaction results in pipeline strain being less than ground strain. Strain gauges traditionally have been used on pipelines in landslide areas to aid in managing pipeline risk. Quadrilaterals may be economical alternatives to placing strain gauges on existing pipelines in areas of active or potential slope movements. A threshold ground deformation or strain is used to trigger more expensive means of evaluating pipeline integrity. Quadrilaterals are relatively inexpensive to install, but must be carefully located and founded deep enough to avoid seasonal shrink-swell effects of the soil. Measurements must be taken with precise instruments (tape extensometer) so that small changes can be detected with acceptable errors. Three contiguous quadrilaterals were installed in Spring 2003 in a landslide-prone area of southern California to aid in monitoring a slope between the main scarp of a recently active landslide and a pipeline bridge foundation. Engineering geologic evaluation supported a conclusion that the rate of headward crest advancement would be slow, but a method of detecting and quantifying slope deformation was needed for operational risk management.
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Peng, Chi-Han, Eugene Zhang, Yoshihiro Kobayashi, and Peter Wonka. "Connectivity editing for quadrilateral meshes." In the 2011 SIGGRAPH Asia Conference. New York, New York, USA: ACM Press, 2011. http://dx.doi.org/10.1145/2024156.2024175.

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Mishiba, Kazu, Masaaki Ikehara, and Keiichiro Shirai. "Quadrilateral Remeshing with Global Alignment." In 2009 IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop. IEEE, 2009. http://dx.doi.org/10.1109/dsp.2009.4785985.

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Connell, Stuart D., D. Graham Holmes, and Mark E. Braaten. "Adaptive Unstructured 2D Navier-Stokes Solutions on Mixed Quadrilateral/Triangular Meshes." In ASME 1993 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/93-gt-099.

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This paper presents a solution adaptive scheme for solving the Navier-Stokes equations on an unstructured mixed grid of triangles and quadrilaterals. The solution procedure uses an explicit Runge-Kutta finite volume time marching scheme with an adaptive blend of second and fourth order smoothing. The governing equations are solved in a 2D, axisymmetric or quasi-3D form. In viscous regions quadrilateral elements are used to facilitate the one dimensional refinement required for the efficient resolution of boundary layers and wakes. The effect of turbulence is incorporated through using either a Baldwin-Lomax or k-ε turbulence model. Solutions are presented for several examples that illustrate the capability of the algorithm to predict viscous phenomena accurately. The examples are a transonic turbine, a nozzle and a combustor diffuser.
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Zhou, Hong, and Nitin M. Dhembare. "The Comparision of Hybrid and Quadrilateral Discretization Models for the Topology Optimization of Compliant Mechanisms." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-62329.

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The design domain of a synthesized compliant mechanism is discretized into quadrilateral design cells in both hybrid and quadrilateral discretization models. However, quadrilateral discretization model allows for point connection between two diagonal design cells. Hybrid discretization model completely eliminates point connection by subdividing each quadrilateral design cell into triangular analysis cells and connecting any two contiguous quadrilateral design cells using four triangular analysis cells. When point connection is detected and suppressed in quadrilateral discretization, the local topology search space is dramatically reduced and slant structural members are serrated. In hybrid discretization, all potential local connection directions are utilized for topology optimization and any structural members can be smooth whether they are in the horizontal, vertical or diagonal direction. To compare the performance of hybrid and quadrilateral discretizations, the same design and analysis cells, genetic algorithm parameters, constraint violation penalties are employed for both discretization models. The advantages of hybrid discretization over quadrilateral discretization are obvious from the results of two classical synthesis examples of compliant mechanisms.
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Li, Wei, Zhuoqi Wu, Ichiro Hagiwara, and Yong Jiang. "Surface Construction Based on Quadrilateral Mesh." In 2011 Fourth International Conference on Information and Computing (ICIC). IEEE, 2011. http://dx.doi.org/10.1109/icic.2011.121.

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Velho, Luiz. "4-8 factorization of quadrilateral subdivision." In the sixth ACM symposium. New York, New York, USA: ACM Press, 2001. http://dx.doi.org/10.1145/376957.376993.

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Reports on the topic "Quadrilateral"

1

D'Azevedo, E. On Optimal Bilinear Quadrilateral Meshes. Office of Scientific and Technical Information (OSTI), March 2000. http://dx.doi.org/10.2172/814808.

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Blacker, T., and M. Stephenson. Paving: A new approach to automated quadrilateral mesh generation. Office of Scientific and Technical Information (OSTI), March 1990. http://dx.doi.org/10.2172/7184374.

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BROCK, J. S. INTEGRATING A BILINEAR INTERPOLATION FUNCTION ACROSS QUADRILATERAL CELL BOUNDARIES. Office of Scientific and Technical Information (OSTI), January 2001. http://dx.doi.org/10.2172/772922.

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Wang, Wenyan, Yongjie Zhang, Guoliang Xu, and Thomas J. Hughes. Converting an Unstructured Quadrilateral/Hexahedral Mesh to a Rational T-spline. Fort Belvoir, VA: Defense Technical Information Center, August 2011. http://dx.doi.org/10.21236/ada555343.

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Lober, R. R., T. J. Tautges, and C. T. Vaughan. Parallel paving: An algorithm for generating distributed, adaptive, all-quadrilateral meshes on parallel computers. Office of Scientific and Technical Information (OSTI), March 1997. http://dx.doi.org/10.2172/469139.

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Manzini, Gianmarco, and Alessandro Russo. Monotonicity conditions in the nodal mimetic finite difference method for diffusion problems on quadrilateral meshes. Office of Scientific and Technical Information (OSTI), May 2013. http://dx.doi.org/10.2172/1079553.

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Ghani, Ejaz, Arti Grover Goswami, and William Kerr. Highway to Success: The Impact of the Golden Quadrilateral Project for the Location and Performance of Indian Manufacturing. Cambridge, MA: National Bureau of Economic Research, November 2012. http://dx.doi.org/10.3386/w18524.

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D`Azevedo, E. F. Are bilinear quadrilaterals better than linear triangles? Office of Scientific and Technical Information (OSTI), August 1993. http://dx.doi.org/10.2172/10179134.

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D'Azevedo, E. F. Are Bilinear Quadrilaterals Better Than Linear Triangles? Office of Scientific and Technical Information (OSTI), January 1993. http://dx.doi.org/10.2172/814567.

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Asvestas, John S. Calculation of Moment Matrix Elements for Bilinear Quadrilaterals and Higher-Order Basis Functions. Fort Belvoir, VA: Defense Technical Information Center, January 2016. http://dx.doi.org/10.21236/ad1001926.

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