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Small Strictly Convex Quadrilateral Meshes of Point Sets
, 2004
"... In this paper we give upper and lower bounds on the number of Steiner points required to construct a strictly convex quadrilateral mesh for a planar point set. In particular, we show that 3⌊n/2 ⌋ internal Steiner points are always sufficient for a convex quadrilateral mesh of n points in the plane. ..."
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In this paper we give upper and lower bounds on the number of Steiner points required to construct a strictly convex quadrilateral mesh for a planar point set. In particular, we show that 3⌊n/2 ⌋ internal Steiner points are always sufficient for a convex quadrilateral mesh of n points in the plane. Furthermore, for any given n ≥ 4, there are point sets for which ⌈(n − 3)/2⌉−1 Steiner points are necessary for a convex quadrilateral mesh.
ABSTRACT Title of Thesis: Analysis and Evaluation of a Shell Finite Element with Drilling Degree of Freedom Name of degree candidate:
"... A at shell nite element is obtained by superposing plate bending and membrane components. Normally, shellelements of this type possess ve degrees of freedom (DOF), three displacement DOF, u, v and w, andtwo inplane rotation DOF, x and y, ateachnode.A sixth degree of freedom, z, is associated with t ..."
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A at shell nite element is obtained by superposing plate bending and membrane components. Normally, shellelements of this type possess ve degrees of freedom (DOF), three displacement DOF, u, v and w, andtwo inplane rotation DOF, x and y, ateachnode.A sixth degree of freedom, z, is associated with the shell normal rotation, and is not usually required by the theory. In practice, however, computational and modeling problems can be caused by a failure to include this degree of freedom in nite element models. This paper presents the formulation and testing of a four node quadrilateralthin at shell nite element, which has six DOF per node. The sixth DOF is obtained by combining by a membrane element with a normal rotation z, the socalled the drilling degree of freedom, and a discrete Kirchho plate element. The at shell has a 24 24 element sti ness matrix. Numerical examples are given for (a) shearloaded cantilever beam, (b) square plate, (c) cantilever Ibeam and (d) folded plate. Performance of the at shell nite element is also compared to a four node at shell element in ANSYS5.0 in case studies (a)(d), and a quadrilateral at shell element from SAP90 in case study (c).DEDICATION For my parents and Aoyasuly. ii ACKNOWLEDGMENTS I would like to sincerely thank my advisor, Professor Mark A. Austin, for his vision, guidance and patience during this project. This work would not have been possible without the assistance of Professor R. L. Taylor, University of California at Berkeley, who provided help and encouragement to pursue this project. My appreciations go also to Professor Peter Chang, who reviewed the thesis carefully and o ered important comments. In addition, I wish to take this opportunity to thank all of the students, faculty and sta
Graduate Group Chairperson
, 2006
"... To my wife Poliana, my daughter Sofia, and my parents Roberto and Dilma. iii Acknowledgments First and foremost, I would like to thank my thesis advisor, Jean Gallier, for his guidance and advice throughout the entire execution of this thesis work. Jean also helped me become a lecturer at the CIS de ..."
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To my wife Poliana, my daughter Sofia, and my parents Roberto and Dilma. iii Acknowledgments First and foremost, I would like to thank my thesis advisor, Jean Gallier, for his guidance and advice throughout the entire execution of this thesis work. Jean also helped me become a lecturer at the CIS department during my last year of my PhD. This job allowed me to stay in the United States for one more year and conclude my PhD studies. I also would like to thank the committee members for their insightful comments
Experimental Results on Quadrangulations of Sets of Fixed Points
"... Abstract We consider the problem of obtaining "nice " quadrangulations of planar sets of points. For many applications "nice " means that the quadrilaterals obtained are convex if possible and as"fat " or squarish as possible. For a given set of ..."
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Abstract We consider the problem of obtaining &quot;nice &quot; quadrangulations of planar sets of points. For many applications &quot;nice &quot; means that the quadrilaterals obtained are convex if possible and as&quot;fat &quot; or squarish as possible. For a given set of points a quadrangulation, if it exists, may not admit all its quadrilaterals to be convex. In such cases we desire that the quadrangulationshave as many convex quadrangles as possible. Solving this problem optimally is not practical. Therefore we propose and experimentally investigate a heuristic approach to solve this problem by converting &quot;nice &quot; triangulations to the desired quadrangulations with the aid of maximummatchings computed on the dual graph of the triangulations. We report experiments on several versions of this approach and provide theoretical justification for the good results obtained with one of these methods. The results of our experiments are particularly relevant for thoseapplications in scattered data interpolation which require quadrangulations that should stay faithful to the original data.
Upper and Lower Bounds for Strictly Convex Quadrilateral Meshes of Point Sets
, 2001
"... In this paper, we give upper and lower bounds on the number of Steiner points required to construct a strictly convex quadrilateral mesh for a planar point set. In particular, we show that 3b 2 c internal Steiner points are always sucient for a convex quadrangulation of n points in the plane. ..."
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In this paper, we give upper and lower bounds on the number of Steiner points required to construct a strictly convex quadrilateral mesh for a planar point set. In particular, we show that 3b 2 c internal Steiner points are always sucient for a convex quadrangulation of n points in the plane. Furthermore, for any given n 4, there are point sets for which d e 1 Steiner points may be necessary for a convex quadrangulation.
A New Analytical Integration Expression Applied To Quadrilateral Finite Elements
"... Abstract—A new analytical integration expression is presented and used to evaluate the element stiffness matrix for the quadrilateral finite elements. For reasons of applications and particularity of the strain based finite elements (higher order shape functions expressed in terms of independent str ..."
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Abstract—A new analytical integration expression is presented and used to evaluate the element stiffness matrix for the quadrilateral finite elements. For reasons of applications and particularity of the strain based finite elements (higher order shape functions expressed in terms of independent strains); it is necessary to introduce irregular forms, which require a special integration technique, and a specific classification in programming level for different geometric forms. To overcome this geometrical inconvenience; the paper presents the new integration expression with validation tests, and it is applied to some quadrilateral finite elements, this will help to extend their applications for the distorted forms and irregular structures. Index Terms — Analytical integration, irregular forms, new expression, quadrilateral element.
Experimental Results on Quadrangulations of Sets of Points
"... We consider the problem of obtaining "nice" quadrangulations of planar sets of points. For many applications "nice" means that the quadrilaterals obtained are convex if possible and as "fat" or as squarish as possible. For a given set of points a quadrangulation, if i ..."
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We consider the problem of obtaining "nice" quadrangulations of planar sets of points. For many applications "nice" means that the quadrilaterals obtained are convex if possible and as "fat" or as squarish as possible. For a given set of points a quadrangulation, if it exists, may not admit all its quadrilaterals to be convex. In such cases we desire that the quadrangulations have as many convex quadrangles as possible. Solving this problem optimally is not practical. Therefore we propose and experimentally investigate a heuristic approach to solve this problem by converting "nice" triangulations to the desired quadrangulations with the aid of maximum matchings computed on the dual graph of the triangulations. We report experiments on several versions of this approach and provide theoretical justification for the good results obtained with one of these methods. 1 Introduction Finite element mesh generation is a problem that has received considerable attention in recent years...
Experimental Results on Quadrangulations of Sets of Fixed Points
, 1997
"... We consider the problem of obtaining "nice" quadrangulations of planar sets of points. For many applications "nice" means that the quadrilaterals obtained are convex if possible and as "fat" or squarish as possible. For a given set of points a quadrangulation, if it e ..."
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We consider the problem of obtaining "nice" quadrangulations of planar sets of points. For many applications "nice" means that the quadrilaterals obtained are convex if possible and as "fat" or squarish as possible. For a given set of points a quadrangulation, if it exists, may not admit all its quadrilaterals to be convex. In such cases we desire that the quadrangulations have as many convex quadrangles as possible. Solving this problem optimally is not practical.