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TECHNICAL PAPERS

Quad-Layer: Layered Quadrilateral Meshing of Narrow Two-Dimensional Domains by Bubble Packing and Chordal Axis Transformation

[+] Author and Article Information
Soji Yamakawa, Kenji Shimada

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213

J. Mech. Des 124(3), 564-573 (Aug 06, 2002) (10 pages) doi:10.1115/1.1486014 History: Received September 01, 2001; Online August 06, 2002
Copyright © 2002 by ASME
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References

Blacker,  T. D., and Stephenson,  M. B., 1991, “Paving: A New Approach to Automated Quadrilateral Mesh Generation,” Int. J. Numer. Methods Eng., 32, pp. 811–847.
Cass,  R. J., and Benzley,  S. E., 1996, “Generalized 3-D Paving: An Automated Quadrilateral Surface Mesh Generation Algorithm,” Int. J. Numer. Methods Eng., 39, pp. 1475–1489.
Owen, S. J., Staten, M. L., Canann, S. A., and Saigal, S., 1998, “Advancing Front Quadrilateral Meshing Using Triangle Transformations,” presented at 7th International Meshing Roundtable, pp. 409–428.
Thompson, D. S., and Soni, B. K., 1999, “Generation of Quad- and Hex-dominant, Semistructured Meshes Using an Advancing Layer Scheme,” presented at 8th International Meshing Roundtable, pp. 171–178.
Shimada, K., Liao, J.-H., and Itoh, T., 1998, “Quadrilateral Meshing with Directionality Control through the Packing of Square Cells,” presented at 7th International Meshing Roundtable, pp. 61–75.
Itoh, T., Shimada K., Inoue, K., Yamada, A., and Furuhata, T., 1998, “Automated Conversion of 2D Triangular Mesh into Quadrilateral Mesh with Directionality Control,” presented at 7th International Meshing Roundtable, pp. 77–86.
White, D. R., 1997, “Redesign of the Paving Algorithm: Robustness Enhancements through Element by Element Meshing,” presented at 6th International Meshing Roundtable, pp. 323–335.
Viswanath, N., Shimada, K., and Itoh, T., 2000, “Quadrilateral Meshing with Anisotropy and Directionality Control via Close Packing of Rectangular Cells,” presented at 9th International Meshing Roundtable.
Tam,  T. K. H., and Armstrong,  C. G., 1991, “2D Finite Element Mesh Generation by Medial Axis Subdivision,” Adv. Eng. Softw., 13, pp. 313–324.
Gürsoy,  H. N., and Patrikalakis,  N. M., 1992, “An Automatic Coarse and Fine Surface Mesh Generation Scheme Based on Medial Axis Transform: Part I Algorithm, Part II Implementation,” Eng. Comput., 8, pp. 121–137, 179–196.
Quadros, W. R., Ramsawami, K., Prinz, F. B., and Gurumoorthy, B., 2000, “LayTracks: A New Approach To Automated Quadrilateral Mesh Generation using MAT,” presented at 9th International Meshing Roundtable, pp. 239–250.
Prasad, L., 1997, “Morphological Analysis of Shapes,” in http://cnls.lanl.gov/Highlights/1997-07/: Los Alamos National Laboratory.
Shewchuk, J. R., 1996, “Triangle: Engineering a 2D Quality Mesh Generator,” presented at First Workshop on Applied Computational Geometry, pp. 124–133.
George, P. L., 1999, “TET MESHING: Construction, Optimization and Adaptation,” presented at 8th International Meshing Roundtable, pp. 133–141.
Shimada, K., Yamada, A., and Itoh, T., 1997, “Anisotropic Triangular Meshing of Parametric Surfaces via Close Packing of Ellipsoidal Bubbles,” presented at 6th International Meshing Roundtable, pp. 375–390.
Shimada,  K., and Gossard,  D. C., 1998, “Automatic Triangular Mesh Generation of Trimmed Parametric Surfaces for Finite Element Analysis,” Computer Aided Geometric Design, 15, pp. 199–222.
Yamakawa, S., and Shimada, K., 2000, “High Quality Anisotropic Tetrahedral Mesh Generation via Ellipsoidal Bubble Packing,” presented at 9th International Meshing Roundtable, pp. 263–273.
Chironis, N. P., and Sclater, N., 1996, Mechanisms and Mechanical Devices Sourcebook, Second ed, McGraw Hill.

Figures

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An example of an input narrow two-dimensional domain and three types of output layered quadrilateral meshes
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Ill-shaped elements caused by uniformly distributing boundary nodes
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Outline of the Quad-Layer method
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Constraining a bubble on a curve
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Variation of Prasad’s algorithm
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Quadrilateral element generation
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Correcting an inverted element by Laplacian smoothing
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Converting part of a mesh into two layers
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Classification of elements
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Quadrilateral mesh of a tire cross-section
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Single-layer mesh with a curvature-based element length distribution function
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A mechanical computing mechanism
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Large deformation finite element analysis of a rubber part

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