Generalization of the Mid-Element Based Dimensional Reduction

[+] Author and Article Information
Krishnan Suresh

Department of Mechanical Engineering, University of Wisconsin, Madison, WIe-mail: suresh@engr.wisc.edu

J. Comput. Inf. Sci. Eng 3(4), 308-314 (Dec 24, 2003) (7 pages) doi:10.1115/1.1631441 History: Received July 01, 2003; Revised October 01, 2003; Online December 24, 2003
Copyright © 2003 by ASME
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Donaghy, R. J., Cune, W. M., Bridgett, S. J., Armstrong, C. G., Robinson, D. J., McKeag, R. M., 1996, “Dimensional Reduction of Analysis Models,” 5th International Meshing Roundtable, Sandia National Laboratories, pp. 307–320.
Kantorovich, L. V., and Krylov, V. I., 1964, Approximate Methods of Higher Analysis, Interscience, New York.
Pilkey, W. D., and Wunderlich, W., 1994, Mechanics of Structures: Variational and Computational Methods, CRC Press, New York.
Shames, I. H., and Dym, C. L., 1985, Energy and Finite Element Methods in Structural Mechanics, McGraw Hill, New York.
Reddy, J. N., 1984, Energy and Variational Methods in Applied Mechanics, John Wiley and Sons, New York.
Babuska,  I., Lee,  I., and Schwab,  C., 1994, “On the A Posteriori Estimation of the Modeling Error for the Heat Conduction in a Plate and its Use for Adaptive Hierarchical Modeling,” Appl. Numer. Math., 14, pp. 5–21.
Wang, C. M., Reddy, J. N., and Lee, K. H., 2000, Shear Deformable Beams and Plates: Relationship to Classical Solutions, Elsevier Science, London.
Strang, G., and Fix, G. J., 1973, An Analysis of the Finite Element Method, Prentice-Hall, New York.
Reissner,  E., 1985, “Reflections on the Theory of Elastic Plates,” J. Appl. Mech., 38(11), pp. 1453–1464.
Vogelius,  M., and Babuska,  I., 1981, “On a Dimensional reduction Method I. The Optimal Selection of Basis Functions,” Math. Comput., 37(155), pp. 31–46.
Madureira, A. L., 1999, “Asymptotics and Hierarchical Modeling of Thin Domains,” Ph.D. thesis, Department of Mathematics, The Pennsylvania State University.
Armstrong,  C. G., 1994, “Modeling Requirements for Finite-Element Analysis,” Comput.-Aided Des., 26 (7) .
Choi,  H. I., Choi,  S. W., and Moon,  H. P., 1997, “Mathematical Theory of Medial Axis Transform,” Pac. J. Math., 181(1), pp. 57–88.
Sherbrooke,  E. C., Patrikalakis,  N. M., and Wolter,  F-E., 1996, “Differential and Topological Properties of Medial Axis Transforms,” Graph. Models Image Process., 58(6), pp. 574–592.
Tam,  T. K. H., and Armstrong,  C. G., 1991, “2D Finite Element Mesh Generation by Medial Axis Subdivision,” Adv. Eng. Software 56(13), pp. 313–324.
Armstrong, C. G., Robinson, D. J., McKeag, R. M., Li, T. S., Bridgett, S. J., Donaghy, R. J., and McGleenan, C. A., 1995, “Medials for Meshing and More,” Proceedings, 4th International Meshing Roundtable, Sandia National Laboratories, Albuquerque.
Price,  M. A., and Armstrong,  C. G., 1995, “Hexahedral Mesh Generation by Medial Surface Subdivision: Part I, Solids With Convex Edges,” Int. J. Numer. Methods Eng., 38(19), pp. 3335–3359.
Armstrong, C. G., Bridgett, S. J., Donaghy, R. J., McCune, R. W., McKeag, R. M., and Robinson, D. J., 1998, “Techniques for Interactive and Automatic Idealization of CAD Models,” Numerical Grid Generation in Computational Field Simulations, Ed. M. Cross, B. K. Soni, J. F. Thompson, J. Hauser, P. R. Eiseman, Proceedings of the 6th International Conference, held at the University of Greenwich, pp. 643–662.
Monaghan, D. J., 1998, “Coupling 1D Beams to 3D Bodies,” Proceedings, 7th International Meshing Roundtable, Sandia National Lab, pp. 285–293.
Sheffer A., Etzion, M., Rappoport, A., and Bercovier, M., 1998, “Hexahedral Mesh Generation using Voronoi Skeletons,” Proceedings of the Seventh International Meshing Roundtable, Michigan.
Armstrong, C. G., and Bradley, B., 1999, “Design Optimization By Incremental Modification Model,” Proceedings, 8th International Meshing Roundtable, South Lake Tahoe, CA, U.S.A., pp. 293–298.
Shim, K. W., Monaghan, D. J., and Armstrong, C. G., 2001, “Mixed Dimensional Coupling in Finite Element Stress Analysis,” Proceedings, 10th International Meshing Roundtable, Sandia National Laboratories, pp. 269–277.
Onodera, M., and Nishigaki, I., 2001, “Medial Surface Generation Technique for CAD-CAE Coupling,” Transactions of the Japan Society for Computational Engineering and Science.
Calabi,  L., and Hartnett,  W. E., 1968, “Shape Recognition, Prairie Fires, Convex Deficiencies and Skeletons,” Am. Math. Monthly, 75, pp. 335–342.
Meshkat,  S. N., and Sakkas,  C. M., 1987, “Voronoi Diagram for Multiply-Connected Polygonal Domains II: Implementation and application,” IBM J. Res. Dev., 31(3), pp. 373–381.
Srinivasan,  V., and Nackman,  L. R., 1987, “Voronoi Diagram for Multiply-Connected Polygonal Domains I: Algorithm,” IBM J. Res. Dev., 31(3), pp. 361–372.
Ramanathan,  M., and Gurumoorthy,  B., 2002, “Constructing Medial Axis Transform of Planar Domains with Curved Boundaries,” Comput.-Aided Des., 35, pp. 619–632.
Sapidis, N. S., and Perucchio, R., 1991, “Domain Delanuay Tetrahedrization of Arbitrarily Shaped Curved Polyhedra Defined in a Solid Modeling System,” Proc. Symposium on Solid Modeling Foundations and CAD/CAM Application, Ed. J. Rossignac and J. Turner, pp. 465–480.
Hoffman, C. M., 1994, “How to Construct the Skeleton of CSG Objects,” Computer-Aided Surface Geometry and Design, Oxford University Press, edited by Bowyer, A., pp. 421–437.
Turkiyyah,  G. M., Storti,  D., Ganter,  M., Chen,  H., and Vimawala,  M., 1997, “An Accelerated Triangulation Method for Computing the Skeletons of Free-form Solid Models,” Comput.-Aided Des. 29(1), pp. 5–19.
Etzion, M., and Rappoport, A., 1999, “Computing the Voronoi Diagram of a 3-D Polyhedron by Separate Computation of its Symbolic and Geometric Parts,” Proceedings, Fifth Symposium on Solid Modeling, Ann Arbor, MI, pp. 167–178.
Etzion,  M., and Rappoport,  A., 2002, “Computing Voronoi Skeletons of a 3-D Polyhedron by Space Subdivision,” Computational Geometry, 21, pp. 87–120.
Blum,  H., and Nagel,  R. N., 1978, “Shape Description using Weighted Symmetric Axis Features,” Pattern Recogn., 10, pp. 167–180.
Nackman,  L. R., 1982, “Curvature Relations in Three-Dimensional Symmetric Axes,” Comput. Graph. Image Process., 20, pp. 43–57.
Bronshtein, I. N., and Semendyayev, K. A., 1985, Handbook of Mathematics, Van Nostrand Reinhold Company, New York, NY.
Kim,  D-S., Hwang,  I-K., and Park,  B-J., 1995, “Representing the Voronoi Diagram of a Simple Polygon using Rational Quadratic Bezier Curves,” Comput.-Aided Des., 27 (8).
Pilkey, W. D., 2002, Analysis and Design of Elastic Beams: Computational Methods, John Wiley & Sons, New York.
Chou, P. C., and Pagano, N. J., 1992, Elasticity: Tensor, Dyadic and Engineering Approaches, Dover Publications, New York.
Rezayat,  M., 1996, “Midsurface Abstraction from 3D Solids Models: General Theory and Applications,” Comput.-Aided Des. 28(11), pp. 905–915.


Grahic Jump Location
Mid-element of a rectangle
Grahic Jump Location
Mid-element dimensional reduction
Grahic Jump Location
Mid-element based decomposition
Grahic Jump Location
Disjoint mid-elements for a dovetail
Grahic Jump Location
The skeleton of the dovetail
Grahic Jump Location
Interior skeletal point
Grahic Jump Location
Geometry of a skeletal curve
Grahic Jump Location
S-Voronoi versus Voronoi decomposition
Grahic Jump Location
S-Voronoi decomposition of dovetail
Grahic Jump Location
Singularity near a reentrant corner
Grahic Jump Location
Computed solution over the skeleton
Grahic Jump Location
Computed solution on the skeleton of a modified L-bracket




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