Constructive Representation of Heterogeneous Objects

[+] Author and Article Information
Ki-Hoon Shin, Debasish Dutta

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125

J. Comput. Inf. Sci. Eng 1(3), 205-217 (Jun 01, 2001) (13 pages) doi:10.1115/1.1403448 History: Received November 01, 2000; Revised June 01, 2001
Copyright © 2001 by ASME
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Bendsoe,  M., and Kikuchi,  N., 1988, “Generating Optimal Topologies in Structural Design Using a Homogenization Method,” Comput. Methods Appl. Mech. Eng., 71, pp. 197–224.
Cherkaev,  A., 1994, “Relaxation of Problems of Optimal Structural Design,” Int. J. Solids Struct., 31, No. 16, pp. 2251–2280.
Ashley,  S., 1991, “Rapid Prototyping Systems,” Mech. Eng. (Am. Soc. Mech. Eng.), pp. 34–43.
Rajagopalan,  S., Goldman,  R., Shin,  K. H., Kumar,  V., Cutkosky,  M., and Dutta,  D., 2001, “Representation of Heterogeneous Objects During Design, Processing and Freeform-Fabrication,” Mater. Des., 22, No. 3, pp. 185–197.
Jackson,  T. R., Liu,  H., Patrikalakis,  N. M., Sachs,  E. M., and Cima,  M. J., 1999, “Modeling and Designing Functionally Graded Material Components for Fabrication With Local Composition Control,” Mater. Des., 20, No. 2/3, pp. 63–75.
Jackson, T., 2000, “Analysis of Functionally Graded Material Representation Methods,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
Kumar, V. Ashok, and Wood, Aaron, 1999, “Representation and Design of Heterogeneous Components,” Proc. SFF Conference, Austin, TX.
Wu, Zhongke, Seah, Hock Soon, and Lin, Feng, 1999, “NURBS-Based Volume Modeling,” Proc. Int. Workshop on Volume Graphics, Swansea, pp. 321–330.
Park, S. M., Crawford R. H., and Beaman, J. J., 2000, “Functionally Gradient Material Representation by Volumetric Multi-Texturing for Solid Freeform Fabrication,” presented at the 11th Annual Solid Freeform Fabrication Symposium, Austin, TX.
Kumar,  V., and Dutta,  D., 1998, “An Approach to Modeling and Representation of Heterogeneous Objects,” ASME J. Mech. Des., 120, No. 4, pp. 659–667.
Kumar, V., 1998, “Solid Modeling and Algorithms for Heterogeneous Objects,” Ph.D. Thesis, Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI.
Requicha,  A., 1980, “Representation for Rigid Solids: Theory, Methods and Systems,” Computing Surveys, 12, No. 4.
Hoffman, C., 1989, Geometric & Solid Modeling, Morgan Kaufmann Publishers.
Liu, H., Cho, W., Jackson, T. R., Patrikalakis, N. M., and Sachs, E. M., 2000, “Algorithms for Design and Interrogation of Functionally Gradient Material Objects,” Proc. ASME 26th Design Automation Conference, Baltimore, MD, Paper No. DETC2000/DAC-14278.
Suresh,  S., and Mortensen,  A., 1997, “Functionally Graded Metals and Metal-Ceramic Composites: Thermomechanical Behavior,” Int. Mater. Rev., 42, No. 3, pp. 85–116.
Shepard, D., 1968, “A Two-Dimensional Interpolation Function for Irregularly Spaced Data,” Proc. 23 Nat. Conf. ACM, pp. 517–524.
Alfeld,  P., 1985, “Multivariate Perpendicular Interpolation,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal., 22, pp. 96–106.
Rvachev, V. L., Sheiko, T. I., Shapiro, V., and Tsukanov, I., 2000, “Transfinite Interpolation Over Implicitly Defined Sets,” Technical Report SAL 2000-1, Spatial Automation Lab., Univ. of Wisconsin.
Rvachev,  V. L., 1967, “Theory of R-Functions and Some Applications,” Naukova Dumka, in Russian.
ACIS Geometric Modeler: Application Guide, 1995, Spatial Technology Inc.
Weiler, K. J., 1986, “The Radial Edge Structure: A Topological Representation for Non-Manifold Geometric Modeling,” in: M. J. Wozny, H. McLaughlin, and J. Encarnacao, eds., Geometric Modeling for CAD Applications, Elsevier Science Publishers, Holland, pp. 3–36.
Bhashyam, S., Shin, K. H., and Dutta, D., 2000, “An Integrated CAD System for Design of Heterogeneous Objects,” Rapid Prototyping J., 6, No. 2, pp. 119–135.
Donomoto T., Miura N., Funatani K., and Miyake N., 1983, SAE Tech. Paper No. 83052, Detroit, MI.


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A prototype of the biomechanical arm
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A heterogeneous modeling space for cylindrical material coordinates
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Effective material function domain
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Geometry-independent material functions
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Distance-based material functions
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Material function coordinates in inverse distance blending
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A simple mold created by a blending function
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Material coordinate transform for sweeping functions
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Material distribution on the cross section of the cooling channel
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Mold assembly embedding conformable cooling channels
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Multiple sets of material composition functions
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Three different hb-sets constructed by a material union operation
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Material intersection, difference, and partition
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Model hierarchy in the constructive representation
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Data structure representing an hp-set
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Data structure representing an h-object
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Construction of the biomechanical arm
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Piston head with Metal Matrix Composite (MMC)



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