Methods to represent and exchange parts consisting of Functionally Graded Material (FGM) for Solid Freeform Fabrication (SFF) with Local Composition Control (LCC) are evaluated based on their memory requirements. Data structures for representing FGM objects as heterogeneous models are described and analyzed, including a voxel-based structure, finite-element mesh-based approach, and the extension of the Radial-Edge and Cell-Tuple-Graph data structures with Material Domains representing spatially varying composition properties. The storage cost for each data structure is derived in terms of the number of instances of each of its fundamental classes required to represent an FGM object. In order to determine the optimal data structure, the storage cost associated with each data structure is calculated for several hypothetical models. Limitations of these representation schemes are discussed and directions for future research also recommended.

1.
Jackson, T. R., 2000, “Analysis of Functionally Graded Material Object Representation Methods,” PhD. thesis, Massachusetts Institute of Technology (http://czms.mit.edu/cho/3dp/publications/trj-thesis.pdf).
2.
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,” Proceedings of 2000 ASME DETC/CIE, 26-th ASME Design Automation Conference, September, 2000, Baltimore, Maryland. p. 141 and CDROM.
3.
Cho, W., Sachs, E. M., Patrikalakis, N. M., Liu, H., Wu, H., Jackson, T. R., tratton, C. C., Serdy, J., Cima, M. J., and Resnick, R., 2001, “Methods for Distributed Design and Fabrication of Parts with Local Composition Control,” Proceedings of the 2001 NSF Design and Manufacturing Grantees Conference, Tampa, FL.
4.
Jackson, T. R., Patrikalakis, N. M., Sachs, E. M., and Cima, M. J., 1998, “Modeling and Designing Components with Locally Controlled Composition,” In D. L. Bourell et al, editor, Solid Freeform Fabrication Symposium, pp. 259–266, Austin, Texas. The University of Texas.
5.
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
,”
Materials and Design
,
20
(
2/3
), pp.
63
75
.
6.
Park, S.-M., Crawford, R. H., and Beaman, J. J., 2001, “Volumetric Multi-Texturing for Functionally Gradient Material Representation,” In D. C. Anderson, and K. Lee, editors, Sixth ACM Symposium on Solid Modeling and Applications, June 6–8, 2001, 216–224. ACM SIGGRAPH.
7.
Kumar, V., and Dutta, D., 1997, “An Approach to Modeling Multi-Material Objects,” In C. Hoffmann, and W. Bronsvort, editors, Fourth Symposium on Solid Modeling and Applications, Atlanta, Georgia, May 14–16, 1997, 336–353, ACM SIGGRAPH.
8.
Kumar
,
V.
, and
Dutta
,
D.
,
1998
, “
An Approach to Modeling and Representation of Heterogeneous Objects
,”
ASME J. Mech. Des.
,
120
, pp.
659
667
.
9.
Kumar
,
V.
,
Burns
,
D.
,
Dutta
,
D.
, and
Hoffmann
,
C.
,
1999
, “
A Framework for Object Modeling
,”
Comput.-Aided Des.
,
31
(
9
), pp.
541
556
.
10.
Bourell, D. L., Crawford, R. H., Marcus, H. L., Beaman, J. J., and Barlow, J. W., 1994, “Selective Laser Sintering of Metals,” In Proceedings of the 1994 ASME Winter Annual Meeting. Chicago, IL. pp. 519–528.
11.
Weiss
,
L. E.
,
Merz
,
R.
,
Prinz
,
F. B.
,
Neplotnik
,
G.
, and
Padmanabhan
,
P.
,
Schultz
,
L.
, and
Ramaswami
,
K.
,
1997
, “
Shape Deposition Manufacturing of Heterogeneous Structures
,”
SME Journal of Manufacturing Systems
,
16
(
4
), pp.
239
248
.
12.
Kaufman
,
A.
,
Cohen
,
D.
, and
Yagel
,
R.
,
1998
, “
Volume Graphics
,”
Computer
,
26
(
7
), pp.
51
64
.
13.
Manohar
,
S.
,
1999
, “
Advances in Volume Graphics
,”
Computers and Graphics
,
23
(
9
), pp.
73
84
.
14.
Chandru
,
V.
,
Manohar
,
S.
, and
Prakash
,
C. E.
,
1995
, “
Voxel-based Modeling for Layered Manufacturing
,”
IEEE Comput. Graphics Appl.
,
15
(
6
), pp.
42
47
.
15.
Pegna, J., and Safi, A., CAD, 1998 “Modeling of Multi-Modal Structures for Freeform Fabrication,” Presentation at Solid Freeform Fabrication Symposium, Austin, Texas. The University of Texas.
16.
Bardis, L., and Patrikalakis, N. M., 1994, Topological Structures for Generalized Boundary Representations, MIT Sea Grant Report 94-22.
17.
Brisson
,
E.
,
1993
, “
Representing Geometric Structures in d Dimensions: Topology and Order
,”
Discrete Comput. Geom.
,
9
, pp.
387
426
.
18.
Hu
,
C.-Y.
,
Patrikalakis
,
N. M.
, and
Ye
,
X.
,
1996
, “
Robust Interval Solid Modeling: Part I, Representations
,”
Comput.-Aided Des.
,
28
(
10
), pp.
807
817
.
19.
Ulichney, R., 1987, Digital Halftoning. Cambridge. MIT Press.
20.
Sachs, E., Haggerty, E. J., Cima, M., and Williams, P., 1993, Three-Dimensional Printing, U.S. Patent No. 5,204,055.
21.
Jakubenas
,
K. J.
,
Sanchez
,
J. M.
, and
Marcus
,
H. L.
,
1998
, “
Multiple Material Solid Free-form Fabrication by Selective Area Laser Deposition
,”
Materials and Design.
19
(1/2) pp.
11
18
. Elsevier Science.
22.
Jackson, I., Xiao, H., Ashtiani, M., and Berber L., 1996. “Stereolithography Model in Presurgical Planning of Craniofacial Surgery,” In D. L. Bourell et al, editor, Solid Freeform Fabrication Symposium. pp. 9–14. Austin, Texas. The University of Texas.
23.
Mazumder
,
J.
,
Choi
,
J.
,
Nagarathnam
,
K.
,
Koch
,
J.
, and
Hetzner
,
D.
,
1997
, “
Direct Metal Deposition of H13 Tool Steel for 3-D Components: Microstructure and Mechanical Properties
,”
J. Met.
,
49
(
5
), pp.
55
60
.
24.
Marsan, A., Kumar, V., and Dutta, D., and Pratz M., 1999, “An Assessment of Data Requirements and Data Transfer Formats for Layered Manufacturing,” NISTIR 6216. Gaithersburg, Maryland. U.S. Department of Commerce.
25.
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, editors, Geometric Modeling for CAD Applications. pp. 3–36. Elsevier Science Publishers, Holland.
26.
Gu¨rso¨z, E. L., Choi, Y., and Prinz, F. B., 1990, “Vertex-Based Representation of Non-Manifold Boundaries,” In M. J. Wozny, J. U. Turner, and K. Preiss, editors. Geometric Modeling for Product Engineering. pp. 107–130. Elsevier Science Publishers, Holland.
27.
Rossignac, J. R., and O’Connor, M. A., 1990, “SGC: A Dimension-Independent Model for Point Sets with Internal Structures and Incomplete Boundaries,” In M. J. Wozny, J. U. Turner, and K. Preiss, editors, Geometric Modeling for Product Engineering. Geometric Modeling for Product Engineering. pp. 145–180. Holland, Elsevier Science Publishers.
28.
Farin, G., Curves and Surfaces for Computer Aided Geometric Design—A Practical Guide, 3rd Edition, Academic Press, Inc., San Diego, CA.
29.
Tuohy
,
S. T.
,
Yoon
,
J. W.
, and
Patrikalakis
,
N. M.
,
1995
, “
Trivariate Parametric B-Splines for Visualization of Ocean Data
,”
In Proceedings of Oceans ’95: Challenges of Our Changing Global Environment.
3
, pp.
1601
1608
. San Diego, CA. 1601–1608. MTS/IEEE Oceanic Oceanic Engineering Society.
30.
Fang
,
L.
, and
Gossard
,
D. C.
,
1995
, “
Multidimensional Curve Fitting to Unorganized Data Points by Nonlinear Minimization
,”
Comput.-Aided Des.
,
27
(
1
), pp.
46
58
.
31.
Seidel
,
H.-P.
,
1990
, “
Symmetric Triangular Algorithms for Curves
,”
Comput.-Aided Des.
,
7
, pp.
57
67
.
32.
Shin
,
K. H.
, and
Dutta
,
D.
,
2001
, “
Constructive Representation of Heterogeneous Objects
,”
ASME J. Comput. Inf. Sci. Eng.
1
(
3
), pp.
205
217
.
33.
Shah, J., and Ma¨ntyla¨, M., 1995, Parametric and Feature-Based CAD/CAM, John Wiley, Inc.
34.
Qian, X., 2000, Feature Methodologies for Heterogeneous Object Realization, PhD. thesis, The University of Michigan.
35.
Qian
,
X.
, and
Dutta
,
D.
,
2001
, “
Feature Based Fabrication in Layered Manufacturing
,”
ASME J. Mech. Des.
,
123
(
3
), pp.
337
345
.
You do not currently have access to this content.