Solidification of metal castings can be modeled by an implicit real-valued function whose behavior is determined by physical parameters prescribed on the boundary of a casting. We show how to construct such functions using theory of R-functions for two-dimensional castings represented by their boundaries. The parameterized form of the constructed functions is convenient for studying, controlling, and optimizing their behavior in terms of the physical parameters specified on the boundary of the casting. The proposed approach can also be used for modeling multiple cavities in a same sand mold, generalizes to three-dimensional castings, and is applicable to other physical phenomena that may be suitable for analysis based on empirical knowledge.

1.
Chvorinov
N.
, “
Theory of Solidification of Casting
,”
Die Giesserei
, Vol.
27
, May 17 to June 14,
1940
, pp.
17
224
.
2.
Hubbard
T. J.
, and
Antonsson
E. K.
, “
Emergent Faces in Crystal Etching
,”
Journal of Microelectromechanical Systems
, Vol.
3
, No.
1
, March
1994
, pp.
19
27
.
3.
Kota
S.
,
Ananthasuresh
G. K.
,
Crary
S. B.
, and
Wise
K. D.
, “
Design and Fabrication of Microelectromechanical Systems
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
116
, December
1994
, pp.
1081
1087
.
4.
Kutsenko, L. H., Computer Graphics in Design Problems, Series “Mathematics and Cybernetics,” No. 8. Znaniye, Moscow, 1990, In Russian.
5.
Kutsenko, L. H., and Markin, L. V., Shapes and Formulas, MAI Publisher, Moscow, 1994, In Russian.
6.
Mikhailov, A. M., Bauman, B. V., and Blagov, B. N., Metal Casting Manufacturing, Machinostroyenie, Moscow, 1987, In Russian.
7.
Neises, S. J., Uicker, J. J., Jr., and Heine, R. W., “Geometric Modeling of Directional Solidification Based on Section Modulus,” AFS Transactions, Vol. 95, 1987.
8.
Ricci
A.
, “
A Constructive Geometry for Computer Graphics
,”
Computer Journal
, Vol.
16
, No.
3
, May
1973
, pp.
157
160
.
9.
Rvachev, V. L., Theory of R-functions and Some Applications, Naukova Dumka, Kiev, 1982, In Russian.
10.
Rvachev, V. L., Geometric Applications of Logic Algebra, Naukova Dumka, Kiev, 1967, In Russian.
11.
Rvachev, V. L., and Sheiko, T. I., “R-functions in Boundary Value Problems in Mechanics,” ASME Applied Mechanics Reviews, Vol. 48, No. 4, April 1995.
12.
Rvachev, V. L., and Shevchenko, A. N., Problem-oriented Languages and Systems for Engineering Computations, Teknika, Kiev, 1988, In Russian.
13.
Shapiro, V., Theory of R-functions and Applications: A Primer, Tech. Report CPA88-3 Cornell Programmable Automation, Cornell University, Ithaca, NY, November 1988.
14.
Shapiro
V.
, “
Real Functions for Representation of Rigid Solids
,”
Computer Aided Geometric Design
, Vol.
11
,
1994
, pp.
153
175
.
15.
Uicker, J. J. Jr., and Sather, L. E., “SWIFT: A Modulus Approach to the Simulation of the Casting Process,” Ductile Iron Solidification Modeling, Vol. 176, 1992.
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