Step function representation of solid models and application to mesh free engineering analysis

Journal of Mechanical Design

Volumn 128, Issue 1, 2006, Pages 46-56

  Kumar, Ashok V ^a   Lee, Jongho ^a  

^a University of Florida   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; COMPUTER SIMULATION; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; SET THEORY;

BOOLEAN OPERATORS; COMPLEX SOLIDS; ENGINEERING ANALYSIS; IMPLICIT EQUATIONS; MESH-FREE METHODS; NONCONFORMING MESH; SOLID MODELS; STEP FUNCTIONS;

SOLIDS;

EID: 33645779491     PISSN: 10500472     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2121743     Document Type: Article

References (38)

1. Mortenson, M. E., 1997, Geometric Modeling, 2nd ed., Wiley Computer Publishing, Wiley, NY.
2. Hoffmann, C., 1989, Geometric and Solid Modeling: An Introduction, Morgan Kaufmann, San Francisco, CA.
3. Mäntylä, M., 1988, An Introduction to Solid Modeling, Computer Science Press, Rockville, Md.
4. Requicha, A. A. G., and Voelcker, H. B., 1982, "Solid Modeling: A Historical Summary and Contemporary Assessment," IEEE Comput. Graphics Appl., 2(2), pp. 9-24.
5. Lee, K., 1999, Principles of CAD/CAM/CAE System, Addison-Wesley, Reading. MA.
6. Requicha, A. A. G., and Voelcker, H. B., 1985, "Boolean Operations in Solid Modeling: Boundary Evaluation and Merging Algorithms," Proc. IEEE, 73(2), pp. 30-44.
7. Bloomenthal, J., 1997, Introduction to Implicit Surfaces, Morgan Kaufmann, San Francisco, CA.
8. Velho, L., Gomes, J., and Figueredo, L., 2002, Implicit Objects in Computer Graphics, Springer-Verlag, NY.
9. Lorensen, W., and Cline, H., 1987, "Marching Cubes: A High Resolution 3D Surface Construction Algorithm," Comput. Graph., 21(4), pp. 163-169.
10. Glassner, A., 1989, An Introduction to Ray Tracing, Academic, London.
11. Bajaj, C., et al., 1995, "Modeling with Cubic A-Patches," ACM Trans. Graphics, 14(2), pp. 103-133.
12. Zhao, H. K., Osher, S., Merriman, B., and Kang, M., 2000, "Implicit and Non-Parametric Shape Reconstruction from Unorganized Data using a Variational Level Set Method," Comput. Via. Image Underst., 80, pp. 295-314.
13. Lim, C. T., Ensz, M. T., Ganter, M. A., and Storti, D. W., 1997, "Object Reconstruction from Layered Data Using Implicit Solid Modeling," J. Manuf. Syst., 16(4), pp. 260-272.
14. Carr, J. C., Beatson, R. K., Cherrie, J. B., Mitchell, T. J., Fright, W. R., McCallum, B. C., and Evans, T. R., 2001, "Reconstruction and Representation of 3D Objects with Radial Basis Functions," pp. 67-76, Proceedings of SI-GRAPH2001.
15. Ohtake, Y., Belyaev, A., Alexa, M., Turk, G., and Seidel, H. P., 2002, "Multi-Level Partition of Unity Implicits," ACM Trans. Graphics, 22(3), pp. 463-470.
16. Pasko, A., Adzhiev, V., Sourin, A., and Savchenko, V., 1995, "Function Representation in Geometric Modeling: Concepts, Implementation and Applications," Visual Comput., 11(8), pp. 429-446.
17. Rvachev, V. L., and Shieko, T. I., 1995, "R-Functions in Boundary Value Problems in Mechanics," Appl. Mech. Rev., 48, pp. 151-188.
18. Lui, G. R., 2003, Mesh Free Methods: Moving Beyond the Finite Element Method, CRC Press, NY.
19. Kantorovich, L. V., and Krylov, V. I., 1958, Approximate Methods of Higher Analysis, Interscience, NY.
20. Shapiro, V., and Tsukanov, I., 1999, "Meshfree Simulation of Deforming Domains," CAD, 31, pp. 459-471.
21. Höllig, K., 2003, "Finite element methods with B-Splines," SIAM Series on Frontiers in Applied Mathematics.
22. Belytschko, T., Parimi, C., Moes, N., Sukamar, N., and Usui, S., 2003, "Structured Extended Finite Element Methods for Solids Defined by Implicit Surfaces," Int. J. Numer. Methods Eng., 56, pp. 609-635.
23. Osher, S., and Fedkiw, R., 2003, "Level Set Methods and Dynamic Implicit Surfaces," Applied Mathematical Sciences, Vol. 153, Springer Verlag, NY.
24. Miura, K. T., Pasko, A. A., and Savchenko, V. V., "Parametric Patches and Volumes in the Functional Representation of Geometric Solids," CSG 96 Set-theoretic Solid Modeling: Techniques and Applications, pp. 217-231.
25. Raviv, A., and Elber, G., 1999, "Three Dimensional Freeform Sculpting via Zero Sets of Scalar Trivariate Functions," Proceedings of the Fifth Symposium on Solid Modeling and Applications, ACM Press, pp. 246-257.
26. Kreyszig, E., 1999, Advanced Engineering Mathematics, 8th ed., Wiley, NY.
27. Zeid, I., 1991, CAD/CAM Theory and Practice, McGraw-Hill, NJ.
28. Hu, Z. J., and Ling, Z. K., 1996, "Swept Volumes Generated by the Natural Quadric Surfaces", Comput. Graphics, 20(2), pp. 263-274.
29. Hui, K. C., 1994, "Solid Modeling with Sweep-CSG Representation," CSG 94 Set Theoretic Solid Modeling: Techniques and Applications, pp. 119-131.
30. Crespin, B., Blanc, C., and Schlick, C., 1996, "Implicit Sweep Objects," Comput. Graph. Forum, 15(3), pp. 165-174.
31. Kumar, A. V., and Yu, L., 2001, "Sequential Constraint Imposition for Dimension-Driven Solid Models", CAD, 33(6), pp. 475-486.
32. Bathe, K. J., 1996, Finite Element Procedures, Prentice Hall, Englewood Cliffs, NJ.
33. Clark, B. W., and Anderson, D. C., 2002, "Finite Element Analysis in 3D Using the Penalty Boundary Method," Proceedings for DETC'02, ASME 2002 Computer and Information in Engineering Conference, Montreal, Canada, Sept. 29-Oct. 2, 2002.
34. Boresi, A. P., Schmidt, R. J., and Sidebottom, O. M., 1993, Advanced Mechanics of Materials, 5th ed., J Wiley, NY.
35. Xu, L., Huang, Z., and Yang, Y., 2004, "Mesh Theory for Toroidal Drive," ASME J. Mech. Des., 126(3), pp. 551-557.
36. Yamakawa, S., and Shimada, K., 2002, "Quad-Layer: Layered Quadrilateral Meshing of Narrow Two-Dimensional Domains by Bubble Packing and Chordal Axis Transformation," ASME J. Mech. Des., 124(3), pp. 564-573.
37. Kumar, A. V., 2000, "A Sequential Optimization Algorithm Using Logarithmic Barriers: Applications to Structural Optimization," ASME J. Mech. Des., 122(3), pp. 271-277.
38. Qian, X., and Dutta, D., 2002, "Physics-Based Modeling for Heterogeneous Objects," ASME J. Mech. Des., 125(3), pp. 416-427.