A B-spline-based approach to heterogeneous objects design and analysis

CAD Computer Aided Design

Volumn 39, Issue 2, 2007, Pages 95-111

  Yang, Pinghai ^a   Qian, Xiaoping ^a  

^a Illinois Institute of Technology   (United States)

Author keywords

B spline finite element; Functionally graded materials; Heterogeneous object model; Integrated design and analysis; Material composite representation

Indexed keywords

COMPUTATIONAL GEOMETRY; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; SPLINES;

B-SPLINE FINITE ELEMENT; INTEGRATED DESIGN AND ANALYSIS; ISOMATERIAL SURFACE; MATERIAL COMPOSITE REPRESENTATION; MATERIAL PROPERTIES;

FUNCTIONALLY GRADED MATERIALS;

EID: 33846596586     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cad.2006.10.005     Document Type: Article

References (30)

1. Huang J., and Fadel G.M. Heterogeneous flywheel modeling and optimization. Journal of Materials and Design 21 (2000) 111-125 [Invited paper]
2. Park SM, Crawford RH, Beaman JJ. Volumetric multi-texturing for functionally graded material representation. In: Sixth ACM symposium on solid modeling and applications. 2001. p. 216-24
3. Pratt MJ. 3D modelling of material property variation for computer aided design and manufacture. In: Proceedings of the SIAM conference on Mathematics of industry: Challenges and frontiers. 2003. p. 58-83
4. Wang M.Y., Chen S.K., Wang X., and Mei Y. Design of multi-material compliant mechanisms using level set methods. ASME Transactions: Journal of Mechanical Design 127 5 (2005) 941-956
5. Patil L, Dutta D, Bhatt A, Jurrens K, Lyons K, Pratt M. Representation of heterogeneous objects in ISO 10303 (STEP). In: ASME international mechanical engineering congress and exposition. 2000
6. Qian X., and Dutta D. Physics-based modeling for heterogeneous objects. ASME Transactions: Journal of Mechanical Design 125 (2003) 416-427
7. Qian X., and Dutta D. Feature based design for heterogeneous objects. Computer-Aided Design 36 12 (2004) 1263-1278
8. Samanta K., and Koc B. Feature-based design and material blending for freeform heterogeneous object modeling. Heterogeneous Object Models and their Applications. Computer Aided Design 37 3 (2005) 287-305 [special issue]
9. Hyun S.J., Kim C., Son J.H., Shin S.H., and Kim Y.S. An efficient shape optimization method based on fem and b-spline curves and shaping a torque converter clutch disk. Finite Elements in Analysis & Design 40 (2004) 1803-1815
10. Kim J., and Paulino G.H. Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials. ASME Journal of Applied Mechanics 69 (2002) 502-514
11. Santare M.H., and Lambros J. Use of graded finite elements to model the behavior of nonhomogeneous materials. ASME Journal of Applied Mechanics 67 (2000) 819-822
12. Kumar V., and Dutta D. An approach to modeling and representation of heterogeneous objects. ASME Journal of Mechanical Design 120 4 (1998) 659-667
13. Jackson T. Analysis of functionally graded material representation methods, Ph.D. thesis. Cambridge (MA): Massachusetts Institute of Technology; 2000
14. Jackson T., Liu H., Patrikalakis N.M., Sachs E.M., and Cima M.J. Modeling and designing functionally graded material components for fabrication with local composition control. Materials and Design 20 2-3 (1999) 63-75
15. Biswas A, Shapiro V. Approximate distance fields for curves and surfaces. Technical report SAL, 2001-3. University of Wisconsin-Madison, Mechanical Engineering Department, SAL; 2001
16. Biswas A., Shapiro V., and Tsukanov I.G. Heterogeneous material modeling with distance fields. Computer Aided Geometric Design (2004) 215-242
17. Martin W, Cohen E. Representation and extraction of volumetric attributes using trivariate splines: A mathematical framework. In: Proceedings of the sixth ACM symposium on solid modeling and applications. 2001. p. 234-40
18. Wu Z, Seah HS, Lin F. NURBS-based volume modeling. In: International workshop on volume graphics. 1999. p. 321-30
19. Hua J., He Y., and Qin H. Trivariate simplex splines for inhomogeneous solid modeling in engineering design. ASME Transactions: Journal of Computing and Information Science in Engineering 5 2 (2005) 149-157
20. Gu P., Dao M., and Asaro R.J. A simplified method for calculating the crack tip field of functionally graded materials using the domain integral. ASME Journal of Applied Mechanics 66 (1999) 101-108
21. Rao B.N., and Rahman S. Mesh-free analysis of cracks in isotropic functionally graded materials. Engineering Fracture Mechanics 70 1 (2003) 1-27
22. Hughes T.J., Cottrell J.A., and Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Computer Methods in Applied Mechanics and Engineering 194 (2005) 4135-4195
23. Kagan P., Fischer A., and Bar-Yoseph P.Z. New B-spline finite element approach for geometrical design and mechanical analysis. International Journal for Numerical Methods in Engineering 41 (1998) 435-458
24. Piegl L., and Tiller W. The NURBS book. 2nd ed. (1997), Springer-Verlag, New York
25. Markworth A.J., Tamesh K.S., and Rarks Jr. W.P. Modeling studies applied to functionally graded materials. Journal of Materials Science 30 (1995) 2183-2193
26. Hashin Z. Analysis of composite materials-A survey. Journal of Applied Mechanics 105 (1983) 481-505
27. Shin K.H., and Dutta D. Process-planning for layered manufacturing of heterogeneous objects using direct metal deposition. Journal of Computing and Information Science in Engineering 2 4 (2002) 330-344
28. Sabin MA. Spline finite elements. Ph.D. thesis. http://www.damtp.cam.ac.uk/user/na/people/Malcolm. 2000
29. Gosz M. Finite element method: Applications in solids, structures and heat transfer (2005), Taylor and Francis CRC Press
30. Press W.H., Teukolsky S.A., Vetterling W.T., and Flannerty B.P. Numerical recipes in C: The art of scientific computing. 2nd ed. (1992), Cambridge University Press, New York