A locally refinable T-spline finite element method for CAD/CAE integration

Structural Engineering and Mechanics

Volumn 30, Issue 2, 2008, Pages 225-245

  Uhm, Tae Kyoung ^a   Kim, Ki Seung ^b   Seo, Yu Deok ^a   Youn, Sung Kie ^a  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

^b LIG Nex1   (South Korea)

Author keywords

Computer aided design (CAD); Computer aided engineering (CAE); Finite element method; Isogeometric analysis; Non uniform rational B splines (NURBS); T splines

Indexed keywords

COMPUTER AIDED ANALYSIS; COMPUTER AIDED DESIGN; COMPUTER AIDED ENGINEERING; INTERPOLATION; NUMERICAL METHODS; SPLINES;

ANALYSIS FRAMEWORKS; CAD/CAE INTEGRATED; CAD/CAE INTEGRATIONS; GEOMETRIC MODELING; ISOGEOMETRIC ANALYSIS; MATHEMATICAL TOOLS; NON-UNIFORM RATIONAL B-SPLINES; T-SPLINES;

FINITE ELEMENT METHOD;

EID: 52249117246     PISSN: 12254568     EISSN: None     Source Type: Journal    
DOI: 10.12989/sem.2008.30.2.225     Document Type: Article

References (33)

1. Bazilevs, Y., Calo, V.M., Zhang, Y. and Hughes, T.J.R. (2006), "Isogeometric fluid-structure interaction analysis with applications to arterial blood flow", Comput. Mech, 38, 310-322.
2. Cho, M. and Roh, H.Y. (2003), "Development of geometrically exact new shell elements based on general curvilinear co-ordinates", Int. J. Numer. Meth. Eng., 56, 81-115.
3. Cirak, F. and Ortiz, M. (2001), "Fully C-conforming subdivision elements for finite deformation thin-shell analysis", Int. J. Numer. Meth. Eng., 51, 813-833.
4. Cirak, F., Ortiz, M. and Schrder, P. (2000), "Subdivision surfaces: a new paradigm for thin-shell finite-element analysis", Int. J. Numer. Meth. Eng., 47, 2039-2072.
5. Cirak, F., Scott, M.J., Antonsson, E.K, Ortiz, M. and Schrder, P. (2002), "Integrated modeling, finite-element analysis, and engineering design for thin-shell structures using subdivision", Comput. Aided Des., 34, 137-148.
6. Cottrell, J.A., Hughes, T.J.R. and Reali, A. (2007), "Studies of refinement and continuity in isogeometric structural analysis", Comput. Meth. Appl. Mech Eng., 196, 4160-4183.
7. Cottrell, J.A., Reali, A., Bazilevs, Y. and Hughes, T.J.R. (2006), "Isogeometric analysis of structural vibrations", Comput. Meth. Appl. Mech. Eng., 195, 5257-5296.
8. Fan, S.C. and Luah, M.H. (1993), "Nine node spline element for free vibration analysis of general plates", J. Sound Tub., 165, 85-100.
9. Guthe, M., Balazs, A. and Klein, R. (2005), "GPU-based trimming and tessellation of NURBS and T-Spline surfaces", ACM T. Graphic, 24, 1016-1023.
10. Hughes, T.J.R., Cottrell, J.A. and Bazilevs, Y. (2005), "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement", Comput. Meth. Appl. Mech. Eng., 194, 4135-4195.
11. Inoue, K., Kikuchi, Y. and Masuyama, T. (2005), "A NURBS finite element method for product shape design", J. Eng Des., 16, 157-174.
12. Kim, J.H., Lee, C.S. and Kim, S.J. (2005), "High-performance domain-wise parallel direct solver for large-scale structural analysis", AIAA J., 43, 662-670.
13. Kim, K.-S. (2007), A study on T-spline Finite Element Analysis with Local Refinement, M.S. Dissertation, KAIST.
14. Kim, K.-S, Seo, Y.-D. and Youn, S.-K. (2007), "Spline-based finite element analysis with T-spline local refinement", Proceeding of the International Conference on Computational Methods (ICCM 2007), Hiroshima, Japan, p. 188.
15. Li, C.J, Wang, R.H. and Zhang, F. (2006), "Improvement on the dimensions of spline spaces on T-Mesh", J. Inf. Comput. Sci., 3, 235-244.
16. Moore, C.J, Yang, T.Y and Anderson, D.C. (1984), "New 48 D.O.F. quadrilateral shell element with variable-order polynomial and rational B-spline geometries with rigid body modes", Int. J. Numer. Meth. Eng., 20, 2121-2141.
17. Mortenson, M.E. (2006), Geometric Modeling, Industrial Press Inc., New York, NY.
18. Natekar, D., Zhang, X. and Subbarayan, G (2004), "Constructive solid analysis: A hierarchical, geometry-based meshless analysis procedure for integrated design and analysis", Comput. Aided Des., 36, 473-486.
19. Pengcheng, S. and Peixiang, H. (1995), "Bending analysis of plates and spherical shells by multivariable spline element method based on generalized variational principle", Comput. Struct., 55, 151-157.
20. Piegl, L.A. and Tiller, W. (1997), The NURBS Book (monographs in visual communication), Springer-Verlag , New York, NY.
21. Rayasam, M., Srinivasan, V. and Subbarayan, G. (2007), "CAD inspired hierarchical partition of unity constructions for NURBS-based, meshless design, analysis and optimization", Int. J. Numer. Meth. Eng., 72, 1452-1489.
22. Rogers, D.F. (2001), An Introduction to NURBS with Historical Perspective, Academic Press, San Diego, CA.
23. Ron, H.Y. and Cho, M. (2004), "The application of geometrically exact shell elements to B-spline surfaces", Comput. Meth. Appl. Mech. Eng., 193, 2261-2299.
24. Roh, H.Y. and Cho, M. (2005), "Integration of geometric design and mechanical analysis using B-spline functions on surface", Int. J. Numer. Meth. Eng., 62, 1927-1949.
25. Sederberg, T.W., Cardon, D.L., Finnigan, G.T, North, N.S, Zheng, J. and Lyche, T. (2004), "T-spline simplification and local refinement", ACM T. Graphie, 23, 276-283.
26. Sederberg, T.W., Zheng, J., Bakenov, A. and Nasri, A. (2003), 'T-splines and T-NURCCs", ACM T. Graphic., 22, 477-484.
27. Shen, P.-C. and Kan, H.-B. (1991), "Multivariate spline element analysis for plate bending problems", Comput. Struct., 40, 1343-1349.
28. Song, W. and Yang, X. (2005), "Free-form deformation with weighted T-spline", Visual Comput., 21, 139-151.
29. Timoshenko, S.P. and Goodier, J.N. (1987), Theory of Elasticity, McGraw-Hill, New York, NY.
30. Uhm, T.-K., Seo, Y.-D., Kim, H.-J. and Youn, S.-K. (2007), "T-spline finite element method with local refinement", Proceedings of 9th U.S. National Congress on Computational Mechanics, San Francisco, U.S., p. 291.
31. Zhang, X. and Subbarayan, G. (2006), "jNURBS: An object-oriented, symbolic framework for integrated, meshless analysis and optimal design", Adv. Eng. Softw., 37, 287-311.
32. Zhang, X., Rayasam, M. and Subbarayan, G. (2007), "A meshless, compositional approach to shape optimal design", Comput. Meth. Appl. Mech. Eng., 196, 2130-2146.
33. Zhang, Y., Bazilevs, Y., Goswami, S., Bajaj, C.L. and Hughes, T.J.R. (2007), "Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow", Comput. Meth. Appl. Mech. Eng., 196, 2943-2959.