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http://dx.doi.org/10.3795/KSME-A.2009.33.2.135

T-spline FEA for Trimmed NURBS Surface  

Kim, Hyun-Jung (KAIST 기계공학과)
Seo, Yu-Deok (KAIST 기계공학과)
Youn, Sung-Kie (KAIST 기계공학과)
Publication Information
Transactions of the Korean Society of Mechanical Engineers A / v.33, no.2, 2009 , pp. 135-144 More about this Journal
Abstract
In this present work, spline FEA for the trimmed NURBS surface of the 2D linear elasticity problem is presented. The main benefit of the proposed method is that no additional efforts for modeling of trimmed NURBS surfaces are needed and the information of the trimming curves and trimmed surfaces exported from the CAD system can be directly used for analysis. For this, trimmed elements are searched by using NURBS projection scheme. The integration of the trimmed elements is performed by using the NURBS-enhanced integration scheme. The formulation of constructing stiffness matrix of trimmed elements is presented. In this formulation, the information of the trimming curve is used for calculating the Jacobian as well as for obtaining integration points. The robustness and effectiveness of the proposed method are investigated through various numerical examples.
Keywords
Trim NURBS Surface; NURBS; T-Spline; Spline FEM;
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Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By SCOPUS : 0
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1 Sevilla, R., Mendez, S. F. and Huerta, A., 2008, “NURBS-Enhanced Finite Element Method(NEFEM),” International Journal for Numerical Methods in Engineering, Vol. 76, pp. 56-83   DOI   ScienceOn
2 Cho, M. and Roh, H. Y., 2003, “Development of Geometrically Exact New Shell Elements Based on General Curvilinear Co-Ordinates,” International Journal for Numerical Methods in Engineering, Vol. 56, pp. 81-115   DOI   ScienceOn
3 Hughes, T. J. R., Cottrell, J. A. and Bazilevs, Y., 2005, “Isogeometric Analysis : CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement,” Computer Methods in Applied Mechanics and Engineering, Vol. 194, pp 4135-4195   DOI   ScienceOn
4 Bazilevs, Y., Calo, V.M., Cottrell, J. A., Hughes, T. J. R., Reali, A., Scovazzi, G., 2007, “Variational Multiscale Residual-Based Turbulence Modeling for Large Eddy Simulation of Incompressible Flows,” Computer Methods in Applied Mechanics and Engineering, Vol. 197, pp. 173-201   DOI   ScienceOn
5 Bazilevs, Y., Calo, V. M., Zhang, Y., Hughes, T. J. R., 2006, “Isogeometric Fluid-Structure Interaction Analysis with Applications to Arterial Blood Flow,” Computational Mechanics, Vol. 38, pp. 310-322   DOI
6 Sederberg, T. W., Zheng, J., Bakenov, A., Nasri, A., 2003, “T-splines and T-NURCCs,” ACM Transactions on Graphics, Vol. 22, pp. 477-484   DOI   ScienceOn
7 Sederberg, T. W., Cardon, D. L., Finnigan, G. T., North, N. S., Zheng, J., Lyche, T., 2004, “T-Spline Simplification and Local Refinement,” ACM Transactions on Graphics, Vol. 23, pp. 276-283   DOI   ScienceOn
8 Cottrell, J. A., Hughes, T. J. R. and Reali, A., 2007, “Studies of Refinement and Continuity in Isogeo-metric Structural Analysis,” Computer Methods in Applied Mechanics and Engineering, Vol. 196, pp. 4160-4183   DOI   ScienceOn
9 Roh, H. Y. and Cho, M., 2004, “The Application of Geometrically Exact Shell Elements to B-Spline Surfaces,” Computer Methods in Applied Mechanics and Engineering, Vol. 193, pp. 2261- 2299   DOI   ScienceOn
10 Roh, H. Y. and Cho, M., 2005, “Integration of Geometric Design and Mechanical Analysis Using B-Spline Functions on Surface,” International Journal for Numerical Methods in Engineering, Vol. 62, pp. 1927-1949   DOI   ScienceOn
11 Cottrell, J. A., Reali, A., Bazilevs, Y., Hughes, T. J. R., 2006, “Isogeometric Analysis of Structural Vibrations,” Computer Methods in Applied Mechanics and Engineering, Vol. 195, pp. 5257-5296   DOI   ScienceOn
12 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,” Computer Methods in Applied Mechanics and Engineering, Vol. 196, pp. 2943-2959   DOI   ScienceOn
13 Sevilla, R., Mendez, S. F., and Huerta, A., 2008, “NURBS-Enhanced Finite Element Method for Euler Equations,” International Journal for Numerical Methods in Fluids, Vol. 57, pp.1051-1069   DOI   ScienceOn
14 Uhm, T. K., Kim, K. S., Seo, Y. D. and Youn, S. K., 2008, “A Locally Refinable T-spline Finite Element Method for CAD/CAE Integration,” Structural Engineering & Mechanics, Vol. 30, pp. 225-245   DOI   ScienceOn
15 Reed, K., Harrod, Jr D., Conroy, W., 1990, “The Initial Graphics Exchange Specification(IGES) (Version 5.0),” US Department of Commerce
16 Piegl, L. A., Tiller, W., 1997, The NURBS Book (Monographs in Visual Communication), Springer-Verlag, New York
17 Timoshenko, S. P. and Goodier, J. N., 1987, “Theory of Elasticity, 3rd edition,” McGraw-Hill, New York
18 Habbitt, K. and Sorensen, Inc., 1998, “ABAQUS Theory Manual, Version 5.8”