Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

T-spline FEA for Trimmed NURBS Surface

트림 NURBS 곡면의 T-스플라인 유한요소해석

  • Published : 2009.02.01
Download PDF
⟨ Previous Next ⟩

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

References

  1. 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 https://doi.org/10.1002/nme.546
  2. 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 https://doi.org/10.1016/j.cma.2004.01.019
  3. 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 https://doi.org/10.1002/nme.1254
  4. 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 https://doi.org/10.1016/j.cma.2004.10.008
  5. 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 https://doi.org/10.1016/j.cma.2007.04.007
  6. 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 https://doi.org/10.1016/j.cma.2005.09.027
  7. 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 https://doi.org/10.1016/j.cma.2007.07.016
  8. 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 https://doi.org/10.1016/j.cma.2007.02.009
  9. 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 https://doi.org/10.1007/s00466-006-0084-3
  10. Sederberg, T. W., Zheng, J., Bakenov, A., Nasri, A., 2003, “T-splines and T-NURCCs,” ACM Transactions on Graphics, Vol. 22, pp. 477-484 https://doi.org/10.1145/882262.882295
  11. 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 https://doi.org/10.1145/1015706.1015715
  12. 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 https://doi.org/10.12989/sem.2008.30.2.225
  13. Reed, K., Harrod, Jr D., Conroy, W., 1990, “The Initial Graphics Exchange Specification(IGES) (Version 5.0),” US Department of Commerce
  14. Piegl, L. A., Tiller, W., 1997, The NURBS Book (Monographs in Visual Communication), Springer-Verlag, New York
  15. 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 https://doi.org/10.1002/nme.2311
  16. 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 https://doi.org/10.1002/fld.1711
  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”