DOI QR코드

DOI QR Code

T-spline Finite Element Method for CAD/CAE Integrated Approach

CAD/CAE 통합 접근을 위한 T-스플라인 유한요소법

  • Published : 2009.02.01

Abstract

T-splines are recently proposed geometric modeling tools. A T-spline surface is a NURBS surface with T-junctions and is defined by a control grid called T-mesh. Local refinement can be performed very easily for T-splines while it is limited for B-splines or NURBS. Using T-splines, patches with unmatched boundaries can be combined easily without special technique. In this study, the analysis methodology using T-splines is proposed. In this methodology, T-splines are used both for description of geometries and for approximation of solution spaces. Two-dimensional linear elastic and dynamic problems will be solved by employing the proposed T-spline finite element method, and the effectiveness of the current analysis methodology will be verified.

Keywords

References

  1. Hughes, T. J. R., Cottrell, J. A. and Bazilevs, Y., 2005, “Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement,” Comput. Methods Appl. Mech. Engrg., Vol. 194, pp. 4135-4195 https://doi.org/10.1016/j.cma.2004.10.008
  2. 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., Vol. 38, pp. 310-322 https://doi.org/10.1007/s00466-006-0084-3
  3. Cottrell, J. A., Reali, A., Bazilevs, Y. and Hughes, T. J. R., 2006, “Isogeometric Analysis of Structural Vibrations,” Comput. Methods Appl. Mech. Engrg., Vol. 195, pp. 5257-5296 https://doi.org/10.1016/j.cma.2005.09.027
  4. Cottrell, J. A., Hughes, T. J. R. and Reali, A., 2007, “Studies of Refinement and Continuity in Isogeometric Structural Analysis,” Comput. Methods Appl. Mech. Engrg., Vol. 196, pp. 4160-4183 https://doi.org/10.1016/j.cma.2007.04.007
  5. 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. Methods Appl. Mech. Engrg., Vol. 196, pp. 2943-2959 https://doi.org/10.1016/j.cma.2007.02.009
  6. Roh, H. Y. and Cho, M., 2004, “The Application of Geometrically Exact Shell Elements to B-Spline Surfaces,” Comput. Methods Appl. Mech. Engrg., Vol. 193, pp. 2261-2299 https://doi.org/10.1016/j.cma.2004.01.019
  7. Roh, H. Y. and Cho, M., 2005, “Integration of Geometric Design and Mechanical Analysis Using B-Spline Functions on Surface,” Int. J. Numer. Meth. Engng.,Vol. 62, pp. 1927-1949 https://doi.org/10.1002/nme.1254
  8. Cirak, F., Ortiz, M. and Schroder, P., 2000, “Subdivision Surfaces: a New Paradigm for Thin-Shell Finite-Element Analysis”, Int. J. Numer. Meth. Engng., Vol. 47, pp. 2039-2072 https://doi.org/10.1002/(SICI)1097-0207(20000430)47:12<2039::AID-NME872>3.0.CO;2-1
  9. Cirak, F. and Ortiz, M., 2001, “Fully $C^1$-Conforming Subdivision Elements for Finite Deformation Thin-Shell Analysis,” Int. J. Numer. Meth. Engng., Vol. 51, pp. 813-833 https://doi.org/10.1002/nme.182
  10. Cirak, F., Scott, M. J., Antonsson, E. K., Ortiz, M. and Schröder P., 2002, “Integrated Modeling, Finite-Element Analysis, and Engineering Design for Thin-Shell Structures Using Subdivision,” Comput. Aided Design, Vol. 34, pp. 137-148 https://doi.org/10.1016/S0010-4485(01)00061-6
  11. Sederberg, T. W., Zheng, J., Bakenov, A. and Nasri, A., 2003, “T-splines and T-NURCCs,” ACM T. Graphic., Vol. 22, pp. 477-484 https://doi.org/10.1145/882262.882295
  12. 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. Graphic., Vol. 23, pp. 276-283 https://doi.org/10.1145/1015706.1015715

Cited by

  1. Study on the Local Refinement in Spline Finite Element Method by Using Hierarchical B-spline vol.34, pp.8, 2010, https://doi.org/10.3795/KSME-A.2010.34.8.1007