Browse > Article
http://dx.doi.org/10.3795/KSME-A.2010.34.8.1007

Study on the Local Refinement in Spline Finite Element Method by Using Hierarchical B-spline  

Hah, Zoo-Hwan (School of Mechanical, Aerospace and Systems Engineering, Division of Mechanical Engineering, KAIST)
Kim, Hyun-Jung (School of Mechanical, Aerospace and Systems Engineering, Division of Mechanical Engineering, KAIST)
Youn, Sung-Kie (School of Mechanical, Aerospace and Systems Engineering, Division of Mechanical Engineering, KAIST)
Publication Information
Transactions of the Korean Society of Mechanical Engineers A / v.34, no.8, 2010 , pp. 1007-1013 More about this Journal
Abstract
A new local refinement scheme for spline finite element method has been proposed; this scheme involves the use of hierarchical B-spline. NURBS has been widely used in CAD; however, the local refinement of NURBS is difficult due to its tensor-product property. In this study, we attempted to use hierarchical B-splines as local refinement strategy in spline FEM. The regions of high gradients are overlapped by hierarchically-created local meshes. Knot vectors and control points in local meshes are extracted from global meshes, and they are refined using specific schemes. Proper compatibility conditions are imposed between global and local meshes. The effectiveness of the proposed method is verified on the basis of numerical results. Further, it is shown that by using a proposed local refinement scheme, the accuracy of the solution can be improved and it could be higher than that of the solution of a conventional spline FEM with relatively lower degrees of freedom.
Keywords
Spline FEM; NURBS; Hierarchical B-spline;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By SCOPUS : 0
연도 인용수 순위
1 Sederberg, T. W., Zheng, J., Bakenov, A. and Nasri, A., 2003, “T-splines and T-NURCCs,” ACM transactions on graphics, Vol. 22, No. 3, pp.477-484.   DOI   ScienceOn
2 Forsey, D. R. and Bartels, R. H., 1988, “Hierarchical B-Spline Refinement,” Computer Graphics, Vol. 22, No. 5, pp. 205-212.   DOI
3 Bazilevs, Y., Calo, V.M., Cottrell, J. A., Evans, J. A., Hughes, T. J. R., Lipton, S., Scott, M. A. and Sederberg, T. W., 2010, “Isogeometric Analysis using T-Splines,” Computer Methods in Applied Mechanics and Engineering, Vol. 199, No. 5, pp. 229-263.   DOI   ScienceOn
4 Uhm, T. K., Kim, K. S., Seo, Y. D. and Youn, S. K., 2009, “T-spline Finite Element Method for CAD/CAE Integrated Approach,” Trans. of the KSME(A), Vol. 33, No. 2, pp. 127-134.   과학기술학회마을   DOI   ScienceOn
5 Piegel, L. A. and Tiller, W., 1997, The NURBS book (Monographs in Visual Communication), Springer-Verlag, New York, pp.142-161.
6 Fish, J., 1992, “The s-Version of the Finite Element Method,” Computers & Structures, Vol. 43, No. 3, pp. 539-547.   DOI   ScienceOn
7 Fernandez-Mendez, S. and Hureta, A., 2004, “Imposing Essential Boundary Conditions in Mesh-Free Methods,” Computer Methods in Applied Mechanics and Engineering, Vol. 193, pp. 1257-1275.   DOI   ScienceOn
8 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