Isogeometric analysis of trimmed NURBS geometries

Computer Methods in Applied Mechanics and Engineering

Volumn 241-244, Issue , 2012, Pages 93-111

  Schmidt, Robert ^a   Wüchner, Roland ^a   Bletzinger, Kai Uwe ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Bending strip; Isogeometric analysis; Isogeometric load design; Kirchhoff Love shell; Multi patch analysis; Trimmed NURBS

Indexed keywords

ISOGEOMETRIC ANALYSIS; KIRCHHOFF-LOVE SHELL; LOAD DESIGN; MULTI-PATCH ANALYSIS; TRIMMED NURBS;

COMPUTATIONAL METHODS; COMPUTER APPLICATIONS;

LOADING;

EID: 84862994818     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2012.05.021     Document Type: Article

References (38)

1. Bazilevs Y., Calo V.M., Cottrell J.A., Evans J.A., Hughes T.J.R., Lipton S., Scott M.A., Sederberg T.W. Isogeometric analysis using T-splines. Comput. Methods Appl. Mech. Engrg. 2010, 199:229-263.
2. Bazilevs Y., Calo V.M., Cottrell J.A., Hughes T.J.R., Reali A., Scovazzi G. Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput. Methods Appl. Mech. Engrg. 2007, 197:173-201.
3. Bazilevs Y., Calo V.M., Hughes T.J.R., Zhang Y. Isogeometric fluid-structure interaction: theory algorithms, and computations. Comput. Mech. 2008, 43:3-37.
4. Belytschko T., Liu W.K., Moran B. Nonlinear Finite Elements for Continua and Structures 2000, Wiley.
5. Borden M.J., Scott M.A., Evans J.A., Hughes T.J.R. Isogeometric finite element data structures based on Bézier extraction of NURBS. Int. J. Numer. Methods Engrg. 2011, 87:15-47.
6. Burkhart D., Hamann B., Umlauf G. Iso-geometric analysis based on Catmull-Clark solid subdivision. Comput. Graph. Forum 2010, 29(5):1575-1784.
7. 1-continuity between two patches of adjacent cubic NURBS surface. Comput. Aid. Des. Comput. Graph. 2007, 15:425-428.
8. Cirak F., Long Q. Subdivision shells with exact boundary control and non-manifold geometry. Int. J. Numer. Methods Engrg. 2011, 10.1002/nme.3206.
9. Cirak F., Ortiz M., Schröder P. Subdivision surfaces: a new paradigm for thin-shell finite-element analysis. Int. J. Numer. Methods Engrg. 2000, 47:2039-2072.
10. E. Cohen, R.F. Riesenfeld, G. Elber, Geometric modeling with splines: an introduction, AK Peters, 2001.
11. De Lorenzis L., Wriggers P., Zavarise G. A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented lagrangian method. Comput. Mech. 2011, 10.1007/s00466-011-0623-4.
12. Dörfel M.R., Jüttler B., Simeon B. Adaptive isogeometric analysis by local h-refinement with T-splines. Comput. Methods Appl. Mech. Engrg. 2010, 199:264-275.
13. Düster A., Parvizian J., Yang Z., Rank E. The finite cell method for three-dimensional problems of solid mechanics. Comput. Methods Appl. Mech. Engrg. 2008, 197:3768-3782.
14. Embar A., Dolbow J., Harari I. Imposing Dirichlet boundary conditions with Nitsche's method and spline-based finite elements. Int. J. Numer. Methods Engrg. 2010, 83:877-898.
15. G. Farin, Curves and Surfaces for CAGD, Morgan Kaufmann, fifth ed., 2002.
16. Farin G., Hoschek J., Kim M.-S. Handbook of Computer Aided Geometric Design 2002, Elsevier Science B.V.
17. Hughes T.J.R., Cottrell J.A., Bazilevs Y. Isogeometric analysis: CAD finite elements NURBS exact geometry and mesh refinement. Comput. Methods Appl. Mech. Engrg. 2005, 194:4135-4195.
18. Hughes T.J.R. The Finite Element Method Linear Static and Dynamic Finite Element Analysis 2000, Dover Publications Inc.
19. Kiendl J., Bazilevs Y., Hsu M.C., Wüchner R., Bletzinger K.-U. The bending strip method for isogeometric analysis of Kirchhoff-Love shell structures comprised of multiple patches. Comput. Methods Appl. Mech. Engrg. 2010, 199:2403-2416.
20. Kiendl J., Bletzinger K.-U., Linhard J., Wüchner R. Isogeometric shell analysis with Kirchhoff-Love elements. Comput. Methods Appl. Mech. Engrg. 2009, 198:3902-3914.
21. Kim H.-J., Seo Y.-D., Youn S.-K. Isogeometric analysis for trimmed CAD surfaces. Comput. Methods Appl. Mech. Engrg. 2009, 198:2982-2995.
22. Kim H.-J., Seo Y.-D., Youn S.-K. Isogeometric analysis with trimming technique for problems of arbitrary complex topology. Comput. Methods Appl. Mech. Engrg. 2010, 199:2796-2812.
23. McNeel, Rhinoceros-NURBS modeling for windows. Website. http://www.rhino3d.com.
24. Mitchell T.J., Govindjee S., Taylor R.L. A method for enforcement of Dirichlet boundary conditions in isogeometric analysis. Recent Developments and Innovative Applications in Computational Mechanics 2011, 283-293. Springer-Verlag. D. Mueller-Hoeppe, S. Loehnert, S. Reese (Eds.).
25. Nguyen-Thanh N., Kiendl J., Nguyen-Xuan H., Wüchner R., Bletzinger K.-U., Bazilevs Y., Rabczuk T. Rotation free isogeometric thin shell analysis using PHT-splines. Comput. Methods Appl. Mech. Engrg. 2011, 200:3410-3424.
26. Parvizian J., Düster A., Rank E. Finite cell method - h- and p-extension for embedded domain problems in solid mechanics. Comput. Mech. 2007, 41:121-133.
27. Piegl L., Tiller W. The NURBS Book 1997, Springer, second ed.
28. Rogers D.F. An Introduction to NURBS with Historical Perspective 2001, Academic Press.
29. Schmidt R., Kiendl J., Bletzinger K.-U., Wüchner R. Realization of an integrated structural design process: analysis-suitable geometric modelling and isogeometric analysis. Comput. Visual Sci. 2010, 13:315-330.
30. Schumaker Larry L. Spline Functions: Basic Theory 2007, Cambridge University Press.
31. Scott M.A., Borden M.J., Verhoosel C.V., Sederberg T.W., Hughes T.J.R. Isogeometric finite element data structures based on Bézier extraction of T-splines. Int. J. Numer. Methods Engrg. 2011, 10.1002/nme.3167.
32. Temizer I., Wriggers P., Hughes T.J.R. Contact treatment in isogeometric analysis with NURBS. Comput. Methods Appl. Mech. Engrg. 2011, 200:1100-1112.
33. Vuong A.-V., Giannelli C., Jüttler B., Simeon B. A hierarchical approach to adaptive local refinement in isogeometric analysis. Comput. Methods Appl. Mech. Engrg. 2011, 200:3554-3567.
34. Wall W.A., Frenzel M.A., Cyron C. Isogeometric structural shape optimization. Comput. Methods Appl. Mech. Engrg. 2008, 197:2976-2988.
35. Zienkiewicz O.C., Taylor R.L., Zhu J.Z. The finite element method, Its Basis and Fundamentals 2005, Elsevier, Oxford. 6th ed.
36. K. Höllig, Finite Element Methods with B-Splines, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2003.
37. Höllig K., Reif U. Nonuniform web-splines. Comput. Aid. Geom. Des. 2003, 20:277-294.
38. Höllig K., Reif U., Wipper J. Weighted extended B-spline approximation of dirichlet problems. SIAM J. Numer. Anal. 2001, 39:442-462.