Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids

Computer Methods in Applied Mechanics and Engineering

Volumn 200, Issue 21-22, 2011, Pages 1892-1908

  Nguyen Thanh, N ^a   Nguyen Xuan, H ^b,c   Bordas, S P A ^d   Rabczuk, T ^a  

^a BAUHAUS UNIVERSITY WEIMAR   (Germany)

^b UNIVERSITY OF NATURAL SCIENCES   (Viet Nam)

^c TON DUC THANG UNIVERSITY   (Viet Nam)

^d CARDIFF UNIVERSITY   (United Kingdom)

Author keywords

Isogeometric analysis; PHT spline; T meshes; T spline

Indexed keywords

COMPLEX GEOMETRIES; ELASTIC SOLIDS; FINITE ELEMENT; ISOGEOMETRIC ANALYSIS; LOCAL REFINEMENT; LOCAL SUPPORT; NON-NEGATIVITY; NUMERICAL EXAMPLE; PARTITION OF UNITY; PHT-SPLINE; POLYNOMIAL SPLINES; SHAPE FUNCTIONS; STANDARD FINITE ELEMENT; T-MESHES; T-SPLINES;

FUNCTION EVALUATION; NUMERICAL METHODS; POLYNOMIAL APPROXIMATION;

SPLINES;

EID: 79952700593     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2011.01.018     Document Type: Article

References (44)

1. 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.
2. Echter R., Bischoff M. Numerical efficiency, locking and unlocking of NURBS finite elements. Comput. Methods Appl. Mech. Engrg. 2010, 199:374-382.
3. Höllig K. Finite Element Methods with B-splines 2003, Society for Industrial and Applies Mathematics, Philadelphia.
4. Sevilla R., Fernandez-Mendez S., Huerta A. Nurbs-enhanced finite element method (NEFEM). Int. J. Numer. Methods Engrg. 2008, 76:56-83.
5. Shaw A., Roy D. NURBS-based parametric mesh-free methods. Comput. Methods Appl. Mech. Engrg. 2008, 197:1541-1567.
6. Szabo B., Duester A., Rank E. The p-version of the finite element method. Fundamentals, Encyclopedia in Computational Mechanics 2004, 1. Wiley, New York, (Chapter 5).
7. Bazilevs Y., Calo V.M., Cottrell J.A., Evans J.A., Hughes T.J.R., Lipton S., Scottand M.A., Sederberg T.W. Isogeometric analysis using T-splines. Comput. Methods Appl. Mech. Engrg. 2010, 199:229-263.
8. Akkerman I., Bazilevs Y., Calo V.M., Hughes T.J.R., Hulshoff S. The role of continuity in residual-based variational multiscale modeling of turbulence. Comput. Mech. 2008, 41:371-378.
9. 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.
10. Cottrell J.A., Reali A., Bazilevs Y., Hughes T.J.R. Isogeometric analysis of structural vibrations. Comput. Methods Appl. Mech. Engrg. 2006, 195:5257-5297.
11. Wall W.A., Frenzel M.A., Cyron C. Isogeometric structural shape optimization. Comput. Methods Appl. Mech. Engrg. 2008, 197:1976-1988.
12. Hughes T.J.R., Reali A., Sangalli G. Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with k-method NURBS. Comput. Methods Appl. Mech. Engrg. 2008, 197:4104-4124.
13. Benson D.J., Hsu M.C., Bazilevs Y., Hughes T.J.R. Isogeometric shell analysis: the Reissner-Mindlin shell. Comput. Methods Appl. Mech. Engrg. 2010, 199:276-289.
14. 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.
15. Cottrell J.A., Hughes T.J.R., Reali A. Studies of refinement and continuity in geometry and mesh refinement. Comput. Methods Appl. Mech. Engrg. 2007, 196:4160-4183.
16. 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.
17. Forsey D., Bartels R. Hierarchical B-spline refinement. Comput. Graphics 1998, 22:205-212.
18. Sederberg T.W., Zheng J., Bakenov A., Nasri A. T-splines and T-NURCCs. ACM Trans. Graphics 2003, 22:477-484.
19. Sederberg T.W., Cardon D.L., Finnigan G.T., North N.S., Zheng J., Lyche T. T-splines and local refinement. ACM Trans. Graphics 2004, 23:276-283.
20. Buffa A., Cho D., Sangalli G. Linear independence of the T-spline blending functions associated with some particular T-meshes. Comput. Methods Appl. Mech. Engrg. 2009, 199(23-24):437-1445.
21. Deng Jiansong, Chen Falai, Li Xin, Hu Changqi, Tong Weihua, Yang Zhouwang, Feng Yuyu Polynomial splines over hierarchical T-meshes. Graph. Models 2008, 70:76-86.
22. Li Xin, Deng Jiansong, Chen Falai Surface modeling with polynomial splines over hierarchical T-meshes. Visual Comput. 2007, 23:1027-1033.
23. Li Xin, Deng Jiansong, Chen Falai Polynomial splines over general T-meshes. Visual Comput. 2010, 26:277-286.
24. Rabczuk T., Belytschko T. Cracking particles: a simplified meshfree methods for arbitrary evolving cracks. Int. J. Numer. Methods Engrg. 2004, 61:2316-2343.
25. Rabczuk T., Belytschko T. Application of particle methods to static fracture of reinforced concrete structures. Int. J. Fract. 2006, 137:19-49.
26. Rabczuk T., Belytschko T. A three dimensional large deformation meshfree method for arbitrary evolving cracks. Comput. Methods Appl. Mech. Engrg. 2007, 196:2777-2799.
27. Rabczuk T., Samaniego E. Discontinuous modelling of shear bands with adaptive meshfree methods. Comput. Methods Appl. Mech. Engrg. 2008, 197:641-658.
28. Rabczuk T., Zi G., Bordas S., Nguyen-Xuan H. A geometrically nonlinear three-dimensional cohesive crack method for reinforced concrete structures. Engrg. Fract. Mech. 2008, 75:4740-4758.
29. Piegl L., Tiller W. The NURBS Book 1997, Springer-Verlag, Berlin. second ed.
30. Salomon David Curves and Surfaces for Computer Graphics 2006, Springer, New York.
31. Sederberg T.W., Zheng J., Bakenov A., Nasri A. T-splines and TNURCCs. ACM Trans. Graphics 2003, 22(3):161-172.
32. Deng Jiansong, Chen Falai, Feng Yuyu Dimensions of spline spaces over T-meshes. J. Comput. Appl. Math. 2006, 194:267-283.
33. Stogner R.H., Carey G.F., Murray B.T. Approximation of Cahn-Hilliard diffuse interface models using parallel adaptive mesh refinement and coarsening with C1 elements. Int. J. Numer. Methods Engrg. 2008, 76:636-661.
34. Rabczuk T., Belytschko T. Adaptivity for structured meshfree particle methods in 2D and 3D. Int. J. Numer. Methods Engrg. 2005, 63(11):1559-1582.
35. Austin Cottrell J., Hughes Thomas J.R., Bazilevs Yuri Isogeometric Analysis: Toward Integration of CAD and FEA 2009, John Wiley & Sons, Ltd., New York.
36. Rabczuk T., Belytschko T., Xiao S.P. Stable particle methods based on Lagrangian kernels. Comput. Methods Appl. Mech. Engrg. 2004, 193:1035-1063.
37. Rabczuk T., Xiao S.P., Sauer M. Coupling of meshfree methods with finite elements: basic concepts and test results. Commun. Numer. Methods Engrg. 2006, 22:1031-1065.
38. Nguyen-Thanh N., Rabczuk T., Nguyen-Xuan H., Bordas S. An alternative alpha finite element method (AαFEM) free and forced vibration analysis of solids using triangular meshes. J. Comput. Appl. Math. 2010, 223(9):2112-2135.
39. Phu N.V., Rabczuk T., Bordas S., Duflot M. Meshless methods: a review and computer implementation aspects, mathematics and computers in simulation. Math. Comput. Simulat. 2008, 79:763-813.
40. Timoshenko S.P., Goodier J.N. Theory of Elasticity 1970, McGraw, New York. third ed.
41. Nguyen-Xuan H., Rabczuk T., Bordas S., Debongnie J.F. A smoothed finite element method for plate analysis. Comput. Methods Appl. Mech. Engrg. 2008, 197:1184-1203.
42. Nguyen-Xuan H., Rabczuk T., Nguyen-Thanh N., Nguyen-Thoi T., Bordas Stephane A node-based smoothed finite element method (NS-FEM) for analysis of Reissner-Mindlin plates. Comput. Mech. 2010, 46:679-701.
43. Nguyen-Thanh N., Rabczuk Timon, Nguyen-Xuan H., Bordas S. An alternative alpha finite element method with stabilized discrete shear gap technique for analysis of Mindlin-Reissner plates. Finite Elem. Anal. Des. 2011, 47(5):519-535.
44. Nguyen-Thanh N., Rabczuk Timon, Nguyen-Xuan H., Bordas S. A smoothed finite element method for shell analysis. Comput. Methods Appl. Mech. Engrg. 2008, 198:165-177.