Weak coupling for isogeometric analysis of non-matching and trimmed multi-patch geometries

Computer Methods in Applied Mechanics and Engineering

Volumn 269, Issue , 2014, Pages 46-71

  Ruess, Martin ^a   Schillinger, Dominik ^b   Özcan, Ali I ^c   Rank, Ernst ^c  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^c TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Finite cell method; Isogeometric analysis; Nitsche's method; Non matching meshes; Trimmed NURBS geometries; Weak coupling

Indexed keywords

FINITE CELL METHOD; ISOGEOMETRIC ANALYSIS; NITSCHE'S METHODS; NON MATCHING MESHES; TRIMMED NURBS; WEAK COUPLINGS;

GEOMETRY; SHIP PROPELLERS;

INTERPOLATION;

EID: 84888121337     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2013.10.009     Document Type: Article

References (99)

1. Hughes T.J.R., Cottrell J.A., Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering 2005, 194:4135-4195.
2. Cottrell J.A., Hughes T.J.R., Bazilevs Y. Isogeometric Analysis: Towards Integration of CAD and FEA 2009, John Wiley & Sons.
3. Evans J.A., Bazilevs Y., Babuška I., Hughes T.J.R. n-Widths, sup-infs, and optimality ratios for the k-version of the isogeometric finite element method. Computer Methods in Applied Mechanics and Engineering 2009, 198(21-26):1726-1741.
4. Schillinger D., Ruess M., Zander N., Bazilevs Y., Düster A., Rank E. Small and large deformation analysis with the p- and B-spline versions of the finite cell method. Computational Mechanics 2012, 50(4):445-478.
5. Grossmann D., Jüttler B., Schlusnus H., Barner J., Vuong A.H. Isogeometric simulation of turbine blades for aircraft engines. Computer Aided Geometric Design 2012, 29(7):519-531.
6. Scott M.A., Li X., Sederberg T.W., Hughes T.J.R. Local refinement of analysis-suitable T-splines. Computer Methods in Applied Mechanics and Engineering 2012, 213-216:206-222.
7. Scott M.A., Simpson R.N., Evans J.A., Lipton S., Bordas S.P.A., Hughes T.J.R., Sederberg T.W. Isogeometric boundary element analysis using unstructured T-splines. Computer Methods in Applied Mechanics and Engineering 2013, 254:197-221.
8. Beirão da Veiga L., Buffa A., Cho D., Sangalli G. Analysis-suitable T-splines are dual-compatible. Computer Methods in Applied Mechanics and Engineering 2012, 249:42-51.
9. Schillinger D., Rank E. An unfitted hp adaptive finite element method based on hierarchical B-splines for interface problems of complex geometry. Computer Methods in Applied Mechanics and Engineering 2011, 200(47-48):3358-3380.
10. Vuong A.V., Giannelli C., Jüttler B., Simeon B. A hierarchical approach to adaptive local refinement in isogeometric analysis. Computer Methods in Applied Mechanics and Engineering 2011, 200(49-52):3554-3567.
11. Schillinger D., Dede' L., Scott M.A., Evans J.A., Borden M.J., Rank E., Hughes T.J.R. An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces. Computer Methods in Applied Mechanics and Engineering 2012, 249-250:116-150.
12. Giannelli C., Jüttler B., Speleers H. THB-splines: the truncated basis for hierarchical splines. Computer Aided Geometric Design 2012, 29(7):485-498.
13. Bornemann B., Cirak F. A subdivision-based implementation of the hierarchical b-spline finite element method. Computer Methods in Applied Mechanics and Engineering 2013, 253:584-598.
14. G. Kuru, C.V. Verhoosel, C. van der Zee, E.H. van Brummelen, Goal-adaptive isogeometric analysis with hierarchical splines, Computer Methods in Applied Mechanics and Engineering (2013), submitted for publication.
15. Nguyen-Thanh N., Nguyen-Xuan H., Bordas S.P.A., Rabczuk T. Isogeometric analysis using polynomial splines over hierarchical t-meshes for two-dimensional elastic solids. Computer Methods in Applied Mechanics and Engineering 2011, 200(21):1892-1908.
16. 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. Computer Methods in Applied Mechanics and Engineering 2011, 200(47):3410-3424.
17. Dokken T., Lyche T., Pettersen K.F. Polynomial splines over locally refined box-partitions. Computer Aided Geometric Design 2013, 30(21):331-356.
18. Cottrell J.A., Reali A., Bazilevs Y., Hughes T.J.R. Isogeometric analysis of structural vibrations. Computer Methods in Applied Mechanics and Engineering 2006, 195:5257-5296.
19. Elguedj T., Bazilevs Y., Calo V.M., Hughes T.J.R. B and F projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements. Computer Methods in Applied Mechanics and Engineering 2008, 197:2732-2762.
20. Auricchio F., da Veiga L.B., Lovadina C., Reali A. The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: mixed fems versus NURBS-based approximations. Computer Methods in Applied Mechanics and Engineering 2010, 199:314-323.
21. Taylor R.L. Isogeometric analysis of nearly incompressible solids. International Journal for Numerical Methods in Engineering 2011, 87(1-5):273-288.
22. Kiendl J., Bletzinger K.U., Linhard J., Wühner R. Isogeometric shell analysis with Kirchhoff-Love elements. Computer Methods in Applied Mechanics and Engineering 2009, 198(49-52):3902-3914.
23. Benson D.J., Bazilevs Y., Hsu M.C., Hughes T.J.R. Isogeometric shell analysis: the Reissner-Mindlin shell. Computer Methods in Applied Mechanics and Engineering 2010, 199:276-289.
24. Echter R., Bischoff M. Numerical efficiency, locking and unlocking of NURBS finite elements. Computer Methods in Applied Mechanics and Engineering 2010, 199:374-382.
25. Benson D.J., Hartmann S., Bazilevs Y., Hsu M.C., Hughes T.J.R. Blended isogeometric shells. Computer Methods in Applied Mechanics and Engineering 2013, 255:133-146.
26. R. Schmidt. Trimming, Mapping, and Optimization in Isogeometric Analysis of Shell Structures, Dissertation, Technische Universität München, 2013.
27. Bazilevs Y., Calo V.M., Hughes T.J.R., Zhang Y. Isogeometric fluid-structure interaction: theory, algorithms and computations. Computational Mechanics 2008, 43:3-37.
28. Bazilevs Y., Hsu M.C., Kiendl J., Wüchner R., Bletzinger K.U. 3D simulation of wind turbine rotors at full scale part II: fluid-structure interaction. International Journal of Numerical Methods in Fluids 2011, 65:236-253.
29. Bazilevs Y., Hsu M.C., Scott M.A. Isogeometric fluid-structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines. Computer Methods in Applied Mechanics and Engineering 2012, 249-252:28-41.
30. 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. Computer Methods in Applied Mechanics and Engineering 2007, 197:173-201.
31. 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. Computational Mechanics 2008, 41:371-378.
32. Gomez H., Calo V.M., Bazilevs Y., Hughes T.J.R. Isogeometric analysis of the Cahn-Hilliard phase-field model. Computer Methods in Applied Mechanics and Engineering 2008, 197:4333-4352.
33. Borden M.J., Verhoosel C.V., Scott M.A., Hughes T.J.R., Landis C.M. A phase-field description of dynamic brittle fracture. Computer Methods in Applied Mechanics and Engineering 2012, 217-220:77-95.
34. Dede' L., Borden M.J., Hughes T.J.R. Isogeometric analysis for topology optimization with a phase field model. Archives of Computational Methods in Engineering 2012, 19:427-465.
35. Liu J., Dede' L., Evans J.A., Borden M.J., Hughes T.J.R. Isogeometric analysis of the advective Cahn-Hilliard equation: spinodal decomposition under shear flow. Computational Physics 2013, 242:321-350.
36. Temizer I., Wriggers P., Hughes T.J.R. Contact treatment in isogeometric analysis with NURBS. Computer Methods in Applied Mechanics and Engineering 2011, 200:1100-1112.
37. Temizer I., Wriggers P., Hughes T.J.R. Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS. Computer Methods in Applied Mechanics and Engineering 2012, 209-212:115-128.
38. De Lorenzis L., Temizer I., Wriggers P., Zavarise G. A large deformation frictional contact formulation using NURBS-based isogeometric analysis. International Journal for Numerical Methods in Engineering 2011, 87(13):1278-1300.
39. 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. Computational Mechanics 2012, 49(1):1-20.
40. Nagy A., Abdalla M.M., Gürdal Z. Isogeometric sizing and shape optimisation of beam structures. Computer Methods in Applied Mechanics and Engineering 2010, 199:1216-1230.
41. Wall W.A., Frenzel M.A., Cyron C. Isogeometric structural shape optimization. Computer Methods in Applied Mechanics and Engineering 2008, 197:2976-2988.
42. Qian X., Sigmund O. Isogeometric shape optimization of photonic crystals via coons patches. Computer Methods in Applied Mechanics and Engineering 2011, 200:2237-2255.
43. Buffa A., Sangalli G., Vazquez R. Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations. Computer Methods in Applied Mechanics and Engineering 2010, 199:1143-1152.
44. Buffa A., Rivas J., Sangalli G., Vázquez R. Isogeometric discrete differential forms in three dimensions. SIAM Journal on Numerical Analysis 2011, 49(2):818-844.
45. Kim H.-J., Seo Y.-D., Youn S.-K. Isogeometric analysis for trimmed CAD surfaces. Computer Methods in Applied Mechanics and Engineering 2009, 198:2982-2995.
46. Rueberg T., Cirak F. Subdivision-stabilised immersed B-spline finite elements for moving boundary flows. Computer Methods in Applied Mechanics and Engineering 2012, 209-212:266-283.
47. Rank E., Ruess M., Kollmannsberger S., Schillinger D., Düster A. Geometric modeling, isogeometric analysis and the finite cell method. Computer Methods in Applied Mechanics and Engineering 2012, 249-250:104-115.
48. Ruess M., Schillinger D., Bazilevs Y., Varduhn V., Rank E. Weakly enforced essential boundary conditions for NURBS-embedded and trimmed NURBS geometries on the basis of the finite cell method. International Journal for Numerical Methods in Engineering 2013, 95(10):811-846. http://dx.doi.org/10.1002/nme.4522.
49. Simpson R.N., Bordas S.P.A., Trevelyan J., Rabczuk T. A two-dimensional isogeometric boundary element method for elastostatic analysis. Computer Methods in Applied Mechanics and Engineering 2012, 209-212:87-100.
50. Auricchio F., Calabrò F., Hughes T.J.R., Reali A., Sangalli G. A simple algorithm for obtaining nearly optimal quadrature rules for NURBS-based isogeometric analysis. Computer Methods in Applied Mechanics and Engineering 2012, 249-252:15-27.
51. F. Auricchio, L. Beirão da Veiga, J. Kiendl, C. Lovadina, A. Reali, Locking-free isogeometric collocation methods for spatial Timoshenko rods, Computer Methods in Applied Mechanics and Engineering (2013). doi:10.1016/j.cma.2013.03.009.
52. Schillinger D., Evans J.A., Reali A., Scott M.A., Hughes T.J.R. Isogeometric collocation: cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations. Computer Methods in Applied Mechanics and Engineering 2013, 267:170-232.
53. Kagan P., Fischer A. Integrated mechanically based CAE system using B-spline finite elements. Computer Aided Design 2000, 32(8-9):539-552.
54. Schmidt R., Kiendl J., Bletzinger K.U., Wüchner R. Realization of an integrated structural design process: analysis-suitable geometric modelling and isogeometric analysis. Computing and Visualization in Science 2009, 13(7):315-330.
55. Cohen E., Martin T., Kirby R.M., Lyche T., Riesenfeld R.F. Analysis-aware modeling: understanding quality considerations in modeling for isogeometric analysis. Computer Methods in Applied Mechanics and Engineering 2010, 199:334-356.
56. M. Ruess, Y. Bazilevs, D. Schillinger, N. Zander, E. Rank, Weakly enforced boundary conditions for the NURBS-based finite cell method, in: J. Eberhardsteiner, H.J. BÂhm, F.G. Rammerstorfer (Eds.), Proc. ECCOMAS, Vienna, Austria, Vienna University of Technology, Austria, 2012.
57. Nitsche J.A. Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1970, 36:9-15.
58. Ruess M., Tal D., Trabelsi N., Yosibash Z., Rank E. The finite cell method for bone simulations: verification and validation. Biomechanics and Modeling in Mechanobiology 2012, 11(3):425-437.
59. Evans J.A., Hughes T.J.R. Isogeometric divergence-conforming B-splines for the steady Navier-Stokes equations. Mathematical Models and Methods in Applied Sciences 2013, 23:1421.
60. Bazilevs Y., Hughes T.J.R. Weak imposition of dirichlet boundary conditions in fluid mechanics. Computers & Fluids 2007, 36:12-26.
61. van Brummelen E.H., van der Zee K.G., Garg V.V., Prudhome S. Flux evaluation in primal and dual boundary-coupled problems. Journal of Applied Mechanics 2012, 79(1):1-8.
62. Hsu M.C., Akkerman I., Bazilevs Y. Wind turbine aerodynamics using ALE-VMS: validation and the role of weakly enforced boundary conditions. Computational Mechanics 2012, 50:499-511.
63. Bazilevs Y., Hsu M.C., Takizawa K., Tezduyar T.E. ALE-VMS and ST-VMS methods for wind-turbine rotor aerodynamics and fluid-structure interaction. Mathematical Models and Methods in Applied Sciences 2012, 22:1-62.
64. Mergheim J., Steinmann P. A geometrically nonlinear FE approach for the simulation of strong and weak discontinuities. Computer Methods in Applied Mechanics and Engineering 2006, 195(37):5037-5052.
65. Hansbo A., Hansbo P. An unfitted finite element method, based on Nitsche's method, for elliptic interface problems. Computer Methods in Applied Mechanics and Engineering 2002, 191:537-552.
66. Schillinger D., Kollmannsberger S., Mundani R.-P., Rank E. The finite cell method for geometrically nonlinear problems of solid mechanics. IOP Conference Series: Material Science and Engineering 2010, 10:012170.
67. D. Schillinger, The p- and B-spline versions of the geometrically nonlinear finite cell method and hierarchical refinement strategies for adaptive isogeometric and embedded domain analysis, Dissertation, Technische Universität München, 2012. http://d-nb.info/103009943X/34.
68. Rogers D.F. An Introduction to NURBS with Historical Perspective 2001, Morgan Kaufman Publishers.
69. Piegl L., Tiller W. The NURBS Book 1997, Springer.
70. Höllig K. Finite Element Methods with B-Splines 2003, Society for Industrial and Applied Mathematics.
71. Rhinoceros - NURBS modeling for Windows, 2012. http://www.rhino3d.com/.
72. Hansbo P. Nitsche's method for interface problems in computational mechanics. GAMM Mitteilungen 2005, 28/2:183-206.
73. Fritz A., Hüeber S., Wohlmuth B. A comparison of mortar and Nitsche techniques for linear elasticity. Calcolo 2004, 41:115-137.
74. Parvizian J., Düster A., Rank E. Finite cell method: h- and p-extension for embedded domain methods in solid mechanics. Computational Mechanics 2007, 41:122-133.
75. Düster A., Parvizian J., Yang Z., Rank E. The finite cell method for three-dimensional problems of solid mechanics. Computer Methods in Applied Mechanics and Engineering 2010, 197:3768-3782.
76. D. Schillinger, M. Ruess, A. Düster, E. Rank, The finite cell method for large deformation analysis, in: Proc. in Applied Mathematics and Mechanics, vol. 11(1), 2011, pp. 271-272.
77. Schillinger D., Düster A., Rank E. The hp-d adaptive finite cell method for geometrically nonlinear problems of solid mechanics. International Journal for Numerical Methods in Engineering 2012, 89:1171-1202.
78. Schillinger D., Cai Q., Mundani R.-P., Rank E. Nonlinear structural analysis of complex CAD and image based geometric models with the finite cell method. Lecture Notes in Computational Science and Engineering 2013, vol. 93:1-23. Springer Berlin Heidelberg, http://dx.doi.org/10.1007/978-3-642-38762-3_1.
79. Yang Z., Ruess M., Kollmannsberger S., Düster A., Rank E. An efficient integration technique for the voxel-based finite cell method. International Journal for Numerical Methods in Engineering 2012, 91:457-471.
80. M. Ruess, V. Varduhn, Z. Yosibash, E. Rank, A parallel high-order fictitious domain approach for biomechanical applications, in: International Symposium on Parallel and Distributed Computing, 2012, pp. 279-285.
81. J.H. Luque Jimenez, I. Papaioannou, M. Ruess, D. Schillinger, D. Straub, Probabilistic model of bone structure based on CT scan data and validation of simulation results using the finite cell method, in: Proc. of the 11th International Conference on Structural Safety & Reliability (ICOSSAR), Columbia University, NYC, 2013.
82. Yang Z., Kollmannsberger S., Düster A., Ruess M., Garcia E.G., Burgkart E., Rank E. Non-standard bone simulation: interactive numerical analysis by computational steering. Computing and Visualization in Science 2012, 14:207-216.
83. Zander N., Kollmannsberger S., Ruess M., Yosibash Z., Rank E. The finite cell method for linear thermoelasticity. Computers & Mathematics with Applicatons 2012, 64(11):3527-3541.
84. Mousavi S.E., Sukumar N. Numerical integration of polynomials and discontinuous functions on irregular convex polygons and polyhedrons. Computational Mechanics 2012, 47(5):535-554.
85. Abedian A., Parvizian J., Düster A., Rank E. The finite cell method for the j2 flow theory of plasticity. Finite Elements in Analysis and Design 2013, 69:37-47.
86. Abedian A., Parvizian J., Düster A., Khademyzadeh H., Rank E. Performance of different integration schemes in facing discontinuities in the finite cell method. International Journal of Computational Methods 2013, 10(3):1-24.
87. Embar A., Dolbow J., Harari I. Imposing Dirichlet boundary conditions with Nitsche's method and spline-based finite elements. International Journal for Numerical Methods in Engineering 2010, 83:877-898.
88. Dolbow J., Harari I. An efficient finite element method for embedded interface problems. International Journal for Numerical Methods in Engineering 2009, 78:229-252.
89. Golub G.H., Van Loan C. Matrix Computations 1996, Johns Hopkins University Press.
90. Parlett B.N. The Symmetric Eigenvalue Problem 1998, Society for Industrial and Applied Mathematics. second ed.
91. Sanders J.D., Dolbow J.E., Laursen T.A. On methods for stabilizing constraints over enriched interfaces in elasticity. International Journal for Numerical Methods in Engineering 2009, 78:1009-1036.
92. Griebel M., Schweitzer M.A. A particle-partition of unity method. Part V: boundary conditions. Geometric Analysis and Nonlinear Partial Differential Equations 2004, 519-542. Springer. S. Hildebrandt, H. Karcher (Eds.).
93. Harari I., Shavelzon E. Embedded kinematic boundary conditions for thin plate bending by Nitsche's approach. International Journal for Numerical Methods in Engineering 2012, 92(1):99-114.
94. Saad Y. Numerical Methods for Large Eigenvalue Problems 2011, Society for Industrial and Applied Mathematics.
95. Zienkiewicz O.C., Taylor R.L. The Finite Element Method - The Basis 2005, vol. 1. Butterworth-Heinemann, sixth ed.
96. Sadd M.H. Elasticity: Theory, Applications, and Numerics 2009, Academic Press.
97. Cottrell J.A., Hughes T.J.R., Reali A. Studies of refinement and continuity in isogeometric structural analysis. Computer Methods in Applied Mechanics and Engineering 2007, 196:4160-4183.
98. Hughes T.J.R. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis 2000, Dover Publications.
99. Schmidt R., Wüchner R., Bletzinger K.-U. Isogeometric analysis of trimmed NURBS geometries. Computer Methods in Applied Mechanics and Engineering 2012, 241-244:93-111.