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Nitsche’s method for two and three dimensional NURBS patch coupling. (English) Zbl 1398.74379

Summary: We present a Nitsche’s method to couple non-conforming two and three-dimensional non uniform rational b-splines (NURBS) patches in the context of isogeometric analysis. We present results for linear elastostatics in two and and three-dimensions. The method can deal with surface-surface or volume-volume coupling, and we show how it can be used to handle heterogeneities such as inclusions. We also present preliminary results on modal analysis. This simple coupling method has the potential to increase the applicability of NURBS-based isogeometric analysis for practical applications.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65D17 Computer-aided design (modeling of curves and surfaces)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S30 Other numerical methods in solid mechanics (MSC2010)
65D07 Numerical computation using splines

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References:

[1] Piegl LA, Tiller W (1996) The NURBS book. Springer, Berlin · Zbl 0828.68118
[2] Rogers DF (2001) An introduction to NURBS with historical perspective. Academic Press, San Diego
[3] Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194(39-41):4135-4195 · Zbl 1151.74419 · doi:10.1016/j.cma.2004.10.008
[4] Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. Wiley, Chichester · Zbl 1378.65009 · doi:10.1002/9780470749081
[5] Kagan P, Fischer A, Bar-Yoseph PZ (1998) New B-spline finite element approach for geometrical design and mechanical analysis. Int J Numer Methods Eng 41(3):435-458 · Zbl 0912.73058 · doi:10.1002/(SICI)1097-0207(19980215)41:3<435::AID-NME292>3.0.CO;2-U
[6] Kagan P, Fischer A (2000) Integrated mechanically based CAE system using B-spline finite elements. Comput Aided Des 32(8-9):539-552 · Zbl 1206.65050 · doi:10.1016/S0010-4485(00)00041-5
[7] Cirak F, Ortiz M, Schröder P (2000) Subdivision surfaces: a new paradigm for thin-shell finite-element analysis. Int J Numer Methods Eng 47(12):2039-2072 · Zbl 0983.74063 · doi:10.1002/(SICI)1097-0207(20000430)47:12<2039::AID-NME872>3.0.CO;2-1
[8] Uhm TK, Youn SK (2009) T-spline finite element method for the analysis of shell structures. Int J Numer Methods Eng 80(4):507-536 · Zbl 1176.74198 · doi:10.1002/nme.2648
[9] Kiendl J, Bletzinger K-U, Linhard J, Wüchner R (2009) Isogeometric shell analysis with Kirchhoff-Love elements. Comput Methods Appl Mech Eng 198(49-52):3902-3914 · Zbl 1231.74422 · doi:10.1016/j.cma.2009.08.013
[10] Benson DJ, Bazilevs Y, Hsu MC, Hughes TJR (2010) Isogeometric shell analysis: the Reissner-Mindlin shell. Comput Methods Appl Mech Eng 199(5-8):276-289 · Zbl 1227.74107 · doi:10.1016/j.cma.2009.05.011
[11] Benson DJ, Bazilevs Y, Hsu M-C, Hughes TJR (2011) A large deformation, rotation-free, isogeometric shell. Comput Methods Appl Mech Eng 200(13-16):1367-1378 · Zbl 1228.74077 · doi:10.1016/j.cma.2010.12.003
[12] Beirão da Veiga L, Buffa A, Lovadina C, Martinelli M, Sangalli G (2012) An isogeometric method for the Reissner-Mindlin plate bending problem. Comput Methods Appl Mech Eng 209-212:45-53 · Zbl 1243.74101 · doi:10.1016/j.cma.2011.10.009
[13] Echter R, Oesterle B, Bischoff M (2013) A hierarchic family of isogeometric shell finite elements. Comput Methods Appl Mech Eng 254:170-180 · Zbl 1297.74071 · doi:10.1016/j.cma.2012.10.018
[14] Benson DJ, Hartmann S, Bazilevs Y, Hsu M-C, Hughes TJR (2013) Blended isogeometric shells. Comput Methods Appl Mech Eng 255:133-146 · Zbl 1297.74114 · doi:10.1016/j.cma.2012.11.020
[15] Kiendl J, Bazilevs Y, Hsu M-C, Wüchner R, Bletzinger K-U (2010) The bending strip method for isogeometric analysis of Kirchhoff-Love shell structures comprised of multiple patches. Comput Methods Appl Mech Eng 199(37-40):2403-2416 · Zbl 1231.74482 · doi:10.1016/j.cma.2010.03.029
[16] Temizer İ, Wriggers P, Hughes TJR (2011) Contact treatment in isogeometric analysis with NURBS. Comput Methods Appl Mech Eng 200(9-12):1100-1112 · Zbl 1225.74126 · doi:10.1016/j.cma.2010.11.020
[17] Jia L (2011) Isogeometric contact analysis: geometric basis and formulation for frictionless contact. Comput Methods Appl Mech Eng 200(5-8):726-741 · Zbl 1225.74097
[18] Temizer İ, Wriggers P, Hughes TJR (2012) Three-dimensional Mortar-Based frictional contact treatment in isogeometric analysis with NURBS. Comput Methods Appl Mech Eng 209-212:115-128 · Zbl 1243.74130 · doi:10.1016/j.cma.2011.10.014
[19] De Lorenzis L, Temizer İ, Wriggers P, Zavarise G (2011) A large deformation frictional contact formulation using NURBS-bases isogeometric analysis. Int J Numer Methods Eng 87(13):1278-1300 · Zbl 1242.74104
[20] Matzen ME, Cichosz T, Bischoff M (2013) A point to segment contact formulation for isogeometric, NURBS based finite elements. Comput Methods Appl Mech Eng 255:27-39 · Zbl 1297.74084 · doi:10.1016/j.cma.2012.11.011
[21] Wall WA, Frenzel MA, Cyron C (2008) Isogeometric structural shape optimization. Comput Methods Appl Mech Eng 197(33-40):2976-2988 · Zbl 1194.74263 · doi:10.1016/j.cma.2008.01.025
[22] Manh ND, Evgrafov A, Gersborg AR, Gravesen J (2011) Isogeometric shape optimization of vibrating membranes. Comput Methods Appl Mech Eng 200(13-16):1343-1353 · Zbl 1228.74062 · doi:10.1016/j.cma.2010.12.015
[23] Qian X, Sigmund O (2011) Isogeometric shape optimization of photonic crystals via Coons patches. Comput Methods Appl Mech Eng 200(25-28):2237-2255 · Zbl 1230.74149 · doi:10.1016/j.cma.2011.03.007
[24] Qian X (2010) Full analytical sensitivities in NURBS based isogeometric shape optimization. Comput Methods Appl Mech Eng 199(29-32):2059-2071 · Zbl 1231.74352 · doi:10.1016/j.cma.2010.03.005
[25] Simpson RN, Bordas SPA, Trevelyan J, Rabczuk T (2012) A two-dimensional isogeometric boundary element method for elastostatic analysis. Comput Methods Appl Mech Eng 209-212:87-100 · Zbl 1243.74193 · doi:10.1016/j.cma.2011.08.008
[26] Scott MA, Simpson RN, Evans JA, Lipton S, Bordas SPA, Hughes TJR, Sederberg TW (2013) Isogeometric boundary element analysis using unstructured T-splines. Comput Methods Appl Mech Eng 254:197-221 · Zbl 1297.74156 · doi:10.1016/j.cma.2012.11.001
[27] Gomez H, Hughes TJR, Nogueira X, Calo VM (2010) Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations. Comput Methods Appl Mech Eng 199(25-28):1828-1840 · Zbl 1231.76191 · doi:10.1016/j.cma.2010.02.010
[28] Bazilevs Y, Akkerman I (2010) Large eddy simulation of turbulent Taylor-Couette flow using isogeometric analysis and the residual-based variational multiscale method. J Comput Phys 229(9):3402-3414 · Zbl 1290.76037 · doi:10.1016/j.jcp.2010.01.008
[29] Nielsen PN, Gersborg AR, Gravesen J, Pedersen NL (2011) Discretizations in isogeometric analysis of Navier-Stokes flow. Comput Methods Appl Mech Eng 200(45-46):3242-3253 · Zbl 1230.76042 · doi:10.1016/j.cma.2011.06.007
[30] Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput Mech 43:3-37 · Zbl 1169.74015 · doi:10.1007/s00466-008-0315-x
[31] Bazilevs Y, Gohean JR, Hughes TJR, Moser RD, Zhang Y (2009) Patient-specific isogeometric fluid-structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device. Comput Methods Appl Mech Eng 198(45-46):3534-3550 · Zbl 1229.74096 · doi:10.1016/j.cma.2009.04.015
[32] Gómez H, Calo VM, Bazilevs Y, Hughes TJR (2008) Isogeometric analysis of the Cahn-Hilliard phase-field model. Comput Methods Appl Mech Eng 197(49-50):4333-4352 · Zbl 1194.74524 · doi:10.1016/j.cma.2008.05.003
[33] Verhoosel CV, Scott MA, Hughes TJR, de Borst R (2011) An isogeometric analysis approach to gradient damage models. Int J Numer Methods Eng 86(1):115-134 · Zbl 1235.74320 · doi:10.1002/nme.3150
[34] Fischer P, Klassen M, Mergheim J, Steinmann P, Müller R (2010) Isogeometric analysis of 2D gradient elasticity. Comput Mech 47:325-334 · Zbl 1398.74329 · doi:10.1007/s00466-010-0543-8
[35] Masud A, Kannan R (2012) B-splines and NURBS based finite element methods for Kohn-Sham equations. Comput Methods Appl Mech Eng 241-244:112-127 · Zbl 1353.82065 · doi:10.1016/j.cma.2012.04.016
[36] Cottrell JA, Reali A, Bazilevs Y, Hughes TJR (2006) Isogeometric analysis of structural vibrations. Comput Methods Appl Mech Eng 195(41-43):5257-5296 · Zbl 1119.74024 · doi:10.1016/j.cma.2005.09.027
[37] Hughes TJR, Reali A, Sangalli G (2008) 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 Eng 197(49-50):4104-4124 · Zbl 1194.74114 · doi:10.1016/j.cma.2008.04.006
[38] Thai CH, Nguyen-Xuan H, Nguyen-Thanh N, Le T-H, Nguyen-Thoi T, Rabczuk T (2012) Static, free vibration, and buckling analysis of laminated composite Reissner-Mindlin plates using NURBS-based isogeometric approach. Int J Numer Methods Eng 91(6):571-603 · Zbl 1253.74007 · doi:10.1002/nme.4282
[39] Wang D, Liu W, Zhang H (2013) Novel higher order mass matrices for isogeometric structural vibration analysis. Comput Methods Appl Mech Eng 260:63-77 · Zbl 1286.74051 · doi:10.1016/j.cma.2013.03.011
[40] Evans JA, Bazilevs Y, Babuška I, Hughes TJR (2009) n-Widths, sup-infs, and optimality ratios for the k-version of the isogeometric finite element method. Comput Methods Appl Mech Eng 198(21-26):1726-1741 · Zbl 1227.65093 · doi:10.1016/j.cma.2009.01.021
[41] Verhoosel CV, Scott MA, de Borst R, Hughes TJR (2011) An isogeometric approach to cohesive zone modeling. Int J Numer Methods Eng 87(15):336-360 · Zbl 1242.74169 · doi:10.1002/nme.3061
[42] Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1):131-150 · Zbl 0955.74066 · doi:10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
[43] De Luycker E, Benson DJ, Belytschko T, Bazilevs Y, Hsu MC (2011) X-FEM in isogeometric analysis for linear fracture mechanics. Int J Numer Methods Eng 87(6):541-565 · Zbl 1242.74105 · doi:10.1002/nme.3121
[44] Ghorashi SS, Valizadeh N, Mohammadi S (2012) Extended isogeometric analysis for simulation of stationary and propagating cracks. Int J Numer Methods Eng 89:1069-1101 · Zbl 1242.74119 · doi:10.1002/nme.3277
[45] Tambat A, Subbarayan G (2012) Isogeometric enriched field approximations. Comput Methods Appl Mech Eng 245-246:1-21 · Zbl 1354.65044 · doi:10.1016/j.cma.2012.06.006
[46] Borden MJ, Verhoosel CV, Scott MA, Hughes TJR, Landis CM (2012) A phase-field description of dynamic brittle fracture. Comput Methods Appl Mech Eng 217-220:77-95 · Zbl 1253.74089 · doi:10.1016/j.cma.2012.01.008
[47] Nguyen VP, Nguyen-Xuan H (2013) High-order B-splines based finite elements for delamination analysis of laminated composites. Compos Struct 102:261-275 · doi:10.1016/j.compstruct.2013.02.029
[48] Nguyen VP, Kerfriden P, Bordas S (2013) Isogeometric cohesive elements for two and three dimensional composite delamination analysis. Compos Part B, 2013. http://arxiv.org/abs/1305.2738 · Zbl 1253.74089
[49] Takacs T, Jüttler B (2011) Existence of stiffness matrix integrals for singularly parameterized domains in isogeometric analysis. Comput Methods Appl Mech Eng 200(49-52):3568-3582 · Zbl 1239.65014 · doi:10.1016/j.cma.2011.08.023
[50] Xu G, Mourrain B, Duvigneau R, Galligo A (2011) Parameterization of computational domain in isogeometric analysis: methods and comparison. Comput Methods Appl Mech Eng 200(23-24):2021-2031 · Zbl 1228.65232 · doi:10.1016/j.cma.2011.03.005
[51] Cohen E, Martin T, Kirby RM, Lyche T, Riesenfeld RF (2010) Analysis-aware modeling: understanding quality considerations in modeling for isogeometric analysis. Comput Methods Appl Mech Eng 199(5-8):334-356 · Zbl 1227.74109 · doi:10.1016/j.cma.2009.09.010
[52] Schmidt R, Kiendl J, Bletzinger K-U, Wüchner R (2010) Realization of an integrated structural design process: analysis-suitable geometric modelling and isogeometric analysis. Comput Vis Sci 13(7):315-330 · Zbl 1216.65019 · doi:10.1007/s00791-010-0147-z
[53] Zhou X and Lu J (2005) Nurbs-based galerkin method and application to skeletal muscle modeling. In Proceedings of the 2005 ACM symposium on solid and physical modeling, SPM ’05. ACM, New York, pp 71-78 · Zbl 0955.74066
[54] Xu G, Mourrain B, Duvigneau R, Galligo A (2013) Optimal analysis-aware parameterization of computational domain in 3D isogeometric analysis. Comput Aided Des 45(4):812-821 · doi:10.1016/j.cad.2011.05.007
[55] Xu G, Mourrain B, Duvigneau R, Galligo A (2012) Analysis-suitable volume parameterization of multi-block computational domain in isogeometric applications. Comput Aided Des 45(2):395-404 · doi:10.1016/j.cad.2012.10.022
[56] Sederberg TW, Zheng J, Bakenov A, Nasri A (2003) T-splines and T-NURCCs. ACM Trans Gr 22:477-484 · doi:10.1145/882262.882295
[57] Bazilevs Y, Calo VM, Cottrell JA, Evans JA, Hughes TJR, Lipton S, Scott MA, Sederberg TW (2010) Isogeometric analysis using T-splines. Comput Methods Appl Mech Eng 199(5-8):229-263 · Zbl 1227.74123 · doi:10.1016/j.cma.2009.02.036
[58] Dörfel MR, Jüttler B, Simeon B (2010) Adaptive isogeometric analysis by local h-refinement with T-splines. Comput Methods Appl Mech Eng 199(5-8):264-275 · Zbl 1227.74125 · doi:10.1016/j.cma.2008.07.012
[59] Scott MA, Borden MJ, Verhoosel CV, Sederberg TW, Hughes TJR (2011) Isogeometric finite element data structures based on Bézier extraction of T-splines. Int J Numer Methods Eng 88(2):126-156 · Zbl 1242.65243 · doi:10.1002/nme.3167
[60] Nguyen-Thanh N, Nguyen-Xuan H, Bordas SPA, Rabczuk T (2011) Isogeometric analysis using polynomial splines over hierarchical t-meshes for two-dimensional elastic solids. Comput Methods Appl Mech Eng 200(21):1892-1908 · Zbl 1228.74091 · doi:10.1016/j.cma.2011.01.018
[61] Nguyen-Thanh N, Kiendl J, Nguyen-Xuan H, Wüchner R, Bletzinger KU, Bazilevs Y, Rabczuk T (2011) Rotation free isogeometric thin shell analysis using PHT-splines. Comput Methods Appl Mech Eng 200(47-48):3410-3424 · Zbl 1230.74230 · doi:10.1016/j.cma.2011.08.014
[62] Rosolen A, Arroyo M (2013) Blending isogeometric analysis and local maximum entropy meshfree approximants. Comput Methods Appl Mech Eng 264:95-107 · Zbl 1286.65025 · doi:10.1016/j.cma.2013.05.015
[63] Nguyen VP, Kerfriden P, Claus S, Bordas SPA (2013) Nitsche’s method for mixed dimensional analysis: conforming and non-conforming continuum-beam and continuum-plate coupling. Comput Methods Appl Mech Eng 2013. http://arxiv.org/abs/1308.2910 · Zbl 1229.74096
[64] Nitsche J (1971) Uber ein variationsprinzip zur losung von dirichlet-problemen bei verwendung von teilraumen, die keinen randbedingungen unterworfen sind. Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg 36:9-15 · Zbl 0229.65079 · doi:10.1007/BF02995904
[65] Hansbo A, Hansbo P (2002) An unfitted finite element method, based on Nitsche’s method, for elliptic interface problems. Comput Methods Appl Mech Eng 191(4748):5537-5552 · Zbl 1035.65125 · doi:10.1016/S0045-7825(02)00524-8
[66] Dolbow J, Harari I (2009) An efficient finite element method for embedded interface problems. Int J Numer Methods Eng 78:229-252 · Zbl 1183.76803 · doi:10.1002/nme.2486
[67] Becker R, Hansbo P, Stenberg R (2003) A finite element method for domain decomposition with non-matching grids. ESAIM Math Modell Numer Anal 37:209-225 · Zbl 1047.65099 · doi:10.1051/m2an:2003023
[68] Hansbo A, Hansbo P, Larson MG (2003) A finite element method on composite grids based on Nitsche’s method. ESAIM Math Modell Numer Anal 37:495-514 · Zbl 1031.65128 · doi:10.1051/m2an:2003039
[69] Sanders J, Puso MA (2012) An embedded mesh method for treating overlapping finite element meshes. Int J Numer Methods Eng 91:289-305 · Zbl 1246.74064 · doi:10.1002/nme.4265
[70] Sanders JD, Laursen T, Puso MA (2011) A Nitsche embedded mesh method. Comput Mech 49(2):243-257 · Zbl 1366.74075 · doi:10.1007/s00466-011-0641-2
[71] Burman E, Hansbo P (2012) Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method. Appl Numer Math 62(4):328-341 · Zbl 1316.65099 · doi:10.1016/j.apnum.2011.01.008
[72] Fernández-Méndez S, Huerta A (2004) Imposing essential boundary conditions in mesh-free methods. Comput Methods Appl Mech Eng 193(1214):1257-1275 · Zbl 1060.74665 · doi:10.1016/j.cma.2003.12.019
[73] Ruess M, Schillinger D, Bazilevs Y, Varduhn V, Rank E (2013) Weakly enforced essential boundary conditions for NURBS-embedded and trimmed NURBS geometries on the basis of the finite cell method. Accepted for publication, Int J Numer Methods Eng · Zbl 1352.65643
[74] Baiges J, Codina R, Henke F, Shahmiri S, Wall WA (2012) A symmetric method for weakly imposing Dirichlet boundary conditions in embedded finite element meshes. Int J Numer Methods Eng 90(5):636-658 · Zbl 1242.76108 · doi:10.1002/nme.3339
[75] Embar A, Dolbow J, Harari I (2010) Imposing Dirichlet boundary conditions with Nitsche’s method and spline-based finite elements. Int J Numer Methods Eng 83(7):877-898 · Zbl 1197.74178
[76] Burman E, Fernández MA (2009) Stabilization of explicit coupling in fluidstructure interaction involving fluid incompressibility. Comput Methods Appl Mech Eng 198(5):766-784 · Zbl 1229.76045 · doi:10.1016/j.cma.2008.10.012
[77] Bazilevs Y, Hughes TJR (2007) Weak imposition of Dirichlet boundary conditions in fluid mechanics. Comput Fluids 36(1):12-26 · Zbl 1115.76040 · doi:10.1016/j.compfluid.2005.07.012
[78] Ruess M, Schillinger D, Bazilevs Y, Rank E (2013) Weakly enforced essential boundary conditions for NURBS-embedded and trimmed NURBS geometries on the basis of the finite cell method. Int J Numer Methods Eng 95(10):811-846 · Zbl 1352.65643 · doi:10.1002/nme.4522
[79] Wriggers P, Zavarise G (2008) A formulation for frictionless contact problems using a weak form introduced by Nitsche. Comput Mech 41(3):407-420 · Zbl 1162.74419 · doi:10.1007/s00466-007-0196-4
[80] Sanders JD, Dolbow JE, Laursen TA (2009) On methods for stabilizing constraints over enriched interfaces in elasticity. Int J Numer Methods Eng 78:1009-1036 · Zbl 1183.74313 · doi:10.1002/nme.2514
[81] Griebel, M.; Schweitzer, MA; Hildebrandt, S. (ed.); Karcher, H. (ed.), A particle-partition of unity method—Part V: boundary conditions, 519-542 (2002), Berlin · Zbl 1033.65102
[82] Rhino. CAD modeling and design toolkit. www.rhino3d.com · Zbl 1228.74077
[83] Hughes TJR (2000) The finite element method: linear static and dynamic finite element analysis. Dover Publications, Mineola
[84] Nayroles B, Touzot G, Villon P (1992) Generalizing the finite element method: diffuse approximation and diffuse elements. Comput Mech 10(5):307-318 · Zbl 0764.65068 · doi:10.1007/BF00364252
[85] Belytschko T, Lu YY, Gu L (1994) Element-free galerkin methods. Int J Numer Methods Eng 37(2):229-256 · Zbl 0796.73077
[86] Liu WK, Jun S, Zhang YF (1995) Reproducing kernel particle methods. Int J Numer Methods Fluids 20:1081-1106 · Zbl 0881.76072 · doi:10.1002/fld.1650200824
[87] Chen JS, Wu CT, Yoon S, You Y (2001) A stabilized conforming nodal integration for Galerkin meshfree methods. Int J Numer Methods Eng 50:435-466 · Zbl 1011.74081 · doi:10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A
[88] Nguyen VP, Rabczuk T, Bordas S, Duflot M (2008) Meshless methods: a review and computer implementation aspects. Math Comput Simul 79(3):763-813 · Zbl 1152.74055 · doi:10.1016/j.matcom.2008.01.003
[89] Borden MJ, Scott MA, Evans JA, Hughes TJR (2011) Isogeometric finite element data structures based on Bézier extraction of NURBS. Int J Numer Methods Eng 87(15):15-47 · Zbl 1242.74097 · doi:10.1002/nme.2968
[90] Henderson A (2007) ParaView guide, a parallel visualization application. Kitware Inc
[91] Ugural AC, Fenster SK (1995) Advanced strength and applied elasticity, 3rd edn. Prentice-Hall, Englewood Cliffs · Zbl 0486.73003
[92] Nguyen VP, Bordas SPA, Rabczuk T (2013) Isogeometric analysis: an overview and computer implementation aspects. Comput Aided Geom Des. http://arxiv.org/abs/1205.2129
[93] Hughes TJR, Reali A, Sangalli G (2010) Efficient quadrature for NURBS-based isogeometric analysis. Comput Methods Appl Mech Eng 199(5-8):301-313 · Zbl 1227.65029 · doi:10.1016/j.cma.2008.12.004
[94] Auricchio F, Calabro F, Hughes TJR, Reali A, Sangalli G (2012) A simple algorithm for obtaining nearly optimal quadrature rules for NURBS-based isogeometric analysis. Comput Methods Appl Mech Eng 249-252:15-27 · Zbl 1348.65059 · doi:10.1016/j.cma.2012.04.014
[95] Fritz A, Hüeber S, Wohlmuth BI (2004) A comparison of mortar and Nitsche techniques for linear elasticity. CALCOLO 41(3):115-137 · Zbl 1099.65123 · doi:10.1007/s10092-004-0087-4
[96] Sukumar N, Chopp DL, Moës N, Belytschko T (2000) Modelling holes and inclusions by level sets in the extended finite element method. Comput Methods Appl Mech Eng 190:6183-6200 · Zbl 1029.74049 · doi:10.1016/S0045-7825(01)00215-8
[97] Sevilla R, Fernández-Méndez S, Huerta A (2008) NURBS-enhanced finite element method (NEFEM). Int J Numer Methods Eng 76(1):56-83 · Zbl 1162.65389 · doi:10.1002/nme.2311
[98] Tornincasa S, Bonisoli E, Kerfriden P, Brino M (2014) Investigation of crossing and veering phenomena in an isogeometric analysis framework. In Proceedings of IMAC XXXII, Orlando pp 3-6 Feb 2014 · Zbl 0983.74063
[99] Ruess M, Schillinger D, Bazilevs Y, Ozcan A, Rank E (2013) Weakly enforced boundary and coupling conditions in isogeometric analysis. In Proceedings of 12th US national congress on computational mechanics. Raleigh, North Carolina, July 22-25 · Zbl 1352.65643
[100] Noels L, Radovitzky R (2006) A general discontinuous Galerkin method for finite hyperelasticity. Formulation and numerical applications. Int J Numer Methods Eng 68(1):64-97 · Zbl 1145.74039 · doi:10.1002/nme.1699
[101] Radovitzky R, Seagraves A, Tupek M, Noels L (2011) A scalable 3D fracture and fragmentation algorithm based on a hybrid, discontinuous Galerkin, cohesive element method. Comput Methods Appl Mech Eng 200(14):326-344 · Zbl 1225.74105 · doi:10.1016/j.cma.2010.08.014
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