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09.02.2022 | Original Article

An efficient automatic mesh generation algorithm for planar isogeometric analysis using high-order rational Bézier triangles

verfasst von: Elias Saraiva Barroso, John Andrew Evans, Joaquim Bento Cavalcante-Neto, Creto Augusto Vidal, Evandro Parente Jr.

Erschienen in: Engineering with Computers | Ausgabe 5/2022

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Abstract

Isogeometric analysis (IGA) is a numerical method that is receiving increasing attention in the last decade. The main goal of IGA is to closely couple geometric modeling with numerical analysis. To that end, in IGA both components use the same geometric representation, e.g., Bézier and NURBS curves and surfaces. However, in many cases, the geometric representation in a CAD system cannot be directly employed in numerical simulation, as only the boundary of the geometry is parametrized. In these cases, an interior parametrization must be constructed before performing isogeometric analysis. This paper presents an algorithm for generation of unstructured geometrically exact meshes composed of rational Bézier triangles of arbitrary degree, and applies it to plane models described by NURBS curves in a Boundary-Representation (B-Rep) scheme. The proposed algorithm respects input discretization and is capable of generating high quality coarse meshes even when high curvature segments are considered. An efficient high-order smoothing step is employed to avoid tangled elements and to improve element quality. The proposed algorithm attains superior performance when compared to a well-known algorithm in the literature, and performs well in the case of complex geometries. High quality meshes were obtained in all examples analyzed. Furthermore, our implementation is efficient, written in C++, and is available as an open-source software

Vorheriger Artikel Interactive PDE patch-based surface modeling from vertex-frames

Nächster Artikel MGNet: a novel differential mesh generation method based on unsupervised neural networks

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Hughes TJRR, 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. https://doi.org/10.1016/j.cma.2004.10.008MathSciNetCrossRefMATH

Piegl L, Tiller W (1995) The NURBS book. Monographs in visual communications. Springer, Berlin. https://doi.org/10.1007/978-3-642-97385-7CrossRefMATH

Auricchio F, Beirão da Veiga L, Buffa A, Lovadina C, Reali A, Sangalli G (2007) A fully “locking-free’’ isogeometric approach for plane linear elasticity problems: a stream function formulation. Comput Methods Appl Mech Eng 197(1–4):160–172. https://doi.org/10.1016/J.CMA.2007.07.005MathSciNetCrossRefMATH

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. https://doi.org/10.1016/j.cma.2009.05.011MathSciNetCrossRefMATH

Cook Robert D, Malkus David S, Plesha Michael E, Witt Robert J (2001) Concepts and applications of finite element analysis, 4th edn. Wiley, HobokenMATH

Cottrell JA, Hughes TJR, Reali A (2007) Studies of refinement and continuity in isogeometric structural analysis. Comput Methods Appl Mech Eng 196(41–44):4160–4183. https://doi.org/10.1016/j.cma.2007.04.007CrossRefMATH

Vuong A-V, Giannelli C, Jüttler B, Simeon B (2011) A hierarchical approach to adaptive local refinement in isogeometric analysis. Comput Methods Appl Mech Eng 200(49–52):3554–3567. https://doi.org/10.1016/J.CMA.2011.09.004MathSciNetCrossRefMATH

Schillinger D, Dedè L, Scott Michael A, Evans John A, Borden Michael J, Rank E, Hughes Thomas JR (2012) Anisogeometric design-through-analysis methodology based on adaptivehierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces. Comput Methods Appl Mech Eng 249–252:116–150. https://doi.org/10.1016/j.cma.2012.03.017CrossRefMATH

Garau EM, Vázquez R (2018) Algorithms for the implementation of adaptive isogeometric methods using hierarchical B-splines. Appl Numer Math 123:58–87. https://doi.org/10.1016/J.APNUM.2017.08.006MathSciNetCrossRefMATH

10.

Sederberg TW, Zheng J, Bakenov A, Nasri A (2003) T-splines and T-NURCCs. ACM Trans Graph 22(3):477. https://doi.org/10.1145/882262.882295CrossRef

11.

Cottrell JAA, Evans JAA, Lipton S, Scott MAA, Sederberg TWW (2010) Isogeometric analysis using T-splines. Comput Methods Appl Mech Eng 199(5–8):229–263. https://doi.org/10.1016/J.CMA.2009.02.036MathSciNetCrossRefMATH

12.

Liu Zhenyu, Cheng Jin, Yang Minglong, Yuan Pei, Qiu Chan, Gao Wei, Tan Jianrong (2019) Isogeometric analysis of large thin shell structures based on weak coupling of substructures with unstructured T-splines patches. Adv Eng Softw 135:102692. https://doi.org/10.1016/J.ADVENGSOFT.2019.102692CrossRef

13.

Dokken T, Lyche T, Pettersen KF (2013) Polynomial splines over locally refined box-partitions. Comput Aided Geom Des 30(3):331–356. https://doi.org/10.1016/J.CAGD.2012.12.005MathSciNetCrossRefMATH

14.

Johannessen KA, Kvamsdal T, Dokken T (2014) Isogeometric analysis using LR B-splines. Comput Methods Appl Mech Eng 269:471–514. https://doi.org/10.1016/J.CMA.2013.09.014MathSciNetCrossRefMATH

15.

Occelli M, Elguedj T, Bouabdallah S, Morançay L (2019) LR B-Splines implementation in the Altair RadiossTM solver for explicit dynamics Iso geometric analysis. Adv Eng Softw 131:166–185. https://doi.org/10.1016/J.ADVENGSOFT.2019.01.002CrossRef

16.

Deng J, Chen F, Li X, Changqi H, Tong W, Yang Z, Feng Y (2008) Polynomial splines over hierarchical T-meshes. Graph Models 70(4):76–86. https://doi.org/10.1016/J.GMOD.2008.03.001CrossRef

17.

Wang P, Jinlan X, Deng J, Chen F (2011) Adaptive isogeometric analysis using rational PHT-splines. Comput Aided Des 43(11):1438–1448. https://doi.org/10.1016/J.CAD.2011.08.026CrossRef

18.

Giannelli C, Jüttler B, Speleers H (2012) THB-splines: the truncated basis for hierarchical splines. Comput Aided Geom Des 29(7):485–498. https://doi.org/10.1016/J.CAGD.2012.03.025MathSciNetCrossRefMATH

19.

Giannelli C, Jüttler B, Kleiss SK, Mantzaflaris A, Simeon B, Špeh J (2016) THB-splines: an effective mathematical technology for adaptive refinement in geometric design and isogeometric analysis. Comput Methods Appl Mech Eng 299:337–365. https://doi.org/10.1016/J.CMA.2015.11.002MathSciNetCrossRefMATH

20.

Mäntylä M (1988) Introduction to solid modeling. Computer Science Press Inc., New York

21.

Stroud I (2006) Boundary representation modelling techniques. Springer, London. https://doi.org/10.1007/978-1-84628-616-2CrossRefMATH

22.

Kang P, Kie Youn S (2015) Isogeometric analysis of topologically complex shell structures. Finite Elem Anal Des 99:68–81. https://doi.org/10.1016/j.finel.2015.02.002MathSciNetCrossRef

23.

Brovka M, López JI, Escobar JM, Cascón JM, Montenegro R (2014) A new method for T-spline parameterization of complex 2D geometries. Eng Comput 30(4):457–473. https://doi.org/10.1007/s00366-013-0336-8CrossRef

24.

Wang W, Zhang Y, Liu L, Hughes TJRR (2013) Trivariate solid T-spline construction from boundary triangulations with arbitrary genus topology. CAD Comput Aided Des 45(2):351–360. https://doi.org/10.1016/j.cad.2012.10.018MathSciNetCrossRef

25.

Liu L, Zhang Y, Hughes TJRR, Scott MA, Sederberg TW (2013) Volumetric T-spline construction using Boolean operations. Eng Comput 30(4):425–439. https://doi.org/10.1007/s00366-013-0346-6CrossRef

26.

Escobar JM, Montenegro R, Rodríguez E, Cascón JM (2014) The meccano method for isogeometric solid modeling and applications. Eng Comput 30(3):331–343. https://doi.org/10.1007/s00366-012-0300-zCrossRef

27.

Akhras HA, Elguedj T, Gravouil A, Rochette M (2016) Isogeometric analysis-suitable trivariate NURBS models from standard B-Rep models. Comput Methods Appl Mech Eng 307:256–274. https://doi.org/10.1016/j.cma.2016.04.028MathSciNetCrossRefMATH

28.

López JII, Brovka M, Escobar JMM, Montenegro R, Socorro GVV (2017) Spline parameterization method for 2D and 3D geometries based on T-mesh optimization. Comput Methods Appl Mech Eng 322:460–482. https://doi.org/10.1016/J.CMA.2017.05.005MathSciNetCrossRefMATH

29.

Shamanskiy A, Gfrerer MH, Hinz J, Simeon B (2020) Isogeometric parametrization inspired by large elastic deformation. Comput Methods Appl Mech Eng 363:112920. https://doi.org/10.1016/J.CMA.2020.112920MathSciNetCrossRefMATH

30.

Engvall L, Evans JA (2016) Isogeometric triangular Bernstein-Bézier discretizations: automatic mesh generation and geometrically exact finite element analysis. Comput Methods Appl Mech Eng 304:378–407. https://doi.org/10.1016/j.cma.2016.02.012CrossRefMATH

31.

Engvall L, Evans JA (2017) Isogeometric unstructured tetrahedral and mixed-element Bernstein-Bézier discretizations. Comput Methods Appl Mech Eng 319:83–123. https://doi.org/10.1016/j.cma.2017.02.017CrossRefMATH

32.

Jaxon N, Qian X (2014) Isogeometric analysis on triangulations. CAD Comput Aided Des 46(1):45–57. https://doi.org/10.1016/j.cad.2013.08.017MathSciNetCrossRef

33.

Xia S, Qian X (2017) Isogeometric analysis with Bézier tetrahedra. Comput Methods Appl Mech Eng 316:782–816. https://doi.org/10.1016/j.cma.2016.09.045CrossRefMATH

34.

Zareh M, Qian X (2019) Kirchhoff-Love shell formulation based on triangular isogeometric analysis. Comput Methods Appl Mech Eng 347:853–873. https://doi.org/10.1016/J.CMA.2018.12.034MathSciNetCrossRefMATH

35.

Liu N, Jeffers AE (2018) A geometrically exact isogeometric Kirchhoff plate: feature-preserving automatic meshing and C1 rational triangular Bézier spline discretizations. Int J Numer Methods Eng 115(3):395–409. https://doi.org/10.1002/nme.5809CrossRef

36.

Jorge L, Cosmin A, Navid V, Naif RTA (2019) Structural shape optimization using Bézier triangles and a CAD-compatible boundary representation. Eng Comput. https://doi.org/10.1007/s00366-019-00788-zCrossRef

37.

Engvall L (2018) Geometrically exact and analysis suitable mesh generation using rational Bernstein-Bezier elements. PhD thesis, University of Colorado

38.

Engvall L, Evans JA (2020) Mesh quality metrics for isogeometric Bernstein-Bézier discretizations. Comput Methods Appl Mech Eng 371:113305. https://doi.org/10.1016/j.cma.2020.113305CrossRefMATH

39.

Dey S, O’Bara RM, Shephard MS (2001) Towards curvilinear meshing in 3D: the case of quadratic simplices. CAD Comput Aided Des 33(3):199–209. https://doi.org/10.1016/S0010-4485(00)00120-2CrossRef

40.

Qiukai L, Shephard MS, Tendulkar S, Beall MW (2014) Parallel mesh adaptation for high-order finite element methods with curved element geometry. Eng Comput 30(2):271–286. https://doi.org/10.1007/s00366-013-0329-7CrossRef

41.

Geuzaine C, Johnen A, Lambrechts J, Remacle JF, Toulorge T (2015) The generation of valid curvilinear meshes. Notes Numer Fluid Mech Multidiscip Des 128:15–39. https://doi.org/10.1007/978-3-319-12886-3_2CrossRef

42.

Roca X, Gargallo-Peiro A, Sarrate J (2011) Defining qualitymeasures for high-order planar triangles and curved mesh generation. In: Proceedings of the 20th international meshing roundtable,IMR 2011, p. 365–383. Springer, Berlin, Heidelberg.https://doi.org/10.1007/978-3-642-24734-7-20

43.

Toulorge T, Geuzaine C, Remacle JF, Lambrechts J (2013) Robust untangling of curvilinear meshes. J Comput Phys 254:8–26. https://doi.org/10.1016/j.jcp.2013.07.022MathSciNetCrossRefMATH

44.

Johnen A, Remacle JF, Geuzaine C (2013) Geometrical validity of curvilinear finite elements. J Comput Phys 233(1):359–372. https://doi.org/10.1016/j.jcp.2012.08.051MathSciNetCrossRef

45.

Gargallo-Peiró A, Roca X, Peraire J, Sarrate J (2015) Distortion and quality measures for validating and generating high-order tetrahedral meshes. Eng Comput 31(3):423–437. https://doi.org/10.1007/s00366-014-0370-1CrossRefMATH

46.

Johnen A, Geuzaine C, Toulorge T, Remacle JF (2018) Efficient computation of the minimum of shape quality measures on curvilinear finite elements. CAD Comput Aided Des 103:24–33. https://doi.org/10.1016/j.cad.2018.03.001MathSciNetCrossRef

47.

Luo XJ, Shephard MS, Lee LQ, Ge L, Ng C (2011) Moving curved mesh adaptation for higher-order finite element simulations. Eng Comput 27(1):41–50. https://doi.org/10.1007/s00366-010-0179-5CrossRef

48.

Ruiz-Gironés E, Gargallo-Peiró A, Sarrate J, Roca X (2019) Automatically imposing incremental boundary displacements for valid mesh morphing and curving. Comput Aided Des 112:47–62. https://doi.org/10.1016/J.CAD.2019.01.001MathSciNetCrossRef

49.

Cardoze D, Cunha A, Miller GL, Phillips T, Walkington N (2004) A bézier-based approach to unstructured movingmeshes. In: Proceedings of the twentieth annual symposium oncomputational geometry—SCG ’04, p. 310, New York, USA, ACM Press. https://doi.org/10.1145/997817.997864

50.

Kadapa C (2019) Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics. Int J Numer Methods Eng 117(5):543–573. https://doi.org/10.1002/nme.5967MathSciNetCrossRef

51.

Manish M, Marcel C (2020) Bézier guarding: precise higher-order meshing of curved 2D domains. ACM Trans Graph (TOG). https://doi.org/10.1145/3386569.3392372CrossRef

52.

Miranda ACO, Meggiolaro MA, Castro JTP, Martha LF, Bittencourt TN (2003) Fatigue life and crack path predictions in generic 2D structural components. Eng Fract Mech 70(10):1259–1279. https://doi.org/10.1016/S0013-7944(02)00099-1CrossRef

53.

Piegl L (1991) On NURBS: a survey. IEEE Comput Graph Appl 11(1):55–71. https://doi.org/10.1109/38.67702CrossRef

54.

Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. Wiley, Chichester. https://doi.org/10.1002/9780470749081CrossRefMATH

55.

Scott MA, Borden MJ, Verhoosel CV, Sederberg TW, Hughes TJRR (2011) Isogeometric finite element data structures based on Bézier extraction of T-splines. Int J Numer Methods Eng 88(2):126–156. https://doi.org/10.1002/nme.3167CrossRefMATH

56.

Thomas DC, Scott MA, Evans JA, Tew K, Evans EJ (2015) Bézier projection: a unified approach for local projection and quadrature-free refinement and coarsening of NURBS and T-splines with particular application to isogeometric design and analysis. Comput Methods Appl Mech Eng 284:55–105. https://doi.org/10.1016/j.cma.2014.07.014CrossRefMATH

57.

Farin G (2002) Curves and surfaces for CAGD a practical guide, vol 3, 5th edn. Morgan Kaufmann Publishers Inc., San Francisco

58.

Mainar E, Peña JM (2006) Evaluation algorithms for multivariate polynomials in Bernstein-Bézier form. J Approx Theory 143(1):44–61. https://doi.org/10.1016/j.jat.2006.05.007MathSciNetCrossRefMATH

59.

Hansford D (2002) Chapter 4–Bézier techniques. In: Gerald F, Josef H, Myung-Soo K (eds) Handbook of computer aided geometric design. Amsterdam, North-Holland, pp 75–109. https://doi.org/10.1016/B978-044451104-1/50005-8CrossRef

60.

Barroso ES, Evans JA, Cavalcante-Neto JB, Vidal CA, Parente JE (2019) An algorithm for automatic discretization of isogeometric plane models. In: XL Iberian Latin-American congress on computational methods in engineering, Natal

61.

Haber R, Shephard MS, Abel JF, Gallagher RH, Greenberg DP (1981) A general two-dimensional, graphical finite element preprocessor utilizing discrete transfinite mappings. Int J Numer Methods Eng 17(7):1015–1044. https://doi.org/10.1002/nme.1620170706CrossRefMATH

62.

Hinz J, Möller M, Vuik C (2018) Elliptic grid generation techniques in the framework of isogeometric analysis applications. Comput Aided Geom Des 65:48–75. https://doi.org/10.1016/j.cagd.2018.03.023MathSciNetCrossRefMATH

63.

Gondegaon S, Voruganti HK (2018) An efficient parametrization of planar domain for isogeometric analysis using harmonic functions. J Braz Soc Mech Sci Eng 40(10):493. https://doi.org/10.1007/s40430-018-1414-zCrossRef

64.

Shephard MS, Flaherty JE, Jansen KE, Li X, Luo X, Chevaugeon N, Remacle JF, Beall MW, O’Bara RM (2005) Adaptive mesh generation for curved domains. Appl Numer Math 52(2–3 SPEC. ISS):251–271. https://doi.org/10.1016/j.apnum.2004.08.040MathSciNetCrossRefMATH

65.

Miranda ACOO, Cavalcante-Neto JB, Martha LF (1999) An algorithm for two-dimensional mesh generation for arbitrary regions with cracks. In: Proceedings 2th Brazilian symposium on computer graphics and image processing, SIBGRAPI 1999, p. 29–38. IEEE Comput Soc, https://doi.org/10.1109/SIBGRA.1999.805605

66.

Freitas MO, Wawrzynek PA, Cavalcante-Neto JB, Vidal CA, Martha LF, Ingraffea AR (2013) A distributed-memory parallel technique for two-dimensional mesh generation for arbitrary domains. Adv Eng Softw 59:38–52. https://doi.org/10.1016/j.advengsoft.2013.03.005CrossRef

67.

Bazilevs Y, Beirão Da Veiga L, Cottrell JA, Hughes TJR, Sangalli G (2006) Isogeometric analysis: approximation, stability and error estimates for h-refined meshes. Math Models Methods Appl Sci 16(7):1031–1090. https://doi.org/10.1142/S0218202506001455MathSciNetCrossRefMATH

68.

Xie ZQ, Sevilla R, Hassan O, Morgan K (2013) The generation of arbitrary order curved meshes for 3D finite element analysis. Comput Mech 51(3):361–374. https://doi.org/10.1007/s00466-012-0736-4MathSciNetCrossRef

69.

Abgrall R, Dobrzynski C, Froehly A (2014) A method for computing curved meshes via the linear elasticity analogy, application to fluid dynamics problems. Int J Numer Methods Fluids 76(4):246–266. https://doi.org/10.1002/fld.3932MathSciNetCrossRefMATH

70.

Poya R, Sevilla R, Gil AJ (2016) A unified approach for a posteriori high-order curved mesh generation using solid mechanics. Comput Mech 58(3):457–490. https://doi.org/10.1007/s00466-016-1302-2MathSciNetCrossRefMATH

71.

Persson P-O, Peraire J (2013) Curved mesh generation and mesh refinement using lagrangian solid mechanics. In: 47th AIAA aerospace sciences meeting including The New Horizons Forum and Aerospace Exposition, Reston, Virigina, American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2009-949

72.

Moxey D, Ekelschot D, Keskin U, Sherwin SJ, Peiró J (2016) High-order curvilinear meshing using a thermo-elastic analogy. CAD Comput Aided Des 72:130–139. https://doi.org/10.1016/j.cad.2015.09.007CrossRef

73.

Cormen TH, Leiserson CE, Rivest RL, Stein C (2009) Introduction to algorithms. The MIT Press, 3rd edn, https://doi.org/10.2307/2583667

74.

Knupp P (2009) Label-invariant mesh quality metrics. In: Proceedings of the 18th international meshing roundtable, IMR 2009, p. 139–155. Springer, Berlin Heidelberg. https://doi.org/10.1007/978-3-642-04319-2_9

75.

Knupp PM (2003) Algebraic mesh quality metrics for unstructured initial meshes. Finite Elem Anal Des 39(3):217–241. https://doi.org/10.1016/S0168-874X(02)00070-7CrossRefMATH

76.

Dunavant DA (1985) High degree efficient symmetrical Gaussian quadrature rules for the triangle. Int J Numer Methods Eng 21(6):1129–1148. https://doi.org/10.1002/nme.1620210612MathSciNetCrossRefMATH

77.

Engvall L (2015) TriGA: triangular IGA

78.

Persson PO (2006) Mesh size functions for implicit geometries and PDE-based gradient limiting. Eng Comput 22(2):95–109. https://doi.org/10.1007/s00366-006-0014-1CrossRef

79.

Geuzaine C, Remacle JF (2009) Gmsh: a 3-D finite element mesh generator with built-in pre- and post-processing facilities. Int J Numer Methods Eng 79(11):1309–1331. https://doi.org/10.1002/nme.2579MathSciNetCrossRefMATH

80.

Zienkiewicz OC, Taylor RL (2000) The finite element method. Butterworth-Heinemann

Titel: An efficient automatic mesh generation algorithm for planar isogeometric analysis using high-order rational Bézier triangles
verfasst von: Elias Saraiva Barroso
John Andrew Evans
Joaquim Bento Cavalcante-Neto
Creto Augusto Vidal
Evandro Parente Jr.
Publikationsdatum: 09.02.2022
Verlag: Springer London
Erschienen in: Engineering with Computers / Ausgabe 5/2022
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI: https://doi.org/10.1007/s00366-022-01613-w

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