Isogeometric analysis based on geometric reconstruction models

Abstract

In isogeometric analysis (IGA), the boundary representation of computer-aided design (CAD) and the tensor-product non-uniform rational B-spline structure make the analysis of three-dimensional (3D) problems with irregular geometries difficult. In this paper, an IGA method for complex models is presented by reconstructing analysis-suitable models. The CAD model is represented by boundary polygons or point cloud and is embedded into a regular background grid, and a model reconstruction method is proposed to obtain the level set function of the approximate model, which can be directly used in IGA. Three 3D examples are used to test the proposed method, and the results demonstrate that the proposed method can deal with complex engineering parts reconstructed by boundary polygons or point clouds.

Graphical abstract

Keywords

isogeometric analysis / reconstruction model / level set function / trimmed element / point cloud

References

[1] HughesT J R, CottrellJ A, BazilevsY. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 2005, 194( 39‒41): 4135– 4195

[2] CottrellJ A, RealiA, BazilevsY. Isogeometric analysis of structural vibrations. Computer Methods in Applied Mechanics and Engineering, 2006, 195( 41‒43): 5257– 5296

[3] WeegerO, WeverU, SimeonB. Isogeometric analysis of nonlinear Euler–Bernoulli beam vibrations. Nonlinear Dynamics, 2013, 72( 4): 813– 835

[4] BensonD J, BazilevsY, HsuM C. A large deformation, rotation-free, isogeometric shell. Computer Methods in Applied Mechanics and Engineering, 2011, 200( 13‒16): 1367– 1378

[5] DengX, KorobenkoA, YanJ. Isogeometric analysis of continuum damage in rotation-free composite shells. Computer Methods in Applied Mechanics and Engineering, 2015, 284 : 349– 372

[6] BazilevsY, DengX, KorobenkoA. Isogeometric fatigue damage prediction in large-scale composite structures driven by dynamic sensor data. Journal of Applied Mechanics, 2015, 82( 9): 091008–

[7] BazilevsY, KorobenkoA, DengX. Fluid-structure interaction modeling for fatigue-damage prediction in full-scale wind-turbine blades. Journal of Applied Mechanics, 2016, 83( 6): 061010–

[8] PengX, AtroshchenkoE, KerfridenP. Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth. Computer Methods in Applied Mechanics and Engineering, 2017, 316 : 151– 185

[9] BazilevsY, CaloV M, HughesT J R. Isogeometric fluid-structure interaction: theory, algorithms, and computations. Computational Mechanics, 2008, 43( 1): 3– 37

[10] HsuM C, AkkermanI, BazilevsY. High-performance computing of wind turbine aerodynamics using isogeometric analysis. Computers & Fluids, 2011, 49( 1): 93– 100

[11] YanJ, DengX, KorobenkoA. Free-surface flow modeling and simulation of horizontal-axis tidal-stream turbines. Computers & Fluids, 2017, 158 : 157– 166

[12] BazilevsY, YanJ, DengX. Computer modeling of wind turbines: 2. Free-surface FSI and fatigue-damage. Archives of Computational Methods in Engineering, 2019, 26( 4): 1101– 1115

[13] WangY, BensonD J. Isogeometric analysis for parameterized LSM-based structural topology optimization. Computational Mechanics, 2016, 57( 1): 19– 35

[14] WangY, XuH, PasiniD. Multiscale isogeometric topology optimization for lattice materials. Computer Methods in Applied Mechanics and Engineering, 2017, 316 : 568– 585

[15] WangZ P, PohL H, DirrenbergerJ. Isogeometric shape optimization of smoothed petal auxetic structures via computational periodic homogenization. Computer Methods in Applied Mechanics and Engineering, 2017, 323 : 250– 271

[16] XieX, WangS, XuM. A new isogeometric topology optimization using moving morphable components based on R-functions and collocation schemes. Computer Methods in Applied Mechanics and Engineering, 2018, 339 : 61– 90

[17] DengX W, WuN, YangK. Integrated design framework of next-generation 85-m wind turbine blade: modelling, aeroelasticity and optimization. Composites Part B, Engineering, 2019, 159 : 53– 61

[18] WangZ P, PohL H. Optimal form and size characterization of planar isotropic petal-shaped auxetics with tunable effective properties using IGA. Composite Structures, 2018, 201 : 486– 502

[19] WangZ P, PohL H, ZhuY. Systematic design of tetra-petals auxetic structures with stiffness constraint. Materials & Design, 2019, 170 : 107669–

[20] BabicB, NesicN, MiljkovicZ. A review of automated feature recognition with rule-based pattern recognition. Computers in Industry, 2008, 59( 4): 321– 337

[21] ZhuX F, HuP, MaZ D. A new surface parameterization method based on one-step inverse forming for isogeometric analysis-suited geometry. International Journal of Advanced Manufacturing Technology, 2013, 65( 9‒12): 1215– 1227

[22] JaxonN, QianX. Isogeometric analysis on triangulations. Computer-Aided Design, 2014, 46 : 45– 57

[23] MartinT, CohenE, KirbyR M. Volumetric parameterization and trivariate B-spline fitting using harmonic functions. Computer-Aided Geometric Design, 2009, 26( 6): 648– 664

[24] XuG, MourrainB, DuvigneauR. Analysis-suitable volume parameterization of multi-block computational domain in isogeometric applications. Computer-Aided Design, 2013, 45( 2): 395– 404

[25] ZuoB Q, HuangZ D, WangY W. Isogeometric analysis for CSG models. Computer Methods in Applied Mechanics and Engineering, 2015, 285 : 102– 124

[26] BazilevsY, CaloV M, CottrellJ A. Isogeometric analysis using T-splines. Computer Methods in Applied Mechanics and Engineering, 2010, 199( 5‒8): 229– 263

[27] ScottM A, LiX, SederbergT W. Local refinement of analysis-suitable T-splines. Computer Methods in Applied Mechanics and Engineering, 2012, 213‒216 : 206– 222

[28] Whetten C, Sederberg M, Scott M. Isogeometric analysis using the *IGA_INCLUDE_BEZIER keyword in LS-DYNA. 2019

[29] KimH J, SeoY D, YounS K. Isogeometric analysis for trimmed CAD surfaces. Computer Methods in Applied Mechanics and Engineering, 2009, 198( 37‒40): 2982– 2995

[30] WangY W, HuangZ D, ZhengY. Isogeometric analysis for compound B-spline surfaces. Computer Methods in Applied Mechanics and Engineering, 2013, 261‒262 : 1– 15

[31] NagyA P, BensonD J. On the numerical integration of trimmed isogeometric elements. Computer Methods in Applied Mechanics and Engineering, 2015, 284 : 165– 185

[32] WangY, BensonD J, NagyA P. A multi-patch nonsingular isogeometric boundary element method using trimmed elements. Computational Mechanics, 2015, 56( 1): 173– 191

[33] RuessM, SchillingerD, BazilevsY. 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

[34] MarussigB, ZechnerJ, BeerG. Stable isogeometric analysis of trimmed geometries. Computer Methods in Applied Mechanics and Engineering, 2017, 316 : 497– 521

[35] GuoY, HellerJ, HughesT J R. Variationally consistent isogeometric analysis of trimmed thin shells at finite deformations, based on the STEP exchange format. Computer Methods in Applied Mechanics and Engineering, 2018, 336 : 39– 79

[36] MarussigB, HughesT J. A review of trimming in isogeometric analysis: challenges, data exchange and simulation aspects. Archives of Computational Methods in Engineering, 2018, 25( 4): 1059– 1127

[37] ParvizianJ, DüsterA, RankE. Finite cell method. Computational Mechanics, 2007, 41( 1): 121– 133

[38] DüsterA, ParvizianJ, YangZ. The finite cell method for three-dimensional problems of solid mechanics. Computer Methods in Applied Mechanics and Engineering, 2008, 197( 45‒48): 3768– 3782

[39] SchillingerD, RuessM. The finite cell method: a review in the context of higher-order structural analysis of CAD and image-based geometric models. Archives of Computational Methods in Engineering, 2015, 22( 3): 391– 455

[40] KamenskyD, HsuM C, SchillingerD. An immersogeometric variational framework for fluid–structure interaction: application to bioprosthetic heart valves. Computer Methods in Applied Mechanics and Engineering, 2015, 284 : 1005– 1053

[41] XuF, SchillingerD, KamenskyD. The tetrahedral finite cell method for fluids: immersogeometric analysis of turbulent flow around complex geometries. Computers & Fluids, 2016, 141 : 135– 154

[42] HuangJ, MenqC H. Automatic CAD model reconstruction from multiple point clouds for reverse engineering. Journal of Computing and Information Science in Engineering, 2002, 2( 3): 160– 170

[43] ManmadhacharyA, KumarR, KrishnanandL. Improve the accuracy, surface smoothing and material adaption in STL file for RP medical models. Journal of Manufacturing Processes, 2016, 21 : 46– 55

[44] WangJ, GuD, YuZ. A framework for 3D model reconstruction in reverse engineering. Computers & Industrial Engineering, 2012, 63( 4): 1189– 1200

[45] RajonD A, BolchW E. Marching cube algorithm: review and trilinear interpolation adaptation for image-based dosimetric models. Computerized Medical Imaging and Graphics, 2003, 27( 5): 411– 435

[46] MontaniC, ScateniR, ScopignoR. A modified look-up table for implicit disambiguation of marching cubes. The Visual Computer, 1994, 10( 6): 353– 355

[47] NewmanT S, YiH. A survey of the marching cubes algorithm. Computers & Graphics, 2006, 30( 5): 854– 879

[48] ChangM, OhJ W, ChangD S. Interactive marching cubes algorithm for intraoral scanners. International Journal of Advanced Manufacturing Technology, 2017, 89( 5‒8): 2053– 2062

[49] DoiA, KoideA. An efficient method of triangulating equi-valued surfaces by using tetrahedral cells. IEICE Transactions on Information and Systems, 1991, 74( 1): 214– 224

[50] TreeceG M, PragerR W, GeeA H. Regularised marching tetrahedra: Improved iso-surface extraction. Computers & Graphics, 1999, 23( 4): 583– 598

[51] GuoD, LiC, WuL. Improved marching tetrahedra algorithm based on hierarchical signed distance field and multi-scale depth map fusion for 3D reconstruction. Journal of Visual Communication and Image Representation, 2017, 48 : 491– 501

[52] ZanderN, BogT, ElhaddadM. FCMLab: a finite cell research toolbox for MATLAB. Advances in Engineering Software, 2014, 74 : 49– 63

[53] VerhooselC V, Van ZwietenG J, Van RietbergenB. Image-based goal-oriented adaptive isogeometric analysis with application to the micro-mechanical modeling of trabecular bone. Computer Methods in Applied Mechanics and Engineering, 2015, 284 : 138– 164

[54] KudelaL, KollmannsbergerS, AlmacU. Direct structural analysis of domains defined by point clouds. Computer Methods in Applied Mechanics and Engineering, 2020, 358 : 112581–

[55] Piegl L, Tiller W. The NURBS Book. New York: Springer, 1997

[56] de BoorC. On calculating with B-splines. Journal of Approximation Theory, 1972, 6( 1): 50– 62

[57] XiaZ, WangQ, WangY. A CAD/CAE incorporate software framework using a unified representation architecture. Advances in Engineering Software, 2015, 87 : 68– 85

[58] RequichaA A G, VoelckerH B. Boolean operations in solid modeling: boundary evaluation and merging algorithms. Proceedings of the IEEE, 1985, 73( 1): 30– 44

[59] HalesT C. The Jordan curve theorem, formally and informally. American Mathematical Monthly, 2007, 114( 10): 882– 894

[60] WangY, BensonD J. Geometrically constrained isogeometric parameterized level-set based topology optimization via trimmed elements. Frontiers of Mechanical Engineering, 2016, 11( 4): 328– 343

[61] Eberly D. Distance between point and triangle in 3D. Geometric Tools, 2008

[62] WangY, LiaoZ, YeM. An efficient isogeometric topology optimization using multilevel mesh, MGCG and local-update strategy. Advances in Engineering Software, 2020, 139 : 102733–

[63] ZhuB, ZhangX, ZhangH. Design of compliant mechanisms using continuum topology optimization: a review. Mechanism and Machine Theory, 2020, 143 : 103622–

RIGHTS & PERMISSIONS

The Author(s) 2021. This article is published with open access at link.springer.com and journal.hep.com.cn.