Please wait a minute...
浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2021, Vol. 55 Issue (1): 135-144    DOI: 10.3785/j.issn.1008-973X.2021.01.016
    
Solid modeling and slicing process of heterogeneous materials based on trivariate T-splines
Bin LI(),Jian-zhong FU*()
College of Mechanical Engineering, Zhejiang University, Hangzhou 310058, China
Download: HTML     PDF(1712KB) HTML
Export: BibTeX | EndNote (RIS)      

Abstract  

A general modeling and manufacturing process that can be used to design, analyze and manufacture heterogeneous material solids was developed in order to apply heterogeneous material solids into additive manufacturing technology. A modeling algorithm for heterogeneous material solids was proposed based on trivariate T-splines. T-mesh was adaptively refined based on the unit cubic. Then the tetrahedral mesh model and its heterogeneous materials were gradually fitted by minimizing the defined energy functional. Adaptive refinement was conducted only in those regions that undergo fine-scale deformation and updated control points were directly inserted in the parametric domain in order to improve computational efficiency. The comparison between trivariate T-splines with adaptive refinement and trivariate NURBS with uniform refinement shows the computational efficiency with much fewer control points. A direct slicing algorithm sliced heterogeneous material solid as the triangular meshes by combining trivariate T-splines and adaptive subdivision process based on the octree structure. The experimental results demonstrated the effectivity and reliability especially for slicing solid heterogeneous objects.

Key words： heterogeneous material      solid modeling      trivariate T-spline      additive manufacturing      direct slicing algorithm     
Received: 24 April 2020      Published: 05 January 2021
CLC:  TH 164  
Corresponding Authors: Jian-zhong FU     E-mail: lib1992@zju.edu.cn;fjz@zju.edu.cn
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Bin LI
Jian-zhong FU
Cite this article:

Bin LI,Jian-zhong FU. Solid modeling and slicing process of heterogeneous materials based on trivariate T-splines. Journal of ZheJiang University (Engineering Science), 2021, 55(1): 135-144.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2021.01.016     OR     http://www.zjujournals.com/eng/Y2021/V55/I1/135


基于三维T样条的异质材料实体建模与切片

为了实现异质材料实体模型应用于增材制造技术的可能性，开发通用的、可同时用于设计、分析和制造异质材料实体模型的建模与制造工艺. 提出基于三维T样条的异质材料实体重建方法，实施自适应细分得到三维T型控制网格. 通过最小化能量泛函逐步拟合四面体网格模型及异质材料属性，使得几何结构和材料分布均得到较高的拟合精度. 为了提高重建过程的计算效率，只对局部误差较大的区域进行自适应细分，在参数域内插入控制点. 采用自适应细分的三维T样条与均匀细分的三维NURBS，分别实施渐进式重建框架. 结果表明，三维T样条能够在达到相似甚至更优的拟合精度的前提下减少冗余控制点. 针对增材制造中的切片工艺，利用适用于异质材料实体模型的直接切片方法，结合三维T样条和基于八叉树结构的自适应细分过程，得到三角网格分层切片结果. 实验结果表明，该算法对异质材料实体模型的直接切片过程是有效和可靠的.


关键词： 异质材料,  实体模型重建,  三维T样条,  增材制造,  直接切片方法 
Fig.1 Modeling framework for solids with heterogeneous materials
Fig.2 Adaptive initialization process for trivariate T-mesh
Fig.3 Progressive modeling framework implemented on lower extremity of femur
Fig.4 Slicing T-meshes based on three different tolerances
Fig.5 Direct slicing results based on slicing T-meshes in Fig.4
Fig.6 Progressive modeling framework implemented on upper extremity of femur
Fig.7 Progressive modeling framework implemented on Rubber Duck
实验模型 三维T样条 nc $ \varepsilon $ ni RS/%
股骨下端 $ G\left({{x}}\right) $ 17 409 0.6 20 86.76
股骨下端 $ M\left({{x}}\right) $ 17 409 0.6 25 90.13
股骨上端 $ G\left({{x}}\right) $ 21 659 0.6 23 85.33
股骨上端 $ M\left({{x}}\right) $ 21 659 0.6 27 88.03
橡皮鸭 $ G\left({{x}}\right) $ 27 455 0.4 23 80.47
橡皮鸭 $ M\left({{x}}\right) $ 27 455 0.4 16 88.66
Tab.1 Modeling results of trivariate T-splines with heterogeneous materials
实验模型 三维NURBS nc $ \varepsilon $ ni RS/%
股骨下端 $ G\left({{x}}\right) $ 68 921 0.6 25 84.57
股骨下端 $ M\left({{x}}\right) $ 68 921 0.6 27 82.66
股骨上端 $ G\left({{x}}\right) $ 64 000 0.6 28 84.62
股骨上端 $ M\left({{x}}\right) $ 64 000 0.6 27 85.92
橡皮鸭 $ G\left({{x}}\right) $ 54 872 0.4 31 83.84
橡皮鸭 $ M\left({{x}}\right) $ 54 872 0.4 19 90.27
Tab.2 Modeling results of trivariate NURBS with heterogeneous materials
Fig.8 Results of direct slicing lower extremity of femur
Fig.9 Results of direct slicing upper extremity of femur
Fig.10 Results of direct slicing Rubber Duck
Fig.11 Results of extracting iso-material surfaces from lower extremity of femur
Fig.12 Results of extracting iso-material surfaces from upper extremity of femur
Fig.13 Results of extracting iso-material surfaces from Rubber Duck
[1]   KOU X Y, TAN S T Heterogeneous object modeling: a review[J]. Computer Aided Design, 2007, 39 (4): 284- 301
doi: 10.1016/j.cad.2006.12.007
[2]   ZHANG B, JAISWAL P, RAI R, et al Additive manufacturing of functionally graded material objects: a review[J]. Journal of Computing and Information Science in Engineering, 2018, 18 (4): 041002.1- 041002.16
[3]   KUMAR V, BURNS D, DUTTA D, et al A framework for object modeling[J]. Computer-Aided Design, 1999, 31 (9): 541- 556
doi: 10.1016/S0010-4485(99)00051-2
[4]   ZHANG Y, HUGHES T J R, BAJAJ C L An automatic 3D mesh generation method for domains with multiple materials[J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199 (5): 405- 415
[5]   YOU Y H, KOU X Y, TAN S T Adaptive tetrahedral mesh generation of 3D heterogeneous objects[J]. Computer-Aided Design and Applications, 2015, 12 (5): 580- 588
doi: 10.1080/16864360.2015.1014736
[6]   HUGHES T J R, COTTRELL J A, BAZILEVS Y Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement[J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194 (39-41): 4135- 4195
doi: 10.1016/j.cma.2004.10.008
[7]   HUA J, HE Y, QIN H. Multiresolution heterogeneous solid modeling and visualization using trivariate simplex splines [C]// Symposium on Solid Modeling and Applications. Genoa: ACM, 2004: 47-58.
[8]   HUA J, HE Y, QIN H Trivariate simplex splines for inhomogeneous solid modeling in engineering design[J]. Journal of Computing and Information Science in Engineering, 2005, 5 (2): 149- 157
doi: 10.1115/1.1881352
[9]   ZHANG Y, BAZILEVS Y, GOSWAMI S, et al Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow[J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196 (29/30): 2943- 2959
[10]   SASAKI Y, TAKEZAWA M, KIM S, et al Adaptive direct slicing of volumetric attribute data represented by trivariate B-spline functions[J]. International Journal of Advanced Manufacturing Technology, 2017, 91 (5-8): 1791- 1807
doi: 10.1007/s00170-016-9800-0
[11]   SEDERBERG T W, ZHENG J, BAKENOV A, et al T-splines and T-NURCCs[J]. ACM Transactions on Graphics, 2003, 22 (3): 477- 484
doi: 10.1145/882262.882295
[12]   SEDERBERG T W, CARDON D, FINNIGAN G, et al T-spline simplification and local refinement[J]. ACM Transactions on Graphics, 2004, 23 (3): 276- 283
doi: 10.1145/1015706.1015715
[13]   ESCOBAR J M, CASCON J M, RODRIGUEZ E, et al A new approach to solid modeling with trivariate T-splines based on mesh optimization[J]. Computer Methods in Applied Mechanics and Engineering, 2011, 200 (45/46): 3210- 3222
[14]   LI B, LI X, WANG K, et al. Generalized polycube trivariate splines [C]// 2010 Shape Modeling International Conference. Aix-en-Provence: IEEE, 2010: 261-265.
[15]   WANG K, LI X, LI B, et al Restricted trivariate polycube splines for volumetric data modeling[J]. IEEE Transactions on Visualization and Computer Graphics, 2012, 18 (5): 703- 716
doi: 10.1109/TVCG.2011.102
[16]   ZHANG Y, WANG W, HUGHES T J R Solid T-spline construction from boundary representations for genus-zero geometry[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 249-252: 185- 197
doi: 10.1016/j.cma.2012.01.014
[17]   WANG W, ZHANG Y, LIU L, et al Trivariate solid T-spline construction from boundary triangulations with arbitrary genus topology[J]. Computer-Aided Design, 2013, 45 (2): 351- 360
doi: 10.1016/j.cad.2012.10.018
[18]   MARTIN W, COHEN E. Representation and extraction of volumetric attributes using trivariate splines: a mathematical framework [C]// Proceedings of the 6th ACM Symposium on Solid Modeling and Applications. New York: ACM, 2001: 234-240.
[19]   LIN H, JIN S, HU Q, et al Constructing B-spline solids from tetrahedral meshes for isogeometric analysis[J]. Computer Aided Geometric Design, 2015, 35-36: 109- 120
doi: 10.1016/j.cagd.2015.03.013
[20]   LENG J, XU G, ZHANG Y Medical image interpolation based on multi-resolution registration[J]. Computers and Mathematics with Applications, 2013, 66 (1): 1- 18
doi: 10.1016/j.camwa.2013.04.026
[21]   JIA Y, ZHANG Y, RABCZUK T A novel dynamic multilevel technique for image registration[J]. Computers and Mathematics with Applications, 2015, 69 (9): 909- 925
doi: 10.1016/j.camwa.2015.02.010
[22]   PAWAR A, ZHANG Y, ANITESCU C, et al DTHB3D_Reg: dynamic truncated hierarchical B-spline based 3D nonrigid image registration[J]. Communications in Computational Physics, 2018, 23 (3): 877- 898
[23]   PAWAR A, ZHANG Y, ANITESCU C, et al Joint image segmentation and registration based on a dynamic level set approach using truncated hierarchical B-splines[J]. Computers and Mathematics with Applications, 2019, 78 (10): 3250- 3267
doi: 10.1016/j.camwa.2019.04.026
[24]   LI B, FU J, ZHANG J Y, et al Slicing heterogeneous solid using octree-based subdivision and trivariate T-splines for additive manufacturing[J]. Rapid Prototyping Journal, 2020, 26 (1): 164- 175
doi: 10.1108/RPJ-11-2018-0287
[1] Xiao-wei LIU,Yun CHEN,Si ZHANG,Kang CHEN. Dynamic monitoring and identification of wire feeder in FDM-based additive manufacturing[J]. Journal of ZheJiang University (Engineering Science), 2021, 55(3): 548-554.
[2] Jun DU,Chen MA,Zheng-ying WEI. Dynamic response of surface morphology of aluminum (Al) deposited layers in wire and arc additive manufacturing based on visual sensing[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(8): 1481-1489.
[3] SHAO Hui-feng, HE Yong, FU Jian-zhong. Research advance of degradable artificial bone with additive manufacturing: customization from geometric shape to property[J]. Journal of ZheJiang University (Engineering Science), 2018, 52(6): 1035-1057.
[4] DU Jun, WANG Xin, REN Chuan-qi, BAI Hao. Morphology analysis of thin-wallparts by metal fused-coating additive manufacturing[J]. Journal of ZheJiang University (Engineering Science), 2018, 52(1): 24-28.