[1]石顺义,郭新泽,周克民.结构拓扑优化数值方法研究进展[J].华侨大学学报(自然科学版),2024,45(2):150-157.[doi:10.11830/ISSN.1000-5013.202312025]
 SHI Shunyi,GUO Xinze,ZHOU Kemin.Research Progress in Numerical Methods of Structural Topology Optimization[J].Journal of Huaqiao University(Natural Science),2024,45(2):150-157.[doi:10.11830/ISSN.1000-5013.202312025]
点击复制

结构拓扑优化数值方法研究进展()
分享到:

《华侨大学学报(自然科学版)》[ISSN:1000-5013/CN:35-1079/N]

卷:
第45卷
期数:
2024年第2期
页码:
150-157
栏目:
出版日期:
2024-03-20

文章信息/Info

Title:
Research Progress in Numerical Methods of Structural Topology Optimization
文章编号:
1000-5013(2024)02-0150-08
作者:
石顺义 郭新泽 周克民
华侨大学 土木工程学院, 福建 厦门 361021
Author(s):
SHI Shunyi GUO Xinze ZHOU Kemin
College of Civil Engineering, Huaqiao University, Xiamen 361021, China
关键词:
结构优化 拓扑优化 数值方法 研究进展
Keywords:
structural optimization topology optimization numerical methods research progress
分类号:
TU4
DOI:
10.11830/ISSN.1000-5013.202312025
文献标志码:
A
摘要:
综述结构拓扑优化数值方法,分析其主要发展趋势。根据不同近似参数比较两类主要优化方法,基于材料的方法借助离散形式的参数描述材料分布场,具有自由度高、描述能力强等优点,基于几何的方法通过描述材料边界形成最优结构,边界清晰且无需后处理。结果表明:放松工程制造约束和提高求解效率是拓扑优化值得深入探索的研究方向,具有广阔的应用前景。
Abstract:
The numerical methods of structural topology optimization are reviewed, and the main trends of the methods are analyzed. By comparison of two main optimization methods based on different approximation parameters, the material-based method describing the material distribution field with the help of discrete form parameters, has the advantages of high degree of freedom and strong descriptive ability; the geometry-based method forming the optimal structure by describing the material boundary, has a clear boundary and does not require post-processing. The result show that relaxing the engineering manufacturing constraints and improving the efficiency of the solution are the research direction worthy of in-depth exploration in topology optimization, and have potential application prospects.

参考文献/References:

[1] BENDS?E M P,SIGMUND O.Topology optimization: Theory, methods, and applications[M].Berlin:Springer Science & Business Media,2003.
[2] ZHU Jihong,ZHANG Weihong,XIA Liang.Topology optimization in aircraft and aerospace structures design[J].Archives of Computational Methods in Engineering,2016,23(4):595-622.DOI:10.1007/s11831-015-9151-2.
[3] XIONG Yulin,ZHAO Zilong,LU Hongjia,et al.Parallel BESO framework for solving high-resolution topology optimization problems[J].Advances in Engineering Software,2023,176:103389.DOI:10.1016/j.advengsoft.2022.103389.
[4] VANEK J,GALICIA J A G,BENES B.Clever support: Efficient support structure generation for digital fabrication[J].Computer Graphics Forum,2014,33(5):117-125.DOI:10.1111/cgf.12437.
[5] 程耿东.实心弹性薄板的最优设计[J].大连工学院学报,1981,20(2):1-11.
[6] BENDS?E M P,KIKUCHI N.Generating optimal topologies in structural design using a homogenization method[J].Computer Methods in Applied Mechanics and Engineering,1988,71(2):197-224.DOI:10.1016/0045-7825(88)90086-2.
[7] BENDS?E M P.Optimal shape design as a material distribution problem[J].Structural and Multidisciplinary Optimization,1989,1(4):193-202.DOI:10.1007/BF01650949.
[8] DíAZ A R,BENDS?E M P.Shape optimization of structures for multiple loading conditions using a homogenization method[J].Structural and Multidisciplinary Optimization,1992,4(1):17-22.DOI:10.1007/BF01894077.
[9] OLHOFF N,BENDS?E M P,RASMUSSEN J.On CAD-integrated structural topology and design optimization[J].Computer Methods in Applied Mechanics and Engineering,1991,89(1):259-279.DOI:10.1016/0045-7825(91)90044-7.
[10] SIGMUND O.Materials with prescribed constitutive parameters: An inverse homogenization problem[J].International Journal of Solids and Structures,1994,31(17):2313-2329.DOI:10.1016/0020-7683(94)90154-6.
[11] PANTZ O,TRABELSI K.A post-treatment of the homogenization method for shape optimization[J].SIAM Journal on Control and Optimization,2008,47(3):1380-1398.DOI:10.1137/070688900.
[12] GROEN J P,WU Jun,SIGMUND O.Homogenization-based stiffness optimization and projection of 2D coated structures with orthotropic infill[J].Computer Methods in Applied Mechanics and Engineering,2019,349:722-742.DOI:10.1016/j.cma.2019.02.031.
[13] GROEN J P,SIGMUND O.Homogenization-based topology optimization for high-resolution manufacturable microstructures[J].International Journal for Numerical Methods in Engineering,2018,113(8):1148-1163.DOI:10.1002/nme.5575.
[14] GROEN J P,STUTZ F C,AAGE N,et al.De-homogenization of optimal multi-scale 3D topologies[J].Computer Methods in Applied Mechanics and Engineering,2020,364:112979.DOI:10.1016/j.cma.2020.112979.
[15] JENSEN P D L,SIGMUND O,GROEN J P.De-homogenization of optimal 2D topologies for multiple loading cases[J].Computer Methods in Applied Mechanics and Engineering,2022,399:115426.DOI:10.1016/j.cma.2022.115426.
[16] WANG Junpeng,WESTERMANN R,WU Jun.A streamline-guided de-homogenization approach for structural design[J].Journal of Mechanical Design,2022,145(2):21702.DOI:10.1115/1.4056148.
[17] ZHOU Ming,ROZVANY G I N.The COC algorithm,Part II: Topological,geometrical and generalized shape optimization[J].Computer Methods in Applied Mechanics and Engineering,1991,89(1):309-336.DOI:10.1016/0045-7825(91)90046-9.
[18] BENDS?E M P,SIGMUND O.Material interpolation schemes in topology optimization[J].Archive of Applied Mechanics,1999,69(9):635-654.DOI:10.1007/s004190050248.
[19] STOLPE M,SVANBERG K.On the trajectories of penalization methods for topology optimization[J].Structural and Multidisciplinary Optimization,2001,21(2):128-139.DOI:10.1007/s001580050177.
[20] GUEST J K,PRéVOST J H,BELYTSCHKO T.Achieving minimum length scale in topology optimization using nodal design variables and projection functions[J].International Journal for Numerical Methods in Engineering,2004,61(2):238-254.DOI:10.1002/nme.1064.
[21] SIGMUND O.Morphology-based black and white filters for topology optimization[J].Structural and Multidisciplinary Optimization,2007,33(4):401-424.DOI:10.1007/s00158-006-0087-x.
[22] 程耿东.关于桁架结构拓扑优化中的奇异最优解[J].大连理工大学学报,2000,40(4):379-383.DOI:10.3321/j.issn:1000-8608.2000.04.001.
[23] GUO Xu,CHENG Gengdong,YAMAZAKI K.A new approach for the solution of singular optima in truss topology optimization with stress and local buckling constraints[J].Structural and Multidisciplinary Optimization,2001,22(5):364-373.DOI:10.1007/s00158-001-0156-0.
[24] BUHL T,PEDERSEN C B W,SIGMUND O.Stiffness design of geometrically nonlinear structures using topology optimization[J].Structural and Multidisciplinary Optimization,2000,19(2):93-104.DOI:10.1007/s001580050089.
[25] SIGMUND O.On the design of compliant mechanisms using topology optimization[J].Mechanics of Structures and Machines,1997,25(4):493-524.DOI:10.1080/08905459708945415.
[26] BONNECAZE R T,RODIN G J,SIGMUND O,et al.Systematic design of phononic band-gap materials and structures by topology optimization[J].Philosophical Transactions of the Royal Society of London.Series A: Mathematical, Physical and Engineering Sciences,2003,361(1806):1001-1019.DOI:10.1098/rsta.2003.1177.
[27] XIE Yimin,STEVEN G P.A simple evolutionary procedure for structural optimization[J].Computers & Structures,1993,49(5):885-896.DOI:10.1016/0045-7949(93)90035-C.
[28] QUERIN O M,STEVEN G P,XIE Yimin.Evolutionary structural optimization(ESO)using a bidirectional algorithm[J].Engineering Computations,1998,15(8):1031-1048.DOI:10.1108/02644409810244129.
[29] YOUNG V,QUERIN O M,STEVEN G P,et al.3D and multiple load case bi-directional evolutionary structural optimization(BESO)[J].Structural and Multidisciplinary Optimization,1999,18(2):183-192.DOI:10.1007/BF01195993.
[30] ZHOU Ming,ROZVANY G I N.On the validity of ESO type methods in topology optimization[J].Structural and Multidisciplinary Optimization,2001,21(1):80-83.DOI:10.1007/s001580050170.
[31] SIGMUND O,PETERSSON J.Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima[J].Structural and Multidisciplinary Optimization,1998,16(1):68-75.DOI:10.1007/BF01214002.
[32] ZHU Jihong,ZHANG Weihong,QIU Kepeng.Bi-directional evolutionary topology optimization using element replaceable method[J].Computational Mechanics,2007,40(1):97-109.DOI:10.1007/s00466-006-0087-0.
[33] HUANG Xiaodong,XIE Yimin.Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method[J].Finite Elements in Analysis and Design,2007,43(14):1039-1049.DOI:10.1016/j.finel.2007.06.006.
[34] DEATON J D,GRANDHI R V.A survey of structural and multidisciplinary continuum topology optimization: Post 2000[J].Structural and Multidisciplinary Optimization,2014,49(1):1-38.DOI:10.1007/s00158-013-0956-z.
[35] SUI Yunkang,YANG Deqing.A new method for structural topological optimization based on the concept of independent continuous variables and smooth model[J].Acta Mechanica Sinica,1998,14(2):179-185.DOI:10.1007/BF02487752.
[36] 隋允康,张学胜,龙连春,等.位移约束集成化处理的连续体结构拓扑优化[J].固体力学学报,2006,27(1):102-107.DOI:10.3969/j.issn.0254-7805.2006.01.018.
[37] 彭细荣,隋允康.有频率禁区的连续体结构拓扑优化[J].固体力学学报,2007,28(2):145-150.DOI:10.3969/j.issn.0254-7805.2007.02.006.
[38] 叶红玲,隋允康.基于ICM方法三维连续体结构拓扑优化[J].固体力学学报,2006,27(4):387-393.DOI:10.3969/j.issn.0254-7805.2006.04.011.
[39] BENDS?E M P,GUEDES J M,HABER R B,et al.An analytical model to predict optimal material properties in the context of optimal structural design[J].Journal of Applied Mechanics,1994,61(4):930-937.DOI:10.1115/1.2901581.
[40] KOCˇVARA M,STINGL M,ZOWE J.Free material optimization: Recent progress[J].Optimization,2008,57(1):79-100.DOI:10.1080/02331930701778908.
[41] HASLINGER J,KOCˇVARA M,LEUGERING G,et al.Multidisciplinary free material optimization[J].SIAM Journal on Applied Mathematics,2010,70(7):2709-2728.DOI:10.1137/090774446.
[42] STINGL M,KOCˇVARA M,LEUGERING G.Free material optimization with fundamental eigenfrequency constraints[J].SIAM Journal on Optimization,2009,20(1):524-547.DOI:10.1137/080717122.
[43] WELDEYESUS A G,STOLPE M.Free material optimization for laminated plates and shells[J].Structural and Multidisciplinary Optimization,2016,53(6):1335-1347.DOI:10.1007/s00158-016-1416-3.
[44] GAILE S,GüNTER L,STINGL M.Free material optimization for plates and shells[C] //IFIP Conference on System Modeling and Optimization.Cracow:[s.n.],2007:239-250.DOI:10.1007/978-3-642-04802-9_12.
[45] HU Jingqiao,LI Ming,YANG Xingtong,et al.Cellular structure design based on free material optimization under connectivity control[J].Computer-Aided Design,2020,127:102854.DOI:10.1016/j.cad.2020.102854.
[46] ZHOU Kemin.Optimization of least-weight grillages by finite element method[J].Structural and Multidisciplinary Optimization,2008,38(5):525-532.DOI:10.1007/s00158-008-0305-9.
[47] ZHOU Kemin,LI Xia.Topology optimization for minimum compliance under multiple loads based on continuous distribution of members[J].Structural and Multidisciplinary Optimization,2008,37(1):49-56.DOI:10.1007/s00158-007-0214-3.
[48] ZHOU Kemin.Topology optimization of truss-like continuum structures for natural frequencies[J].Structural and Multidisciplinary Optimization,2012,47(4):613-619.DOI:10.1007/s00158-012-0870-9.
[49] CUI Hao,ZHOU Kemin.Topology optimization of truss-like structure with stress constraints under multiple-load cases[J].Acta Mechanica Solida Sinica,2019,33(2):226-238.DOI:10.1007/s10338-019-00125-3.
[50] 乔升访,周克民.基于类桁架材料模型的不确定荷载下结构拓扑优化[J].工程力学,2016,33(1):252-256.
[51] CUI Hao,ZHOU Kemin,YANG Zhiyi.Reinforcement layout design of RC structures under multiple load cases using truss-like material model[J].Latin American Journal of Solids and Structures,2020,17(4):1-17.DOI:10.1590/1679-78255930.
[52] OSHER S,SETHIAN J A.Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations[J].Journal of Computational Physics,1988,79(1):12-49.DOI:10.1016/0021-9991(88)90002-2.
[53] SETHIAN J A.Evolution, implementation, and application of level set and fast marching methods for advancing fronts[J].Journal of Computational Physics,2001,169(2):503-555.DOI:10.1006/jcph.2000.6657.
[54] SUSSMAN M,SMEREKA P,OSHER S.A level set approach for computing solutions to incompressible two-phase flow[J].Journal of Computational Physics,1994,114(1):146-159.DOI:10.1006/jcph.1994.1155.
[55] MALLADI R,SETHIAN J A,VEMURI B C.Shape modeling with front propagation: A level set approach[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1995,17(2):158-175.DOI:10.1109/34.368173.
[56] HABER R,BENDSOE M.Problem formulation,solution procedures and geometric modeling-key issues in variable-topology optimization[C]//7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization.Reston:AIAA,1998:4948.
[57] RUITER M J D,KEULEN F V.Topology of optimization: Approaching the material distribution problem using a topological function description[C]//Computational Techniques for Materials, Composites and Composite Structures.Edinburgh:Civil-Comp Press,2000:111-119.
[58] WEI Peng,WANG M Y.Piecewise constant level set method for structural topology optimization[J].International Journal for Numerical Methods in Engineering,2009,78(4):379-402.DOI:10.1002/nme.2478.
[59] OTOMORI M,YAMADA T,IZUI K,et al.Matlab code for a level set-based topology optimization method using a reaction diffusion equation[J].Structural and Multidisciplinary Optimization,2015,51(5):1159-1172.DOI:10.1007/s00158-014-1190-z.
[60] WEI Peng,LI Zuyu,LI Xueping,et al.An 88-line MATLAB code for the parameterized level set method-based topology optimization using radial basis functions[J].Structural and Multidisciplinary Optimization,2018,58(2):831-849.DOI:10.1007/s00158-018-1904-8.
[61] GUO Xu,ZHANG Weisheng,ZHANG Jian,et al.Explicit structural topology optimization based on moving morphable components(MMC)with curved skeletons[J].Computer Methods in Applied Mechanics and Engineering,2016,310:711-748.DOI:10.1016/j.cma.2016.07.018.
[62] ZHANG Weisheng,LI Dong,ZHOU Jianhua,et al.A Moving Morphable Void(MMV)-based explicit approach for topology optimization considering stress constraints[J].Computer Methods in Applied Mechanics and Engineering,2018,334:381-413.DOI:10.1016/j.cma.2018.01.050.
[63] ZHANG Weisheng,LI Dong,YUAN Jie,et al.A new three-dimensional topology optimization method based on moving morphable components(MMCs)[J].Computational Mechanics,2016,59(4):647-665.DOI:10.1007/s00466-016-1365-0.
[64] ZHANG Weisheng,LI Dong,ZHANG Jie,et al.Minimum length scale control in structural topology optimization based on the moving morphable components(MMC)approach[J].Computer Methods in Applied Mechanics and Engineering,2016,311:327-355.DOI:10.1016/j.cma.2016.08.022.
[65] ZHANG Weisheng,YANG Wanying,ZHOU Jianhua,et al.Structural topology optimization through explicit boundary evolution[J].Journal of Applied Mechanics,2016,84(1):1-10.DOI:10.1115/1.4034972.
[66] ZHANG Weisheng,CHEN Jishun,ZHU Xuefeng,et al.Explicit three dimensional topology optimization via moving morphable void(MMV)approach[J].Computer Methods in Applied Mechanics and Engineering,2017,322:590-614.DOI:10.1016/j.cma.2017.05.002.
[67] WEI Peng,MA Haitao,WANG M.The stiffness spreading method for layout optimization of truss structures[J].Structural and Multidisciplinary Optimization,2013,49(4):667-682.DOI:10.1007/s00158-013-1005-7.
[68] NORATO J A,BELL B K,TORTORELLI D A.A geometry projection method for continuum-based topology optimization with discrete elements[J].Computer Methods in Applied Mechanics and Engineering,2015,293:306-327.DOI:10.1016/j.cma.2015.05.005.
[69] ESCHENAUER H A,KOBELEV V V,SCHUMACHER A.Bubble method for topology and shape optimization of structures[J].Structural and Multidisciplinary Optimization,1994,8(1):42-51.DOI:10.1007/bf01742933.
[70] PRAGER W,ROZVANY G I N.Optimal layout of grillages[J].Journal of Structural Mechanics,1977,5(1):1-18.DOI:10.1080/03601217708907301.
[71] SIGMUND O,AAGE N,ANDREASSEN E.On the(non-)optimality of Michell structures[J].Structural and Multidisciplinary Optimization,2016,54(2):361-373.DOI:10.1007/s00158-016-1420-7.
[72] ROZVANY G I N,ONG T G,SZETO W T,et al.Least-weight design of perforated elastic plates: Ⅰ[J].International Journal of Solids and Structures,1987,23(4):521-536.DOI:10.1016/0020-7683(87)90015-1.

相似文献/References:

[1]乔升访,胡杰云,周克民.采用类桁架优化方法研究大跨桥梁的构形[J].华侨大学学报(自然科学版),2016,37(4):431.[doi:10.11830/ISSN.1000-5013.201604008]
 QIAO Shengfang,HU Jieyun,ZHOU Kemin.Structural Topology Optimization of Configuration in Long-Span Bridge Based on Truss-Like Material Model[J].Journal of Huaqiao University(Natural Science),2016,37(2):431.[doi:10.11830/ISSN.1000-5013.201604008]
[2]邓援超,周杨,刘艺,等.折叠电动车主折叠机架的轻量化设计[J].华侨大学学报(自然科学版),2018,39(4):496.[doi:10.11830/ISSN.1000-5013.201711029]
 DENG Yuanchao,ZHOU Yang,LIU Yi,et al.Lightweight Design of Main Folding Frame for Foldable Electric Vehicle[J].Journal of Huaqiao University(Natural Science),2018,39(2):496.[doi:10.11830/ISSN.1000-5013.201711029]
[3]郑伟伟,周克民.应用类桁架模型的连续体拓扑优化方法[J].华侨大学学报(自然科学版),2014,35(3):327.[doi:10.11830/ISSN.1000-5013.2014.03.0327]
 ZHENG Wei-wei,ZHOU Ke-min.Continuum Topology Optimization Based on Truss-Like Model[J].Journal of Huaqiao University(Natural Science),2014,35(2):327.[doi:10.11830/ISSN.1000-5013.2014.03.0327]
[4]李霞,周克民.采用类桁架连续体的桁架结构拓扑优化方法[J].华侨大学学报(自然科学版),2014,35(4):443.[doi:10.11830/ISSN.1000-5013.2014.04.0443]
 LI Xia,ZHOU Ke-min.Topology Optimization Method of Truss Structures Using Truss-Like Continuum[J].Journal of Huaqiao University(Natural Science),2014,35(2):443.[doi:10.11830/ISSN.1000-5013.2014.04.0443]

备注/Memo

备注/Memo:
收稿日期: 2023-12-12
通信作者: 周克民(1962-)男,教授,博士,博士生导师,主要从事计算力学、结构拓扑优化的研究。E-mail:zhoukm@hqu.edu.cn。
基金项目: 国家自然科学基金资助项目(11572131); 福建省科技计划引导性项目(2019H0012)
更新日期/Last Update: 2024-03-20