EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于自适应泡泡法的薄壳结构拓扑优化设计

张华麟 杨东 史之君 蔡守宇

张华麟, 杨东, 史之君, 蔡守宇. 基于自适应泡泡法的薄壳结构拓扑优化设计. 力学学报, 2023, 55(5): 1165-1173 doi: 10.6052/0459-1879-22-562
引用本文: 张华麟, 杨东, 史之君, 蔡守宇. 基于自适应泡泡法的薄壳结构拓扑优化设计. 力学学报, 2023, 55(5): 1165-1173 doi: 10.6052/0459-1879-22-562
Zhang Hualin, Yang Dong, Shi Zhijun, Cai Shouyu. Topology optimization of thin shell structures based on adaptive bubble method. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(5): 1165-1173 doi: 10.6052/0459-1879-22-562
Citation: Zhang Hualin, Yang Dong, Shi Zhijun, Cai Shouyu. Topology optimization of thin shell structures based on adaptive bubble method. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(5): 1165-1173 doi: 10.6052/0459-1879-22-562

基于自适应泡泡法的薄壳结构拓扑优化设计

doi: 10.6052/0459-1879-22-562
基金项目: 国家自然科学基金(11702254), 河南省科技攻关(212102210068)和国家重点研发计划(2017YFB1102800)资助项目
详细信息
    通讯作者:

    蔡守宇, 副教授, 主要研究方向为结构拓扑优化设计. E-mail: caishouyu@zzu.edu.cn

  • 中图分类号: O343.2

TOPOLOGY OPTIMIZATION OF THIN SHELL STRUCTURES BASED ON ADAPTIVE BUBBLE METHOD

  • 摘要: 为有效解决薄壳结构拓扑优化设计难题, 并满足其对分析模型精度和优化结果质量的高要求, 结合等几何壳体分析方法提出一种基于自适应泡泡法的新型拓扑优化设计框架. 等几何分析技术在薄壳分析方面具有天然的优势: 一方面可为薄壳结构建立起精确的NURBS分析模型, 避免了模型转换操作及误差; 另一方面还可保证待分析物理场的高阶连续性, 无需设置转角自由度等. 为了在给定壳面上实现结构的拓扑演化, 借助NURBS曲面(即等几何分析中的薄壳中面)的映射关系, 仅需在规则的二维参数区域内改变结构拓扑即可. 鉴于此, 采用自适应泡泡法在壳面参数区域内开展拓扑优化, 该方法包含孔洞建模、孔洞引入和固定网格分析3个模块, 其在当前工作中分别基于闭合B样条、拓扑导数理论和有限胞元法实现. 其中, 闭合B样条兼具参数和隐式两种表达形式, 参数形式便于在CAD系统中直接生成精确的结构模型; 隐式形式不仅便于开展孔洞的融合/分离操作, 还能与有限胞元法有机结合以替代繁琐的修剪曲面分析方法. 理论分析和数值算例表明, 所提优化设计框架将复杂的薄壳结构拓扑优化问题转化为简单的二维结构拓扑优化问题, 在保证足够分析精度的基础上使用相对很少的设计变量就可得到具有清晰光滑边界且便于导入到CAD系统的优化结果.

     

  • 图  1  带孔薄壳结构建模示意图

    Figure  1.  Schematic diagram of modeling an opening thin shell

    图  2  基于CBS的孔洞表示方式

    Figure  2.  CBS-based hole representation

    图  3  孔洞自适应引入机制示意图

    Figure  3.  Adaptive introduction mechanism of holes

    图  4  有限胞元方法示意图

    Figure  4.  Schematic diagram of the finite cell method

    图  5  受集中垂直载荷的薄壳结构

    Figure  5.  Thin shell subjected to a vertical load

    图  6  薄壳结构拓扑优化过程

    Figure  6.  Topological evolution of the thin shell

    图  7  设计结果的位移云图

    Figure  7.  Displacement contours of the design result

    图  8  柔顺度及体积的收敛曲线

    Figure  8.  The convergent curves for compliance and volume

    图  9  优化结果的CAD模型

    Figure  9.  CAD model of the optimized result

    图  10  不同壳面曲率下的拓扑优化结果对比图(由上至下曲率逐步增大)

    Figure  10.  Comparison of topology optimization design results for different shell curvatures (the curvature gradually increases from top to bottom)

  • [1] 张卫红, 周涵, 李韶英等. 航天高性能薄壁构件的材料−结构一体化设计. 航空学报, 2022, 出版中

    Zhang Weihong, Zhou Han, Li Shaoying, et al. Material-structure integrated design for high-performance aerospace thin-walled component. Acta Aeronautica et Astronautica Sinica, 2022, in press (in Chinese))
    [2] 杨利鑫, 何东泽, 陈强等. 高温环境下大尺度薄壁结构的电性能优化设计. 宇航学报, 2021, 42(9): 1099-1107 (Yang Lixin, He Dongze, Chen Qiang, et al. Electrical performance optimization design of large-scale thin-wall structures in thermal environment. Journal of Astronautics, 2021, 42(9): 1099-1107 (in Chinese)
    [3] 王博, 周子童, 周演等. 薄壁结构多层级并发加筋拓扑优化研究. 计算力学学报, 2021, 38(4): 487-497 (Wang Bo, Zhou Zitong, Zhou Yan, et al. Concurrent topology optimization hierarchical stiffened thin-walled structures. Chinese Journal of Computational Mechanics, 2021, 38(4): 487-497 (in Chinese)
    [4] Träff EA, Sigmund O, Aage N. Topology optimization of ultra high resolution shell structures. Thin-Walled Structures, 2021, 160: 107349 doi: 10.1016/j.tws.2020.107349
    [5] Jiang BS, Zhang JY, Ohsaki M. Shape optimization of free-form shell structures combining static and dynamic behaviors. Structures, 2021, 29: 1791-1807 doi: 10.1016/j.istruc.2020.12.045
    [6] Bendsøe MP, Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 1988, 71(2): 197-224 doi: 10.1016/0045-7825(88)90086-2
    [7] Bendsøe MP, Sigmund O. Topology Optimization: Theory, Methods and Applications. Berlin: Springer Verlag, 2003: 9-24
    [8] Xie YM, Steven GP. A simple evolutionary procedure for structural optimization. Computers and Structures, 1993, 49(5): 885-896 doi: 10.1016/0045-7949(93)90035-C
    [9] 隋允康, 叶红玲. 连续体结构拓扑优化的 ICM 方法. 北京: 科学出版社, 2013

    Sui Yunkang, Ye Hongling. ICM Method for Topology Optimization of Continuum Structures. Beijing: Science Press, 2013 (in Chinese))
    [10] Wang MY, Wang XM, Guo DM. A level set method for structural topology optimization. Computer Methods in Applied Mechanics and Engineering, 2003, 192(1-2): 227-246 doi: 10.1016/S0045-7825(02)00559-5
    [11] Maute K, Ramm E. Adaptive topology optimization of shell structures. American Institute of Aeronautics and Astronautics, 1997, 35: 1767-1773 doi: 10.2514/2.25
    [12] Ansola R, Canales J, Tarrago JA, et al. On simultaneous shape and material layout optimization of shell structures. Structural and Multidisciplinary Optimization, 2002, 24(3): 175-184 doi: 10.1007/s00158-002-0227-x
    [13] 粟华, 陈伟俊, 龚春林等. 环向肋增稳的薄壁圆筒结构定向拓扑优化方法. 宇航学报, 2022, 43(3): 374-382 (Su Hua, Chen Weijun, Gong Chunlin, et al. Oriented topology optimization of thin-walled structure with circumferential rib enhancement of stability. Journal of Astronautics, 2022, 43(3): 374-382 (in Chinese)
    [14] Hassani B, Tavakkoli SM, Ghasemnejad H. Simultaneous shape and topology optimization of shell structures. Structural and Multidisciplinary Optimization, 2013, 48: 221-233
    [15] 牟佳信, 邢彬, 郭梅等. 考虑热、弹、流耦合的航空发动机齿轮箱壳体拓扑优化分析. 机械传动, 2022, 46(2): 127-134 (Mu Jiaxin, Xing Bin, Guo Mei, et al. Topology optimization analysis of aero-engine gearbox housing considering the coupling of thermal elastohydrodynamic lubrication. Journal of Mechanical Transmission, 2022, 46(2): 127-134 (in Chinese)
    [16] 朱润, 隋允康. 基于ICM方法的多工况位移约束下板壳结构拓扑优化设计. 固体力学学报, 2012, 33(1): 81-90 (Zhu Run, Sui Yunkang. Topological optimization design of plate-shell structure under multi-condition displacement constraints based on ICM method. Chinese Journal of Solid Mechanics, 2012, 33(1): 81-90 (in Chinese)
    [17] Huo WD, Liu C, Du ZL, et al. Topology optimization on complex surfaces based on the moving morphable component method and computational conformal mapping. Journal of Applied Mechanics, 2022, 89(5): 051008 doi: 10.1115/1.4053727
    [18] Xu XQ, Gu XD, Chen SK. Shape and topology optimization of conformal thermal control structures on free-form surfaces: A dimension reduction level set method (DR-LSM). Computer Methods in Applied Mechanics and Engineering, 2022, 398: 115183
    [19] Ho-Nguyen-Tan T, Kim HG. An efficient method for shape and topology optimization of shell structures. Structural and Multidisciplinary Optimization, 2022, 65: 119 doi: 10.1007/s00158-022-03213-0
    [20] Ho-Nguyen-Tan T, Kim HG. Level set-based topology optimization for compliance and stress minimization of shell structures using trimmed quadrilateral shell meshes. Computers and Structures, 2022, 259: 106695 doi: 10.1016/j.compstruc.2021.106695
    [21] Meng XC, Xiong YL, Xie YM, et al. Shape-thickness-topology coupled optimization of free-form shells. Automation in Construction, 2022, 142: 104476 doi: 10.1016/j.autcon.2022.104476
    [22] Jiang XD, Zhang WS, Liu C, et al. An explicit approach for simultaneous shape and topology optimization of shell structures. Applied Mathematical Modelling, 2023, 113: 613-639 doi: 10.1016/j.apm.2022.09.028
    [23] Hughes TJR, Cottrell JA, Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 2005, 194(39-41): 4135-4195 doi: 10.1016/j.cma.2004.10.008
    [24] Seo YD, Kim HJ, Youn SK. Isogeometric topology optimization using trimmed spline surfaces. Computer Methods in Applied Mechanics and Engineering, 2010, 199(49-52): 3270-3296 doi: 10.1016/j.cma.2010.06.033
    [25] Kang P, Youn SK. Isogeometric topology optimization of shell structures using trimmed NURBS surfaces. Finite Elements in Analysis and Design, 2016, 120: 18-40 doi: 10.1016/j.finel.2016.06.003
    [26] Zhang WS, Li DD, Kang P, et al. Explicit topology optimization using IGA-based moving morphable void (MMV) approach. Computer Methods in Applied Mechanics and Engineering, 2019, 360: 112685
    [27] Zhang WS, Jiang S, Liu C, et al. Stress-related topology optimization of shell structures using IGA/TSA-based moving morphable void (MMV) approach. Computer Methods in Applied Mechanics and Engineering, 2020, 366: 113036 doi: 10.1016/j.cma.2020.113036
    [28] 蔡守宇, 张卫红, 高彤等. 基于固定网格和拓扑导数的结构拓扑优化自适应泡泡法. 力学学报, 2019, 51(4): 1235-1244 (Cai Shouyu, Zhang Weihong, Gao Tong, et al. Adaptive bubble method using fixed mesh and topological derivative for structural topology optimization. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(4): 1235-1244 (in Chinese)
    [29] Zhang WH, Zhao LY, Gao T, et al. Topology optimization with closed B-splines and Boolean operations. Computer Methods in Applied Mechanics and Engineering, 2017, 315: 652-670 doi: 10.1016/j.cma.2016.11.015
    [30] Parvizian J, Düster A, Rank E. Finite cell method. Computational Mechanics, 2007, 41(1): 121-133 doi: 10.1007/s00466-007-0173-y
    [31] Piegl L, Tiller W. The NURBS Book. 2nd Edition. New York: Springer Verleg, 1997: 117-139
    [32] Kiendl J, Bletzinger KU, Linhard J, et al. Isogeometric shell analysis with Kirchhoff-love elements. Computer Methods in Applied Mechanics and Engineering, 2009, 198(49-52): 3902-3914 doi: 10.1016/j.cma.2009.08.013
    [33] Cirak F, Ortiz M, Schröder P. Subdivision surfaces: a new paradigm for thin-shell finite-element analysis. International Journal for Numerical Methods in Engineering, 2000, 47(12): 2039-2072 doi: 10.1002/(SICI)1097-0207(20000430)47:12<2039::AID-NME872>3.0.CO;2-1
    [34] Nvotny AA, Sokolowski J. Topological Derivatives in Shape Optimization. Heidelberg: Springer-Verlag, 2013
    [35] Sokolowski J, Zochowski A. On the topological derivative in shape optimization. SIAM Journal on Control and Optimization, 1999, 37(4): 1251-1272 doi: 10.1137/S0363012997323230
    [36] Cai SY, Zhang WH, Zhu JH, et al. Stress constrained shape and topology optimization with fixed mesh: A B-spline finite cell method combined with level set function. Computer Methods in Applied Mechanics and Engineering, 2014, 278(15): 361-387
    [37] Svanberg K. The method of moving asymptotes—a new method for structural optimization. International Journal for Numerical Methods in Engineering, 1987, 24(2): 359-373 doi: 10.1002/nme.1620240207
  • 加载中
图(10)
计量
  • 文章访问数:  200
  • HTML全文浏览量:  65
  • PDF下载量:  62
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-11-28
  • 录用日期:  2023-04-03
  • 网络出版日期:  2023-04-04
  • 刊出日期:  2023-05-18

目录

    /

    返回文章
    返回