涉及空腔制造的最小长度尺寸限制的清晰结构拓扑优化设计

doi:10.3901/JME.2019.19.174

机械工程学报 ›› 2019, Vol. 55 ›› Issue (19): 174-185.doi: 10.3901/JME.2019.19.174

• 数字化设计与制造 • 上一篇

涉及空腔制造的最小长度尺寸限制的清晰结构拓扑优化设计

荣见华^1,2, 赵圣佞^1,2, 李方义^1,2, 俞燎宏³, 荣轩霈⁴, 陈成^1,2

1. 长沙理工大学汽车与机械工程学院长沙 410076;
2. 长沙理工大学工程车辆轻量化与可靠性技术湖南省高校重点实验室长沙 410114;
3. 宜春学院物理科学与工程技术学院宜春 336000;
4. 湖南大学汽车车身先进设计制造国家重点实验室长沙 410082

收稿日期:2018-11-19 修回日期:2019-06-04 发布日期:2020-01-07
通讯作者: 李方义(通信作者),男,1978年出生,博士,副教授,硕士研究生导师。主要研究方向为结构动力学与优化设计,可靠分析与设计。mail:lfy703@sina.com
作者简介:荣见华,男,1963年出生,博士,教授,博士研究生导师。主要研究方向为结构动力学与优化设计。E-mail:rongjhua@aliyun.com;赵圣佞,男,1994年出生,硕士研究生。主要研究方向为结构动力学与优化设计。E-mail:1226710184@qq.com;俞燎宏,男,1982年出生,博士,讲师。主要研究方向为结构动力学与优化设计。E-mail:ylh310@163.com;荣轩霈,男,1994年出生,硕士研究生。主要研究方向为结构动力学与优化设计。E-mail:812401736@qq.com;陈成,男,1993年出生,硕士研究生。主要研究方向为结构动力学与优化设计。E-mail:1206509431@qq.com
基金资助:
国家自然科学基金（11772070）、湖南省自然科学基金（2019JJ40296）、江西省教育厅科技项目（GJJ170893）和湖南省教育厅科研项目（17C0044）资助项目。

Clear Structural Topology Optimization Designs Including Minimum Allowable Length Scale Limit on Fabrication Holes

RONG Jianhua^1,2, ZHAO Shengning^1,2, LI Fangyi^1,2, YU Liaohong³, RONG Xuanpei⁴, CHEN Cheng^1,2

1. School of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha 410076;
2. Key Laboratory of Lightweight and Reliability Technology for Engineering Vehicle of Hunan Province, Changsha University of Science and Technology, Changsha 410114;
3. School of Physical Science and Technology, Yichun University, Yichun 336000;
4. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082

Received:2018-11-19 Revised:2019-06-04 Published:2020-01-07

摘要/Abstract

摘要： 针对以结构柔顺度最小为目标函数，涉及空腔制造的最小长度尺寸限制的结构拓扑优化设计问题，提出了一种新的拓扑优化求解方法。首先，为了消除现有的结构实体相及空洞相的相同的光滑Heaviside映射导致的强烈对立矛盾，引入光滑Heaviside映射和修改的光滑Heaviside映射分别进行实体相及空洞相的设计变量过滤；而后，构建了合理和协同的涉及实体相和空洞相的几何最小长度尺寸限制的结构拓扑优化模型；利用MMA算法，形成了一种新的涉及实体相和空洞相的几何最小长度尺寸限制的结构拓扑优化算法。给出的算例结果表明，与现有方法比，该方法可解决结构实体相和空洞相的几何最小长度尺寸控制问题。且所提方法可获得清晰0/1分布的优化结构拓扑。

关键词: 结构拓扑优化, 最小长度尺寸, 可制造性, 滤波器, Heaviside映射

Abstract: For the problem of structural topology compliance minimization with a minimum allowable length scale limit on fabrication holes (void phase), a new topology optimization method of continuum structures with a volume constraint is proposed. Firstly, in order to destroy strong antagonistic contradictions brought by two same smooth Heaviside projections of the solid phase and void phase, a smooth Heaviside projection and a modified smooth Heaviside projection are introduced to make design variable filtering of the solid phase and void phase, respectively. Hence, a reasonable and coordinating structural topology optimization model with the minimum allowable length scale limits on fabrication holes and solid material, is constructed; Being integrated with the MMA algorithm, a new structural topology optimization procedure, dealing with the minimum allowable length scale limits on fabrication holes and solid material, is proposed. It is concluded from given examples that the proposed method can solve the problem of structural topology compliance minimization with the minimum allowable length scale limits on fabrication holes and solid material, and may obtain an optimal topology with more clear 0/1 distribution than the existed methods.

Key words: structural topology optimization, minimum length scale, manufacturability, filters, Heaviside projection

中图分类号:

TH122

荣见华, 赵圣佞, 李方义, 俞燎宏, 荣轩霈, 陈成. 涉及空腔制造的最小长度尺寸限制的清晰结构拓扑优化设计[J]. 机械工程学报, 2019, 55(19): 174-185.

RONG Jianhua, ZHAO Shengning, LI Fangyi, YU Liaohong, RONG Xuanpei, CHEN Cheng. Clear Structural Topology Optimization Designs Including Minimum Allowable Length Scale Limit on Fabrication Holes[J]. Journal of Mechanical Engineering, 2019, 55(19): 174-185.

参考文献

[1] SIGMUND O,MAUTE K. Topology optimization approaches[J]. Structural and Multidisciplinary Optimization,2013,48(6):1031-1055.
[2] 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.
[3] GUO X,CHENG G D. Recent development in structural design and optimization[J]. Acta Mechanica Sinica,2010,26(6):807-823.
[4] GUO X,ZHANG W,ZHONG W. Explicit feature control in structural topology optimization via level set method[J]. Computer Methods in Applied Mechanics and Engineering,2014,272(2):354-378.
[5] ZHANG W,ZHONG W,GUO X. An explicit length scale control approach in SIMP-based topology optimization[J]. Computer Methods in Applied Mechanics and Engineering,2014,282(1):71-86.
[6] WEI P,SHI J,MA H. Integrated layout design of multi-component systems based on stiffness spreading method[C]//7th china-japan-korea joint symposium on optimization of structural and mechanical systems,2012,Huangshan City,Anhui Province.2015:57-57.
[7] LIU J,MA Y. A survey of manufacturing oriented topology optimization methods[J]. Advances in Engineering Software,2016,100:161-175.
[8] VATANABE S L,LIPPI T N,LIMA C R D,et al. Topology optimization with manufacturing constraints:A unified projection-based approach[J]. Advances in Engineering Software,2016,100:97-112.
[9] GUEST J K,PRŃVOST 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.
[10] GUEST J K. Topology optimization with multiple phase projection[J]. Computer Methods in Applied Mechanics and Engineering,2009,199(1):123-135.
[11] ALMEIDA S R M,PAULINO G H,SILVA E C N. A simple and effective inverse projection scheme for void distribution control in topology optimization[J]. Structural and Multidisciplinary Optimization,2009,39(4):359-371.
[12] WANG F,LAZAROV B S,SIGMUND O. On projection methods,convergence and robust formulations in topology optimization[M]. Springer-Verlag. New York,2011.
[13] BRUNS T E,TORTORELLI D A. Topology optimization of non-linear elastic structures and compliant mechanisms[J]. Computer Methods in Applied Mechanics and Engineering,2001,190(26):3443-3459.
[14] SIGMUND O. Morphology-based black and white filters for topology optimization[J]. Structural and Multidisciplinary Optimization,2007,33(4-5):401-424.
[15] GUEST J K,ASADPOURE A,HA S H. Eliminating beta-continuation from heaviside projection and density filter algorithms[J]. Structural and Multidisciplinary Optimization,2011,44(4):443-453.
[16] 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.
[17] PETERSSON J,SIGMUND O. Slope constrained topology optimization[J]. International Journal for Numerical Methods in Engineering,2015,41(8):1417-1434.
[18] ROJAS-LABANDA S,STOLPE M. Automatic penalty continuation in structural topology optimization[J]. Structural and Multidisciplinary Optimization,2015,52(6):1205-1221.
[19] LI L,KHANDELWAL K. Volume preserving projection filters and continuation methods in topology optimization[J]. Engineering Structures,2015(15),85:144-161.
[20] WATADA R,OHSAKI M,KANNO Y. Nonuniqueness and symmetry of optimal topology of a shell for minimum compliance[M]. Springer-Verlag New York, 2011.
[21] STOLPE M,SVANBERG K. On the trajectories of penalization methods for topology optimization[J]. Structural and Multidisciplinary Optimization,2001,21(2):128-139.
[22] GUEST J K. Imposing maximum length scale in topology optimization[J]. Structural and Multidisciplinary Optimization,2009,37(5):463-473.
[23] 邢晓娟,荣见华,邓果. 一种变频率约束限的结构拓扑优化方法[J]. 振动与冲击,2008,27(10):56-60. XING Xiaojuan,RONG Jianhua,DENG Guo. A structural topology optimization method with variable frequency constraints[J]. Journal of Vibration and Shock,2008,27(10):56-60.
[24] 荣见华,葛森,邓果,等. 基于位移和应力灵敏度的结构拓扑优化设计[J]. 力学学报,2009,41(4):518-529. RONG Jianhua,GE Sen,DENG Guo,et al. Structural topological optimization based on displacement and stress sensitivity analyses[J]. Chinese Journal of Theoretical and Applied Mechanics,2009,41(4):518-529.
[25] RONG J H,YI J H. A structural topological optimization method for multi-displacement constraints and any initial topology configuration[J]. Acta Mechanica Sinica,2010,26(5):735-744.
[26] 荣见华,张强,葛森,等. 基于设计空间调整的结构拓扑优化方法[J]. 力学学报,2010,42(2):256-267. RONG Jianhua,ZHANG Qiang,GE Sen,et al. A new structural topological optimization method based on design space adjustments[J]. Chinese Journal of Theoretical and Applied Mechanics,2010,42(2):256-267.
[27] 俞燎宏,荣见华,赵志军,等. 多工况载荷下连续体结构柔顺度拓扑优化问题的新的求解方法[J]. 机械工程学报,2018,54(5):210-219. YU Liaohong,RONG Jianhua,ZHAO Zhijun,et al. A new solving method of the compliance topology optimization problem of continuum structures under multiple load cases[J]. Journal of Mechanical Engineering,2018,54(5):210-219.
[28] RONG J H,YU L H,RONG X P,et al. A novel displacement constrained optimization approach for black and white structural topology designs under multiple load cases[J]. Structural and Multidisciplinary Optimization,2017(2):1-20.
[29] RONG J H,XIAO T T,YU L H,et al. Continuum structural topological optimizations with stress constraints based on an active constraint technique[J]. International Journal for Numerical Methods in Engineering,2016,108(4):326-360.
[30] 石军,荣见华,俞燎宏,等. 考虑载荷随机性的可行域调整的结构拓扑优化设计[J]. 机械工程学报,2017,53(23):116-128. SHI Jun,RONG Jianhua,YU Liaohong,et al. Feasible domain adjustment topology optimization designs of structures under stochastic loads[J]. Journal of Mechanical Engineering,2017,53(23):116-128.
[31] SVANBERG K. The method of moving asymptotes-a new method for structural optimization[J]. International Journal for Numerical Methods in Engineering,1987,24(2):359-373.
[32] SVANBERG K. A class of globally convergent optimization methods based on conservative convex separable approximations[J]. Siam Journal on Optimization,2009,12(2):555-573.

涉及空腔制造的最小长度尺寸限制的清晰结构拓扑优化设计

Clear Structural Topology Optimization Designs Including Minimum Allowable Length Scale Limit on Fabrication Holes

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