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

doi:10.3901/JME.2019.19.174

Abstract

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

CLC Number:

TH122

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.

References

[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.