| Citation: | FU Zhifang, WANG Chunjie. Robust topology optimization of periodic structures under uncertain loading[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(4): 747-753. doi: 10.13700/j.bh.1001-5965.2016.0822(in Chinese)
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This paper proposes a method of structural robust topology optimization under the periodicity constraint. A robust topology optimization model for periodic structures is proposed for linear elastic structures. Then, the formula of the sensitivity number is developed, and the robust topology optimal design of periodic structure under uncertain loadings is performed using soft-kill bi-directional evolutionary structural optimization method. Two numerical examples under different constraints demonstrate the stability of the proposed method. There are significant differences between the optimal structures under deterministic loads and the optimal structures under uncertain loads, and the robust design is more stable than the deterministic design.
| [1] |
WADLEY H N G, FLECK N A, EVAN A G.Fabrication and structural performance of periodic cellular metal sandwich structures[J].Composites Science and Technology, 2003, 63(16):2331-2343. doi: 10.1016/S0266-3538(03)00266-5
|
| [2] |
HUANG, X D, XIE Y M.Optimal design of periodic structures using evolutionary topology optimization[J].Structural and Multidisciplinary Optimization, 2008, 36(6):597-606. doi: 10.1007/s00158-007-0196-1
|
| [3] |
焦洪宇, 周奇才, 李文军, 等.基于变密度法的周期性拓扑优化[J].机械工程学报, 2013, 49(13):132-138. http://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201313020.htm
JIAO H Y, ZHOU Q C, LI W J, et al.Periodic topology optimization using variable density method[J].Journal of Mechanical Engineering, 2013, 49(13):132-138(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201313020.htm
|
| [4] |
荣见华, 廖莺, 赵志军, 等.基于位移约束的类周期性连续体结构拓扑优化设计[J].应用力学学报, 2013, 30(6):876-881. doi: 10.11776/cjam.30.06.B131
RONG J H, LIAO Y, ZHAO Z J, et al.Topology optimization of periodic-like structures with displacement constrains[J].Chinese Journal of Applied Mechanics, 2013, 30(6):876-881(in Chinese). doi: 10.11776/cjam.30.06.B131
|
| [5] |
焦洪宇, 周奇才, 吴青龙, 等.桥式起重机箱型主梁周期性拓扑优化设计[J].机械工程学报, 2014, 50(23):134-139. http://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201423021.htm
JIAO H Y, ZHOU Q C, WU Q L, et al.Periodic topology optimization of the box-type girder of bridge crane[J].Journal of Mechanical Engineering, 2014, 50(23):134-139(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201423021.htm
|
| [6] |
ZUO Z H, HUANG X D, YANG X Y.Comparing optimal material microstructures with optimal periodic structures[J].Computational Materials Science, 2013, 69(1):137-147.
|
| [7] |
LUO Z, TONG L, KANG Z.A level set method for structural shape and topology optimization using radial basis functions[J].Computers and Structures, 2009, 87(7):425-434.
|
| [8] |
GUEST J K, IGUSA T.Structural optimization under uncertain loads and nodal locations[J].Computer Methods in Applied Mechanics and Engineering, 2008, 198(1):116-124. doi: 10.1016/j.cma.2008.04.009
|
| [9] |
DUNNING P D, KIM H A, MULLINEUX G.Introducing loading uncertainty in topology optimization[J].AIAA Journal, 2011, 49(4):760-768. doi: 10.2514/1.J050670
|
| [10] |
CHEN S, CHEN W, LEE S.Level set based robust shape and topology optimization under random field uncertainties[J].Structural Multidisciplinary Optimization, 2010, 41(4):507-524. doi: 10.1007/s00158-009-0449-2
|
| [11] |
CHEN S, CHEN W.A new level-set based approach to shape and topology optimization under geometric uncertainty[J].Structural Multidisciplinary Optimization, 2011, 44(1):1-18. doi: 10.1007/s00158-011-0660-9
|
| [12] |
DUNNING P D, KIM H A.Robust topology optimization:Minimization of expected and variance of compliance[J].AIAA Journal, 2013, 51(11):2656-2664. doi: 10.2514/1.J052183
|
| [13] |
KANG Z, BAI S.On robust design optimization of truss structures with bounded uncertainties[J].Structural and Multidisciplinary Optimization, 2013, 47(5):699-714. doi: 10.1007/s00158-012-0868-3
|
| [14] |
赵军鹏, 王春洁.载荷不确定条件下的结构拓扑优化算法[J].北京航空航天大学学报, 2014, 40(7):959-964. http://bhxb.buaa.edu.cn/CN/abstract/abstract12979.shtml
ZHAO J P, WANG C J.Algorithm of structural topology optimization under loading uncertainty[J].Journal of Beijing University of Aeronautics and Astronautics, 2014, 40(7):959-964(in Chinese). http://bhxb.buaa.edu.cn/CN/abstract/abstract12979.shtml
|
| [15] |
ZHAO J P, WANG C J.Robust topology optimization under loading uncertainty based on linear elastic theory and orthogonal diagonalization of symmetric matrices[J].Computer Methods in Applied Mechanics and Engineering, 2014, 273(2):204-218.
|
| [16] |
罗阳军, 亢战, 邓子辰.多工况下结构鲁棒性拓扑优化设计[J].力学学报, 2011, 43(1):227-234. doi: 10.6052/0459-1879-2011-1-lxxb2010-147
LUO Y J, KANG Z, DENG Z C.Robust topology optimization design of structures with multiple load cases[J].Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(1):227-234(in Chinese). doi: 10.6052/0459-1879-2011-1-lxxb2010-147
|
| [17] |
付志方, 赵军鹏, 王春洁.多工况线性结构稳健拓扑优化设计[J].力学学报, 2015, 47(4):642-650. doi: 10.6052/0459-1879-15-072
FU Z F, ZHAO J P, WANG C J.Robust topology optimization design of structures with multiple load cases[J].Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(4):642-650(in Chinese). doi: 10.6052/0459-1879-15-072
|
| [18] |
XIE Y M, ZUO Z H, HUANG X D, et al.Application of topological optimization technology to bridge design[J].Structural Engineering International, 2014, 24(2):185-191. doi: 10.2749/101686614X13830790993366
|
| [19] |
刘丰睿, 赵丽滨, 韩邦成, 等.磁悬浮控制力矩陀螺框架结构的拓扑优化设计[J].北京航空航天大学学报, 2010, 36(4):455-458. http://bhxb.buaa.edu.cn/CN/abstract/abstract8479.shtml
LIU F R, ZHAO L B, HAN B C, et al.Topology optimization design of frame structure for magnetic suspension control moment gyroscope[J].Journal of Beijing University of Aeronautics and Astronautics, 2010, 36(4):455-458(in Chinese). http://bhxb.buaa.edu.cn/CN/abstract/abstract8479.shtml
|
| [20] |
HUANG X D, XIE Y M.Evolutionary topology optimization of continuum structures:Methods and applications[M].Chichester:John Wiley & Sons, 2010:53-64.
|
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