基于自适应随机抽样敏度分析的双向渐进结构优化方法
Bi-directional evolutionary structural optimization method based on self-adaption and random sampling sensitivity analysis
-
摘要: 为了解决周期循环结构拓扑优化难题,在传统的双向渐进结构优化方法(BESO)的基础上,引入了一种自适应参数策略和随机抽样的方法,提出了基于自适应随机抽样敏度分析的双向渐进结构优化方法,该方法同样适用于非周期结构.以该方法为基础,对Michell桁架结构进行了拓扑优化设计,得到了与理论解一致的结构,并且相对初始结构质量减少了71.5%,说明了所提方法的正确性.基于此方法对多辐板风扇盘进行了结构拓扑优化设计,得到了三辐板风扇盘结构,相比同等设计条件下的参考风扇盘质量减少了17.12%,进一步说明了此方法具有处理复杂周期循环结构拓扑优化设计问题的能力,另外此方法克服了传统双向渐进结构优化方法中容易产生的振荡问题.Abstract: In order to solve the issue of periodic structural topology optimization with design-dependence,the self-adaption strategy and random sampling method were developed,and a topology optimization approach called bi-directional evolutionary structural optimization(BESO) using self-adaption and random sampling sensitivity analysis was proposed based on traditional BESO method.It is also suitable for the non-periodic structures.Based on the approach,the Michell truss structure topological optimization design was carried out,and the optimum structure was obtained in consistence with the theoretical solution.The mass was reduced by 71.5%,compared with the initial structure,showing the proposed method is reasonable;moreover,the multi-web fan disk was designed by the above method,and a new three-web fan disk was obtained.The mass declined by 17.21% in relation to the reference fan disk.The results further illustrates that the method has the ability to cope with the complex issue of periodic structural topology optimization.Additionally,the prone oscillation problems of classical BESO method has been overcome by the algorithm.
-
[1] Rossow H P,Taylor J E.A finite element method for the optimal design of variable thickness sheets[J].AIAA Journal,1973,11(11):1566-1569. [2] Bends E M P,Kikuchi N.Generating optimal topologies in structural design using a homogenization method[J].Computer Method in Applied Mechanics and Engineering,1988,71(2):197-224. [3] Mlejnek H P,Schirrmacher R.An engineer’s approach to optimal material distribution and shape finding[J].Computer Methods in Applied Mechanics and Engineering,1993,106(1/2):1-26. [4] 隋允康.建模变换优化-结构综合方法新进展[M].大连:大连理工大学出版社,1996. [5] Osher S,Sethian J A.Fronts propagating with curvature dependent speed:algorithms based on Hamilton-Jacobi formulations[J].Journal of Computational Physics,1988,79(5):12-49. [6] Xie Y M,Steven G P.Evolutionary structural optimization for dynamic problems[J].Computers & Structures,1996,58(6):1067-1073. [7] 谢亿民,杨晓英,Steven G P.渐进结构优化法的基本理论及应用[J].工程力学,1999,16(6):70-81. XIE Yimin,YANG Xiaoying,Steven G P.The theory and application of evolutionary structure optimization method[J].Engineering Mechanics,1999,16(6):70-81.(in Chinese) [8] Querin O M,Steven G P,Xie Y M.Evolutionary structural optimization(ESO) using a bidirectional algorithm[J].Engineering Computations,1998,15(8):1031-1048. [9] 荣见华,姜节胜,胡德文,等.基于应力及其敏度的结构拓扑渐进优化方法[J].力学学报,2003,35(5):585-591. RONG Jianhua,JIANG Jiesheng,HU Dewen,et al.A structural topplogy evolutiona method based on stresses and their sensitivity[J].Acta Mechanic Sinica,2003,35(5):585-591.(in Chinese) [10] RONG Jianhua.Bi-direction evolutionary optimization of structures with stress and diplacement constrains based on man-made material[M].Beijing:Science Press,2003:1094-1109. [11] Huang X D,Xie Y M.Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials[J].Computational Mechanics,2009,43(3):393-401. [12] Rozvany G I N,Zhou M,Birker T.Generalized shape optimization without homogenization[J].Structural Optimization,2000,20(6):2-11. [13] 刘书田,贺丹.基于SIMP插值模型的渐进结构拓扑优化方法[J].计算力学学报,2009,26(6):761-777. LIU Shutian,HE Dan.SIMP-based evolutionary structural optimization method for topology optimization[J].Chinese Journal of Computational Mechanica,2009,26(6):761-777.(in Chinese) [14] Zhou M,Rozvany G.On the validity of ESO type methods in topology optimization[J].Structural and Multidiscipliary Optimization,2001,21(1):80-83. [15] 刘超.涡轮盘结构拓扑与形状优化方法研究[D].南京:南京航空航天大学,2010. LIU Chao.Topology and shape optimization method for turbine disk[D].Nanjing:Nanjing University of Aeronauticas and Astronautics,2010.(in Chinese) [16] Wadley H N G,Fleck N A,Evan A G.Fabrication and structural performance of periodic cellular metal sandwish structures[J].Computers & structures,2003,63(12):2331-2343. [17] Sigmund O,Torquato S.Design of materials with extreme method[J].Journal of the Mechanics and Physics of Solids,1997,45(6):1037-1067. [18] Zhang W,Sun S.Scal-raleted topology optimization of cellular materials and structures[J].International Journal for Numerical Methods in Engeering,2006,68(9):993-1011. [19] Huang X,Xie Y M.Optimal design of periodic structures using evolutionary topology optimization[J].Struct Multidisc Optim,2008,36(5):597-606. [20] Michell G M.The limits of economy of material in frame-structures[J].Philosophical Magazine:Series 6,1904,47(8):589-597. [21] Querin O M.Evolutionary structural optimisation stress based formulation and implementation[D].Sydney:University of Sydney,1997. [22] 李伦未,陆山.基于ANSYS的多辐板风扇盘结构优化设计技术[J].航空动力学报,2011,10(26):2245-2250. LI Lunwei,LU Shan.Structure optimum design techniques for multi-web fan disk based on ANSYS[J].Journal of Aerospace Power,2011,10(26):2245-2250.(in Chinese)
点击查看大图
计量
- 文章访问数: 1436
- HTML浏览量: 0
- PDF量: 946
- 被引次数: 0