一种基于自适应单元删除率的BESO方法
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摘要
在ESO中采用动态删除率能有效地提高优化效率和稳定性,但现有的动态删除率策略都含有经验参数,确定删除率的过程较为复杂。本文提出了一种用于BESO的无经验参数自适应单元删除率确定方法。通过分析单元删除率对优化稳定性的影响,得到了结构优化过程中单元删除率的理想变化规律和单元灵敏度均匀化信息对删除率的影响情况,并据此分析了经验参数引入的原因,从而构造了评价单迭代步的单元灵敏度均匀化程度指标。然后,基于单迭代步的单元灵敏度均匀化程度指标,构造了全部迭代步信息下的单元灵敏度均匀化程度相对指标,结合单元删除率的推荐范围值,给出了一种自适应于结构优化进程的单元删除率自适应函数。最后,给出了基于自适应单元删除率的BESO方法实现流程。经典算例的结果对比说明,本文方法在保证优化质量相近的情况下,具有更好的优化效率和稳定性。
In ESO,dynamic removal ratio is a strategy that can effectively improve the optimization efficiency and stability.However,the existing dynamic removal ratio strategy contains empirical parameters,and the process of determining removal ratio is quite complex.Therefore,an adaptive element removal ratio determination method which has no empirical parameters for BESO is proposed in this paper.By analyzing the effect of element removal ratio on optimization stability,the ideal trend of element removal ratio and the effect of element sensitivity homogenization information on removal ratio are obtained in the process of structural optimization.Based on these,the reasons for the introduction of empirical parameters are analyzed,and an index of element sensitivity homogenization for evaluating a single iteration step is constructed.Then the relative index of element sensitivity homogenization degree under all iteration step information is constructed.Based on the element sensitivity homogenization index of a single iteration step,a function of element removal ratio adaptive to the process of structural optimization is given in combination with the recommended range of element removal ratio.Finally,the implementation procedure of BESO method based on the adaptive element removal ratio is presented.The comparison results of classical examples show that the proposed method has better optimization efficiency and stability while having similar quality in order aspects.
In ESO,dynamic removal ratio is a strategy that can effectively improve the optimization efficiency and stability.However,the existing dynamic removal ratio strategy contains empirical parameters,and the process of determining removal ratio is quite complex.Therefore,an adaptive element removal ratio determination method which has no empirical parameters for BESO is proposed in this paper.By analyzing the effect of element removal ratio on optimization stability,the ideal trend of element removal ratio and the effect of element sensitivity homogenization information on removal ratio are obtained in the process of structural optimization.Based on these,the reasons for the introduction of empirical parameters are analyzed,and an index of element sensitivity homogenization for evaluating a single iteration step is constructed.Then the relative index of element sensitivity homogenization degree under all iteration step information is constructed.Based on the element sensitivity homogenization index of a single iteration step,a function of element removal ratio adaptive to the process of structural optimization is given in combination with the recommended range of element removal ratio.Finally,the implementation procedure of BESO method based on the adaptive element removal ratio is presented.The comparison results of classical examples show that the proposed method has better optimization efficiency and stability while having similar quality in order aspects.
引文
[1] Xie Y M,Steven G P.A simple evolutionary procedure for structural optimization[J].Computers & Structures,1993,49(5):885-896.
[2] Xie Y M,Steven G P.Evolutionary Structural Optimization [M].Springer,Berlin,1997.
[3] Querin O M,Steven G P,Xie Y M.Evolutionary structural optimisation(ESO)using a bi-directional algorithm [J].Engineering Computations,1998,15(8):1031-1048.
[4] Querin O M,Young V,Steven G P,et al.Computational efficiency and validation of bi-directional evolutionary structural optimisation [J].Computer Me -thods in Applied Mechanics and Engineering,2000,189(2):559-573.
[5] Huang X D,Xie Y M.Topology optimization of nonlinear structures under displacement loading[J].Engineering Structures,2008,30(7):2057-2068.
[6] Huang X D,Xie Y M.A new look at ESO and BESO optimization methods[J].Structural and Multidisciplinary Optimization,2008,35(1):89-92.
[7] Chu D N,Xie Y M,Hira A,et al.Evolutionary structural optimization for problems with stiffness constraints[J].Finite Elements in Analysis and Design,1996,21(4):239-251.
[8] Chu D N,Xie Y M,Hira A,et al.On various aspects of evolutionary structural optimization for problems with stiffness constraints[J].Finite Elements in Ana-lysis & Design,1997,24(4):197-212.
[9] Zhang D K,Zhang W P,He H,et al.A new ERR and strategy for bi-directional evolutionary structural optimization[J].Applied Mechanics and Materials,2012,204:4422-4428.
[10] 罗静,张大可,李海军,等.基于一种动态删除率的 ESO方法[J].计算力学学报,2015,32(2):274-279.(LUO Jing,ZHANG Da-ke,LI Hai-jun,et al.ESO method based on a kind ofdynamic deletion rate[J].Chinese Journal of Computational Mechanics,2015,32(2):274-279.(in Chinese))
[11] Huang X D,Xie Y M.Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials[J].Computational Mecha-nics,2009,43(3):393-401.
[12] Huang X D,Xie Y M.A further review of ESO type methods for topology optimization[J].Structural and Multidisciplinary Optimization,2010,41(5):671-683.
[13] Huang X D,Xie Y M.Convergent and mesh-inde -pendent solutions for the bi-directional evolutionary structural optimization method [J].Finite Elements in Analysis and Design,2007,43(14):1039-1049.
[14] 荣见华.渐进结构优化方法及其应用研究[D].国防科学技术大学,2006.(RONG Jian-hua.Research on Evolutionary Structural Optimization Method and Its Application[D].National University of Defense Technology,2006.(in Chinese))
[15] Huang X D,Xie Y M.Evolutionary Topology Optimization of Continuum Structures:Methods and Applications [M].Wiley,2010.
[16] Huang X D,Xie Y M.Numerical stability and para-meters study of an improved bi-directional evolutionary structural optimization method[J].Structural Engineering and Mechanics,2007,27(1):49-61.
[2] Xie Y M,Steven G P.Evolutionary Structural Optimization [M].Springer,Berlin,1997.
[3] Querin O M,Steven G P,Xie Y M.Evolutionary structural optimisation(ESO)using a bi-directional algorithm [J].Engineering Computations,1998,15(8):1031-1048.
[4] Querin O M,Young V,Steven G P,et al.Computational efficiency and validation of bi-directional evolutionary structural optimisation [J].Computer Me -thods in Applied Mechanics and Engineering,2000,189(2):559-573.
[5] Huang X D,Xie Y M.Topology optimization of nonlinear structures under displacement loading[J].Engineering Structures,2008,30(7):2057-2068.
[6] Huang X D,Xie Y M.A new look at ESO and BESO optimization methods[J].Structural and Multidisciplinary Optimization,2008,35(1):89-92.
[7] Chu D N,Xie Y M,Hira A,et al.Evolutionary structural optimization for problems with stiffness constraints[J].Finite Elements in Analysis and Design,1996,21(4):239-251.
[8] Chu D N,Xie Y M,Hira A,et al.On various aspects of evolutionary structural optimization for problems with stiffness constraints[J].Finite Elements in Ana-lysis & Design,1997,24(4):197-212.
[9] Zhang D K,Zhang W P,He H,et al.A new ERR and strategy for bi-directional evolutionary structural optimization[J].Applied Mechanics and Materials,2012,204:4422-4428.
[10] 罗静,张大可,李海军,等.基于一种动态删除率的 ESO方法[J].计算力学学报,2015,32(2):274-279.(LUO Jing,ZHANG Da-ke,LI Hai-jun,et al.ESO method based on a kind ofdynamic deletion rate[J].Chinese Journal of Computational Mechanics,2015,32(2):274-279.(in Chinese))
[11] Huang X D,Xie Y M.Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials[J].Computational Mecha-nics,2009,43(3):393-401.
[12] Huang X D,Xie Y M.A further review of ESO type methods for topology optimization[J].Structural and Multidisciplinary Optimization,2010,41(5):671-683.
[13] Huang X D,Xie Y M.Convergent and mesh-inde -pendent solutions for the bi-directional evolutionary structural optimization method [J].Finite Elements in Analysis and Design,2007,43(14):1039-1049.
[14] 荣见华.渐进结构优化方法及其应用研究[D].国防科学技术大学,2006.(RONG Jian-hua.Research on Evolutionary Structural Optimization Method and Its Application[D].National University of Defense Technology,2006.(in Chinese))
[15] Huang X D,Xie Y M.Evolutionary Topology Optimization of Continuum Structures:Methods and Applications [M].Wiley,2010.
[16] Huang X D,Xie Y M.Numerical stability and para-meters study of an improved bi-directional evolutionary structural optimization method[J].Structural Engineering and Mechanics,2007,27(1):49-61.