双向渐进结构优化法原理及其动力学优化研究
摘要
针对等效静载荷优化(ESLO)计算效率低、优化流程复杂的问题,将双向渐进结构法引入到等效静载荷优化中。以双向渐进结构法作为优化迭代环方法,对动态响应拓扑优化流程进行了改进,并重新定义了收敛准则;通过2个算例验证了该方法的可行性。研究结果表明,当设计循环次数n大于1时,所提出的方法每次设计外循环消耗的时间小于原始方法消耗的时间,因此整体优化时间减少了;说明该方法适用于结构动态响应拓扑优化,同时效率更高。
引文
[1]BENDSOE M P,SIGMUND O.Topology optimization:Theory,Methods,and Applications[M].New York:Methods and Applications,2003.
[2]BENDSOE M P,KIKUCHI N.Generating optimal t-opologies in structural design using a homogenization method[J].Computer Methods in Applied Mechanics and Engineering,1988,71(2):197-224.
[3]BENDSOE M P.Optimal Shape Design as a Materi-al Distribution Problem[J].Structural Optimization,1989,1(4):193-202.
[4]XIE Y M,STEVEN G P.A Simple Evolutionary Procedure for Structural Optimization[J].Computers and Structures,1993,49(5):885-896.
[5]QUERIN O M,YOUNG V,STEVEN G P,et al.Computational efficiency and validation of bi-directional evolutionary structural optimization[J].Comput.Meth.Appl.Engng,2000(189):559-573.
[6]ROZVANY G I.A critical review of established metho-ds of structural topology optimization[J].Structural and Multidisciplinary Optimization,2009,37(3):217-237.
[7]HUANG X,XIE M.Evolutionary topology optimization of continuum structures:methods and applications[M].John Wiley&Sons,2010.
[8]CHOI S H,KIM S R,PARK J Y,et al.Multi-Objective Optimization Of The Inner Reinforcement For A Vehicle’S Hood Considering Static Stiffness And Natural Frequency[J].International Journal Of Automotive Technology,2007,8(3):337-342.
[9]CHOI K H,PARK J Y,RYU S P,et al.Reliabili ty-Based Topology Optimization Based On Bidirectional Evolutionary Structural Optimization Using Multi-Objective Sensitivity Numbers[J].International Journal Of Automotive Technology,2011,12(6):849-856.
[10]AFIMIWALA K A,MAYNE R W.Optimal Design of an Impact Absorber[J].Journal of Engineering for Industry,Transactions of the ASME 96:124-130.
[11]FOX R L,KAPOOR M P.Structural Optimization in the Dynamic Regime[J].A Computational Approach.AIAA Journal 8:1798-1804.
[12]CHOI W S,PARK G J.Structural Optimization Using Equivalent Static Loads at All the Time Intervals[J].Computer Methods in Applied Mechanics and Engin-eering,2002,191(19-20):2105-2122.
[13]PARK G J,KANG B S.Validation of a Structural Optimization Algorithm Transforming Dynamic Loadsinto Equivalent Static Loads[J].Journal Of Optimizat-ion Theory And Applications,2003,118(1):191-200.
[14]JANG H H,LEE H A,PARK G J.Preliminary Study on Linear Dynamic Response Topology Optimization Using Equivalent Static Loads[J].Transactions of the Korean Society of Mechanical Engineers,2009,33(12):1357-1493.
[15]LEE H A,PARK G J.Nonlinear dynamic response top-ology optimization using the equivalent static loads method[J].Computer Methods in Applied Mechanics and Engineering,2015,283(1):956-970.
[16]苏义脑,唐雪平,陈祖锡.初弯曲纵横弯曲梁的等效载荷法及其应用[J].力学与实践,2004(1):42-44.
[17]黄武龙.基于等效静态载荷方法的大型复杂结构的轻量化设计[D].广州:广东工业大学,2013.
[18]赵礼辉.ESL法在汽车结构优化设计中的应用[D].上海:上海交通大学,2009.
[19]杨志军.基于等效静态载荷原理的高速机构结构拓扑优化方法[J].机械工程学报,2011,9(17):119-126.
[20]芮强,王红岩,田洪刚.基于等效静态载荷法的结构动态优化[J].汽车工程,2014(1):61-65.
[21]KIM E,KIM H,BAEK S,et al.Effective structural o-ptimization based on equivalent static loads combined with system reduction method[J].Structural and Mul-tidisciplinary Optimization,2014,50:775-786.
[22]LEE J Y,PARK G J.Dynamic Response Topology Optimization in the Time Domain Using Equivalent Static Loads[J].AIAA Journal,2012,50(1):226-234.
[2]BENDSOE M P,KIKUCHI N.Generating optimal t-opologies in structural design using a homogenization method[J].Computer Methods in Applied Mechanics and Engineering,1988,71(2):197-224.
[3]BENDSOE M P.Optimal Shape Design as a Materi-al Distribution Problem[J].Structural Optimization,1989,1(4):193-202.
[4]XIE Y M,STEVEN G P.A Simple Evolutionary Procedure for Structural Optimization[J].Computers and Structures,1993,49(5):885-896.
[5]QUERIN O M,YOUNG V,STEVEN G P,et al.Computational efficiency and validation of bi-directional evolutionary structural optimization[J].Comput.Meth.Appl.Engng,2000(189):559-573.
[6]ROZVANY G I.A critical review of established metho-ds of structural topology optimization[J].Structural and Multidisciplinary Optimization,2009,37(3):217-237.
[7]HUANG X,XIE M.Evolutionary topology optimization of continuum structures:methods and applications[M].John Wiley&Sons,2010.
[8]CHOI S H,KIM S R,PARK J Y,et al.Multi-Objective Optimization Of The Inner Reinforcement For A Vehicle’S Hood Considering Static Stiffness And Natural Frequency[J].International Journal Of Automotive Technology,2007,8(3):337-342.
[9]CHOI K H,PARK J Y,RYU S P,et al.Reliabili ty-Based Topology Optimization Based On Bidirectional Evolutionary Structural Optimization Using Multi-Objective Sensitivity Numbers[J].International Journal Of Automotive Technology,2011,12(6):849-856.
[10]AFIMIWALA K A,MAYNE R W.Optimal Design of an Impact Absorber[J].Journal of Engineering for Industry,Transactions of the ASME 96:124-130.
[11]FOX R L,KAPOOR M P.Structural Optimization in the Dynamic Regime[J].A Computational Approach.AIAA Journal 8:1798-1804.
[12]CHOI W S,PARK G J.Structural Optimization Using Equivalent Static Loads at All the Time Intervals[J].Computer Methods in Applied Mechanics and Engin-eering,2002,191(19-20):2105-2122.
[13]PARK G J,KANG B S.Validation of a Structural Optimization Algorithm Transforming Dynamic Loadsinto Equivalent Static Loads[J].Journal Of Optimizat-ion Theory And Applications,2003,118(1):191-200.
[14]JANG H H,LEE H A,PARK G J.Preliminary Study on Linear Dynamic Response Topology Optimization Using Equivalent Static Loads[J].Transactions of the Korean Society of Mechanical Engineers,2009,33(12):1357-1493.
[15]LEE H A,PARK G J.Nonlinear dynamic response top-ology optimization using the equivalent static loads method[J].Computer Methods in Applied Mechanics and Engineering,2015,283(1):956-970.
[16]苏义脑,唐雪平,陈祖锡.初弯曲纵横弯曲梁的等效载荷法及其应用[J].力学与实践,2004(1):42-44.
[17]黄武龙.基于等效静态载荷方法的大型复杂结构的轻量化设计[D].广州:广东工业大学,2013.
[18]赵礼辉.ESL法在汽车结构优化设计中的应用[D].上海:上海交通大学,2009.
[19]杨志军.基于等效静态载荷原理的高速机构结构拓扑优化方法[J].机械工程学报,2011,9(17):119-126.
[20]芮强,王红岩,田洪刚.基于等效静态载荷法的结构动态优化[J].汽车工程,2014(1):61-65.
[21]KIM E,KIM H,BAEK S,et al.Effective structural o-ptimization based on equivalent static loads combined with system reduction method[J].Structural and Mul-tidisciplinary Optimization,2014,50:775-786.
[22]LEE J Y,PARK G J.Dynamic Response Topology Optimization in the Time Domain Using Equivalent Static Loads[J].AIAA Journal,2012,50(1):226-234.