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1、Seediscussions,stats,andauthorprofilesforthispublicationat:https://www.researchgate.net/publication/290493156InvestigationoflocalizedmodesintopologyoptimizationofdynamicstructuresArticle·January2006CITATIONSREADS9833authors:JihongZhuWeihongZhangNorthwesternPolyte
2、chnicalUniversityNorthwesternPolytechnicalUniversity98PUBLICATIONS952CITATIONS411PUBLICATIONS4,735CITATIONSSEEPROFILESEEPROFILEKunfengQiuChinaUniversityofGeosciences(Beijing)62PUBLICATIONS194CITATIONSSEEPROFILESomeoftheauthorsofthispublicationarealsoworkingonthes
3、erelatedprojects:AdditivemanufacturingViewprojectShapepreservingdesignwithstructuraltopologyoptmizationViewprojectAllcontentfollowingthispagewasuploadedbyWeihongZhangon09March2016.Theuserhasrequestedenhancementofthedownloadedfile.第26卷第4期航空学报Vol.26No.42005年7月ACTAA
4、ERONAUTICAETASTRONAUTICASINICAJuly2005文章编号:1000-6893(2005)04-0619-05结构动力学拓扑优化局部模态现象分析朱继宏,张卫红,邱克鹏(西北工业大学中法并行工程联合实验室,陕西西安710072)InvestigationofLocalizedModesinTopologyOptimizationofDynamicStructuresZHUJi-hong,ZHANGWei-hong,QIUKe-peng(Sino-FrenchLaboratoryofConcurre
5、ntEngineering,NorthwesternPolytechnicalUniversity,Xi′an710072,China)摘要:使用拓扑优化技术进行结构自然频率最大化设计时的主要问题是结构空洞区域可能出现的局部模态现象。采用刚度矩阵和质量矩阵求解动力学特征方程,通过算例分析了结构密度差异、惩罚因子对自然频率和模态的影响以及局部模态现象产生的原因。结果表明,由于实体各向同性材料惩罚函数法(SIMP)使用了指数惩罚因子,空洞区域的密度与刚度差异远远大于实体区域,导致空洞区域局部模态的产生。分析了局部模态的产生过
6、程,给出了结构自然频率和模态相对实体-孔洞区域密度的比值以及惩罚因子的变化趋势。同时,基于传统体胞微结构均匀化等效模型方法,提出了描述结构空洞区域的多种体胞微结构,计算证实这些微结构形式均可有效地避免局部模态的发生。关键词:动力学拓扑优化;微结构;局部模态;均匀化方法中图分类号:V215.2;O224文献标识码:AAbstract:Oneofthemainproblemsinthefrequencymaximizationofdynamicstructuresbytopologyoptimiza-tionistheapp
7、earanceoflocalizedmodesinlow-densityareas.Thispaperaimsatinvestigatingtheinherentcausebymeansofnumericalexamples.Basedonthestiffnessandmassmatricesofthestructure,thedynamiccharacteristicequationissolvedtofigureouthowthedensitydifferenceandpenaltyfactoraffectthena
8、turalfrequenciesandmodalvectors.ItisfoundthatduetothepenaltyfactoroftheSIMPmethod,theratioofthedensitytostiffnessisgreaterinthesolidregionthaninthevoidregion.S