结构优化半解析灵敏度分析的改进算法  

Modified semi-analytical sensitivity analysis methods for structural design optimization

作　　者：陈飙松[1,2] 张力丹[1] 鲁一南 程耿东[1] CHEN Biao-song;ZHANG Li-dan;LU Yi-nan;CHENG Geng-dong(State Key Laboratory of Industrial Equipment,Dalian University of Technology,Dalian 116024,China;Jiangsu Research Institute,Dalian University of Technology,Changzhou 213164,China)

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,大连116024 [2]大连理工大学江苏研究院,常州213164

出　　处：《计算力学学报》2018年第5期533-539,共7页Chinese Journal of Computational Mechanics

基　　金：国家重点研发计划(2016YFB0201602);国家自然科学基金(11372064)资助项目

摘　　要：提出了结构半解析灵敏度分析的改进算法,该算法实现简便,对于设计变量摄动步长具有极佳的数值稳定特性。首先,从总体角度推导静力问题半解析法灵敏度分析新算法,提出了位移与应力灵敏度列式,并给出了算法实施途径;然后,将此思路推广于自振频率、屈曲临界荷载和瞬态响应等多种问题,提出了相应的计算步骤。以梁单元与壳单元等典型结构为例,开展了多个算例测试。测试表明,改进算法计算精度和效率均有提升,特别是设计变量步长有更大的数值稳定区域,为复杂工程结构形状优化的灵敏度分析提供了新途径。A modified algorithm for semi-analytical sensitivity analysis is presented in this investigation,which facilitates program implementation and possesses excellent numerical stability stable feature with respect to perturbation step length of design variables.Firstly,a modified semi-analytical sensitivity analysis technique based on global structural equations is proposed for static displacement and stress problems,and its program implementations are provided.Subsequently,the modified method is extended for other analysis tasks including natural frequency,linear buckling and dynamic transient analysis.Meanwhile,the modified method is verified by typical finite element models with beam and shell elements.The results highlight the applicability of the modified method to various analysis types mentioned above,and the accuracy as well as the efficiency is enhanced by the modified methods.Especially,the methods exhibit excellent stable features with respect to perturbation step length of design variables and thus will be more suitable for shape optimization of complex engineering structures.

关 键 词：结构优化 半解析灵敏度分析法 形状优化 改进算法 

分 类 号：O241[理学—计算数学]