工程力学 ›› 2018, Vol. 35 ›› Issue (11): 1-7,16.doi: 10.6052/j.issn.1000-4750.2017.08.0618

• 基本方法 •    下一篇

基于广义模态截断扩增方法的结构频响拓扑变量灵敏度分析

周大为, 陈飙松, 李云鹏, 张盛   

  1. 大连理工大学工业装备结构分析国家重点实验室运载工程与力学学部工程力学系, 大连 116024
  • 收稿日期:2017-08-11 修回日期:2018-03-29 出版日期:2018-11-07 发布日期:2018-11-07
  • 通讯作者: 陈飙松(1973-),男,广东人,教授,博士,从事结构优化及计算力学软件开发研究(E-mail:Chenbs@dlut.edu.cn). E-mail:Chenbs@dlut.edu.cn
  • 作者简介:周大为(1990-),男(满族),吉林人,博士生,从事结构优化及计算力学研究(E-mail:Zhoudw@mail.dlut.edu.cn);李云鹏(1970-),男,辽宁人,硕士,从事计算力学及其软件开发研究(E-mail:lyp@dlut.edu.cn);张盛(1976-),男,吉林人,博士,从事计算力学及其软件开发研究(E-mail:zhangs@dlut.edu.cn).
  • 基金资助:
    国家重点研发计划项目(2016YFB0200702);国家自然科学基金项目(1372064,11761131005);高等学校学科创新引智计划项目(B14013)

SENSITIVITY ANALYSIS OF STRUCTURAL TOPOLOGY DESIGN VARIABLES UNDER HARMONIC EXCITATIONS BASED ON GENERALIZED MODAL TRUNCATION AUGMENTATION METHOD

ZHOU Da-wei, CHEN Biao-song, LI Yun-peng, ZHANG Sheng   

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Facxlty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, China
  • Received:2017-08-11 Revised:2018-03-29 Online:2018-11-07 Published:2018-11-07

摘要: 基于结构拓扑优化设计中的变密度法,采用伴随法推导结构在简谐激励下的频响振幅对单元设计变量的解析灵敏度列式。针对灵敏度数值求解中传统模态位移法引发的低精度问题,通过引入计算成本较低的广义模态截断扩增方法提升灵敏度的计算精度。数值算例将该文方法与全局有限差分法和其他灵敏度计算方法进行了比较。结果证明了该文方法在不同的激励频率及有限元网格密度下高效求解高精度灵敏度的有效性。

关键词: 结构拓扑优化, 解析灵敏度列式, 频响振幅, 伴随法, 模态位移法, 广义模态截断扩增法

Abstract: Based on the variable density method for structural topology optimization, the analytical sensitivity formulation of the frequency response displacement amplitude of structures under harmonic excitations is proposed using the adjoint method. The generalized modal truncation augmentation method is introduced to obtain high accuracy without high computational cost in contrast to the poor accuracy of the traditional modal displacement method in sensitivity computation. Numerical examples are presented to compare the proposed method with the global finite difference method and other computation methods. The computational results demonstrate the effectiveness of the proposed method in computing accurate sensitivities with high efficiency under different excitation frequencies and different densities of finite element meshes.

Key words: structural topology optimization, analytical sensitivity formulation, frequency response displacement amplitude, adjoint method, modal displacement method, generalized modal truncation augmentation method

中图分类号: 

  • O327
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