结构动力响应灵敏度分析伴随法一致性问题研究

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振动与冲击 ›› 2015, Vol. 34 ›› Issue (20) : 167-173.

论文

胡智强1, 马海涛1,2

作者信息 +

On the consistency issue of adjoint methods for sensitivity analysis of dynamic response

HU Zhi-qiang1，MA Hai-tao1,2

Author information +

文章历史 +

摘要

研究结构瞬态动力响应灵敏度分析伴随法可能存在的一致性问题，具体考虑先微分后离散与先离散后微分两种敏度分析方法的计算精度、收敛速度及一致性等。基于动力响应分析的时域显式法基本思想，以更简洁方式推导先离散后微分的伴随法计算列式。结果表明，先微分后离散伴随法一致性问题由计算中所用动力响应结果仅在离散时间点满足运动方程产生的，一致性问题存在不影响该方法的可靠性及应用。

Abstract

The inconsistency issue of adjoint variable methods (AVMs) for sensitivity analysis of transient dynamic responses is investigated. The differentiate-then-discretize and discretize-then-differentiate approaches are considered, focusing on their computational accuracy, convergence rates and result consistency. Based on the basic idea of the ex-plicit time-domain method for dynamic analysis, a concise discretize-then-differentiate AVM formulation is presented. It is found that the inconsistency of the differentiate-then-discretize approach is caused by the fact that numerical solutions for dynamic responses satisfy equations of motion only at integration points in the time domain, and despite this consis-tency problem, this approach is still reliable for sensitivity analysis of dynamic responses.

导出引用

胡智强1, 马海涛1,2. 结构动力响应灵敏度分析伴随法一致性问题研究[J]. 振动与冲击, 2015, 34(20): 167-173

HU Zhi-qiang1，MA Hai-tao1,2. On the consistency issue of adjoint methods for sensitivity analysis of dynamic response[J]. Journal of Vibration and Shock, 2015, 34(20): 167-173

参考文献

[1] 陈太聪,韩大建,苏成. 参数灵敏度分析的神经网络方法及其工程应用[J]. 计算力学学报, 2004, 21(6): 752-756.
CHEN Tai-cong, HAN Da-jian, SU Cheng. Neural network method in parameter sensitivity analysis and its application in engineering [J]. Chinese Journal of Computational Mechanics, 2004, 21(6): 752-756.
[2] 陈钢,赵国忠,顾元宪. 声场-结构耦合系统灵敏度分析及优化设计研究[J]. 振动与冲击, 2007, 26(4): 86-89.
CHEN Gang, ZHAO Guo-zhong, GU Yuan-xian. Sensitivity analysis and design optimization method for acoustic- structural coupled systems[J]. Journal of Vibration and Shock, 2007, 26(4): 86-89.
[3] 毛玉明,郭杏林,赵岩,等. 基于灵敏度分析的结构动态载荷识别研究[J]. 振动与冲击, 2010, 29(10): 1-3.
MAO Yu-ming, GUO Xing-lin, ZHAO Yan, et al. Force iden-tification based on sensitivity analysis method [J]. Journal of Vibration and Shock, 2010, 29(10): 1-3.
[4] 赵杰,李峰,刘录. 基于有限元的超高压管线系统振动特性灵敏度分析 [J]. 振动与冲击, 2014, 33(10): 148-151.
ZHAO Jie, LI Feng, LIU Lu. Vibration characteristic sensitiv-ity analysis based on finite element for ultra-high pressure pipeline systems[J].Journal of Vibration and Shock, 2014, 33(10): 148-151.
[5] Dahl J, Jensen J S, Sigmund O. Topology optimization for transient wave propagation problems in one dimension[J]. Structural and Multidisciplinary Optimization,2008,36:585- 595.
[6] Kang Z, Zhang X P, Jiang S G,et al. On topology optimization of damping layer in shell structures under harmonic excitations[J]. Structural and Multidisciplinary Optimization, 2012, 46: 51-67.
[7] Le C, Bruns T E, Tortorelli D A. Material microstructure optimization for linear elastodynamic energy wave management[J]. Journal of the Mechanics and Physics of Solids,2012, 60: 351-378.
[8] Kang B S, Park G J, Arora J S. A review of optimization of structures subjected to transient loads[J]. Structural and Multi¬disciplinary Optimization,2006, 31: 81-95.
[9] Keulen F V, Haftka R T, Kim N H. Review of options for structural design sensitivity analysis,part 1: linear systems [J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194: 3213-3243.
[10] Jensen J S, Nakshatrala P B,Tortorelli D A. On the consis-tency of adjoint sensitivity analysis for structural optimization of linear dynamic problems[J]. Structural and Multidiscipli-nary Optimization, 2014, 49(5): 831-837.
[11] Bathe K J. Finite element procedures[M]. Prentice-Hall, Englewood Cliffs, New Jersey, 1996.
[12] Kreyszig E. Advanced engineering mathematics (7th edn) [M]. New York:Wiley, 1993.
[13] 苏成,徐瑞.非平稳激励下结构随机振动时域分析法[J]. 工程力学, 2010, 27(12): 77-83.
SU Cheng, XU Rui. Random vibration analysis of structures subjected to non-stationary excitations by time domain method [J]. Engineering Mechanics, 2010, 27(12): 77-83.
[14] Cook R D, Malkus D S, Plesha M E, et al. Concepts and ap-plications of finite element analysis(4th edn)[M]. New York: Wiley,2000.