针对多个设计变量情况下的柔性多体系统灵敏度分析,本文采用伴随变量法对基于绝对节点坐标法建立的柔性多体系统进行了研究。为了验证的该方法的计算效率,分别采用直接微分法和伴随变量法对受重力作用的柔性单摆进行了研究, 结果表明:这两种方法计算结果的误差很小,随着设计变量数量的增加,伴随变量法有更高的计算效率。
Abstract
For multiple design variables, adjoint variable method is applied in sensitivity analysis of flexible multibody systems based on absolute node coordinate formulation. In order to verify the computational efficiency of the method, flexible pendulum under gravity is studied by the direct differentiation method and the adjoint variable method. The results show that the errors between the two methods are small, and the adjoint variable method has higher computational efficiency with increase of design variables.
关键词
多体系统 /
绝对节点坐标法 /
灵敏度 /
伴随变量法
{{custom_keyword}} /
Key words
Multibody system /
Sensitivity /
Absolute node coordinates formulation /
Adjoint variable method
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] 潘振宽,丁洁玉,王钰. 基于隐式微分/代数方程的多体系统动力学设计灵敏度分析方法[J]. 动力学与控制. 2004, 2(2): 66-69.
Pan Zhenkuan, Ding Jieyu, Wang Yu. Design sensitivity analysis of multibody system dynamics descrided by implicit differential/algebraic[J]. Journal of Dynamics and Control. 2004, 2(2): 66-69.
[2] Haug Edward J, and Neel K Mani, Krishnasawami P. Design Sensitivity Analysis and Optimization of Dynamically Driven Systems[M]. Computer Aided Analysis and Optim-ization of Mechanical System Dynamics.Springer Berlin Heidelberg .1983, 555-636.
[3] 康新忠, 王宝元. 机械系统动态优化设计的灵敏度方法[J]. 机械工程学报, 1990, 13(1): 18-23.
Kang Xinzhong, Wang Baoyuan. Sensitivity analysis method of the dynamic optimal design for mechanical systems[J]. Journal of Vibration Engineering. 1990, 13(1): 18-23.
[4] Etman L F P, Van Campen D H, Schoofs A J G. Optimization of multibody systems using approximation concepts[C]//IUTAM.Symposium on Optimization of Mechanical Systems. Netherlands:Springer,1996:81-88.
[5] Li S, Petzold L. Software and algorithms for sensitivity analysis of large-scale differential-algebraic systems[J]. Journal of Computational and Applied Mathematics, 2000, 125: 131-145.
[6] Maly T, Pctzold LR. Numerical methods and software for sensitivity analysis of differential-algebraic systems[J]. Applied Numerical Mathematics, 1996, 20: 57-59.
[7] Shabana A. An absolute nodal coordinates formulation for the large rotation and deformation analysis of flexible bodies[R]. University of Illionis at Chicago, 1996.
[8] Shabana A. Computational continuum mechanics [M]. New York: Cambridge University Press, 2011.
[9] Bonet J, Wood R. Nonlinear continuum mechanics for finite element analysis[M]. Cambridge: Cambridge University Press, 1997.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}