基于结点位移插值的约束子结构界面自由度缩减方法
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摘要
基于结点位移插值原理,建立了约束模态子结构界面自由度的缩减方法,形成了约束子结构模态综合法的二次坐标变换矩阵。通过第二次坐标变换可有效地缩减计算系统的广义自由度,提高计算效率。算例表明,这种缩减方法是合理有效的。该文还讨论了插值基点的选择方式对计算精度的影响,计算结果表明,当选择的插值基点在界面上均匀分布时,计算精度最好。最后,对比了插值域的形状对计算精度的影响,计算结果表明,矩形插值域的计算精度要好于三角形插值域。
Based on a node displacement interpolation formulation,the interface degrees of freedom reduction technique for a constrained substructure was developed in this paper,and the second transformation matrix was constructed for a constrain substructure modal synthesis method.The generalized degrees of freedom of the system were reduced effectively by using the second transformation matrix,thusly the calculating efficiency can be improved.The numerical examples demonstrate that the interface degrees of freedom reduction technique suggested in the paper is reasonable and effective.The influence on the calculation accuracy of the choice of interpolation nodes was discussed,and the numerical results show that the calculation accuracy is the highest if the interpolation nodes uniformly distribute on the interface.At last,the influence on the calculation accuracy of shape of interpolation areas was also studied,and the results indicate that calculation accuracy is higher when using the interpolation areas in the shape of rectangular than the case in the shape of triangle.
Based on a node displacement interpolation formulation,the interface degrees of freedom reduction technique for a constrained substructure was developed in this paper,and the second transformation matrix was constructed for a constrain substructure modal synthesis method.The generalized degrees of freedom of the system were reduced effectively by using the second transformation matrix,thusly the calculating efficiency can be improved.The numerical examples demonstrate that the interface degrees of freedom reduction technique suggested in the paper is reasonable and effective.The influence on the calculation accuracy of the choice of interpolation nodes was discussed,and the numerical results show that the calculation accuracy is the highest if the interpolation nodes uniformly distribute on the interface.At last,the influence on the calculation accuracy of shape of interpolation areas was also studied,and the results indicate that calculation accuracy is higher when using the interpolation areas in the shape of rectangular than the case in the shape of triangle.
引文
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[2]楼梦麟.结构动力分析的子结构方法[M].上海:同济大学出版社,1997:51―214.Lou Menglin.The Substructure method for dynamicanalysis of structures[M].Shanghai:Tongji UniversityPress,1997:51―214.(in Chinese)
[3]Lou M,Ghobarah A,Aziz T S.Application ofwilson-ritz vectors in dynamic substructuring method[J].International Journal of Solids and Structures,1993,30(22):3159―3170.
[4]Lou M,Ghobarah A,Aziz T S.A modal synthesismethod for dynamic substructuring[J].European Journalof Mechanics,A/Solids,1993,12(3):403―416.
[5]楼梦麟,白建方.基于摄动原理的复杂土层地震反应分析的子结构法[J].计算力学学报,2009,26(2):221―225.Lou Menglin,Bai Jianfang.Substructure Method forearthquake response analysis of complicated site soilbased on modal perturbation principle[J].ChineseJournal of Computational Mechanics,2009,26(2):221―225.(in Chinese)
[6]Sung-Kyung Lee,Eun Churn Park,Kyung-Won Min,Ji-Hun Park.Real-time substructuring technique for theshaking table test of upper substructures[J].EngineeringStructures,2007,29:2219―2232.
[7]李玉顺,单炜,李俊华.子结构法拟动力试验技术研究[J].土木工程学报,2010,43(3):119―123.Li Yushun,Shan Wei,Li Junhua.Study on substructurepseudo-dynamic test[J].China Civil Engineering Journal,2010,43(3):119―123.(in Chinese)
[8]许国山,吴斌.采用等效力控制方法的非线性结构实时子结构试验[J].振动工程学报,2010,23(3):237―242.Xu Guoshan,Wu Bin.Real-time substructure testing ofnonlinear structures with equivalent force control method[J].Journal of Vibration Engineering,2010,23(3):237―242.(in Chinese)
[9]王文亮.Hurty-Craig约束模态综合法的动力原理和它的一种变体[J].复旦学报(自然科学版),1982,21(2):121―129.Wang Wenliang.Dynamic principle of Hurty-Craig’smodal synthesis method and its variety[J].Journal ofFudan University(Natural Science Edition),1982,21(2):121―129.(in Chinese)
[10]白建方,楼梦麟.基于动力子结构方法的场地地震反应分析方法[J].震灾防御技术,2008,3(2):145―154.Bai Jianfang,Lou Menglin.The dynamic substructuremethod for seismic response of irregular topography[J].Technology for Earthquake Disaster Prevention,2008,3(2):145―154.(in Chinese)
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