多刚体动力学在结构地震响应分析中的应用
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摘要
该文将多刚体系统动力学理论应用于结构的地震响应分析中;将结构进行多刚体离散,建立了结构的多刚体-铰链-弹簧系统模型,并给出了多刚体离散化模型中弯曲弹簧的等效刚度系数的计算公式;运用多刚体动力学推导了求解结构地震响应的动力学方程,该方程与传统动力学方程的形式相似,可用一般的数值方法求解。该文最后对一单榀建立墙以及一10层剪力墙结构进行了地震响应的时程分析,并将计算结果与有限元方法计算结果进行了比较,两种方法的误差较小。算例结果表明,该文所提出的多刚体动力学用于结构地震反应分析的方法是可行且有效的。
The dynamics theory of multi-rigid body systems was used for analyzing the earthquake response of structures. Based on the multi-rigid body discretization model, a chain multi-rigid body-hinge-spring system model of structures was presented. The calculation formulas of the stiffen coefficients of equivalent springs were then given and the dynamic equations for the earthquake response of structures were derived by the dynamics of multi-rigid body. It is found that the dynamic equation of this method is similar to that of the traditional equation in formulation, and the equation can be solved by the ordinary numerical method. The earthquake responses of a piece of shell wall and a ten-story shell wall structure were analyzed by the method provided in this paper. The analytical results agree well with the results calculated by the finite element method. The numerical results show that this method, applying the dynamics of multi-rigid body to seismic analysis of structures, is feasible and effective.
The dynamics theory of multi-rigid body systems was used for analyzing the earthquake response of structures. Based on the multi-rigid body discretization model, a chain multi-rigid body-hinge-spring system model of structures was presented. The calculation formulas of the stiffen coefficients of equivalent springs were then given and the dynamic equations for the earthquake response of structures were derived by the dynamics of multi-rigid body. It is found that the dynamic equation of this method is similar to that of the traditional equation in formulation, and the equation can be solved by the ordinary numerical method. The earthquake responses of a piece of shell wall and a ten-story shell wall structure were analyzed by the method provided in this paper. The analytical results agree well with the results calculated by the finite element method. The numerical results show that this method, applying the dynamics of multi-rigid body to seismic analysis of structures, is feasible and effective.
引文
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[10]王强,吕西林.离散单元法在框架结构地震反应分析中的应用[J].地震工程与工程振动,2004,24(5):73―78.Wang Qiang,Lu Xilin.Application of DEM to seismic response analysis of frame structures[J].Earthquake Engineering and Engineering Vibration,2004,24(5):73―78.(in Chinese)
[11]王强,吕西林.离散单元法在钢筋混凝土构件非线形反应分析中的应用[J].沈阳建筑大学学报(自然科学版),2005,21(2):91―95.Wang Qiang,Lu Xilin.Application of the DEM to the nonlinear analysis of reinforced concrete members[J].Journal of Shenyang Jianzhu University(Natural Science),2005,21(2):91―95.(in Chinese)
[12]Wang Y.Finite segment model for elastic beams[C]//Midha A.Trends and Developments in Mechanisms,Machines and Robotics,1988:505―507.
[13]Wittenburg J.Dynamics of systems of rigid bodies[M].Teubner,Stuttgart,1977.
[2]马兴瑞,苟兴宇,李铁寿.航天器动力学的发展概况[J].宇航学报,2000,21(3):1―5.Ma Xingrui,Gou Xingyu,Li Tieshou.Development generalization of spacecraft dynamics[J].Journal of Astronautics,2000,21(3):1―5.(in Chinese)
[3]Liu S H,Sun D A,Wang Y S.Numerical study of soil collapse behavior by discrete element modeling[J].Computers and Geotechnics,2003,30:399―408.
[4]Winget J M,Huston R L.Cable dynamics-a finite segment approach[J].Computers and Structures,1976,6(6):475―480.
[5]殷学纲.有限段法在梁非线性振动分析中的应用[J].重庆大学学报,1988,11(11):113―125.Yin Xuegang.Analysis of the nonlinear oscillation of beams by finite segment method[J].Journal of Chongqing University,1988,11(11):113―125.(in Chinese)
[6]殷学纲,杜思义,胡继云.应用多刚体离散化方法对梁的动力屈曲和后屈曲分析[J].应用数学和力学,2005,26(9):1076―1082.Yin Xuegang,Du Siyi,Hu Jiyun.Analysis of dynamical bucking and post bucking for beams by finite segment method[J].Applied Mathematics and Mechanic,2005,26(9):1076―1082.(in Chinese).
[7]李宾,李映辉,殷学纲.大垂度柔索的动力学建模与仿真[J].应用数学和力学,2001,21(6):640―646.Li Bin,Li Yinghui,Yin Xuegang.Dynamics modeling and simulation of flexible cable with large sag[J].Applied Mathematics and Mechanic,2001,21(6):640―646.(in Chinese)
[8]Wang R H,Li Q S,Wu J R.A spatial elastic displacement model for curved box girders with corner stiffeners[J].Computers and Structures,2005,83:1021―1029.
[9]赖明,李英民.剪切型结构地震响应的多刚体离散分析方法[J].建筑结构学报,1994,15(6):17―24.Lai Ming,Li Yingmin.A discrete analysis method of multi-rigid-body model for earthquake response of shear-type structures[J].Journal of Building Structures,1994,15(6):17―24.(in Chinese)
[10]王强,吕西林.离散单元法在框架结构地震反应分析中的应用[J].地震工程与工程振动,2004,24(5):73―78.Wang Qiang,Lu Xilin.Application of DEM to seismic response analysis of frame structures[J].Earthquake Engineering and Engineering Vibration,2004,24(5):73―78.(in Chinese)
[11]王强,吕西林.离散单元法在钢筋混凝土构件非线形反应分析中的应用[J].沈阳建筑大学学报(自然科学版),2005,21(2):91―95.Wang Qiang,Lu Xilin.Application of the DEM to the nonlinear analysis of reinforced concrete members[J].Journal of Shenyang Jianzhu University(Natural Science),2005,21(2):91―95.(in Chinese)
[12]Wang Y.Finite segment model for elastic beams[C]//Midha A.Trends and Developments in Mechanisms,Machines and Robotics,1988:505―507.
[13]Wittenburg J.Dynamics of systems of rigid bodies[M].Teubner,Stuttgart,1977.
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