结构体系动力方程求解的显式积分格式的能耗特性
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摘要
针对作者提出的结构体系动力方程求解的一种显式积分格式,探讨其数值计算能耗特性即算法阻尼特性,导出了其算法阻尼值随体系的物理阻尼和结构体系振动频率值变化的关系,并进一步讨论了该积分格式用于无限介质波动的数值模拟中抑制或消除透射边界引起的计算高频失稳问题,给出了该积分格式与中心差分格式的对比分析算例。
The numerical dissipation property of an explicit time integration scheme is developed for the dynamic equation of structural system. The relations between the degree of numerical dissipation (or algorithmic damping value of the explicit integration scheme) and the physical damping value and free frequency of structural system are deducted. Furthermore a problem was discussed to show the application of the explicit integration scheme to depressing or eliminating the high-frequency instability induced by Local Transmitting Boundary for the numerical analysis of wave motion in infinite domain, and also case studies were given for comparison between the explicit integration scheme and central integration scheme.
The numerical dissipation property of an explicit time integration scheme is developed for the dynamic equation of structural system. The relations between the degree of numerical dissipation (or algorithmic damping value of the explicit integration scheme) and the physical damping value and free frequency of structural system are deducted. Furthermore a problem was discussed to show the application of the explicit integration scheme to depressing or eliminating the high-frequency instability induced by Local Transmitting Boundary for the numerical analysis of wave motion in infinite domain, and also case studies were given for comparison between the explicit integration scheme and central integration scheme.
引文
[1]李小军,廖振鹏,杜修力.有阻尼体系动力问题的一种显式差分解法[J].工程力学,《工程力学》第一届编委会主编,北京科技出版社,1992,471~476;地震工程与工程振动,1992,12(4):74~80.Li Xiaojun,Liao Zhenpeng,Du Xiuli.An explicit finite difference method for viscoelastic dynamic problem[J].Earthquake Engineering and Engineering Vibration,1992,12(4):74~80.(in Chinese)
[2]李小军.非线性场地地震反应分析方法的研究[D].北京:国家地震局工程力学研究所,1993.Li Xiaojun.Study on the method for analysing the earthquake response of nonlinear site[D].Beijing:Institute of Engineering Mechanics,SSB,1993.(in Chinese)
[3]李小军,廖振鹏.非线性结构动力方程求解的显式差分格式的特性分析[J].工程力学,1993,10(2):141~148Li Xiaojun,Liao Zhenpeng.The analysis of the properties of an explicit difference method for solving the nonlinear structural dynamic equations[J].Engineering Mechanics,1993,10(2):141~148.(in Chinese)
[4]李小军,刘爱文.动力方程求解的显式积分格式及其稳定性与适用性[J].世界地震工程,2000,16(2):8~12.Li Xiaojun,Liu Aiwen.Explicit step-by-step integration formulas for dynamic differential equation and their stability and applicability[J].World Information on Earthquake Engineering,2000,16(2):8~12.(in Chinese)
[5]景立平.波动有限方程显式逐步积分格式稳定性分析[J].地震工程与工程振动,2004,24(5):20~26.Jing Liping.Stability analysis of explicit finite element step integral pattern for wave motion[J].Earthquake Engineering and Engineering Vibration,2004,24(5):20~26.(in Chinese)
[6]Li Xiaojun,Liao Zhenpeng,Guan Huimin.An explicit finite element-finite difference method for analyzing the effect of viscoelastic local topography on the earthquake motion[J].ACTA Seismologica Sinica,1995,8(3):447~456.
[7]Liu J B,Sharan S K.Analysis of dynamic contact of cracks in viscoelastic method[J].Computer Methods in Applied Mechanics and Engineering,1995,121:187~200.
[8]涂劲,陈厚群,杜修力.高拱坝非线性地震反应分析中横缝模拟方案研究[J].水力发电学报,2001,(2):18~25.Tu Jin,Chen Houqun,Du Xiuli.A study on the simulation scheme of joints in the nonlinear seismic response analysis of high arch dam[J].Chinese Journal of Hydroelectric Engineering,2001,(2):18~25.(in Chinese)
[9]赵成刚,王进廷,史培新,李伟华.流体饱和两相多孔介质动力反应分析的显式有限元法[J].岩土工程学报,2001,23(2):46~50.Zhao Chenggang,Wang Jinting,Shi Peixin,Li Weihua.Dynamic analysis of fluid-saturated porous media by using explicit finite element method[J].Chinese Journal of Geotechnical Engineering,2001,23(2):46~50.(in Chinese)
[10]Hilber H M,Hughes T T R.Numerical dissipation for time integration algorithms in structure dynamics[J].Earthquake Engineering and Structure Dynamics,1977,5(3):283~292.
[11]Liao Z P,Liu J B.Numerical instabilities of local transmitting boundary[J].Earthquake Engineering and Structure Dynamics,1992,21(1):65~77.
[2]李小军.非线性场地地震反应分析方法的研究[D].北京:国家地震局工程力学研究所,1993.Li Xiaojun.Study on the method for analysing the earthquake response of nonlinear site[D].Beijing:Institute of Engineering Mechanics,SSB,1993.(in Chinese)
[3]李小军,廖振鹏.非线性结构动力方程求解的显式差分格式的特性分析[J].工程力学,1993,10(2):141~148Li Xiaojun,Liao Zhenpeng.The analysis of the properties of an explicit difference method for solving the nonlinear structural dynamic equations[J].Engineering Mechanics,1993,10(2):141~148.(in Chinese)
[4]李小军,刘爱文.动力方程求解的显式积分格式及其稳定性与适用性[J].世界地震工程,2000,16(2):8~12.Li Xiaojun,Liu Aiwen.Explicit step-by-step integration formulas for dynamic differential equation and their stability and applicability[J].World Information on Earthquake Engineering,2000,16(2):8~12.(in Chinese)
[5]景立平.波动有限方程显式逐步积分格式稳定性分析[J].地震工程与工程振动,2004,24(5):20~26.Jing Liping.Stability analysis of explicit finite element step integral pattern for wave motion[J].Earthquake Engineering and Engineering Vibration,2004,24(5):20~26.(in Chinese)
[6]Li Xiaojun,Liao Zhenpeng,Guan Huimin.An explicit finite element-finite difference method for analyzing the effect of viscoelastic local topography on the earthquake motion[J].ACTA Seismologica Sinica,1995,8(3):447~456.
[7]Liu J B,Sharan S K.Analysis of dynamic contact of cracks in viscoelastic method[J].Computer Methods in Applied Mechanics and Engineering,1995,121:187~200.
[8]涂劲,陈厚群,杜修力.高拱坝非线性地震反应分析中横缝模拟方案研究[J].水力发电学报,2001,(2):18~25.Tu Jin,Chen Houqun,Du Xiuli.A study on the simulation scheme of joints in the nonlinear seismic response analysis of high arch dam[J].Chinese Journal of Hydroelectric Engineering,2001,(2):18~25.(in Chinese)
[9]赵成刚,王进廷,史培新,李伟华.流体饱和两相多孔介质动力反应分析的显式有限元法[J].岩土工程学报,2001,23(2):46~50.Zhao Chenggang,Wang Jinting,Shi Peixin,Li Weihua.Dynamic analysis of fluid-saturated porous media by using explicit finite element method[J].Chinese Journal of Geotechnical Engineering,2001,23(2):46~50.(in Chinese)
[10]Hilber H M,Hughes T T R.Numerical dissipation for time integration algorithms in structure dynamics[J].Earthquake Engineering and Structure Dynamics,1977,5(3):283~292.
[11]Liao Z P,Liu J B.Numerical instabilities of local transmitting boundary[J].Earthquake Engineering and Structure Dynamics,1992,21(1):65~77.
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