有阻尼动力方程显式积分方法的精度研究
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摘要
在动力问题分析中,一种好的显式积分方法不仅要具有良好的稳定性,而且还要具有良好的计算精度。对几种有阻尼动力方程显式积分方法的精度问题进行了分析,研究了各自的局部截断误差、数值阻尼比和相对周期误差。这一研究将有助于更加全面地了解这些积分格式的性能。
The accuracy of characteristic analysis is as necessary for an explicit integration scheme as the stability property. In this paper, the accuracy characteristics of several explicit integration schemes for solving the dynamic equation with damping are studied to comprehensively understand their behaviors. The order of accuracy is obtained from local truncation errors. The dissipation and dispersion properties are analyzed. A numerical example is provided to verify the theoretical conclusions. It is shown that the scheme provided by Du et al. is favorable for dynamic analysis.
The accuracy of characteristic analysis is as necessary for an explicit integration scheme as the stability property. In this paper, the accuracy characteristics of several explicit integration schemes for solving the dynamic equation with damping are studied to comprehensively understand their behaviors. The order of accuracy is obtained from local truncation errors. The dissipation and dispersion properties are analyzed. A numerical example is provided to verify the theoretical conclusions. It is shown that the scheme provided by Du et al. is favorable for dynamic analysis.
引文
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[5]杜修力,王进廷.阻尼弹性结构动力计算的显式差分法[J].工程力学,2000,17(5):37~43.Du Xiuli,Wang Jinting.An explicit difference formulation of dynamic response calculation of the elastic structure with damping.Engineering Mechanics,2000,17(5):37~43.(in Chinese)
[6]王进廷,杜修力.有阻尼体系动力分析的一种显式差分法[J].工程力学,2002,19(3):109~112.Wang Jinting,Du Xiuli.An explicit difference method for dynamic analysis of a structure system with damping.Engineering Mechanics,2002,19(3):109~112.(in Chinese)
[7]周正华,周扣华.有阻尼振动方程常用显式积分格式稳定性分析[J].地震工程与工程振动,2001,21(3):22~28.Zhou Zhenghua,Zhou Kouhua.Stability analysis of an integral method for damped vibration equation.Earthquake Engineering and Engineering Vibration,2001,21(3):22~28.(in Chinese)
[8]王进廷,杜修力,张楚汉.瑞利阻尼介质有限元离散模型动力分析的数值稳定性[J].地震工程与工程振动,2002,22(6):18~24.Wang Jinting,Du Xiuli,Zhang Chuhan.Numerical stability of explicit finite element schemes for dynamic systems with Rayleigh damping.Earthquake Engineering and Engineering Vibration,2002,22(6):18~24.(in Chinese)
[9]Belytschko T,Hughes TJR.Computational Methods for Transient Analysis.Vol.1in Computational Methods in Mechanics[M].Amsterdam:Elsevier Science,1983.
[10]Lambert JD.Computational Methods in Ordinary Differential Equations[M].London:John Wiley&Sons,1973.
[2]Tamma K K,Zhou X,Valasutean R.Computational algorithms for transient analysis:the burden of weight and consequences towards formalizing discrete numerically assigned[DNA]algorithmic markets:Wp-family[J].Comput.Methods in Applied Mechanicsand Engineering,1997,149:153~188.
[3]李小军,廖振鹏,杜修力.有阻尼体系动力问题的一种显式解法[J].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)
[4]周正华,李山有,侯兴民.阻尼振动方程的一种显式直接积分方法[J].世界地震工程,1999,15(1):41~44.Zhou Zhenghua,Li Shanyou,Hou Xingmin.An explicit integral method for damped vibration equation[J].World Information of Earthquake Engineering,1999,15(1):41~44.(in Chinese)
[5]杜修力,王进廷.阻尼弹性结构动力计算的显式差分法[J].工程力学,2000,17(5):37~43.Du Xiuli,Wang Jinting.An explicit difference formulation of dynamic response calculation of the elastic structure with damping.Engineering Mechanics,2000,17(5):37~43.(in Chinese)
[6]王进廷,杜修力.有阻尼体系动力分析的一种显式差分法[J].工程力学,2002,19(3):109~112.Wang Jinting,Du Xiuli.An explicit difference method for dynamic analysis of a structure system with damping.Engineering Mechanics,2002,19(3):109~112.(in Chinese)
[7]周正华,周扣华.有阻尼振动方程常用显式积分格式稳定性分析[J].地震工程与工程振动,2001,21(3):22~28.Zhou Zhenghua,Zhou Kouhua.Stability analysis of an integral method for damped vibration equation.Earthquake Engineering and Engineering Vibration,2001,21(3):22~28.(in Chinese)
[8]王进廷,杜修力,张楚汉.瑞利阻尼介质有限元离散模型动力分析的数值稳定性[J].地震工程与工程振动,2002,22(6):18~24.Wang Jinting,Du Xiuli,Zhang Chuhan.Numerical stability of explicit finite element schemes for dynamic systems with Rayleigh damping.Earthquake Engineering and Engineering Vibration,2002,22(6):18~24.(in Chinese)
[9]Belytschko T,Hughes TJR.Computational Methods for Transient Analysis.Vol.1in Computational Methods in Mechanics[M].Amsterdam:Elsevier Science,1983.
[10]Lambert JD.Computational Methods in Ordinary Differential Equations[M].London:John Wiley&Sons,1973.
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