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无条件稳定的更新精细积分方法
引用本文:汪梦甫.无条件稳定的更新精细积分方法[J].固体力学学报,2006,27(3):311-314.
作者姓名:汪梦甫
作者单位:湖南大学土木工程学院,长沙,410082
摘    要:提出将Pade逼近与精细积分方法中的指数矩阵运算技巧结合起来,建立了精细积分法的更新形式及计算过程,对该更新精细积分方法的稳定性进行了论证与探讨.结果表明,该更新精细积分方法是无条件稳定的,整个积分方法的精度取决于所取Pade逼近的阶数与高斯积分点的数量.数值例题也显示了该方法的高效率及其可行性.

关 键 词:结构动力学  时程分析  指数矩阵运算  无条件稳定
修稿时间:2005年11月8日

AN UNCONDITIONAL STABLE PRECISE TIME STEP INTEGRATION METHOD OF STRUCTURAL DYNAMIC ANALYSIS
Wang Mengfu.AN UNCONDITIONAL STABLE PRECISE TIME STEP INTEGRATION METHOD OF STRUCTURAL DYNAMIC ANALYSIS[J].Acta Mechnica Solida Sinica,2006,27(3):311-314.
Authors:Wang Mengfu
Abstract:The precise time step integration method proposed for linear time-invariant homogeneous dynamic system can give precise numerical results approaching to the exact solution at the integration points.However,it is a conditional stable algorithm,so it is dubious when this algorithm is used in the nonlinear dynamic response analysis.By combining the Pade approximation with the 2N calculation technique of matrix exponential function in the precise time step integration method,a new precise time step integration method(that is renewal precise time step integration method) is proposed.The proposed method in this paper is an unconditionally stable algorithm with an arbitrary order of accuracy.Numerical example is given to demonstrate the validity and efficiency of the algorithm.
Keywords:structural dynamics  time step integration method  calculation technique of matrix exponential function  unconditionally stable algorithm
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