非线性动力分析的广义精细积分法

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (21) : 220-226.

论文

非线性动力分析的广义精细积分法

王海波，何崇检

作者信息 +

Generalized precise time domain integration method for nonlinear dynamic analysis

WANG Haibo, HE Chongjian

Author information +

文章历史 +

摘要

针对非线性动力状态方程，结合广义精细积分法和预估-校正法，提出了用于非线性动力分析的广义精细积分法。首先，在任一时间子域内，对计算过程中待求的vk+j/m(j=1,2,…m)，利用当前时刻的vk进行预估。然后，将离散的非线性项用拉格朗日插值多项式展开并视为外荷载，结合广义精细积分法即可求解非线性系统的动力响应。该方法计算格式统一，易于编程，与四种单步法、一次预-校法及预估校正-辛时间子域法进行数值比较，计算结果表明，该方法具有很高的精度、稳定性及较高的效率。可用于多自由度结构体系的非线性动力反应分析。

Abstract

For the state equation used for nonlinear dynamics system, the generalized precise time step integration method for nonlinear dynamics system is proposed with the combination of the generalized precise time step integration method and predict-correct method. Firstly, in any time-subdomain, the vk is used to estimate the unknown vk+j/m(j=1,2,…m) in the process of computation. And then the discrete nonlinear terms are expanded by using Lagrange interpolation polynomial and treated as load. As a result ,the generalized precise time step integration method can be used to calculate dynamic response, which is an unified computational and easy programming method. Compared with the four single-step methods, one predict-correct method or the predictor-corrector symplectic time-subdomain algorithm, the numerical results show that the proposed method is more highly accurate and stable, capable of keeping appropriate efficiency. The algorithm can be used to calculate the nonlinear dynamic responses of structural systems with multi-degrees of freedom.

导出引用

王海波，何崇检. 非线性动力分析的广义精细积分法[J]. 振动与冲击, 2018, 37(21): 220-226

WANG Haibo, HE Chongjian. Generalized precise time domain integration method for nonlinear dynamic analysis[J]. Journal of Vibration and Shock, 2018, 37(21): 220-226

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