针对非线性动力状态方程 ，结合精细积分法和Romberg数值积分，对计算过程中待求的vk+j/m(j=1,2,…m)，利用当前时刻vk，通过二阶龙格库塔法进行预估，提出了一种避免状态矩阵求逆的高效精细积分单步法。该方法计算格式统一，易于编程，通过选取m值，可进行不同计算精度的计算。与两种单步法、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，该方法具有高精度、高效率及较好的稳定性。在求解多自由度、强非线性动力响应问题中具有较大优势。
Abstract
For the state equation used for nonlinear dynamics system, an efficient precise integration single-step method is proposed with the combination of the precise integration method and Romberg numerical integration. In the process of computation, the state matrix inversion is avoided and vk is used to estimate the unknown vk+j/m(j=1,2,…m) by the two-order Runge-Kutta method. The algorithm has an uniform computing scheme, which makes programming more simple. Moreover, it applies to diverse computations for different accuracies by controlling the value of m. Compared with two 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 effcient, capable of keeping computation stability. The efficient precise integration single-step method is more advantageous to computate MDOF, strongly nonlinear dynamic responses.
关键词
非线性动力方程 /
精细积分法 /
Romberg数值积分 /
龙格库塔法 /
单步法
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Key words
nonlinear dynamic equations /
precise integration method /
Romberg numerical integration /
Runge-Kutta method /
single-step method
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