用于非线性动力分析的一种高效精细积分单步法

发布时间：2018-10-26 13:51

【摘要】：针对非线性动力状态方程v=H·v+f(v,t),结合精细积分法和Romberg数值积分,对计算过程中待求的v_(k+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 nonlinear dynamic equation of state (VX H v f (VT), combining the precise integration method and the Romberg numerical integration, the vk / j / m (J _ (k / j / m) (J _ (k / j / m), which is to be solved in the process of calculation, is studied. , m), uses the current time vk, to predict by the second order Runge-Kutta method and proposes an efficient precise integration single-step method to avoid the inversion of the state matrix. This method has the advantages of uniform calculation format and easy programming. By selecting m value, different calculation accuracy can be carried out. Compared with two single-step methods, one-step precalibration method and predictor-correction-symplectic time subdomain method, the numerical results show that the proposed method has high accuracy, high efficiency and good stability. It has great advantages in solving multi-degree-of-freedom and strongly nonlinear dynamic response problems.
【作者单位】：中南大学土木工程学院;
【基金】：国家自然科学基金(50908230)
【分类号】：O241.4

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