非线性动力学系统的精细逐块积分求解方法

A Precise Block-by-Block Integration Method for Nonlinear Dynamic Systems

针对非线性动力学系统提出了一种精细逐块求解的积分方法。通过引入逐块积分格式和精细积分算法,典型的非线性动力微分方程最终可被转换为容易求解的逐块代数方程组。由于这种隐式积分格式具有高精度和稳定性,相比于四阶Runge-Kutta方法和Newmark方法,此方法可以对非线性动力系统应用较大的步长。此外,此方法对具有奇异或接近奇异的系统矩阵的动力学系统仍然有效。数值算例验证了此方法的有效性。

This paper proposes a precise block-by-block integration method for nonlinear dynamic systems.By applying the block-by-block method and the precision integration scheme,the classic nonlinear differential governing equations are converted into algebraic equations within each block,which is favorable to solve.Due to the high accuracy and stability of this implicit integration scheme,a large step size can be utilized for nonlinear dynamic systems comparing with those of the fourth order Runge-Kutta method and the Newmark method.In addition,the proposed method is also effective for dynamic systems with a singular or close to singular system matrix.Numerical examples are given to verify the proposed method.