非线性动力方程的改进分段直接积分法

详细信息

IMPROVED SEGMENTED-DIRECT-INTEGRATION METHOD FOR NONLINEAR DYNAMIC EQUATIONS

(1. School of Civil Engineering and Architecture, Central South University, Changsha, Hunan 410075, China; 2. College of Civil Engineering, Hunan City University, Yiyang, Hunan 413000, China)

摘要: 对现有的求解非线性动力方程的分段直接积分方法进行了改进，提出了新的预估式。该方法为显式预估-校正、自起步的单步四阶精度的精细积分算法，避免了对求导。算例表明：该文改进方法可用于求解多自由度、强非线性、非保守系统的动力响应问题；对研究解的稳定性也是一个有效的工具，而且比现有的分段直接积分方法和经典的Runge-Kutta方法计算精度高。
- 非线性动力方程 /
- 分段直接积分法 /
- 精细积分法 /
- 预估-校正 /
- Runge-Kutta方法
Abstract: The present segmented-direct-integration method is improved for nonlinear dynamic systems governed by the equation , and new predict formulas are proposed. As a precise integration method with explicit, predict-correct, self-starting and four order accuracy, the improved method is not necessary to differentiate . Numerical examples show that the improved method is suitable for multi-degrees of freedom, strongly nonlinear and non-conservative dynamic systems, even effective in studying stability of solution. Moreover, the improved method has higher accuracy than the present segmented-direct-integration method as well as classical Runge-Kutta integration method.
- nonlinear dynamic equations /
- segmented-direct-integration method /
- precise integration method /
- predict-correct /
- Runge-Kutta integration method