非线性动力方程的改进分段直接积分法  

IMPROVED SEGMENTED-DIRECT-INTEGRATION METHOD FOR NONLINEAR DYNAMIC EQUATIONS

作　　者：王海波[1,2] 余志武[1] 陈伯望[2] 

机构地区：[1]中南大学土木建筑学院,湖南长沙410075 [2]湖南城市学院土木工程学院

出　　处：《工程力学》2008年第9期13-17,22,共6页Engineering Mechanics

基　　金：国家自然科学基金项目(50438020;10572153);湖南省教育厅科研项目(05B063;05A070)

摘　　要：对现有的求解非线性动力方程v=H.v+f(v,t)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f(v,t)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。The present segmented-direct-integration method is improved for nonlinear dynamic systems governed by the equation v = H. v ＋ f（v,t）, 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 f（v,t）. 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.

关 键 词：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 

分 类 号：O322[理学—一般力学与力学基础] TU311.3[理学—力学]