非线性动力方程的增维精细积分法  

Increment-dimensional precise integration method for nonlinear dynam icequation

作　　者：张素英[1] 邓子辰[1] 

机构地区：[1]西北工业大学工程力学系,西安710072

出　　处：《计算力学学报》2003年第4期423-426,共4页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金 (1 9872 0 57);霍英东青年教师基金 (71 0 0 5);教育部高校博士点专项基金(2 0 0 1 0 6990 1 6);航空科学基金 (0 0 B530 0 6);大连理工大学工业装备结构分析国家重点实验室开放基金资助项目

摘　　要：对线性定常结构的动力系统提出的精细积分法 ,能得到在数值上逼近于精确解的结果。但是对于非齐次动力方程却涉及到矩阵求逆的困难 ,而且通常与时间有关的非齐次项不能进入精细积分的细化过程。采用增维的方法 ,将非齐次动力方程化为齐次方程 ,在实施精细积分的过程中不必进行矩阵求逆。这种处理方法对于程序实现和提高数值计算的稳定性十分有利 ,而且在大型问题中可明显提高计算效率 ,数值算例显示本文方法是有效的。The precise integration method proposed for linear-invariant dynamic system can give precise numerical results approaching to the exact solution at the integration points. However, it is more or less difficult when the algorithm is used to the non-homogeneous dynamic system due to the inverse matrix calculations, and the non-homogeneous vector with relation to time variable do not be considered in the process of division of the precise integration. The original non-homogeneous equation is converted into homogeneous equation by means of increment-dimensional method. Then, precise integration method can be used and the inverse matrix need not be computed in the integration. The present method is not only benefit to both programming implementation and improving the numerical stability, but also more efficient to the large-scale problem. The numerical examples show the validity and efficiency of the method.

关 键 词：非线性动力方程 增维精细积分法 动力系统 非齐次动力方程 数值计算 线性定常结构 

分 类 号：O19[理学—数学] O241.7[理学—基础数学]