辛数值流形时间子域法  

Symplectic numerical manifold time-subdomain method

作　　者：黄伟江[1,2] 罗恩[1] 章学军[1,3] 

机构地区：[1]中山大学应用力学与工程系,广州510275 [2]广州市建筑科学研究院有限公司,广州510440 [3]广东省建筑科学研究院,广州510500

出　　处：《中国科学（G辑）》2009年第10期1487-1494,共8页

基　　金：国家自然科学基金资助项目(批准号:10172097;10772203)

摘　　要：基于多自由度系统相空间非传统Hamilton变分原理,提出了一种结构动力响应分析的新方法-辛数值流形时间子域法.该方法在时间子域上应用数值流形方法,基于Lagrange分片函数,构造非差分格式.证明了这种辛算法是无条件稳定的,并给出算法的改进递推方法.通过两个不同类型算例的计算结果表明,这种在Hamilton体系下的辛算法的精度和计算效率都明显高于国际上常用的Wilson-θ法和Newmark-β法,是一种高性能、高质量和高精度的算法.Based on the unconventional Hamilton variational principle in phase space for elastodynamics of multidegree-of-freedom system, a symplectic algorithm which is called symplectic numerical manifold time-subdomain method is proposed. A non-difference scheme is constructed by ap- plying numerical manifold method with Lagrange interpolation polynomial to the time subdomain. And the improved recurrence scheme of the algorithm is developed. It is also proved that the presented symplectic algorithm is an unconditionally stable one. And its improved algorithm is proposed. From the results of the two numerical examples of different types, it can be seen that the accuracy and the computational efficiency of the new method excel obviously those of widely used Wilson-θ and Newmark-β methods. This symplectic algorithm in Hamilton system is a highly efficient one with better computation performance.

关 键 词：辛数值流形时间子域法 多自由度系统 结构动力响应 相空间非传统Hamilton 变分原理 

分 类 号：O302[理学—力学]