求解非线性结构动力方程的预估校正-辛时间子域法  

Predictor-corrector symplectic time-subdomain algorithm for nonlinear dynamic equations

作　　者：李纬华[1] 王堉[1] 罗恩[1] 

机构地区：[1]中山大学工学院,广州510275

出　　处：《计算力学学报》2014年第4期453-458,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(10772203;11202247);教育部博士点新教师基金(20100171120007)资助项目

摘　　要：提出了求解非线性结构动力方程的预估校正-辛时间子域法。首先,将结构非线性动力方程转换为状态空间方程,在任一时间子域内利用改进的欧拉法对各离散时刻的状态变量值进行预估和校正。然后,将离散的非线性项用Lagrange插值多项式展开并视为外荷载,结合辛时间子域法即可求解非线性动力系统的响应。这种方法不必对状态矩阵求逆,无需计算高阶导数,计算简单,格式统一,易于编程。算例结果表明,本文方法具有较高的计算精度、效率和稳定性,是一种求解非线性结构动力方程的有效方法。A predictor-corrector symplectic time-subdomain algorithm for nonlinear dynamic equations is presented in this paper .Firstly ,nonlinear dynamic equations are transformed into state space equations . Taking advantage of improved Euler’s method ,state variable values at discrete moment are predicted and corrected in any time-subdomain .And then ,the discrete nonlinear terms are expanded by using Lagrange interpolation polynomial and treated as load .As a result ,a new symplectic time-subdomain algorithm can be used to calculate dynamic response ,w hich is a unified computational and easy programming method with no need for inverse matrix and higher derivative .The results of numerical examples show that the method is an effective algorithm with highly computational accuracy ,efficiency and stability for solving nonlinear dynamic equations .

关 键 词：非线性动力方程 辛时间子域法 改进欧拉法 变分原理 预估校正 

分 类 号：O322[理学—一般力学与力学基础]