非线性结构动力方程的自适应步长数值算法  

Adaptive step numerical algorithm for nonlinear structural dynamic equations

作　　者：王海波[1] 王鸿燊 纪海潮 WANG Hai-bo;WANG Hong-shen;JI Hai-chao(School of Civil Engineering,Central South University,Changsha 410075,China)

机构地区：[1]中南大学土木工程学院,长沙410075

出　　处：《计算力学学报》2024年第6期1045-1052,共8页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(50908230)资助项目.

摘　　要：基于Runge-Kutta法实现对时间步长的自适应选择,研究提高非线性结构动力方程的计算精度。利用Runge-Kutta公式的局部截断误差,得出误差估计值ξ_(n+1),根据ξ_(n+1)的大小自适应调节时间步长的大小,为算法提供一个判断语句,其能使算法流程图更加多样性。将该思想应用于经典Runge-Kutta算法和精细Runge-Kutta算法中,得到自适应步长的经典Runge-Kutta算法和精细Runge-Kutta算法,使算法的时间步长依赖于给定的每步误差限值,提高计算精度,数值算例论证了本文方法的有效性。In this paper,we examine the enhancement of computational accuracy of nonlinear structural dynamic equations by using adaptive selection of the time step based on Runge-Kutta method.The local truncation error of Runge-Kutta formula is used to obtain the error estimate value ξ_(n+1),and the size of the time step is adaptively adjusted according to the sizes of ξ_(n+1),providing ξ_(n+1) judgment statement for the algorithm,which can make the flow chart of the algorithm more diverse.This idea is applied to the classical Runge-Kutta algorithm and the fine Runge-Kutta algorithm,and the adaptive step sizes of the classical Runge-Kutta algorithm and the fine Runge-Kutta algorithm are obtained,so that the time step size of the algorithm is dependent on the given error limit of each step to improve the calculation accuracy.Numerical examples demonstrate the validity of the proposed ideas.

关 键 词：非线性动力方程 自适应步长 精细积分法 RUNGE-KUTTA法 

分 类 号：O322[理学—一般力学与力学基础]