计算力学学报2024，Vol.41Issue(6)：1045-1052,8.DOI:10.7511/jslx20230406003
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
摘要
Abstract
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 ζn+1,and the size of the time step is adaptively adjusted according to the sizes of ζn+1,providing ζn+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Key words
nonlinear dynamic equation/adaptive step/precise integration/Runge-Kutta分类
数理科学引用本文复制引用
王海波,王鸿燊,纪海潮..非线性结构动力方程的自适应步长数值算法[J].计算力学学报,2024,41(6):1045-1052,8.基金项目
国家自然科学基金(50908230)资助项目. （50908230）
