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| Adaptive step numerical algorithm for nonlinear structural dynamic equations |
| Received:April 06, 2023 Revised:May 28, 2023 |
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| DOI：10.7511/jslx20230406003 |
| KeyWord:nonlinear dynamic equation adaptive step precise integration Runge-Kutta |
| Author | Institution |
| 王海波 |
中南大学 土木工程学院, 长沙 |
| 王鸿燊 |
中南大学 土木工程学院, 长沙 |
| 纪海潮 |
中南大学 土木工程学院, 长沙 |
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| 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 ξn+1,and the size of the time step is adaptively adjusted according to the sizes of ξn+1,providing ξn+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. |
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