| 结构动力方程求解的改进-精细Runge-Kutta方法 |
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| 引用本文： | 张继锋,邓子辰,张凯.结构动力方程求解的改进-精细Runge-Kutta方法[J].应用数学和力学,2015,36(4):378-385. |
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| 作者姓名： | 张继锋 邓子辰 张凯 |
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| 作者单位： | 西北工业大学 力学与土木建筑学院, 西安 710072 |
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| 基金项目： | 国家自然科学基金(重点项目)(11432010);国家重点基础研究发展计划(973计划)(2011CB610300);111引智计划项目(B07050);高校博士点基金(20126102110023)~~ |
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| 摘 要： | 在已有精细Runge-Kutta(龙格-库塔)方法的基础上，考虑了状态空间方程非齐次项的特点和外荷载的特殊性，提出了求解结构动力方程的改进精细Runge-Kutta方法.通过对矩阵进行分块计算，在利用原有精细Runge-Kutta方法高精度的同时进一步提高了计算效率，有利于大型结构的长时间仿真.将改进精细Runge-Kutta方法应用于结构动力方程求解，为其求解提供一种新方法.数值算例表明了改进方法的正确性和有效性.
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| 关 键 词： | 结构动力方程 精细积分 简化计算 Runge-Kutta方法 |
| 收稿时间： | 2014-12-30 |
An Improved Precise Runge-Kutta Method for Structural Dynamic Equations |
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| ZHANG Ji-feng
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DENG Zi-chen
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ZHANG Kai.An Improved Precise Runge-Kutta Method for Structural Dynamic Equations[J].Applied Mathematics and Mechanics,2015,36(4):378-385. |
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| Authors: | ZHANG Ji-feng DENG Zi-chen ZHANG Kai |
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| Institution: | School of Mechanics and Civil Engineering & Architecture, Northwestern Polytechnical University, Xi’an 710072, P.R.China |
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| Abstract: | Based on the precise Runge-Kutta method, in view of the characteristics of the non-homogeneous terms of the state space equations and the particular distribution of the loads, a new improved precise Runge-Kutta method was presented for solving the structural dynamic equations. Through partitioning of the related state space matrices, the improved method not only inherited the advantage of high precision of the precise Runge-Kutta method, but also greatly promoted the computational efficiency, making it suitable for solving large-scale structural dynamic problems and conducting long-time simulations. The results of numerical examples show the correctness and validity of the proposed simplified method. |
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| Keywords: | structural dynamic equation precise integration simplified calculation Runge-Kutta method |
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