结构动力方程求解的改进精细Runge-Kutta方法  

An Improved Precise Runge-Kutta Method for Structural Dynamic Equations

作　　者：张继锋[1] 邓子辰[1] 张凯[1] 

机构地区：[1]西北工业大学力学与土木建筑学院,西安710072

出　　处：《应用数学和力学》2015年第4期378-385,共8页Applied Mathematics and Mechanics

基　　金：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)~~

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.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 e- quations. Through partitioning of the related state space matrices, the improved method not on- ly 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 dy- namic problems and conducting long-time simulations. The results of numerical examples show the correctness and validity of the proposed simplified method.

关 键 词：结构动力方程 精细积分 简化计算 RUNGE-KUTTA方法 

分 类 号：O313[理学—一般力学与力学基础]