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刘广,刘济科,陈衍茂.基于Wilson-θ和Newmark-β法的非线性动力学方程改进算法
An improved algorithm for nonlinear dynamic systems based on Wilson-θ and Newmark-β method[J].计算力学学报,2017,(4):433~439
基于Wilson-θ和Newmark-β法的非线性动力学方程改进算法
An improved algorithm for nonlinear dynamic systems based on Wilson-θ and Newmark-β method
An improved algorithm for nonlinear dynamic systems based on Wilson-θ and Newmark-β method
投稿时间:2016-06-10  修订日期:2016-12-20
DOI:10.7511/jslx201704006
中文关键词:  Wilson-θ  Newmark-β  非线性动力学方程  猜测解  迭代校正
英文关键词:Wilson-θ method  Newmark-β method  nonlinear dynamic system  guess solution  iterative correction
基金项目:国家自然科学基金(11272361,11572356,11672337)资助项目.
作者单位E-mail
刘广 中山大学 力学系, 广州 510275  
刘济科 中山大学 力学系, 广州 510275  
陈衍茂 中山大学 力学系, 广州 510275 chenymao@mail.sysu.edu.cn 
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中文摘要:
      Wilson-θ法和Newmark-β法是非线性动力学方程求解的常用方法。它们的一个基本步骤是,将方程改写为增量平衡的形式,在每一个积分步长内用状态参量修正平衡方程的系数矩阵,其本质是在单个步长内对系统的非线性环节进行了线性化处理。本文基于增量思想分别改进了Wilson-θ法和Newmark-β法,根据即时解给出下一步的猜测解,然后对猜测解进行迭代校正,最终得到收敛的近似解。算例表明,改进算法的精度更高,且收敛准则简单。更为重要的是,本文方法无须对非线性项进行线性化处理,因而计算效率更高,适应范围更广。
英文摘要:
      When using Wilson-θ or Newmark-β method to solve nonlinear dynamic equations,usually,we rewrite the equations in the form of incremental equilibrium equations.The coefficient matrix has to be updated in each integral step according to the state variables.In essence,this procedure is to linearize the considered nonlinear system in a single time step.It is usually difficult,however,to handle some strongly nonlinear problems with multiple-degrees-of-freedom.By using an incremental process,in the paper a new fast algorithm was proposed based on Wilson-θ method or Newmark-β method.According to the obtained solution at one time point,we present an initial guessed solution at the next time instant.Then the guessed solution can converge to the true solution via iterative corrections.Numerical examples show that,using the presented fast algorithm together with Wilson-θ method or Newmark-β method,one can get highly accurate solutions.Moreover,the presented algorithm can provide us with a simple way to adjust the convergence as necessary.As the presented methods avoid linearization of the considered nonlinear dynamic systems,they are not only more applicable but also more computationally efficient.
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