计算力学学报2017，Vol.34Issue(4)：433-439,7.DOI:10.7511/jslx201704006
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
摘要
Abstract
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.关键词
Wilson-θ法/Newmark-β法/非线性动力学方程/猜测解/迭代校正Key words
Wilson-θ method/Newmark-β method/nonlinear dynamic system/guess solution/iterative correction分类
数理科学引用本文复制引用
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[J].计算力学学报,2017,34(4):433-439,7.基金项目
国家自然科学基金(11272361,11572356,11672337)资助项目. （11272361,11572356,11672337）
