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王海波,何崇检,贾耀威.增维精细积分法的适用范围研究[J].计算力学学报,2019,36(5):618~623
增维精细积分法的适用范围研究
Study on the application scope of the precise time-integration with dimension expanding method
投稿时间:2018-07-09  修订日期:2018-11-23
DOI:10.7511/jslx20180709003
中文关键词:  增维精细积分法  傅里叶级数  叠加原理  线性化假设  递推算法
英文关键词:the precise time-integration with dimension expanding method  Fourier series  superposition principle  linearized hypothesis  recursive algorithm
基金项目:国家自然科学基金(50908230)资助项目.
作者单位E-mail
王海波 中南大学 土木工程学院, 长沙 410075 haibarg@163.com 
何崇检 中南大学 土木工程学院, 长沙 410075  
贾耀威 中南大学 土木工程学院, 长沙 410075  
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中文摘要:
      对线性定常结构动力系统提出的增维精细积分法,能够将非齐次动力方程转化为齐次动力方程,不用对状态矩阵求逆就能方便高效地求解出结构的动力响应。本文在仔细分析增维精细积分法性质的基础上,提出了其适用条件,进一步拓宽了其应用范围,并给出了将荷载项展开成傅里叶级数时,相应增维精细积分法的表达式。同时,在一个时间步长内,通过对非齐次项作线性化假设,成功地将增维精细积分法应用到了非线性动力分析领域。本文方法计算格式统一,易于编程,具有很高的计算效率。数值算例证明了本文方法的有效性。
英文摘要:
      The precise time-integration with dimension expanding method can transform the non-homogeneous dynamic equation into a homogeneous dynamic equation.Therefore the state matrix inversion is avoided and the dynamic response of structure can be solved easily.On the basis of careful analysis of the properties of the precise time-integration with dimension expanding method,the application conditions are proposed and its application scope is further expanded.And the expression of the corresponding precise time-integration with dimension expanding method is given when the load term is expanded into a Fourier series.At the same time,in a time step,by making the linear assumption of inhomogeneous terms,this paper successfully applies the precise time-integration with dimension expanding method to nonlinear dynamic analysis.This method has unified mathematical format,convenience in computer programming and high computational efficiency.Numerical examples demonstrate the effectiveness of this method.
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