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

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。

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.