精细时程法在大型结构动力响应中的应用

精细时程法涉及到稠密矩阵，计算量大，需要大量的存储空间，适合自由度数较少的简单结构。根据指数矩阵的Taylor展开和矩阵指数函数的性质来计算指数矩阵，结合动力方程的稀疏变换和积分方程的级数解，避开稠密矩阵，给出了精细时程法在大型结构动力响应中的一种推广应用，并设计了相应的时程积分算法。整个算法仅涉及一个稀疏矩阵，对存储空间的要求很低，能应用于大型结构的动力响应分析。最后给出了算例验证。

Application of Precise Time-integration Method for Dynamic Response Analysis of Large-scale Structures

The precise time-integration method has the advantages of high precision, high efficiency, absolute stability and etc. But the method needs a great deal of memory and computing time because of dense matrices. So the method suits simple structures that have fewer degrees of freedom. Based on Taylor series of the exponential matrix and the property of exponential function, the exponential matrix was calculated. In order to avoid dense matrices, the sparse transform of dynamic equations and series solution of integral equations were also employed. Thus an algorithm for dynamic response analysis of large-scale structures was designed. The algorithm only related to a sparse matrix and needed little memory. So it could be employed in dynamic response analysis of large-scale structures. Finally, some numerical examples were presented to demonstrate the algorithm.