精细积分方法的评估与改进

详细分析了结构动力分析的精细积分方法的稳定性、计算精度，在此基础上提出了对现有精细积分方法的改进策略。算例证实了本文对精细积分方法改进的科学性与可行性。

Assessment and improvement of precise time step integration method

In this paper, the numerical stability and the computation accuracy of precise time step integration method are discussed in detail. It is shown that the precise time step integration method is conditionally stable and this time integration scheme has inherent algorithmic damping, algorithmic period error and algorithmic amplitude decay, but the stability conditions and the computation accuracy requirements of this time integration scheme are easy to satisfy for the discretized structural models. Based on the above results, the optimum values of the truncation order L and 2-division order N are presented, the Gauss quadrature method is used to improve the computation accuracy of precise time step integration method, a new precise time step integration method is established. The proposed method avoids the inverse matrix calculation and the simulation of the applied loading and improves the computing efficiency. In particular, the proposed method is independent to the quality of the matrix H]. If the matrix H] is singular or nearly singular, the advantage of the method is remarkable. Finally, a numerical example verified the validity of the selections of L and N and the feasibility of improvement of precise time step integration method.