精细积分方法的稳定性和精度分析

分析了结构动力分析的精细积分方法的稳定性、精度和计算工作量,讨论了离散时间间隔、指数矩阵幂级数展开式的截断阶数L以及2N类算法的阶数N的优化问题.说明了精细积分方法是条件稳定的.综合考虑稳定性、精度和计算工作量,判定截断阶数L取4时精细积分方法的总体效果最好,并给出了N的参数优化公式.最后给出2个例题验证了稳定性和精度分析的正确性.

Stability and Precision Analysis for Precise Integration Method

The precise integration method, one of the direct integration methods for problems in structural dynamics, was analyzed. Several comments were made on its formulation, numerical stability, computational accuracy and cost. The method is conditionally stable and belongs to the category of explicit time integration methods. The precise integration method is based on the 2 N type algorithm for computation of exponential matrix. It controls the order N to satisfy the accuracy requirement. Its numerical results have excellent correlation. According to the analytic results, the numerical stability, computational accuracy and cost depend to a large degree on the selection of the parameters, time division, truncation order and order of 2 N type algorithm. Then the optimal formulation of parameters was given. And several points about the precise integration method were illuminated theoretically. Finally, two numerical examples verified the validity of the stability, precision and the optimal formulation.