结构动力方程的显式级数积分格式

Explicit integral method with Taylor series for structural dynamic equation

将Newmark-β法中常平均加速度法的基本假定与精细指数算法结合,根据指数矩阵的Taylor级数展开式,提出了动力方程的显式级数解,并设计了相应的时程积分算法。该算法的精度可根据Taylor级数展开式的项数进行灵活控制。算例的结果表明:在满足稳定性条件的前提下,随着时间步长的增加,其精度优于传统的时程积分法。通过稳定性的分析,指出其稳定性条件是显然满足的。

Combining the precise exponential matrix calculation with the basic assumptions of constant average acceleration method of the Newmark family, explicit integral method with Taylor series and its algorithm are put forward. The accuracy of the algorithm can be controlled by choosing the number of Taylor series expansion. Results of the example show that the accuracy of the algorithm is better than that of traditional scheme with the increase of time step depending on the stable conditions. The analysis of stability shows the stable conditions are obviously satisfied.