基于Newmark法的一种新精细直接积分法

A new direct precise integration scheme based on Newmark method

将Newmark法中常平均加速度法的基本假定引入结构动力微分方程中,运用指数矩阵的精细运算技巧和精度较高的柯特斯积分格式逐步积分,形成新精细直接积分法。与精细时程积分法相比,文中方法在将二阶微分方程降为一阶时,方程的数量没有增加,其迭代公式明显。文中对该方法的稳定性进行分析。结果表明该方法虽是条件稳定的,但其稳定性条件非常容易满足。数值例题显示了本文新精细直接积分法的精度。

Basic assumptions of constant average acceleration method were introduced into dynamic differential equation. And the new equation could be integrated step by step with precise exponential matrix calculation and Cotes integration. Therefore the new direct precise integration scheme was put forward. Compared with precise time - integration method, number of equations was not increased when the order of differential equation was reduced to one with the new scheme. And interval formulas were apparent. In this paper, the stability of the new scheme was analyzed. Results show that the proposed method is a conditionally stable algorithm. But it is very easy to satisfy these conditions. Numerical examples are given to demonstrate the accuracy of the algorithm.