结构动力方程的更新精细积分方法

RENEWAL PRECISE TIME STEP INTEGRATION METHOD OF STRUCTURAL DYNAMIC ANALYSIS

将高斯积分方法与精细积分方法中的指数矩阵运算技巧结合起来,建立了精细积分法的更新形式及计算过程,对该更新精细积分方法的稳定性进行了论证与探讨。在实施精细积分过程中不必进行矩阵求逆,整个积分方法的精度取决于所选高斯积分点的数量。这种方法理论上可实现任意高精度,计算效率较高,其稳定性条件极易满足。数值例题也显示了这种方法的有效性。

The precise time step integration method proposed for linear time-invariant homogeneous dynamic system can give precise numerical results approaching to the exact solution at the integration points.However,it is more or less difficult when the algorithm is used to the non-homogeneous dynamic systems due to the inverse matrix calculation and the simulation accuracy of the applied loading.By combining the Gauss quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method,a new precise time step integration method (that is renewal precise time step integration method) is proposed.The new method avoids the inverse matrix calculation and the simulation of the applied loading and improves the computing efficiency.In particular,the 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.The proposed method in this paper is a unconditionally stable algorithm having an arbitrary order of accuracy.Numerical examples are given to demonstrate the validity and efficiency of the algorithm.