结构动力方程的高斯精细时程积分法

对线性定常结构动力系统提出的精细积分方法,能够得到在数值上逼近于精确解的结果,但是对于非齐次动力方程涉及到矩阵求逆的困难,计算精度取决于非齐次项的拟合精度等问题。提出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,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,而且计算效率较高,数值例题显示了方法的有效性。

GAUSS PRECISE TIME-INTEGRATION OF STRUCTURAL DYNAMIC ANALYSIS

The precise time-integration method proposed for linear time-invariant dynamic systems can give precise numerical results approaching the exact solution at the integration points. However, difficulty arises when the algorithm is applied to the non-homogeneous dynamic systems due to the inverse matrix calculation and the simulation of the applied loading. By combining the Gauss quadrature with the calculation technique of matrix exponential function in the precise time-integration method, a new precise time-integration method, Gauss precise time-integration method, is proposed. The new method avoids the inverse matrix calculation and the simulation of the applied loading and improves the computing efficiency. The order of accuracy is selectable in the method. A numerical example is given to demonstrate the validity and efficiency of the method.